1182 
negative, then we may place this last group, after reversion of its 
sign, before the first group and combine them to one single group. 
We have deduced this by indicating that from both the series (18 
and 19) the same P,7’ diagram-type results. 
Now we shall indicate that both series may be converted mutually 
and in what way this can take place. 
We write reaction (1) when we put » + 2—r for the sake of. 
abbreviation 
a, FP, +a, Py. + Arn Era + ag Fy +... + oy F, =0 … (41) 
we assume that @,—; is positive, and that a,...a, are negative, so 
that those last form a separate negative group, just as group U in 
(18). We represent the ratios by u,...«,, so that 
Oy > My > Darl Dole > Dr 
is satistied. Reaction (2) now passes into : 
wal, + pga, +. + ur Ar Fe + tates +... + Hal, =0 (42) 
It follows from (41) and (42) 
(ua, FY +. + (aar Pr + (faa Pe +... + (a, =O (48) 
wherein % is arbitrary. We choose % in such a way that 
iE Ao Ss eas alleen er a flea (ie!) 
is satisfied. 
The negative coeff. of #.../, from (41) become positive in (438) ; 
the coefficients of /’,..: F, keep all the same sign. We place the 
positive group 4... £, at the beginning of the series ; then we obtain 
(Ua-%) 0g: F' ye 4- + (Uy -*) ay (u, Ba, PH + (Ue -1-#)a2 Eri = 90 (45) 
wherein the coefficient of the first term is positive | viz. u, — «<0 
and a, < 0]. Now we take u, > 0, so that also x > 0. We write for (42): 
—Urar Py — ... -— wy ay Ea, Ke Ur der Er = 0 (46) 
so that also herein the first term is positive | viz. uw: > 0 and a, < 0]. 
Now we shall show that condition (3) is satisfied. We write this: 
RSS gS SSS re ee AN 
wherein : 
he semi A en dn ef 
Us—X 
Now we have: 
—Uj — Hg (tj — lg) 
45 hg == = = - (48) 
Up % Ug—% ne (Up —*)(Uq—*) 
When we apply (48) every time for two values of 4, and i, 
which sueceed one another, consequently for 4, and 2,, for 2, and 2,, 
ete. and also for 2, en A,, then we find when we take (44) into 
consideration 
