290 Mi\ Herapath on the Causes, Laws, and principal [Apkii,' 



much more direct and rigorous than the one in that proposition ; 

 for which reasons it will enable us presently to consider one or 

 two points of our theory that we could not before, at least in the 

 manner we are now enabled to. 



(Jor, 2. — The motions and directions of two balls being given, 

 and the direction in which they strike one another being also 

 given, the motions and directions of them 

 after the stroke may be found. Let A C, 

 B C, be the two given motions previous to 

 the contact, and let E C F be the direction 

 in which the balls strike. Upon E F let fall 

 the perpendiculars A E, B F ; and from the 

 points E, F, draw E 6, F «, respectively 

 equal and parallel to F B, E A ; join a C, 

 h C ; and a C will be the motion of A, and 

 h C that of B after the impulse. 



Qor^ 3. — From this cor. it foUovvs, that the compound motion 

 of the bodies is the same before and after the impulse. For 

 draw A D equal and parallel to C B, and join D C, which will 

 be the compound motion of the bodies before the impulse. 

 Likewise draw 6 A, B a, and h D. Then because E A, F a, and 

 E 6, F B, are equal and parallel, A /;, a B, are equal and parallel; 

 and because A D, C B, are equal and parallel, 6 D, C a, are also 

 equal and parallel ; but by the preceding cor. a C is the motion 

 of A, and b C that of B after the stroke ; D C is, therefore, the 

 motion compounded of these motions. The same D C has also 

 been shown to be the motion compounded of the motions of the 

 bodies before the stroke ; whence the motion compounded of 

 the motions before the stroke is the same as the motion com- 

 pounded of the motions after the stroke. Consequently, the 

 motion of the common centre of gravity of the bodies receives 

 no change from the coUision. 



Cor. 4. — The same inferences that we have drawn in the pre- 

 ceding cor. might have been easily drawn from other premises. 

 For since action and reaction are equal and contrary, the motion 

 of each body is equally affected by the stroke ; and whatever is 

 gained by the one in any direction is lost by the other in the 

 same direction ; so that the aggregate motion of the bodies in 

 any direction is always the same, unless some extraneous force 

 interferes. 



Scholium, 



Having now brought our theory of coRision as far as it will be 

 wanted in the subsequent part of the memoir, I shall omit the 

 more intricate problems connected with it, and shall only stop, 

 before I proceed to the theory of gases, to consider another 

 error in the old theory, and to clear up one or two points in the 

 new, where, I think, from the novelty of the views and a natural 

 prejudice in favour of preconceived notions, objections may 

 arise. 



