86 A NEW METHOD OF DETERMINING 
With this value of cos*?@,and r= a, cos “py — &7 cos J, 
we find 
Pr. __ dCos*e,—e,.71 cos f --r cos f (E cos *¢,--e)--r sin -4 Cos *¢, 
Pi My) COS *Qy 
__ a cos*g,--r cos f. cos*g, +r sin f.7 Cos *¢g, , 
Ms COS *¢g, (1—2e,E—cos *¢, & — cos *gy7 2 
and hence 
ai saritdh, aiken 
1+&—.cos f-+-7.— . sin 
mh a : 
7. 1— 2e,—cos’¢,€’— cos’, 
From 
GO Ui, df dz 
a tb @a ° de” 
and 
df __  ky/p(.--m) 
ae r ? 
we have 
df a 
di. — %- » - COs >. 
In like manner we find 
lf 2 ; 
 — n=". cos op. 
dz } 
We have therefore 
dz 
