( 119 ) 
The integration according to w may directly be executed. It yields 
for the three cases: 
Pe) en 
IF dw = 5 
a 
if 2l — 
b 
If we substitute in this equation for each case the proper limits 
and if we then-add the results for the three cases, then we get: 
tu 
. / el! 
2] 2 + ah bh { que! bh gn’ fu 4} + 
b 
0 0 
+ ant} ast buut — qu’ bw} | cos p (1! —u) du dul. 
In the exponent of a we have neglected the term 27 as it is small 
compared with the other terms. If we arrange the terms in another 
way and again suppress the constant factors we may write the 
integral in the following form : 
hw 
ffe) 5 cos p (u —u) du dul + 
0) . 
0 
tw 
UF a) 1 u a —u. 
+ {fee (*) (5) COS plu — u) du dies Ata», (55 
00 
Integrating partially we find: 
uy 
(Ya \u 1 Ha \t ; uy p ity u 
| — cos plu —u)du—=— Jeo plu —u) | —— SUN plu —u) du= 
. l a / iy? oat ase h 
0 l 9 i‘ l 
) ) 
nd 
Db 
1 : fa \u la p a 2 u lu p a \% f 
ee — cos plu — U) | — sn plu —%)|) — | cos plu — u)du 
lo jr a x ob lo de b 
From which follows: 
j a ae ; ; 
u L —{ — COS Pu } —p sin p 
a aise sh nd ast clean? 
| — [COS plu — u)du— LES d a 
b ot » 
rte 8 
) 
0 
In the same way we have: 
as B. rd ! $ ' 
2 =| 008 — psinp 
vaN b b oo pu psimpu 
— eos plu —u)du= See 2 ; 
b in = os 
— D 
b / 
0 
