Recent Progress in Theoretical Physics. 257 



CiL^^ ^ + ir=o. (5) 



\ dr / dr dr 



Let us consider the dynamical condition that the raj may be of 

 constant intensity, that is, that r may be constant. 

 Lagrange's equation for the force in r becomes 



d_ 



dt 



Since r is constant the first term vanishes. We have therefore 

 the equation 



__^ + ^=0. (6) 



dr dr 



in which q is supposed to be given, and we are to determine the 



value of the angular velocity 6, which we may denote by its actual 



value, n. 



The kinetic energy, T^ contains one term involving ?i^ ; other 



terms may contain products of n with other velocities, and the 



rest of the terms are independent of n. The potential energy, F, 



is entirely independent of n. The equation is, therefore of the 



form 



An^ + Bn + C= 0. (7) 



This being a quadratic equation, gives two values of n. It ap- 

 pears from experiment that both values are real, that one is posi- 

 tive and the other negative, and that the positive value is numeri- 

 cally the greater. Hence, if A is positive, both B and C are neg- 

 ative ; for, if n^ and 71^ are the roots of the equation, 



A {n, + 7io) + B = 0. (8) 



The coefficient B, therefore, is not zero, at least when magnetic 

 force acts on the medium. We have, therefore, to consider the 

 expression B71, which is the part of the kinetic energy involving 

 the first power of n, the angular velocity of the disturbance. 



Every term of T is of two dimensions as regards velocity. 

 Hence the terms involving n must involve some other velocit3^ 

 This velocity cannot be r or q, because, in the case we consider, 

 r and q are constant. Hence it is a velocity which exists in the 

 medium independently of that motion which constitutes light. It 

 must also be a velocity related to n in such way that when it is 

 multiplied by n the result is a scalar quantity, for only scalar 

 quantities can occur as terms in the value of T, which is itself 

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