of Electrons in an Elastic Solid JEiher. 145 



where \, /a, v are any three Unities. We may take 



Xco= — So>V- *, fia>= — Sa>V- /3, V(o= — So>V. 7j 



so that 



m(Vv)=iSViV 2 V3Sa 1 /S 2 7 3 . 



Thus we have the fundamental theorem 



??*(<£ + \/r, (f) + -\|r, (£ -f yfr) — Hi ((£</><£) -f om (<j><f>yfr) + 3m {(f>^^r) 



Here as a special case we may put </> = a scalar a, ^ = %, 

 when we get 



x* 4- aW + W + m'" E .'' n -t- 3a? 2 m(ll^) + 3o?wi(l^x) 



Or we may put 4> = v, ^r=JVe( ), (f> + yjr = v and so on. The 

 cubic of % is 



and it may be written 



% 3 -ox 2 . i»(ii%)+3x • ^ < ( 1 %x)~^(yxx) =°-J 



w of equation (29) may be expressed in terms of s\ s", s'" 

 thus. From (26), (27), (28) we have 



2(e 1 '-2^ 1 )=2(*"-^), 



Hence 



and 



or 



22/# 1 =l*' 2 -s" + 5 '", 

 m,/A = 36*" + (16 + i'-)s" 2 + §(± 1 - 2b)s'». . (48) 



Th. 11 shows that for our purposes we may omit from to 

 any constant multiples of m', m", m" f . Let us do this and 

 also omit fourth order terms, so that now for the first time 

 must we assume the strain small. Put v for the modified 

 value of w. Thus 



t-IA = tt(m' 2 -e*) + {±!> + {c)ni , [m / + (m /2 -2m'' -e 2 )] 

 " +i(±l-26)(-m ,3 +4m / m' , +mV~2Se^€), 

 Phil. Mag. S. 6. Vol. 19. No. 109. Jan. 1910. L 



