1815.} On the Collision of Hard Bodies. 415 
and imperfect hardness ; but the result of the inquiry is commonly 
referred to bodies possessing the quality in an absolute degree, 
though it is manifestly derived from the properties of matter which 
is comparatively soft or pliant. ‘The fundamental theorem is com- 
monly expressed in the following manner, or nearly so. If two 
perfectly hard bodies impinge upon each other, they will move 
together after collision with the velocity due to their common centre 
of gravity before and after impact, or else both will remain at rest. 
The arguments advanced in support of the proposition may be thus 
stated. When a perfectly hard body, A, impinges directly on ans 
other perfectly hard body, B, part of A’s motion is transferred to 
, by the action of A; and an equal quantity is taken from A by 
the re-action of B. Thus is the velocity of B augmented, and that 
of A diminished, until they become equal, when action and re- 
action ceases: but it is the velocity of the bodies which is changed 
by collision, not the momentum of the system; therefore the 
velocity of A and B becomes equal to that of their common centre 
of gravity, from the force of impact; consequently if the centre of 
gravity be without motion, A and B are reduced to a state of rest. 
Such are the arguments advanced in support of the proposition : 
but if only part of A’s momentum be transferred to B, and that 
gradually too until these velocities become equal, the centre of 
gravity of A will in the mean time approach that of B. In other 
words, the figures of both bodies will be changed ; consequently 
they are imperfectly hard and inelastic. 
After making the preceding remarks on the fundamental theorem 
relating to the doctrine of collision in general, 1 will endeavour to 
investigate the effects which really would result from the impact of 
bodies possessing the quality of hardness in an absolute degree. 
For this purpose the reader is requested to form the simple diagram 
for himself, which is easily done, and will spare the editor a little 
unnecessary trouble. : 
Let A, B, F, G, &c. be a row of circles touching each other 
externally in succession. Also let the right line, C D, pass through 
their centres, and the figure is complete. 
Prop. \.—\f a perfectly hard body, A, moving in the direction 
CD with the momentum M, impinge upon a perfectly hard 
body, B, at rest, A will loose all its momentum, which will be 
transferred to B in the same direction, C D; for as soon as A and 
B come into contact, their centres of gravity will cease to approach 
by definition; therefore A will exert its momentum, M, collectively 
upon B in the direction C D, no regard being had to time; and B 
will re-act in the same manner with an equal force in the direction 
DC; i.e. A will be urged in opposite directions by equal forces, 
one of which is its own momentum; therefore A will lose all its 
motion : but B is urged in the line C D with the momentum of A 
only; therefore M, or this momentum, will be transferred to By 
Q. E.D. 
Cor.—If A in motion impinge upon B at rest, the first in a row 
