96 



Prof. F. Slate on Electron 



tc 



Thus /(K) will have a root less than - unless a l5 a 2 ...a n 

 are all zero. ' 



Hence the whirling speed is a maximum when all the bays 

 are equal. 



In the case o£ two bays the restriction that the a's are 

 small may be removed, so that it can rio-orously be proved 

 that the greatest possible whirling speed is reached when 

 the bays are equal, but this theorem does not appear to have 

 been proved for any greater number of bays. 



The introduction of the function /(K) is due to Mr. Berry, 

 and the author has extended its use to any number of bays. 



V. Electronic Energy and Relativity. 

 By Prof. Frederick Slate *. 



THE modus operandi characteristic of relativity proves to 

 be working in disguised agreement with what Newton's 

 equations also teach, when these are properly written to 

 include variable inertia f- The older problem of motion 

 resisted proportionally to the square of speed has furnished 

 the principal key in this reconciling dissection, after its 

 equation of motion was put into a form inspired by a 

 prospect of making it a model for electrons. That problem 

 is surprisingly interwoven with our attempted analvsis. 

 It allows aspects to be rated normal under its general type 

 that had once seemed exceptional. Especially is this true of 

 vital relations for energy, where correspondences show that 

 are of first importance to recognize. 



The equation of rectilinear motion, and the recasting of it 

 with the aid of terminal velocity (i\) referred to are 



|; «P-®)J^^ 



(a) P-R = m, 



(1) 



In (b) that factor occurs directly, whose different powers 

 run through all the calculations of relativity. Much can be 

 made to grow out or its striking property that links an 

 arithmetical and an harmonic mean : 



+ 



»i— v_J \v 1 +v l l\Vi — v/ v-s — v 2 



(2) 



* Communicated by the Author. 



J - Slate, Phil. Mag. April 1920, p. 433 ; July 1920, p. 31. This is a 

 continuation of those papers, carrying- on their plan and their notation 

 consistently. They are cited as {!.), (II.) To avoid wasteful repetition, 

 free reference is made to results alreadv recorded there. 



+ See (II.), eq. (8). 



