472 Mr. S. H. Burbury on the 



is the same for all classes of molecules of the same gas what- 

 ever their absolute speeds in space, no distinction being drawn 

 between those classes which have great and those which have 

 small absolute speeds. 



I propose to show (as has been already proved by Boltz- 

 mann) that, in order to represent the true motion of the dif- 

 fusing gas, it is necessary to make a, the small additional 

 translation-velocity, a function of the absolute velocity of 

 the molecules, those classes which have greater absolute velo- 

 city having greater translation-velocity ; and that Professor 

 Tait's hypothesis, making a constant, is inconsistent with 

 steady motion. It is sufficient to prove this for the imaginary 

 case of two gases, of which the molecules of one have the 

 same mass and the same diameter as those of the other. 



3. At any point in the tube let us take two parallel sections, 

 A and A', each of unit area, distant hx from each other. The 

 volume of the cylinder whose bases are A and A' is hx. We 

 will call it our element of volume. At A let n x be the number 

 of molecules of gas I., n 2 the number of molecules of gas II., 

 per unit of volume. Then at A' the respective numbers will be 



drh *„ „„j „ , dn a « . n^ • - " ■ dn. __ dn 



i x + -j— hx, and n 2 + — - Bx ; that is, since 



and 



dx dx ' dx dx 



dn 2 ~ ,, T 



Wir— -T- ox for gas 1., 



n 2 + -f^$w for gas II. 



At A the number of molecules of gas I. in unit volume 

 whose velocities, irrespective of direction, lie between v and 

 v + dvj shall be denoted by nif(v)dv. We will call them the 

 class v. Those members of the class v whose directions of 

 motion make with the axis of the tube angles between ijr and 

 y}f i-d-ty shall be called the class (v, yjr). Their number in the 

 gas at rest would be 



nif{v~)dv -J sin yjr d^. 



In the moving gas it will be 



n \f( v ) dv J sin yjr d-\jr 



+ -| n^v) dv - cos yjr sin yjr d-yjr ; 



a being the mean translation-velocity for the class v, whether 

 that be a function of v or not. 



4. Let us now find the number of molecules of the class 



