132 Dr Glasher, On expressions for the [Nov. 14, 
equal to zero in the formule for ©, (x), O(«), ©, (x) and making 
x very small in the formula for ©,(@), 
Nae 4 {= 2i+sin 2. (2 a 
an JaruJo cosh 2¢— cos 2t oa eh 
wt eo a 20 
ee * Jp 0 cosh 2¢ — cos 2¢ ex i 
t 
Jk'p = We 
Af simi — sim 2t . in (=) d 
1 jus 0 cosh 2¢+ cos 24> be 
_ 4 [% sinh 2¢+ sin 2¢ (2) at 
orp o cosh 2¢ + cos2t 
— sinh ¢ cos t+ cosht sin ¢ =i e& ai 
cosh 2¢ — cos 2¢ 
_ 8 /* sinhtcost—cosht¢sint os (= 
* a cosh 2¢ — cos 2¢ ) a 
vf J orp 0 
= 8 [° (Cc+Ss)sinh 2t—(Co—Ss)sin 2¢ . (2° 
vk Jap (cosh 2¢ + cos 2¢)? oy iD ae 
8 r (Ceo—Ss) sinh 2¢+ (Ce + Ss) sin 2¢ e a 
~ lien: (cosh 2¢ + cos 2¢)” ie Fie ee 
where, for brevity, S, C, s, c are used to denote 
sinh t, coshé, sint, cost. 
The occurrence of the term a in the second of the formule 
for J/p and ./kp is due to the fact that the integral 
Sua t 
| =——7 Cos (=) dt 
0 +2 bo 
is no longer equal to we “ when « is zero, the value of the integral 
being then zero. If therefore we put x= ye in the general formule 
we must, corresponding to the term wre e “ in the series, introduce 
separately the term = , as this term is not included in the value 
be 
of the integral expression, 
