1033 
mR, +r Rk, +...+5,8, +88, +...+¢7, HUT, == 
a,A,+a,A,+...+6,B,+0,B,+...t¢,C,+¢,C,+..+d,D,+d,D,+..° 
in which the reaction-coefficients 7, 7,... ete. are however unknown, 
but they are all positive. The sum of the reaction-coefficients at the 
right and at the left of the sign of equation must be the same. We 
find from fig. 3 for the reaction of the phases with respect to 
curve (R,); 
rR, +7',k, +..-+8,8,+8,8,+...+¢,7,+¢,T,4+. | 
+a@,A,+a@,A,+-°=6,B8,4 0,B,4.-.. - (2) 
0 +¢,€,+...4+d,D,+d,D,+... \ 
in which the reaction-coeffieients are still also unknown, but they 
are all positive. Also again the sum of the reaction-coefficients at 
the right and at the left of the sign of equation must be the same. 
We multiply (1) by 2 and deduct (2) therefrom; we find: 
ar, + (ar, as) Big exe 0 (as, —s')) 8, Hi (Js, —s',) S, “Phe 
aie (At, —t') Lp El (at, —t',) T, n= 
aA, + (da, +a',) A, + (Aa, + @’,) A, +... + (4b,—0',)B, +\ . (3) 
(4b, —b',) B, +... + (dere) C, + (Ae, el C, +... 
+ (Ad,—d',) D, + (ad,—d',) D, +... 
In this equation (3) the coefficient a’, of the phase A, is always 
positive. 
In order to find from (3) the reaction with respect e.g. to curve 
(C{), we put: 
(1) 
c 
ac,—c', = 0 consequently A= —. . . .,.. (4) 
Cy 
Hence we find some conditions, which the reaction-coefficients in 
(1) and (2) must satisfy. It is apparent viz. from fig. 3 that all the 
curves of the bundles (7’), (A) and (B) are situated on the same 
side of curve (C,) as curve (A,). As in (3) the coefficient of A, is 
positive, the coefficients of A,, A,,... and B,, B,... in (3) must be 
also positive and those of the phases 7’, 7.,,... negative. The first 
condition, viz. that the coefficients of A,, A,,... are positive, is 
satisfied; we write the two other conditions: 
b! b', b' t! Oe 
NE dee (6) 
b, b, b, t t, 
in which 2 has the value, indicated in (4). 
Further it is apparent from fig. 3 that the curves (C,), (C), … 
and the bundles D),(R) and (S) are situated on the other side of 
curve (C,) as curve ‘A,). Hence it follows that in (8) the coefficients 
