THE INDEX SYMBOL IN THE CALCHLUS OE OPEEATIONS. 
41 
then 
{a, b, c, dXDj, A)" 
=(aAc4lVj,Vif-2(aAc41Vj,7iX%MT-(a,b,c,clXVjMt^^^^ Vi)-h2(a,b,c,dJVj,7d\ 
which may be symbolically represented thus : 
(a, b, c, dJBj, Vi)' = (a, b, c, dX (V^- Vi) 1 * ) 
{% vy (Vj v.) 2 
I (y;- v,r (Vj vif (Vj v,) 
And generally, 
(a, 5,.. ]S;..D,.,V, I (..V, V,) 1 
(..yvi)’ (..v,-v,) 
* 
Moreover, if 
(..v;v:)^ (..v,v:)^ (..v,Vi) .. 
(..v;vi)" (..v^v;)“-‘ . . (..v.vo 
u= 2(1“' 2“" , . )a’“' xp . . 
Then, understanding that the order of multiplication must be preserved, as in the case 
of two variables, 
d d d d 
>'( • . VyVi)w= 2F{. . , 2(a,+l)£^“% S(«,+l)£^^'^'-j(l“- 2“^ . . )A-t‘ At • • 
Again, if 
U^I •• ^22 0522^1 “l“/322A2•• 
DjD, — V2V1 — |(aiia2i+/3iia22+ •• )Aid-(aii^2iH“/^ii/^22 4‘ ••)'*^2+ • • } 
|(®12®^21 “f" /3 i 2®22“1~ jA") “h (0^12/321 “f"/4)2/l22“l“ • •' | 
ci 
dX] 
_d_ 
dx^ 
Then 
