the Molecular Velocities in Gases. 

 velocity may correspond to eo. We shall thus have 



h -nv, . 7 co" co' 



— = \ t COS I, -V, — T — • 



53 



To simplify this value, let B', C denote two points of 7 the 

 distance between which is not very small relatively to the 

 dimensions of 7 ; let B, C be the corresponding points of co", 

 and let us draw C W equal and parallel to B / C / . The point 



Gr being at first in C the contact was in C; a motion of trans- 

 lation bringing Gr to B', the point of S which was in C comes 

 to B"; at that instant the contact being in B, let T T be the 

 tangent plane common to S and S'. The point B" being 

 upon S, and C upon S', the distance of each from the tangent 

 plane is, as we know, an infinitesimal of the second order. 

 Therefore the straight line C W makes with the plane an infi- 

 nitely small angle; and it is the same with B / C. The same 

 could be said of B"D', D' being another point of 7. Therefore 

 the plane of y, in its entirety, is parallel to the plane of a/', 

 and consequently to that of co' ' . 



Next let us call M specially the centre of the circle co, the 

 points M', M." being those which correspond to it; it is evi- 

 dent that the ratios — j — 7 ? ~ do not change if we alter the 



CO CO CO ' ° 



form of the elements, provided that they exactly correspond 

 to one another and, further, are still at the same place — that 

 is to say, contain M, or MS, or M" ; we have, then, co = 4&/ cos i, 

 a relation previously found for a rectangular form. "We shall 

 moreover substitute 



lr=AM"), ^=F(M",S): 



the second of these indicates that -~ depends at the same time 

 on the position of M" and that of S relatively to S' ; and the 



