WILLIAM L. CLEMENTS
ich herrlene Elu
Raie
en saben to 14268
Chinle - 1945. El-
manzie din 428
ESTC 105429



AN
EXPLICATION
OF THE
FIRST
CAUSES
0 F
Action in MATTER;
* AND OF THE
CAUSE
OF
GRAVITATION.
By CADWALLADER: COLDEN.
N E W.Y OR K:
Printed in the Year, MDCCXLV.
And London Reprinted: for J. BRINDLEY,
Bookfeller to His Royal Highneſs, the Prince
of WALES, at the Feathers in New Bond-
ftreet1746.
( Price One Shilling.)

LO

[iii
KERANCINHA
ΤΟ
JAMES ALEXANDER, Elg;
AT
NE W - Y OR K.
Athing halten
Y
in tretters
SIR,
OU have obliged me exceedingly big
my
3 actin love
the trouble and care you have taken
in examining the papers I ſent to
you, for that purpoſe. You will ;' He maring
now find the number of lines in ſeveral places , the luryhing Porn
conßderably increaſed; becauſe I find it difficult
to convey new conceptions of things to others
; 3 Ile Elastil,
with that conciſeneſs
, I at firſt intended, and ranking power
which require a method of thinking entirely dif-
ferent from that, which, perhaps, has become
habitual to them: but I muſt have been tedious
if
A 2

iv DEDICATION.
if I had not left fome ſteps to be ſupplied by
the reader. For the ſame reaſon, I have not
followed a method ſtrictly mathematical, but ſuch
as I thought would more eaſily lead the mind of
the reader; step by ſtep, into the ſame concep-
tións I have. An adequate idea of any com-
plicated matter cannot at once be formed; and
therefore the difficulties which may ariſe in the
firſt steps, cannot be eaſily removed, till the con-
ception of the whole matter is cleared up by go-
ing further on. I have likewiſe, in ſeveral
ſteps, taken different methods of conveying and
clearing up the ſame conception: becauſe the
ſame man at different times, and different men
at all times, receive any idea more eaſily in one
way than in another.
THE deſign of theſe papers is ſo exceeding
hardy, that I have all the reaſon in the world
to be diffident of myſelf. To attempt to efta-
bliſh new principles in phyſics, different from
thoſe of all writers before me; to attempt to
explain the cauſe of gravitation, after all the
great men in philofophy. have failed, and after
fir ISAAC NEWTON ſtopt port, as at an en--
quiry not furmountable by his fagacity, which
had diſcovered fo many wonders : when I confi-
der this, I have reaſon to fear, that this at-
tempt will not only be blamed, as bold and raſh,
but will be look' d on as ſo vain and fooliſh, as
not to deferve, a reading, or any conſideration,
However, after having for a confiderable time
revolved

DEDICATION.
revolved it in my mind, and conſidered every ob-
jection which occurr'd to me, with all the care
and impartiality that I am capable of; the
truth of the principles which I now advance,
ftill appear with ſo much evidence to me, that
I can no longer doubt of their certainty. Tho®
1 may not pretend to have acquired a perfect
and adequate conception of what I treat, or
that I have fallen upon the beſt method of con-
veying to others, the conceptions which I have
formed myſelf, on this ſubject; the force of the
evidence on my mind, is as ſtrong as that of
day-light after the ſun is up in cloudy wea-
ther.
IF the ſubje&t of the following ſheets were
a mere piece of curioſty, in an abſtruſe point;
it will even as fuch (if well performed) be
very acceptable to curious men: but it has likes
wiſe opened to me, a prospect of great improve-
ment in all the uleful ſciences in human life. I
expect that not only for ISAAC NEWTON's
theorems, in his Principia, may be explained
more eaſily from theſe principles, without the
aſſiſtance of the conic ſections ; but that more
eaſy and certain methods may be found for de-
termining the orbits of the planets, and even of
the moon, and of forming equations for that
purpoſe, than can be done from other princi-
ples. Of how great conſequence this may be in
geography and navigation, they beſt know, who
think that no method for diſcovering longitude

vi
DEDICATION.
at fea, can ſucceed, till the moon's place cah
be determined at all times with ſufficient exact-
neſs. It gives me likewiſe a profpext of im-
provement in ſeveral other parts of phyſics.
Upon the whole then; the evidence of truth, and
the uſefulneſs of the ſubject of the following
Sheets, as they appear to me, I hope will gain
a favourable conſtruction of my intention in
printing only ſo many copies of them, as may
be ſufficient to ſubmit my thoughts to the exa-
mination of the learned ; and without any de-
fign of troubling the world any further on this
ſubject, but according to the reception theſe
Jheets ſhall have with proper judges.
old;
I have likewiſe another reaſon for my print-
ing in the manner I do, that as I think theſe
diſcoveries certain and uſeful, I would not
have them loft to the world.
I am grown
I am not ſo much at eaſe as is neceſſary
to proſecute fuch fudies to any length, and
I want many things neceſſary for this pur-
poſe : theſe, then, may ſerve as hints to
others of much greater abilities than I can
pretend to: and though what I have done,
be not ſufficient to ſet the truth in a
clear light; others may be able to clear it of
thoſe obfcurities, that I have not been able to
I have already gone ſo far, as to ap-
ply theſe principles to ſeveral phenomena and
caſes in gravitation : but I ſhall ſtop short
in this publication, with finiſhing the sheet,
wbare
remove.

DEDICATION.
vii
where the explication of gravitation in gene-
ral ends, till I ſhall know the judgment of
thers; and then, if I find it will be accepta-
ble, I may add as far as my time and capacity
shall allow me to proceed.
NOW, fir, if you approve of theſe reaſons
for my printing the following ſheets; I hope
you
will allow me publickly to acknowledge your
kindneſs, in examining and making remarks on
the firſt draught of them : that if theſe papers
have any merit to preſerve themſelves from ob-
livion; they may continue to our children, the
memory of the friendſbip that has for many
years ſubfiſted between us ;
and that I may
have the pleaſure while alive, of fancyiug,
that if any bereafter ſhall think of my name,
they will at the ſame time believe, that I ever
was, as I now am, with great eſteem,
Your moſt affectionate Friend,
and moſt humble Servant,
CADWALLADER COLDEN.
Coldingham, in the Pro-
vince of New York,
December 10, 1745


(9)
3
AN
EXPLICATION
OF THE
FIRST CAUSES
OF
Action in Matter, &c.
Ο Η Α Ρ. Ι.
Of the primary material agents; or,
the firſt principles in phyſics.
"A
NY thing is ſaid to be extended,
or extenſion is an eſſential
pro-
perty of that thing, when we
cannot conceive it without li-
mits, or bounds, or ſhape; or when we can-
not form any conception of it, without
per-
ceiving at the ſame time, that it is capable of
being greater or ſmaller ; capable of addition
B
or

( 10 )
or diviſion, as conſiſting of parts, or as being
diviſible into parts : for that property is eſſen-
tial to any thing, without which we cannot
form
any conception of that thing. There-
fore,
2. Every thing conceived as quantity, is
extended.
3. A thing is ſaid to be impenetrable, when
it excludes every thing elſe from the ſpace
which it occupies. Every thing, which we
conceive as diſtinct from another, neceſſarily
includes this
property : for the moment that
we ſuppoſe, that two things abſolutely occu-
ру the ſame ſpace, all diſtinction ceaſes in
our conception of them; and therefore the
one or other, as to us, becomes a non-entity,
or that of which we have no conception.
4. Every thing, which is conceived as ex-
tended and impenetrable, I call Matter.
5. Then if matter be taken in this large
ſenſe of the word, which, I think, is the
common acceptation of it; we muſt allow
that there are different kinds or ſpecies of
matter, diſtinguiſhed by manifeſt eſſential
properties, peculiar to each fort, and incon-
fiftent with the eſſential properties of the o-
thers: which I propoſe to thew more parti-
cularly by what follows.
6. There is ſome thing endowed with a
certain kind of force or power, by which it
refifts every alteration of its preſent ſtate,
whether it be in motion or at reft: this is
commonly called, the power of reſiſtance, and
by

(11)
by fir ISAAC Newton, vis inertia. There
can be no doubt of ſomething poffeffing this
property, or that is endowed with this
power
or force: for it is ſo generally obſerved in e-
very thing, which is the object of our ſenſa-
tions, that this power is generally attributed
to all matter. But how truly this is done,
will better appear after we have conſidered
the nature of this power; which however
will not be found eaſy for us to do, ſeparate-
ly from other ſpecies of matter : becauſe all
the ideas we form of power, or force, or of
action, are generally taken from matter in
motion; and therefore we cannot eaſily con-
ceive any action without motion.
. Yet it is
evident, that motion ought by no means to
enter into our conception of this
power
of
reſiſting; for it exerts its force at reſt as well
as in motion.
7. In order to form an adequate notion of
this power or force, I ſhall obſerve, 1. That
this power or force cannot proceed from a
meer want of action: for the power of re-
fiſting is ſometimes greater, at other times
lefs; fometimes it is able to reſiſt a greater
force, at other times only a leſs : but a meer
want can never be greater or leſs; it is a non-
entity, and cannot be of any quantity either
great or ſmall: it can have no power or force;
for it is a negation of all power or force.
No kind of motion can enter into the con-
ception of the manner of action in the pow-
er : for in the idea of motion we muſt con-
B 2
ceive
2.

( 12 )
ceive ſome kind of tendency or direction
from one place or point towards another
place or point. If then the idea of reſiſting
has any thing in common with motion, it
muſt oppoſe motion more in one direction
than in another, more when the motion
which it oppoſes is in an oppoſite direction
to the direction of reſiſtance, than when both
directions tend the ſame way: but reſiſtance
oppoſes motion in all directions; therefore
nothing of motion can properly enter into
the conception of it. 3. This power equally
exerts its force, whether it be in motion or at
reſt: for when two quantities of this reſiſting
power are different while at reſt, the one
greater than the other; if they be put in
motion, that quantity which reſiſted moſt
while at reſt, will likewiſe reſiſt moſt while
in motion. 4. The effects of this power ap-
pear in a kind of obſtinacy, by which it op-
poſes all other power or force. It does not
deſtroy the oppoſite power, but only oppoſes
its action, and in ſome caſes (as will be
ſhewn afterwards) continues the effect of ac-
tion of the other powers, which would other-
wiſe ceafe. Neither can the power or force
of reſiſting be deſtroyed by an oppoſite pow-
er : for if this power be effential to any thing,
(as we ſhall afterwards prove) it cannot be
deſtroyed without annihilating the thing it-
felf. This power, and every part of it, or
particle, exerts its force or action in all di-
rections: for it, and every part of it, equally
oppoſes,
5.

(13)
oppoſes, reſiſts or leſſens the action of other
powers, in whatever direction they be applied,
6. The thing or being which exerts this pow-
er or force, is truly an agent; it is a principle
which acts of itſelf, without the force, pow-
er or agency of any other thing: for, ſince its
whole power or force is exerted in oppoſing
the actions of all other power or force, it
cannot receive its power or force from that
which it oppoſes. Therefore,
8. The thing endowed with the power of
reſiſtance, or vis inertia, is an agent, or ac-
tive ſubſtance, ſubſiſtence, exiſtence, or be-
ing, endowed with a certain power or force,
whereby it perſiſts in its preſent ſtate, and
oppoſes or refifts all other power that would
change that ſtate, whether it be in motion or
at reit; and thereby weakens, or renders
more or leſs ineffectual, the action of all o-
ther power or force: which force it exerts in
a manner peculiar to itſelf, and different from
all other natural agents. Force without ac-
tion, is a contradiction in terms; yet we are
ſo accuſtomed to join motion with all action,
that I find it very difficult to convey any no-
tion of action or agency in the power of re-
fiſting, tho? it demonſtrably be an agent or
acting principle.
9.
This
power of reſiſting, or vis inertie,
may be conſidered as quantity: for it is every
day, and in all places, obſerved to be greater
or leſs : It is capable of being augmented or
leſſened; of conſequence it is contained with-
in

( 14 )
erting this
in fome bounds or limits: it is of ſome ſhape,
parts may be taken from it, or added to it,
that is, it is extended. Indeed we can form
no conception of it, without conceiving it as
exiſting within fome bounds or other : and
therefore extenſion is eſſential to the agent ex-
power.
10. Again, it is impoſſible to conceive this
power of reſiſting, without fuppofing at the
fame time, that this agent is impenetrable ;
that no other power can at the ſame time
poffefs the ſame place : for as this agent acts
by reſiſting other power or force; the thing
which it refifts muſt occupy a different place,
otherwiſe we cannot conceive the one as re-
fiſting the other : therefore impenetrability is
an effential property of the reſiſting agent:
And of conſequence,
agent endowed with, or exerting
the power or force of reſiſting, is a ſpecies of
There is no great difficulty of form-
ing a conception of this agent, as a ſpecies of
matter, or as being extended and impenetra-
ble; every object of our ſenſes round us, raiſes
this idea in our mind: but I have taken this
method of proving it, the more eaſily to ap-
ply this reaſoning to ſome other agents, which
we are not accuſtomed to conſider in this
II. The
matter.
manner.
12. It is generally concluded, that the force
of reſiſtance is in proportion to the quantity
of matter reſiſting : becauſe a greater quantity
of reſiſting matter; requires a greater force to
move

(15)
move it. But it muſt be obſerved, that in
conſidering this reſiſting matter, there are two
different ways of conſidering it as quantity:
either the quantity of extenſion (its bulk) or
the quantity of its force. When we ſay two
powers producing the ſame effect'are equal,
we then mean only as to the quantity of
force; but two different quantities may have the
fame force : there may therefore be different
ſpecies of this reſiſting matter, in which the
proportions of their force to their bulk may
be different; and, as theſe different propor-
tions may be infinite in number, the different
ſpecies of refiſting matter may be infinitely
different. No experiment, which only de-
termines the force of two different agents to
be equal, does, for that reaſon, determine
that their bulk is ſo likewife. From fir
ISAAC NEWTON's diſcovery of the infinitely
different ſpecies of light, it is poſſible there
may be as many different ſpecies of reſiſting
matter; and if there be, we may hope that a
method may be diſcovered to demonſtrate this.
Before fir Is A AC's diſcovery, light was uni-
verſally thought to be homogeneous; and yet
he has ſo clearly demonſtrated the contrary,
that none can doubt of its being the very re-
verſe, that it conſiſts of an infinite variety of -
ſpecies. Could any man have imagined, that
this diſcovery, which had avoided all the cu-
rious reſearches of philoſophers to his day, was
made by ſo ſimple and common a contrivance,
as a triangular glaſs-priſm? Glaſs and priſms
had

( 16 )
had been known and in uſe many ages, and
in all that time it was never imagined that
any ſuch diſcovery could be made : who then
can ſay what diſcoveries may be made, when
ſuch another genius as fir ISAAC Newton's
Shall appear in the world?
13. We daily obſerve, that ſome things
move, or paſs from one place to another :
the power of reſiſting is ſo very different from
that of moving, that they can in no manner
be conceived as the effects of the ſame agent,
or of the fame cauſe. We every day ob-
ſerve, that ſome things in motion, loſe their
motion; that the ſame things again, or o-
ther things at reſt acquire motion, and things
moving with ſmall velocity acquire greater
velocity: this motion then muſt either be by
fome power, force or agency in the moving
thing itſelf, or it muſt be the effect of ſome
other power without it: this other thing muſt
be of itſelf an agent, and has the power of
moving eſſential to it; or it muſt be put in
motion by a third thing, and ſo on; we muſt
then at laſt reſt in ſomething to which the
power of moving is eſſential, or we muſt al-
low, that an effect can be produced without
a cauſe: this thing then, to which motion is
eſſential, which moves by its own natural
force, muſt be an agent, which has its active
principle in itſelf.
14. We every day perceive different quan-
tities of motion, or its force or power ſome-
times greater, ſometimes leſs, and we per-
ceive

(17)
ceive it in different places : we cannot then
otherwiſe conceive it than as bounded, or of
ſome ſhape, and as conſiſting of parts; and
therefore extenſion is eſſential to the idea
thereof. We every day likewiſe ſee refiſting
matter put in motion by this agent; therefore
they muſt be impenetrable to each other : for
otherwiſe we cannot conceive the one as mo-
ving, the other as reſiſting; neither can we
otherwiſe conceive them as diſtinct beings,
without diſtinct places. This moving agent,
or this thing endowed with the power of mo-
ving, is a ſpecies of matter. When we ſee a
ſmall ſpark gradually ſet a large city all in a
blaze, can any man imagine that there is no
more motion in all the parts of the city, thus
on fire together, than there was in the firſt
little ſpark that began the fire? That there is
no more power or force in this prodigious
fire, than there was in the ſcarce diſtinguiſh-
able ſpark which began it ? But if there be
not ſuppoſed fomething mixed in the mate-
rials of the city thus on fire, which has a pow-
er of moving of itſelf; all the prodigious force
of motion in the city thus on fire, muſt be
ſuppoſed in the firſt little ſpark which be-
gan the fire : for nothing can give what it
has not. There are innumerable other Phæ-
nomena, which evidently ſhew, that ſome
parts of matter are ſelf-moving agents, and
which ever move, unleſs hindered by the ſu-
perior force of reſiſting matter; and that as
ſoon as the reſiſting power is by any means re-
с
moved,

( 18 )
moved, the ſelf-moving matter immediately
recovers its motion.
15. Since the reſiſting and moving agents
are ſo very contrary to each other in their na-
ture, reſiſting motion and ſelf-moving, that it
is impoſſible to conceive them as exiſting in
the ſame thing, or that any one thing can have
both powers eſſential to it; we muſt then be
very careful not to attribute theſe different
powers, and inconſiſtent modes of action to
the ſame agent: which however, from what
follows, it will appear, is not eaſy for us to a-
void,
16. Suppoſe that two quantities of the mo-
ving agent, or two particles of moving mat-
ter (for both theſe expreſſions fignify the
ſame thing) move towards each other with
the ſame force, in oppoſite directions, what
will happen after their meeting? If you ſay,
that they will ſtop each other, and remain at
reſt; I deny it; becauſe motion never de-
ſtroys motion, or leſſens it: it is the property
of reſiſting matter only to ſtop, lefſen, or ren-
der ineffectual the force of the moving mat-
I ſhall aſk, what is it in the oppoſite
motions which deſtroys motion ? If you fay,
that it is their mutual reſiſtance; I anſwer,
they have no reſiſtance. I have proved (7,
8, 13, 14, 15,) that the power of reſiſt-
ing and moving, can never exiſt in the
ſame agent; and therefore two particles of
moving matter
in the
proper
fenſe of the word, reſiſt each other's motion.
What
ter.
cannot,

( 19 )
What then, you'll ſay, muſt happen after the
meeting of theſe two oppoſite movers? They
muſt either return back, or go off together,
or from each other, in ſome direction or o-
ther. I don't at preſent enquire which of
theſe will happen; all that I aſſert is, that
motion will not be lefſen'd in this caſe, in ei-
ther one or the other, or in both taken toge-
ther ; the change of direction only ſeems à
neceſſary conſequence of their impenetrability.
The truth of this appears in the meeting of
two quantities of elaſtic matter ; the motion
in this caſe is no way lefſened by the oppoſite
motions: it muſt then be ſomething elſe than
motion which leſſens or deſtroys it; for nothing
deſtroys itſelf, or its own force. We muſt care-
fully diſtinguiſh the effects which are necef-
ſary conſequences of impenetrability, from
thoſe which are the conſequences or the ef-
fects of the reſiſting agent; without this care,
we ſhall often run ourſelves into confuſion,
becauſe of a faulty habit, which every one
acquires, of confounding theſe very diſtinct
properties in matter, impenetrability and re-
fiſtance. The reaſon of this is, that all our
ideas of motion are taken from reſiſting mat-
ter in motion, which is endowed with both
theſe properties.
17. Suppoſe next, that two quantities of
matter meet, the one of the moving agent,
the other of the reſiſting, what will happen?
If the reſiſting power be greater, or equal to
the moving power, it will ſtop the action of
C
the

( 20 )
the moving power, and both remain at reft,
tho' the force, or endeavour, or power to
move, ſtill remain in the moving power; but
if the moving power be greater or ſtronger
than the reſiſting, then the moving power will
only loſe part of it's motion, and both will
move together, with the remaining force of
motion : this becomes a compound quantity,
endowed with both motion and reſiſtance. It
is not my preſent buſineſs to proſecute this
more particularly, but only to give general no-
tions of theſe two different agents, and of their
manner of acting.
18. Again, fuppoſe that this united
quan-
tity of the moving and reſiſting agents, be by
ſome means ſeparated; I ſay, that the mo-
ving matter will, the moment after it is ſepa-
rated from the reſiſting matter, recover its firſt
and original action of moving, or its whole
motion : and the reſiſting matter will conti-
nue its motion in the ſame manner, or with
the ſame velocity it did, while joined with the
moving matter; and this by its power of re-
ſiſtance: for this power or force confifts in
perſiſting in whatever ſtate it is at any time in,
and in oppoſing all change of that ſtate. As
the degree of velocity, with which it moves,
is the ſtate in which every part of that quan-
tity of reſiſting matter is in at the time; the
force of reſiſting all change, or perſiſting in
that ſtate, in two different quantities ſo mo-
ving, will be as the quantities themſelves; and
in different quantities moving with different
velocities,

( 21 )
velocities, as the velocities multiplied into the
reſpective quantities of reſiſtance. This force
is called Momentum, by fir ISAAC NEWTON,
and is by him rightly diſtinguiſhed from mo-
tion: for it is plain, they ariſe from the ac-
tions of agents effentially different in their na-
ture and manner of acting. It is likewiſe
evident, that any quantity of reſiſting matter,
moving thus by motion communicated to it,
loſes the whole, or ſome part of its motion,
every time it meets with any other quantity of
reſiſting matter, and never of itſelf recovers
that motion again. The laws of this com-
municated motion (Momentum) being moſt
common to our obfervation, are well deſcri-
bed by philoſophers: but the laws, by which
the primary agents act, are little underſtood,
though they be truly the cauſe of all the Phæ-
nomena in nature, and therefore deſerve the
trouble of further enquiry.
19. But befides theſe two powers, the one
reſiſting, oppoſing or fupprefſing motion, or
any alteration of its preſent ſtate; the other a
felf-moving power, always changing or en-
deavouring to change its place, by moving in
ſome one direction or other; there is a third
kind of force or power obſerved, by which
the parts of this thing receive any impreſſion
or action from any other agent, either the mo-
ving or reſiſting agent; and by a kind of re-
acting force communicates this action to all
things round it, as by a kind of expanſion of
action, or ſuch kind of action as ſeems to
proceed

( 22 )
proceed from a center of every part, in ſtrait
lines to the ſurface: and this reaction is al-
ways obſerved to be equal to the force im-
preſſed. As we take our idea of this power
from elaſtic bodies, whoſe parts, if by any
force compreſſed nearer, endeavour to recede,
and reſtore themſelves with a force equal to
that which compreſſed them; and thereby e-
qually preſs every thing round them, which
oppoſes the reſtoring of them to their firſt
ſituation; it is uſually called elaſtic force.
20. Now it is plain, that this elaſtic or ex-
panſive force cannot be the effect of the re-
fiſting agent: for the whole power of the re-
fiſting agent is exerted in preſerving its pre-
fent ſtate, and oppoſing all change; but the
very idea of this includes a perpetual endea-
vour of change by expanſion. Again, the
reſiſting power is exerted in oppoſing, leſſen-
ing and rendering ineffectual all motion ; but
this power, by its reaction, preſerves the mo-
tion impreſs'd upon it in its full force, and
only alters the direction. Neither can it be
the effect of the moving power : for the mov-
ing power exerts its force only in one di-
rection; but this power exerts its force in all
directions from every point. This then muſt
be the force or power of an agent eſſentially
different from both the reſiſting and moving
agents: for the effect of this power cannot
be produced by either of thoſe agents fingly,
or by both jointly. The whole manner of
action in this agent is fingular and peculiar to
itſelf,

( 23 )
any other
itſelf. This power neither reſiſts nor moves,
and exerts no kind of action of itſelf, with-
out the concurrence of ſome other power; fo
that in the abſence of other powers, it muſt
be conceived as in perfect inaction. Its po-
wer conſiſts in this, that every part of it rem
ceives the impreſſion or action of
contiguous power; and by a kind of expan-
fion, or elaſticity, or reaction, every part re-
flects or expands that action which it received,
in every direction, in an oppoſite direction as
well as in the direct, and thereby communi-
cates it to the adjacent parts.
It muſt be
conceived as exiſting alternately in two dif-
ferent ſtates; the one of receiving, the o-
ther of reflecting, expanding, or reacting:
it receives in one direction, and reflects in
every direction: it has no manner of acting
peculiar to itſelf, independently of the other
powers; but receives any manner of action,
either that of the reſiſting or moving power;
and then, if this elaſtic matter be ſuppoſed
to fill the ſpace between any other ſpecies of
matter, by a power peculiar to itſelf, it
communicates the action of the one to the
other at a diſtance, which otherwiſe could
not be done : ſo that it is the general medium,
by which all action is communicated to any
diſtance from the acting power. This po-
wer of reaction, and reflecting any force im-
preſſed upon it, is the power peculiar to this
ſpecies of matter; and it exerts this power in
a manner fimilar to the manner of acting of
any

( 24 )
any other
power,
from which it receives its
action.
21. The reſiſting power is negative to eve-
ry other power, to the elaſtic power as well
as the moving: for reſiſtance muſt leffen e-
very other action; and whatever leffens or
weakens any action, is negative to that action.
Therefore, in whatever degree the action of
the reſiſting power is communicated to any
part or particle of the elaſtic power, in the
ſame degree the action of reacting or reflect-
ing (which is the proper and peculiar action
of elaſtic matter) is leſſened: but the moving
and elaſtic power being no way negative to
each other, in no manner leſſen or weaken
each others action. For the ſame reaſon, the
action of ſeveral quantities of the ſame po-
wer, acting in oppoſite directions, are in their
directions negative to each other; becauſe it
is impoſſible they both can at the ſame time
take their full effect: but the reaction of the
elaſtic power, in the direction oppoſite to the
direction of the action which it reflects, is
not negative to that action, becauſe performed
at different times; as is evident from the i-
dea of receiving and reflecting. Hence the
action of every power muſt not be conceived
as one continued act, but as a great many re-
peated acts or momentaneous vibrations; and
that the reaction of the elaſtic power is in
the interval of theſe acts or vibrations. This
alternate action and reaction, or alternate fy-
ſtole and diaſtole, or undulating vibration is
par-

( 25 )
particularly obſerved by Sir Isaac NEWTON,
in the paſſage of light thro' any
medium.
22. This expanſive or elaſtic force has been
uſually attributed to the ſhape of the parts
which compoſe the elaſtic body. They are
ſuppoſed to be fpirial ſprings, like watch-
{prings : but why a ſpiral ſhape, or any ſhape,
or any manner of arranging the parts of any
thing, ſhould give that thing any power which
it had not before, is to me inconceivable. It
is plain from common obſervation, that no
Shape can give an elaſtic force to lead; a ſpi-
ral of lead is as little elaſtic as a ſtrait line of
lead.
23. As we cannot conceive this expanſive or
laſtic
power, otherwiſe than as conſiſting of
parts, every one of which exerts its reactive
force, as it were in lines from the centre of
every part to its ſurface, and every part as
acting upon all the ſurrounding parts, and
acted upon by them; the agent exerting this
force cannot be conceived otherwiſe than as
extended and impenetrable; and therefore,
that it is a ſpecies of matter.
24. It follows then, from the whole of
what has been ſaid, that theſe ſpecies of mat-
ter above deſcribed, are agents or acting prin-
ciples; that each has a power or force pecu-
liar to itſelf, differing from the others in its
eſſence and manner of acting. Whether
there be any more ſpecies of matter, is not
eaſy to determine, tho' moſt of the ancients
agree in this number. That theſe three are
ef-
D

( 26 )
eſſentially diſtinct, I can make no doubt. If
there be any other diſtinct ſpecies of matter,
it muſt likewiſe be an active principle: for
we can have no idea of any thing but what a-
riſes from action, and there can be no proper-
ty without ſome power or force. For this rea-
fon ſome of the ancient philoſophers ſaid, all
nature is alive; that is, all nature is active.
Try to deſcribe matter without action, po-
wer, or force, the whole deſcription muſt
conſiſt of negatives, that is, it muſt be the
deſcription of no thing; and then it very cer-
tainly follows, that no thing or no being ex-
ifts no where. The word matter, defined
to be a thing without action, without power,
or force or property is ſynonymous to the word
no-thing; and then I think it requires no
great penetration to demonſtrate, that it ex-
iſts no where, or is not: and yet this is the
ſum of fome late learned and elaborate diſa
courſes.
25. The quantity of power, or the quan-
tity of matter, are fimilar expreſſions; that
is, a cubic inch, for example, of refifting,
moving, or elaſtic matter, has half the
quan-
tity of reſiſtance, motion or elaſticity, that
two cubic inches of the fame power or ſpe-
cies of matter have; but the manner of ex-
power, or degree of action, or of
force, is as great in the cubic inch as in the
two inches. Or more generally, every part
of any ſpecies of matter has the power of
acting in as great a degree as the whole has :
for
erting that

( 27 )
Since power
for where any power is eſſential, there can be
nothing in the thing itſelf to obſtruct the ex-
ertion of that power, and any. external ob-
ſtruction is not ſuppoſed. It is neceſſary
therefore, to diſtinguiſh carefully between the
quantity of power, and the degree of force,
or of action, or of the manner of exerting
that power: for velocity, for example, from
the higheſt or quickeſt that can be conceived,
to the floweſt, may be divided into infinite
degrees; and all theſe degrees are different
manners of exerting the moving power.
is the effence or fubftance of the
thing, nothing can communicate its power;
for that would be to tranſubſtantiate or to
create : but every power can communicate a
different degree of action or manner of acting,
to another, and therefore it cannot properly
be faid, that any power communicates any
quantity of power to another, but only ſome
certain degree of force or manner of acting.
And the only effects or alterations, which
any power or agent can produce on another,
is to communicate to this other, ſome degree
of its action, or manner of acting.
26. The degree of action communicated, is
always in the ratio of the quantity of the act-
ing to the receiving power. Thus, if any
quantity of moving power communicate any
degree of motion to a cubic inch of the refift-
ing power, or of the elaſtic, it will commu
nicate but half that degree to two cubic inch
es: ſo that the degree communicated does
D 2
23
not

( 28 )
not conſiſt in the abſolute quantity of the act-
ing power, but in the ratio it has to the re-
ceiving power.
do nota
27. This communicated action, or the ef-
fects of different powers, muſt be different
according to the nature or different manner of
acting. Thus, if any degree of motion be
communicated, it cannot be augmented by
the addition of a leſs degree, in the ſame direc-
tion; as the velocity of a ball moving at the
rate of ten miles in an hour, cannot be aug-
mented by the action of a ball moving at the
rate of nine miles in the ſame time. Indeed,
the firſt can receive no impulfe or action from
the latter ; and therefore there can be no ad-
dition of different degrees of motion in the
ſame direction : but it is otherwiſe in the re-
fiſting power.
16 orli bros o'o
28. Though the degree of reſiſtance com-
municated, be always in the ratio of the re-
fiſting power to the receiving, as in the mo-
ving, the effects ariſing from it are different
from what they are in the moving: becauſe it
exerts its action not in one ſingle direction,
as the moving power, but in every
direction.
For example, if any quantity of reſiſting
matter communicate to a quantity of elaſtic
matter, a degree of reſiſtance, as 10, and a-
nother quantity of refifting matter commu-
nicate to another quantity of elaſtic matter, a
degree of reſiſtance as 5; whenever theſe two
quantities of elaſtic matter are contiguous,
their ſeveral degrees of actions muſt be united
in

( 29 )
in the reaction, which is exerted or expand-
ed in all directions; and therefore, in the re-
action, the degree of action between theſe
two, will be equal to 15 degrees of reſiſtance :
For fince the action of reſiſtance is negative
to the other action, and thereby leffens it; it
is evident, that, though the moving power
be leſſened in any degree by a ſtrong action,
it may be ſtill further leſſened by the appli-
cation of a weaker action.
29. However, there ſtill remains a diſtinc-
tion to be obſerved between the effects of the
power itſelf, and of the action communicated
to another thing: for example, any quantity of
elaſtic matter, having any degree of reſiſtance,
or of motion, communicated to it, cannot
communicate a greater degree than what it
has received ; if it communicate the whole
degree to another inch of elaſtic matter, it
cannot communicate a greater degree to half
an inch. It is otherwiſe as to the power it-
ſelf: for, if it communicate a degree, as 10,
to any quantity, it will communicate a de-
gree, as 20, to half that quantity. And it is
likewiſe to be obſerved, that though the de-
gree of communicated action cannot, by being
communicated to a leſs quantity, be increaſed;
yet it may be leffened by being communica-
ted to a greater.
30. If upon further inquiry into the nature
and manner of acting of theſe ſeveral agents, ,
ſome of the moſt general phænomena in na-
ture become plain, and eaſy to our concep-
23VID
tion,

( 30 )
tion, and which have hitherto puzzled the
greateſt philoſophers; it will be a ſtrong ad-
ditional proof of what has been advanced.
My next attempt ſhall be, to ſhew this in
fome inſtances; and before I proceed, I ſhall
only obſerve, that perhaps the chymiſts aim
at the ſame thing I do, in the three princi-
ples which they eſtabliſh, viz. Salt, Sulphur,
and Mercury : By Salt, they may intend the
reſiſting matter or power ; by the action of
which chiefly the parts of matter (as will be
afterwards ſhewn) attract each other, or are
kept in union: By Sulphur, the moving mat-
ter, by which, motion, or that kind of ac-
tion, which is moſt evident to our ſenſes, is
produced; and by Mercury, the elaſtic mat-
ter, by which (like a meſſenger) the action of
one is carried thro' any diſtance to another,
and like Mercury or Proteus, takes or imitates
the action of either of the others: but the
inquiring into the opinions of philoſophers on
this ſubject, is beſide my preſent purpoſe.
POSTSCRIPT.
-0%
IM
AM very
AM ſenſible how difficult it is to con-
vey any new conceptions of things, or
which are contrary to notions confirmed by
long habits. This was the caſe of fir ISAAC
Newton's Theory of Light and Colours. It
was violently oppoſed by ſome of the greateſt
philoſophers at that time ; and every one per-
ceives

(31)
ceives, on his firſt reading of that book, with
what reluctancy he yields to the evidence of
truth, which forces his affent. What can
ſeem more abſurd to common obſervers, than
to be told, that there is no colour in any body
we ſee; that all colours are only in the light,
and that white is made up of a mixture of all
colours ? Tell this to any man not converfant
in that theory, and he'll immediately think,
that you are a fool, or deſign to play the fool;
and yet there is no man, who underſtands fir
ISAAC's book, that can doubt of the truth of
theſe things. After we have been accuſtomed
to the reaſonings and ideas communicated by
fir ISAAC NEWTON, we find no difficulty in
theſe conceptions, which ſeemed at firſt the
moſt difficult to conceive ; and I preſume,
that after a cloſe attention and repeated reflex-
ions, the reader will find the fame eaſineſs
with reſpect to the doctrine here delivered.
I find moſt people ſtartled, when I tell
them, that the reſiſtance of a body at reſt,
or without motion, is performed by ſome ac-
tion in the refifting body. When a body at
reſt, or without motion, reſiſts, does it do any
thing ?--- or nothing? If it do nothing, it does
not reſiſt; if it do any thing, it muſt act ;and
if it act, there muſt be action without mo-
tion. It is ſurprizing, to find it ſo difficult
for a thinking being, to conceive action with
out motion. When a man thinks he does
ſomething, then thinking is acting, or is a
kind of action ; but this action cannot be
con

( 32 )
conceived as conſiſting either in motion, or in
reſiſting, or in reflecting motion : it is a kind
of action different from every one of theſe.
But I find it is expected, that I ſhould ex-
plain the Modus or manner of acting in refift-
ing matter ; otherwiſe it is concluded, that the
whole theory is defective and uncertain. Tho'
I cannot explain the modus, or manner of act-
ing, when I think; I hope none will deny,
that I do or can think: but I will ſay more ;
we cannot explain the modus or manner of
acting of any ſimple power, no not of the
moving power. When a quantity of moving
matter puts another quantity of matter into
motion, what conception have we of the mo-
dus, or of the manner of acting? If it be ſaid,
to be by puſhing or preſſing the body which
it moves ; I muſt aſk again, what idea have
you of puſhing or preſing ? Have you any o-
ther idea, but that the moving body communi-
cates motion to the body which it puſhesor pref-
ffes ? Asto my part, I can form no other concep-
tion of puſhing or preſſing; and if any other can;
I ſhall be exceedingly pleas'd to ſee its modus,
or manner of acting explained: ’till this be
done, I ſhall preſume to ſay, that we may
have as clear and diſtinct a conception of the
modus, or manner of acting in reſiſting mat-
ter, as of the action of moving matter; that
is, that reſiſting matter communicates its acti-
on to the matter on which it acts. I muſt
likewiſe add, that we have no idea of any
thing but of action; and that all ideas ariſe
from

( 33 )
from the communication of ſome kind of actiot
to the thinking thing or being : fimple ideas aa
riſe from the actions of fimple powers, and
complex ideas from the complicated actions
of ſeveral ſimple powers: no ſimple idea can
be explained; as I think is confeſſed by all ;
and the explication of complex ideas, is the
Thewing of what ſimple ideas they are com-
pounded. Let any man ſhew any idea, which
does not evidently ariſe from ſome action or
other, if he can.
In the laſt place, I muſt obſerve, that,
tho' I call that matter or power; elaſtic mata
ter, which reflects any action, or conveys any
action from the acting matter or agent, to
any diſtance from it (being a term uſed by
fir Isaac Newton, and other philoſophers);
yet
the action of this elaſtic matter muſt not
be conceived as in any manner ſimilar to that
of elaſtic bodies, ſuch as a ball of ivory; but
as a kind of action fingular and peculiar to
itſelf, and which cannot be explained by any
fimilitude to the action of any other thing,
no more thản the actions of reſiſting or think-
ing can be explained by any fimilitude to the
action of moving. Therefore, if one ſhould
imagine, the elaſtic matter to conſiſt of in-
numerable ſmall globules, (as of ivory) whoſe
parts being preſſed together, rebound with
the fane force with which they are com-
preſſed; he would have no conception of the
elaſtic matter which I mean. The actions of
E
all

( 34 )
all firſt principles, and the ideas of them,
muſt be all fimple; nothing of ſhape, or of
parts, or of number, or of any thing like
compoſition, can enter into theſe ſimple ac-
tions, or into the ideas of them : for other-
wiſe they cannot be ſimple. In any concep-
tion of globules, they muſt be conceived as
conſiſting of parts; which being preſſed near-
er to each other, endeavour to ſeparate again :
and as this cannot be conceived otherwiſe than
as in motion, ſuch elaſtic power can never re-
flect or continue any other action but that of
motion. Theſe parts which are thus ſuppo-
ſed to contract and dilate, have either the
fame elaſtic power, or not: if they have not,
then an aggregate has a power which no part
of it has: if they have the ſame power, they
muſt be again compounded of others, till we
come at laſt, in conception at leaſt, to ſuch
as are not compounded; theſe, then muſt
have this elaſtic power without any contrac-
tion or dilatation of parts. If it be ſaid, that
this divifion into parts goes on in infinitum ;
and therefore can never be reduced to fingle
parts: in this caſe we muſt ſuppoſe that the
aggregate
has power or action which none of
its parts have; and that the power of reflec-
ting or reacting conſiſts only in number, and
not in the thing itfelf. It is true, that in ma-
chines, and ſuch like aggregates, there is a
kind of compound action, which none of the
parts have ſeparately; and by this the ma-
chine

( 35 )
chine or aggregate becomes a kind of unity,
or tò év, as the Greeks expreſs it); for its ef-
fence is deſtroyed by diviſion, and it no long-
er remains the ſame thing but every one
eaſily perceives, that no machine can be a
ſimple being, nor its action fimple, but is the
complication of the actions of ſeveral ſimple
actions; and therefore the nature of all ma-
chines, and the manner of their acting can
be explained; but the manner of acting of
fimple beings, as before obſerved, cannot be
explained.
Canleg
bowiod bolso
en
C Η Α Ρ. ΙΙ.
Of Æther and Gravitation.
31. SR
31.
IR ISAAC NEWTON, with wondern
ful fagacity, has diſcovered, that Gra-
vitation is an effect of ſome cauſe or agent,
which
operates in
every part of the univerſe
of which we have any knowledge; and he
has deſcribed its manner of acting, ſo far as
can be concluded from the effects: but what
that cauſe is, whether it acts by attraction or
pulſion, he has no where determined. And
tho' in ſeveral parts of his writings in the
laſt editions) he has more exprefly declared
his opinion, that the agent which makes all
badies
E 2

( 36 )
bodies gravitate towards each other, acts by
pulfion; yet the manner he has taken to ex-
plain this pulfion, has not given that general
ſatisfaction which the other parts of his wri-
tings have; and he having at firſt explained
himſelf, as done by attraction, his followers
Have frequently been puzzled, and foreigners
have received a prejudice to the whole of
that doctrine. Suppoſe that gravitation be by
attraction, how can two bodies be ſuppoſed
mutually to draw each other, without ſome-
thing like ſtrings paſſing between them? but
the free motion of any other body between
theſe two, ſhews, that there can be nothing
of that kind between them. Again, the
force of gravitation towards any body being
at every diſtance reciprocally, as the ſquares
of the diſtances, ſeems to ſhew, that gravi-
tation is the effect of fome emanation from
the attracting body: for the force of the e-
manation of any vertue, proceeding from a-
ny body, as a center in ſtrait lines, is at e-
very diſtance reciprocally, as the ſquares of
the diſtances; which is demonſtrated by dr.
Gregory, in the 48th propoſition of the firſt
book, and 57th propoſition of the third
book of his Aſtronomy. But this no way lef-
fens the difficulty: for how can we conceive,
that an emanation or motion from any body,
can make another move towards it. Theſe
difficulties, and ſome others, have prevented
the general reception of a doctrine, which
evidently agrees with all phænomena. If I
can

( 37 )
can fhew then, how gravitation is perform-
ed, ſo as one may be able to form a clear
conception of the ſame, conſiſtently with all
manner of acting, of which we have any
certain knowledge, and founded on the prin-
ciples before explained; I hope to do ſome-
thing that will be aeceptable to the curious.
32. Sir ISAAC ſuppoſes, that there is a
fine ſubtile fluid, or medium, expanded thro
the univerſe, which he calls Æther. This
occupies all the ſpace not filled with other
matter, and permeates all the interſtices or
paſſages, which are in or between bodies.
He brings ſeveral proofs of the exiſtence of
ſuch a medium, in the 18th and 21ſt que-
ries, at the end of his opticks, and in ſeve-
ral other places of that book. Every philo-
fopher almoſt has ſuppoſed the exiſtence of
fome ſuch thing; all agreeing, that it is im-
poſſible to account for the general and con-
ſtant phænomena, without the exiſtence of
ſuch a medium. We have no way of diſco-
vering the exiſtence of any phyſical agent,
thing or being, but by the mediatę or im-
mediate impreſſion it makes on our ſenſes.
We only diſcover the agent by the effects,
and the manner of its acting, by a continued
obſervation of effects. If then from a ge-
neral obſervation of many perpetual phæno-
mena, and of the particularities in them,
they appear to be the effects or action of an
elaſtic agent, (19, 20,) and neceffarily fol-
low, if ſuch an elaſtic agent exiſt; we thero-
by

( 38 )
by have the ſame proof of the exiſtence of
ſuch an agent, that we have of the exiſtence
of reſiſting matter, or of moving matter : for
neither our ſenſes nor our ideas reach to the
things or ſubſtances themſelves. We have no
idea or conception of any thing other than of
its power or force, or of the action or manner
of its exerting that power or force. By the
effects of the reſiſting or moving matter, ei-
ther mediately or immediately on our ſenſes,
we conclude that ſuch powers exiſt; and no
otherwiſe have we any proof of their exi-
ſtence : ſo that I preſume to give the ſame
proof of the exiſtence of æther, (or of an
elaſtic medium) that can be given of the
exiſtence of any thing whatſoever, that does
not immediately ſtrike our ſenſes.
33. Suppoſe then a line of elaſtic matter,
a, b, c, d, e, f, g, conſiſting of any num-
ber of particles or parts; then if any im-
preffion be made, or action communicated
on a, it will communicate the whole of the
impreſſion or action, and the whole force it
received, to b, and b in like manner will
communicate the whole force to c, and c
to d, and ſo on, thro' the whole length of
the line, however long it be: and with what-
ever force a preſſes b, with the ſame force
b in its reaction will preſs a, and ſo c will
preſs b, &c. the reaction will every where
be equal. If you ſay, that a communicates
lefs to b, than it received, and bleſs to c;
the communicated force continually decrea-
ſing

( 39 )
оо
оооо
fing, by reaſon of the reſiſtance of the ſeves
ral parts: I ſay, that
you
have not fufficient
attention to the caution given before (16,
20): for elaſtic matter has no power of re-
ſiſting in itſelf.
34. Suppoſe again, any tri-
angular ſurface, filled with par-
ticles of elaſtic matter, or of æ-
ther, in ſuch manner, that the
number of particles in each rank or line con-
tinually increaſe equally: then whatever de-
gree of action be communicated, by any
power whatfoever, to the fingle particle at
the top, it will communicate one half of
that degree to each of the two particles in
the next rank, and one third of that force
or degree of action to each particle in the
third rank, and one fourth to each particle
in the fourth rank, &c. For, ſince the fin-
gle particle communicates the whole force
or degree of action which it received, to
two particles, it cannot communicate more
than one half to each, otherwiſe it muſt
give what it has not received; nor does it
communicate leſs, becauſe there is no refift-
ance to leſſen it. Then the force or degree
of action, in this caſe communicated to each
particle in each rank, will be as the diſtance
of the rank applied to the force or degree of
action of the firſt particle ; that is, as 1,
3, , , ;, &c. Now it is plain, that the
difference between 1 and i, is greater than
and, and the difference between and ,
is

( 40 )
is greater than between and Ă, and ſo on :
likewiſe, 1:1::2:1, and ; : :: 3 : 2,
and :::4:3. Therefore, theſe conti-
nually decreaſe reciprocally, to an increaſing
arithmetical progreſſion. Then the degree of
force communicated to each particle of the
feveral ranks, will, in the ſeveral ranks be in
the ratio of 'numbers decreaſing reciprocally to
arithmetical increaſing proportionals. Then
by the reaction of the æther, in this triangular
ſurface of it, each particle of the outermoſt
or fartheſt line or rank, from the ſummit or
point, will communicate the degree of force
or of action which it received, to the parti-
cles in the next line or rank within it, to
which the direction of its reaction can go.
This ſecond rank, having its communicated
degree of action thus augmented, will, by its
reaction, communicate its degree of action to
the particles of the line or next rank within
it, in like manner; and thereby this third line
or rank of æther, will have its degree of ac-
tion augmented in the ratio of the firſt and
ſecond lines or ranks; and in like manner
the fourth will be augmented by the addi-
tion of the firſt or outermoft, ſecond and
third; and the fifth by that of the firſt, ſe-
cond, third and fourth. Thus the force or
degree of action of the ſeveral ranks or lines
in this triangular ſurface of æther, being thus
changed by a continued addition of their ra-
tio's, in an order reciprocal or contrary to
the natural or direct order of increaſing ratio's,
the

( 41 )
the ratio of force communicated to the fin
gle particle at the ſummit, will become 15;
the ratio or degree of force communicated to
each of the two particles in the next will be
10; to each of the three next 6; to each of the
four next 3; and that of each of the five out-
ermoſt will be 1: and the differences of de-
grees of action communicated by the reaction
to the particles in each line, from the ſum-
mit or ſingle particle, will be, 5, 4, 3, 2, 1,
or decreaſing arithmetical proportionals.
35. In order to underſtand the nature of
reciprocal ratio's, it is to be obſerved, that as
the direct are the ratio's of quantities greater
than unity ; fo the reciprocal are the ratio's
of quantities leſs than unity; and that unity
is the common meaſure, to which both are
referred. Therefore the ratio's of equidiſtant
terms from unity of fimilar ſeries, the one
increaſing, and the other decreaſing, are al-
ways the ſame. So likewiſe, if any addi-
tion, ſubſtraction, multiplication, or diviſion,
of any number of terms of the direct or in-
creaſing ſeries be made; and a like addition,
ſubſtraction, multiplication or diviſion of the
correſpondent equidiſtant terms from unity,
of the decreaſing or reciprocal ratio; the ram
tio ariſing from ſuch addition, ſubſtraction,
multiplication or diviſion, will in both ſeries
be the ſame. Theſe two ſeries then are pro-
perly thus expreſſed, (&c. *; } î 1, },
1 &c.) that is, 2:1:: 1:1, 3:1::1:5
and 4: 18:1:1 &c. Then 2+3:15:1
F
T.

( 42 )
: + or 5:1::1:5, and the ſum of
all, 10:1::1:*. For the denominators
in the reciprocal, are indexes of the fame ra-
tio's, that the integers or numerators are in
the direct. Therefore the reciprocal ratio's
may be as well expreſſed by negative num-
bers, thus, -2, -3, -4, &c. as by the frac-
tions; they both equally ſhewing the ratio to
unity. Therefore, whatever be the product
of two or more ſeries of increaſing ratio's
from unity, however combined, the fame
product will ariſe from the ſimilar combina-
tion of ſimilarly decreaſing ſeries from unity;
and the one may be ſubſtituted in the place
of the other. But to avoid miſtakes, it muſt
be carefully obſerved, that what is here af-
firmed, is not of the quantities themſelves,
but of their ratio's only.; and this diſtinction
between the ratio's of quantities and the quan-
tities themſelves, is conſtantly to be kept in
mind; for otherwiſe many difficulties may
ariſe, or objections be made to what follows,
only from not obſerving this diſtinction : for
generally, I treat of only the ratio's of quan-
tities, and not of the quantities themſelves.
36. But in the caſe of the triangular ſurface
of æther here put, the æther is ſuppoſed to
be bounded; which cafe really never hap-
pens, becauſe the æther is expanded through
the univerſe: therefore, though I put it for
the more eaſy conception of the ratio of ac-
țion communicated, this fuppofition is in fe-
veral refpects defective in giving a true con-
ception

(43)
ception of the reaction of the æther: and, as
the action of reſiſting matter is negative to all
other power ; the general ſuppoſition of any
action cannot fo clearly ſhew that of the re-
fiſting power. Let us ſuppoſe then, an un-
bounded ſurface of æther; then if any point
be taken in this furface, and the action of the
reſiſting power be communicated from this
point in all directions; theſe directions be-
come ſo many radii from this point. From
the ſame point divide the ſurface into any
number of circles, ſo that their radii be in-
creaſing arithmetical proportionals; the cir-
cumferences of theſe circles muſt likewiſe be
increaſing arithmetical proportionals. Now,
by 'the ſame reaſoning uſed in the caſe of
the triangular ſurface of æther, the ratio of
action communicated to the particles of æ-
ther in each circumference, muſt be in the
reciprocal ratio of the radii, or of the cir-
cumferences themſelves; and the reaction in
the ſame direction or radius, muſt be reci-
procal to increaſing numbers, whoſe diffe-
rences are arithmetical proportionals. But as
this ratio of increaſe of the reaction is fun-
damental in the idea of the manner of act-
ing of the æther; it may be neceſſary to ex-
plain this more fully, in order to give an ad-
equate conception of it. The reaction or re-
flection of action of every particle of æther
(20) is equal in every direction; then if
any
particle b, in any of theſe circumferences be
taken, and two other contiguous particles, a
F2
and

( 44 )
a,
a;
and c, in the ſame circumference, one on
each fide; the action communicated to theſe
three particles being in each equal, the reac-
tion of b, in the direction of the circumfe-
rence, muſt be made null (21) towards
by the equal and oppoſite reaction of and
its reaction towards c, be made null by the
reaction of c: therefore the particles of æ-
ther can have no reaction in the directions of
theſe circumferences. Again, take any num-
ber of contiguous particles, a, b, c, d, &c.
all in the fame radius or direction to the
center, but each in different circumferences
ſince the action of the reſiſting power com-
municated to their ſeveral particles, is reci-
procal to their diſtance from the center, or
is leſs in the ratio of their diſtance; and,
the reſiſting power is negative (21) to every
other
power;
the
power of reacting or re-
flecting any action, muſt be leſs in the
par-
ticles nearer to the center, than in thoſe fur-
ther from it; and conſequently the particles
further from the center, muſt have a ſtrong-
er reaction, or force of reflecting, than thoſe
that are nearer: then there can be no reac-
tion in the direction from the center; for the
ſtronger and contrary action muſt annul the
weaker in contrary directions (21) : therefore
all reaction in the direction of every radius
muſt be towards the center; and being in all
inſtantaneous (21), the action of the far-
theſt diſtant particles muſt ſtrengthen or in-
creaſe the action of the nearer to the cen-
ter,
as

( 45 )
ter. For the action muſt in one inſtant be
communicated to the outmoſt extent, and the
reaction made through the parts in the next
inſtant.
37. Suppoſe in the third place, a cone of
ſuch elaſtic particles or of æther, and that
this cone is divided tranſverſely to its axis,
into any number of parallel ſegments or cir-
cular ſurfaces : in this caſe the content of each
ſegment or circular ſurface is as the ſquares
of their diſtances from the ſummit of the
cone. Then any force or degree of action
communicated from the ſummit, or ſingle
particle at the top, to each particle in each
circular ſurface, will be as the force impref-
ſed upon the first particle applied to the
ſquares of the diſtances, or reciprocally as
the ſquares of the diſtances. And the force
communicated to each particle in one circle,
and to each particle in the next contiguous
circle, is reciprocally as the ſquares of their
diſtances from the top of the cone: that is,
as I, 4, 5, it is, &c. Therefore by a fi-
milar reaſoning to that in the preceding pa-
ragraphs, the force or degree of reaction of
the æther in the ſeveral ſurfaces, will be reci-
procal to a ſeries of increaſing numbers,
whoſe differences increaſe as the ſquares of
arithmetical proportionals, or reciprocal to
theſe numbers 1, 5, 14, 30, 55, &c.
38. In the fourth place, ſuppoſe a particle
of this elaſtic matter placed in the center of
a ſphere of the ſame matter, and that this
ſphere

( 46 )
ſphere be divided into any number of concen-
tric ſpherical ſurfaces. Now, ſince the con-
tents of theſe ſpherical ſurfaces are as the
ſquares of their diſtances from the center,
any
force communicated from the center to
every particle in each reſpective ſpherical ſur-
face, is as the force at the center applied to the
ſquares of their diſtances, or reciprocally as
the ſquares of increaſing arithmetical propor-
tionals; and the reaction will be reciprocal to
an increaſing ſeries, whoſe differences increaſe
as the ſquares of arithmetical proportionals :
for the reaſoning in this and the preceding
cafe is entirely the ſame.
39. Now, fince elaſtic matter communi-
cates any impreſſion or force made upon it, in
the manner above deſcribed ; let there be
any
quantity of reſiſting matter placed any where
in the æther, which is ſuppoſed to extend all
over the univerſe : this reſiſting matter is an
agent continually and neceſſarily acting and ex-
erting force, (8) and muſt therefore commu-
nicate its action or manner of acting, to the
parts of the æther contiguous to it, and they
to others next to them. (20) Therefore calling
any quantity of teſiſting matter a body; and
ſuppoſing a ſpherical body placed in the æther,
and the æther round it divided into any num-
ber of ſpherical ſurfaces, concentric with the
fphere of reſiſting matter : then the force im-
preſſed by the reſiſting agent, which is here
ſuppoſed a ſpherical body, will be communi-
çated to the particles in each ſpherical ſurface

( 47 )
40. Then if
of æther, in a ratio reciprocal to the ſquares
of their diſtances. (38) And therefore by the
reaction as above deſcribed, the elaſtic force
of every particle of æther ſurrounding the re-
fiſting body in its action of reflecting the ac-
tion of any motion, will be leſſened in a ratio
reciprocal to increaſing numbers, whoſe diffe-
rences are increaſing ſquares of arithmetical
proportionals : for the action or force of re-
fifting matter, is to obſtruct or leſſen, or is
negative to the action of all other power or
force.
any moving thing or power or
agent, be placed within this ſphere of æther,
ſurrounding the reſiſting body; it will by the
reaction in the æther of its own action be
preſſed on all ſides by the elaſtic particles of
æther, whoſe force of reaction increaſes reci-
procally, as in the preceding paragraph. There-
fore, that thing will be more preſſed on the
ſide which is from that body, than on the fide
towards it, and muſt therefore approach to-
wards the body, every where with a force
equal to the difference of force of the elaſtic
particles of æther, on the oppoſite ſides of the
thing. But theſe differences are every where
(39) reciprocally as the ſquares of the diſtan-
ces: therefore every body will ſeem to at-
tract another in motion, with a force every
where reciprocal to the ſquares of the diſtan-
ces from that body; though more properly
ſpeaking, this thing is repelled towards the
body, by the elaſtic force of the æther before
deſcribed ;

( 48 )
deſcribed ; or if the æther be put in motion
from any cauſe (as it muſt conſtantly be by the
continued tranſmiſſion of light from the ſun,
planets and ſtars) the reaction of this motion
will be ſtronger on one ſide of a body at reſt,
within the ſphere to which the action of the
reſiſting body is communicated, than on the
other ſide; and thereby this body will be re-
pelled towards the other body, within whoſe
ſphere of æther the action of the reſiſting bo-
dy is communicated.
41. Here again, before I proceed further,
I muſt take notice of an objection which pro-
bably will ariſe from the commonly received
idea of reſiſtance, and which I obſerve is apt
to return, notwithſtanding what has been al-
ready wrote to prevent it. One is apt to think,
that refiſtance is one ſingle act, which only
happens when two bodies in motion, and in
oppoſite directions, meet each other; or when
a ſmall body in motion meets a greater one at
reſt, where after the firſt ſhock they both re-
main at reſt, and all action is ſuppoſed to
ceaſe. Since then (it may be ſaid, reſiſtance
is only a fingle act, whatever impreſſion be
made by it on the æther, it can only be mo-
mentary; and all action between the reſiſting
body and the æther muſt afterwards ceaſe. I
have already endeavoured to explain this (16,
17, 24, 25,) and I ſhall only now repeat, that
the miſtake proceeds from thinking that there
is no action, but what conſiſts in motion; but
as reſiſtance is a power eſſential to one ſpecies
of

( 49 )
of matter (24, 25,) this ſpecies can nevet
ceaſe in exerting this power, or muſt be con-
tinually in action: and as this action of reſiſt-
ance is contrary to, or negative of motion,
nothing of motion can enter the
proper con-
ception of it. Suppoſe that any quantity of
reſiſting matter meet a quantity of moving
matter, and by its action of reſiſting, ſtop
the motion or action of the moving matter;
and that immediately after this momentary
ſtop, the reſiſting matter ceaſes to act or to
reſiſt, muſt not then the moving matter re-
cover its action or motion, ſince there is no-
thing to reſiſt or hinder it? Power and force,
and conſequently action, is eſſential to both
theſe ſpecies of matter; and in this caſe, while
both remain at reſt, they both exert their
force or power: but their actions being con-
trary and equal, and negative of each other,
the degree of action in each becomes =0.
But as there is nothing in the elaſtic
power
contrary to, or negative of either the reſiſting
or moving powers, it equally receives the
action of both; and every part of elaſtic mat-
ter reflects the actions of both, with the ſame
degree of force with which they were impreſ-
fed.
42. Now, ſuppoſing any ſpherical quantity
of refifting matter to be placed in the æther,
the action of the reſiſting matter will be com-
municated in the manner deſcribed (38). If
then any body without motion, be placed
within the ſphere of æther, to which the
G
action

( 50 )
action of the reſiſting matter is communica-
ted; this body can have no motion, either to-
wards the reſiſting matter, or from it, or in
any direction : for ſince the action of reſiſting
matter is negative of motion, and the æther
of itſelf has neither the action of reſiſting
nor of moving, and motion is not ſuppoſed
to be communicated to the æther otherwiſe ;
this body thus placed in the æther, can ac-
quire no motion, but muſt remain in any
place in that ſphere where it ſhall happen to
be placed. But if this body move, or have
the action of moving, or if motion be com-
municated to this ſphere of æther from any
other caufe; then the reflection of the acti-
on of motion, from the ſeveral particles of
æther, will be different : ſo that the reflexion
will be always leſs in the particles nearer to
the reſiſting matter; becauſe the reflexion of
the action of the reſiſting matter, at the ſame
time communicated to theſe particles of e-
ther, is negative to the action of motion, and
greater the nearer theſe particles are to the re-
fiſting matter. Then any thing or body in
this caſe, placed within this ſphere of æther,
will have the action of motion more ſtrongly
impreſſed or reflected upon it, by the æther
on the fide furtheſt diſtant from the reſiſting
matter, than on the ſide neareſt to it: and
the difference of the force of reflexion on
theſe two oppoſite ſides, being every where
within that ſphere reciprocally, as the ſquares
of the diſtance from the reſiſting matter ; that
body

(51)
body will be repelled towards the reſiſting
matter, by a force or degree of velocity, eve-
ry where reciprocal to the ſquares of the dif-
tance from the reſiſting matter.
43. It follows then, that no ſpecies of
matter has in itſelf a power of attracting any
other, or of gravitating towards
any
other ;
but that this apparent attraction or gravitation,
is truly and really performed by pulſion, or
more properly is the effect of the joint actions
of the moving, reſiſting and elaſtic powers :
however, as the Copernican aſtronomers ſpeak
of the motion of the fun and ſtars, tho' they
know that they are ever at reſt; ſo I think it
may be allowed me, to treat of attraction
and gravitation, and to conſider this apparent
action as if it were real; tho' I be perſwaded,
that the notion of attraction and
gravitation
ariſes from a falſe conception of things; and
therefore I ſhall next ſhew, how far this the-
ory agrees with the general phænomena of
attraction and gravitation.
44. Every ſpherical ſolid may be conſidered
as compoſed of ſpherical ſurfaces, and the
ratio of every outer ſurface to the next conti-
guous ſurface within, increaſes as arithmetical
proportionals; for the ratio's between any
quantities increaſe as the differences of theſe
ratio's of quantities, and the differences of
the ratio's of theſe ſurfaces are arithmetical
proportionals: therefore the ratio's of the de-
grees of force, which every ſpherical ſurface
of the body from the center Qutwards, ſhall
G 2
com-

( 52 )
communicate to the ſurface of æther next with-
in it, will increaſe as arithmetical proportio-
nals, or as the numbers 1, 2, 3, 4, 5,&c. Then
the force of reſiſtance communicated to the
ſeveral ſurfaces, by reaction of the æther, will
become as 5, 5+4=9, 5+4+3=12, &c. or
as theſe numbers, 5, 9, 12, 15, 15. There-
fore the force of attraction within any body,
will be as the differences of theſe numbers, or
every where as the diſtance from the center of
a ſpherical body. Here it is to be obſerved,
that ſince the degree of action communicated
to the æther within a ſpherical body, increaſes
directly from the center, and is not leſſened
reciprocally, as without the body; the degree
of action from the reflexion of the æther, is
increaſed by a direct addition of the ratio's,
not by a reciprocal addition, as without the
body.
45. This may be otherwiſe demonſtrated
thus: of all the directions or lines paſſing thro*
any particle of a ſphere, that is the longeſt
within the ſphere which paſſes through the
center; therefore that line in a ſpherical quan-
tity of reſiſting matter, has more reſiſting mat-
ter in it, than any other line of the fame
{phere not paſſing through the center: conſe-
quently the elaſticity of all the particles of
æther in that line muſt be more leſſened than
of thoſe in any other line; and therefore the
Țeaction of every particle of æther muſt be in
the direction or line paſſing thro' the center.
Likewiſe the length of every line within the
ſphere,

( 53 )
Tphere, paſſing thro' any particle of the ſphere
and the center, is longer on that ſide of the
particle on which the center is, than on the
oppoſite fide towards the ſurface, and conſe-
quently the elaſticity or reaction is moſt lef-
fened on that fide; the reaction of
every par-
ticle muſt be towards the center of the ſphere.
Again, fince every line of a ſphere paſſing
thro' the center, is equally divided at the
center, the oppoſite directions of reaction in
every line muſt be equal at the center; and
therefore the reaction of the æther at the cen-
ter muſt be =0. And ſince the differences
of the lengths of the lines paſſing thro' every
particle and the center, on one ſide, and
the oppoſite ſide of that particle, increaſe as
the diſtance of the particle from the center,
the differences of the ratio of force or degree
of reaction in every particle, muſt be as it's
diſtance from the center. The ſame kind of
reaſoning may eaſily be applied to the ſphere
of æther ſurrounding a body of reſiſting mat-
ter, and to which the action of the reſiſting
body is communicated.
46. Then, if any ſpherical body be placed
any where in an unlimited quantity of æther,
and the æther be ſuppoſed to be divided, as
well within the body as without it, into any
number of ſpherical ſurfaces, concentric with
the ſpherical body; the elaſtic force of the æ-
ther will be at leaſt at the center, and will con-
tinually increaſe from the center, but in dif-
ferent ratio's within the body and without it,
Within

(54)
Within the body it increaſes as the ſquares of
the diſtance from the center, ſo that the diffe-
rences between each two ſpherical ſurfaces
within the body, are directly as their diſtance
from the center : but without the ſphere the
elaſtic force increaſes reciprocally, as num-
bers whoſe differences are ſquares of the di-
ſtance of the ſurface from the ſpherical body;
and the difference of force of elaſticity, be-
tween each two elaſtic particles is reciprocally,
as the ſquares of the diſtance from the ſphe-
rical body.
47. Gravitation towards any ſpherical bo-
dy, is directed in lines tending to the center of
that body, and may be repreſented by two dif-
ferent decreaſing progreſſions, the greateſt term
of both which is common to both, and at the
ſurface of the ſpherical body; one of which
progreffions decreaſes towards the center re-
ciprocally, as the diſtance from the ſurface,
and the other decreaſes from the ſurface out-
wards reciprocally, as the ſquares of the di-
ſtance from the ſurface. Thus, if C be put
for the center of any ſphere, S its ſurface, and
A the limit of or extremity,
to which the action of the C-
ſphere is communicated in
ebf
any line paſſing through the center : then if
CS and S A be each equally divided at a
and b, the ratio or degree of gravitation will
be twice as great from S to a as from a to C,
and four times as great from b to S as from A
to b, or in the reciprocal ratio a C of a S
and
S
4
cad

( 55 )
and Ab of S b. Again, if C S and S À
be each divided into three parts, Cc, cd, d S
and Se, ef, f A; then the force of gravita-
tion will be three times greater from S to d
than from C to c; and twice greater from d to
Cg than from c to C; but the gravitation from
e to S, will be nine times greater than from
A to f, and four times greater from f to e,
than from A to f. Therefore,
48. Into whatever number of parts the di-
ſtance to which the action of reſiſting matter
extends, or the force of attraction: the ratio
or force of gravitation in each of theſe parts
may
be found: but if the diſtance be divided
infinitely, the degree of gravitation will be-
come an infinite ſeries, increaſing reciprocally
to the ſquares of the diſtances from the re-
fiſting body.
49. Then an infinite ſeries of proportionals
increaſing reciprocally as the diſtances, or di-
rectly as the diſtances, or reciprocally as the
ſquares of the diſtances, may be in any finite
diſtance; and if the ratio's or differences be-
tween any finite parts of ſuch infinite ſeries be
finite, the diſtance to which all the ſeries ex-
tends muſt be finite. Therefore, if the ratio
of the attraction of the ſun, or of the pla-
nets, can be determined in any finite diſtances,
the diſtance to which the attraction of he
fun and planets extends, may be finite and
may
be determined: therefore it is not uni-
verſally true, that all bodies mutually attract
each other.
50, If

( 36 )
17; and the
2,
2
go. If the velocity (or the times being re-
ciprocal to the velocities) with which any bom
dy paſſes by gravitation, thro' three equal and
continued diſtances, be given, the diſtance to
the limit of attraction, or to the extent of ac-
tion of the reſiſting body (which is ſuppoſed
to attract) on the æther, may be found thus:
fuppoſe the velocities be 36, 45, 55; then
55-45=10, and 45–36=9, fince 10 and 9
differ only by unity; it ſhews, that the di-
ftance where the velocity was 55, was the tenth
of ſuch diſtances from the limit of attraction ;
but if the three velocities be 64, 81, 100,
the differences will be
19
and
19+1=
difference of theſe numbers is then
10, and 17+1=9; which ſhews, that theſe
velocities were acquired in the gth and 10th
of ſuch equal diſtances from the limit of at-
traction: the ſame reſult will be if the velo-
cities were 15, 32, 51; for the velocities are
as the ſquares of the diſtances, and the diffe-
rences of theſe ſquares are as the diſtances.
51. Here it may be obſerved, that ſince
lines are compoſed of points, and ſurfaces of
lines, fo folids of ſurfaces; a triangular ſur-
face may be conceived as compoſed of an in-
finite number of lines, increaſing in an arith-
metical progreffion: fo likewiſe cones may
be conceived as compounded of an infinite
number of ſurfaces continually increaſing, ſo
that the differences between them are increa-
ſing arithmetical proportionals; therefore in-
ſtead
2

( 57 )
ſtead of a ſeries produced by the continual
addition of arithmetical proportionals, or by
the continual addition of the ſquares of arith-
metical proportionals, we ſhall hereafter fay,
a ſeries of the ſquares of arithmetical propor-
tionals, or a ſeries of their cubes. It is true,
that theſe infinite numbers are not perfect
ſquares and cubes of arithmetical proportio-
nals, but as the number of terms increaſe,
they come nearer and nearer to the truth, and
in infinite ſeries they are perfect ſquares and
cubes: for if any triangular ſurface, for ex-
ample, be ſuppoſed to be divided into any
ſmall number of lines, theſe lines muſt have
ſome breadth; then the oppoſite ſides of the
triangle, in which the lines terminate, will
not be ſtrait lines, but like ſo many ſteps of
ſtairs; but the more of theſe ſteps, they
muſt be the ſmaller, and the differences of
the lines leſs; and therefore if the number of
lines be infinite, the ſteps muft vaniſh, and
the ſides become ſtrait lines. Now, if the
parts of the æther be infinitely ſmall (as we
have reaſon to think, and may perhaps after-
wards be proved) there muſt be an infinite
number of ſurfaces of æther in every finite
ſpace; and therefore we may properly ſay,
that theſe ſeries compoſed of increaſing
ſquares are truly ſolids or cubes: for all fimi-
lar folids are as the cubes of their homologous
fides ? And if from obſervation it ſhall ap-
pear, that the ſeries of elaſticity of the æther
(as above deſcribed) at ſeveral diſtances, is
H
per-

( 58 )
4
Perfectly as the cubes of theſe diſtances, the
particles of æther muſt be infinitely ſmall.
See Wallis's Arithmetica Infinitorum.
52. Suppoſe any cubical quantity of reſiſting
matter be divided into any number of ſquare
ſurfaces, all equal to the fide of the cube;
then the action of each of theſe ſurfaces
communicated to the ſurface of æther, conti-
guous to the fide or ſurface of the cubical bo-
dy, will be as foHows: calling each ſquare
fürface, into which it is divided, x, that of
the outermoſt will be 13 of the next
of the next * of the
third of the fourth c. &c. and the acti-
on communicated to the ſurface of æther
contiguous to the cubical body, by the cubi-
cal body, will be equal to the ſum of the
actions of all the ſquare ſurfaces, which
compoſe it. But, by 21 Prop. of dr. Wal-
bis's Arithmetica Infinitorum, the ſum of an
infinite ſeries of the ſquares of arithmetical
decreaſing proportionals is equal to one third
of the ſum of as many furfaces, all equal to
the greateſt; that is, in this cafe of ſo many all
equal to the ſquare ſurface of the cubical body:
conſequently the force of attraction of every
quantity of reſiſting matter, is equal to one
third of the quantity of matter. (3538,
39, 47, 48, 49.) Therefore, we do
53. In ſeveral quantities of matter increa-
fing, as the cubes of arithmetical proportio-
nals, the differences between the quantity of
matter, and force of attraction increaſe con-
tipually, as the cubes of arithmetical pro-
portionals:

( 59 )
portionals: for ſuppoſing three cones or pyra-
mids, A, B, C, of equal height, but the ba-
ſes to be of A as I, of B as 2, and of C as
3; then A will repreſent the force of attrac-
tion, C the quantity of matter, and B the
difference between the force of attraction and
quantity of matter. Now at the points in
their ſummits, all theſe three cones or pyra-
mids are equal, or their differences are = 0;
and if the axis's of theſe cones or pyramids
be equally divided from the points in their
ſummits, and they be likewiſe infinitely con-
tinued; each will be from their ſummits
cubes of arithmetical proportionals increaſing
infinitely: therefore, in ſeveral quantities of
matter increaſing, &c. Sir ISAAC NEWTON,
and ſeveral after him, have obſerved, that the
force of attraction in little bodies, at the point
of contact, is prodigiouſly greater, in propor-
tion to their bulk, than that of great bodies
at their ſurfaces; but I know not that any
have aſſigned the reaſon of this, or have
yen a rule for diſcovering theſe differences.
54. If then three homogeneous bodies, in-
creaſing as the cubes of arithmetical propor-
tionals, be taken, and the force of attraction
of each of theſe at their furfaces, or at any
equal diſtance from their ſurface, be diſcove-
red; the force of attraction of all other bo-
dies homogeneous to them, may be diſco-
vered by a ſimilar method to that in Par. 50.
Experiments perhaps may be contrived on.
theſe principles, to diſcover whether bodies
H 2 O
be
gle

( 60 )
be homogeneous or not, and whether there
be different ſpecies of reſiſting matter, (12)
differing in their force of attraction, as the .
rays of light in their refrangibility.
55. The diſtance, extent or radius of the
ſphere of æther, to which the action of
any
body or quantity of refifting matter is com-
municated, is much longer in little bodies, in
proportion to their bulk, than in great bodies:
for the extent or number of terms of any
fe-
ries decreaſing, as the cubes or as the ſquares
of decreaſing arithmetical proportionals, is as
the cube root or ſquare root of the higheſt or
firſt term of each ſeries. And this holds true
in infinite ſeries as well as finite; for exam-
ple, ſuppoſe two quantities, one as 100, the
other as 300; their force of attraction at the
ſurface is as 33 and 100, and the extent of
their attraction nearly, as 6 and 10. Again,
if the quantities of reſiſting matter be as 300
and
3000, their force of attraction will be as
100 and 1000, and the extent of their at-
traction as 10 and not quite 32.
56. Suppoſe any body or quantity of re-
Gifting matter, or of moving matter, or of both
reſiſting and moving matter, mixed in one
body, placed within the ſphere of æther,
to which the action of reſiſtance of any other
body is communicated, and that motion by
any means be communicated to the fame
ſphere (42); then the firſt body will appear
to be attracted, or to gravitate towards the
quantity of reſiſting matter: and tho' theſe
apparent actions of the attracting and gravi-
tating

(61)
gating bodies, really ariſe from the ſame cauſe
yet the force of gravitation in different gravi-
tating bodies, may be very different from the
force of attraction in the fame bodies. For
gravitation is cauſed by the action of the æ-
ther on every particle or part of the gravita-
ting body, on the parts of the moving matter
contained in that body as well as on the re-
fiſting; and tho' there be different ſpecies of
reſiſting matter, the action of the æther may
be equal on all of them, and they may all e-
qually gravitate ; but the force of attraction in
different bodies, is only as the reſiſting matter
in theſe bodies; neither is it as the quantities
themſelves: therefore, by obſerving the dif-
ferences of attraction and gravitation in the
fame bodies, and by contriving proper experi-
ments for that purpoſe, or perhaps by obſer-
ving the phænomena of the great heavenly
bodies; the quantities of reſiſting matter and
moving matter in theſe ſeveral bodies, or in
the great heavenly bodies, may be diſcovered, ,
and whether there be different ſpecies of re-
fiſting matter. Here, I ſuppoſe, that the æ-
ther acts upon every part or particle of bodies,
and freely permeates between and round all
the parts of every body: it is beſide my pre-
ſent purpoſe to prove this
, but pethaps it may
be afterwards done, when it can be ſhewn by
what power, force or action, the parts of bo-
dies cohere.
57. I ſhall next proceed to fhew, the
joint acțion of two diſtinct bodies or quanti
ties

(( 62 )
or 2 X.
that of 33
ties of refifting matter, on the æther 'round
them, or on the æther between them and on
their outer fides. But, to make this the
more clear to readers, who have not a di-
ſtinct notion of reciprocal ratio's, I ſhall firſt
obſerve, that if there be
any force or action of any A_3_23_B
power decreaſing in the
line A B reciprocally, as the diſtance from A;
then if that line be divided equally in 2, the
force in 2 B will be of that in A 2;
but if the diſtance be taken from B, and
B 2 be I or *, 2 A will be 2
If the line be divided into 3 parts, as A 3,
33, 3B; then if the diſtance be taken from
A, and the force in A
3
be 1,
will be i, and that of 3 B will be that
is, reciprocal to the diſtance from A: but if
the diſtance be computed from B, and the
force in
3
B be 1, that of 33 will be 2,
and of 3 A will be 3, directly as the di-
stance from B; and ſo in like manner into
whatever number of parts the line A B is
divided. Therefore the direct ratio's may
be well ſubſtituted in the place of the reci.
procal: for it is evident, they are the ſame
confidered in a different manner; this is true
not only in ratio's directly or reciprocally as
the diſtances, but in ratio's likewife as the
çubes or ſquares of the diſtances, and in
any
ſeries of decreaſing or increaſing ratio's; for
the ſame are increaſing ratio's, if the ſmalleſt
term be the firſt and be made unity, which
are

( 63 )
187)
are decreaſing when the greateſt term is put
firſt, or made unity, and thereby becomes re.
ciprocal to the former.
58. If two equal ſpherical bodies be pla-
ced within the diſtance, to
which the actions of the
reſiſting matter in each ex-
tend, or within each other's
ſpheres of attraction; the
æther will have its elaſtici-
ty lefſened by both, in a
ratio reciprocal to the cubes
of the diſtances from each,
as in the margin.
Let there be two quanti-
ties of reſiſting matter, whoſe
force or action on the con-
tiguous ſurface of æther in
each, is equal to 1240, and
that theſe two bodies are
placed at the extremity of
each other's ſpheres of at-
traction; then the æther
between theſe two bodies
muſt have its elaſticity lef-
fened, in a ratio reciprocal
to the cubes of the diſtances
of each, or in the order and
ratio of the numbers 1240,
1015, 819, &c. in the two
firſt lines of numbers; and
the elaſticity of the æther is
lefſened by the action of both theſe bodies,
221,
5,
153,
34,
408, 425, 476, 561, 680, 833, 1020,
91, 140, 204, 285, 385, 506, 650, 819, 1015, 1240,
17, 51, 85, 119, 153, 187,
17, 51, 85, 119,
34. 34, 341 349
1240, 1015, 819, 650, 506, 385, 285, 204, 140, 91, 55, 30, 14,
1241, 1020, 833, 680, 561, 476, 425, 408, 425, 476, 561, 680, 833, 1020, 1241,
17,
30, 55,
1020, 833, 680, 561, 476, 425, 408,
221, 187, 153, 119, 85, 51,
187, 153, 119, 85% 51, 17,
342 343 34, 34; 34; 3.4.3
5, 14,
1,
25

( 64 )
ås the ſums of the terms of theſe two lines
of numbers, or as the numbers 1241, 1020,
833, &c. in the third line of numbers : but
the fums of the terms of two equal oppoſite
progreſſions, each increaſing the contrary
way,
as the cubes of the diſtances, are as
the ſquares of the diſtances from the middle
point; and the differences between theſe
terms increaſing as the ſquares of the di-
ſtances are directly as the diſtances, or as
221, 187 in the fifth line, or are arithmeti-
cal proportionals.
59. The greateſt force of the elaſticity of
the æther between two equal bodies, is in
the middle point between them: for the ſum
of the terms of two oppoſitely decreaſing e-
qual progreſſions, continually decreaſe to that
point from the greateſt point of each pro-
greffion; and the ſum of the terms in this
caſe, is the ratio in which the elaſticity of
the æther is leffened : therefore a third ſmall
body, placed any where between this middle
point and either of the bodies, muſt be re-
pelled and gravitate towards that body. But
it is to be obſerved, that ſuch third bodies can
only gravitate towards either of the other
two, which have their abfolute force of at-
traction leſs than that compound force at the
diſtance at which the third body is placed :
for if the abſolute force be greater, they wil
likewiſe attract the other, and a ſmall body
placed exactly in the middle between two
equal large bodies, will remain at reft.
60. This
ز

( 65 )
60. This middle point between equal boa
dies, is called the Limit of their ſeveral at-
tractions: and to find the limit of attraction
between unequal bodies, which by any force
are kept at the ſame diſtance, firſt find the
diſtance from the greater body, at which the
force of its attraction is equal to the abſolute
force of the leſs body; then if the fmaller bo-
dy be placed nearer to the greater, or at that
diſtance, there is no attraction to the ſmaller bo-
dy; but if it be placed further from the greater
body than this diſtance, then the middle di-
ſtance between the ſmaller body and this di-
ſtance, is the limit of attraction between the
two unequal bodies : for from that place where
the force of attraction of the greater body, is
equal to the abſolute force of attraction of the
tmaller body, the elaſticity of the æther in the
ſpace between this place and the ſmaller body,
is lefſened in the ſame manner as between
equal bodies.
61. If two bodies, a greater and a ſnaal-
ler, be ſo placed, that the attraction of the
greater body, at the diſtance at which the
ſmaller is placed, be greater than the abſo-
lute force of the ſmaller, then this fmaller
body cannot attract a third body, placed any
where between them ; but if the ſmaller bo-
dy be removed to a greater diſtance, then a
third little body may be ſo placed between
them, as to be attracted by the ſmaller body,
and the diſtance at which the ſmaller body
can attract a third, will always increaſe as its
I
di-

( 66 )
diſtance from the greater body increaſes. This
may be of uſe to explain many phænomena
among ſmall or little bodies, where the di-
ſtance between them is continually changing,
or is by ſome force or other changed.
62. If two ſpherical bodies be retained by
any force within the ſpheres of each other's
attraction, at the ſame diſtance, ſuch as that
a third body at ſome diſtance or other may
be
attracted to either one of them; and that a
ſurface be ſo extended from the limit of their
ſpherical attractions, in the line connecting
their centers, that the ratio of the diſtances
of every point in that ſurface to the two bo-
dies be the fame, as the ratio of the diſtance
of the limit of attraction in the line connect-
ing their centers to the fame bodies; then a
third little body placed any where from the
point of limit in this furface, will be attract-
ed towards this point of limit : and if the
little body be placed any where out of this
ſurface on either ſide of the line connecting
the centers of the greater bodies, the little bo-
dy will be attracted towards that of the two
greater bodies, between which and that fur-
face it is placed: but this little body will not
move in a ftrait line to the center of that bo-
dy, but in a curve line, whoſe curvature con-
tinually decreaſes as it approaches to that bo-
dy. This paragraph is to be underſtood with
this limitation, that the third little body be
bodo
b placed

( 67 )
placed in the ſurface extended from the point
of limit, ſo as to be in ſome ſenſe really be-
tween the two great bodies; that is, ſo as
that a line from the center of the third little
body drawn to the center of the greateſt, do
not interfect that ſurface.
63. Therefore if two unequal bodies be
kept at the fame diſtance, a little body no
where gravitates to the center of gravity of
theſe two bodies.
64. If two ſpherical bodies be ſo far pla-
ced within the ſphere of each other's attrac-
tion, that it extends beyond the other body;
then the force of gravitation of a third little
body to either one of them, while in the
line paffing through the centers of the two
bodies, is reciprocally as the diſtance from
that body to which it gravitates, or directly
as the diſtance from the limit, while it is
between the two bodies, but reciprocally as
the ſquares of the diſtances, when on the O-
ther ſide of either of them : the force of at-
traction of each of theſe two bodies on the
oppoſite ſide to each other, is increaſed in
the ſame manner, as if their quantity were
increaſed by a quantity of reſiſting matter,
equal to the force of the other at the di-
ſtance at which the other is placed. Thus,
ſuppoſing the abſolute force of each of theſe
two bodies to be 1240, and that the bodies
were placed within the ſphere of each o-
ther's attraction, as theſe numbers are in the
I 2
example

( 68 )
ز
4.
42
43
69, 115, 161, 274, 232, 194, 160, 130, 104,
OT,
1012, 1035, 1104, 1219,
1380, 1106, 874, 680, 520, 390,
42,
232,
38,
4,
46,
42,
42
69, 05,
46,
23.
46,
239
9045, 1240, 1015, 819, 650, 506, 385, 285, 204, 140,
1106, 1380, 1219, 1104, 1035, 1012, 1033, 1104, 1219, 138
40,
115,
46,
9', 140,
274,
example in the margin; where the firſt and
fecond lines of numbers
are as the ſeparate forces
of theſe two bodies, at
the ſeveral diſtances ;
the third line is as their
united force at the fame
diſtances; and the lines
under it fhew the dif-
ferences between the
terms of this united
force, and the force
wherewith a third body
gravitates to either of
them.
65. But in a circle
drawn from one body,
as a center through the
center of the other, the
force of the æther in-
creaſes reciprocally, as
the cubes of the di-
ſtances from the body
through which the cir-
cle paſſes, but is at all
theſe diſtances further
leſſened equally, by the
force of the central bo-
dy at that diſtance. Thus
in the example in the
margin, the force of the
central body on the body
through

( 69 )
140, and
thro' which the circle paſſes, is
therefore their united force there is 1240 +
140= 1380, and at ſeveral diſtances from this
body equidiſtant from the other, it is, 1015+
140 = 1155, 819 + 140=959, 650 + 140
=790, &c. then the force of gravitation in
this circle to the body through which it paſſes,
is the ſame every where, that it would be to
that body were it placed fingly by itſelf; be-
cauſe the differences between the terms, are
in both caſes the fàine.
66. It is likewiſe evident from the numbers
in 58 and 64, that the differences of the elaf-
ticity of the æther in the line paffing through
the centers of two bodies, placed within the
fphere of each others attraction, are different
from what they are when either of the bodies
are placed fingle; and if they remove from
each other, decreaſe in the ſpace between theſe
bodies reciprocally, as the cubes of the di-
ſtances of the other from that body: for theſe
differences are made by a continual addition
of the cubes of an arithmetical progreſſion;
and therefore, that the differences of the force
of attraction in the ſame caſes decreaſe reci-
procally, as the ſquares of the fame diſtances:
for the differences of differences increaſing as
the cubes are as the ſquares. But ſince the
differences of the elaſticity of the æther in
the ſame line, but on the other ſides of theſe
bodies, increaſe reciprocally, as the cubes of
the diſtances in the ſame caſe; the difference
of the force of attraction will be reciprocally,
as

( 70 )
as
the ſquares of the diſtances from either bo-
dy: therefore, as two bodies approach to each
other, the force of their attraction in the line
paffing through their centers, decreaſes in the
ſpace between them reciprocally, as the ſquares
of their diſtances; but on the other ſide of
them increaſes reciprocally as the ſquares of
their diſtances.
67. Hence the gravitation of the moon in
one half of her orbit, from the quadratures
to the oppoſition, and from the oppoſition to
the oppoſite quadrature is increaſed every
where reciprocally, as the ſquares of the earth's
diſtance from the fun; but in the other half
of her orbit, her gravitation is decreaſed every
where reciprocally, as the ſquares of the earth’s
diſtance from the fun: and the moon gravi-
tates in her conjunctions, towards either the
fun or the earth, not reciprocally to the ſquares
of the diſtances, but reciprocally to the di-
ftances themſelves,
68. I ſhall, in the laſt place, apply this
theory of the æther and of gravitation to a
moſt remarkable phænomenon, which puzzled
all the philoſophers till fir ISAAC NEWTON
explained it; I mean, the tides of the fea.
Any fluid on the ſurface of the earth will be
lefs preſſed in the places and near them) where
the ſurface is cut by a line paffing thro' the
centers of the moon and earth, than where
the furface is cut by a plain perpendicular to,
that line, and paſſing thro' the center of the
carth; for the elaſticity of the æther being
every

( )
every where equally leſſened, on the ſurface
of any ſpherical body, by the reſiſting matter
of that body, there can be no difference occa-
fioned by it, in any part of the ſurface: but
the elaſticity of the æther at the ſurface of the
earth next the moon, is more lefſened by the
refiſting matter in the moon, than at the di-
ftance of the earth's center from the moon,
and more at the center than at the ſurface
fartheſt from the moon : but of any
three
terms of a progreſſion, increaſing as the cubes
of arithmetical proportionals, twice the mid-
dle term is leſs than the ſum of the firſt and
third term ; therefore, the two oppoſite fur-
faces of the earth, cut by a line paſſing thro'
the centers of the earth and moon, will be
leſs preffed than any two oppoſite ſurfaces of
the earth, cut by a plain perpendicular to that
line, and paſſing thro' the center of the earth;
and if by any means the preſſure of the æther
on the oppofite ſides of a ſpherical body be
unequal, (47) it muſt become on each ſide e-
qual to half the ſum of the preſſure of both
the oppoſite fides, by the point of equal pref-
ſure, in the body when fingle, being moved
in the line connecting the centers of the two
bodies towards the fide which is leaſt preffed.
This perhaps may appear more plainly, by
obſerving the ratio's of elaſticity of the æther
in Par. 64, 65, thus:
1035

( 72 )
1039
T104
1219
680
1380 1106
874
161
274 232 194
69
115
in
799 959
1155
1380 1155 959 790
169 196
225 225 196 169
where the firſt line of numbers fhews the ra-
tio of elaſticity of the æther on both ſides of
one of the bodies, and which at the diſtance
of its center from the other body is = 1380,
and at every two equal diſtances from the
center, are 1219 +1106=2325, 1104 + 874
=1978, 1035 + 680=1715. The ſecond
line Thews the differences of the elaſticity of
the æther on each ſide of the ſame body,
equal diſtances in that line, or the ratio of
gravitation, viz. 161 + 274 = 435, 115+
232 = 347, 69 + 194 = 263. The third
line ſhews the ratio of elaſticity at the ſame
diſtances in the ſpherical ſurface, every where
equally diſtant from the center of the other
body, where 1155 + 1155 = 2310, 959 +
959 = 1918, 790 +790=1580. And the
laſt line ſhews the ratio of gravitation in the
ſame ſpherical ſurface, and at the ſame
diſtances 225 + 225
= 450, 196 + 196
= 392, 169 + 169 = 338.
greater than 2310, 1978-is greater than 1918,
and
1715 is greater than 1580: therefore the
elaſticity of the æther is more leſſened in the
line connecting the centers of two bodies, than
in the ſpherical ſurface in parts æquidiſtant
from the other body. Again, 435 is leſs
than 450, 347 is leſs than 397, and 263 than
338, or the ratio or force of gravitation is al-
this
Now 2325 is

(73)
Ways greater at the ſame diſtances in the ſphe-
tical ſurface, every where æquidiſtant from
the other body, than in the line connecting
the centers of the two bodies; and in diſtan-
ces near the center of the body thro' which
this ſpherical ſurface paſſes, it coincides with
a plain normal to the line paſſing thro' the
centers of the two bodies:
So far as I have now gone, I think fufficient
to ſhew the agreement of this theory with fe-
veral general phænomena, and may ſerve to
fhew the method of applying it to others, and
to the peculiarities of particular caſes, when
any fhall think proper to take the trouble of
doing it. I am perſwaded, it might have
been put into a ſtrictly mathematical demon-
ftrative method, by feparating the definitions,
axioms, and lemmata from other ſciences into
their proper order, and by deducing the the-
orems from thence; but I was of opinion,
that the method which I have taken, is more
proper for conveying new conceptions, and
ſuch as have not been before received: nei-
ther could that method have been purſued
within the compafs I had ſet to myſelf. Be-
fides, I believe, that the evidence of the truth
of it is much ſtronger, by fhewing its agree-
ment with nature in every inſtance, than by
the moft pompous demonſtration : for how
often have the greateſt men erred in their de-
ductions in this method. For this reaſon, I
had a ſtrong inclination to have thewed the
K
con-

( 74 )
conformity of this theory with the motion of
the planets, by Thewing in the phænomena
of their motion, the force and ratio of the mo-
ving power; and likewiſe in many phænome-
na obſerved by fir ISAAC Newton; in his
Optics, by which, I think, I might have il-
luſtrated many things not touched in fir Is A-
Ac's theory; and more particularly to have
given (if I be not much deceived) a new
theory of the moon : but I have too good
reaſon to conclude, that in my preſent cir-
cumſtances I ſhall never be able to accompliſh
it. I thought, however, it may be of ſome
uſe to give theſe hints to the learned, which
I have been able in ſome meaſure to digeſt,
that thereby others, more capable than my
ſelf, may improve them to the benefit of the
publick. Sir Isaac has taken wonderful
pains, and many of his followers fince have
been indefatigable in applying his theory of
the moon to practice ; but after all, I do not
find that they have been able to form tables fo
uſeful in practice as was expected, and which
in all caſes agree with obſervation : I may
therefore be allowed to ſuſpect, that his the-
ory.
is in ſome meaſure defective.
Since theſe ſheets were ſent to the preſs, I
obtain’d mr. Flamſteęd's Hiſtoria cæleſtis'; and
as one gạeat advantage of the doctrine above
deliver'd, is, that it gives an eaſy and certain
method of forming equations for the planets
motions and orbits; which by all other me-
thods, which I have ſeen, ſeems to be very
difficult

( 75 )
difficult and perplexing: I form'd equations
for the earth, fo far as to aſſure my ſelf, by
ſeveral calculations in different parts of her or-
bit, that this theory agrees with the phæno-
mena to as great an exactneſs as I expected.
If I be not much miſtaken, this theory and
mr. Flamſteed's, obſervations, will mutually
prove the accuracy of each other, I have
fallen (I think) on a method in proving this,
independent of refractions and of the latitude,
different from that which mr. Flamſteed takes
in his prolegomena, and which has one ad-
vantage above his, that it is leſs complicated,
requires fewer data or things to be known,
and conſequently is leſs ſubject to error.
Some thoughts may have occurred to my
imagination in thinking ſo long as I have al-
ready on this ſubject, which may not readily
to men of more ſkill and knowledge. Si De-
us nobis hæc otia fecerit, that I could
be enabled
to digeft into order, and demonſtrate theſe
thoughts without prejudice, or rather with
ſome advantage to thoſe cares which every
man ought to have near his heart, and which
fpeculative ſtudies are apt to make him neg-
lect; I ſhould think it the greateſt happineſs
that can befal me in the laſt ſtage of my life,
to be thus uſeful with the greateſt pleaſure to
.
my ſelf
Namque erit ille mibi ſemper Deus: illius arama
Sæpe tener noſtris cb ovilibus imbuet agnus.
F Ι Ν Ι
S.




c
Colden, Caldkwallader
1746
co