Prof. Clausius on the Conduction of Heat by Gases* 517 



molecule ; for it is the molecules which strike each other, and, 

 after the rebound, leave the stratum with altered directions and 

 velocities, which we have agreed to call the molecules emitted 

 from the stratum. 



We will call the probability of one molecule striking another 

 while traversing the infinitely small space ds, as we have done 

 in § 9, ads ; and our business is now to make a closer approxi- 

 mation to the value of a. 



In my former memoir* I have determined the value of a for 

 the case of a molecule moving in a space containing very many 

 other molecules in a state of rest, and there I found 



7T0 2 



where p is the radius of the sphere of action of a molecule, in 

 the sense indicated in the paper quoted, and \ is the interval 

 which would exist between every pair of neighbouring molecules 

 if, instead of the irregular distribution of them which occurs in 

 reality, the molecules had a regular cubical arrangement (that 

 is, if the entire space were divided up into small cubical spaces, 

 and the centres of the molecules were at the corners of the 

 cubes). Instead of the magnitude X, we may likewise introduce 

 N, the number of the molecules existing in a unit of space. 

 There must indeed be as many molecules in a unit of space 

 as there are such cubical spaces with the side X contained in it ; 



hence we have N = r-g, whereby the last equation is transformed 



int0 «=7rp 2 N. ...... (25) 



This expression for a admits of being easily modified so as to be 

 likewise applicable to the case in which the other molecules are 

 in motion instead of being at rest. 



If we denote the likelihood that there is of the molecule under 

 consideration striking another during the element of time dt 3 by 

 adtj and regard ds as the space traversed during the time dt, 

 we get 



adt=ads; (26) 



ds 

 or, putting v in place of -j, that is to say, the velocity of the 



molecule in question, 



a = av (27) 



Substituting here for a its value as deduced in (25), we have 



a = irp^v (28) 



* Phil. Mag. S. 4. vol.xvii. p. 87. 



