of Polarization Plane in an Aeoloiropic Medium. 2*21 



become (3) and (4) respectively. This statement can easily 

 be verified independently of " M. T. E." 



In the language of " M. T. E." this is equivalent to taking 

 for the standard position not the actual fixed position of 

 matter, but a homogeneously strained (% _1 ) state of that. 



By suitably choosing % we can make either c or ft a 

 constant scalar. It will be sufficient to consider only one of 

 these cases. 



Let w! '= /Mi fi 2 f i*>3 , where /*/, fi 2 ', y% are the actual prin- 

 cipal inductivities (/. e., w! stands towards p! asm towards %). 

 Put 



X = ™'~ k ^ (9) 



Thus 



m = m r ~ l j (10) 



and equation (8) becomes 



B' = mft/ilB, D' = in'i^D, [. . . (11) 



fJb = 1, C == fA f ~* C' IJJ~*, J 



Since now in eq. (4) fi = l, we see at once that in the ideal 

 space denoted by p, H, D, &c. the wave-surface of propagation 

 of H and E or B and D will be a Fresnel surface, and the 

 corresponding index-surface will be its polar reciprocal. 



The equation of this ideal wave-surface being expressed in 

 terms of p, the true wave-surface will be obtained by straining 

 by the function ^ or m'~i pji because p' — XP' ^ ne ideal 

 index-surface is the polar reciprocal of the ideal wave-surface, 

 and similarly for the actual surfaces. Hence, by the lemma 

 above, the actual index- surface is obtained from the ideal by 

 straining by ^ /_1 or ml* p/~K 



This change of variables from p to p' thus enables us to 

 reduce the finding of the wave-surface from the index-surface 

 to the ordinary Fresnel case, and thus saves us from the only 

 part of Mr. Heaviside's investigation which is very complex. 



If we notice that in equation (1) above the relation between 

 a f and <r is the ordinary intensity relation, and remember that 

 p' and a' are naturally taken as the coordinate vectors of 

 points on the wave- and index-surfaces respectively ; and if 

 we bear in mind the fundamental properties of intensities and 

 fluxes, we shall find that all Mr. Heaviside's results for the 

 actual case can be written down from the corresponding ones 

 for the simplified ideal case. For instance, if we show in the 

 simplified case that 



a = VBD/iS(BH + DE), 



S2 



