of Electrons in an Elastic Solid yEther. 131 



expression. If z is a scalar function uf x-> ^ ne differential 

 operator G is defined by 



is=-Bdjffbt£ (12) 



Thus Q is a symbolic Unity capable of explicit expression. 



w is a function of v, and is therefore a function of x- 

 For such a function there is of course a definite connexion 

 between Q" and 9. It is easily proved to be 



a=r& (13) 



Since 2 is self-conjugate it follows that not d but GT' is 

 self-conjugate and T _1 G is self-conjugate. It may be shown 

 that the necessary and sufficient condition for z to be a mere 

 function of v is that T^CLr is self -conjugate. 



In (11) and (12) ?, £ are used with their usual bilinear 

 meanings given by 



Q(?,0=Q(m)+QO;jQ+Q(M), 

 Q(Si, Si, &, &)=Qte h h + Qft hhi) + ••• - 



The meanings now defined of the symbols 



a, a, e, f, g, 



e, f\ g, w, »i', m", »i r ", », ?i', ?tf, to', 



\7,T, <©,<£', 



e, f, ??, p, p', *i &', w, %, &), 



will be rigorously adhered to in this paper, and will not be 

 explained as required. The same remark applies to the use 

 of the dash for the conjugate of a Unity, so that, for instance, 

 %' is the conjugate of %; and to the bar for the self-conjugate 

 part of a Unity, so that for instance v is the self-conjugate 

 part of v. Note that there are three several uses of the dash 

 .above ; (1) linity self-conjugacy ; (2) orders as with m\ m", 

 m'"; (3) reference to the actual as opposed to the standard 

 state as with n', w' f d%', p, ds '. The use of numerical suffixes 

 is mainly confined, but we need not be rigorous in this 

 custom, to the purpose of denoting the symbol to which a 

 c inferential operator such as V or Q applies. £i, f J5 f 2 , £> 

 may be regarded as of this nature, since they may be replaced 

 by Vi> Pi> V* P* 



K2 



