and if the Moon were in the variable ecliptic, its latitude would be sin </>'sin (v — a); 
that is, the latitude, measured from the variable ecliptic, is = s — sin <£' sin (v — a'); or, 
putting 
s /} the Moon’s latitude, measured from the variable ecliptic, 
we have 
s = sin 0' sin (v — a) + s r 
Hence, disregarding the variations of cf>', a, we have 
ds . , . /. ds, 
; = sm <f> cos (v-a) + -^; 
ds 
and substituting these values of s, and s', we find 
s cos (v ~ v )~^ v s i n ( v ~ v ) ~ s ' 
d 9 
= S / COS (V — V ) — ~ sin (V — V') 
+ sin <£' -jsin (v — a) cos (v — v') — cos (v — a) sin (v — v) — sin (v — a') 
= s y cos (v — v') — — sin (v — v'); 
ds d£l dil , oN d£l 
dv di-“d ! 7 (1 + s) dF 
* f ^ 
cos (v — v') -Is, cos (v s ^ n ( v ; 
which, neglecting the periodic terms, is 
2 „,2 "/ ’ 
_ mu 
= & —-s,: 
and then