428 Prof. Clausitis on the Conduction of Heat by Gases. 

 But by equation (1), 



A A '' 



and A, p, and e bciug independent of p,, we thus obtain 



»-i^;'; • n 



Putting here for U the series given in (I.), and denoting the 

 fraction -r- by /*, we obtain 



H=A(l+2j / i«+|$-|W+..:). . . (II.) 



The factor /* differs from 1 only by a quantity of the second 

 order in relation to e ; and putting, according to equation (4), 

 the value Vu*-\-p*e* for A, we have 



h =^wm =1 - l A e " + - •'■ (8) 



The system of motion produced by adding the common com- 

 ponent velocity pe to the perfectly regular system, in which an 

 equal number of molecules move in every direction, is completely 

 defined by the equations (I.) and (II.) 



§ 7. The system of motion so defined corresponds to the 

 motions of the molecules emitted from a stratum, in case the 

 normal variations only are regarded. To obtain the motions 

 which actually exist, the accidental variations spoken of in § 3 

 must also be taken into account. 



It is plainly impossible to do this by determining the motions 

 of each individual molecule ; but the rules of probabilities enable 

 us to establish certain general principles for a large number of 

 molecules. Maxwell has thus deduced a formula purporting to 

 represent the manner in which the various existing velocities are 

 distributed among the molecules. It is not, however, necessary 

 for our present purpose to enter upon this ; it is sufficient if it 

 be granted that the accidental variations occur to an equal extent 

 in all directions, and that therefore in a quantity of gas, whose 

 temperature and density are uniform throughout, the same num- 

 ber of molecules move in every direction, and that the mean 

 velocity in all directions is the same. 



It is indeed easy to see in this case that the accidental varia- 

 tions cannot in any degree contribute to cause more vis viva to 

 traverse a given plane in one direction than in the opposite 

 direction, since, whatever may be their individual effects, their 

 influence must be the same in both directions. We may there- 

 fore entirely disregard the accidental variations in deducing the 



