114 M O T 
firft, there mud be a fupply from fome foreign caufe; 
which in a perpetual motion is excluded. Or, fecondly, 
all refinance from the fridlion of the parts of matter mtift 
be removed ; which necefiarily implies a change in the na¬ 
ture of things'. For, by the fecond law of nature, the 
changes made in the motions of bodies are always pro¬ 
portional to the imprefled moving force, and are pro¬ 
duced in the fame diredlion with it; no motion then can 
be communicated to any engine, greater than that of the 
firft force imprefled. But, on our earth, all motion is per¬ 
formed in a refilling medium, and mull, therefore, of ne- 
ceffity be retarded ; confequently, a confiderable quantity 
of its motion will be fpent on the medium. Nor is there 
any engine or machine in which all fridlion can be avoid¬ 
ed f there being in nature no finch thing as exadl fmooth- 
nefis, or perfect coneruity j the manner of the cohefion of 
the parts of bodies, the final 1 proportion the folid matter 
bears to the vacuities between them, and the nature of 
thofe conftituent particles not admitting it. This.fric- 
tion, therefore, will alfio in time fenfibly diminilh the im- 
prelfed, or communicated, force ; fio that a perpetual mo¬ 
tion can never follow, unlefis the communicated force be 
fo much greater than the generating force, as to recom- 
penfe the diminution made, therein by all thefe caufies : 
but nil dnt quod non habet; and the generating force can- 
' not communicate a greater degree of motion than it hath 
itfielf. Or, thirdly or laltly, there mull be fome method 
of gaining a force equivalent to what is loll, by the artful 
dilpolition and combination of mechanic powers; to which 
laft point, then, all endeavours are to be directed ; but 
how, or by what means finch force lliould be gained, is Hill 
a myltery ! The multiplication of powers or forces, it is 
certain, avails nought; for what is gained in power is Hill 
lolb in time, fio that the quantity of motion Hill remains 
the fame. This is an inviolable law of nature ; by which 
nothing is left to art, but the choice of the feveral combi¬ 
nations that may produce the fame eftedl. 
Although it is allowed, that, by the refolution of force, 
there is a gain orincreafe of the abfolute quantity of force, 
as the two forces in the fides of the parallelogram taken 
together exceed the force in the diagonal which is re- 
folved into them, yet you cannot proceed refolving mo¬ 
tion in infinitum by any machine whatfoever; but thofe 
you have refolved mull be again compounded, in order to 
make a continual movement, and the gain obtained by the 
refolution will be loft again by the compofition. In like 
manner, if you fiuppofe two bodies to be perfectly elallic, 
and that the fmaller body llrikes the other at reft, there will 
be an increafe of the abfolute quantity of force, becaufie 
the ftriking body will be refledled ; but, if you fiuppofe 
them both to turn round any centre, after the ftroke, fo 
as to meet again, this increafe of force will be loll, and 
their motion will be reduced to its firft quantity. Such a 
■ gain, therefore, of force, as mull be afterwards loft in the 
adlions of the bodies, can never produce a perpetual move¬ 
ment. There are various ways, belides thefe, by which 
abfolute force may be gained j but, fince there is always 
an equal gain in oppofite diredlions, and no increafe ob¬ 
tained in the fame diredlion, in the circle of actions ne- 
ceflary to make a perpetual movement, this gain mull be 
prefently loft, and will not ferve for the neceftary expenle 
of force employed in overcoming fridlion, and the refin¬ 
ance of the medium. We may obferve, therefore, that, 
though it could be fhown, that in an infinite number of 
bodies, or in an infinite machine, there could be a gain of 
force for ever, and a motion continued to infinity, it does 
not follow that a perpetual movement can be made. That 
which was propofed by M. Leibnitz, in Auguft 1690, in 
the Leipfic Adts, as a confequence of the common ellima- 
tion of the forces of bodies in motion, is of this kind, and 
for this and other reafons ought to be rejedted. 
The poflibility of a perpetual motion has been urged 
from the followingfipecious argument. Lettheheight AB, 
fig. 4, be divided into four equal parts AC, CD, DE, EB: 
fiuppofe the body A to acquire, by the delcent A C, a ve- 
1 O N. 
locity, as 1 ; and this motion, by any contrivance, to be 
tranfmitted to an equal body B : then let the body A, by 
an equal defeent CD, acquire another degree of motion, 
as 1, to be tranfmitted likewife to the fame body B, which 
in this manner is fuppofed to acquire a motion, as 2, that 
is fufticient to carry it upwards from B to A; and, be- 
caufe there yet remain the motions which A acquires by. 
the defeents D E and E B, that may be fufticient to keep 
an engine in motion, while B and A afeend and defeend 
by turns, it is hence^concluded, that a fufticient gain of 
force may be obtained in this manner, fo as to produce a 
perpetual movement. But it fhould be con fid ered, that 
two equal fucceflive impuifes, adling upon the fame body, 
will not produce a motion in itdouble of that which would 
be generated by the firft impulfe ; becaufe the fecond im¬ 
pulse has necefiarily a lefs eftedl upon the body, which is 
already in motion, than the firft impulfe which added upon 
it while at reft. In like manner, if there is a third and 
fourth impulfe, the third will have lefs efxecl than the fe¬ 
cond, and the fourth lefs than the third. Hence it ap¬ 
pears, that a motion as 2, in the preceding cafe, cannot 
be produced in B, by the two fucceflive impuifes tranf¬ 
mitted from A, each of which is as 1. Maclauriu's 1 View, 
'SfC. book ii. c. 3. 
The perpetual motion has indeed been thequickfand of 
mechanicians,asthe quadrature ofthe circle, the trifedlion 
of an angle, &c. have been that of geometricians; and, as 
thofe who pretend to have difeovered the folution of the 
latter problems are, in general, perfons Icarcely acquainted 
with the principles of geometry, thofe who fearch for, or 
imagine they have found, the perpetual motion, are always 
men to whom the moft certain and invariable truths in 
mechanics are unknown. 
It may be demonftrated indeed, to all thofe capable of 
reafoning in a found manner on thofe fciences, that a per¬ 
petual motion is impoflible ; for, to be poftible, it is ne- 
ceflary that the effedt fhould become alternately the caufe, 
and the caufe the effect. It would be neceftary, for ex¬ 
ample, that a weight, raifed to a certain height by another 
weight, fhould in its turn raife the fecond weight to the 
height from which it defeended. But, according to the 
laws of motion, all that a defeendin'g weight could do, in 
the moll perfedl machine which the mind can conceive, is 
to raife another in the fame time to a height reciprocally 
proportional to its mafs. But it is impoflible to conftrudl 
a machine in which there (hall be neither fridlion nor the 
refiftance of fome medium to be overcome ; confequently, 
at each alternation of afeentand defeent,fome quantity of 
motion, however fmall, will always be loft; each time 
therefore, the weight to be raifed will afeend to a lefs 
height; and the motion will gradually flacken, and at 
length ceafe entirely. 
A moving principle has been fought for, but without 
fuccefs, in the magnet, in the gravity ofthe atmofphere, 
and in the elafticity of bodies. If a magnet be diipofed 
in luch a manner as to facilitate the afeenuon of a weight, 
it will afterwards oppofe its defeent. Springs, after being 
unbent, require to be bent by a new force equal to that 
which they exercifed ; and the gravity of the atmofphere, 
after forcing one fide of the machine to the loweft point, 
muft be- itfelf raifed again, like any other weight, in order 
to continue its adlion. 
We fhall however give an account of fome attempts 
that have been made to obtain a perpetual motion, becaufe 
they may ferve to amufe the reader, as well as to fhow 
how much fome perfons have fuffered themfelves to be 
deceived on this fubject. 
Fig. 5. reprefents a large wheel, the circumference of 
which is furnifhed, at equal diftances, with levers, each 
bearing at its extremity a weight, and movable on a hinge, 
fo that in one diredlion they can reft upon the circumfe¬ 
rence, while on the oppofite fide, being carried away by 
the weight at the extremity, they are obliged to. arrange 
themfelves in the diredlion of the radius continued. 
This being fuppofed, it is evident that, when the whee 
1 turns 
