;nO PP.OFESSOK G. H. DAKWIX OX THE PEAK-SHAPED EIOrPE 
Hence it follows that we have the identity 
1—K 
I y " I '* n o • .1 o n • 0 i •» ,i „2 f — W") (sill" 0 — CO”) 1-5“ 
— C'K' siir y = C-K' sin- y - LI - L _ 
ro" — 1 /a:- o)- — 1 ft)- (1/A- — ar) (1 — uy)w- 
— ft)-) 
Putting ft)' = - , 
-,A + -TT —- -.+0' Sin- y = -- . -T-r (1 — '^)(l — - sin-1/) (1 — cos- (p). 
(/~ K~ — rr fr ' (K' — v") Slin \/r q- q~ 
This expression, together A\ ith those for x, i in (8), enables ns to write doAvn the 
results at once. As before, I drop the several factors as being redundant for most 
})nrposes. 
From (y) 
{v) 1^1 (/^) Cl {(p) = z , Pi^ (v) Pi^ (g) {(P) = x, 1 ^ 1 ^ (v) (g) ((/)) = ij 
From (lU) 
(18). 
.T /.■> 
T'l ^ 
(z^) ll-i (g) C-: {<p) and (v) (g) iiix {(/>) = <fx' + ^ f 
K — q 
+ 0^7'sin'7 • (H^), 
where 
so tliat 
7' = ;^ [1 -f- k' d" (1 — k'V'-)^] , and k' = q- 
■_AT 
1 - -p ’ 
o /o 
T'l 
- 7 
, = 1 - 27A 
From (11), ( 1^)5 and (13) 
Pi' O) Pi' ()*) C,' (4>) = .fi, IPi’ (li) IS,’ (fi) Si’ {4>) = '/■■. P,’ (v) Pc’ ((i) Si’ {X) = •’■y 
. . . (ilO). 
From (14) 
^^3 {^) 1^3 (/^) C 3 {(p) and {v) ^^ 3 - (g) Cy- {(p) = ■- {q'x^ + -J 
whei-e 
so that 
From (15) 
i ir - q -z' 
K” — 7" 
4- c-(fq ~ sill' y) 
5==f[l + «’:F{l -tK’ + «*)’], and = 
(- 1 ). 
o /a 
T'l ~ 
a:'- — If 
, = 3 - 47 b 
Ps^ {^) Po^ (/^) {<\>) and P.d {v) PyS (g) (T/ (</,) = .r [q\,r + 4 ^. V' - '/'z 
K 7 
+ (-Y 7 ''sin-y) . (LA’), 
