1184 
with the groups A, R, B and S. Both the series are, however, the 
same as in (17); when we go in fig. 3 (V), starting from bundle A 
towards the right, then series (17) follows; when we go, however, start- 
ing from.S towards the right or the left, then the above series follow. 
We can also deduce this property without using the P,7-diagram. 
For this we form from (41) and (42) the two new reaction-equations : 
(u, — *) a, Fy +... + (uy, — 2%) a, Fy +... + (4 — 2X) ar Fy =0 (509) 
(u, —l) a, FH... + (uy —l) ay Fy +... + (ur—!) a, F, = 0 (502) 
wherein we give arbitrary values to / and z. As we are allowed 
to always take the last group in (41) positive, we suppose a, > 0. 
We distinguish three principal cases. 
JE ATE See IES CAD ES. Th Soa SSS 
Principal case I. We may distinguish three cases: 
a. u, >landl>x; 6. u, >landi<z; ce. l> 4, therefore 1 >~x. 
Now we can show that the equations (50¢) and (50%) satisfy con- 
dition (3), if we take them in the given or in opposite order of 
succession as it appears necessary. |The reader, to whom we leave 
this deduction, has to bear in mind that the coefficient of the first 
term must be positive in both equations; in the case c this term is 
negative in (50%), so that we have to reverse all signs of (50%)|. 
As all signs: of (50°) are the same as in (41) the series of signs 
of (50%) is, therefore, the same as that of (41). 
Principal case II. We distinguish three cases: 
a) l>wu,,and/>x; 6) l>u,and/< x; c) /<u, therefore /< x. 
It appears that the series of signs of (50° is the same as that in (41). 
Principal case III. u, > x > u, 
We take x between the two ratios w,—; and u, which succeed 
one another, so that is satisfied: 
By > ssi Se Sot ya St ey Se Se os Sb 
We assume that in (41) the phases #,..,../: belong to the 
same series of signs; a;..da,..a; are, therefore, all either positive 
or negative. We write (50,) and (50,) in the order of succession: 
AE a 
(«—p,)a,F, +... (#—pa)acPs + ... (gag =O 
(—py)ayF, + ..-(—uz)azF, +... (l—u,)a,F, a ord | _ (604) 
-.-(l—u,)a,F, .. . (l—ug)azl; +... lugar = 0 
We distinguish again three cases viz. : 
a) l>p,andl >=; 6) 4>p,andl <x; c) 1<u, therefore 1< x. 
When we take care that in all those cases the coefficient of the 
