176 Mr. A. M c Aulay on a Modification 



(p. 690) of ' Electromag.' For brevity I must refrain from 

 redescribing my methods and notation and must constantly 

 refer the reader to the original paper. 



Pkop. If r a , r b be fluxes, V-r^Ta/D is an intensity, D, ~D' 

 being the densities of matter in the standard and present 

 positions respectively. [In the original paper D was used for 

 electrical density and D m for material density.] By this is 

 meant that Vt^t^/D' bears the same relation to Yr a Tb/T> as 

 does <j' to cr in equations (5) § 7 of ' Electromag."' 



To prove, we have 



rJ=m- l xTa, Tj=mr l x T b, D'=m _1 D. 

 Hence 



YrjT b '/T)'=m-iY X T aX T b /B=^YT a T b /T>. 



3. It may be noticed that the investigation in ' Electro- 

 mag.' is not apparently complete for a perfect dielectric, 

 though in a sense the equations are correct. For such a 

 dielectric x is zero, and it would seem to follow from equa- 

 tion (28) § 50 that since e = 0, ^1=0. This, however, is 

 not true, for in this case we have the condition Syd = 0, 

 which introduces a new term into equation (28). It is easy 

 to see, however, that the case is met by ignoring equation (28) 

 § 50 and putting E of equation (29) equal to zero ; for D and 

 d have now the same meaning, and account has been taken in 

 equation (29) of SyD = 0. Since in the present paper E of 

 equation (29) is always zero, we will use E to stand for the 

 E of § 61 (except that it is best to define it not as RK but 

 as —aVh or, what is the same in the present case, — bV0» 

 Thus E' will have the meaning usually given to E. 



4. For a fluid we have for the V of § 51, 



l'= -DV 2 /2 + w) + (27rK'- 1 D' 2 -^H ,2 /87r), . . (1) 



where iv is the ordinary potential energy per unit mass due 

 to compression or rarefaction, and is therefore a function of 

 D' only ; and where K7, yj are scalars, which also can only 

 be functions of D'. 

 Thus 



07' = aD'. dZ'/aD'sdCm-^D . "dV/bW 



[' Electromag.' § 54, equation (10)]. Hence [ibid. § 54, 

 equation (20)], 



[0']=D'3Z'/&D', 



or [ibid, equation (21)] 



<frf« -0+ ?e )-27rK / - 1 D'( )D'-^'H'( )H'/8w, . (2) 



