On Machines in GensraL ^515 



system, the relative velocity of all these adjacent corpilstlfcs 

 which act upon each other^ taken two by two^ will be tid- 

 ihing at the rirst instant. This being granted, let us callow 

 the absolute velocity which m will have in the first rnstant, 

 in virtue of this geometrical movement, and z the angle coiii- 

 prehended between the directions of tc and U ; it is clclir 

 that the corpuscles m will not tend to approach or recede 

 from each other in virtue of the velocities 2/, if we su'ppose 

 them animated at the same time with these velocities u and 

 velocities U ; nor will they tend more to approach or recede 

 if animated with the mere velocities U : thcretbrc the re- 

 ciprocal action exercised among the different parts of the 

 system will be the same, whether each molecule be anima- 

 ted with the sino-|e velocitv U, or with the two velocities u 

 and U : but if each molecule was animated with the single 

 velocity U, it is plain that there would be equilibrium': 

 thus, if it was animated at once with the two velocities U 

 and ?/, or with a single velocity the result of both, U will 

 still be the velocity lost by tn ; and u will be the real velocity 

 after the reciprocal action : thus, by the same reasoning by 

 which we had the fundamental equation (E) we shall also 

 have srritiU cosine z = (F) ; second fundamental equa- 

 tion. 



It is very easy at present to resolve the problem which we 

 propose for the preceding equation necessarily taking place, 

 whatever be the value of u and its direction, provided the- 

 movement to which it refers be geometrical : it is clear that 

 by successively attributing to that indeterminate different 

 values and arbitrary directions, we shall obtain all the ne- 

 cessary equations among the unknown quantities, upon 

 which depends the solution of the problem and of quantities 

 either given or taken at pleasure. 



XVII. In order to place this solution in the clearest light, 

 • it will be sutlicient to give an example of it. 



Let us suppose therefore that tlie whole system is reduced 

 to an assemblage of bodies united to each other by inflexible 

 rods, in such a manner that all the parts of the system 

 should be forced always to preserve their same respective 



4 positions; 



