PROCEEDINGS OF SECTION A. 201 
From (27) and (29) 
ee ae. Wa (ucos 2pm + v sin 2 pz) aotae 
4 py (pw? + v*) K y, ae 
pa. Wa(usin2pe -veos2pum) , ~”™ 
4pv (ee tv) Kk 
Hence from (30) and (31), observing that (u + »?)*"K=(\ at + K) 
rat Wa K 
#5 (14 ve )= 2 (¥ee-') 
1.6:, 
ey 
i Wa ( Y E a 1 
TS a ra (32) 
2% ( Like ee ) 
Hence finally 
7 ae = POI a8) 8 
4 pv (we + v) paver PTR | {wcoswo tr sinwof e 
=f {cos ye (2 — 0) - v. stn, fe.(2. a7 = 0) Ta ih deg cha me 
ra ce 
Wa 1 - Vv @ @ 
"4 Aa 
27 ( uae ya) Qa? £1) A. (33) 
If K is small compared with Y G «a? and with > a4, the last 
tN tie, Oe eR ae . 
term in (33) becomes 274, (, , da and the limiting 
Vas 
W 
value towards which ¢ tends § =’%= ae oe 
T 274 1 = Aa 
YG 
— PA 
if » is so large that e may be neglected, we have when 9 = 0 
{calling ¢t’=t) +t)t’=t, + Maciel, 3 tig rags WO 2 
Reh Va + py (mw? + v2) K 
KE 
and when 6=7_, W 
a A at and ?¢’ rapidl 
27a Lh ote apl ap- 
7 ( + °) pidly ay 
proaches the value t’z, ... Se Hes Yee, ee (34) 
