56 Mr. J. P. Dalton on the 



Since <J> is a linear function of the velocities 



2 u r , <&=0. 



r—1 aU r 



Hence dH = ^ ^ jL(rf N ) = o by (49) and (50). 



Therefore as I have already argued, a steady magnetic 

 field has no effect. The same argument does not hold for a 

 steady electric field. For in arriving at the equations (30) 

 electrostatic energy is supposed included in H. Its presence 

 already determines the canonical distribution from which 

 the motion starts. 



§ 8. Conclusions. 



To save the "sether" it is necessary to give up the 

 classical mechanics. This paper shows that the theory of 

 radiation can proceed without using the principle of minimum 

 action. A formula for the complete radiation naturally 

 suggested is 



K 



E x = S7rm\- 4 {l + K 1 \0 (e* -l)}" 1 , 



k x and k are arbitrary constants. This gives a result similar 

 to Hayleigh's for large values of \6, a result similar to 

 Wien's for small values. 



June 10,1912. 



JfT. Note on the Energetics of the Induction Balance. By 

 John P. Dalton, M.A., B.Sc, Department of Physics, 

 University College, Dundee *. 



§ 1. |~N the generalized induction balance in which each 

 A arm contains resistance, inductance, and capacity: 

 (i.) steady balance is conditioned by the usual Wheatstone 



relationship between the resistances; 

 (ii.) an approximate impulsive balance is given by zero 

 integral extra-current in the galvanometer ; while 

 (iii.) true impulsive balance necessitates zero extra- current 

 in the galvanometer at any time. 



Heavisidef used his operational method to solve the case 



* Communicated by Professor Wm. Peddie, B.Sc, F.R.S.E. 

 t O. Heaviside, ' Electrical Papers/ ii. p. 280. 



