520 Frof. Clausius on the Conduction of Heat by Gases. 



accordingly, if we neglect terms of the second or higher degrees 

 in the expression sought for for R, we may disregard the quan- 



tity ^-tyy -— , whereby the calculation becomes very much sim- 

 plified. 



The equation for R then becomes 



R = V'g Vl^oi^ V'Vv. .... (35) 

 But , by equation (9), 



V=U- £,»+..., 



so that, by developing the foregoing equation according to s as 

 far as the term of the first degree, it is transformed into 



And substituting for s in this expression the mean value s, we 

 obtain instead of R the mean value R : thus 



R = \/2 \fl-cos<l> VTv(l-ll^ fJL^: . (36) 



In place of U and s we will now put the values given for them 

 in (1) and (18), which, neglecting terms of the second and 

 higher degrees, are as follows : — 



s =ce; 



at the same time we will put 



v=u + $, (37) 



where S may denote any magnitude of the order of e. Then we 

 get 



R= •g •1-cob^|[«+ -B+ l(p-c j)/xe] ; 



flu 

 or, substituting q for p — c-j- i as we have done already in (19), 



!■= tfZ \/l-co8<l>(u+i$+iqtJt,e). . . . . (38) 

 This expression must be multiplied by I, which is represented, 

 according to (VII.), disregarding the higher terms, by 1 — -fxe. 



