52.2 Prof. Clausius on the Conduction of Heat by Gases. 

 Thereby, substituting also u + 8 for v, wc get 



«=- 7r/ o 2 N^+-S+— ^cos^ej, . . . (42) 



a= | VN ( 1 _i! +] L, C0S ^). . . (43) 



The unknown quantity p can still be eliminated from these 

 expressions. For assuming, as a particular case, that the given 

 molecule, as well as all the other molecules present, has the 

 velocity u, we have 8=0 and q=-Q; whence it results that 



a = f 7 r / o 2 N. ...... (44) 



Further, according to § 9, the fraction - represents the mean 



length of excursion between any two impacts, whence we obtain 

 for the .mean length of excursion the following expression : — 



3 1 g 



4 7rp 2 N ' 



In order to render the signification of this expression still more 

 special, so that it may represent the normal mean length of excur- 

 sion, which we have denoted by e, we only require to substitute 

 for N, which signifies the number of molecules contained in a 

 unit of volume, the particular value which corresponds to the 

 normal condition of the gas. Distinguishing this value by N , 

 we obtain 



6= !^n - • • • • • • < 45 ) 



Eliminating p 2 from the above expressions by means of the 

 equation, they become 



N e\ sm 10 2 u/ v J 



We see from these expressions that the quantities a and a are 

 dependent on the velocity and direction of motion of the given 

 molecule, and further, since N and u are functions of x, that 

 they are dependent upon the position of the particular stratum 

 in which we consider the motion j\ 



* I have already given this value for the mean length of excursion, in 

 the ease in which all the velocities are equal, in my former paper (Pogg. 

 Ann. vol. cxv. p. 249), but without the details of calculation. 



f Maxwell has not in his calculations sufficiently attended to the de- 

 pendence of the quantity a, on various circumstances, inasmuch as he treats 



