516 Prof. Clausius on tlie Conduction of Heat by Gases, 



E-0, "J 



F = constant quantity, \ .... (21) 

 G= constant quantity, J 



which we will now apply to the expressions already arrived at 

 for E, F, and G. 



The first equation gives, if we neglect the term Xe 3 , 



q + uq'=0, 



which determines the ratio between the coefficients q and q 1 , 

 namely, 



<?=-l ; < 33 ) 



Hence equation (IV.) takes the following form, if we at the same 

 time introduce into it the value of i given in (20) : — 



I = l-|/,6 + rV-i)^+ (VII.) 



The second of the foregoing equations (VI.), neglecting Xje 2 , 

 S ives Nw 2 = const (23) 



N determines the density of the gas at the point in question, 

 and w 2 is proportional to its absolute temperature ; whence it 

 follows that the product of the density into the absolute tempe- 

 rature, or, what comes to the same thing, that the pressure must 

 be the same throughout the whole mass of gas — a result which 

 might also have been assumed as self-evident at starting. 



Finally, touching the magnitude G. On applying to the last 

 of the equations (VI.) the equation (22), and neglecting the 

 term X 2 e 3 , it becomes 



G = lkmm*qe (VIII.) 



But since, according to what precedes, Nw 2 is a constant quan- 

 tity, and k, m, and e are essentially constants, it follows that, if 

 G is to be, as in fact it must be, constant, 



q = constant quantity (24) 



In order to determine the conduction of heat without consi- 

 dering the magnitude e, which I have discussed in my former 

 paper, it now only remains to determine this one constant quan- 

 tity q. 



V. Relation between the molecules existing simultaneously in a 

 given stratum and those emitted from the same stratum. 



§ 17. In order to find how many molecules are emitted from 

 a stratum, we must know how great is the likelihood that a mole- 

 cule, while traversing the stratum, will strike against another 



