of Electrons in an Elastic Solid SEtlier. 139 



w is a symmetrical function of e, f, a, the same in form at 

 all points of space, e and %e (meaning e + f+g) are not 

 simple functions of rj and its space derivatives, though 

 %(e + ^e 2 ) is such a simple symmetrical function. Another 

 is 



%e + %/{/ + efg — m' + m " -f m!" = m i 



say. Any rational function of m l9 e+ %e 2 , f+if*, 9+°9~ 

 which is symmetrical in e, /, g is expressible in terms of 77 

 and its space derivatives, and the degree in y is the same as 

 the degree in e,f,g. We therefore seek the three simplest 

 symmetrical functions of the kind. These are s f of the first 

 and second orders, s" of the second and third orders, and 

 s"' of the third and fourth orders, where 



s'=te + $Ze 2 , (26) 



*'=J-m l =2Qfi-Jjj)-efg, . . . (27) 



s»> = s"-$[i(e + yr-(f+if 2 )(9 + kr)] ' 

 =&[-e*+fg(f+g)-2efg] +#(_*+ */y) L (28) 



=i(-^+/+r/)(^-/-fr/)(^+/-^)(i-r^>- 



We are guided to $" by getting rid of the first order terms 

 and to s'" by getting rid of the second order terms by sub- 

 tracting an appropriate function from s" . 



Let w be as simple a function of sf s s", s'" as it can be. 

 If w is a mere multiple of s' the consequences are remarkable 

 and unexpected, and seem to have a distinct bearing on the 

 properties of actual aether. I have been acquainted with 

 the properties of the medium thus constituted for a long- 

 time, but till lately had supposed them to be of mere mathe- 

 matical interest. For the present let it suffice to say, thai 

 though very suggestive, they do not altogether meet present 

 requirements. 



We will be influenced in our choice of w chiefly by the 

 ordinary assumption that w is a true minimum for e=f="g = 0. 

 This excludes a mere multiple of *" and suggests the sum of 

 multiples of s" and s' 2 . This carries us necessarily as far as 

 the fourth order, so that it would be an artificial restriction 

 to exclude a term in s'". 



The form which it is convenient to use is 



iclA=±p>'' + bZ(f l --g i y + ic(Xe i y, . . (29) 

 where A, b, c are positive constants, and 



