81 
From (16) dx — m^/ (a - bf + <r 
ST- 
,jnd 
cos. - 
/ .. m0\ 
1 1 - cos - T j 
dd 
1 + cos. 
mQ 
a- x— \/ (a - bf + c“ 
1 - cos. 
md 
/ . bV , c2 _ -hf + <?{ 3 ^ (g - 0!+ -jV .*-_«} 
(s-6)+c- - m0\ 2 
^ 1 - cos. -g - ) 
| (V>3 6) 2 + c 2 + a - &)Cos.m0 j 
} 3 y/ (a - b) 2 + c 2 + b — a j 
Substitute these values in (15) observing the change in the 
limits, then 
v — 
m 
V 3 y/ (a - bf + c 2 - + 6 - 
a 
. /a - a -</ (a- bf + c 2 
+ ■yj (a - bf + c 
2 /ct- a 
-cos -M 
m \a- a 
) 
2 _/a-(Z-y/(a- bf + c\ 
• ‘U-/3 + ^ Awj 
—cos, 
pn 
dd 
v 1 + 
^/(a-bf + c 2 + a-b 
3 V ( a ~ bf + c 2 + b- a 
. cos.mfl 
.(17) 
It is readily seen that 3 (a - 6) 2 + c 2 + 6 - a is a positive 
quantity whatever may be the values of a , 5, c. The 
coefficient of cos.m0 is a proper fraction, therefore, equation 
(17) may be written as follows : 
m 
dd 
V 3\/ (a - bf + c 2 + b - a 
fOi 
m 
^ -s/1 + ncos.mQ 
i m 
IIMMMIMMII (18) 
where »= H V /;-^ + ^, + g - a , 
*>v (<x-6) 2 + c 2 + 6-a J a '~ (l + \/ (a-bf + c 2 
and Cos4 _ a ~ \/ (a- b f + c 2 
of “/3 + v'(o"-5) 2 + c 2 
