48 M. C. Cellerier on the Distribution of 



plane is not altered by the collision; otherwise the sum of the 

 vires vivos of translation would also be so. 



In regard to the solidity so far as the collision is concerned, 

 let us remark that the trajectory of one of the centres of gra- 

 vity is composed of two straight lines joined by a curve cor- 

 responding to the period of mutual action. In the case of two 

 springs bending one another this curve has a certain extent; 

 for two solid spheres it is reduced to a point. More precisely, 

 if a denotes the displacement of the centre of gravity of a mo- 

 lecule during the collision (that is to say. during the sensible 

 action of another molecule), and d the distance of the two 

 centres at that instant, the condition of solidity consists in a 

 being imperceptible compared with d. 



This is only a consequence of the gaseous constitution of 

 which we wish to calculate the effect ; for this calculation 



consists in regarding as negligible the ratio -j n d' being the 



mean distance traversed by a molecule between two successive 

 collisions. It is so also for gases strongly compressed ; for 

 such was the case in one of the principal experiments from 

 which the nothingness of the internal work has been concluded. 

 Now, if a body in the solid state pass to that of a compressed 

 gas occupying either eight times or twenty-seven times its 

 original volume, the mean interval between two neighbouring 

 molecules is merely doubled or trebled. At the distance of 

 the original interval they certainly act the one upon the other; 

 and it is evident that in the gaseous state they can hardly be 

 displaced the distance d without collision : therefore d and d' 



are quite of the same order of magnitude ; and if j, is negli- 

 gible, so is -y 



It is moreover easy to see, for solid molecules it is true, that 

 the degree of incompressibility of a body serves as a measure 

 for that of its molecules. If two equal masses, divided each 

 into n parts, collide with great force, the stress borne by one 

 part will be the same as if it had been isolated and received 

 the impact of one part only. If in that case it is sensibly 

 compressed, as much will happen when it forms part of the 

 mass, and this will be compressed in the same proportion. 



We shall examine some particular cases of molecular mo- 

 tions before attacking the general question ; but first some 

 remarks are necessary in order to avoid repetitions. 



(1) The unit of length is supposed to be chosen so that the 

 total volume comprised in the enclosure is the unit, although 

 it be very great. Even when the molecules are divided into 



