538 On the Distribution of a Gas in an Electrical Field. 

 fairly well with these experimental results if F 2 lies between 



The distance between the striae depends on the diameter 

 of the discharge-tube. It is possible that the solution of the 

 general differential equation for % would lead to this, but it 

 seems hopeless to attack the equation for two dimensions. 



Another interesting deduction from the solution above, 

 which has been verified experimentally since I made the 



calculation, is that while ^ is periodic in the striae the 

 potential % is not periodic. 



The equation cosh — ^~ — = sn (A#-j-/3, k) may be trans- 

 formed into 



sin yjr=/ji sn (v,k)*, 

 where ^ is a linear function of %, 



jju some constant, 

 k some modulus. 



Now this equation is just of the same form as that for the 

 motion of a simple pendulum under gravity, yjr being the angle, 

 and v the time, and we know that when the pendulum makes 

 complete revolutions it is possible to express yjr as equal to 

 fjuv and a series of periodic terms. 



Thus, x m general is a linear function of oc and a series of 

 periodic terms. 



% must be real, and the series convergent. This will 

 depend on the particular circumstances. That the series must 

 converge to zero in one case is obvious, for if there are no 

 free atoms %=Acc+B is a complete solution of the equation. 



Further, ~ is periodic, although •% is not so. 



I understand that from measurements of ^ in the striae, % is 

 just of the nature we have found, while Mr. H. A. Wilson, 



at the Cavendish Laboratory, finds that —■ is periodic. 



d 2 x 



* In the equation ^p =87re ^N^i 2 sinh (eA^-hoe) put 



eh x -\-»—i^, 

 x = it : 

 and we get d 2 v|/- 



l^ja" = —STre 2 h s/ N^ sin yfr, 



which is the equation of motion of a simple pendulum. 



