292 Mr, Herapath on the Causes, Laws, and principal [April, 



bodies. Then because the bodies are perfectly hard, the strokes 

 will be equally diffused, and felt in every part of the impinging 

 bodies ; and, therefore, every part of the impinging bodies wiU 

 equally contribute to the stroke. And the same things will 

 evidently hold good if each impinging mass, instead of being 

 one entire body, be composed of two or more moving along in 

 contact with a common velocity, provided the centres of gravity 

 of all the bodies and their points of contact be all in the line in 

 which the impulse is given. Again, because the bodies struck 

 are equal and similar, and the strokes are made similarly and with 

 equal velocities ; the strokes, as far as they depend upon these 

 circumstances, must be identically the same. Therefore, what- 

 ever be the difference in the intensities of the strokes, it is 

 wholly attributable to the difference in the masses of the 

 impinging bodies. But we have already shown that the stroke 

 is the same, under certain conditions, whether the impinging 

 body be one or several bodies in contact. If, therefore, we 

 conceive the greater impinging body to be composed of two, one 

 of which is equal to the other impinging body, then, since the 

 mere contact of the two parts can have no influence in augment- 

 ing or diminishing the intensity of coUision due to either of them 

 separately, the intensity of the impulse of the other body, and of 

 the part which is equal to it, are consequently equal. But 

 because every part of the impinging body equally contributes^to 

 the stroke, the intensity of the impulse due to a part, whether 

 that intensity be equivalent to the whole, or only to a portion of 

 the momentum, is to the intensity due to the whole of the body 

 as the part is to the whole. The ratio, therefore, of the impulses 

 is equal to the ratio of the impinging bodies. 



When a hard ball strikes another hard ball at rest, in the hne 

 of its motion, the effect of the collision is a mutual change of 

 state. And since by cor. 1 to the preceding prop, this is true 

 without regard to the relative masses of the balls : it follows that 

 a body in a state of free and perfect quiescence, however 

 small it might be, will destroy the motion of another body how- 

 ever large and however great its momentum. Thus then a single 

 particle of matter, of the smallest dimensions, to which a very 

 small force would give a velocity sufficiently great to avoid a 

 stroke from a very large body, moving with a much greater 

 momentum, may, if struck, when at rest, stop another of any 

 dimensions and moving with any force. This conclusion, which, 

 at first view, appears to throw an air of improbabihty over the 

 theory, will, upon a closer inspection, be found to be perfectly 

 natural and correct. For the effect in motion on either of the 

 balls is equal to the intensity of the impulse, and that intensity, 

 by the aforesaid cor. and by a variety of other considerations 

 which it would be tedious to state, is equal to the momentum of 

 the moving body. It is, therefore, not on the relative magnitudes 

 of the bodies that the change of motion depends, but on the 



