200 
MESSRS. A. E. H. LOVE AND F. B. PIDDUCK 
and along BC, where s = and r decreases from W to r', we have 
V XT , T t \ , /I 3 \ 4 fFi(o- + w) 
Z = Kj + Lj (r-SiH - r- —-- 
\cr dcrj { cr 
|V__5V = (si + 7- ; )(gi ^)fe + r )' i (20-180^+420f-280r), 
dr r + s (r + sf 
, = (r—r') {s x — s') 
(r' + s') (r + Sj) 
The value of Z at (/, s') can be regarded as a sum of terms with the coefficients 
Z B , hi, l x , ccr 0 10 /945a, ct 0 , , K 1; L 1; A 0 , A 1; ... , 
and each of these terms may be found from the formula for Z (rs') by performing the 
integrations where necessary. The result will be to exhibit Z ( r', s') as a sum of terms 
with these coefficients. 
27. Determination of the Second Middle Wave. —No integration is needed in order 
to obtain the term which has Z B as a factor, but it is important to observe that V n , 
as a function of r' and s', can be expressed either in the form 
or in the form 
v„ = | (R,+s.) (± I fe + _ + . 4 +'±M 
1 3 yr tz-R,) 4 (/+«,)* ! 
V u = f(R 1 + Sl ) igX 
cr 
We shall suppress the accents on r' and s' so as to express the value of Z at ( r, s). The 
term with coefficient Z B is 
-I (R,+s,) z c (i £J j(gx D 1 p , ±M‘ 
cr 
The term with coefficient h x is 
2 ki p J f ( s - s ,)«(s + R,)n . 
cr 
The term with coefficient l x is 
(SR^A^-g) (^R^ j , 
cr 
The terms with coefficients ccr™/M5a and a 0 are 
cr 0 10 i \/l 0 
° — +a ° 
945a 
1 ( s — s l 
a VRj + Si 
1 + 4 
s + Ri 
Rj + 
+ 10 
+ 20 
£+RiV 
Ri + Sj 
g + Ri X3 
v Ri+5j 
+ 35 
s + Rj 
Ri + s x J J _ 
