528 Mr. J. H. Jeans on the 



angle In the neighbourhood of a point at which X vanishes 

 (a nucleus), the graph for X will approximate to the upper 

 halves of two parabolas, the axes of which coincide with the 

 axis of the graph. The latera recta of the parabolas will be 

 in the ratio of k x to k 2 , the concavity of the larger being- 

 turned towards the cathode. 



§ 18. Let f be the value of X which corresponds to rj, the 

 critical value of y below which the differential equation (8) 

 ceases to hold. If we can find out in what way f depends 

 upon the pressure and current, we shall have obtained some 

 indication of the closeness of approximation which is to be 

 looked for. 



Let Nj be the large value of n l corresponding to the value 

 f of X. At the point at which n ± attains this value, dyjdx 

 will be very nearly equal to 47n'/& 1 , so that we have approxi- 

 mately, by equation (5) 



« _ 1 f . k 2 4ttH 



i 



The value of f is therefore seen to be 7 M . , and since k A 



may be supposed to vary inversely as p, the pressure of the 



gas, this will be proportional to £- • If we suppose that the 



critical value f always corresponds to the same volume 

 density of ions, we shall have for the relation between f , p, 

 and i, 



where C is a constant so long as we are dealing with the 

 same gas. 



We must therefore expect that the value of X below which 

 the experimental graph begins to appreciably differ from the 

 ideal mathematical graph, will decrease as the product pi 

 decreases. The graphs which approximate most closely to the 

 ideal form demanded by theory, ought to be those for which 

 this product has the smallest value, and an inspection of the 

 graphs of Graham and Wilson seems to show that this is the 

 case. 



§ 19. A further cause of disagreement between the graphs 

 of theory and observation may perhaps be found in the 

 intermittence of the current. The theoretical graph gives the 

 distribution of potential-gradient on the assumption that the 

 current is steady throughout. If the current is in any way 





