1821.] Phenomena of Heat, Gases, Gravitation, S^c, 291 



According to the commonly received theory of coUision, when 

 a hard body strikes another at rest, the two bodies proceed toge- 

 ther with a common velocity. Now if these bodies have no kind 

 of attraction, they do not press after collision ; and, consequently, 

 either of them may be taken away without affecting the motion 

 of the other. Hence the motion which the body that was quies- 

 cent has acquired is proportional to the intensity of the impulse, 

 and may be taken as a measure of it. Therefore, if the body A 

 with a velocity of a strike the quiescent body B, the velocity of 



the balls after the stroke will, by the old theory, be -- — - , and 



the intensity of the stroke -r — :g. The ball B and other things 

 remaining the same, if, instead of A we substitute a ball 71 times 

 greater, the intensity of the stroke would be — ^^ — ^; and there- 

 fore the ratio of these two strokes is that of ?z A + B to n 

 (A + B). That is, if two perfectly hard balls strike similarly 

 and with equal velocities, two similar, hard, and equal balls, 

 B, B, at rest, the ratio of the strokes will be that of w A + B to 

 w (A + B). But by our first cor. to the preceding prop, the 

 ratio of these intensities should be that of \ to n\ and the same 

 is true by the third prop. The ratio of the strokes, therefore, as 

 given in the two theories, differs materially. When the ratio of 

 the stroke of a less to that of a greater body, under the same 

 circumstances of action is considered, it is greater in the old 

 than in the new theory, and conversely ; and in all cases, except 

 one ; namely, the collision on a fixed plane, the intensity of the 

 blow is less in the old than in the new theory. It is not an easy- 

 thing to examine the truth of either of these theories by direct 

 experiment ; except, perhaps, in the case that I have mentioned 

 in the scholium of prop. 2, for want of perfectly hard bodies to 

 experiment on ; but probably, in the absence of experiment, the 

 perfect coincidence of phsenomena, and the consequences that I 

 have drawn, from these new principles of coUision in the follow- 

 ing theory of gaseous bodies, will be admitted to amount, as 

 nearly to an experimental proof as the nature of the subject 

 allows. 



Besides the methods we have adopted to consider various 

 points in the coUision of hard bodies, there are several others, all 

 of which, however, come to the same thing ; but the following 

 method of examining the case of this schol. which has occurred 

 to me while I have been writing this part of the memoir, appears 

 to be so independent of previous considerations that I have beea 

 tempted to give it. Setting aside aU idea whether the bodies 

 after coUision do or do not continue together, let us only suppose 

 that they are absolutely hard, that the two quiescent ones are. 

 perfectly equal, and that the other bodies before the strokes, 

 have equal velocities, and move simUarly upon the quiesc^rit 



t2 



