308 
rROFE.SS(JK G. II. DAIGMX OX THE PEAR-SHAPED FIGURE 
It' we put 
4 +A 
we iind 
and 
5(1—^) 
3 ^ - 5r 
= 9. 
• o i ^ 0 
o — 4^^- 
Therefore, with tlie above alternative form for (f, 
53. M and i/-W = ~0^- 
^ 1^3 {fx) and (/x) = — sin ^ ( 1 — — siiT 6 
C,{^) and = (1 - tIcos2<^)(1 - K-^cos~cf>f 
9.~ / 
(14). 
Again in the two cases where the type is OOC Ave found 
p=‘ (") (a=^ i. 
Putting 
we find 
and 
T. 
o 
K" 
T = 
K~ 
3 - /3 + 2/U 
5(l-/3) ’ 
|(L +2,c2a:(I 
n 2 — 5(f 
Q '.-r o ■ 
1 — 4^' 
«= + 4a)5), 
'J'herefore, A\'ith the above alternative form for (f, 
eus ( I — ry-yi 11"-vlr) 
P.;' {^) and P;.®(/x) = 
siir’ \lr 
Ps^ (p.) and (p) = — [ I — K' siir 0)- 1 — t •‘’in" B 'j 
(^ 3 ' {(f)) and (iTs® {(f>) = cos (1 — cos" 
( 15 ). 
In the tAvo cases Avhere the type is OOS Ave found 
P 3 ' (v) and \^J^{p) — (h- - “ ')' 
