260 G. PLARR ON THE ELIMINATION OF a, £, y, ETC. 
I =— SI 
(23) Il = Sll+ VU 
IIT =—SII + VII 
1V = + Sil. 
With the help of this we need occupy ourselves with the expression of IT only. 
Besides the formula of definition of II = 2apa, we have formula (18), and 
introducing VI = 0 into (16) we get for VII, namely, the vector of II: 
(24) . WU Fes as 
(25) VII =— 23V(aV a). 
As we have expressed a, ales etc., by the help of a, so we will now express 
ba, &B, &., by the help of a, and II. 
In treating (24) successively by S.a., S.6., S.y. we get 
S<da =— 5 Sal 
¢ able 
(26) Sg =—} Sel 
Sy =— 5 Syl. 
Then by (21) we get 


ee ee: 
Viste Sage cae ) 
=+ 2 > ae [aSaw, — a,Saa | 


By the expression (18) of IT this is 


So that we have the three values: 

Vda = a5 SI— 52 eh Daa 
(27) Vap=£.5 Sl —5>| a Sae 
Vey =.5 8-32 Day . 

When these results are not to be used for differentiation, then we may — 
identify in it a, 8, y, respectively with a, B, y, so that wnder the restriction just 1 
expressed we have: 

