36 PHYSICS. 
Scotland (1772), to amount to 54 seconds, and obtained from this the mean 
density of the earth at 4.45. 
f. Of Impact. 
In most cases the forces by which a body is moved, act only on a small 
part of the molecules of which it is composed, and yet all parts of the body 
move, those struck as well as those not touched. Thus, for example, a 
billiard ball rolls along, although, strictly speaking, only a small part is 
struck by the player. The motion must therefore be uniformly distributed 
to all the molecules; this takes place, however, in an infinitely short time, 
and the force has then passed on into the body, and distributed itself in it 
uniformly. The body thus impelled will continue incessantly to move in 
the direction of the impulse with uniform velocity, unless hindered by fric- 
tion or the resistance of the atmosphere. The action of the force is there- 
fore momentary ; its effect, however, unlimited. 
Under such circumstances the body receives the force, and one and the 
same force acting upon different bodies must produce very different 
motions ; a force which can impel a small body with tolerable swiftness 
may hardly move a larger. It is usually said that this difference depends 
upon the weight, but this is not the case ; else, if the body ceased to be heavy, 
the same force would impel all bodies with equal velocity. This, however, 
does not follow, as even in vacuo the same force must produce a less 
velocity, as the matter to be moved is greater; and the theory of mechanics 
teaches us that the same force operating upon different bodies, communi- 
cates to them velocities which are inversely as their masses, that is, as the 
quantity of their matter. Consequently, the same force that would impel a 
mass with a velocity = 1, would impel one of ten times the greater mass with 
one tenth of the velocity. Multiplying each of these masses by their velo- 
city, the produets will be equal; this product is called the quantity of motion, 
or the momentum. Machines cannot increase the quantity of motion, as 
they do not generate force, but only change the kind of motion. Thus a 
laborer can, by means of a rope which passes over a fixed pulley, easily 
raise 25 pounds to a height of 23 feet in a second; if, however, the rope 
were laid over a wheel and axle, where the latter should have a four times 
smaller diameter, the laborer, with the same exertion of strength as before, 
would easily raise four times the weight, but would require four fold the 
time. 
If a body in inotion meet one that is stationary but movable, it imparts to 
this latter a part of its motion, without thereby changing the quantity of 
motion ; for if the striking body did not rebound in consequence of its elas 
ticity, and if the blow were a central one, both bodies after the blow would 
move in the same direction, but always in mutual relation to their masses. 
The velocity after impact can therefore very readily be obtained by dividing 
the velocity of the moving body by the sum of the masses of the moving and 
the stationary body. Suppose a bal] moving witha velocity of 1400 feet ina 
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