272 
Pp 
o regions of p factors corresponding with x’? and also the o regions 
q 
of q factors, corresponding with y’? ete. in all possible o9/o/.... 
Je 
ways, adding them and finally dividing by g/o/.... Then n, may 
be written 
Je Pe 9, 
n, — Az ty -.-:; 
where in the way known from symbolism of invariants o,o, 
different equivalent quantities n,, n, .... are to be introduced in 
order to avoid ambiguities’). Then the given form is also obtained by 
at ere ( Bik aye 
VE ie | Pos “a oen 
P 
p q 
According to theorem IL we have now: 
5 P US. q a. 
Bp Gx) (oy. ya 
p 4 
pore raed) long 
= (EL Oi. x’) YL Hy . y) 435 
p q 
p p q q P Pq 
When we write *Lna, = u,’in, = Vv, ete. and m=uy..., then 
we have 
ee es Po De deld ved 
Jem 1 Wy ems (TURD. @) el ie 
P v q 
P P 
m is the only affinor of this shape that when transvected with r’ 
P P 
gives Fm. In fact every affinor m, that can be written in the form 
P p q 
m, == CL Mz) (VL m,) Ae 
P 
and gives zero when transvected with r’ is identically zero. In fact, as we 
D 
have supposed that x’ may obtain all values that are solutions of 
p p p 
the equation ‚„Lx' =x’; we thus may take for x’ 
e ’ ? 
x == aL S ihe On Sp ’ 
where s,‚...,sS’, are not-ideal different sets of variables and the 
q 
same holds for y’, ete. Then we have: 
P P p 
; 4g 
0=m, = CL il) 2 oh Ss, sieke Sp iP (YL m,,) : yb tr zee ty’}? eves 
a= (“7 ti ’ Ds) | vL q t? PE 
== (CL ML) Sie Sone My) ty tee. tan 
P q 
P 
=S eens enn tT 
P 
1) Comp. Die direkte Analysis zur neueren Relativitätstheorie, p. 11, 17. 
