47* VISCOSITY OF GASES 447 



18* without hesitation, taking the forward motion to be uniform 

 within each layer, but to differ from one layer to another. 



In the formulae w r hich we introduce with this assumption we 

 must partly alter the meaning of the symbols, in order to be able 

 to retain the notation employed in the last two paragraphs and 

 the system of rectangular coordinates there introduced. We had 

 before denoted by s the angle which the direction of motion of 

 the particle under consideration makes with the direction of the 

 forward velocity o of the flowing gas ; instead of cos s we have 

 now to put sin s cos 0, if, as hitherto, we take the direction of 

 flow coincident with that of the ^/-axis. Corresponding to this 

 assumption we replace the letter o by v f , to which we leave the 

 meaning it has hitherto had. The formulas of the preceding 

 paragraphs are thereby changed so far that the exponent 

 which occurs in Maxwell's formula, is to be replaced by 



q = m<*) + v wv sn s cos ^. 



The number B of collisions which a single particle undergoes 

 on the average in unit time, and the number of paths which it 

 begins in unit time, are calculated just as if the gas were at rest. 

 For, firstly, with our assumption the speed of flow alters by only 

 vanishingly small quantities with the region in which the paths 

 of the molecules considered lie ; and, secondly, the calculation of 

 31* teaches that with an unequal distribution of the forward 

 motion the number of collisions is altered only by quantities of 

 the order of the square of the differences of the speeds. 



We put therefore 



dy dzN(km/7r)%e~ q Re~ Brl "u> 2 dt*> dr cos s sin s ds d<f> 



for the number of particles which pass through the surface-element 

 dy dz in unit time, having started from the volume-element 

 r 2 dr sin s ds d$, B retaining its former meaning. 



Each of these particles possesses the momentum mw sin s cos <j> 

 in the direction of the y-axis ; hence the momentum which is 

 carried across the element dy dz in unit time is 



sfoo foo r$7r (-27T -Br/o, a 



Q = dydz mN(km]rrY dw \ dr ds dA'Be ' e a * sin 2 s cos s cos <b; 



Jo Jo Jo Jo 



and this expression gives the momentum Q lt which is carried 

 across in the direction of decreasing x, if the value v' lt as defined 

 in 45*, is substituted for v' in q, and also the momentum Q 2 , 



