PROCEEDINGS OF SECTION A. 199 
so that we have 
vo f a 8) 
=(AcosuO+Bsinud)e + | (A cosu(27-0)+B sin yp (2 7-8) 
E a? 
hat +K ci) 
we have at once 
du v0 v(27-6) 
Tp= A+ UB) {cos uO x e —cosu(27r-8) xe i 
v8 (27 — 6) 
+ (— wA+yB) fe sin wO—e sin (2 m6) (16) 
d2u ve y (27-6) ) 
=7 aa A+2yuvB) {e cos wO+e cos pm (2 w— 8) 
gpa vy (2 7-8) 2 
= (2uvA +B) je sin 48 +e sin p (2 -8)} (7) 
aS a - ve v(27-90) } 
ee (14+-2¢?)A+p(1— 2? )B) }e ) ¢ cos —e Cos p. (2 7 — 9) 
( :, v(27 6) 
+ \u(r-202)A-v(rt2n7) Bh f Ve sinwO—e sin w (2-0) (18) 
vo vy (2 r—-8@) 
1+ u 
a= (t= 4 ut yt) Ang uy 3 ye cos LO+e cos uw (2 r— 9) i 
( cay El VBE vy (27-8) i 
a Te Peal ae 2, EG. Vane sin uw (2 7-9) a) 
and these satisfy (10). 
From (6) and (8) 
dv | oe ace 
do*"-YG| a? \d@ 
Hence 
dv d? u E 
Nat as sds 20 
ao =you d @? + (vow = +YG on 
Hence if we write for short 
vA —-pB=A',pA+rB=P,rvA+pB=C, —-pA+vB=D, 
we have 
F Ja E 
Diet Fi Wl Nal °K) 
l we } A’cos 20+ B! sin pb a 
Yep? nae 2 ) 
Fs sa i = cos w(2m7-—6)+ B’ sinp(2a7- at, eae al 
Mee ie |C’ cos 0+ D'sin pot .”° 
YG OV— $0 cos wlam- 0) +D’sin p (2-0) ¢ .” 27-9 
(21) 
