122 Dr. L. Silberstein on General Relativity 



Again the fourth o£ (II a), for £ = 4, compared with the 

 second of (II) gives 



F 14 = -i <£ 1? etc. 



and at the same time cr 4 = — =p. Finally, the first of (II) , 



y/gu 



compared with (II a) for i=l, 2, 3 gives, as the remainder 

 of the required dictionary, 



F 23 



= M 1 a Ail, etc . . q- 1= pVl , etc, 

 V /7 v — a^a,A 



The relations between the forces and the polarizations, which 

 are obviously of prime importance, follow at once. In fact, 

 by (35) which for orthogonal coordinates becomes 



F" = FJ.^ , (35 a) 



we have M^ = Wlii/g^, Ej. = Si\/^44 ? and s0 . on - 



Thus, for any orthogonal system of curvilinear coordinates 

 u\ collecting the scattered formulae, 



F 23 =3fti S/gvgsto etc.; F U = E! V -g n , etc 

 F 23 = M 1 \/^ 1 , etc.; F"=— ®!-7=i 



#11#44 ^ ' ( 37 ) 



o"! = , --, etc., cr 4 = — , 



V -^11^44 ^#44 



where w l9 t> 2 , v 3 are the components of v along the curvi- 

 linear " axes " u u u 2i u z and similarly for the remaining four 

 vectors ; and the relations between the forces and polariza- 

 tions assume the remarkably simple form 



3y?=- 7 ='M, g= ~=E. . . . (38) 



V#44 V#44 



These latter are the simple relations supplementing (I) 



and (II). If w 4 is used as time, — 7= plays the part of 



V #44 

 magnetic " permeability," and at the same time of dielectric 



" permittivity." Of course, according to (36), dt = du 4: \/g u 

 would be the more appropriate time-element in the system 

 under consideration. And if g a is 1 or any constant, then 



