( 754 ) 
It is necessary then for all values of 9,,9.,-+++@n—1 that the 
closing side of the broken line be greater than c and taking into 
consideration the two integral-theorems, serving as starting point, we 
conclude that the integrals IV’, and |W, have both become zero. 
3. We might ask whether results as arrived at above are also attained 
when the functions J (ua) behind the sign of integration have not 
all the same parameter. The following operation shows that this is 
partly the case. Supposing that Wo ys. +) fn are numbers greater 
than rv, then under a definite condition the evaluation of the integrals 
oo 
: el pb. s du 
Wi J’+1 (uc) Js(ua,) J*(ua,)... T° "(uan) i 
a, a,%2.. A7 ; urn 
0 
le 2) 
c+? fb: du 
W.= 
y--2 i 7 de 
sa poe fy (uc) J(ua,) J'2(ua,). . « J" (uay) — EE 
ke Gj 
can be reduced to that of the integrals W, and W,,. 
For the reduction of W, and W, we can repeatedly apply the 
formula *) 
ie 
(wa) 
J#(ua) = ui i J (ua cos a) cos} a sin®?*-”—1 ada. 
AI ur 
We obtain in this way 
il 2 
W 
ZT 2-1 rn 2 [4 —2v—1 d 
== ; cos a, sine ada 
3 5 
VENI AUS P). 1 1 1 
= 
sf cos®*Hl a, sin 2#n—2—1 ade, X 
Plu) 
oo 
F1 du 
/ — | JH! (we) J? (wa, cos a,) … J' (war cos an) — 
(a, cos @,)’ … (an cos Gy)’ win)" 
0 
1 = 
W. —= e 7g 2x1 nm —2¥—1 
5 gE ia =), cos a, sin” a,da, 
pe 
2. 
costa, sin? Pl oden X 
pee Fa 
1) Nrersen, page (81, 
