42 
MR. K. TERAZAWA ON PERIODIC DISTURBANCE OF LEVEL 
Substituting these values of integrals in (9), we have 
1 
ahqpz 
a, = ———■ 
2 p 
+ 
- (r < a) 
a 
_0 ( r>a)_ 
ahgp (X + 2p) 
2 p (X + p) 
OLZw x Z (V — Cl ) r r.[ \-| 
- o 2 a’l \ D’Vi - 
2 a vtt? (v) 
2 cltt 
r~ 
~(r < a) 
S - 
a 
_ > 
_0 ( r > a)_ 
-\ -(gjC«! +J/]) 
9 9 
r—ar 
. - ~ 
aa~ irara. 
+ 
2 (■>’■ — «■) P(«)-e,r f / r \l l /oo\ 
P' (u) 
in which the simplest value of v, i.e., n — 0, n' = 0 in (i.) of (18) is taken as the 
representative. 
At the surface it reduces simply to 
U). = 7 ^d—'f' b -U + e^)- 
where 
jfJL 
(\ + p) 
ir 1 a 
Cti'a" 
7®i 
a - -- 
(23) 
Ci = 
2 i 2 
a + r 
Sara ’ 
= — 
a 2 + r 2 — Sar 
Sara 
= 
a 2 + r + Sar 
Sara 
■ (24) 
Similarly for the value of ( Cr 1 ) we have 
du z \ _ ligp (X + 'Zp) 
Sr /o 2p (X + p.) it 
■ aa 2 {k<h<’h->h)- 
(25) 
For practical purposes of calculation, it will be very convenient to transform the 
expressions into J acobi’s q series ; q being defined by 
q = e' 
T = 
CO3 
cofi 
After Weierstrass, if we put 
l _ ( e i — £3)*—(g t —ea) 1 _ (r + a) 1 - \ r —«[* 
(e\—e^f‘ J r(e l — e^ (r + a)* + \r—a\ i ’ 
then q can be computated from 
«=i + 2 (i/ +i5 (iy +i5o (ir +o ^ i7 >- 
