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A  treatise  of 
the  system  of  the  world 

Isaac  Newton,  Andrew  Motte 


CE  LIVRE  A  ETfc  UONNlt 

a  la  BIBLIOTIIEQUE  CANTONALE 
ET  UNIVERSITAIRE 


/PATRW 


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A 


T  R  E  A  T  I  S  E 

O  F  T  HE 

SYSTEM 

ft  • 

OF  T  H  £ 

W  O  R  L  D. 

BY 

Sir  ISA  A  C  °NE  WTON. 


Tranliated  into  English. 


LONDON: 

Printed  for  F.  Fayram  at  the  South  En¬ 
trance  under  the  Royal  Exchange. 

M  DCG  XXV111. 


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'J  iOS'l 


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C  iii  ] 


PREFACE- 

IH  the  beginning  of  the  third  book 
of  the  Mathematic  alTrinciples 
of  Natural  Thilofophy  of  the 
late  illujlrious  Sir  Isaac  Newton, 
he  acquaints  us,  “  that  he  had  once 
“  compofed  that  book  in  a  popular 
“  method  that  it  might  be  gene - 
“  rally  read ;  but  that  afterwards 
“to  avoid  the  difputes  which  might 
“  arife,  if  thofe  who  were  unac- 
“  quainted  with  the  principles  laid 
“  down  in  the  preceding  books,  and 
“  full  of  the  prejudices  which  many 
“ years  had  made  natural  to  them, 
“  Jhould  take  it  in  hand,  he  put 
“  the  [ubjlance  of  that  book  into 
“  proportions  in  the  mathematical 
“  way,  that  it  might  be  read  by 
“  thofe  only  who  had  Jludied  the 
<e  principles  beforehand.  ”  The  pre¬ 
judices  that  great  Man  apprehend- 

A  2,  ed, 


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iv  PREFACE. 
ed,  when  the  principles  huhereby  he 
explained  the  appearances  of  Na¬ 
ture  were  new ,  are  now  jo  well 
dijjipated  by  the  univerfal  applaufe 
and  approbation  they  have  been 
juftly  attended  with,  that  his  rea- 
fon  for  fupprejjing  that  perform¬ 
ance  being  entirely  ceafed ,  we  think 
the  fame  may  be  very  acceptable 
to  the  IVorld.  And  to  render  it 
the  more  ujeful  to  our  countrymen , 
we  chufe  to  give  it  in  a  careful 
tranflation  rather  than  in  the  ori¬ 
ginal  Latin. 

That  this  work  as  it  is  here  pub - 
lijhed  is  genuine,  will  fo  clearly 
appear  by  the  intrinfic  marks  it 
bears,  that  it  will  be  but  lofing 
words  and  the  Readers  time  to 
take  pains  in  giving  him  any  other 
fatisfa&ion.  It  will  be  more  con¬ 
venient  to  clear  the  way  for  thofe 
who  are  lefs  acquainted  with  the 
fubjeft ,  by  a  Jhort  account  of  Aftro - 
nomy,  and  the  ft  ate  it  was  in  when 
the  Author  wrote  j  by  which  the 

curious 


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PREFACE.  y 
curious  difcoveries  therein  contain¬ 
ed  will  he  the  better  underjlood ’ 

By  the  imperfection  of  our  fenfe 
it  comes  to  pafs,  that  the  ap - 
pearances  of  the  heavens  and 
heavenly  bodies  are  entirely  diffe¬ 
rent  from  what  they  really  are  in 
themfelves.  The  Sun,  the  Moon , 
the  other  ‘Planets,  and  the  fixed 
Stars ,  appear  to  the  eye  only  like 
f mall  circles  or  like  points  of  lights 
at  equal  dijlances  from  us  ;  flick¬ 
ing  to  the  top  of  a  blue  hemifphe- 
rical  vault,  not  very  far  from  the 
Earth,  which  it  feems  to  touch  on 
every  fide  near  the  horizon.  And 
this  blue  vault  turning  upon  its  axis, 
thefe  bodies  being  carried  round 
with  it,  rife  and  fet  alternately , 
and  fo  prefent  themfelves  in  order 
to  the  fever al  parts  of  the  Earth . 

But  our  reafon  ajjijled  by  geome- 
try,  opens  to  us  a  very  diff  erent 
fcene.  It  Jhews  us  an  immenfe 
ocean  of  celeftial  f pace  fpreading 

A3  it 


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Vi  PREFACE. 
it  felf  on  all  hands  from  our  Earth 
without  poffibility  that  any  limits 
Jhould  he  fit  to  it .  That  the  fede¬ 
ral  heavenly  "bodies  that  fiem  to 
our  eye  fo  [mall ',  and  equally  dif- 
t ant from  us ,  are  in  reality  of  pro¬ 
digious  magnitudes ,  and  placed  at 
vajl  and  very  different  intervals 
from  the  Earth  and  each  other ,  in 
that  boundlefs  abyjs .  Thefe  things 
were  long  ago  known  and  confint - 
ed  to  by  all  j  but  the  ex  all  form 
in  which  thefe  bodies  and  the 
Earth  are  fituate  with  refpeffi  to 
each  other  in  that  immenfity  of 
fpace,  was  not  well  fettled  till  a- 
boutfixty years  ago  ;  at  which  time 
fiftronomers  generally  agreed  in 
the  following  Syftem.  That  the 
Sun,  though  it  feems  to  move,  is 
indeed  fixed  and  quiefcent  in  a  cer¬ 
tain  given  part  of  the  celeftial  re¬ 
gions.  That  at  a  great  diflance 
from  thence  that  Tlanet  we  call 
Mercury  goes  round  him  in  an  orbit 
either  circular  or  very  nearly  fo, 
in  the  centre  of  which  the  Sun  is. 


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PREFACE.  vii 
That  at  a  yet  greater  diftance  the 
Tlanet  Venus  revolves  about  the 
Sun  in  like  manner.  That  next  to 
Venus  the  Earth  goes  round  the 
Sun,  turning  at  the  fame  time  upon 
its  axis,  and  attended  by  the  Moon  j, 
which  revolves  about  the  Earth  as 
the  Earth  does  about  the  Sun.  That 
the  other  Tlanet s.  Mars,  'Jupiter, 
and  Saturn ,  move  alfo  round  the 
Sum  in  like  orbits  with  the  others  ; 
the  twolafl  being  obferved  to  have 
Satellites  or  Moons  revolving  about 
them,  as  our  Earth  has  its  Moan. 
j$U  this  is  reprefented  in  the  com¬ 
mon  figures  of  the  Solar  or  Copcrni- 
can  Syftem. 

But  Jtjlron&mers  did  not  flop 
here.  They  not  only  found  the  or* 
der  in  which  the  ‘Planets  move, 
and  the  Jituation  of  their  orbits  ; 
but  the  fagatiom  Kepler  made  alfo 
the  following  great  difcoveries  con¬ 
cerning  the  lams  of  their  motions. 
Thejivfl,  that  all  the  Tlanet s,  m 
A  4  moving 


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viii  PREP1  'A*  C  E. 

moving  round  the  Sun ,  defcribe,  by 

radii  drawn  to  the  Sun ,  areas  pro¬ 
portional  to  the  times :  and,  fecond- 
ly,  that  the  cubes  of  their  dijlances 
increafe  in  the  fame  proportion  as 
the  fquares  of  their  periodical 
times ,  or  that  the  dijlances  and 
periodical  times  are  in  a  fejquiah 
teral  ratio. 

It  may  be  proper,  before  we  pro¬ 
ceed,  to  explain  the  meaning  of 
thej'e  two  more  fully.  Suppofe 
DEF,  A B G,  to  be  the  orbits  of 
two  Planets  A  and  D,  revolving 
about  the  Sun  at  C  ;  now  if  right 
lines  be  conceived  to  join  A  /o  C, 
and  D  to  C,  then  will  the  area  de¬ 
ferred  by  the  right  line  CA,  in 
the  motion  of  the  ‘Planet  A,  be 
ever  proportional  to  the  time  in 
which  that  area  is  deferibed.  And 
the  time  in  which  the  Planet  A 
moves  from  A  to  Ba  is  to  the  time 
of  its  whole  revolution,  as  the  area 
A  C  B,  is  to  the  whole  area  A  B  G  A. 

Ltkewife 


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X  P  R  E  F  A  C  E. 

Likewife  the  area  sdefcribed  by  the 
right  tine  CD;  intbe  motion  of  tht* 
Tlanet  D,  is  ever  as  the  time  in 
which  that  area, is  defcribed'.  jind 
the  time  m  which  '  the  Tlanet  15^ 
moves  from  D  to  E,  is  to  the  trait is* 
of  its  whole  revolution ,  astheared\ 
D  C  E,  is  to  the  whole  area  DEED*  > 
So  alfo  we  may  fuppofe  a  Tlanet y 
moving  in  an  orbit  A  B DC,  of  an v 
elliptical  figure,  in  whofe  focus  at  St 
the  Sun  is.  Here  the  Sun  willbe\ 
nearer  to  feme  parts  of  the  orbits 
than  to  others,  as  to  A  and\&^ 
more  than  to  C  and  D.  In  this\ 
cafe,  if  areas  proportional  to  the  \ 
times  are  defcribed  by  radii  drawn  * 
to  the  Sun  at  S,  by  how  much  the 
diftance  C  S  or  D  S  is  greater  than 
A  S  or  BS,  by  fo  much  will  the  arc 
CD  defcribed  in  any  given portiiMy 
of  time,  be  lefs  than  the  arc  A  B 
defcribed  in  the  fame  time,  ^ 

this,  as  was  faid,  is  what  we'  mean  \ 
by  this  great  law  of  proportionality 


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P  R  E  F  A  C  E.  ■  xi 

the 

tnfofim spfsthe  fPhmetS\abe  jubjebf. 

%\\  %m  \  ';V.»\  V  U'-*  .  \  (  ■  \  ■ 

Vik,  the  M%i,pi*oe  )  we,  may  ex~ 
f€ki»  Mt  'litti&  \  the  'nattcre  >  of  the 
other  heat  of  <  tbd  plddets  rhotions. 
The  meaning  4s.  ims;  that  if  we 
td&eitife  cubes  of  the  difiances  of 
any  ikboTiamts,  as.  Venus,  mid 
Mart  (whibh  are  known  hy  afire* 
nomical  calculation  and  obfervO> 
twtof)\and  the  fquareS  of  the  per&  \ 
cdtiurt  times  cf  the  fame  Ticmets, 
(kkobm  by  the  fame  methods  f)  theft  \ 
f(ndr.  numbers  will)  be,  in  proper*, 
tioks:  Athatft,  the  fquare  of  the ■> 
tmsem  which  Venus  moves  m  the 
orbtt  D  RF,  is  to  the  Jquare  of\ 
the.thnC' m  which  Mars  moves  trt 
thexcrbith  BG,  as  the  cube  of  the 
di/ianee^GD,  is  to  the  cube  of  the 
dJ$Once\&h.'  jind  quantities  in 
thaf  proportion  are  f aid  Jo  have  a 
f  fqmalteral  ratio  to  eachoiher.  v 

•'  •0\Yv\«->n  » .  v  -  •  >.  •  ...  -:\  ■  t.. 

Yv 

This 


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xii  PREFACE. 

This  was  the  fate  of  the  afro- 
nomy  of  the  Tlanets ,  when  Sir 
Isaac  Newton  wrote.  As  to 
the  Comets,  they  were  generally 
thought  to  move  uniformly  in  right 
lines  through  the  celefial  [paces, 
and  not  to  defcrihe  any  orbit  recur¬ 
ring  into  it  [elf,  or  at  all  incurva - 
ted  j  and  it  was  a  prevailing  opi¬ 
nion,  that  at  the  time  tho[e  bodies < 
were  vifible,  their  motions  were 
performed  in  the  regions  beyond 
Saturn. 

•  .  .  ,  v  ..  \\ 

There  remained  one  thing  fari 
ther  to  be  known,  which  was,  the 
cauf  which  retains  the  Tlanetfm 
thofe  regular  motions  which  [hey  arp 
found  to  revolve  with  For  fine# 
projected  bodies,  impelled  by  a/ingle 
force ,  move  by  their  own  nature; 
uniformly  along  the  right  lm[s  id 
which  the  forces  that  impel  thent 
are  dire&ed,  without  any  peffibifity 
of  [(deviating from  tho[e  rectilinear 
paths  [  it  follows  that  bodies,  tike 
the.  TldpetSf  that  move  id  curyp 


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PREFACE.  xiii 

lines ,  mujl  be  aCted  on  by  more  for¬ 
ces  than  one,  or  by  fome  compound 
f<vrce,  drawing  them  out  of  the 
right  lines  they  naturally  tend  to 
defcribe.  The  queflion  then  was , 
of  what  nature  that  force  is  which 
is  diffufed  through  fo  vajl  an  ex¬ 
tent  as  that  of  the  Vianet  ary  Sy- 
flern ,  and  which  feems  tobe fimple 
and  uniform,  by  its  uniform  effects 
above-mentioned,  of  the  proportio¬ 
nality  of  the  areas  and  times  j  and 
the  fefquialteral  ratio  of  the  di- 
Jtance's  and  periods,  [aid  above  to 
be  collected  from  the  obfervations. 

*  To  this  end  the  Author  did  not* 
frame  hypothefes  as  other  philofo- 
pherj  ufed  to  do,  but  fet  himfelf  to 
efdynine  the  phenomena  them - 
TelveSy  by  mathematical  reafoning. 
Ana  fir Ji  of  all,  he  found  that  bo- 
a\is  fle [bribing  areas  proportional 
Ip  'thCpibiCl'1  by  radii  drawn  to  any 
point  ' are  impelled  by  fwo^ 

m&JMM  °f  whkh  ***•' 

itpaafly  endeavour  to  fly  off  in  the 
'  tangents 


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xiv  PREFACE. 
tangents  of  the  orbits  they  defcribe, 
and  by  the  other ,  which  continually 
impells  them  to  the  given  point, 
they  are  with-held  from  doing  fo, 
and  retained  in  thofe  curvilinear 

Since  then  the  Tlanets  by  radii 
drawn  to  the  Sun  defcribe  areas 
proportional  to  the  times,  it  fol¬ 
lows  that  the  compound  force  which 
beeps  them  in  their  regular  motv 
ons  according  to  that  law,  is  com * 
pounded  of  two  forces ;  one  of 
which  impells  them  according  to 
the  tangents  of  their  orbits,  and 
the  other  impells  them  towards  the 
Sun  the  firft  of  which  we  may  call 
the  Trojeftile,  the  other  the  Centri¬ 
petal  Force. 

Now  by  this  difeovery  we  have 
made  a  great  advance,  havingft ymd, 
Firft,  that  this  phenomenon  of 
the  motions  of  the  Tlanets  may  be 
accounted  for  by  two  fuch  forces ; 
and.  Secondly,  that  the  centripetal 
force  is  directed  to  one  fixed  and 


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PREFACE!.  xv 
given  place,  the  Sun's  centre ;  and 
not  to  any  uncertain  and  wandring 
places ;  which  would  have  made 
our  future  /peculations  very  intri¬ 
cate ,  if  it  had  proved  fo.  IVhat 
the  caufe  is  of  this  force ,  we 
do  not  yet  pretend  to  determine ; 
our  bujinejs  is,  fince  fuch  a  force 
is  found  to  exift,  to  [e arch  into  the 
properties  and  proportions  of  that 
force,  before  we  think  of  enquiring 
into  the  caufe  of  it. 

The  next  queflion  is  then  what  . 
proportion  two  centripetal  forces 
actually  bear  to  one  another  in  two 
different  Tlanets.  For  forces  being 
menfurable  quantities,  are  capable 
of  being  compared  together  as  to 
proportion  ;  which  proportion  may 
be  exprejjed  by  numbers ;  in  the 
fame  manner  as  the  proportions 
of  any  two  lines ,  weights ,  &c. 
And  fince  the [e  two  forces  actually 
exijl,  and  operate  upon  the  Tlanets \ 
they  mujl  of  courje  bear  fome  cer- 
tain proportion  to  each  other ,  if  that 

could 


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xvi  PREFACE. 
could  be  found  out .  They  mufl  be 
either  equal  in  all  the  Tlanets ,  or 
greater  in  the  near  eft,  and  lefs  in 
the  more  remote ,  or  vice  verfa. 

The  inveJTtgation  of  thefe  pro¬ 
portions  is  a  mathematical  pro¬ 
blem  j  which  the  Author  ftolves  by 
finding  that  if  federal  bodies  re¬ 
volve  about  a  centre  in  ftuch  orbits 
(i is  the  Tlanets,  and  the  times  of 
their  periods  be  to  each  other  in  a 
fteftqmalteral  ratio,  their  centripe¬ 
tal  forces  willbe  reciprocally  as  the 
fquares  of  the  diftances  from  the 
centre .  Whence  it  follows  that 
fince  the  Tlanets  move  about  the 
Sun  in  periods  having  that  ratio 
to  each  other,  their  centripetal 
forces  towards  the  Sun  are  reci¬ 
procally  as  the  fquares  of  their  dif¬ 
tances  from  the  Suit , 

There  is  therefore  a  virtue  dif- 
fufed  throughout  the  whole  Tlane- 
tary  fyftem  by  which  the  Tlanets 
are  obliged  t  o  tend  on  all  fide s  to¬ 
wards 

y\  . 


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PREFACE.  xvii 
wards  the  Sun  placed  in  the 
common  center  or  focus  of  their 
orbits  j  and  whole  effect  is  always 
in  the  reciprocal  duplicate  ratio  of 
-  the  diflances  from  the  Sun. 

This  is  a  difcovery  for  which  we 
are  beholden  to  the  penetrating 
genius  of  our  great  Author.  Our 
next  enquiry  mujl  be,  whence  this 
virtue  is  propagated.  For  though 
we  know  fuch  a  virtue  exi/ls ,  we 
are  not  yet  certain  whence  it  is 
produced. 

To  fet  us  fome thing  more  for¬ 
ward  in  this  fe arch,  the  Author 
has  dij covered  and  demon  fir  at  edly 
mathematical  reafoning,  that  if  a 
globe  is  compofed  of  particles  to 
each  of  which  there  tend  centripe¬ 
tal  forces  that  are  in  the  recipro¬ 
cal  duplicate  ratio  of  the  diflances 
from  the  particles,  the  centripetal 
forces  tending  to  the  whole  globe 
will  be  alfo  in  the  fame  ratio , 
Therefore ,  fmce  there  are  centri¬ 
petal  forces  tending  to  the  whole 
body  of  the  Sun  which  are  in  that 
reciprocal  duplicate  ratio  of  the 

*  B  dif- 


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xviii  P  R  E  F  A  C  E. 
diflances,  it  follows  that  each  /ingle 
particle  of  the  Suns  body  has  fuch 
centripetal  forces  tending  to  it  act¬ 
ing  in  the  very  fame  ratio.  So  that 
we  fee  the  deflexion  of  the  Tlanets 
from  the  rectilinear  paths  into  the 
curve  orbits  they  defer ibe,  is  occa- 
fioned  by  a  certain  property  of  the 
parts  of  which  the  Sun  is  compofed ', 
which  by  fome  hidden  virtue ,  either 
by  attractions  propagated from  thofe 
parts  or  by  impulfes  directed  to 
them ,  oblige  the  Tlanets  to  tend 
towards  the  Suns  body  perpetually, 
with  forces  that  are  in  the  reci¬ 
procal  duplicate  ratio  of  the  dijlati- 
ces  from  the  Sun.  This  virtue  we 
will  name  an  attractive  virtue ; 
though  the  effect  thereof  is  more 
probably  caufed  by  an  impulfe  from 
without  the  attracted  body,  rather 
than  by  any  thing  emitted  from 
that  which  is  faid  to  attract.  But 
fince  the  names  of  things  are  arbi¬ 
trary,  and  after  this  caution  pre- 
mifed,  this  name  cannot  mijlead 
us,  we  ufe  it  for  the  convenience 
of  brevity. 


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PREFACE,  ;rix 
But  by  the  laws  of  motion  recei¬ 
ved  by  all  philo fophers,  it  is  certain 
that  if  the  particles  of  the  Sun  at¬ 
tract  the  particles  of  the  Planets , 
thefe  latter  mu  ft  alfo  equally  and 
mutually  attract  the  former.  And 
if  Jo,  it  follows  that  the  particles 
of  the  Sun  and  of  the  "Planets  are, 
in  refpeCt  of  this  attractive  virtue , 
entirely  fimilar.  By  Planets ,  I  here 
mean  the  primary.  But  fince  there 
can  be  no  pretence  of  reafon  to  ima¬ 
gine  that  the  fecondary  Planets  are 
in  this  ref  pelt  different  from  the 
primary ,  it  follows  that  all  the  bo¬ 
dies  in  the  Planetary  Syftem  are 
endued  with  this  virtue ,  of  attract¬ 
ing  others  in  the  reciprocal  dupli¬ 
cate  ratio  of  their  difances  from 
the  attracted  body.  And  if  every 
fingle particle  of  each  body  be  fepa- 
rately  endued ,  as  was  Jhewn  above, 
with  this  virtue,  it  follows  that 
where  a  number  of  thofe  particles 
are  united  in  one  body,  the  entire 
force  of  that  whole  body  will  be  cx- 
teris  paribus  as  the  number  of  thofe  r 
particles  j  that  is,  as  its  quantity 
*  B  x  of 


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XX  PREFACE. 

of  matter.  And  fo  the  attractive 
virtue  of  all  bodies  will  be  cseteris 
paribus  as  their  quantity  of  matteri 
Therefore  all  the  Tlanets  may  be 
confidered  as  centers  and  four ces  of 
this  attractive  force  which  [oreads 
it  [elf  about  them  on  all  fiaes ,  at¬ 
tracting  towards  them  from  all 
quarters,  all  bodies  that  are  not 
hindered  by  a  more  forcible  attra¬ 
ction  to  [ome  other  body.  This  is 
farther  confirmed  by  the  revolution 
of  fecondary  Tlanets  about  fome  of 
the  frimary,  ( as  about  the  Earth, 
Jupiter  and  Saturn)  according  to 
the  fame  laws,  which  the  primary 
ob [erve  about  the  Sun,  as  to  the  pro¬ 
portionality  of  times  and  area's, 
and  the  Je[quialteral  ratio  of  the 
dijlances  and  periods :  and  the fame 
thing  appears  by  the  fenftble  effects 
of  the  Moon  upon  the  Earth.  All 
which  demon  fir  ate  that  an  attrac¬ 
tive  virtue  is  propagated from  tho[e 
bodies ,  of  the  very  fame  kind  with 
that  which  is  propagated  from  the 
Sun , 


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And 


PREFACE.  xxi 

And fince,  as  was  fttewn  above,  the 
centripetal  forces  of  the  Sun  and  pri¬ 
mary  Planets  are  in  a  given  ratio  to 
the  periods  and  diftances  of  the  pri¬ 
mary  ‘Planets  about  the  Sun ,  and  of 
the  fecondary  about  the  primary ,  it 
follows  that  we  may  mathematically 
invejligate  from  the  phenomena  the 
proportions  which  the  centripetal for¬ 
ces  of  thofe  celeftial  bodies  jeverally 
bear  to  each  other  ;  and  from  thence 
judge  of  the  effects  they  are  fever  ally 
like  to  produce  in  the  Syftem  of  the 
Wi nld.  And  the  doing  this  is  the  J'ub- 
jeCt  of  the  fir  ft  part  of  this  trad. 

The  fum  therefore  of  thefe  new 
inventions  is  contained  in  this  great 
and  univerfal  truth ,  and  its  corolla¬ 
ries,  That  all  bodies  through  the  whole 
folar  Syftem  \and  therefore  through¬ 
out  the  univerfe,  as  we  have  all  the 
reafon  that  can  be  to fuppofe~\  at  trad, 
or  {which  is  the  term  ufed  mojl  ge¬ 
nerally)  gravitate  towards ,  each  other 
•with  forces  that  are  as  their  quan¬ 
tities  of  matter  dire  Cl ly ,  and  as  the 
fquares  of  their  dijtances  from  each 
other  reciprocally . 


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On 


xxii  PREFACE. 

On  this  great  foundation  the  Au¬ 
thor  builds  two  important  difcoveries , 
entirely  new ;  the  firfl  relating  to 
the  Moon  and  the  tides ;  the  fecond 
relating  to  the  motions  of  the  Comets, 
and  the  figure  of  their  orbits 

AJironomers  have  always  found  the 
Moons  motion  to  be  [abject  to  fo 
many  and  various  irregularities  that 
they  could  never  bring  their  tables  to 
anfwer  to  it,  with  any  thing  near  the 
exa&nefs  they  could  do  in  the  other 
Tlanets.  And  befides,  the  Thano- 
mena  they  obferved  in  her  motion 
were  in  them/ elves  very  odd  and  fur- 
prizing,  there  being  no  example  of  the 
like  in  any  of  the  other  Tlanets.  But 
from  that  great  law  of  nature,  above- 
mentioned,  the  true  fource  of  thofe 
irregularities  has  been  mojl  clearly 
laid  open  by  this  great  writer.  And 
from  the  fame  principles  that  won¬ 
derful  Thaenomenon  of  the  ebbing  and 
flowing  of  the  fea,  is  here  alfo  mojl 
•' plainly  deduced. 

The  AJlronomy  of  Comets  was  en¬ 
tirely  unknown  till  the  time  this  Trail 
was  written.  The  figure  of  the  paths 


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PREFACE.  xxiii 
they  defcribed ,  the  regions  through 
'which  they  faffed  when  they  were  vi- 
Jible  to  us ,  andthofe  to  which  they  af¬ 
terwards  went ,  were  quite  miftdken 
hy  all  the  Afronomers.  But  they  are 
now  fo  clearly  made  known  to  us  by 
the  Author  s  means 9  that  nothing  is 
wanting  to  compleat  that  Aftronomy 
hut  length  of  time  and  opportunities 
of  obfervations.  The  conflruCtion  of  a 
Comet's  trajectory  with  which  this 
Treatife  is  concluded  being  different 
from  that  in  the  Trincipia ,  it  will 
probably  be  acceptable  to  fome  to  fee 
one  of  thofe  e ff ays  that  are  f aid  by  the 
Author  {in  the  ‘Principia )  to  be  made 
by  him  towards  the  foluiion  of  that 
great  and  difficult  problem. 

Some  per  Jons  will  probably  be  ready 
to  enquire  what  is  the  caufe  of  this 
hidden  virtue  of  gravity  which  is  here 
attributed  to  the  heavenly  bodies.  To 
this  the  only  anfwer  is,  that  this  caufe 
is  as  yet  one  of Nature sfecrets :  and 
perhaps  it  will  ever  remain  fo.  ' Tis 
only  plain  from  mathematical  reafon - 
ing  and  undoubted  obfervation,  that 
fuch  a  virtue  exifts  and  operates  in  the 

Syftem 

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xxiv  PREFACE. 

Byftem  of  the  ‘Planets,  and  that  ac¬ 
cording  to  the  laws  above  mentioned. 
Till  a  better  explication  be  found  we 
may  very  well  refolve  it  into  the  IVill 
of  the  All-wife  and  Almighty  Crea¬ 
tor ,  who  when  he formed  and  difpofed 
thefe  bodies ,  by  this  invifible  bond 
made  them  faft  for  ever  and  ever: 
and  gave  them  a  law  which  lhall  not 
he  broken. 

The  reader  is  de fired  to  obferve  that 
the  references  to  propofitions  cited  in 
the  original ',  are  omitted,  fo  that  many 
things  he  will  find  herein  ajferted, 
mujl  be  taken  upon  truft.  The  reafon 
of  this  is,  that  the  great  work  of  the 
Trincipia  in  which  thofe  propofitions 
were  contained,  appears  to  have  been 
put  into  a  very  different  form  after 
this  Trad  was  written,  and  many 
things  were  added  and  altered  there¬ 
in.  This  alteration  caufed  fo  much 
confufion  in  the  citations,  that  it  was 
thought  bejl  to  leave  them  all  out ;  one 
or  two  excepted  which  efcaped  our 
notice ,  arid  have  crept  in  by  overfight. 


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OF 


t  i  1 

ar, ■*»•>■>«  ..«■  ■  if  ht 


OF  THE 

SYSTEM 

OF  THE 

WORLD- 


IT  was  the  ancient  opinion  of  not  a 
few  in  the  earlieft  ages  of 
philofophyjThat  the  fixed  £ 

Stars  flood  immoveable  in 
the  higheft  parts  of  the  world ;  that  un¬ 
der  the  Fixed  Stars  the  Planets  \tere 
carried  about  the  Sun;  that  the  Earth, 
a$  one  of  the  Planets,  defcribed  an  an¬ 
nual  courfe  about  the  Sun,  while  by 
a  diurnal  motion  it  wa9  in  the  mean 
time  revolved  about  its  own  axe  ;  and 
that  the  Sun,  as  the  common  fire  which 
ferved  to  warm  the  whole,  was  fixed  • 
in  the  center  of  the  Univerfe. 

This  was  the  philofophy  taught  of 
old  by  'Philolausy  Arifiarchus  of  Sa¬ 
mos,  Plato  in  his  riper  years,  and  the 
Whole  fed:  of  the  'Pythagoreans .  And 
this  was  the  judgement  of  Anaximan - 
B  der* 


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OF  THE  SYSTEM 

der ,  more  ancient  than  any  of  them,  and 
of  that  wife  king  of  the  Romans  Numa 
! Tom  ft  lius ;  who  as  a  fymbol  of  the  fi¬ 
gure  of  the  World  with  the  Sun  in  the 
center,  ere&ed  a  temple'  in  honour  of 
V ?J1a,  of  a  round  form,  and  ordained  per¬ 
petual  fire  to  be  kept  in  the  middle  of  it. 

The  Egyptians  were  early  oblervers 
of  the  heavens.  And  from  them  pro¬ 
bably  this  philofophy  was  fpread  abroad 
among  other  nations.  For  from  them 
it  was.  and  the  nations  about  them,  that 
the  Greeks ,  a  people  of  themfelves  more 
adduced  to  the  ftudy  of  philology  than 
of  nature,  derived  their  firft  as  well  as 
founded:  notions  of  philofophy.  And 
in  the  veftal  ceremonies  we  may  yet 
trace  the  ancient  fpirit  of  the  Egyptians. 
For  it  was  their  way  to  deliver  their 
myfteries,  that  is  their  philofophy  of 
things  above  the  vulgar  way  of  think¬ 
ing,  under  the  veil  of  religious  rites  and 
hieroglyphick  fymbols. 

It  is  not  to  be  denied  but  that  Ana x- 
agoras,  ‘Democritus  and  others  did  now 
and  then  ftart  up,  who  would  have  it 
that  the  Earth  poflefled  the  center  of 
the  World,  and  that  the  Stars  of  all  forts 
were  revolved  towards  the  weft,  about 
the  Earth  quiefeent  in  the  center,  fome 
at  a  fwifter,  others  at  a  flower  rate. 

'  However, 


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bF  THE  WORLD. 

However,  it  was  agreed  on  both  fides, 
that  the  motions  of  the  celeftial  bodies 
were  performed  in  {paces  altogether  free, 
and  void  of  refiftancc.  The  whim  of 
folid  orbs  was  of  a  later  date,  introdu* 
ced  by  Eudoxus ,  Calippus  and  Arijlo - 
tie ;  when  the  ancient  philofophy  be¬ 
gan  to  decline,  and  to  give  place  to  the 
new  prevailing  fictions  of  the  Greeks. 

But  above  all  things  the  phenomena 
of  Comets  can  by  no  means  conlift  with 
the  notion  of  folid  orbs.  The  Chalde¬ 
ans ,  the  moll  learned  aftronomers  of 
their  time,  looked  upon  the  Comets 
(which  of  ancient  times  before  had  been 
numbered  among  the  celeltial  bodies) 
as  a  particular  fort  of  planets,  which 
delcribing  very  eccentric  orbits,  prefent- 
ed  themfelves  to  our  view  only  by  turns, 
viz.  once  in  a  revolution  when  they 
defcended  into  the  lower  parts  of  their 
orbits. 

And  as  it  was  the  unavoidable  confe* 
quence  of  the  hypothefis  of  folid  orbs. 
While  it  prevailedjthat  the  Comets  lhould 
be  thruft  down  below  the  Moon  ;  fo  no 
fooner  had  the  late  obfervations  of  aftro¬ 
nomers  teftored  the  Comets  to  their  an¬ 
cient  places  in  the  higher  heavens,  but 
thefe  celeftial  (paces  were  at  once  cleared 
of  the  incumbrance  of  folid  orbs,  which 
B  x  by 


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4 


OF  THE  SYSTEM 

by  thefe  obfervations  were  broke  into 
pieces  and  difcarded  for  ever. 

The  principle  ofcir-  WHENCE  it  W4S  that  the  PI*, 

cuiar  motion  in  free  nets  came  to  be  retained  with* 
fpace3‘  in  any  certain  bounds  in  thefe 

free  (paces,  and  to  be  drawn  off  from  the 
re&i linear  courfes,  which,  left  to  them- 
felvcs,  they  fhould  have  purfoed*  into  re-  f 
gular  revolutions  in  curvilinear  orbits, 
are  queftions  which  we  do  not  know  how 
the  ancients  explained.  And  probably 
it  was  to  give  iome  fort  of  fatisfaCtioa 
to  this  difficulty  that  folid  orbs  were  in¬ 
troduced. 

The  later  philofophers  pretend  to  ac¬ 
count  for  it,  either  by  the  a&ion  of 
certain  vortices,  as  Kepler  and  Ties 
Cartes ;  or  by  fome  other  principle  of 
impulfe  or  attraction,  as  Borelli ,  Hook* 
and  others  of  our  nation.  For  from 
the  laws  of  motion  it  is  molt  certain  that 
thefe  effe&s  mult  proceed  from  the  ac¬ 
tion  of  fome  force  or  other. 

But  our  purpofe  is  only  to  trace  oof 
the  quantity  and  properties  of  this  force 
from  the  phenomena,  and  to  apply  what 
We  difcover  in  fome  fimple  cafes,  as 
principles,  by  which,  in  a  mathematical 
Way,  we  may  eftimate  the  effects  there- 
of  in  more  involved  cafes.  For  it  would 
be  endlefs  and  unpoffible  to  bring  every 

par- 


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OF  THE  WORLD. 

particular  to  direCt  and  immediate  ob¬ 
servation. 

We  laid,  in  a  mathematical  way ,  to  a- 
void  all  queftions  about  the  nature  or 
quality  of  this  force,  which  we  would 
not  be  underftood  to  determine  by  any 
hypothecs  and  therefore  call  it  by  the 
general  name  of  a  centripetal  force,  as 
it  is  a  force  which  is  directed  towards 
feme  center ;  and  as  it  regards  more  par¬ 
ticularly  a  body  in  that  center,  we  call 
it  circum  -  lolar ,  circum-terreftrial,  cir- 
cum-jovial,  and  in  like  manner  in  re- 
(peCt  of  other  central  bodies. 

That  by  means  of  centripetal  forces, 
the  Planets  may  be  retained 
in  certain  orbits,  we  may  eafily 
underftand,  if  we  confider  the 
motions  of  projectiles.  For  a  ftone  pro¬ 
jected  is  by  the  prefliire  of  its  own  weight 
forced  out  of  the  rectilinear  path, 
which  by  the  projection  alone  it  Ihould 
have  purlued,  and  made  to  defcribe  a 
curve  line  in  the  air ;  and  through  that 
crooked  way  is  at  laft  brought  down  to 
the  ground.  And  the  greater  the  velo¬ 
city  is  with  which  it  is  projected,  the 
farther  it  goes  before  it  falls  to  the 
Earth.  We  may  therefore  fuppoie  the 
velocity  to  be  lo  encrealed,  that  it 
would  deicribe  an  arc  of  i,  i,  5, 10, 100, 
B  3  1000 


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6 


OF  THE  SYSTEM 

jooo  miles  before  it  arrived  at  the 
Earth,  till  at  laft  exceeding  the  limits  of 
the  Earth,  it  Ihould  pafs  quite  by  with¬ 
out  touching  it. 

Let  A  F 13  reprefent  the  (urface  of  the 
Earth,  C  its  center,  V  D,  V  E,  V  F,  the 
curve  lines  which  a  body  would  de- 
fcribe  if  projected  in  an  horizontal  di¬ 
rection  from  the  top  of  an  high  moun¬ 
tain,  fucceflively  with  more  and  more 
velocity.  And,  becaufe  the  celeftial  mo¬ 
tions  are  fcarcely  retarded  by  the  little 
or  no  refillance  of  the  ipaces  in  which 
they  are  performed  ;  to  keep  up  the  pa¬ 
rity  of  cafes,  let  us  fuppole  either  that 
there  is  no  air  about  the  Earth,  or  at 
Jeaft  that  it  is  endowed  with  little  or  no 
power  of  refilling.  Aud  for  the  lame 
reafon  that  the  body  projeded  with  a 
lefs  velocity,  defcribes  the  lelTer  arc  VD, 
and  with  a  greater  velocity,  the  greater 
arc  V  E,  and  augmenting  the  velocity, 
it  goes  farther  and  farther  to  F  and  G ; 
if  the  velocity  was  Hill  more  and  more 
augmented,  it  would  reach  at  laft  quit? 
beyond  the  circumference  of  the  Earth, 
and  return  to  the  mountain  from  which 
it  was  projected. 

And  fince  the  area’s,  which  by  this 
motion  it  defcribes  by  a  radius  drawn 
fo  the  center  of  the  Earth,  from  the 


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'Digitized  by  v^ooQle 


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OF  THE  WORLD.  7 

principles  of  geometry  are  demonftrated  Prof- 1«. 
to  be  proportional  to  the  times  in  which 
they  are  defcribed ;  its  velocity,  when 
it  returns  to  the  mountain,  will  be  no 
lefs  than  it  was  at  firft  ;  and  retaining 
the  fame  velocity  it  will  delcribe  the 
fame  curve  over  and  over,  by  the  lame 
law. 

But  if  we  now  imagine  bodies  to  be 
projected  in  the  directions  of  lines  pa¬ 
rallel  to  the  horizon  from  greater  heights, 
as  of  5,  io,  loo,  1000  or  more  miles, 
or  rather  as  many  femi-diameters  of  the 
Earth  ;  thole  bodies,  according  to  their 
different  velocity,  and  the  different  force 
of  gravity  in  different  highths,  will  de- 
fcribe  arcs  either  concentric  with  the 
Earth,  or  varioully  excentric,  and  go  on 
revolving  through  the  heavens  in  thole 
trajectories  juft  as  the  Planets  do  in  their  ^ 
orbs. 


As  when  a  ftone  is  projected  oblique¬ 
ly,  that  is,  any  way  but  in  the  , 

perpendicular  direftion.the  per-  "“'.T"’' 
petual  defleCtion  thereof  towards 
the  Earth  from  the  right  line  in  which 
it  was  projected,  is  a  proof  of  its  gravi¬ 
tation  to  the  Earth,  no  lels  certain  than 
its  direct  defcent  when  only  fuffered  to 
fall  freely  from  reft  ;  fo  the  deviation  of 
bodies,  moving  in  free  Ipaces,  from  rec- 
B  4  tilinear 


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8 


OF  THE  SYSTEM 

tiliaear  paths,  and  perpetual  deflexion 
therefrom  towards  any  place,  is  a  lure 
indication  of  the  exiftence  of  feme  force, 
which  from  all  quarters  impells  thole 
bodies  towards  that  place. 

And  as  from  the  luppoled  exiftence 
of  gravity,  it  oecefiarily  follows  that  all 
bodies  abput  the  Earth  mull  prefs  down¬ 
wards,  and  therefore  mnft  either  de- 
fcend  dire<5tly  to  the  Earth,  if  they  are 
let  fall  from  reft,  or  at  leaf):  perpetually 
deviate  from  right  lines  towards  the 
Earth,  if  they  are  proje&ed  obliquely  \ 
f o  from  the  fiippofed  exiftence  of  a  force 
directed  to  any  center,  it  wiU  follow  by 
the  like  oeceflity,  that  all  bodies,  upoq 
which  this  forpe  a<fts,  mull  either  de- 
fcend  dire&ly  to  that  center,  or  at  leaft 
deviate  perpetually  towards  it  from  right 
lines,  if  otherwife  they  ifliould  have  mo¬ 
ved  obliquely  in  thefe  right  lipes. 

And  from  the  motions  given  we  may 
infer  the  forces,  or  from  the  forces  gi¬ 
ven  we  may  determine  the  motions,  by 
mathematical  rcafoning. 

If  the  Earth  is  fiippofed  to  Hand  Hill, 
and  the  fixed  Stars  to  be  revol- 
SlSiS  ved  in  free  i’paccs,  in  the  ipace  of 
motion  of  the  rtarj.  14  hours,  it  is  certain  the  forces; 

by  which  the  fixed  Scars  arc  re- 


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9 


OF  THE  WORLD. 

rained  in  their  orbs,  are  not  dire&ed  to  the 
Earth,  but  to  the  centers  of  the  ieveral 
orbs,  that  is,  of  the  feveral  parallel  cir¬ 
cles,  which  the  fixed  Stars,  declining  to 
one  fide  and  the  other  from  the  Equator, 
describe  daily.  Allb  that  by  radii  drawn  P[°P-  '• 
to  the  liters  of  thole  orbs,  the  fixed  *  e^m’ 
Stars  defcribe  area’s  exadtly  proportio¬ 
nal  to  the  times  of  defcription.  Then 
becaufe  the  periodic  times  are  equal,  ic 
follows  that  the  centripetal  forces  are  as 
the  radii  of  the  leveral  orbs  ;  and  that 
they  will  perpetually  revolve  in  the  lame 
orbs.  And  the  like  conlequcnces  may 
be  drawn  from  the  fuppofed  diurnal  mo¬ 
tion  of  the  planets. 

That  forces  lhould  be  directed  to  no 
Body  on  which  they  phyfically  depend, 
but  to  innumerable  imaginary 
points  in  the  axe  of  the  Earth  The  '"congruous 
is  an  hypothefis  too  incongru-  fu^E”softhl* 
ous.  ’Tis  more  incongruous 
Bill  that  thofe  forces  lhould  increale  ex- 
adtly  in  proportion  of  the  distances  from 
this  axe.  For  this  is  an  indication  of  an 
increale  to  immenfity,  or  rather  to  infi¬ 
nity  ;  whereas  the  forces  of  natural 
things  commonly  decreafe  in  receeding 
from  the  fountain  from  which  they 
flow.  But  what  it  yet  more  ablurd, 
peither  are  the  area’s,  deferibed  by  the 


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JO  OF  THE  SYSTEM 

lame  Star,  proportional  to  the  times, 
nor  are  its  revolutions  performed  in  the 
fame  orb.  For  as  the  Star  recedes  from 
the  neighbouring  pole,  both  area's  aod 
orb  increaie  ;  and  from  the  increafe  of 
or.  i .  the  area,  it  is  demonftrated  that  the  forces 
prep.  2.  are  not  dire&ed  to  the  axe  of  the  Earth. 
And  this  difficulty  arifes  from  the  two¬ 
fold  motion  that  is  obferved  in  the  fixed 
Stars,  one  diurnal  round  the  axe  of  the 
Earth,  the  other  exceeding  flow,  round 
the  axe  of  the  ecliptic.  And  the  ex¬ 
plication  thereof  requires  a  compofition 
of  forces  fo  perplexed  and  fo  variable, 
that  it  is  hardly  to  be  reconciled  with 
any  phyfical  theory. 

That  there  are  centripetal  forces  ac¬ 
tually  directed  to  the  bodies  of 
That  there  is  a  cen-  the  Sun,  of  the  liarth,  and  other 

Uipeta'  force  really  pjaners  thus  j  jnfer. 
directed  to  the  cen-  * 

ter  of  every  planet.  The  Moon  revolves  about 
our  Earth,  and  by  radii  drawn 
to  its  center,  delcribes  area’s  nearly  pro¬ 
portional  to  the  times  in  which  they  are 
deferibed  ;  as  is  evident  from  its  velo¬ 
city  compared  with  its  apparent  diame¬ 
ter.  For  its  motion  is  flower,  when  its 
diameter  is  leis,  ( and  therefore  its  dis¬ 
tance  greater')  and  its  motion  is  fwifter 
when  its  diameter  i§  greater. 


The 


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OF  THE  WORLD. 

The  revolutions  of  the  latellits  of 
Jupiter  about  that  planet  are  more  re¬ 
gular.  For  they  defcribe  circles  concen¬ 
tric  with  Jupiter  by  equable  motions,  as 
exactly  as  our  fenfes  can  diftinguilh. 

And  lo  the  fatellits  of  Saturn  are  re¬ 
volved  about  this  planet  with  motions 
nearly  circular  and  equable,  fcarcely 
disturbed  by  any  eccentricity  hitherto 
obferved. 

That  Venus  and  Mercury  are  revol¬ 
ved  about  the  Sun  is  demonltrable  from 
their  Moon -like  appearances.  When 
they  Ihine  with  a  full  face,  they  are  in 
thole  parts  of  their  orbs  which  in  relpedt 
of  the  Earth  lie  beyond  the  Sun  ;  when 
they  appear  half  foil,  they  are  in  thole 
parts  which  lie  over  againft  the  Sun ; 
when  horned,  in  thofe  parts  which  lie 
between  the  Earth  and  the  Sun,  and 
iometimes  they  pafs  over  the  Sun’s  dife, 
when  diredtly  interpofed  between  the 
Earth  and  the  Sun. 

And  Venus,  with  a  motion  almoft 
uniform,  deferibes  an  orb  nearly  circu¬ 
lar  and  concentric  with  the  Sun. 

But  Mercury,  with  a  more  eccentric 
motion,  makes  remarkable  approaches 
to  the  Sun,  and  goes  off  again  by  turns  $ 
but  it  is  always  fwifter  as  it  is  near  to 
the  §un,  and  therefore  by  a  radius  drawn 

to 


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It 


OF  THE  SYSTEM 

to  the  Sac,  dill  describes  area’s  pro¬ 
portional  to  the  times. 

Laftly,  that  the  Earth  describes  about 
the  Sun,  or  the  Sun  about  the  Earth,  by 
a  radius  from  the  one  to  the  other,  areas 
ext&iy  proportional  to  the  rimes,  is  de- 
monftrable  from  the  apparent  diameter 
of  the  Sun  compared  with  its  apparent 
motion. 

Thefe  are  agronomical  experiments, 
from  which  it  follows  by  geometrical 
reasoning,  that  there  arc  centripetal  for¬ 
ces,  actually  directed  (either  accurately 
or  without  confiderable  errour)  to  the 
centers  of  the  Earth,  of  Jupiter  of  Sa¬ 
turn,  and  of  the  Sun.  In  Mercury, 
Venus,  Mars,  and  the  lefler  planets, 
where  experiments  arc  wanting,  the  ar¬ 
guments  from  analogy  mull  be  allowed 
in  their  place. 

That  thole  forces  decreafe  in  the  du- 

Tbat  thofe  wntripe.  Plicate  proportion  of  the  diftan- 
tai  forces  decree  in  ceS  from  the  center  of  every  pla- 

t’ion^f'Sdrftan^e,  net,  appears  by  Cor. 6. Prop. 4. 
from  the  center  of  For  the  periodic  times  of  the  la- 
every  planet.  tcilits  of  Jupiter  are,  one  to  an¬ 

other,  in  the  fefquipiicate  proportion  of 
their  diftances  from  the  center  of  this 

This  proportion  has  been  long  ago 
obferved  in  thofe  fatellits.  And  Mr. 

Flam - 


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13 


OF  THE  WORLD. 

Flamjieedi  who  had  often  meafured 
their  diftances  from  Jupiter  by  the  mi¬ 
crometer,  and  by  the  eclipfes  of  the  fa- 
tellits,  wrote  to  me,  that  it  holds  to  all 
the  accuracy  that  poffibly  can  be  dift 
cerned  by  our  fenfes.  And  he  lent  me 
the  dimensions  of  their  orbits  taken  by 
the  micrometer  and  reduced  to  the  mean 
diftaoce  of  Jupiter  from  the  Earth  or 
from  the  Sun,  together  with  the  times 
of  their  revolutions,  as  follows  : 


The  greateft  elonga¬ 
tion  of  the  fatellits 

The  periodic  times 

from  the  center  of 

of  their  revolutions. 

Jupiter  as  feen  from 
the  Sun. 

1  h  n 

d.  1).  '  » 

tft 

l  48  or  108 

1  18  28  3$ 

i 

3  oi  or  181 

3  13  17  54 

3d- 

4  4<?  or  28  6 

8  134  or  493 j 

7  03  5  9 

4th. 

16  18  5  13 

Whence  the  fefcjuiplicate  proportion 
may  be  eafily  feen.  For  example,  the 
i6d.  i8h  o i^'isto  the  time  i* 

1,8  b.  28 /.  as  493^'x  c<> 

*o8 11  x  V 108'',  negle&ing  thofe  final! 
fractions  which,  in  obierving  cannot  be 
certainly  determined 

Before  the  invention  of  the  microme¬ 
ter,  the  fame  diftances  were  detertaared 
in  lemi- diameters  of  Jupiter,  thus  : 

Dii- 


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OF  THE  SYSTEM 


Diftance  of  the  : 

ijl. 

id. 

3  *. 

4  th. 

By  Galil<eo 

6 

10 

1 6 

28 

Simon  Marius 

6 

10 

1 6 

2  6 

CaJJini 

5 

8 

*3 

*3 

Sorelli  more 
exaftly 

J-r 

8 1 

14 

*4r 

After  the  invention  of  the  micrometer. 


By  <Tocivnley 

5,51 

8,78 

13,47 

24,72 

Flamfteed 

5,31 

8,55 

13,98 

24,23 

More  accurately 
by  the  eclipfes 

5,578 

8,875  J 

14, *59 

24,903 

And  the  periodic  times  of  thole  la- 
tellits,  by  the  oblervations  of  Mr.  Flam- 
Jleed, are  i  d.  18  h.  28'  36^(3  d.  13  h.  17' 

54/r 1 7 d.  3h.  5"9'  36"  |  i6d.  i8h. 

13^  j  as  above. 

And  the  dillances  thence  computed 
are  578  |  8,878  |  14,168  |  24,968  |  ac¬ 
curately  agreeing  with  the  dillances  by 
oblervation. 

CaJJini  allures  us  that  the  lame  pro¬ 
portion  is  obferved  in  the  circum-latur- 
nal  planets.  But  a  longer  courle  of  ob- 
fervations  is  required  before  we  can 
have  a  certain  and  accurate  theory  of 
thofe  planets* 


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OF  THE  WORLD.  i$ 

In  the  circum-folar  planets.  Mercury 
and  Venus,  the  fame  proportion  holds 
with  great  accuracy  according  to  the 
dimenuons  of  their  orbs,  as  determined 
by  the  obfervations  of  the  beft  Aftrono- 
mers. 


That  the  fuperiour 
planets  are  revolved 
about  the  Sun,  and 
by  radii  drawn  to  the 
Sun,  deferibe  area’s 
proportional  to  the 
times. 


That  Mars  is  revolved  about  the 
Sun,  is  demonftrated  from  the 
phales  which  it  ihews,  and  the 
proportion  of  its  apparent  dia¬ 
meters.  For  from  its  appear¬ 
ing  full  near  conjunction  with 
the  Sun  and  gibbous  in  its  qua¬ 
dratures,  it  is  certain  that  it  furrounds 
the  Sun 

And  fince  its  diameter  appears  about 
five  times  greater,  when  in  oppofition 
to  the  Sun,  than  when  in  conjunction 
therewith,  and  its  diftance  from  the 
Earth  is  reciprocally  as  its  apparent  dia¬ 
meter,  that  diftance  will  be  about  5" 
times  lefs,  when  in  oppofition  to,  than 
when  in  conjunction  with,  the  Sun.  But 
in  both  cafes  its  diftance  from  the  Sun 
will  be  near  about  the  fame  with  the 
diftance  which  is  inferred  from  its  gib¬ 
bous  appearance  in  the  quadratures. 
And  as  it  encompafles  the  Sun  at  almofl: 
equal  diftances,  but  in  refpeCt  of  the 
Earth  is  very  unequally  diftant }  lo  by 
radii  drawn  to  the  Sun  it  defcribeS 

area’s 


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i6 


OF  THE  SYSTEM 

area’s  newly  uniform,  but  by  radii 
drawn  to  the  Earth,  it  is  fbmetimcs 
fwifr,  fbmctrmes  flattonary,  and  ibme- 
times  retrograde. 

That  Jupiter,  in  a  higher  orb  than 
Mars,  is  likewife  revolved  about  the 
Sun,  with  a  motion  nearly  equable,  as 
Well  in  diftance  as  in  the  area’s  defcri- 
bed,  I  infer  thus. 

Mr.  Flamjieed  affured  me  by  letters* 
that  all  the  edipfes  of  the  innermoft  fa- 
tellite,  which  hitherto  have  been  well 
obferved,  do  agree  with  his  theory  for 
nearly,  as  never  to  differ  therefrom  by 
two  minutes  of  time ;  that  in  the  ont- 
moft,  the  errour  is  little  greater  ;  in  the 
outmoft  but  one,  fcarcely  three  times 
greater ;  that  in  the  innermoft  but  one* 
the  difference  is  indeed  much  greater* 
yet  fb  as  to  agree  as  nearly  with  his 
computations,  as  the  Moon  does  with 
the  Common  tables.  And  that  he  com¬ 
putes  thofe  eclipfes  only  from  the  mean 
motions  corrected'  by  the  equation  of 
light  difcovered  and  introduced  by  Mr. 
Rower.  Suppofing  then  that  the  theory1 
differs  by  a  lefs  errour  than  that  of 
from  the  motion  of  the  outmoft  fatdlite 
as  hitherto  defcribed ;  and  taking  as  the 
periodic  time  16  d.  18  b.  y'  13^  to  1/ 
in  time,  fo  is  the  whole  circle  or  360°  to 

the 


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OF  T  k  E  WORLD. 

tfie  arc  i'  48 11 ;  the  errour  of  Mr.  Flam - 
fieed’s  Computation  reduced  to  the  fatel- 
lite’s  orbit,  willbelefs  than  i>  48 /f,  that 
is,  thd  longitude  of  the  fatellite,  as  feen 
frofcn  the  center  of  Jupiter,  will  be  de¬ 
termined  with  a  lefs  erf  our  thah  1'  48". 
But  when  the  latellite  is  in  the  middle  of 
the  Ihadow,  that  longitude  is  the  fame 
with  the  heliocentric  longitude  of  Ju-' 
£iter.  And  therefore  the  hypothefis 
Which  Mr.  Flamjteed  follows,  viz.  the 
Copernican  as  improved  by  Kepler ,  and 
(as  to  the  motion  of  Jupiter)  lately 
corrected  by  himfelf,  rightly  reprefents 
that  longitude  within  a  lels  errour  than 
i,48//.  But  by  this  longitude,  toge¬ 
ther  with  the  geocentric  longitude,  which 
is  always  eafily  found,  the  diftance  of 
Jupiter  from  the  Sun  is  determined  : 
Which  inuft  therefore  be  the  very  lame 
with  that  which  the  hypothefis  exhibits. 
For  that  greateft  erroUr  of  1'  48''  that 
can  happen  in  the  heliocentric  longitude 
is  almoft  inlenfible,  and  quite  to  be  neg- 
te&ed,  and  perhaps  may  arile  from  lome 
jet  undilcovered  eccentricity  of  the  fa- 
tellite.  But  when  both  longitude  and 
diftance  are  rightly  determined,  it  fol¬ 
lows  of  necefiity,  that  Jupiter  by  radii 
drawn  to  the  Sun,  defcribes  area’s  lo 


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1.8  OF  THE  SYSTEM 

conditioned  as  the  hypothefis  requires, 
that  is,  proportional  to  the  times. 

And  the  fame  thing  may  be  conclu¬ 
ded  of  Saturn  from  his  fatellite  by  the 
obfervations  of  Mr.  Huygens  and  Dr. 
Halley  j  though  a  longer  ieries  of  obfer¬ 
vations  is  yet  wanting  to  confirm  the 
thing,  and  to  bring  it  under  a  fufficiently 
exadt  computation. 

For  if  Jupiter  was  viewed  from  the 
Sun,  it  would  never  appear  re- 
That  the  forec  which  troorade  nor  ftationary,  as  it  is 
CnLilnZt  f«n  fometio.es  from  the  Earth, 

ted,  not  to  the  Earth  alw^YS  tO  gO  forward  With 

but  to  the  Sun.  a  motion  nearly  uniform.  And 
from  the  very  great  inequality  of  its  ap¬ 
parent  geocentric  motion,  we  infer  that 
the  force  by  which  Jupiter  is  turned 
out  of  a  re&ilinear  courle  and  made  to 
revolve  in  an  orb,  is  not  dire&ed  to  the 
center  of  the  Earth.  And  the  lame  ar¬ 
gument  holds  good  in  Mars  and  in  Sa¬ 
turn.  Another  center  is  therefore  to 
be  looked  for,  about  which  the  a- 
rea’s  delcribed  by  radii  intervening, 
may  be  equable.  And  that  this  is  the 
Sun,  we  have  proved  already  in  Mars 
and  Saturn  nearly,  but  accurately 
nough  in  Jupiter.  It  may  be  alledged 
that  the  Sun  and  Planets  are  impelled 


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19 


OF  THE  WORLD. 

by  lome  other  force,  equally  and  in 
the  direction  of  parallel  lines.  But  by 
Inch  a  force  no  change  would  happen  in 
the  lituation  of  the  Planets  one  to  an¬ 
other,  nor  any  fenfible  effect  follow  ; 
but  our  bufinefs  is  with  the  caufes  of 
fenfible  effe&s.  Let  us  therefore  negle<^ 
every  fuch  force  as  imaginary  and  pre¬ 
carious,  and  of  no  ufe  in  the  phenome¬ 
na  of  the  heavens  ;  and  the  whole  re¬ 
maining  force  by  which  Jupiter  is  im¬ 
pelled,  will  be  dire&ed  to  the  center  of 
the  Sun.  The  argument  from  analogy 
proves  the  lame  thing  in  Mars  and  Sa¬ 
turn  ;  and  in  Saturn,  it  may  be  made 
out  dire&ly  from  its  latellite  by  the  ob- 
fervations  of  Mr.  Huygens  and  Dr.  Hal¬ 
ley ,  though  a  longer  feries  of  obferva- 
tions  is  required  for  the  confimation  of 
it. 

Thb  diftances  of  the  Planets  from  the 
Sun  come  out  the  fame,  whe-  That  the  drcum.fo. 
thcr,  with  Tytho,  we  place  the  lar  force  throughout 

Earth  in  the  center  of  the  fyf-  Jle 

tem,  or  the  Sun  with  Coper-  f«h  in  the  duplicate 

nicus:  and  we  have  already  Pr°Pomo"  of  'J1* 

.  .  i  r  i-n  J  diftances  from  the 

proved  that  thele  durances  are  sun. 
true  in  Jupiter. 

Kepler  and  Bullialdus  have,  with 
greac  care,  determined  the  diftances  of 
the  planets  from  the  Sun.  And  hence 
C  i  it 


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io 


OF  THE  SYSTEM 

it  is  that  their  tables  agree  beft  with  the 
heavens.  And  in  all  the  Planets,  in  Ju¬ 
piter  and  Mars,  in  Saturn  and  the 
Earth,  as  Well  as  in  Vends  and  Mer¬ 
cury,  the  cubes  of  their  diftances  are  as 
the  fquares  of  their  periodic  times ;  and 
therefore  the  centripetal  circum-lolar 
force,  throughout  all  the  planetary  re¬ 
gions,  decreafes  in  the  duplicate  propor¬ 
tion  of  the  diftances  from  the  Sun.  In 
examining  this  proportion,  we  are  to 
ule  the  mean  diftances,  or  the  tranfverle 
femi-axes  of  the  orbits,  and  to  negledb 
thole  little  fractions,  which,  in  defining 
the  Orbits,  may  have  arole  from  the  in- 
fenfibleerrours  of  oblervation,  or  may  be 
alcribed  to  other  cauies  which  we  lhall 
afterwards  explain.  And  thus  we  lhall 
always  find  the  faid  proportion  to  hold 
exa&ly.  For  the  diftances  of  Saturn, 
Jupiter,  Mars,  the  Earth,  Venus  and 
Mercury  from  the  Sun  drawn  from  the 
obfervations  of  Aftronomers,  are,  ac¬ 
cording  to  the  computation  of  Kepler , 
as  the  numbers  951000,519650,152350, 
100000,72400,38806  ;  by  the  compu¬ 
tation  of  Bullialdus,  as  the  ntimbers, 
9541 98,522  5  20,1 52350, 100000, 7x398, 
38585  j  and  from  the  periodic  times 
they  come  out  953806,520116,152399, 
100000,72333,38710.  Their  diftan¬ 
ces, 


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IX 


OF  THE  WORLD. 

CCS,  according  to  Kepler  and  Bull'tal- 
dus ,  fearcely  differ  by  any  fenfible  quan¬ 
tity,  and  where  they  differ  moft,  the 
diftances  drawn  from  the  periodic  times 
fall  in  between  them. 


That  the  circum-terreftrial  force  like 
wile  decreafes  in  the  duplicate 
proportion  of  the  diftances, 
thus  I  infer. 

The  mean  diftance  of  the 
Moon  from  the  center  of  the 
Earth,  is  in  femi-diameters  of 
the  Earth,  according  to  *Pto- 
lomy^  Kepler  in  his  Ephemerides ,  Bui¬ 
lt  aldus,  Hevelius  and  Ricciolus ,  59  ;  ac¬ 
cording  to  Flatnfteed  59  according  to 
Tycho  to  Vendelin  60,  to  Coperni¬ 
cus  60 j,  to  Kircher 


That  the  circum-ter¬ 
reftrial  force  decrea¬ 
fes  in  the  duplicate 
proportion  of  the 
diftances  from  the 
Earth  proved  in  the 
hypothecs  of  the 
Earth’s  being  at  reft. 


But  Tycho  and  all  that  follow  his  ta¬ 
bles  of  refraeftion,  making  the  refracti¬ 
ons  of  the  Sun  and  Moon  (altogether 
againft  the  nature  of  light)  to  exceed 
thofe  of  the  fixed  Stars,  and  that  by  a- 
bout  four  or  five  minutes  in  the  hori¬ 
zon,  did  thereby  augment  the  horizon¬ 
tal  parallax  of  the  Moon,  by  about  the 
like  number  of  minutes,  that  is,  by  a- 
bout  the  izth  or  15th  part  of  the  whole 
parallax.  CorreCt  this  errour,and  the  difi 
$nce  will  become  60  or  61  femi-diame- 


C  3  ters 


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21 


OF  THE  SYSTEM 

ters  of  the  Earth,  nearly  agreeing  with 
what  others  have  determined. 

Let  us  then  alTume  the  mean  didance 
of  the  Moon,  6  o  femi-diameters  of  the 
Earth,  and  its  periodic  time  in  relpe& 
of  the  fixed  Stars,  17 d.  7 h.  43',  as 
Adronomcrs  have  determined  it.  And 
a  body  revolved  in  our  air,  near  the  fur- 
face  of  the  Earth  fuppofed  at  red,  by 
means  of  a  centripetal  force,  which 
Ihould  be,  to  the  lame  force  at  the  di£ 
tanceof  the  Moon,  in  the  reciprocal  du¬ 
plicate  proportion  of  the  didances  from 
the  center  of  the  Earth,  that  is,  as  $6qq 
to  1  ;  would  (lecluding  the  refidance  of 
the  air)  compleat  a  revolution  in  1  h. 
14',  17".  „ 

Suppole  the  circumference  of  the 
Earth  to  be  1x3149600  Tarts  feet,  as 
has  been  determined  by  the  late  menlu- 
ration  of  the  French :  and  the  lame  bo¬ 
dy,  deprived  of  its  circular  motion,  and 
falling  by  the  impulfe  of  the  lame  cen¬ 
tripetal  force  as  before,  would,  in  one 
fecond  of  time,  defcribe  15  f,  Tarts 
feet. 

This  we  infer  by  a  calculus,  ahd  it 
agrees  with  what  we  .oblerve  in  all  bo¬ 
dies  about  the  Earth.  For  by  the  exjpe- 
riments  of  pendulums,  and  a  computa¬ 
tion 


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*3 


OF  THE  WORLD. 

tion  raifed  thereon,  Mr.  Huygens  has 
demonftrated  that  bodies  falling  by  all 
that  centripetal  force,  with  which  (of 
whatever  nature  it  is)  they  are  impelled 
near  the  furface  of  the  Earth,  do,  in  one 
fecond  of  time,  defcribe  15  lT  Tans 
feet. 


But  if  the  Earth  is  fuppoled  to  move, 

the  Earth  and  Moon  together  pJme  pr0ved  in 

will  be  revolved  about  their  the  hypothefis  of  the 
_ Earth’s  motion. 

common  center  or  gravity. 

And  the  Moon  will  in  the  fame  perio¬ 


dic  time  17  d.  7  h  43',  with  the  fame  cir- 
cum-terreftrial  force,  diminilhed  in  the 


duplicate  proportion  of  the  diftance,  de- 
fcribe  an  orbit,  whole  femi-diameter  is 
to  the  femi-diameter  of  the  former  orbit. 


that  is,  to  60  femi-diametersof  the  Earth, 
the  fum  of  both  the  bodies  of  rhe  Earth 


and  Moon  to  the  firft  of  two  mean  pro- 
portionals  between  thisfiim  and  the  body 
of  the  Earth ;  that  if  we  fuppofe  the 
Moon  (on  account  of  its  mean  appa¬ 
rent  diameter  3 1  ir)  to  be  about  ,V  of  the 

Earth,  as  43  to  yV.  41x43]%  or  as  a* 
bout  128  to  117.  And  therefore  the 
femi-diameter  of  the  orbit,  that  is,  the 
diftance  between  the  centers  of  the 
Moon  and  Earth,  will  in  this  cafe  be  60  4 
femidiameters  of  the  Earth,  almoft  the 
fame  with  that  afligned  by  Copernicus, 
'  t  '  C  4  which 


Digitized  by  LjOOQle 


OF  THE  SYSTEM 

which  the  Tychonic  obfervations  by  no 
means  difprove.  And  therefore  the  du¬ 
plicate  proportion  of  the  decrement  of* 
the  force  holds  good  in  this  diftance. 
I  have  negledted  the  increment  of  the 
orbit,  which  ariles  from  the  a&ion  of 
the  Sun,  as  inconfidcrable.  But  if  that  is 
fubdutfted,  the  true  diftance  will  re¬ 
main,  about  6of  femidiameters  of  the 
Earth. 


But  further,  this  proportion  of  the 
The  decrement  of  decrement  of  the  forces  is  con- 

tSfc a^pTojor^nof  firmed  ^  the  eccentricity  of 
the  diftances  from  the  Planets,  and  the  very  flow 
&**££?■£;  motion  of  their  apfes.  For  in 
the  eccentricity  of  no  other  proportion^  could  the 
ihe  planer*,  and  the  circum-folar  planets,  'once  in 

their  apfes.  every  revolution  delcend  to 

their  leaft  and  once  afcend  to  their 
greatcft  diftance  from  the  Sun,  and  the 
places  of  thole  diftances  remain  immo¬ 
vable.  A  fmall  efrour  from  the  dupli¬ 
cate  proportion,  would  produce  a  mo¬ 
tion  of  the  aples,  confiderable  in  every 
revolution,  but  in  many  enormous.  - 
’  But  now  after  innumerable  revolu¬ 


tions,  hardly  any  luch  ifiotion  has  beeh 
perceived  in  the  orbs  of  the  circum-fo¬ 
lar  planets.  Some  Aftronomers  affirm, 
that  there  is  no  fuch  motion,  others  red** 
kon  it  hq  greater  than  what  may  eaftiy 
v  *  artle 


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OF  THE  WORLD.  if 

arife  from  the  caules  hereafter  to  be  sS- 
figned,  and  is  of  no  moment  in  the  prp- 
fent  queftion. 

We  may  even  negledt  the  motion  pf 
the  Moon’s  apfe,  which  is  far  greater 
than  in  the  circum -Tolar  planets,  a- 
mounting  in  every  revolution  to  three 
degrees.  And  from  this  motion  it  is 
demonftrable,  that  the  circum-terreftrial 
force  decreafes  in  no  lefs  than  the  du¬ 
plicate,  but  fgr  lefs  than  the  tripli¬ 
cate  proportion  of  the  diftance.  For 
if  the  duplicate  proportion  was  gradu¬ 
ally  changed  into  the  triplicate,  the  mo¬ 
tion  of  the  apfe  would  thereby  increafe 
to  infinity ;  and  therefore,  by  a  very 
finall  mutation,  would  exceed  the  mo¬ 
tion  of  the  Moon’s  apfe.  This  flow 
motion  arifes  from  the  a&ion  of  the 
circum-folar  force,  as  we  lhall  afterwards 
explain.  But  fecluding  this  caufe,  the 
apfe  or  apogeon  of  the  Moon  will  be 
fixed,  and  the  duplicate  proportion  of 
the  decreafe  of  the  circum-terreftrial 
force  in  different  diftances  from  the 
Earth,  will  accurately  take  place. 

Now  that  this  proportion  has  been 
pftablifhed,  w?  may  compare  The  quantity  of  the 
the  forces  of  the  fevcral  planets  r°'“; 
gmong  themfelvcs.  planet*.  The  dr¬ 

ip  the  mean  diftance  of  Ju-  *um-folar  very  great. 

piter 


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1 6  OF  THE  SYSTEM 

piter  from  the  Earth,  the  greateft  elon¬ 
gation  of  the  outmofl  fatellite  from  Ju¬ 
piter’s  center  (  by  the  obfervations  of 
Mr.  Flamfteed)  is  8'  isft.  And  there¬ 
fore  the  diftance  of  the  fatellite  from  the 
center  of  Jupiter,  is  to  the  mean  diftance 
of  Jupiter  from  the  center  of  the  Sun, 
as  1x4  to  5'2ora,  but  to  the  mean  dif¬ 
tance  of  Venus  from  the  center  of  the 
Sun,  as  114  to  7134.  And  their  perio¬ 
dic  times  are  16 £d.  and  xi4fd.  And 
from  hence  (according  to  Cor.  x.  Fro^. 
4.)  dividing  the  difiances  by  the  fquares 
of  the  times,  we  infer  that  the  force  by 
which  the  fatellite  is  impelled  towards 
Jupiter,  is  to  the  force  by  which  Ve¬ 
nus  is  impelled  towards  the  Sun,  as  44Z 
to  143.  And  if  we  diminifh  the  force, 
by  which  the  fatellite  is  impelled  in 
the  duplicate  proportion  of  the  diftance 
1x4  to  7x34,  we  fhall  have  thecircum- 
jovial  force,  in  the  diftance  of  Venus 
from  the  Sun,  to  the  cirCum-folar  force 
by  which  Venus  is  impelled,  as  {4<»  to 
143,  or  as  1  to  1 100.  Wherefore  at 
equal  diftances,  the  circum  -  fblar  force 
is  1100  times  greater  than  the  circum- 
jovial. 

And  by  the  like  computation,  from 
the  periodic  time  of  the  fatellite  of  Sa¬ 
turn  1 5  d.  xxih.  and  its  greateft  elongation 

from 

% 


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OF  THE  WORLD.  ij 

fromSaturn, while  that  planet  is  in  ks  mean 
diftance  from  us,  3 1  20";  it  follows 
that  the  diftance  of  this  fatellite  from 
Saturn’s  center,  is  to  the  diftance  of 
Venus  from  the  Sun,  as  92  $  to  7234; 
and  from  thence  that  the  abfolute  cir- 
cum-folar  force  is  2360  times  greater 
than  the  abfolute  circum-faturnial. 

From  the  regularity  of  the  heliocen¬ 
tric  and  irregularity  of  the  geo- 
centric  motions  of  Venus,  of 
Jupiter,  and  the  other  planets, 
it  is  evident  that  the  circum-terreftrial 
force,  compared  with  the  circum-folar, 
is  very  final!. 

Ricciolus  and  Vendel'tn  haveleverally 
tried  to  determine  the  Sun’s  parallax', 
from  the  Moon’s  dichotomies  obferved 
by  the  telefcope,  and  they  agree  that  it 
does  not  exceed  half  a  minute. 

Kepler  from  Tycho's  obfervations  and 
his  own,  found  the  parallax  of  Mars 
infenfible,  even  in  oppofition  to  the  Sun, 
when  that  parallax  is  fbmething  greater 
than  the  Sun’s. 

Flamjieed  attempted  the  fame  paral¬ 
lax  with  the  micrometer  in  the  perigeon 
pofition  of  Mars,  but  never  found  it 
above  25"  ^  and  thence  concluded  the 
Sun’s  parallax  at  mod  10^. 

Whence 


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*8  OF  THE  SYSTEM 

Whence  it  follows  that  the  diliance 
of  the  Moon  from  thp  Earth  bears  no 
greater  proportion  to  the  diftance  of  the 
Earth  from  the  Sun,  than  2.9  to  10000  ; 
nor  to  the  diliance  of  Venus  from  the 
Sup,  than  19  to  7233. 

From  which  diftances,  together  with 
the  periodic  times,  by  the  method  a- 
bove  explained  it  is  eafy  to  infer,  That 
the  abfoiute  circum-folar  force  is  greater 
than  the  abfoiute  circum-terreftrial  force 
at  leaft  119400  times. 

And  though  we  were  only  certain, 
from  the  obfervations  of  Ricciolus  and 
Vendelin ,  that  the  Sun’s  parallax  was 
lels  than  half  a  minute,  yet  from  this  it 
will  follow,  that  the  abfoiute  circum-fo- 
lar  force  exceeds  the  abfoiute  circum- 
terreftrial  force  8500  times. 

By  the  like  Computations  I  happen- 
The  apparent  dia-  cd  to  dilpover  an  analogy  that 
meters  of  the  pia-  is  qbferved  between  the  forces 
and  the  bodies  of  the  Planets. 
But  before  I  explain  this  analogy,  the 
apparent  diameters  of  the  Planets  in 
their  mean  diftances  from  the  Earth, 
muft  be  firft  determined. 

Mr.  Flamji eed,  by  the  micrometer, 
paeafured  the  diameter  of  Jupiter  40"  or 
4l,,»  the  diameter  of  Saturn’s  png  jo!*, 

and 


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OF  THE  WORLD. 

and  the  diameter  of  the  Sun  about  31'. 

13". 

But  the  diameter  of  Saturn  is  to  the 
diameter  of  the  ring,  according  to  Mr. 
Huygetis  and  Dr.  Halley ,  as  4  to  9  ;  ac¬ 
cording  to  Galletiusy  as  4  to  10 ;  and 
according  to  Hook  (by  a  telelcope  of  &o 
feet)  as  i  to  12.  And  from  the  mean 
proportion  5  to  1 2,  the  diameter  of  Sa¬ 
turn’s  body  is  inferred  about  21". 

Such  as  we  have  laid  are  the  appa- 
rent  magnitudes.  But  becaufe  Th.  „,„ai00  of 
Of  the  unequal  refrangibility  of  the  apparent  diame- 
light,  all  lucid  points  are  dila-  ters- 
ted  by  the  telelcope,  and  in  the  focus  of 
the  objective  glafs  poflefs  a  circular 
fpace,  whofe  breadth  is  about  the  50th 
part  of  the  aperture  of  the  glafs. 

It  is  true,  that  towards  the  circumfe¬ 
rence,  the  light  is  fo  rare  as  hardly  to 
move  the  fenfe,  but  towards  the  middle, 
where  it  is  of  greater  denlity,  and  is 
fenfible  enough,  it  makes  a  fmall  lucid 
circle,  whole  breadth  varies  according  to 
the  lplendour  of  the  lucid  point,  but  is 
generally  about  the  3d,  or  4th,  or  jth 
part  of  the  breadth  of  the  whole. 

Let  A  B  D  reprelenc  the  circle  of  the 
whole  light,  P  the  fmall  circle  of  the 
denier  and  dearer  light,  C  the  center  of 

both ; 


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OF  THE  SYSTEM 

both  ;  C  A,  C  B  femi-diameters  of  the 
greater  circle  containing  a  right  angle 
at  C ;  A  C  B  E  the  fquare  comprehend¬ 
ed  under  thefe  femi-diameters,  A  B  the 
diagonal  of  that  Iquare  ;  E  G  H  an  hy¬ 
perbola  with  the  center  C  and  afymptotes 
C  A,  C  B  ;  P  G  a  perpendicular  ere&ed 
from  any  point  P  of  the  line  B  C,  and 
meeting  the  hyperbola  in  G,  and  the 
right  lines  A  B,  A  E  in  K  and  F  :  and 
the  denfity  of  the  light  in  any  place  P, 
will,  by  my  computation,  be  as  the  line 
FG»  and  therefore  at  the  center  infinite, 
but  near  the  circumference  very  (mail. 
And  the  whole  light  within  the  fmali 
circle  P  Q  is  to  the  whole  without,  as 
the  area  of  the  quadrilateral  figure 
C  A  K  P  to  the  triangle  P  K  B.  And  we 
are  to  underftand  the  fmali  circle  P  Q^to 
be  there  terminated,  where  F  G  the  den¬ 
sity  of  the  light  begins  to  be  left  than 
what  is  required  to  move  the  fenfe. 

Hence  it  was  that  at  the  diftance  of 
191381  feet,  a  fire  of  3  feet  in  diameter, 
through  a  telefcope  of  3  feet,  appeared 
to  Mr.  Tic  art  of  8".  in  breadth,  when  it 
ihould  have  appeared  only  of  3".  14'". 
And  hence  it  is  that  the  brighter  fixed 
Stars  appear  through  the  telelcope,  as 
of  5"  or  6"  in  diameter,  and  that  with  a 


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OF  THE  WORLD. 

good  full  light,  but  with  a  fainter  light 
they  appear  to  run  out  to  a  greater 
breadth.  Hence  likewife  it  was  that  He- 
* velius ,  by  diminifhing  the  aperture  of 
the  telefcope,  did  cut  off  a  great  part  of 
the  light  towards  the  circumference,  and 
brought  the  dife  of  the  Star  to  be  more 
diftinCtly  defined,  which  though  hereby 
diminifhed,  did  yet  appear  as  of  5"  or 
6"  in  diameter.  But  Mr.  Huygens  only 
by  clouding  the  eye-glafs  with  a  little 
frnoak,  did  lb  effectually  extinguifh  this 
fcattered  light,  that  the  fixed  Stars  ap¬ 
peared  as  meer  points,  void  of  all  fenli- 
ble  breadth.  Hence  alfo  it  was  that 
Mr.  Huygens ,  from  the  breadth  of  bo¬ 
dies  interpofed  to  intercept  the  whole 
light  of  the  Planets,  reckoned  their  dia¬ 
meters  greater  than  others  have  meafu- 
red  them  by  the  micrometer.  For  the 
fcattered  light  which  could  not  be  fecn 
before  for  the  ftronger  light  of  the  Pla¬ 
net,  when  the  Planet  is  hid  appears 
every  way  further  fpread.  Laflly  from 
hence  it  is  that  the  Planets  appear  fo 
(mail  in  the  dife  of  the  Sun,  being  leflen- 
ed  by  the  dilated  light.  For  to  Heveliusf 
Galletius ,  and  Dr.  Halley ,  Mercury  did 
not  feem  to  exceed  ix"  or  15".  And 
Venus  appeared  to  Mr.  Crabtrie  only. 
V-.  i".  to  Horrox  but  i'.  ix",  though 

by 


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OF  tkt  SYSTEM 

by  the  menfurations  of  Hevelius  and 
Hugenius  without  the  Suu’s  difc,  it 
ought  to  have  been  feen  at  leaft  i\  14". 
Thus  the  apparent  diameter  of  the 
Moon,  which  in  1684,  a  few  days  both 
before  and  after  the  Sun’s  eclipfe,  was 
meafured  at  the  obfervatory  of  Farit 
31'.  30";  in  the  eclipfe  it  lelf  did  not 
feem  to  exceed  ?o/  or  3o/.  05".  And 
therefore  the  diameters  of  the  Planets 
are  to  be  diminifhed,  when  without  the 
Sun,  and  to  be  augmented  when  within 
it  by  fome  feconds.  But  the  errours 
feem  to  be  lefs  than  ufual  in  the  menfu¬ 
rations  that  are  made  by  the  microme¬ 
ter.  Sb  from  the  diameter  of  the  fha- 
dow,  determined  by  the  eclipfes  of  the 
fatellites,  Mr.  Flamjleed  found  that  the 
diameter  of  Jupiter,  was  to  the  greateft 
elongation  of  the  outmoft  fatellite  as  1! 
to  24,903.  Wherefore  fince  that  don- 
gationds  8'.  13'',  the  diameter  of  Jupi¬ 
ter  will  be  39  i"  ;  and  rejedhog  the 
lcattered  light,  the  diameter,  found  by 
the  micrometer  40"  or  41",  will  be  re¬ 
duced  to  39^ .  And  the  diameter  of  Sa¬ 
turn  zi't,  is  to  be  diminifhed  by  the 
like  corre&ion,  and  to  be  reckoned  20" 
or  fomething  lefs.  But  ( if  I  am  not 
miftakenj  the  diameter  of  the  Sun,  be- 

£aufe 


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33 


OF  THE  WORLD. 

caufe  of  its  ftronger  light  is  to  be  dimi- 
niih’d  fomething  more,  and  to  be  reck¬ 
oned  about  31'.  or  )zr.  6 fl. 

That  id  near  an  analogy  Ihould  be 
found  among  bodies  of  magni-  why  the  denfIty  k 
tudes  lo  different,  is  nbt  with-  greater  in  Tome  otthe 
out  lome  myltery.  planets*  ,and  'ef* in 

T  *  J  -  J  -  others  *  but  the  for- 

it  may  be  that  the  remoter  ces  in  ail  are  as  their 
Planets,  for  want  of  heat,  have  9uantitie* of  matter* 
not  thole  metallic  fubftances  and  pon¬ 
derous  minerals  with  which  our  Earth 
abounds  ;  and  that  the  bodies  of  Venus 
and  Mercury*  as  they  are  more  expoled 
to  the  Sun’s  heat,  are  alfo  harder  baked 
and  more  compact. 

For  from  the  experiment  of  the  burn- 
ing  glafs,  we  lee  that  the  heat  increales 
With  the  denfity  of  light.  And  this 
denfity  increales  in  the  reciprocal  du¬ 
plicate  proportion  of  the  diftance  from 
the  Sun.  From  whence  the  Sun's  heat 
in  Mercury  is  proved  to  be  feven-fold 
its  heat  in  our  lummer  leafons.  But 
With  this  heat  our  water  boyls ;  and 
thofe  heavy  fluids,  quickfilver  and  the 
jpirits  of  vitriol,  gently  evaporate,  as  I 
have  tryed  by  the  thermometer.  And 
therefore  there  can  be  no  fluids  in  Mer¬ 
cury,  but  what  are  heavy,  and  able  to 
hear  a  great  heat,  and  from  which  fub- 
D  fiances 


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34 


OF  THE  SYSTEM 
fiances  of  great  denfity  may  be  nou- 
rifh’d. 

And  why  n<jt?  if  God  has  placd 
different  bodies  at  different  diftances 
from  the  Sun,  fo  as  the  dtnfer  bodies 
always  pofiefs  the  nearer  places,  and 
each  body  enjoys  a  degree  of  heat  Writa¬ 
ble  to  its  condition,  and  proper  for  its 
nourifhment.  From  this  confederation 
it  will  beft  appear  that  the  weights 
of  all  the  Planets  are  one  to  another  as 
their  forces. 

But  1  fhould  be  glad  the  diameters 
of  the  Planets  were  more  accurately 
meaiured.  And  that  may  be  done,  if  a 
lamp,  fet  at  a  great  diftance,  is  made  to 
fhine  through  a  circular  hole,  and 
both  the  hole  and  the  light  of  the  lamp  are 
fo  diminifhed  that  the  ipe&rum  may  ap¬ 
pear  through  the  telefcope  juft  like  the 
Planet,  and  may  be  defined  by  the  fame 
meafure.  Then  the  diameter  of  the  hole 
will  be  to  its  diftance  from  the  objective 
glafs,  as  the  true  diameter  of  the  Pla¬ 
net  to  its  diftance  from  us.  The  light 
of  the  lamp  may  be  diminifhed  bv  the 
interpofition  either  of  pieces  of  cloath, 
or  of  fmoaked  glafs. 


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OF  THE  WORLD.  3* 

O  f  kin  to  the  analogy  we  have  been 
deferibing,  there  is  another  Another  analogy 
obferved  betwen  the  forces  and 
the  bodies  attradied.  Since  the  in  the  esieftui  bo- 
action  of  the  centripetal  force  d,c,• 
upon  the  Planets  decreafes  in  the  dupli¬ 
cate  proportion  of  the  distance,  and  the 
periodic  time  increafesin  the  fefquiplicate 
thereof,  it  is  evident  that  the  a  diions  of 
the  centripetal  force,  and  therefore  the 
periodic  times,  would  be  equal  in  equal 
Planets,  at  equal  diftances  from  the  Sun ; 
and  in  equal  diftances  of  unequal  Pla¬ 
nets,  the  total  adtions  of  the  centripetal 
force  would  be  as  the  bodies  of  the 
Planets.  For  if  the  actions  were  not 
proportional  to  the  bodies  to  be  moved, 
they  could  not  equally  retradi  thefe  bo¬ 
dies  from  the  tangents  of  their  orbs,  and 
force  them  to  revolve  in  equal  orbs,  in 
equal  times.  Nor  could  the  motions  of 
the  fatellites  of  Jupiter  be  lb  regular,  if 
it  was  not  that  the  circum-lblar  force 
was  equally  exerted  upon  Jupiter  and 
all  its  fatellites  in  proportion  of  their  fe- 
veral  weights.  And  the  fame  thing  is 
CO  be  laid  of  Saturn  in  refpedf  of  its  la- 
tellite,  and  of  our  Earth  in  refpedf  of 
the  Moon.  And  therefore  at  equal  di-  . 
fiances,  the  a&ion  of  the  centripetal 
force  is  equal  upon  all  the  Planets,  in 
D  x  pro* 


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3<* 


OF  THE  SYSTEM 
proportion  of  their  bodies,  or  of  the 
quantities  of  matter  in  their  feveral  bo¬ 
dies  :  and  for  the  fame  reafon  mult  be 
the  fame  upon  all  the  particles  of  the 
lame  fize,  of  which  the  planet  is  com- 
pofed.  For  if  the  a&ion  was  greater 
upon  fomc  fort  of  particles  than  upon 
others  then  in  proportion  to  their  quan¬ 
tity  of  matter,  it  would  be  alfo  greater 
or  lefs,  upon  the  whole  Planets,  not  in 
proportion  of  the  quantity  only,  but 
like  wife  of  the  fort  of  the  matter 
more  copioufly  found  in  one,  and 
more  fparingly  iu  another. 

In  fuch  bodies  as  are  found  on  our 
Earth  of  very  different  forts,  I 

Proved  in  terreftrial  cxamjned  this  analogy  With 

boJie*’  great  accuracy.  . 

If  the  action  of  the  circumterreurial 
force  is  proportional  to  the  bodies  to 
be  moved,  it  will  move  them  with  equal 
velocity  in  equal  times,  and  will  make 
all  bodies  let  fall  to  defcend  through 
equal  fpaces  in  equal  times  ;  and  all  bo¬ 
dies  hung  by  equal  threads,  to  vibrate  in 
equal  times.  If  the  adion  of  the  force 
was  greater,  the  times  would  be  lets.  It 
that  was  lefs,  thefe  would  be  greater 
But-ft  has  been  long  ago  obferved  by 
others,  that  ( allowance  being  made  for 


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OF  THE  WORLD. 

the  frnall  refiftance  of  the  Air)  all  bo¬ 
dies  delcend  through\equal  lpaces  in 
equal  times.  And,  by  the  help  of  pen¬ 
dulums,  that  equality  of  times  may  be 
diftinguilh’d  to  great  exadhnefs. 

I  tryed  the  thing  in  gold,  filver,  lead, 
glafs,  land,  common  laic,  wood,  water 
and  wheat.  I  provided  two  equal 
wooden  boxes.  I  filled  the  one  with 
wood,  and  fufpended  an  equal  weight  of 
gold  ( as  exactly  as  1  could  )  in  the 
center  of  ofcillation  of  the  other.  The 
boxes  hung  by  equal  threads  of  1 1  feet, 
made  a  couple  of  pendulums  perfe&ly 
equal  in  weight  and  figure,  and  equally 
expo  led  to  the  refiftance  of  the  air. 
And  placing  the  one  by  the  other,  I  ob- 
ferved  them  to  play  together,  forwards 
and  backwards,  for  a  long  while,  with 
equal  vibrations.  And  therefore  the 
quantity  of  matter  in  the  gold  was  to 
the  quantity  of  matter  in  the  wood,  as 
the  adtion  of  the  motive.force  upon  all 
the  gold,  to  the  atftion  of  the  lame  upon 
all  the  wood,  that  is,  as  the  weight  of 
the  one  to  the  weight  of  the  other. 

And  by  thele  experiments,  in  bodies 
of  the  lame  weight,  I  could  have  dif- 
covered  a  difference  of  matter,  lefs  than 
the  thoulandth  part  of  the  whole. 

D  3  Since 


Digitized  by  L^ooQle 


38 


OF  THE  SYSTEM 

Since  the  action  of  the  centripe- 
The  affinity  cf  thofe  tal  force  upon  the  bodies  at- 
anaiogies.  tradted,  is,  at  equal  diftances, 

proportional  to  the  quantities  of  mat¬ 
ter  in  thole  bodies ;  reafon  requires 
that  it  fliould  be  alio  proportional  to  the 
quantity  of  matter  in  the  body  at¬ 
tracting. 

For  all  aCtion  is  mutual,  and  makes 
the  bodies  mutually  to  approach  one 
to  the  other,  and  therefore  mull  be  the 
lame  in  both  bodies.  It  is  true  that  we 
may  confidcr  one  body  as  attracting, 
another  as  attracted.  But  this  diftin&ion 
is  more  mathematical  than  natural.  The 
attraction  is  really  common  of  either  to 
other,  and  therefore  of  the  fame  kind  in 
both. 

And  hence  it  is  that  the  attractive 
force  is  found  in  both.  The  Sun 
n  ccinci  enc  f  attracts  Jupiter  and  the  other 
Planets.  Jupiter  attracts  its  iatellites. 
And  for  the  lame  reafon,  the  fatellites 
aCt  as  well  one  upon  another  as  upon 
Jupiter,  and  all  the  Planets  matually 
one  upon  another. 

And  though  the  mutual  actions  of 
two  Planets  may  be  diftinguilhed  and 
confidered  as  two,  by  which  each  at- 
tfaCJs  the  qther ;  yet  as  thofe  a&ions 

are 


Digitized 


by  Google 


OF  THE  WORLD. 

arc  intermediate,they  don’t  make  two, but 
one  operation  between  two  terms.  Two 
bodies  may  be  mutually  attracted,  each 
to  the  other,  by  the  contraction  of  a 
cord  interpoled.  There  is  a  double 
cauie  of  action,  to  wit,  the  dilpofition 
of  both  bodies,  as  well  as  a  double  ac¬ 
tion  in  fo  far  as  the  adtion  is  confidered 
as  upon  two  bodies.  But  as  betwixt  two 
bodies  it  is  but  one  tingle  one.  ’Tis 
not  one  adtion  by  which  the  Sun  at¬ 
tracts  Jupiter,  and  another  by  which  Ju¬ 
piter  attrads  the  Sun.  But  it  is  one  ac¬ 
tion  by  which  the  Sun  and  Jupiter  mu¬ 
tually  endeavour  to  approach  each  the 
other.  By  the  adtion  with  which  the 
Sun  attradts  Jupiter,  Jupiter  and  the  Sun 
endeavour  to  come  nearer  together, 
and  by  the  adtion,  with  which  Jupiter 
attracts  the  Sun,  likewife  Jupiter  and 
the  Sun  endeavour  to  come  nearer  to¬ 
gether.  But  the  Sun  is  not  attracted  to¬ 
wards  Jupiter  by  a  two-fold  adtion,  nor 
Jupiter  by  a  two-fold  adtion  towards 
the  Sun :  but  ’tis  one  tingle  interme¬ 
diate  adtion,  by  which  both  approach 
nearer  together. 

Thus  iron  draws  the  load-ftone,  as 
well  as  the  load-ftone  draws  the  iron. 
For  all  iron  in  the  neighbourhood  of  the 
load- Hone  draws  other  iron.  But  the 
D  4  adtion 


Digitized  by  LjOOQle 


•40 


OF  THE  SYSTEM 

aCtion  betwixt  the  load-ftone  and  iron 
is  Single,  and  is  confidered  as  Tingle  by 
the  philofophers.  The  adtion  of  iron 
upon  the  load-ftone  is  indeed  the  adtion 
of  the  load  ftone  betwixt  it  felf  and  the 
iron,  by  which  both  endeavour  to  come 
nearer  together.  And  To  it  manifestly 
appears  For  if  you  remove  the  load^ 
ftone,  the  whole  force  of  the  iron  al- 
moft  ceafes. 

In  this  fenfe  it  is  that  we  are  to  con¬ 
ceive  one  Single  adtion  to  be  exerted  be¬ 
twixt  two  Planets,  arifing  from  the  con- 
fpiring  natures  of  both.  And  this  adtion 
Standing  in  the  fame  relation  to  both, 
if  it  is  proportional  to  the  quantity  of 
matter  in  the  one,  it  will  be  alio  propor¬ 
tional  to  the  quantity  of  matter  in  the 
other. 

Perhaps  it  may  be  objected,  that 
That  the  forces  of  according  to  this  philofophy, 
fmaii  bodies  are  in-  all  bodies  Should  mutually  at- 
fenfioie.  tradt  one  anotf,£ri  contrary 

to  the  evidence  of  experiments  in  ter- 
reftrial  bodies.  But  I  anfwer,  that  the 
experiments  in  terreftrial  bodies  come  to 
no  account.  For  the  attractions  of 
homogeneous  Spheres  near  their  Surfaces, 
are  as  their  diameters.  Whence  a  Sphere 
of  one  foot  in  diameter,  find  of  a  lifce 

nature 

;  i- 


Digitized  by  LjOOQle 


4* 


OF  THE  WORLD. 

nature  to  the  Earth,  would  attract  a 
final  1  body  plac’d  near  its  furface  with  a 
force  about  20000000  times  Ids,  than 
the  Earth  would  do  if  placed  near  its 
furface.  But  fo  finall  a  force  could  pro¬ 
duce  no  fenfible  effect.  If  two  luch 
fpheres  were  diftant  but  by  i  of  an  inch, 
they  would  not  even  in  (paces  void  of 
refinance,  come  together  by  the  force 
of  their  mutual  attraction  in  lels  than  a 
months  time.  And  lefs  fpheres  will 
come  together  at  a  rate  yet  (lower,  viz. 
in  the  proportion  of  their  diameters. 
Nay  whole  mountains  will  not  be  (uffi- 
cient  to  produce  any  (enfible  effect.  A 
mountain  of  an  hemifpherical  figure, 
three  miles  high,  and  fix  broad,  will  not 
by  its  attraction,  draw-  the  pendulum 
2  minutes  out  of  the  tree  perpendi¬ 
cular.  And  ’tis  only  in  the  great  bo¬ 
dies  of  the  Planets  that  thefe  forces  are 
to  be  perceiv’d,  unlefs  we  may  reafon  a- 
bout  fmaller  bodies  in  manner  follow¬ 
ing- 


Let 


Digitized  by  LjOoq  le 


4* 


OF  THE  SYSTEM 


Let  A  BCD  reprefent  the  globe 
of  the  Earth,  cut,  b  jr  any  plane 
which not»wWt»«l-  AC,  into  two  parts  A C B, 
5SCST3  and  A  CD.  The  part  ACB 
tcireftrial  bearing  upon  the  part  A  CD 

proportional  totheir  ^  &  ^  ^  whole  Weight. 

. . Lc  cao  da*  part  iCD  tf 

tain  this  prefTore  and  continue  un¬ 
moved,  if  it  is  not  oppofed  by  an  equal 
contrary  prellure.  And  therefore  the 
parts  equally  prels  each  other  by  their 
weights,  that  is,  equally  attract  each  o- 
ther,  and  if  feparated  and  let  go  would 
fall  towards  each  other  with  velocities 


reciprocally  as  the  bodies.  All  which 
we  may  try  and  lee  in  the  load-ftone, 

whofe 


Digitized  by  LjOOQle 


43 


OF  THE  WORLD. 

whole  attracted  part  does  dot  propell  the 
part  attracting,  but  is  only  Hopped  and 
fuftained  thereby. 

Suppofe  now  that  ACB  reprelents 
Ibme  fmall  body  on  the  Earth’s  furface  ; 
and  becaule  the  mutual  attractions  of 
this  particle  and  of  the  remaining  part 
of  the  Earth  towards  each  other,  are 
equal ;  but  the  attraction  of  the  parti¬ 
cle  towards  the  Earth  (  or  its  weight ) 
is  as  the  matter  of  the  particle  (  as  we 
hare  proved  by  the  experiment  of  the 
pendulums)  the  attraction  of  the  Earth 
towards  the  particle,  will  Jikewile  be  as 
the  matter  of  the  particle.  And  therefore 
the  attractive  forces  of  all  terreftrial  bo¬ 
dies,  will  be  as  their  leveral  quantities 
of  matter. 


Prov*d  that  the  fame 
forces  tend  toward* 
the  celeftial  bodies* 


The  forces,  which  are  as  the  matter 
in  terreftrial  bodies  of  all  forms, 
and  therefore  are  not  mutable 
with  the  forms,  mult  be  found 
in  all  forts  of  bodies  whatfo- 
ever,  celeftial  as  well  as  terreftrial,  and  be 
in  all  proportional  to  their  quantities  of 
matter,  becaule  among  all  there  is  no 
difference  of  lubftance,  but  of  modes 
and  forms  only.  But  in  the  celeftial  bo¬ 
dies,  the  lame  thing  is  likewife  proved 
thus.  We  have  Ihewed,  that  the  aCfcion 
f  of 


Digitized  by  LjOOQle 


44 


OF  THE  SYSTEM 
of  the  circumfolar  force  upon  all  the 
Planets  (  reduced  to  equal  diftances)  is 
as  the  matter  of  the  Planets  ;  That  the 
a&ion  of  the  circumjovial  force  upon  the 
fatellites  of  Jupiter  obferves  the  fame 
law  ;  and  the  fame  thing  is  to  be  laid  of 
the  attra&ion  of  all  the  Planets  towards 
every  Planet.  But  thence  it  follows 
that  their  attra&ive  forces  are  as  their 
feveral  quantities  of  matter. 

As  the  parts  of  the  Earth  mutually  at- 
That  from  the  furfa*  trad  one  another  ^  fo  do  thole 
ce.  of  the  Planets,  of  all  the  Planets.  If  Jupiter  and 

their°fbrces *decreafe  *tS  fatellites  Were  brought  tOge- 
in  the  duplicates  but,  ther,and  formed  into  one  globe  ; 

w'tl>out  doubt,  they  would 
on  of  the  diftances  continue  mutually  to  attract 
from  their  centers.  one  another  as  before.  And  on 

the  other  hand,  if  the  body  of  Jupiter 
was  broke  into  more  globes,  to  be  lure, 
thefe  would  no  lefs  attract  one  another 
than  they  do  the  fatellites  now.From  thefe 
attractions  it  is  that  the  bodies  of  the 
Earth,  and  all  the  Planets  affeCt  a  fphe- 
rical  figure,  and  that  their  parts  cohere, 
and  are  not  difperfed  through  the  Ether. 
But  we  have  before  proved  that  thefe 
forces  arife  from  the  univerfal  nature  of 
"  jpatter,  and  that  therefore  the  force  of 
any  whole  globe  is  made  up  of  the  feveral 

forces 


Digitized  by  LjOOQle 


OF  THE  WORLD.  4y 

forces  of  all  its  parts.  And  from  thence 
it  follows,  that  the  force  of  every  par¬ 
ticle  decreafes  in  the  duplicate  propor¬ 
tion  of  the  diftance  from  that  particle ; 
and  that  the  force  of  an  entire  globe* 
reckoning  from  the  furface  outwards, 
decreafes  in  the  duplicate,  but  reckon¬ 
ing  inwards,  in  the  fimple  proportion 
of  the  diftances,  from  the  centres,  if 
the  matter  of  the  globe  be  uniform. 

And  though  the  matter  of  the  globe, 
reckoning  from  the  center  towards  the 
furface,  is  not  uniform ;  yet  the  de- 
creafe  in  the  duplicate  proportion  of  the 
diftance  outwards  would  take  place,  pro¬ 
vided  that  difformity  is  fimilar  in  pla- 
ces  round  about  at  equal  diftances  from 
the  center.  And  two  fuch  globes  will 
attract  one  the  other  with  a  force  de- 
creafing  in  the  duplicate  proportion  of 
the  diftance  between  their  centers. 

Wherefore  the  abfolute  force  of 
every  globe  is  as  the  quantity  ThequantitIesoffhe 
of  matter  which  the  globe  con-  forces  and  of  the  mo- 
tains.  But  the  motive  force  by  gjyjgj in  the 
which  every  globe  is  attratfed 
towards  another,  and  which,  in  terref- 
trial  bodies,  we  commonly  call  their 
weight,  is  as  the  content  under  the 
quanties  of  matter  in  both  globes  apply  - 

ed 

/ 


Digitized  by  LjOOQle 


4$  OF  THE  SYSTEM 

ed  to  the  fquare  of  the  diftance  be¬ 
tween  their  centers  ;  to  which  force  the 
quantity  of  motion,  by  which  each  globe 
in  a  given,  time  will  be  carried  towards 
the  other,  is  proportional.  And  the 
accelerative  force,  by  which  every  globe 
according  to  its  qqantity  of  matter  is 
artra&ed  towards  another,  is  as  the 
quantity  of  matter  in  that  other  globe 
applyed  to  the  fquarc  of  the  diftance  be¬ 
tween  the  centers  of  the  two  ;  to  which 
force,  the  velocity,  by  which  the  at¬ 
tracted  globe  will,  in  a  given  time,  be 
carried  towards  the  other,  is  proportio¬ 
nal.  And  from  thefe  principles  well 
underftood,  it  will  be  now  eafy  to  de¬ 
termine  the  motions  of  the  celeftial  bo¬ 
dies  among  themlelves. 

From  comparing  the  forces  of  the 
AKhta  Planets  one  with  another,  we 
revolve  about  the  have  above  leen  that  the  cir- 
Sun*  cum-folar  does  more  than  a 

thoufand  times  exceed  all  the  reft.  But 
by  the  adion  of  a  force  fo  great,  it  is 
unavoidable  but  that  all  bqdies  within, 
pay  and  far  beyond  ,  the  bounds  of 
the  planetary  fyftem,  muft  defeend  di¬ 
rectly  to  the  Sun,  unlefs  by  other  mo¬ 
tions  they  are  impelled  towards  other 
parts.  Nor  is  our  Earth  to  be  excluded 

from 


Digitized  by  v^ooQle 


47 


OF  THE  WORLD. 

from  the  number  of  fiich  bodies.  For 
certainly  the  Moon  is  a  body  of  the 
fame  nature  with  the  Planets,  and  {ob¬ 
ject  to  the  lame  attractions  with  the 
other  Planets,  feeing  it  is  by  the  circum- 
terreftrial  force  that  it  is  retained  in  its 
orbit.  But  that  the  Earth  and  Moon  are 
equally  attracted  towards  the  Sun,  we 
have  above  proved :  We  have  likewife 
before  proved,  that  all  bodies  are  fub- 
jedt  to  the  lame  common  laws  of  attrac¬ 
tion.  Nay,  fuppofing  any  of  thole  bo¬ 
dies  to  be  deprived  of  its  circular  mo¬ 
tion  about  the  Sun,  by  having  its  diftance 
from  the  Sun  we  may  find  in  what 
Ipace  of  time  it  would,  in  its  delcenr, 
arrive  at  the  Sun  ^  to  wit,  in  half  that 
periodic  time,  in  which  the  body  might 
be  revolved  at  one  half  of  its  former 
diftance  j  or,  in  a  Ipace  of  time  that  is 
to  the  periodic  time  of  the  planet  as  i 
to  4  V  x'  As  that  Venus  in  its  de¬ 
le  ent  would  arrive  at  the  Sun  in  the 
fpace  of  40  days,  Jupiter  in  the  Ipace 
of  two  years  and  one  month ;  and  the 
£arth  and  Moon  together  in  the  fpace 
of  66  days  and  19  hours.  Bat  fmce  no 
inch  thing  happens,  it  muft  needs  be 
that  tbofe  bodies  are  moved  towards 
other  parts.  Nor  is  every  motion  faffi- 
cient  for  this  purpofe.  To  binder  Inch 

a 


Digitized  by  LjOOQle 


4*  OF  THE  SYSTEM 

a  defcent,  a  due  proportion  of  velocity 
is  required.  And  hence  depends  the 
force  of  the  argument  drawn  from  the 
retardation  of  the  motions  of  the  Pla¬ 
nets.  Unlefs  the  circum-folar  force  de- 
creafed  in  the  duplicate  ratio  of  their 
increafmg  flownef*  the  excefs  thereof 
would  force  thofe  bodies  to  defcend  to 
the  Sun.  For  inftance*  if  the  motion 
{cater is  paribus)  was  retarded  by  one 
half,  the  planet  would  be  retained  in  its 
orb  by  one  fourth  of  the  former  circum- 
folar  force,  and  by  the  excefs  of  the 
other  three  fourths  would  defcend  to  the 
Sun.  And  therefore  the  Planets  (Sa¬ 
turn,  Jupiter,  Mars,  Venus,  and  Mer¬ 
cury)  are  not  really  retarded  in  their 
perigees,  nor  become  really  ftarionary 
or  regreffive  with  flow  morions.  All 
thefe  are  but  apparent,  and  the  abfo- 
lute  motions,  by  which  the  Planets 
continue  to  revolve  in  their  orbits,  are 
always  dire<5t  and  nearly  equable.  But 
that  fuch  motions  are  performed  about 
the  Sun,  we  have  already  proved  j  and 
therefore  the  Sun,  as  the  center  of  the 
abfolute  motions,  .is  quiefeent.  For  we 
can  by  no  means  allow  quiefcence  to 
the  Earth,  leaft  the  Planets  in  their  pe¬ 
rigees  fhould  indeed  be  truly  retarded, 
and  become  truly  flationary  and  regret 

five^ 


Digitized  by  LjOOQle 


49 


OF  THE  WORLD. 

live,  and  fo  for  want  of  motion  Ihould 
defcend  to  the  Sun.  Bat  further,  fince 
the  Planets  (Venus,  Mars,  Jupiter  aad 
the  reft)  by  radii  drawn  to  the  Sun  de- 
fcribe  regular  orbits,  and  area’s  ( as  we 
have  fhewed)  nearly  and  to  fenfe  pro¬ 
portional  to  the  times  j  it  follows  that 
the  Sun  is  moved  with  no  notable  force, 
unlefs  perhaps  with  fuch  as  all  the  Pla¬ 
nets  are  equally  moved  with,  accord¬ 
ing  to  their  feveral  quantities  of  matter, 
in  parallel  lines,  and  fo  the  whole  fyf- 
tem  is  transferred  in  right  lines.  Re- 
jed  that  tranftation  of  the  whole  fyftem, 
and  the  Sun^will  be  almoft  quiefcent  in 
the  center  thereof.  If  the  Sun  was  re¬ 
volved  about  the  Earth,  and  carried  the 
other  Planets  round  about  it  felf,  the 
Earth  ought  to  attrad  the  Sun  with 
a  great  force,  but  the  circum-lblar  Pla¬ 
nets  with  no  force  producing  any  fenfi- 
ble  effed,  which  is  abfurd.  Add  to 
this,  that  if  hitherto  the  Earth,  becaule 
of  the  gravitation  of  its  parts,  has  been 
placed  by  moft  authors  in  the  lowermoft 
region  of  the  Univerle  ;  now  for  better 
reafon,  the  Sun  poftefted  of  a  centripe¬ 
tal  force  exceeding  our  terreftrial  gravi¬ 
tation  a  thoufand  times  and  more,  ought 
to  be  deprefled  into  the  lowermoft  place, 
and  to  be  held  for  the  center  of  the  fyf- 
E  urn. 


Digitized  by  LjOOQle 


fo  OF  THE  SYSTEM  * 

tem.  And  thus  the  true  dHpofitron  of 
the  whole  fyftem  will  be  more  fullly  and 
more  exa&ly  underftood. 


That  the  common 
center  of  gravity  of 
all  the  Planets  is 
quiefeent.  That  the 
Sun  is  agitated  with 
a  very  flow  morion. 
Thismotion  defined. 


Because  the  fixed  Stars  are  qniefi 
cent  one  in  refpedt  of  another, 
we  may  confider  the  Son,  Earth 
and  Planets  as  one  fyftem  of 
bodies  carried  hither  and  thi¬ 
ther  by  various  motions  among 
themfelves,  and  the  com¬ 
mon  center  of  gravity  of  all  will  ei¬ 
ther  be  quiefeent,  or  move  uniformly 
forward  in  a  right  line:  In  which  cale 
the  whole  fyftem  will  likewife  move 
uniformly  forward  in  right  lines.  But 
this  is  an  hypothefis  hardly  to  be  ad¬ 
mitted.  And  therefore  fetting  it  afide, 
that  common  center  will  be  quiefeent. 
And  from  it  the  Sun  is  never  far  remo¬ 
ved.  The  common  center  of  gravity 
of  the  Sun  and  Jupiter  fells  on  the  fur- 
fece  of  the  Sun.  And  though  all  the 
Planets  were  placed  towards  the  feme 
parts  from  the  Sun  with  Jupiter,  the 
common  center  of  the  Sun  and  all  of 
them  would  fcarcely  recede  twice  as  far 
from  the  Sun’s  center.  And  therefore 


though  the  Sun,  according  to  the  vari¬ 
ous  fituation  of  the  Planets,  is  varioufly 
agitated  and  always  wandering  to  and 

fro 


Digitized  by  v^ooQle 


51 


OF  THE  WORLD. 

fro  with  a  flow  motion  of  libration,  yet 
it  never  recedes  one  entire  diameter  of 
its  own  body  from  the  quieicent  center 
of  the  whole  Syftem.  But  from  the 
weights  of  the  Sun  and  Planets  above 
determined,  and  the  fituation  of  all  a- 
mong  themfelves,  their  common  center 
of  gravity  may  be  found,  and  this  being 
given,  the  Sun’s  place  to  any  fuppoled 
time  may  be  obtained. 


About  the  Sun  thus  librated  the 
other  Planets  are  revolved  in  ThattheP 
elliptic  orbits,  and,  by  radii  vertbelefs 
drawn  to  the  Sun,  defcribe  a-  ^ing'"^!! 
tea’s  nearly  proportional  to  the  the°sun  5 ; 
times,  as  was  explained  before.  ‘j"  drawni 
If  the  Sun  was  quieicent,  and  the  pcrtionai 
other  planets  did  not  adt  mutu- 
ally  one  upon  another,  their  orbits  would 
be  elliptic,  and  the  area’s  exadtly  propor¬ 
tional  to  the  times.  But  the  adtions  of 
the  Planets  among  themlelves,  compa¬ 
red  with  the  a&ions  of  the  Sun  on  the 
Planets*  are  of  no  moment,  and  pro¬ 
duce  no  fenfible  errours.  And  thole 
errours  are  lels  in  revolutions  about  the 


That  the  Planets  ne- 
vertbelefs  are  revol¬ 
ved  in  ellipfes,  ha¬ 
ving  their  foci  in 
the  Sun  j  and  by  ra¬ 
dii  drawn  to  the  Sun 
defcribe  areals  pro¬ 
portional  to  the 


Sun  agitated  in  the  manner  but  now  de- 
fcribed,  than  if  thole  revolutions  were 
made  about  the  Sun  quiefcent,  efpeci- 
ally  if  the  focus  of  every  orbit  is  placed 
Ei  in 


Digitized  by  LjOOQle 


5* 


OF  THE  SYSTEM 

in  the  common  center  of  gravity  of  all 
the  lower  included  Planets:  viz.  the  fo¬ 
cus  of  the  orbit  of  Mercury,  in  the  cen¬ 
ter  of  the  Sun  ;  the  focus  of  the  orbit  of 
Venus,  in  the  common  center  of  gra¬ 
vity  of  Mercury  and  the  Sun  ;  the  focus 
of  the  orbit  of  the  Earth,  in  the  common 
center  of  gravity  of  Venus,  Mercury 
and  the  Sun  ;  and  fo  of  the  reft.  And  by 
this  means  the  foci  of  the  orbits  of  all 
the  Planets  except  Saturn,  will  not  be 
fenfibly  removed  from  the  center  of  the 
Sun,  nor  will  the  focus  of  the  orbit  of 
Saturn  recede  fenftbly  from  the  com¬ 
mon  center  of  gravity  of  Jupiter  and 
the  Sun.  And  therefore  aftronomers 
are  not  far  from  the  truth,  when  they 
reckon  the  Sun’s  center  the  common 
focus  of  all  the  planetary  orbits.  In  Sa¬ 
turn  it  felf,  the  errour  thence  arifing 
does  not  exceed  i  \  45^.  And  if  its 
orbit,  by  placing  the  focus  thereof  in  the 
common  center  of  gravity  of  Jupiter 
and  the  Sun  lhall  happen  to  agree  better 
with  the  phenomena,  from  hence  all 
that  we  have  faid  will  be  farther  con¬ 
firmed. 


If 


Digitized  by  LjOOQLc 


53 


OF  THE  WORLD. 

If  the  Sun  was  quiefcent  and  the 
Planets  did  not  ad  one  on  an-  of  the  diraenfion$ 
other  the  aphelions  and  nodes  of  the  orbit*,  and  of 
of  their  orbits  would  likewile  be  ,h'  i"°,,ons  of  *•?*'' 

.  r  I*  *  apnehons  and  nodes. 

quieicent.  And  the  longer  axes 
of  their  elliptic  orbits  would  be  as  the 
cubic  roots  of  the  fquares  of  their  perio¬ 
dic  times  :  And  therefore  from  the  gi¬ 
ven  periodic  times  would  be  alfo  given. 

But  thofe  times  are  to  be  meafured  not 
from  the  equino&ial  points,  which  are 
moveable  ;  but  from  the  firft  Star  of 
Aries.  Put  the  lemi-axe  of  the  Earth’s 
orbit  iooooo,  and  the  femi-axes  of  the 
orbits  of  Saturn,  Jupiter,  Mars,  Venus,  and 
Mercury,  from  their  periodic  times  will 
comeout  95-3806,510116,1 5-1369,7x3  3  3, 

38710  refpe&ively.  But  from  the  Sun’s 
motion  every  femi-axe  is  encreafed  by 
about  one  third  of  the  diftance  of  the 
Sun’s  center  from  the  common  center 
of  gravity  of  the  Sun  and  Planet.  And 
from  the  actions  of  the  exteriour  Planets 
on  the  interiour,  the  periodic  times  of 
the  interiour  are  fomething  protra&ed 
though  Icarcely  by  any  fenfible  quin- 
tity  ;  and  their  aphelions  are  transfer¬ 
red  by  very  flow  morions  in  confequen- 
tia.  And  on  the  like  account  the  pe¬ 
riodic  times  of  all,  efpecially  of  the  ex¬ 
teriour  Planets,  will  be  prolonged  by 
E  3  the 


Digitized  by  LjOOQle 


54 


OF  THE  SYSTEM 

the  a&ions  of  the  comets,  if  any  fiich 
there  are,  without  the  orb  of  Saturn, 
and  the  aphelions  of  all  will  be  thereby 
carried  forwards  in  confequentia.  But 
from  the  progrefs  of  the  aphelions,  the 
regrefs  of  the  nodes  follows.  And  if 
the  plain  of  the  Ecliptic  is  quiefcent,  the 
regrefs  of  the  nodes  will  be  to  the  pro- 
grels  of  the  aphelion  in  every  orbit,  as 
the  regrefs  of  the  nodes  of  the  Moon’s 
orbit  to  theprogreis  of  its  apogaeon  near¬ 
ly,  that  is,  as  about  ioto  21.  But  aftro- 
nomical  obfervations  feem  to  confirm 
a  very  flow  progrefs  of  the  aphelions, 
and  a  regrefs  of  the  nodes  in  refpe&  of 
the  fixed  Stars.  And  hence  it  is  pro¬ 
bable,  that  there  are  comets  in  the  regi¬ 
ons  beyond  the  Planets,  which  revol- 
v  • '  3  in  very  eccentric  orbs,  quickly  fly 
tlnough  their  perihelion  parts,  and  by 
an  exceeding  flow  motion  in  their  aphe¬ 
lions,  fpend  almofl  their  whole  time  iu 
the  regions  beyond  the  Planets ;  as  we 
fhall  afterwards  explain  more  at  large. 


The 

AM  the  motions  of 
the  Moon  that  have 
hith«  rto  been  ob¬ 
served  by  aftrcno. 
mers,  derived  from 
the  foregoing  prin¬ 
ciples. 


Planets  thus  revolved  about 
the  Sun,  may  at  the  fame 
time  carry  others  revolving  a- 
bout  themfelyes  as  fatellites  or 
Moons.  But  from  the  a&ion 
of  the  Sun,  our  Moon  muft 
move  with  greater  velocity, 

and. 


Digitized  by  LjOOQle 


55 


OF  THE  WORLD. 

and,  by  a  radius  drawn  to  the  Earth, 
defcribe  an  area  greater  for  the  time  ;  it 
mud  have  its  orbit  left  curve,  and  there¬ 
fore  approach  nearer  to  the  Earth,  in 
thve  fyzygies  than  in  the  quadratures, 
except  in  ib  far  as  the  motion  of  eccen¬ 
tricity  hinders  thole  effe&s.  For  the 
eccentricity  is  greateft  when  the  Moon’s 
apogaeon  1$  in  the  fyzygies,  and  leaft 
when  the  fame  is  in  the  quadratures ; 
and  hence  it  is  that  the  perigeon-Moon 
is  fwifter  and  nearer  to  us,  but  the  apo- 
gaeon-Moon  flower  and  farther  from  us, 
in  the  fyzygies  than  in  the  quadratures. 
But  further,  the  apogaeon  has  a  progref- 
five,  and  the  nodes  a  regreflive  motion, 
both  unequable.  For  the  apogaeon  is 
more  fwiftly  progreflive  in  its  fyzygies, 
more  llowly  regreflive  in  its  quadratures, 
and  by  the  excefs  of  its  progrefs  above 
its  regrefs  is  yearly  transferred  in  confe- 
quentia :  but  the  nodes  are  quiefcent  in 
their  fyzygies,  and  moil  fwiftly  regrel- 
five  in  their  quadratures.  But  further 
(till,  the  greateft  latitude  of  the  Moon  is 
greater  in  its  quadratures  than  in  its  fy¬ 
zygies  ;  and  the  mean  motion  fwifter 
in  the  aphelion  of  the  Earth  than  in  its 
perihelion.  More  inequalities  in  the 
Moon’s  mption  have  not  hitherto  been 
taken  notice  of  by  aftronomers.  But 
E  4  all 


Digitized  by  L^ooQle 


56  OF  THE  SYSTEM 

all  thefe  follow  from  our  principles,  and 
are  known  really  to  exid  in  the  heavens. 
And  this  may  be  feen  in  that  mod  in¬ 
genious,  and,  if  I  miftake  not,  of  all  the 
mod  accurate,  hypothefis  of  Mr.  Hor- 
rox ,  which  Mr.  Flamfteed  has  fitted 
to  the  heavens.  But  the  adronomical 
hypothefes  are  to  be  corrected  in  the 
motion  of  the  nodes.  For  the  nodes 
admit  the  greated  equation  or  prodha- 
phazrefis  in  their  o<dants,  and  this  ine¬ 
quality  is  mod  conlpicuous,  when  the 
Moon  is  in  the  nodes,  and  therefore 
alfo  in  the  odtanrs.  And  hence  it  was 
that  Tycho  and  others  after  him  referred 
this  inequality  to  the  ocdants  of  the 
Moon,  and  made  it  mendrual.  But  the 
reafons  by  us  adduced  prove  that  it 
ought  to  be  referred  to  the  odants  of 
the  nodes,  and  to  be  made  annual. 

Beside  thole  inequalities  taken  no- 
......  ,  rice  of  by  adronomers,  there 

uneqmbie  motions  are  yet  lome  others,  by  which 
ti  at  hitherto  have  the  Moon’s  motions  are  lo  difi 

not  been  obferved.  turbgtJ}  hitherto  by  no 

law  could  they  be  reduced  to  any  cer¬ 
tain  regulation.  For  the  velocities  or 
horary  motions  of  the  apogee  and  nodes 
of  the  Moon,  and  their  equations,  as 
well  as  the  difference  betwixt  the  great- 


Digitized  by  LjOOQle 


57 


OF  THE  WORLD. 

eft  eccentricity  in  the  fyzygies  and  the 
leaft  in  the  quadratures,  and  that  inequa¬ 
lity  which  we  call  the  variation,  in  the 
progrefs  of  the  year  are  augmented  and 
diminilhed  in  the  triplicate  ratio  of  the 
Sun’s  apparent  diameter.  Beftde  that, 
the  variation  is  mutable  nearly  in  the 
duplicate  ratio  of  the  time  between  the 
quadratures.  And  all  thole  inequalities 
are  fomething  greater  in  that  part  of  the 
orbit,  which  relpe&s  the  Sun,  than  in  the 
oppofite  part,  but  by  a  difference  that 
is  icarcely  or  not  at  all  perceptible. 

By  a  computation  which  for  bre- 
Titles  fake  I  don’t  defcribe,  I  ^  ^  o( 
alio  find,  that  the  area  which  ,he  Moon  from  the 
the  Moon,  by  a  radius  drawn  ^arth  *°  any  £iven 
to  the  Earth,  defcribes  in  the  time‘ 
feveral  equal  moments  of  time  is  nearly  as  . 
the  fum  of  the  number  a-37TV  and  verfed 
fine  of  the  double  diftance  of  the  Moon 
from  the  neareft  quadrature  in  a  circle 
whole  radius  is  unity  ;  and  therefore 
that  the  fquare  of  the  Moon’s  diftance 
from  the  Earth,  is  as  that  fum  divided 
by  the  horary  motion  of  the  Moon. 

Thus  it  is  when  the  variation  in  the  oc¬ 
tants  is  in  its  mean  quantity.  But  if 
the  variation  is  greater  or  lels,  that  ver- 
fed  fine  mull  be  augmented  or  diminilh¬ 
ed 


Digitized  by  LjOOQle 


OF  THE  SYSTEM 
ed  in  the  fame  ratio.  Let  aftronomers 
try  how  exa&ly  the  diftances  thus  found 
will  agree  with  the  Moon’s  apparent 
diameters. 


The  motions  of  the 
fatellites  of  Jupiter 
and  Saturn,  derived 
from  the  motions 
of  our  Moon. 


From  the  motions  of  our  Moon  we 
may  derive  the  motions  of  the 
Moons  or  Satellites  of  Jupiter 
and  Saturn.  For  the  mean  mo* 
tion  of  the  nodes  of  the  out- 
moft  fatellite  of  Jupiter  is  to 
the  mean  motion  of  the  nodes  of  our 
Moon  in  a  proportion  compounded  of 
the  duplicate  proportion  of  the  periodic 
time  of  the  Earth  about  the  Sun,  to  the 
periodic  time  of  Jupiter  about  the  Sun, 
and  the  fimple  proportion  of  the  perio¬ 
dic  time  of  the  fatellite  about  Jupiter  to 
the  periodic  time  of  our  Moon  about 
the  Earth,  and  therefore  thole  nodes, 
in  the  Ipace  of  an  hundred  years,  are 
carried  8°  14'  backwards,  or  in  ante¬ 
cedents,  The  mean  motions  of  the 
nodes  of  the  inner  (atellites  are  to  the 
(  mean  )  motion  of  ( the  nodes  of)  the 
outmolt  as  their  periodic  times  to  the 
periodic  time  of  this,  by  the  lame  co¬ 
rollary,  and  are  thence  given.  And  the 
motion  of  the  apfis  of  every  fatellite  in 
confequentia  is  to  the  motion  of  its 
nodes  in  antecedents,  as  the  motion 

of 


Digitized  by  LjOOQle 


OF  THE  WORLD.  f9 

of  the  apogee  of  our  Mood,  to  the  mo¬ 
rion  of  its  nodes  (by  the  fame  corolla¬ 
ry)  and  is  thence  given.  The  variation 
of  a  fatellite  feen  from  Jupiter  is  to  the 
variation  of  our  Moon,  in  the  lame 
proportion,  as  the  whole  motions  of 
their  nodes  refpedhvely ,  during  the 
times,  in  which  the  fatellite  and  our 
Moon  (after  parting  from)  are  revolved 
(again)  to  the  Sun  by  the  fame  corolla¬ 
ry  ;  and  therefore  in  the  outmolt  latel- 
lite  the  variation  does  not  exceed  sr/. 

From  the  lrnall  quantity  of  thole 
inequalities  and  the  llownefs  of  the  mo¬ 
tions,  it  happens  that  the  motions  of 
the  latellites  are  found  to  be  lo  regular, 
that  the  more  modern  aftronomers  ei¬ 
ther  deny  all  motion  to  the  nodes,  or 
affirm  them  to  be  very  llowly  regref- 
five. 

Wh  i  l  e  the  Planets  are  thus 
revolved  in  orbits  about  remote  ^he0"“e,fald 
centers,  in  the  mean  time  they  stars,  are  revolved 
make  their  leveral  rotations  a-  eciu^'f  motion* 

L  ,  about  tneir  proper 

bout  their  proper  axes ;  the  axes.  And  that  (per. 
Sun,  in  x6  days ;  Jupiter,  in  haps)  «hofe  mown. 

,  7  _  J .  in  are  the  molt  fit  for 

9h.  56  ;  Mars,  in  14  f  h;  Venus,  the  equation  of  time. 

in  13  h;  and  that  in  plains  not 

much  inclined  to  the  plain  of  the  E- 

pliptic,  and  according  to  the  order  of 


Digitized  by  LjOoq  le 


6o 


OF  THE  S  YSTEM 

the  figns,  as  allronomers  determine 
from  the  Ipots  or  macula^  that  by 
turns  prelent  themlelves  to  our  fight  in 
their  bodies.  And  there  is  a  like  revo¬ 
lution  of  our  Earth  performed  in  24 
And  thole  motions  arc  neither  accele¬ 
rated  nor  retarded  by  the  a&ions  of  the 
centripetal  forces.  And  therefore  of 
all  others  they  are  the  moll  equable  and 
moll  fit  for  the  menluration  of  time. 
But  thole  revolutions  are  to  be  reckon¬ 
ed  equable,  not  from  their  return  to 
the  Sun  but  to  fome  fixed  Star.  For  as 
the  pofition  of  the  Planets  to  the  Sun 
is  unequably  varied,  the  revolutions  of 
thofe  Planets  from  Sun  to  Sun  are  ren¬ 
dered  unequable. 


I  n  like  manner  is  the  Moon  revolved 
about  its  axe  by  a  motion  moll 

Ifc  ^uable  in  refpetf  Of  the  fixed 

a  diurnal  ipotion  a.  Stars,  VJZ>.  in  X J  \  7  **  a, 

irSS&r'jS  th”is>  ii'hefpace  of  afyde-' 
thence arife.  real  month;  lo  that  this  diur¬ 

nal  morion  is  equal  to  the  mean 
motion  of  the  Moon  in  its  orbit.  Up¬ 
on  which  account,  the  fame  face  of  the 
Moon  always  refpe&s  the  center  about 
which  this  mean  motion  is  performed, 
that  is,  the  exteriour  focus  of  the  Moon’s 
orbit  nearly.  And  hence  ariles  a  de¬ 
flexion 


Digitized  by  LjOoq  le 


6i 


OF  THE  WORLD. 

flexion  of  the  Moon’s  face  from  the 
Earth,  fbmetimes  towards  the  eaft,  at 
other  times  towards  the  weft,  accord¬ 
ing  to  the  pofition  of  the  focus  which 
it  refpe&s  ;  and  this  deflexion  is  equal 
to  the  equation  of  the  Moon’s  orbit  or 
to  the  difference  betwixt  its  mean  and 
true  motions.  And  this  is  the  Moon’s 
libration  in  longitude.  But  it  is  like- 
wife  affe&ed  with  a  libration  in  latitude 
arifing  from  the  inclination  of  the 
Moon’s  axe  to  the  plain  of  the  orbit  in 
which  the  Moon  is  revolved  about  the 
Earth,  For  that  axe  retains  the  fame  pofi¬ 
tion  to  the  fixed  Stars  nearly,  and  hence 
the  poles  prefent  themfelves  to  our  view 
by  turns  :  as  we  may  underftand  from 
the  example  of  the  motion  of  the  Earth, 
whole  poles,  by  reafon  of  the  inclination 
of  its  axe  to  the  plain  of  the  Ecliptic,  are 
by  turns  illuminated  by  the  Sun.  To 
determine  exactly  the  pofition  of  the 
Moon’s  axe  to  the  fixed  Stars,  and  the 
variation  of  this  pofition,  is  a  problem 
worthy  of  an  aftronomer. 

B  y  reafon  of  the  diurnal  re- 
volutions  of  the  Planets,  the 
matter  which  they  contain  en-  of  the  libratory  mo- 
deavours  to  recede  from  the  ”on°fth,e“e‘of‘he 

...  .  ,  Earth  and  Planets. 

axes  of  this  motion  ;  and  hence 

i  the 


Digitized  by  LjOOQle 


6x  OF  THE  SYSTEM 

the  fluid  parts  rifing  higher  towards 
the  equator  than  about  the  poles,  would 
Jay  the  folid  parts  about  the  equator 
under  water,  if  thole  parts  did  not  rife 
alio.  Upon  which  account  the  Planets 
are  fomething  thicker,  about  the  equator 
than  about  the  poles,  and  their  equi¬ 
noctial  points  thence  become  regreflive, 
and  their  actions  by  a  motion  of  nuta¬ 
tion,  twice  in  every  revolution  librate 
towards  their  ecliptics,  and  twice  re¬ 
turn  again  to  their  former  inclina¬ 
tion.  And  hence  it  is  that  Jupiter, 
viewed  through  very  long  telefcopes, 
does  not  appear  altogether  round,  but 
having  its  diameter  that  lies  parallel 
to  the  Ecliptic,  fomething  longer  than 
that  which  is  drawn  from  north  to 
ibuth. 

And  from  the  diurnal  motion 
That  th J  fea  ought  and  the  attractions  of  the 
twice  to  flow,  aud  Sun  and  Moon,  our  Sea  ought 

twice  to  ebb  every  .  ,r  <  ^  ?  „ 

day ,  that  the  higheft  twice  to  rife  and  twice  to  fall 
water  muft  fall  out  every  day,  as  well  Lunar  as 

te/the  appuinToi  the  Solar^  and  the  greateft  hight  of 
luminaries  to  the  me-  the  water  to  happen  before  the 

ridianofthepl.ee.  fixth  houf  of  eithef  day>  and 

after  the  twelfth  hour  preceding.  By 
the  flownefs  of  the  diurnal  motion,  the 
flood  is  retraded  to  the  nth  hour, 

and 


Digitized  by  LjOOQle 


*3 


OF  THE  WORLD. 

and  by  the  force  of  the  motion  of  reci¬ 
procation  it  is  protra&ed  and  deferred 
till  a  time  nearer  to  the  fixth  hour.  But 
till  that  time  is  more  certainly  deter¬ 
mined  by  the  phenomena,  chooling  the 
middle  between  thole  extreme3, why  may 
we  not  conje&ure  the  greatefl:  height  of 
the  water  to  happen  at  the  third  hour  ? 
for  thus  the  water  will  rile  all  that  time 
in  which  the  force  of  the  luminaries  to 
raife  it  is  greater,  and  will  fall  all  that 
time  in  which  their  force  is  lefs  ;  viz. 
from  the  9th  to  the  3  d  hour  that  force  is 
greater,  and  from  the  3d  to  the  9th  it  is 
lefs.  The  hours  I  reckon  from  the  ap- 
pulfe  of  each  luminary  to  the  meridian 
of  the  place,  as  well  under  as  above  the 
horizon  ;  and  by  the  hours  of  the  lu¬ 
nar  day  I  underftand  the  24th  parts  of 
that  time,  which  the  Moon  Ipends  be¬ 
fore  it  comes  about  again  by  its  apparent 
diurnal  motion  to  the  meridian  of  the 
place,  which  it  left  the  day  before. 

But  the  two  motions  which  the  two 
luminaries  raife  will  not  ap-  Tbat  the 
pear  diltinguilhed,  but  will  make  tides  happen  in  the 

fyzygies  of  the  lumL 

naries,  the  lead  in  their  quadratures  ;  and  that  at  the  third  hour 
after  the  appulfeofthe  Moon  to  the  meridian  of  the  place.  But 
that  out  of  the  fyzygies  and  quadratures  thofe  greateft  and  lead 
tides  deviate  a  little  from  that  third  hour  towards  the  third  hour 
after  the  appulfe  of  the  Sun  to  the  meridian. 

a 


Digitized  by  LjOoq  le 


<4 


OF  THE  SYSTEM 

a  certain  mixt  motion.  In  the  conjun¬ 
ction  or  oppolition  of  the  luminaries, 
their  forces  will  be  conjoined  and  bring 
on  the  greateft  flood  and  ebb.  In  the 
quadratures  the  Sun  will  raife  the  wa¬ 
ters  which  the  Moon  deprefleth,  and  de-. 
prefs  the  waters  which  the  Moon  rai- 
Feth,  and  from  the  difference  of  their  for¬ 
ces, the  fmalleft  of  all  tides  will  follow. 
And  becaufe  (  as  experience  tells  us)  the 
force  of  the  Mopn  is  greater  than  that 
of  the  Sun,  the  greateft  height  of  the 
water  will  happen  about  the  third  lunar 
hour.  Out  of  the  fyzygies  and  qua¬ 
dratures  the  greateft  tide,  which  by  the 
(ingle  force  of  the  Moon  ought  to  fall 
out  at  the  third  lunar  hour,  and  by  the 
fmgle  force  of  the  Sun  at  the  third  fb- 
lar  hour,  by  the  compound  forces  of 
both  muft  fall  out  in  an  intermediate 
time  that  approaches  nearer  to  the  third 
hour  of  the  Moon  than  to  that  of 
the  Sun :  And  therefore  while  the  Moon 
is  palling  from  the  fyzygies  to  the  qua¬ 
dratures,  during  which  time  the  3d  hour 
of  the  Sun  precedes  the  3d  of  the  Moon ; 
and  that  by  the  greateft  interval  a  little 
after  the  o&ants  of  the  Moon ;  and  by 
like  intervals,  the  greateft  tide  will  fol¬ 
low  the  3d  lunar  hour,  while  the  Moon 
is  palling  from  the  quadratures  to  the 
fyzygies.  But 


Digitized  by  LjOoq  le 


OF  THE  WORLD.  6s 


But  the  effeds  of  the  luminaries 
depend  upon  their  diftances  .  .. 

from  the  Earth.  For  when  greateftwhenthelu! 
they  are  left  diftant,  their  ef-  mi,)aries  are  ia  their 
fe<fts  are  greater,  and  when  per,seel' 
more  diftant  their  effafts  are  left*  and 
that  in  the  triplicate  proportion  of  their 
apparent  diameters.  Therefore  it  is  that 
the  Sun  in  the  winter  time,  being  then 
in  its  perigee,  has  a  greater  effe<ft,  and 
makes  the  tides  in  the  fyzygies  fome- 
thing  greater,  and  thole  in  the  quadra¬ 
tures  iomething  left  than  in  the  fummer 
feafon  ;  and  every  month  the  Moon, 
while  in  the  perigee,  raileth  greater  tides 
thap  at  the  diftance  of  iy  days  before 
or  after,  when  it  is  in  its  apogee. 
Whence  it  comes  to  pals  that  two  high- 
eft  tides  do  not  follow  one  the  other,  in 
two  immediately  fucceeding  fyzygies. 


The  effe<ft  of  either  luminary  doth 
Jikewile  depend  upon  its  decli-  T.  .  .. 

nation  or  diftance  from  the  greateft about'h* 
equator.  For  if  the  luminary  <Ju,noxe*. 

Was  placed  at  the  pole,  it  would  con* 
ftantly  attra<ft  all  the  parts  of  the  wa¬ 
ters,  without  any  intention  or  rcmiflion 
of  its  a&ion,  and  could  cauie  no  reci¬ 
procation  of  motion.  And  therefore  a$ 
the.  luminaries  decline  from  the  equa- 
F  tot 


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66 


OF  THE  SYSTEM 

tor  towards  either  pole,  they  will  by  de¬ 
grees  lole  their  force,  and  on  this  account 
will  excite  lefler  tides  in  the  folftitial  than 
in  the  equino&ial  lyzy  iges.  But  in  thefol- 
ftitial  quadratures,  they  will  raife  greater 
tides  than  in  the  quadratures  about  the 
equinoxes;  becaufe  the  force  of  the  Moon, 
then  fituated  in  the  equator, moft  exceeds 
the  force  of  the  Sun.  Therefore  the 
greateft  tides  fall  out  in  thole  lyzygies, 
and  the  leaft  in  thole  quadratures  ;  which  j 
happen  about  the  time  of  both  equinox¬ 
es.  And  the  greateft  tide  in  the  lyzy¬ 
gies  is  always  fucceeded  by  the  leaft 
tide  in  the  quadratures,  as  we  find  by 
experience.  But  becaule  the  Sun  is  lefs 
diftant  from  the  Earth  in  winter  than  in 
fummer,  it  comes  to  pals  that  the 
greateft  and  leaft  tides  more  frequently  j 
appear  before  than  after  the  vernal  equi¬ 
nox  ;  and  more  frequently  after,  than 
before  the  autumnal. 

Moreover  the  effects  of  the  lu- 
.  minaries  depend  upon  the  lati- 

tudes  of  places.  Let  A/EP 
greater  and  lefs  ai-  reprelent  the  Earth,  on  all 
ternateiy.  fides  covered  with  deep  wa¬ 

ters  ;  C  its  center  ;  P,  p  its  poles ;  A  E 
the  equator ;  F  any  place  without  the 
equator  ;  F  f  the  parallel  of  the  place ; 

D  d  the  correfpondent  parallel  on  the 

other 


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OF  THE  WORLD. 


67 


Other  fide  of  the  equator ;  L  the  place 
which  the  Moon  poflels‘d  three  hours 
before ;  H  the  place  of  the  Earth  di- 
tedtly  under  it ;  h  the  oppofite  place ; 
K,  k  the  places  at  90  degrees  diftance  ; 
C  H,  C  h  the  greateft  heights  of  the  Sea 
from  the  center  of  the  Earth,and  CK,C/£, 
the  leafl:  heights  :  and  if  with  the  axes 
H  h,  K  k%  an  elliple  is  defcribed,  and 
by  the  revolution  of  that  elliple  about 
its  longer  axe  H  h,  a  fpheroid  H  P  K 
bpk  is  formed ;  this  Ipheroid  will  near¬ 
ly  reprelent  the  figure  of  the  Sea ;  and 
C  F,  C  f  C  D,  C  </,  will  reprelent  the 
figure  of  the  Sea  in  the  places  F,  f,  D* 
d.  But  further,  if  in  the  faid  revolution 
of  the  elliple  any  point  N  defcribes  the 
circle  N  M,  cutting  the  parallels  F 
D  d  in  any  places  R,  T,  and  the  equa- 
F  %  tor 


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OF  THE  SYSTEM 
tor  A  E  in  S  ;  C  N  will  reprefent  the 
height  of  the  Sea  in  all  thofe  places, 
R,  S,  T,  fituated  in  this  circle.  Where¬ 
fore  in  the  diurnal  revolution  of  any 
place  F,  the  greateft  flood  will  be  in  F, 
at  the  3  d  hour  after  the  appulfe  of  the 
Moon  to  the  meridian  above  the  ho¬ 
rizon  ;  and  afterwards  the  greateft  ebb 
in  Q_  at  the  3d  hour  after  the  fetting 
of  the  Moon,  and  then  the  greateft  flood 
in  ft  at  the  3d  hour  after  the  appulfe  of 
the  Moon  to  the  meridian  under  the  hori¬ 
zon,  and  laftly  the  greateft  ebb  in  Q, 
at  the  3d  hour  after  the  rifing  of  the 
Moon ;  and  the  latter  flood  in  f,  will 
be  left  than  the  preceding  flood  in  F. 
For  the  whole  Sea  is  divided  into  two 
huge  and  hemifoherical  floods,  one  in 
the  hemifphere  K  H  k  C,  on  the  north- 
fide,  the  other  in  the  oppofite  hemis¬ 
phere  KHfC,  which  we  may  there¬ 
fore  call  the  northern  and  the  fouth- 
ern  floods.  Thefe  floods  being  always 
oppofite  the  one  to  the  other,  come  by 
turns  to  the  meridians  of  all  places  after 
the  interval  of  it  lunar  hours.  And  - 
feeing  the  northern  countries  partake 
more  of  the  northern  flood,  and  the 
fouthern  countries/  more  of  the  fouth- 
ern  flood,  thence  arife  tides  alternately 
greater  and  lefs  in  all  places  without  the 
equator,  in  which  the  luminaries  rife 


*  Digitized  by  LaOOQle 


OF  THE  WORLD.  «9 

and  fer.  .  But  the  greater  tide  will  hap¬ 
pen  when  the  Moon  declines  towards 
the  vertex  of  the  place,  about  the  3d 
hour  after  the  appulfe  of  the  Moon  to 
the  meridian  above  the  horizon;  and 
when  the  Moon  changes  its  declinati¬ 
on,  that  which  was  the  greater  tide  will 
be  changed  into  a  leffer,  and  the  great- 
ell  difference  of  the  floods  will  fall  out 
about  the  times  of  the  folflices,  efpecial- 
ly  if  the  afcending  node  of  the  Moon  is 
about  the  firft  of  Aries.  So  the  morn¬ 
ing  tides  in  winter  exceed  thofe  of  the 
evening,  and  the  evening  tides  exceed 
thofe  of  the  morning  in  fuminer;  at 
i Plymouth  by  the  heighth  of  one  foot, 
but  at  Briftolby  the  heighth  of  15  Inch¬ 
es,  according  to  the  oblervations  of 
Colefrefs  and  Sturmy . 

But  the  motions  which  we  have 
been  defcribing  foffer  fbme  That  by  the  confer, 
alteration  from  that  force  of  ™£nd  XX  Vhe 
reciprocation  which  the  waters  difference  of  the  tide* 
having  once  received,  retain  a 
little  while  by  their  vts  tnjita.  happen  that  the 
Whence  ic  comes  to  p«fs  chat 
the  tides  may  continue  for  tome  after  the  fyzygy. 
time,  though  the  a&ions  of  the  luminaries 
fhould  ceafe.  This  power  of  retaining 
the  imprefled  motion  lefiens  the  diffe¬ 
rence  of  the  alternate  tides,  and  makes 
F  3  thofe 


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Google 


70 


OF  THE  SYSTEM 

thofe  tides  which  immediately  fucceed 
after  the  lyzygies  greater,  and  thole 
which  follow  next  after  the  quadratures 
Ids.  And  hence  it  is  that  the  alternate 
tides  at  Ply  moth  and  Brijlol ,  do  not  dif¬ 
fer  much  more  one  from  the  other,  than 
by  the  height  of  a  foot  or  of  iy 
inches,  and  that  the  greateft  tides  of  all 
at  thole  ports  are  not  the  firft  but  the 
third  after  the  lyzygies. 

And  belides  all  the  motions  are  re¬ 
tarded  in  their  paflage  through  lhallow 
channels,  fo  that  the  greateft  tides  of 
all  in  fome  ftreights  and  mouths  of  ri¬ 
vers,  are  the  fourth  or  even  the  fifth 
after  the  fyzygies. 

I  r  may  alfo  happen  that  the  great¬ 
eft  tide  may  be  the  fourth  or 
fifth  after  the  fyzygies,  or  fall 
tarded  by  inopedi-  out  yet  later,  becaule  the  mo¬ 
ments  in  its  chan-  tjons  [fo  Sea  are  retarded  in 

**  palling  through  lhallow  places 

towards  the  lhores.  For  lo  the  tide 
arrives  at  the  weftern  coaft  of  Ireland 
at  the  third  lunar  hour,  and  an  hour  or 
two  after,  at  the  ports  in  the  fouth- 
ern  coaft  of  the  fame  Illand,  as  alfo  at 
the  iflands  C&ffiterides  commonly  Sor¬ 
tings  ;  then  fuccefiively  at  Falmouth , 
‘Plymouth ,  Portlands  the  ifle  of  Height, 
Winchejler ,  Plover ,  the  mouth  of  the 

Thames, 


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7* 


OF  THE  WORLD. 
Thames ,  and  London-Bridge ,  (pending 
ix  hours  in  this  paflage.  But  further 
the  propagation  of  the  tides  may  be  ob> 
ftru&ed  even  bythe  channels  of  the  ocean 
it  (elf,  when  they  are  not  of  depth  e- 
nough  ;  for  the  flood  happens  at  the 
third  lunar  hour  in  the  Canary  1  (lands, 
and  at  all  thofe  weflern  coafts  that  lie 
towards  the  Atlantic  ocean, as  of  Ireland, 
France ,  Spain,  and  all  Africa  to  the 
Cape  of  Good-hofe ,  except  in  fome  (hal¬ 
low  places,  where  it  is  impeded  and  falls 
out  later  ;  and  in  the  (heights  of  Gib¬ 
raltar,  where  by  real'on  of  a  motion  pro¬ 
pagated  from  the  Mediterranean  Sea  it 
flows  (boner.  But  palling  from  tho(e 
coafts  over  the  breadth  of  the  ocean  to 
the  coafts, of  America. ,  the  flood  arrives 
flrft  at  the  moft  eaftern  (hoars  of  Brajile , 
about  the  fourth  or  fifth  lunar  hour,  then 
at  the  mouth  of  the  river  of  the  Ama¬ 
zons,  at  the  6th  hour,  but  at  the  neigh¬ 
bouring  i Hands,  at  the  4th  hour ;  after¬ 
wards  at  the  iflands  of  Bermudas  at  the 
7th  hour,  and  at  port  bt .Auguftin  in 
Florida  at  7 f .  And  therefore  the  tide 
is  propagated  through  the  ocean  with  a 
flower  motion  than  it  (hould  be  accord¬ 
ing  to  the  courfe  of  the  Moon ;  and  this 
retardation  is  very  neceflary,  that  the 
Sea  at  the  fame  time  may  fall  between 
Bra  file  and  new  France ,  and  rife  at  the 
F  4  Cana- 


Digitized  by  LjOoq  le 


7%  .  OF  THE  SYSTEM 

Canary  Iflands,  and  on  the  coafts  of 
Europe  and  Africa^  and  viceverfa.  For 
■  the  Sea  cannot  rife  in  one  place  but  by 
felling  in  another.  And  it  is  probable 
that  the  Pacific  Sea  is  agitated  by  the 
feme  laws.  For  in  the  coafts  of  Chili 
and  Peru,  the  flood  is  laid  to  happen 
at  the  3d  lunar  hour.  But  with  what 
velocity  it  is  thence  propagated  to  the 
eaftern  coafts  of  Japan,  the  'Philippine 
and  other  iflands  adjacent  to  China ,  I 
have  not  yet  learned. 

Farther  it  may  happen,  that  the 
That  from  the  impe-  tide  may  be  propagated  from 
?nTn!of«  c«r,w  the  ocean  through  different 

fnd  inoars,  various  .  ,  p  , 

phenomena  do  a-  channels  towardsthe  lame  port, 
rifa,  as  that  the  fea  an(j  may  pafs  quicker  through 

f very  day.  lome  channels  than  through 

others,  in  which  cafe  the  feme  tide,  di¬ 
vided  into  two  or  more  fucceeding  one 
another,  may  compound  new  motions 
of  different  kinds.  Let  us  fuppofe  one 
tide  to  be  divided  into  two  equal  tides ; 
the  former  whereof  precedes  the  other 
by  the  fpace  of  6  hours  j  and  happens 
at  the  3d  or  X7th  hour  of  the  appulfe 
of  the  Moon  to  the  meridian  of  the  port. 
If  the  Moon  at  the  time  of  this  appulfe 
to  the  meridian  was  in  the  equator,every 
fix  hours  alternately  there  would  arife 
filial  flopds?  wh|ch  meeting  with  as  ma- 

<>? 


Digitized  by  L^ooQle 


7i 


OF  THE  WORLD, 
ny  equal  ebbs,  would  lo  ballance  one 
the  ocher,  chat  for  chat  day  the  water 
would  flagnate  and  remain  quiet.  If 
the  Moon  then  declined  from  the  equa¬ 
tor,  the  tides  in  the  ocean  would  be  al¬ 
ternately  greater  and  lels  as  was  faid. 
And  from  thence  two  greater  and  two 
lefter  tides  would  be  alternately  propa¬ 
gated  towards  that  port.  But  the  two 
greater  floods  would  make  the  greateft 
height  of  the  waters  to  fall  out  in  the 
middle  time  betwixt  both,  and  the  great¬ 
er  and  lefler  floods  would  make  the 
waters  to  rile  to  a  mean  height  in  the 
middle  time  between  them,  and  in  the 
middle  time  between  the  two  lefler 
floods  the  waters  would  rile  to  their 
leaft  heighth.  Thus  in  the  Ipace  of  14 
hours,  the  waters  would  come,  not  twice 
but,  once  only  to  their  greateft,  and  once 
only  to  their  lead  height ;  and  their 
greateft  height,  if  the  Moon  declined 
towards  the  elevated  Pole,  would  hap¬ 
pen  at  the  6th  or  3d  hour  after  the  ap- 
pulfe  of  the  Moon  to  the  meridian,  and 
when  the  Moon  changed  its  declination 
this  flood  would  be  changed  into  an  ebb. 

Of  all  which  we  have  an  example  in 
the  port  of  Batjbam ,  in  the  kingdom  of 
‘Futtquin,  in  the  latitude  of  ao°.  fo' 
north.  In  that  port  op  the  day  which 
.  '  follows 


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74 


OF  THE  SYSTEM 

follows  after  the  paflage  of  the  Moon 
over  the  equator  the  waters  Magnate  : 
When  the  Moon  declines  to  the  north, 
they  begin  to  flow  and  ebb,  not  twice  as 
in  other  parts,  but  once  only  every 
day,  and  the  flood  happens  at  the  let¬ 
ting,  and  the  greateft  ebb  at  the  rifeing 
of  the  Moon.  This  tide  encreafeth 
with  the  declination  of  the  Moon,  till 
the  7th  or  8th  day,  then  for  the  7th  or 
8th  day  following,  it  decreafeth  at  the 
lame  rate  as  it  had  increafed  before,  and 
cealeth  when  the  Moon  changerh  its  de¬ 
clination.  After  which  the  flood  is 
immediately  changed  into  an  ebb ;  and 
thenceforth  the  ebb  happens  at  the  fet- 
ting,  and  the  flood  at  the  rifing  of  the 
Moon  ;  till  the  Moon  again  changes  its 
declination.  There  are  twb  inlets  from 
the  ocean  to  this  port ;  one  more  diredfc 
and  fhort  between  the  ifland  Hainan 
and  the  coaft  of  Quantung,  a  province 
of  China ;  the  other  round  about  be¬ 
tween  the  fame  ifland  and  the  coaft  of 
Cochim  :  And  through  the  fhorter  paf- 
fage  the  tide  is  fooner  propagated  to 
Batjham. 


In 


Digitized  by  LjOOQle 


OF  THE  WORLD.  yf 

I  n  the  channels  of  rivers,  the  influx 
and  reflux  depends  upon  the 
current  of  the  rivers,  which  ob-  tideswubinthechan- 
ffru&s  the  ingrefs  of  the  waters  *>«)*  of  river*  are 
from  the  Sea,  and  promotes  r«h.S“  " 
their  egrefs  to  the  Sea,  making 
the  ingrefs  later  and  flower,  and  the 
egrefs  foonerand  farter.  And  hence  it  is, 
that  the  reflux  is  of  longer  duration  than 
rhe  influx,  efpecially  far  up  the  rivers, 
where  the  force  of  the  Sea  is  lefs.  So 
Sturmy  tells  us,  that  in  the  river  Avon 
3  miles  below  Briftol ,  the  water  flows 
pnly  5  hours,  but  ebbs  feven.  And 
without  doubt  the  difference  is  yet  great¬ 
er  above  Briftol ,  as  at  Careflxam  or  the 
Bath.  This  difference  does  likewife  de¬ 
pend  upon  the  quantity  of  the  flux  and 
reflux.  For  the  more  vehement  motion 
of  the  Sea  near  the  fyzygies  of  the  lu¬ 
minaries  more  eafily  overcoming  the 
refiftance  of  the  rivers,  will  make  the 
ingrefs  of  the  water  to  happen  fooner 
and  to  continue  longer,  and  will  there¬ 
fore  diminifh  this  difference.  But  while 
the  Moon  is  approaching  to  the  fyzy¬ 
gies,  the  rivers  will  be  more  plentifully 
filled,  their  currents  being  obrtru&ed  by 
the  greatnefs  of  the  tides,  and  there¬ 
fore  will  fomething  more  retard  the  re¬ 
flux  of  the  Sea  a  little  after,  than  a  little 

before 


Digitized  by  L^ooQle 


7 6  OF  THE  SYSTEM 

before  the  lyzygies.  Upon  which  ac¬ 
count  the  flowed  tides  of  all  will  not 
happen  in  the  lyzygies,  but  prevent 
them  a  little.  And  I  obferved  above, 
that  the  tides  before  the  fyzygies  were 
allb  retarded  by  the  force  of  the  Sun. 
And  from  both  caules  conjoined,  the  re¬ 
tardation  of  the  tides  will  be  both  great¬ 
er  and  looner  before  the  lyzygies.  All 
which  I  find  to  be  lo,  by  the  tide-tables 
which  Flamfteed  has  compoled  from  a 
great  many  oblervations. 


By  the  laws  we  have  been  defcribiug, 
That  the  tides  are  the  times  of  the  tides  are  go- 
greater  in  greater  yerned.  But  the  greatnels  of 

greater  *on  the  Chores  the  tides  depends  Upon  the 

of  continents  than  oreatnefs  of  the  Seas.  Let  C 
reprdcnt  the  center  of  the 
yet  greater  in  Qiallow  Earth,  E  A  D  B  the  OVal  fi- 
SiSa.a'sS  gate  of  the  Sea,  C  A  the  long- 


er 


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77 


OF  THE  WORLD. 

er  iemiaxe  of  this  oval,  C  B  the  ihort- 
er  infilling  at  right  angles  upon  the  for¬ 
mer,  D  the  middle  point  between  A  and 
B,  and  E  C  F  or  e  C  f  the  angle  at  the 
center  of  the  Earth,  lubtended  by  the 
breadth  of  the  Sea  that  terminates  in  the 
ihores  E,  F  ;  or  e,  f.  Now  fuppofing 
that  the  point  A  is  in  the  middle  be¬ 
tween  the  points  E,  F,  and  the  point  D 
in  the  middle  between  the  points  e,  f ; 
if  the  difference  of  the  heights  C  A,  C  B 
repreient  the  quantity  of  the  tide  in  a 
very  deep  Sea  iurrounding  the  whole 
Earth  j  tne  excels  of  the  height  C  A 
above  the  height  C  E  or  C  F,  will  re¬ 
preient  the  quantity  of  the  tide  in  the 
middle  of  the  Sea  E  F  terminated  by  the 
ihores  E,  F :  and  the  excels  of  the  height 
C  e  above  the  height  C  f,  will  nearly 
repreient  the  quantity  of  the  tide  on  the 
Ihores  of  the  lame  Sea.  Whence  it  ap¬ 
pears  that  the  tides  are  far  lels  in  tne 
middle  of  the  Sea,  than  at  the  Ihores ; 
and  that  the  tides  at  the  Ihores  are 
nearly  as  E  F  the  breadth  of  the  Sea,  not 
exceeding  a  quadrantal  arc.  And  hence 
it  is  that  near  the  equator,  where  the 
Sea  between  Africa  and  America  is  nar¬ 
row,  the  tides  are  far  lefs  than  towards 
either  fide  in  the  temperate  Zones, 
where  the  Seas  are  extended  wider,  or  on 

almoft 


Digitized  by  LjOOQle 


7* 


OF  THE  SYSTEM 

almoft  all  the  Ihores  of  the  Pacific  Sea* 
as  well  towards  America  as  towards 
China ,  and  within  as  well  as  without 
the  tropicks  ;  and  that  in  iflands  in  the 
middle  of  the  lea  they  Icarce  rile  higher 
than  x  or  3  feet,  but  on  the  ihores 
of  great  continents  are  3  or  4  times 
greater  and  above,  cfpecially  if  the  mo¬ 
tions  propagated  from  the  ocean  are  by 
degrees  contra&ed  into  a  narrow  fpace, 
and  the  water,  to  fill,  and  empty  the 
bays  alternately,  is  forced  to  flow  and 
ebb  with  great  violence  through  ihalloW 
places ;  as  at  Tlymouth  and  Chef  flow- 
Bridge  in  England ,  at  the  mount  of 
St.  Michael  and  town  of  Avranches  in 
Normandy ,  and  at  Cambaja  and  ‘Pegu 
in  the  Eaji  Indies.  In  which  places, 
the  fea  hurried  in  and  out  with  great 
violence,  iometimes  lays  the  ihores  un¬ 
der  water,  fometimes  leaves  them  dry 
for  many  miles.  Nor  is  the  force  of 
the  influx  and  efflux  to  be  broke  till  it 
has  railed  or  deprefied  the  water  to  40 
or  50  feet  and  more.  Thus  alio  long 
and  ihallow  ftreights  that  open  to  the 
fea  with  mouths  wider  and  deeper  than 
the  reft  of  their  channel,  (fuch  as  thofe 
about  Britain ,  and  the  Magellanic 
S freights  at  the  eaftern  entry)  will  have 
a  greater  flood  and  ebb,  or  will  more 

*  intend 


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Google 


19 


OF  THE  WORLD. 

intend  and  remit  their  courle,and  there¬ 
fore  will  rife  higher  and  be  deprefled 
lower.  On  the  coafts  of  South  Ame¬ 
rica, ,  ’tis  faid  that  the  'Pacific  Sea  in  its 
reflux  fometimes  retreats  two  miles,  and 
gets  out  of  fight  of  thole  that  ftand  on 
ihoar.  Whence  in  thefe  places  the 
floods  will  be  alio  higher.  Gut  in 
deeper  waters  the  velocity  of  influx  and 
efflux  is  always  lefs,  and  therefore  the 
alcent  and  defcent  is  lb  too.  Nor  in 
fuch  places  is  the  ocean  known  to  a- 
fcend  to  more  than  6,  8,  or  io  feet.  The 
quantity  of  the  afcent  I  compute  in  the 
following  manner. 


Earth,  P  the  Moon,  PAGB  the 
Moon’s  orbit.  In  QP  take  QK 
equal  to  QS  and  Q_L  to  QK 
in  the  duplicate  ratio  of  QK 
to  QP.  Parallel  to  P  S  draw 


"the  force  of  the  Sun 
to  difturb  the  moti- 
on s  of  the  moon 
computed  from  the 
foregoing  principles. 


L  M ;  and  fuppoflng  the  mean  quantity 


of 


Digitized  by  LjOOQle 


80  OF  THE  SYSTEM 

of  the  circum-lolar  force  directed  to* 
wards  the  Earth  to  be  reprelented  by 
.  the  diftance  QS  or  QK,  QL  will  re- 
prefent  the  quantity  thereof  direded  to* 
wards  the  Moon.  But  that  force  is 
compounded  of  the  parts  QM,  L  M  j 
of  which  the  force  L  M,  and  that  part 
of  QM  which  is  reprelented  by  SM  do 
dilturb  the  motion  of  the  Moon  (as 
is  evident  from  mathematical  reafon- 
ing).  In  lb  far  as  the  Earth  and  Moon 
are  revolved  about  their  common  cen* 
ter  of  gravity,  the  Earth  will  be  liable 
to  the  a&ion  of  the  like  forces.  But 
we  may  refer  the  fums  as  well  of  the 
forces  as  of  the  motions  to  the  Moon, 
and  repreient  the  fums  of  the  forces,  by 
the  lines  S  M  and  M  L,  which  are  pro¬ 
portional  to  them.  The  force  L  M,  in 
its  mean  quantity,  is  to  the  force  by 
which  the  Moon  may  be  revolved  in  an 
orbit  about  the  Earth  quiefcent  at  the 
diftance  P  S,  in  the  duplicate  ratio  of 
the  Moon's  periodic  time  about  the 
Earth  to  the  Earth’s  periodic  time  about 
the  Sun,  that  is,  in  the  duplicate  ratio  of 
17  d.  7  h.  43 to  36 j* d.  6  h.  9*.  or  as  1000 
to  178715-,  or  1  to  178IT.  The  force 
by  which  the  Moon  may  be  revolved 
about  the  Earth  in  reft,  at  the  diftance 
P  S  of  6of  femi- diameters  of  the  Earth, 

Is 


Digitized  by  LjOoq  le 


OF  THE  WORLD.  8l 

is  to  the  force  of  gravity  on  the  Earth’s 
furface  as  i  to  60  £  x  60  f  ;  and  therefore 
the  mean  force  M  L  is  to  the  force  of  gra¬ 
vity  as  i  to  6of  x  <5o  |  x  178  ?r.  Whence 
the  force  SM  will  be  alfo  given  from  the 
proportion  of  the  lines  S  M,  M  L.  And 
thele  are  the  forces  of  the  Sun,  by  which 
the  Moon’s  motions  are  diflurbed. 


If  from  the  Moon’s  orbit  we  defcend 
to  the  Earth’s  furface  thofe  The  foM  of the  Sim 
forces  will  be  diminilhed  in  the  to  move  the  fea 
ratio  of  the  diftances  60  f  and  comPuted* 

1  ;  and  therefore  the  force  LM  will 
then  become  60  ±  x  60  f  x  1 7B  fr  x  60  * 
times  lefs  than  the  force  ofgravity  .But  this 
force  a&ing  equally  every  where  upon 
the  Earth,  will  fcarcely  effe<3:  any  change 
on  the  motion  of  the  Sea,  and  therefore 
may  be  negle&ed  in  the  explication  of 
that  motion.  The  other  force  S  M,  in 
places  where  the  Sun  is  vertical  or  in 
their  nadir,  is  triple  the  quantity  of  the 
force  ML,  and  therefore  but  60  £  x  60  | 

X  59  f?  or  13184000  times  lefs  than  the 
force  of  gravity. 


G 


Sup- 


Digitized  by  L^ooQle 


S*  OF  THE  SYSTEM 

Suppose  now  ADBE  to  reprefent 
The  height  of  the  the  fpherical  furface  of  the 
tide  under  the  equa-  Earth,  a  D  b  E  the  furface  of 

fo[ceariof8«Je°msI,n!  the  water  over-fpreading  it,  C 
computed.  the  center  of  both,  A  the  place 

to  which  the  Sun  is  vertical,  B  the  place 
oppofite ;  D,  E,  places  at  90  degrees 
diftance  from  the  former ;  ACEw/H 


right  angled  cylindric  canal  paffing  thro’ 
the  Earth’s  center.  1  he  force  SM  in  any 
place  is  as  the  difrance  of  the  place  from 
the  plain  D  E,  on  which  a  line  from  A 
to  C  infifts  at  right  angles,  and  therefore 
in  the  part  of  the  canal  which  is  repre- 
fented  by  E  C  /  jw,  is  of  no  quantity  but 
in  the  other  part  AC  Ik,  is  as  the  gra¬ 
vity 


Digitized  by  L^ooQle 


OF  THE  tORLD. 

Vity  at  the  feveral  heights.  For  in  de¬ 
fending  towards  the  center  of  the 
Earth,  gravity  is  every  where  as  the 
height.  And  therefore’  the  force  SiV£ 
drawing  the  water  upwards  will  dimi- 
nifli  its  gravity  in  the  leg  AC  Ik  of  the 
Canal  in  a  given  ratio  ;  upon  which  ac¬ 
count  the  water  will  alcend  in  this  leg, 
till  its  defe<ft  of  gravity  is  fupplyed  by 
its  greater  height,  nor  will  it  reft  in  an 
equilibrium,  till  its  total  gravity  becomes 
equal  to  the  total  gravity  in  EC  Im  the 
other  leg  of  the  canal.  Becaufe  the  gra¬ 
vity  of  evefy  particle  is  as  its  diftance 
from  the  Earth’s  center,  the  weight  of 
the  whole  water  in  either  leg  will  in- 
creafe  in  the  duplicate  ratio  of  the 
height ;  and  therefore  the  height  of  the 
water  in  the  leg  AC  Ik  will  be  to  the 
height  thereof  in  the  leg  C/«E  in 
the  fubduplicate  ratio  of  the  number 
13184001  to  13184000,  or  in  the  ratid 
of  the  number  16374001  to  26374000, 
and  the  height  of  the  water  in  the  leg 
E  C  Im  to  the  difference  of  the  heights* 
as  16374000  to  i.  But  the  height  in 
the  leg  EC/m  is  of  19615843  Tar  is  feet, 
as  has  been  lately  found  by  the  men- 
furation  of  the  French.  And  therefore 
fey  the  preceding  analogy,  the  difference 
of  the  heights  comes  oat  9  inches  of 
G  i  the 


Digitized  by  LjOOQle 


84 


OF  THE  SYSTEM 
the  ‘Paris  foot ;  and  the  Sun’s  force  will 
make  the  height  of  the  Sea  at  A  to  ex¬ 
ceed  the  height  of  the  fame  at  E  by  9 
inches.  And  though  the  water  of  the 
canal  AC  E  m Ik  be  fuppofed  to  be  fro¬ 
zen  into  a  hard  and  folid  confiftence, 
yet  the  heights  thereof  at  A  and  E, 
and  all  other  intermediate  places  would 
frill  remain  the  fame. 

Let  A  a  reprefent  that  excefs  of 
.  .  height  of  nine  inches  at  A,  and 
dfa  */  the  excefs  of  height  at  any 

ids,  anting  from  the  other  place  h ;  and  upon  D  C 
sun’*  force,  compu-  jec  fajj  tjje  perpendicular  fGt 

meeting  the  globe  of  the  Earth 


inF.  Andbecaufe  the  diftance  of  the 
Sun  is  fo  great  that  all  the  right  lines 

drawn 


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Google 


OF  THE  WORLD. 

drawn  thereto  may  be  considered  as 
parallel,  the  force  SM  in  any  place 
F,  will  be  to  the  fame  force  in  the  place 
A,  as  the  fine  F  G  to  the  radius  A  C. 
And  therefore  Since  thofe  forces  tend  to 
the  Son  in  the  dire&ion  of  parallel  lines, 
they  will  generate  the  parallel  heights 
F/i  A  a  in  the  Same  ratio ;  and  there¬ 
fore  the  figure  of  the  water  D faeb 
will  be  a  Spheroid  made  by  the  revolu¬ 
tion  of  an  ellipSe  about  its  longer  axe 
ab.  And  the  perpendicular  height  fb 
will  be  to  the  oblique  height  F/as  fG 
to  fCy  or  as  F  G  to  A  C  ;  and  therefore 
the  height  fh  is  to  the  height  A  a  in  the 
duplicate  ratio  of  F  G  to  A  C,  that  is, 
in  the  ratio  of  the  verfed  Sine  of  double 
the  angle  D  Cf  to  double  the  radius, 
and  is  thence  given.  And  hence  to  the 
feveral  moments  of  the  apparent  revo¬ 
lution  of  the  Sun  about  the  Earth,  we 
may  infer  the  proportion  of  the  aScent 
and  defeent  of  the  waters  at  any  given 
place  under  the  equator,  as  well  as  of 
the  diminution  of  that  aScent  and  de¬ 
scent,  whether  arifing  from  the  latitude 
of  places  or  froorthe  Sun's  declination ; 
viz.  That  on  account  of  the  latitude  of 
places,  the  aScent  and  defeent  of  the  lea 
is  i#  all  places  diminished  in  the  dupli- 
G  3  cate 


Digitized  by  LjOOQle 


86  OF  THE  SYSTEM 

cate  ratio  of  the  co-fines  of  latitude  ;  and 
on  account  of  the  Sun’s  declination,  the 
afcent  and  defcent  under  the  equator  is 
diminilhed  in  the  duplicate  ratio  of  the 
co  fine  of  declination.  And  in  places 
without  the  equator,  the  half  lum  of  the 
morning  and  evening  afcents  (  that  is, 
the  mean  afcent)  is  diminilhed  nearly 
In  the  lame  ratio. 

Let  S  and  L  refpeftively  reprefent 
the  forces  of  the  Sun  and  Moon 
the*  tides  ^under1  the  placed  in  the  equator,  and  sit 
equator,  in  the  fyzy-  their  mean  diftances  from  the 
SjttS  Earth,  r  the  radius,  r  and  tr  thy 
forces  of  both  Sun  verled  fines  of  double  the  con^ 
9nd  Moon.  plements  of  the  Sun  and  Moon*S 

declinations  to  any  given  time,  D  and 
E  the  mean  apparent  diameters  of  the 
Sun  and  Moon  :  and,  luppofing  F  and 
G  to  be  their  apparent  diameters  to  that 
given  time,  their  forces  to  raiie  the 
tides  under  the  equator  will  be,  in  the 

vG*  t F  *  .  . 

fy^ygirs.  J7jfr  L  +  ^757  S,  m  the 

,  v  G’  !F'  , 

quadratures,  L  —  S. 

And  if  the  lame  ratio  is  likewile  obler- 
ved  under  the  parallels,  from  obferva- 
tions  accurately  made  in  pur  northern 

■  climates. 


Digitized  by  L^ooQle 


OF  THE  WORLD.  *7 

climates,  we  may  determine  the  pro¬ 
portion  of  the  forces  L  and  S ;  and  then 
by  means  of  this  rule  predict  the  quan¬ 
tities  of  the  tides  to  every  lyzygy  and 
quadrature. 

At  the  mouth  of  the  river  Avon, 
three  miles  below  Brijioly  in 
foring  and  autumn,  the  whole 
alcent  of  the  water  in  the  con-  and  the  height  of  th« 
jundion  or  oppofition  of  the  ^om' anfin^ 
luminaries  (by  the  obfervation  coinpute  * 
of  Sturmy)  is  about  45^  feet,  but  in  the 
quadratures  only  15.  Becaufe  the  ap¬ 
parent  diameters  of  the  luminaries  are 
not  here  determined,  let  us  a  flu  me  them 
in  their  mean  quantities,  as  well  as  the 
Moon’s  declination  in  the  equino&ial 
quadratures,  in  its  mean  quantity,  that 
is,  13  i  0 ;  and  the  verled  fine  of  double 
its  complement  will  be  1681,  fuppofing 
the  radius  to  be  1000.  But  the  decli¬ 
nations  of  the  Sun  in  the  equinoxes  and 
of  the  Moon  in  the  fyzygies  are  of  no 
quantity,  and  the  verfed  fines  of  dou¬ 
ble  the  complements  are  each  2.000. 

Whence  thofe  forces  become  L  -}-  S  in 

the  fyzygies,  and  L  «—  S  in  the 
J  JO  zooo 

quadratures,  refpe&ively  proportional 
to  the  heights  of  the  tides  of  45  and  x$ 

G  4  feet. 


Digitized  by  LjOOQle 


OF  THE  SYSTEM 

feet,  or  of  9  and  y  paces.  And  there¬ 
fore  multiplying  the  extremes  and  the 

means  we  have  5  L  +  5  S  =  — L 

aooo 


—  9  S,  or  L  = 


18000 


S  =  S’  hr  S. 


5*38 

But  further,  I  remember  to  have  been 
told,  that  in  iummer  the  afeent  of  the 
lea  in  the  fyzygies,  is  to  the  afeent 
thereof  in  the  quadratures  as  about  5  to 
4.  In  the  Iblftices  themfelves  it  is  pro¬ 
bable  that  the  proportion  may  be  Ibme- 
thing  lels,  as  about  6  to  5: ;  whence  it 
would  follow  that  L  is  =  yj  S.  [For 

,  ,  .  1682  ¥  .  1681 

then  the  proportion  is  ^-77  L  -f- 


lOOO 


aooo 


1681 


S  :  L— - S  : 6 :  5-1  Till  we  can 

.  .  XOOO  J  J 


more  certainly  determine  the  propor¬ 
tion  from  obfervation,  let  us  aflume 
L  =  s’fS  ;  and  fince  the  heights  of 
the  tides  are  as  the  forces  which  excite 
them,  and  the  force  of  the  Sun  is  able 
to  raile  the  tides  to  the  height  of  nine 
Ruches,  the  Moon’s  force  will  be  lufh- 
cient  to  raile  the  lame  to  the  height  of 
four  feet.  And  if  we  allow  that  this 
height  may  be  doubled,  or  perhaps  tri¬ 
pled  by  that  force  of  reciprocation 

■  -  whiefj 


Digitized  by  LjOOQle 


h 


OF  THE  WORLD. 

which  we  obferve  in  the  motion  of  the 
waters,  and  by  which  their  motion  once 
begun  is  kept  up  for  ibme  time,  there 
will  be  force  enough  to  generate  all  that 
quantity  of  tides,  which  we  really  find 
in  the  ocean. 

T  h  u  s  we  have  feen  that  thele  forces 
are  fufficient  to  move  the  lea. 

But,  lb  far  as  I  cun  obferve, 

they  will  not  be  able  to  pro-  are  fcarce  fenfible  by 
duce  any  other  efied :  fenfible 
On  OUr  Earth.  For  lince  the  they  raifcinthefea. 
weight  of  one  grain  in  4000 
is  not  fenfible  in  the  niceft  ballance; 
and  the  Sun’s  force  to  move  the  tides  is 
13187000  lefs  than  the  force  of  gra¬ 
vity  ;  and  the  lum  of  the  forces  of  both 
Moon  and  Sun,  exceeding  the  Sun’s 
force  only  in  the  ratio  of  6  >-  to  1,  is  ftill 
above  ioooooo  times  lefs  than  the  force 
of  gravity  j  it  is  evident  that  both  for¬ 
ces  together  are  foo  times  lels  than 
what  is  required  fenfibly  to  increafe  or 
diminifh  the  weight  of  any  body  in  a 
ballance.  And  therefore  they  will  not 
lenfibly  move  any  fufpended  body ;  nor 
will  they  produce  any  fenfible  effe<3: 
on  pendulums,  barometers,  bodies  fwim- 
ming  in  ftagnant  water,  or  in  the  like 
finical  experiments.  In  the  atmofphere 
1  *  ■*  y  indeed 


Digitized  by  LjOOQle 


90 


OF  THE  SYSTEM 

indeed  they  will  excite  fuch  a  flux  and 
reflux  as  they  do  in  the  lea,  but  with 
fo  fmall  a  motion  that  no  fenfible  wind 
will  be  thence  produced. 

I  f  the  efFe&s  of  both  Moon 
That  the  body  of  the  and  Sun  in  railing  the  tides,  as 
more  denfe  than  the  well  as  their  apparent  diameters 
body  of  the  Sun.  were  equal  among  themfelves, 
their  ablolute  forces  would  be 
as  their  magnitudes.  But  the  efie& 
of  the  Moon  is  to  the  cffedt  of  the  Sun 
as  about  y  f  to  1  ;  and  the  Moon’s  dia* 
meter  lefs  than  the  Sun’s  in  the  ratio  of 
51  i  to  31  {  or  of  45;  to  4 6.  Now  the 
force  of  the  Moon  is  to  be  increaled  in 
the  ratio  of  the  effe&  dire&ly,  and  in 
the  triplicate  ratio  of  the  diameter  in- 
verlely.  Whence  the  force  of  the  Moon 
compared  with  its  magnitude  will  be  to 
the  force  of  the  Sun  compared  with  its 
magnitude  in  the  ratio  compounded  of 
5 1  to  1,  and  the  triplicate  of  4?  to  4 6 
inverfely,  that  is,  in  the  ratio  of  about  5  h 
*  to  1.  And  therefore  the  Moon  in  re* 
fpedf  of  the  magnitude  of  its  body,  has 
an  ablolute  centripetal  force  greater  than 
the  Sun  in  relpe&  of  the  magnitude  of 
its  body,  in  tne  ratio  of  y?*  to  x,  and 
is  therefore  more  denfe  in  the  fame  ra* 
tio. 


Digitized  by  v^ooQle 


9* 


OF  THE  WORLD. 

I  n  the  time  of  27  d.  7  h.  43'.  in  which 
the  Moon  makes  its  revolution  „ 

about  the  Earth,  a  Planet  may  more  denfe  than  the 
be  revolved  about  the  Sun  at  Earth  in  a  ratio  of  a- 
the  diftance  of  18,954  diame-  boutJto** 
ters  of  the  Sun  from  the  Sun’s  center, 
fuppofing  the  mean  apparent  diameter 
of  the  Sun  to  be  And  in  the 

fame  time  the  Moon  may  be  revolved 
about  the  Earth  at  reft,  at  the  diftance 
of  30  of  the  Earth’s  diameters.  If' in 
both  cafes  the  number  of  diameters  was 
the  fame,  the  abfolute  circum-terreftrial 
force  would  be  to  the  abfolute  circum- 
folar  force  as  the  magnitude  of  the  Earth 
to  the  magnitude  of  the  Sun.  Becaufo 
the  number  of  the  Earth’s  diameters  is 
greater  in  the  ratio  of  30  to  18,954,  the 
body  of  the  Earth  will  be  Iefs  in  the  tri¬ 
plicate  of  that  ratio,  that  is,  in  the  ra¬ 
tio  of  341  to  1.  Wherefore  the  Earth’s 
force,  for  the  magnitude  of  its  body,  is 
to  the  Sun’s  force,  for  the  magnitude  of 
its  body,  as  3  f*  to  i,  and  confoquently 
the  Earth’s  denfity  to  the  Sun’s  will  be 
in  the  fame  ratio.  Since  then  the  Moon’s 
denfity  is  to  the  Sun’s  denfity  as  5?* 
to  1,  the  Moon’s  denfity  will  be  to  the 
Earth’s  denfity  as  5^  to  344,  or  as  13 
to  16.  Wherefore  fince  the  Moon’s 
pagnitnde  is  to  the  Earth’s  magnitude 


Digitized  by  v^ooQle 


9*  OF  THE  SYSTEM 

as  about  i  to  41  r,  the  Moon’s  abfolute 
centripetal  force  will  be  to  the  Earth’s 
abloJure  centripetal  force  as  about  x  to 
19,  and  the  quantity  of  matter  in  the 
Moon  to  the  quantity  of  matter  in  the 
Earth  in  the  lame  ratio.  And  hence 
the  common  center  of  gravity  of  the 
Earth  and  Moon  is  more  exadly  deter¬ 
mined  than  hitherto  has  been  done. 
From  the  knowledge  of  which  we  may 
now  infer  the  Moon’s  diftance  from  the 
Earth  with  greater  accuracy.  But  I 
would  rather  wait  till  the  proportion  of 
the  bodies  of  the  Moon  and  Earth  one 
to  the  other  is  more  exa&ly  defined 
from  the  phenomena  of  the  tides,  hop¬ 
ing  that  in  the  mean  time  the  circumfe¬ 
rence  of  the  Earth  may  be  meafured  * 
from  more  diftant  ftations  than  any  bo¬ 
dy  has  yet  employed  for  this  purpofe. 

Tpys  I  have  given  an  account  of 
_ .  l  tii.  r  the  fyftem  of  the  Planets.  As  to 

Of  the  diftance  of  ,  >  ,  ~  1  r  11  r 

the  fixed  surt.  the  fixed  Stars,  the  fmallnels 
of  their  annual  parallax  proves 
them  to  be  removed  to  immenfe  ds (lan¬ 
ces  from  the  fyftem  of  the  Planets. 
That  this  parallax  is  lefs  than  one  mi¬ 
nute  i$  moll  certain ;  and  from  thence 
it  follows  that  the  diftance  of  the  fixe$ 
Stars  is  above  180  titties,  greater  than  the 

diftance 


Digitized  by  v^ooQle 


9? 


OF  THE  WORLD. 

diftance  of  Saturn  from  the  Sun.  Such 
as  reckon  the  Earth  one  of  the  Planets 
and  the  Sun  one  of  the  fixed  Stars,  may 
remove  the  fixed  Stars  to  yet  greater 
diftances  by  the  following  arguments. 
From  the  annual  motion  of  the  Earth 
there  would  happen  an  apparent  tranf- 
pofition  of  the  fixed  Stars,  one  in  re* 
fpeV  of  another,  almoft  equal  to  their 
double  parallax.  But  the  greater  and 
nearer  Stars*  in  refpeV  of  the  more  re¬ 
mote  which  are  only  feen  by  the  tcle- 
fcope,  have  not  hitherto  been  obferved 
to  have  the  leaft  motion.  If  we  fhould 
fuppofe  that  motion  to  be  but  lefs  than 
ao^.  the  diftance  of  the  nearer  fixed 
Stars  would  exceed  the  mean  diftance  of 
Saturn  by  above  1000  times.  Again* 
the  difc  of  Saturn,  which  is  only  17". 
or  18".  in  diameter,  receives  but  about 

- -1 - of  the  Sun’s  light.  For  fo 

a  100000000 

much  lefs  is  that  difc  than  the  whole 
fphericai  furface  of  the  orbit  of  Saturn. 
Now  if  we  fuppofe  Saturn  to  reflect  a- 
bout  £  of  this  light,  the  whole  light  re¬ 
lieved  from  its  illuminated  hemifphere 

Will  be  about - -1 — —  of  the  whole 

4100000000 

light  emitted  from  the  Sun's  hemi¬ 
fphere. 


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OF  THE  SYSTEM 

Iphere.  And  therefore  fince  light  is  ra¬ 
refied  in  the  duplicate  ratio  of  the  dis¬ 
tance  from  the  luminous  body,  if  the 
Sun  was  10000-^/42.  times  more  diftant 
than  Saturn,  it  would  yet  appear  as  lu¬ 
cid,  as  Saturn  now  does  without  its  ring, 
that  is,  fomething  more  lueid  than  a  fix¬ 
ed  Star  of  the  firfi  magnitude.  Let  us 
therefore  fiippofe  that  the  distance  from 
Which  the  Sun  would  Ihine  as  a  fixed 
Star  exceeds  that  of  Saturn  by  about 
10000  times,  and  its  apparent  diameter 
will  be  7V.  i6vi.  and  its  parallax  arifing 
from  the  annual  motion  of  the  Earth 
13'"'.  And  fo  great  will  be  the  difiance, 
the  apparent  diameter,  and  the  parallax, 
of  the  fixed  Stars  of  the  firfi  magnitude 
in  bulk  and  light  equal  to  our  Sun; 
Some  may  perhaps  imagine  that  a  great 
part  of  the  light  of  the  fixed  Stars  is  in¬ 
tercepted  and  loft  in  its  paftage  through 
io  vaft  fpaces,  and  upon  that  account 
pretend  to  place  the  fixed  Stars  at  near¬ 
er  difiances.  But  at  this  rate  the  remo¬ 
ter  Stars  could  be  fcarce  leem  Suppoie 
for  example  that  $  of  the  light  perilh  in 
its  paflage  from  the  neareft  fixed  Stars 
to  us,  and  $  will  twice  perilh  in  its  paf- 
fege  through  a  double  fpace,  thrice  thro* 
a  triple,  and  fo  forth.  And  therefore  the 
fixed  Stars  that  are  at  a  double  difiance 

will 


Digitized  by  LjOOQle 


9f 


OF  THE  WORLD. 

will  be  1 6  times  more  obfcure,  viz. 
4  times  more  obicarc  on  account  of  the 
diminifhcd  apparent  diameter ;  and  a- 
again,  4  times  more  on  account  of  the 
loft  light.  And  by  the  fame  argumenr, 
the  Axed  Stars  at  a  triple  diftance,  will 
be  9  x  4  X  4  or  144  times  more  obfcure, 
and  thole  at  a  quadruple  diftance  will 
be  16x4X4X4  or  1014  times  more 
obfcure.  But  fo  great  a  diminution  of 
light  is  no  ways  confiftent  with  the  phe¬ 
nomena  and  with  that  hypothefis  which 
places  the  fixed  Stars  at  different  diftan- 
ces. 


The  fixed  Stars  being  therefore  at 
fiich  vaft  diftances  from  one 
another,  can  neither  attract  each  T,hat  the,  Co,mets  ** 

r  n  1  1  n.  1  often  as  they  become 

other  lenfibly,  nor  be  attra&ed  vifibie  to  u%  are 
by  our  Sun.  But  the  Comets  "«arer  th?n  Jupiter, 
muft  unavoidably  beaded  on  prailax inTongi" 
by  the  circum-folar  force.  For 
as  the  Comets  were  placed  by  aftrono- 
toers  above  the  Moon  becaule  they 
Were  found  to  have  no  diurnal  parallax ; 
fi>  their  annual  parallax  is  a  convincing 
proof  of  their  defcending  into  the  regi¬ 
ons  of  the  Planets.  For  all  the  Comets 
Which  move  in  a  dired  courle,  accord¬ 
ing  to  the  order  of  the  figns,  about  the 
end  of  their  appearance  become  more 

than 


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96 


OF  THE  SYSTEM 

than  ordinarily  (low,  or  retrograde,  if 
the  Earth  is  between  them  and  the  San  j 
and  more  than  ordinarily  fwift,  if  the 
Earth  is  approaching  to  a  heliocentric 
oppofition  with  them.  Whereas  on  the 
other  hand,  thole  which  move  againft 
the  order  of  the  figns  towards  the  end 
of  their  appearance,  appear  fwifter  than 
they  ought  to  be  if  the  Earth  is  between 
them  and  the  San  ;  and  (lower,  and  per¬ 
haps  retrograde,  if  the  Earth  is  in  the 
other  fide  of  its  orbit.  This  is  occafi- 
oned  by  the  motion  of  the  Earth  in  dif¬ 
ferent  fituations.  If  the  Earth  go  the 
lame  way  with  the  Comet,  with  a  fwift¬ 
er  motion,  the  Comet  becomes  retro¬ 
grade  ;  if  with  a  (lower  motion,  the  Co¬ 
met  becomes  (lower  however  ;  and  if 
the  Earth  move  the  contrary  way,  it  be¬ 
comes  fwifter.  And  by  colle&ing  the 
differences  between  the  (lower  arid 
fwifter  motions,  and  the  lums  of  the 
more  (wift  and  of  the  retrograde  moti¬ 
ons,  and  comparing  them  with  the  fitu- 
ation  and  motion  of  the  Earth  from 
whence  they  ari(e,  I  found,  by  means 
of  this  parallax,  that  the  diftances  of  the 
Comets  at  the  time  they  ceafe  to  be  vifi- 
ble  to  the  naked  eye,  is  always  lefs  than 
the  diftance  of  Saturn ;  and  generally 
even  Ids  than  the  diftance  of  Jupiter. 

3  The 


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97 


OF  THE  WORLD. 

The  lame  thing  may  be  collected 
from  the  curvature  of  the  way  T,„  fimt 
of  the  Comets.  Thele  bodies  from  their  parallax 
go  on  nearly  in  great  circles  ,n  la,,,u<le* 
while  their  motion  continues  fwift  ;  but 
about  the  end  of  their  courfe,  when  that 
part  of  their  apparent  motion,  which  a- 
riles  from  the  parallax,  bears  a  greater 
proportion  to  their  whole  apparent  mo¬ 
tion,  they  commonly  deviate  from  thole 
circles ;  and  when  the  Earth  goes  to  one 
fide,  they  deviate  to  the  other.  And 
this  deflexion^  becaufe  of  its  correlpond- 
ing  with  the  motion  of  the  Earth,  mud 
arile  chiefly  from  the  parallax  ;  and  the 
quantity  thereof  is  fo  confiderable,  as 
by  my  computation,  to  place  the  dis¬ 
appearing  Comets  a  good  deal  lower 
than  Jupiter.  Whence  it  follows,  that 
when  they  approach  nearer  to  us  in  their 
perigees  and  perihelions,  they  often  de- 
fcend  below  the  orbits  of  Mars  and  the 
inferiour  Planets. 

Moreover,  this  neamels  of  the 
Comets  is  confirmed  by  the  an-  The  fame  eJ 
nual  parallax  of  the  orbit,  in  fo  otherwife  by  the  pa- 
far  as  the  fame  is  pretty  nearly  rallax> 
collected  by  the  luppofition  that  the 
Comets  move  uniformly  in  right  lines. 

The  method  of  collecting  the  diftance 
H  of 


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OF  THE  SYSTEM 

of  a  Comet  according  to  this  hypothe¬ 
cs  from  four  obfervations ,  (firft  at¬ 
tempted  by  Kepler*  and  perfe&ed  by 
Dr.  Wallis  and  Sir  Chrift.  Wren')  is  well 
known.  And  the  Comets  reduced  to 
this  regularity  generally  pals  through 
the  middle  of  the  planetary  region.  So 
the  Comets  of  the  years  1607  and  1618 
as  their  motions  are  defined  by  Kepler 
palled  between  the  Sun  and  the  Earth  ; 
that  of  the  year  1664  below  the  orbit  of 
Mars ;  and  that  in  1680  below  the  orbit 
of  Mercury,  as  its  motion  was  defined 
by  Sir  Chrift .  Wren  and  others.  By  a 
like  rectilinear  hypothefis ,  Heveltus 
placed  all  the  Comets  about  which  we 
have  any  obfervations,  below  the  orbit 
of  Jupiter.  ’Tis  a  falfe  notion  therefore, 
and  contrary  to  aftronomical  calculation, 
which  lome  have  entertained,  who  from 
the  regular  motion  of  the  Comets,  either 
remove  them  into  the  regions  of  the 
fixed  Stars,  or  deny  the  motion  of  the 
Earth }  whereas  their  motions  cannot  be 
reduced  to  perfect  regularity,  unlels  we 
luppofe  them  to  pafs  through  the  re¬ 
gions  near  the  Earth  in  motion.  And 
thefe  are  the  arguments  drawn  from  the 
parallax,  lo  far  as  it  can  be  determined 
without  an  exaCt  knowledge  of  the  or¬ 
bits  and  motions  of  the  Comets. 

The 


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99 


OF  THE  WORLD. 

The  near  approach  of  the  Comets  is 
further  confirmed  from  the  light  Frora  the  )ight  of|he 
of  their  beads.  For  the  light  of  comets  heads  it  is 
a  celdtial  body,  illuminated  by 
the  San,  and  receding  to  re-  Saturn,  Jupiter,  and 
mote  parts,  is  diminilhed  in  the  evcnoflhe  Eaitb- 
quadruplicate  proportion  of  the  diftance, 
to  wit,  in  one  duplicate  proportion  on 
account  of  the  increafe  of  the  diftance 
from  the  Sun ;  and  in  another  duplicate 
proportion,  on  account  of  the  decreal’e 
of  the  apparent  diameter.  Hence  it  may¬ 
be  inferred,  that  Saturn  being  at  a  dou¬ 
ble  diftance,  and  having  its  apparent 
diameter  nearly  half  of  that  of  Jupiter, 
mull  appear  about  1 6  times  more  obfcure ; 
and  that  if  its  diftance  were  4  times 
greater,  its  light  would  be  156  times 
Jefs  j  and  therefore  would  be  hardly  per¬ 
ceivable  to  the  naked  eye.  But  now  the 
Comets  often  equal  Saturn’s  light,  with¬ 
out  exceeding  him  in  their  apparent 
diameters.  So  the  Comet  of  the  year 
1678,  according  to  Dr.  Hook's  obferva- 
tions,  equalled  in  brightnefs  the  lighr  of 
a  fixed  Star  of  the  firft  magnitude,  and 
its  head,  or  the  Star  in  the  middle  of  the 
coma,  appeared,  through  a  telefcope  of 
x$  foot,  as  lucid  as  Saturn  near  the  hori¬ 
zon.  But  the  diameter  of  the  head  was 
only  zf'f ;  that  is,  almoft  the  fame  with 
H  x  the 


Digitized  by  LjOOQle 


loo 


OF  THE  SYSTEM 

the  diameter  of  a  circle  equal  to  Saturn 
and  his  ring.  The  coma  or  hair  fur¬ 
rounding  the  head  was  about  ten  times 
as  broad ;  namely,  4  }  min.  Again,  the 
leaft  diameter  of  the  hair  of  the  Comet 
of  the  year  1681,  oblerved  by  Mr.  Flam - 
jleed  with  a  tube  of  16  foot,  and  meafii- 
red  with  the  micrometer,  was  a*.  o". 
But  the  nucleus,  or  Bar  in  the  middle, 
icarce  poflefled  the  tenth  part  of  this 
breadth,  and  was  therefore  only  ii//.  or 
\xr.  broad.  But  the  light  and  cleameft 
of  its  head  exceeded  that  of  the  year 
1 680,  and  was  equal  to  that  of  the  Stars 
of  the  firft  or  fecond  magnitude.  More¬ 
over,  the  Comet  of  the  year  1665'  in 
April,  as  Hevelius  informs  us.  exceed¬ 
ed  almoft  all  the  fixed  Stars  in  (plendor ; 
and  even  Saturn  it  lelf,  as  being  of  a 
much  more  vivid  colour.  For  this  Co¬ 
met  was  more  lucid  than  that  which  ap¬ 
peared  at  the  end  of  the  foregoing  year, 
and  was  compared  to  the  Stars  of  the 
firft  magnitude.  The  diameter  of  the 
coma  was  about  6>.  but  the  nucleus, 
compared  with  the  Planets  by  means  of 
a  telefcope,  was  plainly  leis  than  Jupiter, 
and  was  fometimes  thought  left,  fome- 
times  equal  to,  the  body  of  Saturn  with¬ 
in  the  ring.  To  this  breadth  add  that 
of  the  ring,  and  the  whole  face  of  Sa¬ 
turn 


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OF  THE  WORLD. 

tarn  will  be  twice  as  great  as  that  of  the 
Comet,  with  a  light  not  at  all  more  in¬ 
tend  :  and  therefore  the  Comet  was 
nearer  to  the  Sun  than  Saturn.  From 
the  proportion  of  the  nucleus  to  the 
whole  head  found  by  thefe  obfervations, 
and  from  its  breadth,  which  feldom  ex¬ 
ceeds  8'  or  n'i  it  appears  that  the  Stars 
of  the  Comets  are  mod  commonly  of 
the  lame  apparent  magnitude  as  the 
Planets  ;  but  that  their  light  may  be 
compared  oftentimes  with  that  of  Sa¬ 
turn,  and  lometimes  exceeds  it.  And 
hence  ’tis  certain  that  in  their  perihelia 
their  diftances  can  fcarce  be  greater  than 
that  of  Saturn.  At  twice  that  diftance, 
the  light  would  be  four  times  lefs,  which 
befides  by  its  dim  palenefs  would  be  as 
much  inferiour  to  the  light  of  Saturn,  as 
the  light  of  Saturn  is  to  the  fplendour  of 
Jupiter.  But  this  difference  would  be 
eafily  obferved.  At  a  diftance  ten  times 
greater  their  bodies  mad  be  greater  than 
that  of  the  Sun  ;  but  their  light  would 
be  ioo  times  fainter  than  that  of  Saturn. 
And  at  diftances  ftill  greater  their  bodies 
would  far  exceed  the  Sun :  but  being  in 
fuch  dark  regions,  they  mud  be  no  lon¬ 
ger  vifible.  So  impoftible  is  it  to  place 
the  Comers  in  the  middle  regions  be¬ 
tween  the  Sun  and  fixed  Stars,  account- 
H  3  ing 


10$ 


Digitized  by  LjOOQle 


102 


OF  THE  SYSTEM 

ing  the  Sun  as  one  of  rhe  fixed  Stars* 
For  certainly  they  would  receive  no 
more  light  there  from  the  Sun,  than  we 
do  from  the  greateft  of  the  fixed  Stars. 

So  far  we  have  gone  without  confider* 
ing  that  obfeuration  which  Comets  fuf- 
fer  from  that  plenty  of  thick  fmoak 
which  encompafteth  their  heads,  and 
through  which  the  heads  always  fhew 
dull  as  through  a  cloud.  For  by  how 
much  the  more  a  body  is  obfeured  by 
this  fmoak,  by  fo  much  the  more  near 
it  mud  be  allowed  to  come  to  the  Sun  , 
that  it  may  vie  with  the  Planets  in 
the  quantity  of  light  which  it  refle&s. 
Whence  it  is  probable  that  the  Comets 
ddeend  far  below  the  orbit  of  Saturn,  as 
we  proved  before  from  their  parallax. 
But  above  all,  the  thing  is  evinced  from 
their  tails,  which  mud  be  owing  either 
to  the  Sun’s  light  reflected  from  a  fmoak 
arifing  from  them  and  difperfing  it  felf 
through  the  /Ether,  or  to  the  lights  of 
their  own  heads. 

In  the  former  cafe  we  mud  fhorten 
the  diftance  of  the  Comets,  leaft  we  be 
obliged  to  allow  that  the  fmoak  arifing 
from  their  heads  is  propagated  through 
fuch  a  vaft  extent  of  (pace,  and  with 
fuch  a  velocity  of  expanfion  as  will 
feem  altogether  incredible.  In  the  lat¬ 
ter 


Digitized  by  LjOOQle 


103 


OF  TH«  WORLD. 

ter  cafe  the  whole  light  of  both  head 
and  tail  muft  be  afcribed  to  the  central 
nucleus.  But  then  if  we  fuppofe  all  this 
light  to  be  united  and  condenled  within 
the  difc  of  the  nucleus,  certainly  the 
nucleus  will  by  far  exceed  Jupiter  it 
felf  in  Iplendour,  elpecially  When  it  e- 
mits  a  very  large  and  lucid  tail.  If 
therefore  under  a  lefs  apparent  diameter 
it  refle&s  more  light,  it  muft  be  much 
more  illuminated  by  the  Sun,  and  there¬ 
fore  much  nearer  to  it.  So  the  Comet 
that  appeared  Dec.  12.  and  if.  O.  S. 
Anno  1679, at  £he  time  it  emitted  a  very 
Ihining  tail,  whole  iplendour  was  equal 
to  that  of  many  Stars  like  Jupiter  if  their 
light  were  dilated  and  fpread  through 
io  great  a  (pace,  was,  as  to  the  magni¬ 
tude  of  its  nucleus,  lels  than  Jupiter,  (as 
Mr.  Flamfleed  obferved)  and  therefore 
was  much  nearer  to  the  Sun.  Nay,  it 
was  even  lefs  than  Mercury.  For  on 
the  17th  of  that  month, when  it  was 
nearer  to  the  Earth,  it  appeared  to  Caf- 
fiui  through  a  telefcope  of  3  f  foot  a  lit¬ 
tle  left  than  the  globe  of  Saturn.  On 
the  8th  of  this  month,  in  the  morning. 
Dr.  Halley  law  the  tail,  appearing  broad 
and  very  Ihort,  and  as  if  it  role  from  the 
body  of  the  Sun  it  felf,  at  that  time 
very  near  its  rifing.  Its  form  was  like 
H  4  that 


Digitized  by  LjOOQle 


iC4 


OF  THE  SYSTEM 

that  of  an  extraordinary  hright  cloud  ; 
nor  did  it  difappear  till  the  Sun  it  felf 
began  to  be  feen  above  the  horizon.  Its 
iplendour  therefore  exceeded  the  light 
of  the  clouds  till  the  Sun  role,  and  far 
furpafled  that  of  all  the  Stars  together, 
as  yielding  only  to  the  immediate  bright- 
jiefs  of  the  Sun  it  felf.  Neither  Mercu¬ 
ry,  nor  Venus,  nor  the  Moon  it  felf 
are  feen  lo  near  the  rifing  Sun.  Imagine 
all  this  dilated  light  colleded  together, 
and  to  be  croudcd  into  the  orbit 
of  the  Comet’s  nucleus  which  was 
Jefs  than  Mercury  ;  by  its  fplendour 
thus  increafed,  becoming  fo  much  more 
confpicuous,  it  will  vaftly  exceed  Mer¬ 
cury,  and  therefore  muft  be  nearer  to 
the  Sun.  On  the  nth  and  15-th  of 
the  lame  month  this  tail  extending  it 
ielf  over  a  much  greater  fpace,  appeared 
more  rare;  but  its  light  was  ftill  lb  vi¬ 
gorous  as  to  become  vifible  when  the 
fixed  Stars  were  hardly  to  be  feen,  and 
foon  after  to  appear  like  a  fiery  beam 
lhining  in  a  wonderful  manner.  From 
its  length,  which  was  40  or  50  deg.  and 
its  breadth  of  x  deg.  we  may  compute 
what  the  light  of  the  whole  muft  be. 


This 


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Google 


OF  THE  WORLD.  ioj 

This  near  approach  of  the  Comets 
to  the  Sun  is  confirmed  from 
the  fituation  they  are  feen  in  £>  S?\x£!3[ 
when  their  tails  appear  moft  re-  nari  fplendour  of 
fptadent.  For  when  the  head 
paffes  by  the  Sun  and  lies  hid 
under  the  folar  rays,  very  bright  and 
fhining  tails  like  fiery  beams  are  laid  to 
i!7ue  from  the  horizon  ;  but  afterwards 
when  the  head  begins  to  appear,  and  is 
gpt  farther  from  the  Sun,  that  fplendour 
always  decreafes  and  turns  by  degrees 
into  a  palenefs,  like  to  that  of  the  milky 
way,  but  much  more  fenfible  at  firft  \ 
after  that  vanifhing  gradually.  Such  was 
that  mod  refplendent  Comet  deferibed 
by  Ariftotle ,  Lib.  i.  Meteor .  6.  ‘  The 
‘  head  thereof  could  not  be  feen  becaufe 

*  it  let  before  the  Sun,  or  at  lead  was  hid 
f  under  the  Sun’s  rays  ;  but  the  next  day 
‘  it  was  feen  as  well  as  might  be ;  for  ha¬ 
lving  left  the  Sun  but  a  very  little  way  it 

*  let  immediately  after  it.  And  the  feat- 
‘  tered  light  of  the  head  obfeured  by  the 
‘  too  great  fplendour  (of  the  tail)  did  not 
‘yet  appear.  But  afterwards  (fays  Art- 

*  Jiotle)  when  the  fplendour  of  the  tail 
‘  was  now  diminifhed,  (the  head  of)  the’ 

*  Comet  recovered  its  native  brightnefs. 

‘  And  the  fplendour  of  its  tail  reached 
‘  now  to  a  third  part  of  the  heavens*  (that 

is 


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io6 


OF  THE  SYSTEM 

Is  to  <So°.)  ‘  It  appeared  in  the  winter 
‘leafon,  and  riling  to  Orion's  Girdle, 

‘  there  vanilhed  away.’  Two  Comets  of 
the  lame  kind  are  delcribed  by  JuftiMy 
lib.  37.  which  according  to  his  account 
‘  Ihined  lo  bright  that  the  whole  heaven 

*  leemed  to  be  on  fire ;  and  by  their  great- 

*  nels  filled  up  a  fourth  part  of  the  hea- 
‘  yens,  and  by  their  fplendour  exceeded 

*  that  of  the  Sun.*  By  which  Jaft  words  a 
near  polition  of  thele  bright  Comets  and 
the  riling  or  fetting  Sun  is  intimated. 
We  may  add  to  thefe  the  Comet  of  the 
year  1101  or  1106,  *  the  ftar  of  which 
‘  was  fmall  and  oblairc  (like  that  of  1 680) 

*  but  the  fplendour  arifing  from  it  ex¬ 
tremely  bright,  reaching  like  a  fiery 
‘  beam  to  the  Eaft  and  North,*  as  Heve- 
lius  has  it  from  Simeon  the  monk  of 
* Durham .  It  appeared  at  the  beginning 
of  February  about  the  evening  in  the 
loath- weft.  From  this  and  from  the  li- 
tuation  of  the  tail  we  may  infer  that  the 
head  was  near  the  Sun.  Matthew  Far  is 
lays,  ‘  it  was  about  one  cubit  from  the 

‘  Sun  ;  from  the  third’  [  or  rather  the  * 
fixth]  ‘  to  the  ninth  hour  lending  out  a 
‘Jong  ftream  of  light.*  The  Comet  of 
1164  in  July,  or  about  the  foiftice,  pre¬ 
ceded  the  riling  Sun,  fending  out  its 
beams  with  3  great  light  towards  the 

weft 


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OF  THE  WORLD. 

weft  as  far  as  the  middle  of  the  heavens. 
And  at  the  beginning  it  alcended  a  little 
above  the  horizon ;  but  as  the  Sun  went 
forwards  it  retired  every  day  farther 
from  the  horizon,  till  it  palled  by  the 
very  middle  of  the  heavens.  It  is  laid 
to  have  been  at  the  beginning  large  and 
bright,  having  a  large  coma,  which  de¬ 
cayed  from  day  to  day.  It  is  defcribed 
in  Append.  Matth.  *Parif  Hifl.  Ang. 
after  this  manner.  An.  Chrifti  i  x6$. 
4  there  appeared  a  Comet  lb  wonderful, 
*  that  none  then  living  had  ever  feen  the 
‘  like.  For  riling  from  the  eaft  with  a 
4  great  brightnefs,  it  extended  it  lelf  with 
4  a  great  light  as  far  as  the  middle  of  the 
4  hemifphere  towards  the  weft.’  The  La¬ 
tin  original  being  fomewhat  barbarous 
and  obfcure,  it  is  here  fubjoined.  Ab 
orient e  entm  cum  magno  fulgore  fur- 
gens ,  ufque  ad  medium  hem'tfpharii 
verjus  Occident em,  omnia perlucide per- 
trahcbat.  In  the  year  1401  or  1401, 
the  Sun  being  got  below  the  horizon, 
there  appeared  in  the  weft  a  bright  and 
ihining  Comet  lending  out  a  tail  upwards 
in  fplendour  like  a  flame  of  fire,  and  in 
form  like  a  fpear,  darting  its  rays  from 
weft  to  eaft.  When  the  Sun  was  funk 
below  the  horizon,  by  the  luftre  of  its 
own  rays  it  enlightned  all  the  borders 


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toy 


io& 


OF  THE  SYSTEM 

of  the  Earth,  not  permitting  the  other 
Stars  to  fhew  their  light,  or  the  (hades 
of  night  to  darken  the  air,  becaufe  its 
light  exceeded  that  of  the  others,  and 
extended  it  felf  to  the  upper  part  of  the 
heavens,.6te.  Mift .  Byzant.  <Duc.  Mich . 
Nepot.  From  the  dtuation  of  the  tail 
of  this  Comet,  and  the  time  of  its  firft 
appearance,  we  may  infer  that  the  head 
was.  then  near  the  Sun,  and  went  farther 
from  him  every  day.  For  that  Comet 
continued  three  months.  In  the  year 
1 5x7,  Aug.  it.  about  four  in  the  morn¬ 
ing,  there  was  (een  almod  throughout 
Europe ,  a  terrible  Comet  in  Leo ,  which 
continued  flaming  an  hour  and  a  quar¬ 
ter  every  day.  It  role  from  the  ead, 
and  afccnded  to  the  (outh  and  wed  to  a 
prodigious  length.  It  was  mod  confpi- 
cuous  to  the  north,  and  its  cloud  (that 
is  its  tail)  was  very  terrible  ;  having, 
according  to  the  fancies  of  the  vulgar, 
the  form  of  an  arm  a  little  bent,  holding 
a  fword  of  a  vad  magnitude.  In  the 
year  1618,  in  the  end  of  November , 
there  began  a  rumour,  that  there  appear¬ 
ed  about  Sun  rifing  a  bright  beam,  which 
was  the  tail  of  a  Comet,  whole  head  was 
as  yet  concealed  within  the  brightnefs 
of  the  lblar  rays.  On  Nov.  14.  and  from 
that  time  the  comet  it  felf  appeared  with 

at 


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'OF  THE  WORLD. 

!a  bright  light,  its  head  add  tail  being 
extremely  refplendent.  The  length  of 
the  tail,  which  was  at  firft  io  or  30 
deg.  increafed  till  ‘December  9.  when  it 
arofe  to  75^  deg.  but  with  a  light  much 
more  faint  and  dilute  than  at  the  begin¬ 
ning.  In  the  year  1668,  March  y. 
N.  S.  P.  Valent.  Eftancius  being  in 
Brafile ,  faw  a  comet  near  the  horizon 
in  the  fouth-wed.  Its  head  was  fmall, 
and  fcarce  dilcernible,  but  its  tail  ex¬ 
tremely  bright  and  refulgent,  fb  that  the 
reflexion  of  it  from  the  fea  was  eafily 
feen  by  thofe  who  flood  upon  the  fhore. 
This  great  fplendour  laded  but  three 
days,  decreaung  very  remarkably  from 
that  time.  The  tail  at  the  beginning 
extended  it  felf  from  wed  to  fouth,  and 
in  a  (ituation  almod  parallel  to  the  ho¬ 
rizon,  appearing  like  a  finning  beam  23 
deg.  in  length.  Afterwards  the  light  de- 
creafing,  its  magnitude  increafed  till  the 
Comet  ceafed  to  be  vifible.  So  that 
CaJJini  at  Bologna  faw  it  (Mar.  10.  11. 

riling  from  the  horizon  31  deg.  in 
length.  In  ‘Portugal  it  is  laid  to  have 
taken  up  a '  fourth  part  of  the  heavens, 
(that  is,  4?  deg.)  extending  it  felf  from 
wed  to  ead  with  a  notable  brightnefs ; 
though  the  whole  of  it  was  not  feen,  be* 
caule  the  head  in  this  part  of  the  world 

always 


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I  to 


Of  THE  SYSTEM 

always  lay  bid  below  the  horizon.  Front 
the  increale  of  the  tail  it  is  plain  that 
the  head  receded  from  the  Son,  and  was 
neared  to  it  at  the  beginning  when  the 
tail  appeared  brighted. 

To  all  thefe  we  may  add  the  comec 
of  1680,  whole  wonderful  Iplendour  at 
the  conjunction  of  the  head  with  the 
Sun  was  above  delcribed.  But  lb  great 
a  Iplendour  argues  the  comets  of  this 
kind  to  have  really  palled  near  the  foun¬ 
tain  of  light ;  elpecially  lince  the  tails 
never  ihine  fo  much  in  their  oppoficioa 
to  the  Sun ;  nor  do  we  read  that  fiery 
beams  have  ever  appeared  there. 

Lastly,  the  fame  thing  is  inferred 

The  fame  proved  thc  °f  he*k  “► 

from  the  light  of  creafing  in  the  recefs  of  the  co- 
their  head*,  ai 1  being  mets  from  tJjC  Earth  towards 

greater  ctteris  paribus  .  .  ,  r  •  t  • 

when  they  come  near  the  Sun,  and  decreafing  in  their 
t»  the  sun.  return  from  the  Sun  towards 

the  Earth.  For  lo  the  lad  comet  of  the 
year  1665",  (by  the  obfervation  of  He- 
•velius)  from  the  time  that  it  was  fird 
leen  was  always  lofing  of  its  apparent 
motion,  and  therefore  had  already  pat 
led  its  perigee,  yet  the  fplendour  of  its 
head  was  daily  increafing,  till  being  hid 
by  the  Sun’s  rays,  the  comet  ceaied  to 
appear.  The  Comet  of  the  year  1683, 

(by 


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tit 


OF  THE  WORLD. 

(by  the  obfervation  of  the  lame  Heve- 
lius)  about  the  end  of  July,  when  it 
firft  appeared,  moved  at  a  very  flow 
rate,  advancing  only  about  40  or  4? 
minutes  in  its  orbit  in  a  day’s  time.  But 
from  that  time  its  diurnal  motion  was 
continually  upon  the  increaie  till  Sep¬ 
tember  4.  when  it  arofe  to  about  £  de¬ 
grees.  And  therefore  in  all  this  inter¬ 
val  of  time  the  Comet  was  approaching 
to  the  Earth.  Which  is  likewiie  proved 
from  the  diameter  of  its  head  meafured 
with  a  micrometer.  For  Auguft  the  6th 
Hevelius  found  it  only  6K  £;/.  including 
the  coma ;  which  September  z.  he  obfer- 
ved  7".  And  therefore  its  head  ap¬ 
peared  far  lels  about  the  beginning  than 
towards  the  end  of  its  motion,  though  a- 
bout  the  beginning,  becaufe  nearer  to  the 
Sun,  it  appeared  far  more  lucid  than  to¬ 
wards  the  end,  as  the  fame  Hevelius 
declares.  Wherefore  in  all  this  interval 
of  time,  on  account  of  its  reeds  from 
the  Sun,  it  decreafed  in  fplendour,  not- 
withftanding  its  accefs  towards  the 
Earth.  The  comet  of  the  year  1618, 
about  the  middle  of  ^December,  and  that 
of  the  year  1680,  about  the  end  of  the 
fame  month,  did  both  move  with  their 
greateft  velocity,  and  were  therefore 
then  in  their  perigees.  But  the  greateft 

Iplen- 


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lit 


OF  T H IS  SYSTEM 

fplendour  of  their  heads  was  leen  twd 
weeks  before  when  they  had  juft  got 
clear  of  the  Sun’s  rays.  And  the  great- 
eft  fplendour  of  their  tails  a  little  more 
early,  when  yet  nearer  to  the  Sun.  The 
head  of  the  former  Comet,  according  to 
the  obfervations  of  Cyfatus ,  'Dec.  r. 
appeared  greater  than  the  Stars  of  the 
firft  magnitude,  but  in  the  lplendour 
and  brightnefs  of  its  light,  a  great  deal. 
Jan.  7.  Kepler  being  uncertain  about 
the  head,  left:  off  oblerving.  Dec.  iz. 
the  head  of  the  laft  Comet  w'as  feen  and 
obferved  by  Flamfteed at  the  diftance  of 
9  degrees  from  the  Sun ;  which  a  Star 
of  the  third  magnitude  could  hardly 
have  been.  December  if  and  17,  the 
fame  appeared  like  a  Star  of  the  third 
magnitude,  its  fplendour  being  diminifh- 
ed  by  the  bright  clouds  near  the  fetting 
Sun.  Dec.  26.  when  it  moved  with  the 
greateft  fwiftnefs,  and  was  almoft  in  its 
perigee,  it  was  inferiour  to  Os  cPegafii 
a  Star  of  the  third  magnitude.  Jan.  3 .  it 
appeared  like  a  Star  of  the  fourth.  Jan.  9. 
like  a  Star  of  the  fifth.  Jan.  1 3.  it  difap- 
peared  by  reafon  of  the  brightnels  of  the 
Moon  which  was  then  in  its  increafe. 
Jan.  2f.  it  was  fcarce  equal  to  the  Stars 
of  the  feventh  magnitude.  If  we  take 
equal  times  on  each  hand  of  the  perigee, 


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OF  THE  WORLD.  iij 

the  heads  placed  at  remote  diftances 
Would  have  fhined  equally  before  and 
after,  becaufe  of  their  equal  diftances 
from  the  Earth.  That  in  one  cafe  they 
Aimed  very  bright,  and  in  the  other 
Vanifhed,  is  to  be  afenbed  to  the  near- 
iiefs  of  the  Sun  in  the  firft  cafe,  and  his 
diftance  in  the  other.  And  from  the 
great  difference  of  the  light  in  thefe  two 
cafes,  we  infer  its  great  nearnefs  in  the 
firft  of  them.  For  the  light  of  the  Co¬ 
mets  ufes  to  be  regular,  and  to  appear 
greateft  when  their  heads  move  the 
fwifteft,  and  are  therefore  in  their  peri¬ 
gees  ;  excepting  in  fo  far  as  it  is  increa- 
fed  by  their  nearnefs  to  the  Sun. 

From  thefe  things  I  at  laft  difeover- 
td  why  the  Comets  frequent  fo  .  c  , 
much  the  region  of  the  Sun.  If  by  the  great  number 
they  were  to  be  feen  in  the  re-  of  comet*  feen  m 
gions  a  great  way  beyond  Sa«  ,here8lon<>  theSuo* 
turn,  they  muft  appear  oftner  in  thofe 
parts  of  the  heavens  that  are  oppofire  ro 
the  Sun.  For  thofe  which  are  in  that  fl- 
tuation  would  be  nearer  to  the  Earth ; 
and  the  interpofition  of  the  Sun  would 
obfeure  the  others*  But  looking  over 
the  hiftory  of  Comets,  I  find  that  four 
or  five  times  more  have  been  feen  in  the 
bemifphere  toward  the  Sun,  than  in  the 
I  oppofite 


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:i4  OF  THE  SYSTEM 

oppofite  hemifphere ;  befides,  without 
doubt,  not  a  few  which  have  been  hid 
by  the  light  of  the  Sun.  For  Comets 
defending  into  our  parts  neither  emit 
tails,  nor  are  fo  well  illuminated  by  the 
Sun  as  to  dilcover  themfelves  to  our 
naked  eyes,  till  they  are  come  nearer  to 
us  than  Jupiter.  But  the  far  greater 
part  of  th  it  iphasrical  (pace,  which  is  de- 
fcribed  about  the  Sun  with  fo  fmall  an 
interval,  lies  on  that  fide  of  the  Earth 
which  regards  the  Sun,  and  the  Comets 
in  that  greater  part  are  more  ftrongly  il¬ 
luminated  as  being  for  the  mod  part 
nearer  to  the  Sun.  Befides,  from  the 
remarkable  eccentricity  of  their  orbits 
it  comes  to  pafs  that  their  lower  apfides 
are  much  nearer  to  the  Sun  than  if  their 
revolutions  were  performed  in  circles 
concentric  to  the  Sun. 

Hence  alfo  we  underftand  why  the 
this  alfo  confirmed,  tails  of  the  Comets,  while  their 

by  the  greater  mag-  heacjs  are  defending  towards 
nitude  and  fplendour  .  ,  °  n  „ 

of  the  tails  after  the  the  Sun,  always  appear  lhort 
conjunaion  of  the  ancj  rarC}  and  are  leldcim  laid  to 

f£f bdlorhe.the  Sun'  have  exceeded  is  or  20  deg.  in 
length  ;  but  in  the  recels  of  the  heads 
from  the  Sun  often  fliine  like  fiery  beams, 
and  foon  after  reach  to  40,  fo,  60,  70 
deg.  in  length,  or  more.  This  great 

Iplendour 


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OF  THE  WORLD, 
fplendour  and  length  of  the  tails  arifes 
from  the  heat  which  the  Sun  communi¬ 
cates  to  the  Comet  as  it  pafles  near  it. 

And  thence  I  think  it  may  be  concluded 
that  all  the  Comets  that  have  had  fuch 
tails  have  palled  very  near  the  Sun. 

Hence  alfo  we  may  collet  that 
the  tails  arife  from  the  atmof- 
phercS  of  the  heads.  But  we  Jhat  *he  ar,r= 
nave  had  three  leveral  opinions  of  the  Comets, 
about  the  tails  of  Comets.  For 
fome  will  have  it,  that  they  are  nothing 
elle  but  the  beams  of  the  Sun’s  light 
tranfmitted  through  the  Comets  heads* 
which  they  fuppofe  to  be  tranfparent  : 
others,  that  they  proceed  from  the  rc- 
fra&ion  which  light  fullers  in  palling 
from  the  Cornets  head  to  the  earth  :  and 
laftly,  others,  that  they  are  a  fort  of 
clouds  or  vapour  conftantly  riling  from 
the  Comets  heads,  and  tending  towards 
the  parts  oppofite  to  the  Sun.  The 
firft  is  the  opinion  of  fuch  as  are  yet  un¬ 
acquainted  with  opticks.  For  the  beams 
of  the  Sun  are  not  leen  in  a  darkned 
room,  but  in  conlequence  of  the  light 
that  is  refle&ed  from  them,  by  the  little 
particles  of  dull  and  finoak  which  are  al-  , 
ways  flying  about  in  the  air.  And 
hence  it  is,  that  in  air  impregnated  with 
I  %  thick 


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u6 


OF  THE  SYSTEM 

thick  finoak  they  appear  with  greater 
brighmefs,  and  are  more  faintly  and 
more  difficultly  feen  in  a  finer  air.  But 
in  the  heavens,  where  there  is  no  mat¬ 
ter  to  refledt  the  light  they  are  not  to 
be  lecn  at  all.  Light  is  not  feen  as  it  is 
in  the  beams,  but  as  it  is  thence  reflec¬ 
ted  to  our  eyes.  For  vifion  is  not  made 
but  by  rays  falling  upon  the  eyes  ;  and 
therefore  there  mufl  be  fome  refle&ing 
matter  in  thofe  parts  where  the  tails  of 
Comets  are  feen  ;  and  fo  the  argument 
turns  upon  the  rhird  opinion.  For  that 
refie&ing  matter  can  be  no  where  found 
but  in  the  place  of  the  tail,  becaufe 
otherwile,  fiuce  all  the  ccleftial  ipaces 
are  equally  illuminated  by  the  Sun’s 
light,  no  part  of  the  heavens  could  ap¬ 
pear  with  more  iplendour  than  another. 
The  fecond  opinion  is  liable  to  many 
difficulties.  The  tails  of  Comets  are  ne¬ 
ver  feen  variegated  with  thole  colours, 
which  ever  uie  to  be  infcparable  from 
refradtion.  And  the  diftindt  tranfmiffion 
of  the  light  of  the  fixed  Stars  and  Pla¬ 
nets  to  us,  is  a  demonftration  that  the 
sether  or  ccleftial  medium  is  not  endow¬ 
ed  with  any  refradtive  power.  For  as 
to  what  is  alledged  that  the  fixed  Stars 
have  been  fometimes  feen  by  the  Egyp¬ 
tians ,  environed  with  a  coma  or  capil- 

litiujn, 


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OF  THE  WORLD. 
Jitium,  becaufe  that  has  but  rarely  hap¬ 
pened,  it  is  rather  to  be  afcribed  to  a 
cafual  refraction  of  clouds,  as  well  as 
the  radiation  and  fcinrillation  of  the  fix¬ 
ed  Stars  to  the  refractions  both  of  the 
eyes  and  air.  For  upon  applying  a  tele- 
fcope  to  the  eye,  thofe  radiations  and 
icintillations  immediately  difappear.  By 
the  tremulous  agitation  of  the  air  and 
afcending  vapours  it  happens  that  the 
rays  of  light  are  alternately  turned  afide 
from  the  narrow  fpace  of  the  pupil  of 
the  eye ;  but  no  luch  thing  can  have 
place  in  the  much  wider  aperture  of  the 
object-glafe  of  a  telefcope.  And  hence 
it  is,  that  a  fcintillarion  is  occafioned 
in  the  former  cafe,  which  ceales  in  the 
latter.  And  this  ceflation  in  the  latter 
cafe  is  a  demonflration  of  the  regular 
tranfmifTion  of  light  through  the  hea¬ 
vens  without  any  fenflble  refraction. 
But  to  obviate  an  objection  that  may  be 
made  from  the  appearing  of  no  tail  in 
fuch  Comets  as  mine  but  wit;h  a  faint 
light,  as  if  the  fecondary  rays  were  then 
too  weak  to  affect  the  eyes,  and  for  this 
reafon  it  is  that  the  tails  of  the  fixed 
Stars  do  not  appear ;  we  are  to  con- 
fider,  that  by  the  means  of  telefcopes 
the  light  of  the  fixed  Stars  may  be  aug¬ 
mented  above  an  hundred  fold,  and  yet 
I  3  no 


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ii8 


OF  THE  SYSTEM 

no  tails  are  feen  That  the  light  of  the 
Planets  is  yet  more  copious  without 
any  tail,  but  that  Comets  are  feen  fome- 
times  with  huge  tails,  when  the  light  of 
their  heads  is  but  faint  and  dull.  For  io 
it  happened  in  the  Comet  of  the  year 
1680,  when  in  the  month  of  ‘December 
it  was  fearcely  equal  in  light  to  the 
Stars  of  the  fecond  magnitude,  and  yet 
emitted  a  notable  tail,  extending  to  the 
length  of  40°,  50°,  6o°,  or  70°,  and 
upwards  ;  and  afterwards  on  the  17th 
and  28th  of  January ,  when  the  head 
appeared  but  as  a  Star  of  the  7th  mag¬ 
nitude  ;  but  the  tail,  (as  was  faid  above) 
with  a  light  that  was  fenfible  enough 
though  faint,  was  ftretched  out  to  6  or 
7  degrees  in  length,  and  with  a  languilh- 
ing  light,  that  was  more  difficultly  feen, 
even  to  ix°.  and  upwards.  But  on  the 
prh  and  10th  of  February ,  when  to  the 
naked  -eye  the  head  appeared  no  more 
through  a  telefeope,  I  viewed  the  tail  of 
i°.  in  length.  But  further,  if  the  tail 
was  owing  to  the  refradfcion  of  the  ce- 
leftial  matter,  and  did  deviate  from  the 
pppofition  of  the  Sun,  according  as 
the  figure  of  the  heavens  requires  ; 
that  deviation,  in  the  lame  places  of  the 
heavens,  Ihould  be  always  dire&ed  to¬ 
wards  the  fame  parts.  But  the  Comet 


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OF  THE  WORLD. 

of  the  year  1680  Dec.  28  d.  8  * h.  P.  M. 
at  London  was  feen  in  x  89.  41'  with 
latitude  north  a8°.  6L  while  the  Sun 
was  in  vs  18  °.  26  f.  And  the  Comet  of 
the  year  15 77,  December  19,  was  in 
H  8°.  41^  with  latitude  north  z8°.  40/. 
and  the  Sun  as  before  in  about  180.  z6f. 
In  both  cafes  the  fituation  of  the  Earth 
was  the  fame,  and  the  Comet  appeared 
in  the  fame  place  of  the  heavens ;  yet 
in  the  former  cafe  the  tail  of  the  Comet 
(as  well  by  my  obfervations  as  by 
the  obfervations  of  others  )  deviated 
from  the  oppofitiOn  of  the  Sun  to¬ 
wards  the  north  by  an  angle  of  44  de¬ 
grees,  whereas  in  the  latter  there  was 
(according  to  the  obfervation  of  Tycho ) 
a  deviation  of  zi  degrees  towards  the 
fouth.  The  refraction  therefore  of  the 
heavens  being  thus  difproved,  it  remains 
that  the  phenomena  of  the  tails  of  Co¬ 
mets  rnuft  be  derived  from  fbme  reflect¬ 
ing  matter.  That  vapours  fufficient  to 
fill  fuch  immenfe  fpaces  may  arife  from 
the  Comets  atmofpheres,  may  be  eafily 
underftood  by  what  follows. 

I 


I  4  lx 


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119 


no  OF  THE  SYSTEM 

I  t  is  well  known  that  the  ait  near  the 
That  the  a, rand  *a-  furface  of  our  Earth  poflefles  a 
pour  in  the  ceieftiai  fpace  about  noo  times  greater 

menfe  rarhy  ind  than  Water  °(  thc  fame  Weight. 

that  a  fmaii  auan:it?  And  therefore  a  cyiindric  co- 

&rs“&r!f.  1“»"  of ™  »°°  ft?  hish:  ft 

the  phxnomena  of  ( f  equal  weight  with  a  cyltn- 
the  tails  of  Comets.  ^  cf  water  of  the  fame  breadth 

and  but  one  foot  high.  But  a  cylinder 
of  air  reaching  to  the  top  of  the  at« 
mofphcre  is  of  equal  weight  with  a 
cylinder  of  water  about  3  3  foot  high ; 
and  therefore  if  from  the  whole  cylin¬ 
der  of  air,  the  lower  part  of  jiqo  foot 
high  is  taken  away,  the  remaining  up¬ 
per  part  will  be  of  eqgal  weight  with  a 
cylinder  of  wa'er  31  foot  high  Where¬ 
fore  at  the  height  of  1100  feet  or  two 
furlongs,  the  weight  of  the  incumbent  air 
is  lcfs,  and  coniequently  the  rarity  of 
the  comprefTed  air  greater  than  near  the 
furface  of  the  Earth  in  the  ratio  of  3  3  to 
32-.  And  having  this  ratio,  we  may 
compute  the  rarity  of  the  air  in  all 
places  whatfoever,  fuppofing  the  expan¬ 
sion  thereof  to  be  reciprocally  propor¬ 
tional  to  its  compreffiori  and  this  pro¬ 
portion  has  been  proved  by  the  experi¬ 
ments  of  Hook  and  others.  The  reiult 
of  the  computation  I  have  let  down  in 
the  following  table,  in  the  frit  column 

of 


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OF  THE  WORLD, 
of  which  you  have  the  height  of  the  air 
in  miles  whereof  4000  make  a  femi-dia- 
meter  of  the  Earth ;  in  the  lecond  the 
comprefiion  of  the  air,  or  the  incumbent 
weight ;  in  the  third  its  rarity  or  ex* 
panfion,  fuppofing  gravity  to  decreaie 
in  the  duplicate  ratio  of  the  distances 
from  the  Earth’s  center.  And  the  Latin 
numeral  characters  are  here  ufed  for  cer¬ 
tain  numbers  of  ciphers,  as  o,xvii  1114 
for  o , 00000000000000000 1124,  and 
16956x7  for  16956000000000000000. 

A  I  R*S 


rH  eight. 

Comprefiion. 

- -  T  - '■> 

Expanfion. 

O 

33 

I 

5 

1 7,85 1  S' 

1,8486 

IO 

9>67i7 

3,415* 

^o 

i,8f2 

*»,57* 

40 

0,15-15- 

136,83 

400 

o,xvii  1114 

16956  XV 

4000 

o,cv  4465 

739°7  cii 

40000 

o,cxcii  1618 

20163  clicxxix 

400000 

o,ccx  7895 

41798  ccvii 

4000000 

■  o,ccxii  9878 

334*4  ccix 

Infinite. 

o,ccxii  6041 

54611  ccix 

But  from  this  table  it  appears  that  the 
?ir>  in  proceeding  upwards,  is  rarified  in 
fuch  manner,  that  a  Ijpherc  of  that  air 

whicft 


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Ill 


OF  THE  SYSTEM 

which  is  neared  to  the  Earth  of  but  one 
inch  in  diameter,  if  dilated  with  an  e- 
quai  rarefaction  with  that  of  the  air  at 
the  height  of  ten  femidiamcters  of  the 
Earth,  would  (ill  up  more  (pace  than  is 
contained  in  the  whole  heavens  on  this 
fide  the  fixed  Stars,  according  to  the 
preceding  computation  of  their  didance. 
And  though  by  reafon  of  the  far  grea¬ 
ter  thicknefs  of  the  atmofpheres  of  Co¬ 
mets,  and  the  great  quantity  of  the  cir- 
cum-folar  centripetal  force  it  may  hap¬ 
pen  that  the  air  in  the  celedial  {paces, 
and  in  the  tails  of  Comets,  is  not  fo 
vadly  rarified  ;  yet  from  this  computa¬ 
tion  it  is  plain,  that  a  very  fmall  quan¬ 
tity  of  air  and  vapour  is  abundantly  fuffi- 
cient  to  produce  all  the  appearances  of 
the  tails  of  Comets.  For  that  they  are  in¬ 
deed  of  a  very  notable  rarity  appears  from 
the  fhining  of  the  Stars  through  them.  The 
$itmofphere  of  the  Earth,  illuminated  by 
the  Sun’s  light,  though  but  of  a  few 
miles  in  thicknefs,  oblcures  and  extin- 
guiihes  the  light,  not  only  of  all  the 
Stars,  but  even  of  the  Moon  it  felfj 
whereas  the  fmallcd  Stars  are  feen  to 
fhine  through  the  immenfe  thicknefs  of 
the  tails  of  Comets,  likewile  illuminated 
by  the  Sun,  without  the  lead  diminution 
pf  their  fplendour. 

•  KETLER 


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113 


OF  THE  WORLD. 

KETLE  R  afcribes  the  afeent  of 
the  tails  of  Comets  to  the  at- 
molpheres  of  their  heads,  and  SS2 

their  direction  towards  the  parts  may  arife  from  the 
oppofite  to  the  Sun,  to  the  ac-  thc»f 

tion  of  the  rays  of  light,  car¬ 
rying  along  with  them  the  matter  of  the 
Comets  tails.  And  without  any  great 
ipcongruity  we  may  fuppole  that,  in  lo 
free  fpaces,  fo  fine  a  matter  as  that  of 
the  Ether  may  yield  to  the  aCtion  of 
the  rays  of  the  Sun’s  light,  though  thofe 
rays  are  not  able  fenfibly  to  move  the 
grols  lubftances  in  our  parts,  which  are 
clogged  with  (o  palpable  a  refiftance. 
Another  author  thinks  that  there  may  be 
a  fort  of  particles  of  matter  endowed  with 
a  principle  of  levity  as  well  as  others  are 
with  a  power  of  gravity;  that  the 
matter  of  the  tails  of  Comets  may  be  of 
the  former  lort,  and  that  its  alcent  from 
the  Sun  may  be  owing  to  its  levity. 

But  confidering  the  gravity  of  terreftial 
bodies  is  as  the  matter  of  the  bodies, 
and  therefore  can  be  neither  more  nor 
Ids  in  the  lame  quantity  of  matter,  I 
am  inclined  to  believe  that  this  alcent 
may  rather  proceed  from  the  rarefaction 
of  the  matter  of  the  Comets  tails.  The 
afeent  of  fmoak  in  a  chimpey  is  owing 
to  the  impulle  ©f  the  air,  \yith  which 


Digitized  by  LjOOQle 


1X4 


OF  THE  SYSTEM 

it  is  entangled.  The  air  ratified  by  heat 
afcends,  becaufe  its  fpecifick  gravity  is 
diminiihed,  and  in  its  afcent  carries  a- 
long  with  it  the  linoak  with  which  it  is 
ingaged.  And  why  may  not  the  tail  of 
a  Comet  rile  from  the  Sun  after  the  lame 
manner  ?  For  the  Sun’s  rays  do  not  a <51 
any  way  upon  the  mediums  which  they 
pervade,  but  by  refle&ion  and  refrac¬ 
tion.  And  thole  refle&ing  particles 
heated  by  this  adion,  heat  the  matter  of 
the  Ether  which  is  involved  with  them. 
That  matter  is  rarefied  by  the  heat 
which  it  acquires,  and  becaufe  by  this 
rarefa&ion  the  Ipecifick  gravity,  with 
which  it  tended  towards  the  Sun  before, 
is  diminiihed,  it  will  afcend  therefrom 
like  a  ftream,  and  carry  along  with  it 
the  refle&ing  particles  of  which  the  tail 
of  the  comet  is  compofed  the  impulfe 
of  the  Sun’s  light,  as  we  have  laid, 
promoting  the  afcent. 


That  the  tails  do  in¬ 
deed  arife  from  thofe 
atmofpheres,  proved 
from  fcveral  of  their 
phsenomen*. 


Bur  that  the  tails  of  Comets  do  arife 
from  their  heads  and  tend  to¬ 
wards  the  parts  oppofite  to  the 
Sun,  is  further  confirmed  from 
the  laws  which  the  tails  ob- 
ferve.  For  lying  in  the  plains 
of  the  Comets  orbit  which  pafs  through 
the  Sun,  they  conllantly  deviate  from 

the 


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US 


OF  THE  WORLD. 

the  oppofition  of  the  Sun,  towards  the 
parts  which  the  Comets  heads  in  their 
progrefs  along  thole  orbits  have  left. 
And  to  a  fpedator  placed  in  thole 
plains,  they  appear  in  the  parts  di- 
re&ly  oppofite  to  the  Sun.  But  as  the 
fpe&ator  recedes  from  thole  plains, 
their  deviation  begins  to  appear,  and 
daily  becomes  greater.  Ana  the  devi¬ 
ation  cateris paribus  appears  lefs,  when 
the  tail  is  more  oblique  to  the  orbit  of 
the  Comet,  as  well  as  when  the  head  of 
the  Comet  approaches  nearer  to  the 
Sun  ;  elpecially  if  the  angle  of  deviation 
is  ellimated  near  the  head  of  the  Comer. 
Farther,  the  tails  which  have  no  devia¬ 
tion  appear  llreight,  but  the  tails  which 
deviate  are  likewife  bended  into  a  cer¬ 
tain  curvature.  And  this  curvature  is 
greater  when  the  deviation  is  greater ; 
and  is  more  fenfible  when  the  tail  cate - 
ris  paribus  is  longer  :  for  in  the  Ihort- 
er  tails  the  curvature  is  hardly  to  be 
perceived.  And  the  angle  of  deviation 
is  lefs  near  the  Comet’s  head,  but  greater 
towards  the  other  end  of  the  tail,  and 
that  becaufe  the  lower  fide  of  the  tail 
regards  the  parts  from  which  the  devia¬ 
tion  is  made,  and  which  lie  in  a  right 
line,  drawn  out  infinitely  from  the  Sun 
through  the  Comet’s  head.  And  the 
tails  that  are  longer  and  broader,  and 

lhine 


Digitized  by  LjOOQle 


ii6 


OF  THE  SYSTEM 
ftiine  with  a  ftronger  light,  appear  more 
relplendent  and  more  exa&ly  defined  on 
the  convex  than  on  the  concave  fide. 
Upon  which  accounts  it  is  plain  that 
the  phenomena  of  the  tails  of  Comets 
depend  upon  the  motions  of  their  heads* 
and  by  no  means  upon  the  places  of  the 
heavens  in  which  their  heads  are  feen* 
and  that  therefore  the  tails  of  the  Co¬ 
mets  do  not  proceed  from  the  refra&ion 
of  the  heavens,  but  from  their  own 
heads,  which  furnilh  the  matter  that 
forms  the  tail.  For  as  in  our  air  the 
fmoak  of  a  heated  body  alcends  either 
perpendicularly  if  the  body  is  at  reft,  or 
obliquely,  if  the  body  is  moved  oblique¬ 
ly  ;  lo  in  the  heavens  where  all  the  bo¬ 
dies  gravitate  towards  the  Sun,  finoak 
and  vapour  mult  (as  we  have  already 
laid)  afcend  from  the  Sun,  and  either 
rile  perpendicularly  if  rhe  fmoaking 
body  is  at  reft,  or  obliquely  if  the  body* 
in  the  progreis  of  its  motion,  is  al¬ 
ways  leaving  thofe  places  from  which 
the  upper  or  higher  parts  of  the  vapours 
had  rilen  before.  And  that  obliquity  will 
be  lefs,  where  the  vapour  afceuds  with 
more  velocity,  to  wit,  near  the  fmoak* 
ing  body  when  that  is  near  the  Sun. 
For  there  the  force  of  the  Sun  by  which 
the  vapour  afcends  is  ftronger.  But  be- 
caufe  the  obliquity  is  varied,  the  colomn 


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ii7 


OF  THE  WORLD. 

of  vapour  will  be  incurvated  \  and  be- 
caufe  the  vapour  in  the  preceding  fide  is 
fomething  more  recent,  that  is,  has  a- 
feended  iomething  more  lately  from  the 
body,  it  will  therefore  be  fomething 
more  denfo  on  that  fide,  and  mult  on 
that  account  reflect  more  light  as  well 
as  be  better  defined  ;  the  vapour  on  the! 
other  fide  languifhing  by  degrees  and 
vanifhing  out  of  fight. 

B  u  t  it  is  none  of  our  prefont  bufinefs 
to  explain  the  caufes  of  the  ap¬ 
pearances  of  nature.  Let  thofe 
things  which  we  have  laft  laid  below  the  orbit  of 
be  true  or  falle,  we  have  at  leaft  ^ercui7  *  proved 
made  out  in  the  preceding  dif- 
courfe,  that  the  rays  of  light  are  direct¬ 
ly  propagated  from  the  tails  of  Comets 
in  right  lines  through  the  heavens,  in 
which  thofe  tails  appear  to  the  lpeCta- 
tors  where- ever  placed ;  and  confe- 
quently  the  tails  mult  afeend  from  the 
heads  of  the  comets  towards  the  parts 
oppolite  to  the  Sun.  And  From  this 
principle  we  may  determine  the  limits 
of  their  diltances  in  manner  following. 

Let  S  reprefent  the  Sun,  T  the  Earth, 

S  T  A  the  elongation  of  a  Comet  from 
the  Sun,  and  AT  B  the  apparent  length 
of  its  tail.  And  becaule  the  light  is 
propagated  from  the  extremity  of  the 


Digitized  by  LjOOQle 


ixS  OF  THE  SYSTEM 

tail  in  the  direction  of  the  right  line 
TB,  that  extremity  muft  lie  fomewhere 
in  the  line  TB.  Suppofe  it  in  D,  and  join 
D  S  cutting  TA  in  C.  Then  becaufe 
the  tail  is  always  ftretched  out  towards 
the  parts  nearly  oppofite  to  the  Sun  ; 
and  therefore  the  Sun,  the  head  of  the 
Comer,  and  the  extremity  of  the  tail  lie 
in  a  right  line,  the  Comet's  head  will  be 
found  in  C.  Parallel  to  TB  draw  S  A, 


meeting  the  line  TA  in  A,  and  the  Co¬ 
met’s  head  C  muft  neceflarily  be  found 
between  T  and  A ;  becaufe  the  extre¬ 
mity  of  the  tail  lies  lome where  in  the 
infinite  line  T  B,  and  all  the  lines  S  D 
which  can  polfibly  be  drawn  from  the 
point  S  to  the  line  TB,  muft  cut  the 
line  TA  fomewhere  between  T  and  A. 

Where- 


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OF  THE  WORLD. 

Wherefore  the  diftance  of  the  Comet 
from  the  Earth  cannot  exceed  the  inter¬ 
val  TA,  nor  its  diftance  from,  the  Sun 
the  interval  SA  beyond,  or  ST  on  this 
fide,  the  Sun.  For  inftance,  the  elonga¬ 
tion  of  the  Comet  of  1680  from  the  Sun 
Dec.  1  2.  was  90.  and  the  length  of  its 
tail  3  50.  at  leaft.  If  therefore  a  triangle 
TSA  is  made  whofe  angle  T  is  equal  to 
the  elongation  90.  and  angle  A  equal  to 
ATB  or  to  the  length  of  the  tail,  viz. 
35°.  then  SA  will  be  to  S  T,  that  is,  the 
line  of  the  greateft  poftible  diftance  of 
the  Comet  from  the  Sun,  to  the  femi- 
diameter  of  the  orbis  ihagnus,  as  the 
fine  of  the  angle  T  to  the  fine  of  the  an¬ 
gle  A,  that  is,  as  about  3  to  11.  And 
therefore  the  Comet  at  that  time  was 
lels  diftant  from  the  Sun  than  by  of 
the  Earth’s  diftance  from  the  fame,  and 
confequently  either  was  within  the  orbit 
of  Mercury,  or  between  that  orbit  and 
the  Earth.  Again,  'Dec.  zi.  the  elon¬ 
gation  of  the  Comet  from;  the  Sun  was 
315®,  and  the  length  of  its  tail  70°. 
Wherefore  as  the  fine  of  32 1°  to  the 
fine  of  7G0,  that  is,  as  4  to  7,  lb  was  the 
limit  of  the  Comet’s  diftance  from  the 
Sun  .to  the  diftance  of  the  Earth  from' 
the  Sun,  and  confequently  the  Comet 
flad  not  then  got  without  the  orbit  of 
K  Venus: 


12* 


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130 


OF  THE  SYSTEM 

Venus.  ‘Dec.  a8.  the  elongation  of  the 
Comet  from  the  Sun  was  55°.  and  the 
length  of  its  tail  $6°.  And  therefore  the 
limit  of  the  Comet’s  diftance  from  the 
Sun  was  not  yet  equal  to  the  diftance  of 
the  Earth  from  the  fame,  and  confe- 
quently  the  Comet  had  not  then  got 
without  the  Earth’s  orbit.  But  from  its 
parallax  we  find  that  its  egrels  from  the 
orbit  happened  about  Jan.  5.  as  well  as 
that  it  had  delcended  far  within  the  or¬ 
bit  of  Mercury.  Let  us  fuppofe  it  to 
have  been  in  its  perihelion  Dec.  the  8th 
when  it  was  in  conjunction  with  the 
Sun,  and  it  will  follow  that  in  the  jour¬ 
ney  from  its  perihelion  to  its  exit  out 
of  the  Earth’s  orbit,  it  had  fpent  ag 
days ;  and  conlequently  that  in  the  x6 
or  days  following,  in  which  it  ceafed 
to  be  further  feen  by  the  naked  eye,  it 
had  fcarce  doubled  its  diftance  from  the 
Sun.  And  by  limiting  the  diftances  of 
other  Comets  by  the  like  arguments  we 
come  at  laft  to  this  conclufion,  That  all 
Comets  during  the  time  in  which  they 
are  vifible  by  us,  are  within  the  corn- 
pals  of  a  fpherical  ipace  deferibed  about 
the  Sun  as  a  center,  with  a  radius  dou¬ 
ble,  or  at  moft  triple  of  the  diftance  of 
the  Earth  from  the  Sun. 


And 


Digitized  by  LjOOQle 


OF  THE  WORLD.  *31 

And  hence  it  follows  that  the  Co¬ 
mets,  during  the  whole  time  of  ‘ 
their  appearance  unto  us,  being  ™tVhe  CoTt5 
Within  the  lphere  of  activity  of  tion*,  having  one  fo. 
the  cir  cum-folar  force,  and  there-  c“* in  ,he  cen‘er  ®f 
fore  agitated  by  the  impulfe  of  radii'  draw/w  th« 
that  force,  will  (for  the  fame  centfr  do  deffribe 
reafon as  the  Planets)  be  made  ioih*  times.0"10"*1 
to  move  in  conic  fe&ions  that 
have  one  focus  in  the  center  of  the  Sun, 
and,  by  radii  drawn  to  the  Sun,  to  de- 
fcribe  area’s  proportional  to  the  times. 

For  that  force  is  propagated  to  an  im- 
menfe  diftance,  and  will  govern  the  mo¬ 
tions  of  bodies  far  beyond  the  orbit  of 
Saturn. 


There  are  three  hypothefes  about 
Comets.  For  fome  will  have  That  thofe  conic- 
it  that  they  are  generated  and  ^a™fa*re 
perilh,  as  often  as  they  ap-  from  the  velocity  «f 
pear  and  vanifh ;  others  that  theC®®*«. 
they  come  from  the  regions  of  the  fix¬ 
ed  Stars,  and  are  feen  by  us  in  their 
pafiage  through  the  fyftem  of  our  Pla¬ 
nets  ;  and  laftly,  others  that  they  are 
bodies  perpetually  revolving  about  the 
Sun  in  very  eccentric  orbits.  In  the 
firft  cafe,  the  Comets,  according  to  their 
different  velocities,  will  move  in  conic 
fedtions  of  all  forts  ;  in  the  fecond  they 
K  a  will 


Digitized  by  LjOOQle 


13* 


OF  THE  SYSTEM 

will  deferibe  hyperbola’s,  and  in  either 
of  the  two  will  frequent  indifferently 
all  quarters  of  the  heavens  as  well 
thole  about  the  poles  as  thofe  towards 
the  Ecliptic  ;  in  the  third  their  motions 
will  be  performed  in  ellipfes  very  ec¬ 
centric  and  very  nearly  approaching  to 
parabola’s.  But  ( if  the  law  of  the  Pla¬ 
nets  is-obferved)  their  orbits  will  not 
much  decline  from  the  plain  of  the  E- 
diptic.  And  fo  far  as  1  could  hitherto 
obferve  the  third  cafe  obtains.  For  the 
Comets  do  indeed  chiefly  frequent  the 
zodiac  and  fearce  ever  attain  to  a  helio¬ 
centric  latitude  of  40®.  And  that  they 
move  in  Orbits  very  nearly  parabolical, 
I  infer  from  their  velocity.  For  the  ve¬ 
locity  with  which  a  parabola  is  deferi- 
Eed,  is  every  where  to  the  velocity  with 
which  a  Comet  or  Planet  may  be  revol¬ 
ved  about  the  Sun  in  a  circle  at  the 
fame  diflance,  in  the  fubduplicate  ratio 
of  a  to  1.  And  by  my  computation  the 
Velocity  of  Comets  is  found  to  be  much 
about  the  fame.  I  examined  the  thing 
by  inferring  nearly  the  velocities  from 
the  diftances,  and  the  diftances  both 
from  the  parallaxes  and  the  phenomena 
of  the  tails,  and  never  found  theerrours 
Of  excels  or  defeat  in  the  velocities 
greater  than  what  might  have  arofe  from 


Digitized  by  LjOoq  le 


*33 


OF  THE  WORLD. 

the  errours  in  the  diftanccs  colle&ed 
after  that  manner.  But  I  likewife  made 
ule  of  the  reafoning  that  follows. 

Supposing  the  radius  of  the orbis 
magous  to  be  divided  into  1000  In  what  fpace  of 
parts :  Let  the  numbers  in  the  »me  Comets  defcri- 
firft  column  of  the  following  tra* 

&  jeftories  pals  through 

table  reprelent  the  durance  of  the  fphere  of  the  or- 
the  vertex  of  the  parabola  from  b,smjgnus- 
the  Sun’s  center,  exprefled  by  thole 
parts  ;  and  a  Comet  in  the  times  ex- 
prelled  in  Col  x  will  pals  from  its  pe¬ 
rihelion  to  the  lurface  of  the  Iphere 
which  is  deferibed  about  the  Sun  as  a 
center  with  the  radius  of  the  orbis  mag¬ 
nus  ;  and  in  the  times  exprefled  in  Col. 

3,  4,  and  it  will  double,  triple,  and 
quadruple  that  its  distance  from  the 
jSun. 


K  3  Tabi«e 


Digitized  by  LjOOQle 


*34 


OF  THE  SYSTEM 


Table  I. 


The  dif- 
tance  of 
a  Comet’s 
perihelion 
from  the 
Sun’s  cen¬ 
ter. 

The  time  of  a  Comet’s  paflage  from  its  pe¬ 
rihelion  to  a  diftance  from  the  Sun  equal  to 

r 

the  rad. 
of  the  or- 
6  is  mag. 

To  its 
double. 

To  its 
triple. 

1 

To  its 
quadruple. 

d.  h .  *. 

d.  h.  *. 

d.  h. 

d.  h.  . 

0 

*7  n 

77.  16  28 

14*  *7  *4 

219  17  30 

5 

27  16  07 

77  «  >+ 

10 

27  ax  00 

78  06  24 

ao 

28  06  40 

78  20  13 

144  OJ  19 

221  08  54 

4° 

2901  32 

791*  33 

So 

30  1*3  26* 

82  04  56 

160 
'  320 

33  05  29 
37  *3  46 

86  10  *6 
93  *3  38 

153  16  08 

»3*  11  19 

*  640 

37  09  49 

105  ox  28 

1280 

2560 

1 06  06  35 

200  06  43 

I47  22  31 

*97  03  46 

300  06  03 

[This  table,  here  corre&ed,  is  made  on  the  fuppofition 
that  the  Earth’s  diurnal  motion  is  juft  59'*  and  the 
meafure  of  one  minute  loofely  0,2909,  in  refpeft  of 
the  radius  1000.  If  thofe  meafures  are  taken  true, 
the  true  numbers  of  the  table  will  all  come  out  lefs. 
But  the  difference,  even  when  greateft,  and  to  the 
quadruple  of  the  Earth’s  diftance  from  the  Swy  a* 
mounts  only  to  16 &  55#0 


The 


Digitized  by  LjOOQle 


OF  THE  WORLD. 
The  time  of  a  Comet's  in. 


*35 


,  _  ,  c  .  At  what  time  Comets 

grefs  into  the  iphere  or  the  or-  enter  into  and  pars 

bis  roagnus,  or  of  its  egrefs  from  »“  °f 

the  fame  may  be  inferred  near¬ 
ly  from  its  parallax,  but  with  more  ex¬ 
pedition  by  the  following 


Table  II. 


The  apparent 
elongation  of 
a  Comet  from 
the  Sun. 

Its  apparent  diur¬ 
nal  motion  in  its 
own  orbit. 

Its  distance  from 
the  Earth  in  parts, 
whereof  the  radius 
of  the  orbis  mag¬ 
nus  contains  iooq. 

Direft 

Retrog. 

6o° 

*<•  18' 

oo°  20 

1000 

*5 

2  38 

00  35 

844 

7  o 

2  55 

00  57 

684 

7* 

3  07 

01  09 

618 

7+ 

3  23 

01  29 

55i 

76 

3  *3 

01  45 

484 

7* 

4  10 

02  12 

416 

So 

4  47 

02  49 

347 

8a 

5  45 

03  47 

278 

84  - 

7  »* 

05  20 

209 

86 

10  17 

08  19 

140 

88 

18  37 

16  39 

70 

90 

Infinite 

Infinite 

■ 

00 

The  ingrefs  of  a  Comet  into  the 
fphere  of  theorbis  magnus,  or  w  wte 
its  egreis  from  the  lame  happens  -  - 

at  the  time  of  its  elongation 
from  the  Sun  exprefled  in  Col. 
j.  againft  its  diurnal  motion. 

K  4 


the  Comets  of  i68<^ 
palled  through  the 
Iphere  of  the  orbis 
magnus. 

So 


Digitized  by  LjOOQle 


i3/T  OF  THE  SYSTEM 

So  in  the  Comet  of  1681,  Jan.  4. 
the  apparent  diurnal  motion  in  its  orbit 
was  about  30.  ojr'.  and  the  correlpond- 
ing  elongation  71 }°.  And  the  Comet 
had  acquired  this  elongation  from  the 
Sun  Jan.  4.  about  fix  in  the  morning. 
Again  in  the  year  1680,  November  11. 
the  diurnal  motion  of  the  Comet  that 
then  appeared,  was  about  4  •-  °.  and  the 
correfiponding  elongation  79  f  happened 
Nov.  10.  a  little  before  mid-night.  Now 
at  the  times  named  thele  Comets*  had 
arrived  at  an  equal  diftance  from  the 
Sun  with  the  Earth,  and  the  Earth  was 
then  ahnofi  in  its  perihelion.  But  the 
fufi  table  is  fitted  to  the  Earth’s  mean 
difiance  from  the  Sun  afliuned  of  1000 
paus ;  and  this  diftanee  is  greater  by 
iiich  an  excels  of  lpace  as  the  Earth 
might  dcfcribe,  by  its  annual  motion, 
in  one  days  time,  or  the  Comet,  by  its 
motion,  in  16  hours.  To  reduce  the 
Comer  to  this  mean  difiance  of  1000 
parts  wc  add  thole  16  hours  to  the  for? 
mer  time  and  fubdutfi  them  from  the 
latter  ;  and  thus  the  former  becomes 
Jan.  4d.  10I).  after  noon,  the  latter 
Nov.  10.  about  fix  in  the  morning.  But 
from  the  tenour  and  progrels  of  the  di¬ 
urnal  motions  it  appears  that  both  Co¬ 
pers  were  ifl  conjunction  with  the  Sun 

between 


Digitized  by  LjOOQle 


*37 


OF  THE  WORLD. 

between  Dec.  7.  and  Dec.  8.  And 
from  thence  to  Jan.  4d.  ioh.  afternoon 
on  one  fide,  and  to  Nov.  iod.  61*.  of  the 
morning  on  the  other,  there  are  about 
28  days.  And  fo  many  days  (by  Tar 
ble  1.)  the  motions  in  parabolic  trajec¬ 
tories  do  require. 

But  though  we  have  hitherto  con- 
fidered  thole  £omets  as  two, 
yet  from  the  coincidence  of  That  *^efe  were  “«* 

*.  .  .1  ,  two,  but  one  and 

their  perihelions  and  agreement  the  fame  Comet, 

Of  their  Velocities,  it  iS  proba-  what  orbit  and  with 

l?le,  that  in  efFed  they  were  but  Smet^as'^arried 
one  and  the  fame.  And  if  lo,  through  the  heaven* 
the  orbit  of  this  Comet  mult  aaiy.  m°re  **’ 
have  either  been  a  parabola  or 
at  leaft  a  conic  fediort  very  little  differ¬ 
ing  from  a  parabola,  and  at  its  vertex 
almoft  in  contad  with  the  lurface  of  the 
Sun.  For  by  Tab.  2.  the  diftance  of  the 
Comet  from  the  Earth  Nov.  10.  was  a- 
bout  360  parts,  and  Jan.  4.  about  630. 

From  which  diftances,  together  with  its 
longitudes  and  latitudes,  we  infer  thedif- 
rance  of  the  places  in  which  the  Comet 
was  at  thole  times,  to  have  been  about 
280 :  the  half  of  which,  viz.  140  is  aq 
ordinate  to  the  Comet’s  orbit,  cutting 
off  a  portion  of  its  axe  nearly  equal  to 
fa  radius  of  the  orbis  qaagmjs,  that  is  to 

1000 


Digitized  by  LjOoq  le 


OF  THE  SYSTEM 

iooo  parts.  And  therefore  dividing  the 
fquare  of  the  ordinate  140  by  ioco  the 
iegment  of  the  axe,  we  find  the  latus  re- 
<fium  19, 1 6,  or  in  a  round  number  20. 
The  fourth  part  whereof  $  is  the  di£ 
fence  of  the  vertex  of  the  orbit  from 
the  Sun’s  center.  But  the  time  corre- 
fponding  to  the  difiance  of  5  parts  in 
Tab .  1.  is  ^7i.  i6h.  /.  In  which  time, 
if  the  Comet  moved  m  a  parabolic  or¬ 
bit,  it  would  have  been  carried  from 
its  perihelion  to  the  fiirface  of  the 
lphere  of  the  orbis  maguus  deferibed 
with  the  radius  iooo,  and  would  have 
Ipent  the  double  of  that  time,  viz. 
5fd.  8  J*.  in  the  whole  courle  of  its  mo¬ 
tion  within  that  lphere :  And  lb  in  fa<fi 
it  did.  For  from  Nov.  iod.  6h.  of  the 
morning,  the  time  of  the  Comet’s  in- 
greis  into  the  lphere  of  the  orbis  magnus, 
to  Jan.  4d.  ioh.  after  noon,  the  time  of 
its  egrels  from  the  fame,  there  are  y?4. 
i6h.  The  linall  difference  of  7$h.  in 
this  rude  way  of  computing  is  to  be 
negle&ed,  and  perhaps  may  arile  from 
the  Comet’s  motion  being  Ibme  linall 
matter  llower,  as  it  mufi  nave  been  if 
the  true  orbit  in  which  it  was  carried 
was  an  ellipfe.  The  middle  time  be¬ 
tween  its  ingrefs  and  egrels  was  ‘De¬ 
cember  8d.  oib.  of  the  morning.  And 


Digitized  by  LjOOQle 


OF  THE  WORLD. 

therefore  at  this  time  the  comet  ought 
to  have  been  in  its  perihelion.  And  ac¬ 
cordingly  that  very  day, juft  before  Sun- 
riling,  Dr.  Halley  (as  we  faid)  law  the 
tail  ihort  and  broad,  but  very  bright 
tiling  perpendicularly  from  the  horizon. 

From  the  polition  of  the  tail,  it  is  cer¬ 
tain  that  the  Comet  had  then  crofted 
over  the  Ecliptic,  and  got  into  north- 
latitude,  and  therefore  had  palled  by  its 
perihelion  which  lay  on  the  other  lide 
of  the  Ecliptic,  though  it  had  not  yet 
come  into  conjunction  with  the  Sun. 

And  the  Comet,  being  at  this  time  be¬ 
tween  its  perihelion  and  its  conjunction 
with  the  Sun,  mull  have  been  in  its  peri¬ 
helion  a  few  hours  before.  For  in  lo 
near  a  diftance  from  the  Sun  it  muft 
have  been  carried  with  great  velocity, 
and  have  apparently  deicribed  almoft 
half  a  degree  every  hour. 

By  like  computations  I  find  that  the 
Comet  of  i<Si8  entered  the  Wlth  ^  Telotl 
Iphere  of  the  orbis  magnus  jDe-  Comets  are  carried. 
cember  7.  towards  Sun  -  letting.  b?  more  “• 
But  its  conjunction  with  the 
Sun  was  Nov.  9,  ono,  about  x8  days  in¬ 
tervening,  as  in  the  preceding  Comet. 

For  from  the  lize  of  the  tail  of  this,,  in 
which  it  was  equal  to  the  preceding,  it 
*  '  is 


Digitized  by  v^ooQle 


*4© 


OF  THE  SYSTEM 


is  probable  that  this  Comet  likewife  did 
come  almoft  into  a  contact  with  the 
Son.  Four  Comets  were  feen  that  year, 
of  which  this  was  the  laft.  The  fecond, 
which  made  its  firft  appearance  Octo¬ 
ber  31.  in  the  neighbourhood  of  the  ri- 
fing  Sun,  and  was  foon  after  hid  under 
the  Sun's  rays,  I  iulped  to  have  been 
the  fame  with  the  fourth,  which  emer¬ 
ged  out  of  the  Sun’s  rays  about  Nov.  9. 
To  thefe  we  may  add  the  Comat  of 
1 607,  which  entered  the  fpherc  of  the 
orbis  magnus  Sept.  14 \0.  S.  and  arrived 
at  its  perihelion -diftance  from  the  Sun 
about  O Bober  19,  35  days  intervening. 
Its  perihelion'diftance  fubtended  an  ap¬ 
parent  angle  at  the  Earth  of  about  23 
degrees,  and  was  therefore  of  390  parts. 
And  to  this  number  of  parts  about  34 
days  correfpond  in  Tab.  1.  Further, 
the  Comet  of  1665  entered  the  iphere  of 
the  orbis  magnus  about  March  17,  and 
came  to  its  perihelion  about  April  16. 
30  days  intervening.  Its  perihelion- 
diftance  fubtended  an  angle  at  the  Earth 
of  about  leven  degrees,  and  therefore 
was  of  1x2  parts:  and  corresponding 
to  this  number  of  parts,  in  Tab.  1 .  we 
find  30  days.  Again,  the  Comet  of 
i68x  entered  the  Iphere  of  the  orbis 
magnus  about  Aug.  11.  and  arrived  at 


its 


Digitized  by  v^ooQle 


OF  THE  WORLD.  14* 

its  perihelion  about  Sept.  16.  being  then 
diftant  from  the  Sun  by  about  570 
parts,  to  which,  in  Tab.  1.  belong  334 
days.  Laftly,  that  memorable  Comet 
of  Kegiemontanusi  which  in  1471  was 
carried  through  the  cireum-polar  parts 
of  our  northern  hemifphere  with  fuch 
rapidity  as  to  defcribe  40  degrees  in  6ne 
day,  entered  the  fphere  of  the  drbis 
magnus  Jan.  zi.  about  the  time  that  it 
was  palling  by  the  pole,  and  haftening 
from  thence  towards  the  Sun,  was  hid 
under  the  Sun’s  rays  about  the  end  of 
February.  Whence  ’tis  probable  that 
30  days  or  a  few  more  were  Ipent  be¬ 
tween  its  ingrefs  into  the  fphere  of  the 
orbis  magnus  and  its  perihelion.  Nor 
did  this  Comet  truly  move  with  more 
velocity  than  other  Comets,  but  owed 
the  grcatnefs  of  its  apparent  velocity  to 
its  palTing  by  the  Earth  at  a  near  difc 
tance. 

I  t  appears  then  that  the  velocity  of 
Comets,  fo  far  as  it  can  be  de- 
terminal  by  thefe  rude  ways  of 
computing,  is  that  very  velo-  me»  propofed. 
city  with  which  parabola’s,  or 
ellipfes  near  to  parabola’s,  ought  to  be 
deicribed.  And  therefore  the  didance 
between  a  Comet  and  the  Sun  being 

given. 


Digitized  by  LjOOQle 


OF  THE  SYSTEM 

given,  the  velocity  of  the  Comet  is 
nearly  given.  And  hence  arifes  this 
problem. 

The  relation  betwixt  the  velocity  of  a 
Comet,  and  its  diftance  from  the  Sun's 
center  being  given,  the  Comets  tra¬ 
jectory  is  required. 

If  this  problem  was  reiolved,  we 
ihould  thence  have  a  method  of  deter¬ 
mining  the  trajectories  of  Comets  to  the 

freateft  accuracy.  For  if  that  relation 
e  twice  affamed,  and  from  thence  the 
trajectory  be  twice  computed,  and  the 
errour  of  each  trajectory  be  found  from 
obfervations,  the  aflumprion  may  be 
corrected  by  the  Rule  of  Falfe,  and  a 
third  trajectory  may  thence  be  found 
that  will  exactly  agree  with  the  obfer¬ 
vations.  And  by  determining  the  tra¬ 
jectories  of  Comets  after  this  method, 
we  may  come  at  laft  to  a  more  exad 
knowledge  of  the  parts  through  which 
thofe  bodies  travel,  of  the  velocities 
with  which  they  are  carried,  what  fore 
of  trajectories  they  deferibe,  and  what 
are  the  true  magnitudes  and  forms  of 
their  tails  according  to  the  various  dif- 
tances  of  their  heads  from  the  Sun  ; 
whether  after  certain  intervals  of  time. 


Digitized  by  LjOOQle 


OF  THE  WORLD. 

the  fame  Comets  do  return  again,  and 
in  what  periods  they  compleat  their  fe> 
veral  revolutions.  But  the  problem 
may  be  relolved  by  determining  firft  the 
hourly  motion  of  a  Comet  to  a  given 
time  from  three  or  more  obfervations, 
and  then  deriving  the  trajectory  from 
this  motion.  And  thus  the  invention 
of  the  trajectory  depending  on  one  ob« 
fervation  and  its  hourly  motion  at  the 
time  of  this  obfervation  will  either  con¬ 
firm  or  difprove  it  felf.  For  the  con- 
clufion  that  is  drawn  from  the  motion 
only  of  an  hour  or  two  and  a  falfe  hy- 
pothefis,  will  never  agree  with  the  mo¬ 
tions  of  the  Comets  from  beginning  to 
end.  The  method  of  the  whole  compu¬ 
tation  is  this. 

Lem.  i.  To  cut  two  right  lines  OR, 
TP  given  in  pofition,  by  a  third 
right  line  RP,  io  as  TRP  may  to  the  foluti 
be  a  right  angle,  and,  if  another  Problem* 
right  fine  SP  is  drawn  to  any  given 
point  S,  the  folid  contained  under  this 
line  SP,  and  the  fquare  of  the  right  line 
OR  terminated  at  a  given  point  O,  may 
be  of  a  given  magnitude. 

It  is  done  by  linear  defeription,  thus. 
Let  the  given  magnitude  of  the  folid  be 
M4  x  N.  From  any.  paint  r  of  the  right 

line 


Digitized  by  LjOOQle 


**4 


Of  THE  SYSTEM 

line  OR  eredfc  the  perpendicular  rp 
meeting  TP  in  p.  Then  through  the 
points  Sp  draw  the  line  S  q  equal  to 

In  like  manner  draw  three  or 

Or* 

more  right  lines  S  x  q ,  S  3  q ,  &c.  And 
a  regular  line  qxqiq  drawn  through  all 
the  points  qxqiq,  &c.  will  cut  the 
right  line  TP  in  the  point  P,  from 
which  the  perpendicular  PR  is  to  be 
lei  fall  Q.E.F. 


By  trigonometry  thus.  Afliiming  the 
right  line  TP  as  found  by  the  preceding 
fnethod,  the  perpendiculars  TR,  SB  in 
the  triangles  TPR,  TPS  will  be  thence 
given,  and  the  fide  S  P  in  the  triangle 

SBP 


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6f  ?HE  WORLd  145* 

M*vN 

5BP,  as  well  as  the  errour  — — — — SP. 

OR1 

Let  this  errour,  fuppofe  D,  be  to  a  new 
eritour,  fuppofe  E,  as  the  errour  x/  z  f 
±  3/  3  q  to  the  errour  z/  3/  ;  or  as  the 
errour  z/  z  ^  +  D  to  the  errour  2/P ; 
and  this  new  errour  added  to  or  fubduCted 
from  the  length  TP  will  give  the  correct 
length  TPtE.  The  inipeCtion  of  the 
figure  will  fhew  whether  we  are  to  add 
or  to  fubtraCt.  And  if  at  any  time  there 
ihould  be  uie  for  a  further  correction* 
the  operation  may  be  repeated. 


By  arithmetic  thus.  Suppoie  the 
thing  done*  and  let  TP±f  be  The  fign  ±  Ae- 
the  correCt  length  of  the  line  n^es+or  — -  am- 
TP  found  by  delineation;  and  ftSSfiw thecon- 
the  corredt  lengths  of  the  lines  trary  fign. 

T  D 

OR,  BP  and  S  P  will  be  OR  ± 


BP  f  f  and  VSPi±xBPe±ei 
_  M*xN 

OR±zORxTR  ,  TR* 

TP  *  T P*  e 
Whence  by  the  method  of  converging 

feries’s,  we  have  S  P  ±  —  e  4.  SB-  ee. 


OR1 


OR* 

L 


OR4 


And 


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i+6 


QF  THE  SYSTEM 


And  fox'  the  given  co-efficients 


M*N 

OR* 


cn  .  BP,M‘NM‘N  SB*  „ 

*  *  SP  ± OR*  ’OR4  *SP*  pU  * 


F  F 

ting  F,  and  carefully  obferving 

the  ligns,  we  find  G  H  —  e*  =  H  e,  or 

Grr  —  =  e.  Whence,  neglecting  the 
H 

cz 

very  fmall  term  — ,  e  comes  out  equal 


6 

to  G.  If  the  errotir  —  is  not  delpica- 

H 

Q* 

ble,  take  e  =  G  —  — . 

H 

And  if  is  to  be  jobferved,  that  here  a 
general  method  is  hinted  at  for  folving 
the  more  intricate  fort  of  problems,  as 
well  by  trigonometry  as  by  arithmetic, 
without  thole  perplexed  computations 
and  refolutions  of  affected  equations, 
which  hitherto  have  been  in  ufo. 

Lem.  x.  To  cut  three  right  lines  gi¬ 
ven  in  pofition  by  a  fourth  right  line 
that  lhall  pals  through  a  point  afiigned 
in  any  of  the  three,  and  lo  as  its  inter¬ 
cepted  parts  lhall  be  in  a  given  ratio  one 
to  the  other. 


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OF  THE  WORLD. 

Let  A  B,  A  C,  B  C  be  the  right  lines 
given  in  pofition,  and  fuppofe  D  to  be 
the  given  point  in  the  line  AC.  Parallel 
to  AB  draw  DG  meeting  BC  in  G.  And, 


taking  GF  to  BG  in  the  given  ratio, 
draw  FD  E  ;  and  FD  will  be  to  DE  as 
FG  to  BG.  Q.E.F. 

By  trigonometry  thus.  In  the  trian¬ 
gle  CGD,  all  the  angles  and  the  fide  CD 
are  given,  and  from  thence  its  remain¬ 
ing  fides  are  found  ;  and  from  the  given 
rations,  the  lines  G  F  and  B  E  are  alfo 
given. 

Lem.  3.  To  find  and  reprelent  by  a 
linear  delcription  the  hourly  motion  of 
a  Comet  to  any  given  time. 

From  obfervations  of  the  beft  credit, 
let  three  longitudes  of  the  Comet  be 
given,  arid  iuppofing  ATR,  RTB  to  be 
their  differences  ;  let  the  hourly  motion 
be  required  to  the  time  of  the  middle 

obfer- 


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OF  THE  SYSTEM 
obfervation  TR.  By  Lem.  z.  draw  the 
right  line  ARB,  io  as  its  intercepted 
parts  AR,  RB  may  be  as  the  times  be¬ 
tween  the  obfervations.  And  if  we 
fuppofe  a  body  in  the  whole  time  to 
defcribe  the  whole  line  AB  with  an  e- 


<jual  motion,  and  to  be  in  the  mean 
time  viewed  from  the  place  T,  the  appa¬ 
rent  motion  of  that  body  about  the  point 
R,  will  be  nearly  the  fame  with  that  of 
the  Comet  at  the  time  of  the  obftrva- 
tion  TR. 

The  fame  more  accurately. 

Let  To,  Tb  be  two  longitudes  given 
at  a  greater  diftance  oh  one  fide  and  oh 
the  other ;  and  by  Lem .  z.  draw  the 
right  line  alkb  fo  as  its  intercepted  parts 
a  R,  R  £  may  be  as  the  times  between 
•  -  .  '  •  -  -  the 


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the  obfervations  tfTR,  RTf  Suppofe 
this  to  cat  the  lines  TA,  TB  in  D  and 
E.  And  becaufe  the  errour  of  the  in¬ 
clination  TRtf  increafes  nearly  in  the 
duplicate  ratio  of  the  time  between  the 
obfervations,  draw  FRG,  lo  as  either  the 
angle  D  R  F  may  be  to  the  angle  A  R  F, 
or  the  line  D  F  to  the  line  AF,  in  the 
duplicate  ratio  of  the  whole  time  be¬ 
tween  the  obfervations  a  TB  to  the 
whole  time  between  the  obfervations 
AT  B,  and  ufe  the  line  thus  found  F  G 
in  place  of  the  line  AB  found  above. 

It  will  be  convenient  that  the  angles 
ATR,  RTB,  *TA,  BT b  be  no  lefs 
than  of  ten  or  fifteen  degrees,  the  times 
correlponding  no  greater  than  of  eight 
or  twelve  days,  and  the  longitudes  ta- 
]ken  when  the  Comet  moves  with  the 
greateft  velocity.  For  thus  the  errours 
of  the  obfervations  will  bear  a  lefs  pro¬ 
portion  to  the  differences  of  the  longi¬ 
tudes. 

Lem.  4.  To  find  the  longitudes  of  a 
Comet  to  any  given  times. 

It  is  done  by  taking,  in  the  line  F  G, 
the  diftances  Rr,  Kp  proportional  to 
the  tiroes,  and  drawing  the  lines  Tr, 
T  p.  The  way  of  working  by  trigono¬ 
metry  is  manifeft. 

*-  ' 

Lem. 


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ijo  bF  THfc  SYSTEM 

Lem,  5.  To  find  the  latitudes. 

On  TF,  TR,TG,  as  radius’s,  at  right 
angles  ereCt  F  R  P,  G  g  tangents  of 
the  obferved  latitudes  ;  and  parallel  to 
fg  draw  PH.  The  perpendiculars  r/, 
p-ur  meeting  P  H  will  be  the  tangents  of 
the  fought  latitudes  to  T  r  and  Ty  as 
radius’s. 

^rob.  i.  From  the  aflumed 
The  problem  fefol-  ratio  of  the  velocity  to  deter- 
yed’  mine  the  traje&ory  of  a  Comet. 

Let  S  reprelent  the  Sun,  £,T,t  three 
places  of  the  Earth  in  its  orbit  at  equal 


diftances,/,P,ar  as  many  correfponding 
places  of  the  Comet  in  its  trajectory,  fo 
as  the  diftances  interpofed  betwixt  place 
and  place  may  anfwer  to  the  motion  of 
one  hour,  /r,  PR,  <srf  perpendiculars 

let 


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QF  THE  WORLD.  %si 

let  fall  on  the  plain  of  the  ecliptic,  and 
rRj)  the  veftige  of  the  traje&ory  in 
this  plain.  Join  S/,  SP»  S<cr,  SR,  ST, 
tr ,  TR,  rp,  TP  ;  and  let  tr,  Tp  meet 
in  O,  TR  will  nearly  converge  to  the 
fame  point  O,  or  the  errour  will  be  in- 
confiderable.  By  the  premtfed  lemma’s, 
the  angles  rOR,  ROj>  are  given,  as 
well  as  the  ratio’s pr  to  tr,  PR  to  TR, 
and  <a to  to  t p.  The  figure  tTrO  is 
likewife  given,  both  in  magnitude  and 
pofition,  together  with  the  diftance  S  T 
and  the  angles  STR,  PTR,  STP.  Let 
us  aflume  the  velocity  of  the  Comet,  in 
the  place  P,  to  be  to  the  velocity  of  a 
Planet,  revolved  about  the  Sun  in  a  cir¬ 
cle,  at  the  fame  diftance  SP,  as  V  to  i, 
and  we  fhall  have  a  line  p  P  nr  to  be  de¬ 
termined,  of  this  condition,  that  the 
fpace  p  <ar,  defcribed  by  the  Comet  in 
two  hours,  may  be  to  the  fpace  Vxtr 
(that  is,  to  the  fpace  which  the  Earth 
defcribes  in  the  fame  time  multiplied  by 
the  number  V  )  in  the  fubduplicate  ratio 
of  ST,  the  diftance  of  the  Earth  from 
the  Sun,  to  S  P  the  diftance  of  the  Co¬ 
met  from  the  Sun ;  and  that  the  fpace 
P  P,  defcribed  by  the  Comet  in  the  firft 
hour,  may  be  to  the  fpace  P-sr  defcribed 
by  the  Comet  in  the  fecond  hour,  as 
the  velocity  in  p,  tp  the  velocity  in  P, 

*  that 


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Of  the  system 

that  is,  in  the  lubduplicate  ratio  of*  the 
diflance  SP  to  the  didance  Sp,  or  id 
the  ratio  of  a  S  P,  to  $  P+S P-  For  in 
this  whole  work  I  negle&  fmall  frac¬ 
tions  that  can  produce  no  ienfible  er- 
rour. 

In  the  fird  place  th£n,  as  mathema¬ 
ticians  in  the  refolution  of  adedted  e- 
quations,  are  wont,  for  the  fird  eflayj 
to  adume  the  root  by  conjedhire;  fo,  in 
this  analytical  operation,  I  judge  of  {he: 
fought  didance  TR,  as  I  bed  ,  can  by 
conjecture.  Then  by  Lem.  i'  I  draw 
rp,  firdfuppofing  r  R  equal  to  Rp,  and 
again  (after  the  ratio  of  SP  to  S/  is 
difcovered)  fo  as  rR  may  be  td  Rp,  as 
fcSPto  SP-j-S/,  and  I  find  the  rations 
of  the  lines p<&,  r?  and  O  R  one  to  the 
other.  Let  M  be  to  Vx  t  t  •  as  O  R  to 
pur  ;  and  becaufe  the  fquare  of  is 
to  the  lquare  of  Vx  ?  t,  as  S  T  to  S  P, 
we  ihall  have  ex  a  quo  OR*  toJVT  as 
ST  to  SP,  and  therefore  the  folia  OR* 
X  SP  equal  to  the  given  folid  M*  X  ST. 
Whence  (fuppofing  the  triangles  S  TP, 
PTR  to  be  now  placed  in  the  lame 
plain)  TR,  TP,  SP,  PR  will  be  given 
by  Lem.  i.  All  this  I  do,  fird  by  de¬ 
lineation  in  a  rude  and  hady  way,  then 
by  a  new  delineation  with  greater  care, 
and  ladly,  by  an  arithmetical  computa- 
•  *  ’  tion. 


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OF  *HE  WORLD. 

tibn.  Then  I  proceed  to  determine 
the  pofitioh  of  the  lines  r  p,  p  w  with 
the  greateft  accuracyj  together  with  the 
nodes  and  inclination  of  the  plain  S /  ©• 
to  the  plain  of  the  ecliptic  ;  and  in  that 
plain  S/-BT,  I  delcribe  the  trajedory  in 
which  a  body  let  go  from  the  place 
P  in  the  direction  of  the  right  line  /-nr* 
would  be  carried  with  a  velocity  that  is 
to  the  velocity  of  the  Earth,  as  ]>  &  to 
Vy.tr.  Q.E.F. 

Trob.  i.  To  corred  the  alTiimed  ra¬ 
tio  of  the  velocity  and  the  trajedory 
thence  found. 

Take  an  obfervation  of  the  Comet 
about  the  end  of  its  appearance,  or  any 
bther  obfervation  at  a  very  great  dif 
tace  from  the  obfervations  bled  before* 
and  find  the  interfedion  of  a  right  line 
drawn  to  the  Comet,  in  that  obferva¬ 
tion,  with  the  plain  S/>  >arr  as  well  as 
the  Comet’s  place  in  its  trajectory  to 
the  time  of  the  obfervation.  if  that  in¬ 
terfedion  happens  in  this  place,  it  is  a 
proof  that  the  trajedory  was  right  de¬ 
termined.  If  otherwile,  a  new  number 
V  is  to  beaflumed,  and  a  new  trajec¬ 
tory  to  be  found,  and  then  the  place  of 
the  Comet  in  this  trajedory  to  the 
time  of  that  probatory  obfervation,  and 
the  intetfedion  of  a  right  line  drawn 

M  to 


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QF  THE  SY$T?M 

to  the  Comet,  with  the  plain  of  the 
trajectory  are  to  be  determined  as 
before.  And  by  comparing  the  va¬ 
riation  of  the  errour  with  the  variation 
of  the  other  quantities,  we  may  con¬ 
clude,  by  the  Rule  of  Three,  how  far 
thofe  other  quantities  ought  to  be  vari¬ 
ed  or  corre&ed,  fo  as  the  errour  may 
become  as  fmall  as  pofiible.  And  by 
means  of  thefe  corrections  we  may  have 
the  trajectory  exactly,  providing  the 
oblervations,  upon  which  the  compu- 
tion  was  founded,  were  exaCt,  and  that 
we  did  not  err  much  in  the  atfumption 
a  of  the  quantity  V  for  if  we  did,  the 
operation  is  to  be  repeated  till  the  tra¬ 
jectory  is  exactly  enough  determined. 
Q.  E.  F. 


FINIS. 

/£joi y—.' fX  * 

nlAUSA^n  r  f) 

£  jjT ■  T>  I -'Is 


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E  R  R  A  T  A. 

Preface,  page  if.  line  4.  from  the  bottom, 
dele  two.  Pag.  *3.  line  ip.  read  as  the  fum  &c. 
Pag.  43.  lin.  6.  for  and  read  then.  Pag.f  3.  lin.  17. 
between  fzoi  16  and  71 333  infert  if  13pp.  In  the 
Scheme  pag.  84.  draw  a  line  from  b  through  C  to 
A.  Pag.  up.  lin.  7.  read  about  VS  18®.  z6'.  Pag. 
1 34.  the  firft  number  in  col.  f .  fhould  have  flood 
even  with  thofe  in  the  other  four. 


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