(158) 
- Then substituting for 8,, &, 8 and p, q, r their values, 
with sin « for tan « as is permissible, we have 
l  C—A 
00 —= — SsinaCos |? + nt }» 
A 
à à ; ‘C— A 
sin 60% —= — Sin asin | + + F nt). 
| C— A 
de + COS 00) — tan À SIn & COS nt, 
de LE TA 
— —= — NSINASIN| 9 + -——n" 
dt (+ A } 
re Bag TRE C — A ) 
SNn6— — — nsinasin|s + nl |» 
di RE OA 
de dy 
— + COS — —= n. 
dt dt 
We now differentiate the first three of these equa- 
tions, and only retaining terms of the first order add 
them respectively to the second three. We thus obtain 
es l d: est es) 
— (9+ 00) =—n sin eue, TEA Ne : 
7 crRt ndt A OCT ar 
d 
sin (8 + ©6) T (y + dy) 
d? . C—A CE 
=n sin «| 1 —— : cos (; + à nt |» 
ndt A 
u dp) + 6 + 08 set + dy) 
—— ee —— ! 
D (8 + de) + cos (6 + 03) T(b + dé 
C — A . . “ 
n lan À sin & so 
= | — 
