Radiation and Electromagnetic Theory. 313 



The first is effected by putting /-/r = 2Rr + r 2 , and the 

 second by making the self-induction a maximum. We shall 

 now see how the third can be effected. 



P — P 



The difference in phase when ~ — ^ 2 is a maximum is 



given by equation (5). 1 1 + "2 



Replacing sin 2a and cos 2a by their corresponding values, 

 we get 



Pi-P 2 2RZn(R + r) 



P 2 + P2 ~ y (2Rr + r 2 ){4R 2 /V + (2Rr + r 2 + l 2 n 2 ) 2 \ 



= 2B(R + r) (6) 



\/mrTr~ 2 ^{2U + r) 2 + r 2 + (^ 



This is a maximum when l 2 n 2 = 2Rr + r 2 , that is when the 

 difference in phase is 90°; and it will be found that the self- 

 induction can be altered to a considerable extent above or 

 below this value, without affecting the control materially. 



Taking into consideration, then, the fact that the self- 

 induction is not constant, but varies to a certain extent with 

 the current, and that in any case it is only possible to measure 

 it approximately, it seems advisable to adjust it in such a 

 manner as to make l 2 n 2 sls nearly as possible equal to 2Rr-}-^ 2 . 



This allows a large margin either way without any appre- 

 ciable loss of control, damps down the surging currents, and 

 finally avoids all fluctuation in the external circuit by keeping 

 constant the total power given out by the two alternators. 



I have to thank Professor Grreenhill for suggestions and 

 for verification of the formulas involved. 



XXXII. Radiation and Electromagnetic Tlieory. 

 By R. Hargreaves*. 



§ 1-3. Radiation formulae connected with change of period in reflexion 



at a moving surface. Connexion with laws of Stefan and Wien. 



§ 4-8. Refraction. Formula for pressure. 



§ 9-12. Electromagnetic waves viewed from a moving standpoint. 



Fresnefs formula. Aberration. 



§ 13-16. Reflexion and refraction. Application to formulae in first 



section. Calculation of pressure, &c 

 § 17-19. Introduction of charge and current into the equations. Electro- 

 magnetic momentum or momentum of radiation. 



REFLEXION at a moving surface has certain distinct 

 features : the angles of incidence and reflexion are 

 unequal, the periods of the incident and reflected waves are 

 different. At the same time energy is converted to mecha- 

 nical work by the action of pressure on a moving surface. 

 * Communicated by the Author. 



