260 



Mr. J. H. Jeans on the 



as B, 0, or D in fig. 5, we should not only have an infinite 

 volume-density of ions, but also all the ions would be at rest. 



It has, however, been already pointed out (§ 2) that as y 

 becomes indefinitely small, the equation from which our 

 solution has been derived ceases to hold. New forces come 

 into play, with the result that the graph representing the 

 actual values of y ceases any longer to satisfy the differential 

 equation which holds elsewhere. And if these forces are 

 forces which prevent the volume-density of ions from becoming 

 infinite (as must be the case if the ions are of finite size), 

 the change in the differential equation will be of such a nature 

 as to prevent the graph from ever meeting the axis. 



Let us imagine that rj is some small value of y, such that 

 these forces do not produce any effect till y falls below a 

 certain value rj, but that for values of y less than rj the 

 equations of § 3 cease to hold. 



In iig. 6 let A be the anode, ABODE the axis along 

 which y = 0, Imn . . . . the line y=y. 



Fig. 6. 



Starting from the point a! in the anode, such that the value 

 of y is less than the critical value y ly let the graph be drawn 

 as in fig. 5 until it meets the line y = v in some point m. 

 And after the graph has reached this line, let it be continued 

 so as to satisfy the true differential equation which holds when 

 y is less than r]> 



The graph must either remain in the region in which y is 

 less than 77, or else emerge from this region at some point n 

 in I m n . . . . If in the limit we assume rj to be very small, 

 the former alternative need not be considered. Beyond n 



