through Gases between Parallel Plates. 241 



Besides this solution, there is another corresponding to the 

 case where C x is zero, and when therefore the transformation 

 from to (j> fails. 



In this case the relation between y and v can be expressed 

 directly without the use of an auxiliary variable, and may 

 readily be shown to be 



/l — e 2c 1 — e , f 2c , / '2a -» . /10X 



± 2 V^r.V-TI^ lo ={l^2e ± Vl^e^ = " + 0OnSt - (l2 > 



The solution (11) may be somewhat simplified in form, 

 for if we put 



<£ 1- e = cosh <D } 

 and substitute the values of c and a, we get 



4-7T r — 6 C d(0 , -i _L 



cosh 1 " 



^^^i^MJ^+M' 



(13) 



where ^/a is to be employed with the same sign in both 

 places and where 



Ki + R,' 



or R 2 



€ = 



Rj + R 2 ' 

 according as the pressure is such as to make 



a = 47T0B.!, 



or a=47rcR 2 « 



The integrals in (13) may be evaluated in finite form 



when — — is an integer, and when therefore the velocity of 



one ion is an exact multiple of the velocity of the other. 

 In other cases they may be easily calculated*. 

 The other solution (12) may be put in the form 



, 9 l-eR 2 -R 11 f Sire / 1 1 v _ / a 1 



±2^/ 6(l ~ € J KlR ^ = ^ + const. . (14) 



4 



* The author has calculated a table of these integrals for e= ~? which 



is approximately one of the values for the case of air. This he hopes to 

 give in a supplementary paper at an early date. 



Phil. Mag. S. 6. Vol. 10. No. 56. Aug. 1905. R 



