524 



Mr. J. H. Jeans on the 



to a single convolution of this curve about the point T, the 

 curve being confined within the area A^GrcBOA. The range 

 of possible values for -sr n , it is easy to see, will be the line 

 Tc, the limiting values being Ue and UT. Similarly the 



Fig. 8. 



range of possible values for vrp will be bT, and so on. Now 

 the ratio of Tc to bT depends on, and is roughly of the same 

 order as, the ratio of TU to TS, and therefore of k 2 to h x ;. 

 and direct experiment shows that this ratio is large. 



As we pass along the graph away from the anode, the curve 

 in fig. 8 will revolve about T in a left-handed direction. All 

 the curves which meet STU within the range Tc must, by 

 the time they reach TS, be compressed into a smaller range 

 Tb. Hence if S^r n) $vr p , . . . are the variations which occur 

 in passing from any one curve to an adjacent curve, we may 



reasonably expect that -~—^ will be large. 



Passing beyond p the curve enters the region y <i). In 

 this region the form of the curves is entirely unknown, but 

 there are no grounds for supposing that the curves which 

 have cut ST within a range bT will spread out so as to cut 

 TU in a range comparable with TC. The supposition upon 

 which we shall proceed is, that if we for the moment regard 



k 2 /ki as very great, then £— will either be finite or will be 



of a lower order of small quantities than k— - . 



Hence there are reasons for supposing that ^ — will be- 



