M E C H A N I C S'. 
animal is obliged to renew bis efforts. The velocity of 
the machine would now he confiderably increafed, were 
it not that the fly now afts as a refitting power, and the 
greateft part of the fuperfiuous motion is lodged in it, fo 
that the increafe of velocity in the machine is fcarcely per¬ 
ceptible. Thus the animal has time to reft until the ma¬ 
chine again requires an increafed impulfe, and fo on al¬ 
ternately. The cafe is the fame with a machine moved by 
water, or by a weight; for, though the (trengfh of thefie 
does not exhauft itfelf like that of an animal, yet the 
yielding of the parts of the machine renders the impulfe 
much lei's after it begins to move. Hence its velocity is 
accelerated for l'ome time, until the impulfe becomes fo 
fmali, that the machine requires an increafe of power to 
keep up the neceffary motion. Hence the machine flackens 
its. pace, the water meets with more refiftance, and of 
confequence exerts its power more fully, and the machine 
recovers its velocity. But, when a fly is added to the 
other parts, this-afls fir ft as a power of refiftance, fo that 
the machine cannot acquire the velocity it would other- 
wife do. When it next begins to yield to the preflu re of 
the water, and the impulfe of courfe to flacken, the fly 
communicates part of its motion to the other parts ; fo 
that, if the machine be well made, there is very little 
difference in the velocity perceptible. The truth of what 
is here advanced will eafily be feen, from confidering the 
inequality of motion in a clock when the pendulum is 
off, and how very regularly it goes when regulated by the 
pendulum which here afls as a fly. Flies are particularly 
ufeful in any kind of work which is done by alternate 
ftrokes, as the lifting of large peftles, pumping of water. 
See. In this cafe the weight of the wheel employed is a 
principal objeff; and the method of calculating this is to 
compare it with the weight to be raifed at each ftroke of 
the machine. Thus, fuppofe it were required to raife a 
peftle 30 pounds weight to the height of one foot 60 times 
in a minutes Let the diameter of the fly be feven feet, 
and fuppofe the peftle to be lifted once at every revolu¬ 
tion of the fly; we mult then confider what weight palling 
through az feet in a fecond will be equivalent to 30 
pounds moving through one foot in a fecond. This will be 
30—22 or 1-3^- pounds. Were a fly of this kind to be ap¬ 
plied, therefore, and the machine fet going, the fly would 
juft be able to lift the peftle once after the moving power 
■was withdrawn; but, by increafing the weight of the fly 
to 10, iz, or 20, pounds, the machine when left to itfelf 
would make a confiderable number of ftrokes, and be 
worked with much lefs labour than if no fly had been 
ufed, though no doubt at the firit it would be found a 
confiderable incumbrance to the motion. This is equally 
applicable to the a£tion of pumps; but the weight which 
can be moft advantageoufly given to a fly has never yet 
been determined. It is certain, however, that the fly 
4pes not communicate any abfolute increafe of power to 
the machine; for, if a man or other animal is not able 
to fet any engine in motion without a fly, he will not be 
able to do it though a fly be applied; nor will he be able 
to keep it in motion, thougli fet going with a fly, by 
means of a greater power. This may feem to be contra¬ 
dicted by the example of a common clock ; for, if the 
pendulum be once flopped, the weight is not able to fet 
it in motion again, though it will keep it going when 
Once put in motion by an external power. This, how¬ 
ever, depends not upon any infufficiency of the weight, but 
on the particular mechanifm of the crown-wheel; which 
as fuch, that, when once the pendulum is flopped, it would 
require a much greater weight than that commonly ap¬ 
plied to fet it in motion; and, if the ufual weight were to 
aft fairly, it would be more than fufficient to move all 
the machinery, and make the pendulum vibrate alfo with 
much greater force than it does. 
Of the COLLISION or IMPULSION of BODIES. 
Definition 1. When a body, moving with a certain velo¬ 
city, Itrikes another body, either at reft or in motion, the 
Vox,.XIV. No. 1001. 
6:37 
one is fa'id to impinge againft, or to impel, the other. 
This effert has been diftinguifhed by the names collifton, 
impullion or impulfe, percufllon, and impact. 
Defi. 2, Thecollifion or impuifion of two bodies is faid 
to be diredl, when the bodies move in the fame ftraight 
line, or when the point in which they Ifrike each other is 
in the ftraight line which joins their centres of gravity. 
When this is not the cafe, the impulfe is faid to be oblique. 
Defi. 3. A hard body is one which is not fufceptible of 
compreflion by any finite force. An elafiic body is one 
fufceptible of compreflion, which recovers its figure with 
a force equal to that which comprefies it. A Joft body 
is one which does not recover its form after compreflion. 
There does not exift in nature any body which is either 
perfectly hard, perfectly elaftic, or perfectly foft. Every 
body with which we are acquainted poflefles elafticity in 
fome degree or other. Diamond, cryftal, agate, &c, 
though among the hardeft bodies, are highly elaftic ; and 
even clay itfelf will in fome degree recover its figure after 
compreflion. It is neceffary, however, to confider bodies 
as hard, foft, or elaftic, in order to obtain the limits be¬ 
tween which the required refults mud be contained. 
Defi. 4., The mafs of a body is the fum of the material 
particles of which it is compofed ; and the momentum, or 
moving force, or quantity of motion, of any body, is the 
produfl arifing from multiplying its mafs from its velocity. 
Prop. XXIV. Two hard bodies B, B', with velocities V, V', 
fir iking each other perpendicularly , will be at refi after impulfe, 
if their velocities are inverfely as their mafifes. 
1. When the two bodies are equal, their velocities mu ft be 
equal in the cafe of an equilibrium after impulfe; and 
therefore, B : B' = V' : V, or B V = B' V*; for, if they 
are not at reft after impulfe, the one mult carry the other 
along with it; but, as their maffes and velocities are equal, 
there can be no reafon why the one lhould carry the other 
along with it. 
2. If the one body is double of the other, or B = i B', we 
fliould have V' =2 zV'. Now in (lead of B we may lubfti- 
tute two bodies equal to B', and inftead of V' we may 
fubllitute two velocities equal to V, with which the bo¬ 
dies R' maybe conceived to move; confequently we have 
2 B'x V=B'XiV; or B' : 2B'=V : 2V; but 2V is the 
velocity of B', and V is the velocity of iB'; therefore, 
when one body is double of the other, they will remain 
at reft when the maffes of the bodies are inverfely as their 
velocities. 
In the fame way the propofition may be demonftrated 
when the bodies are to one another in any commenfurable 
proportion. 
Prop. XXV. To find the common velocity v of two hard 
bodies B, B‘, whofie velocities are V, V', after firiking each 
other perpendicularly. —If the bodies have not equal quan¬ 
tities of motion they cannot be in equilibria after impulfe. 
The one will carry the other along with it; and, in con¬ 
fequence of their hardnefs, they will remain in contact, 
and move with a common velocity v. 
Cafe 1. In order to find this, let us firft fuppofe B f to be 
at reft, and to be ftruck by B in motion. The quantity 
of motion which exifts in B before impulfe is B V ; and, 
as this is divided between the two bodies after impulfe, 
it muft be equal to the quantity of motion after impulfe. 
But v X B-J- B' is the quantity of motion after impulfe ; 
therefore,!/x B-j-ft' — BV, and —. 
Cafe 2. Let us now fuppofe that both the bodies are in 
motion in the fame direction that B follows B'. In order 
that B may impel B', we muft have V greater than V'. 
Now we may conceive both the bodies placed upon a plane 
moving with the velocity V', The body B', therefore, 
vvhofe velocity is V' equal to that of the plane, w ill be at 
reft upon the plane, while the velocity of B with regard 
to E', or the plane, will be V — V'; confequently, the 
bodies are in the fame circumltances as if B' were at reft, 
and B moving with the velocity V — VL Therefore, by 
7 Z the 
