526- Prof. Clausius on the Conduction of Heat by Gases. 



The determination of the coefficient ^e gives at the same time, 

 as a consequence of equation (22) , also the value of q'. The series 

 in equations (III.) and (IV.), which express the land of motion 

 of the molecules existing simultaneously in a stratum, are there- 

 fore known as far as is necessary for our purpose ; that is, in 

 each series, besides the term which is independent of €, that one> 

 which contains its first power is known*. 



VI. Final Conclusions. 



§ 23. Having in the preceding pages ascertained the value 

 of the necessary coefficients, we may now proceed to draw con-, 

 elusions from the equations that have been established, as to the 

 condition of the "gas" and the' conduction of heat taking place 

 within it. 



In § 16 we found that q must be a constant quantity; and 

 if, instead of q, we put its value, we may accordingly write 



1 du 



^= constant. 



The same section further teaches us that 



~Nu 2 = const.; 

 and by multiplying these two equations, we have 



w 2 -t-= const (52) 



But, since the quantity w 2 is proportional to the absolute tempe- 

 rature T, we may put 



u — const. V'T, 



and hence the last equation becomes 



VT-^ = const (53) 



By integrating this equation, an equation of the following form 



* In the terms of the second degree we meet with the quantities q x 2 , r, 

 and r', which can be determined in the same way as q by carrying out the 

 calculations further. Without here dwelling upon this extension of the 

 calculations, which presents no difficulty whatever in regard to principle, I 

 will merely quote the values of these quantities which are so arrived at : 

 namely, 



2 41 2 



50 y 



,_ 266 (f 

 r 17-25 w 2 ' 



