MECHANIC S. 
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t ied on to’an infinite feries of folutions, in each of which 
the fame precife difficulty will recur, without our at all 
approaching to the removal of it. Whence, according to 
the mathematical doctrine of ultimate ratios, not even an 
infinite feries, were that poflible in this cafe, could remove 
it. We mull:, therefore, flop foinewhere, and fuppofe the 
requifite motion to be imparted to the'fuppofed fubtle 
matter, by fomething which is not matter ; i. e. fince God 
is the ultimate author of all motion, we mult fuppofe him 
to be immaterial.” 
Equilibrium may be defined generally, as an equality of 
weights, powers, or forces, of any fort. Bodies at rcjl are 
in a Hate of equilibrium, when they are folicited by va¬ 
rious forces in different directions in fucli a manner as to 
be completely balanced, and have no tendency to move 
in any direction. Bodies in uiotion are in a ftate of equi¬ 
librium, when the refinance to motion and the power pro¬ 
ducing it are fo adjufted, that the refult fhall be uniform 
motion. An accurate knowledge of both kinds of equili¬ 
brium is indifpenfably neceffary, in order that the theory 
may be applied to good practical purpofes. 
We may now define fomewhat more diftinCHy the 
fcience of Mechanics ; it comprifes the doCtrine of the 
reft, the equilibrium, and the motion, of bodies. It may 
be divided into Mechanics, properly fo called, and Hy¬ 
draulics ; the firft comprifes Statics, which has for its ob- 
jeCI the balanced reft of folid bodies ; and Dynamics, 
which confiders the motion of folid bodies. The latter 
comprifes Hydroftatics, which relates to the refting equi¬ 
librium of non-elaftic fluid bodies •, and Hydrodynamics, 
which treats of fuch bodies in motion. To thefe mult 
likewife be added Pneumatics, which comprehends the 
doCtrine of the weight, preifure, and effects of elaliic 
fluids, as air, &c. 
Of the LAWS of MOTION. 
The firft law of motion is, “ That a body always per¬ 
feveres in a ftate of reft, or of uniform motion in a right 
line, till by fome external influence it be made to change 
its ftate.” That a body, of itfelf, perfeveres in its ftate 
of reft, is matter of molt common and general obferva- 
tion, and is what fuggefts to us the paflive nature of body ; 
but that it likewife, of itfelf, perfeveresin its Itatd of mo¬ 
tion, as well as of reft, is not altogether fo obvious, and 
was not underltood, for fome time, by philofophers them- 
felves, when they demanded the caufe of the continuation 
»f motion. It is eafy, however, to fee that this laft is as 
general and conftant a law of nature as the firft. Any 
motions we produce, hereon the earth, foon languifli,and 
at length vanifh ; whence it is a vulgar notion that, in 
general, motion diminifhes and tends always toward reft. 
.But this is owing to the various refiftances which bodies 
here meet with in their motion, efpecially from friftjon, 
«r their rubbing upon other bodies in their progrefs, by 
which their motion is chiefly confumed. For when, by 
any contrivance, this -friction is much diminifhed, we al¬ 
ways find that the motion continues for a long time. 
Tiius, when the friction of the axis is leflened by friCiion- 
wheels applied to it, and turning round with it, the great 
wheel will fcmetimes continue to revolve for half an hour ; 
and, when a brafs top moves on a very fmall pivot on a 
glafs plane, it will continue in motion very fmoothly for 
a great number of minutes. A pendulum, fufpended in 
an advantageous manner, will vibrate for a great while, 
notwithttanding the reiiftance of the air. Upon the whole, 
it appears, that, if the friction and other refiftances could 
be taken quite away, the motions would be perpetual. 
But what lets this in the cieareft light, is, that a body 
placed on the deck, dr in the cabin, of a (hip, continues 
there at reft while the motion of the fhip remains uni¬ 
form and (teady ; and the fame holds of a body that is 
carried along in any fpace that lias, itfelf, an uniform 
motion in a right line. For, if a body in motion tended 
*o reft, that which is in the cabin of a fhip ought to fall 
lback towards the item, which would appear as iurprifing, 
when the motion of the fliip is uniform and fteady, as iP 
the body ftiould, of itfelf, move towards the ftern when 
the fiiip is at reft. It is for this reafon that the uniform 
motion of the earth upon its axis has no effect on the mo¬ 
tion of the bodies at the furface ; that the motion of a 
fliip carried aucay with a current is infenfible to thole in 
the fliip, unlefs they have an opportunity to ciifcover it 
by objects which they know to be fixed, as the fliores, 
and the bottom of the fea, or by altronomicai obferva- 
tions; and that the motions of the planets-and comets, in 
the free celeftial fpaces, require no new impuiles to per¬ 
petuate them. 
It is a part of the fame law, that a body never changes 
the direction of its motion, of itfelf, but by fome exter¬ 
nal influence 01 ly ; and it is as natural a confequence of 
the paflive nature of body, as that it never changes its 
velocity of itfelf. As body has no felf-motive power, or 
fpontaneity, if it were to change its direction, how could 
it determine itfelf to any one direClion rather than to an¬ 
other? This part of the law is likewife confirmed by' 
conftant experience. If upon any fmooth plane a globe 
of an uniform texture be projected, it proceeds always in 
a right line, without-turning to either fide, till its motion 
be extinguifhed by the friction of the plane and refin¬ 
ance of the air. It is true, that, in certain cafes, a ball 
proceeds upon a billiard-table firft in a right line, and, af¬ 
terwards, returns of itfelf a little way in the fame right 
line; but this arifes from the ball’s having a motion upon 
its axis, with a direction contrary to that of its progreflive 
motion on the table ; which, when the progreflive mo¬ 
tion is deflroyed by the friction, brings the ball back 
again, till this motion is likewife deflroyed by the fame 
friction. When a ball is projected in the air, its gravity 
indeed bends its motion into a curve, but it continues to 
move in a plane of its firft projection perpendicular to tha 
horizon, without turning to either fide of that plane ; 
unlefs in fome cafes, when, becaufe of its motion upon 
its axis, the re-a&ion of the air makes it deviate fome- 
what from it. If bodies changed the direction of their 
motion of themfelves, they could not continue at reft in 
a fpace that is carried uniformly forward in a right line ; 
as they are always found to do. As body, therefore, is 
paflive in receiving its motion and the direction of its mo¬ 
tion, fo it retains them or perfeveres in them, without 
any change, till it be aCted upon by fomething external. 
This law is now generally received upon the beft evi¬ 
dence, but was not clearly underftood even fo lately as 
in Kepler’s time. From this law alfo it appears, why 
we enquire not, in philofophy, concerning the caufe of 
the continuation of the reft of bodies, or of their uniform 
motion in a right line; but, if amotion begin, or if a 
motion already produced is either accelerated or retarded, 
or if the direction of the motion is altered, an enquiry 
into the power or caufe that produces this change is a 
proper fubjeft of philofophy; the chief bufinefs of which 
(as fir Ifaac New'ton obferves) is to difcover the powers 
that produce any given motions; or, when the powers 
are given, to trace the motions that are produced by them. 
The fecond general law of motion is, “ That the change 
of motion is proportional to the force imprelfed, and is 
produced in the right line in which that force aCts.’* 
Thus, when a motion is accelerated, as that of a heavy 
body defeending in the vertical line, the acceleration is 
proportional to the power that ads upon the body. If a 
body defeend along an inclined plane, the acceleration of 
the motion along the plane is proportional, not to the to¬ 
tal force of gravity, ,but to that part only which ads in the 
direCIion of the plane, as wiL) better appear when we com® 
to treat of the refolution of motion. When a fluid aCts 
upon a body, as water or air upon the vanes of a mill, or 
wind upon the fails of a fliip, the acceleration of the mo¬ 
tion is not proportional to the whole force of thofe fluids, 
but to that part only w hich is imprefled upon the vanes or 
fails, which depends upon theexcefs of the velocity of ths 
fluid above the velocity which the vane or fail has already 
acquired; 
