THE LATITUDE-VARIATION TIDE. 
105 
of which the least square solution is 
h = h' + h" } 
3, = <V + C„/' • 
S« = SJ+S vi \ 
where 
U = — 2 TL 
( 3 ) 
m 
(7/ = (—) P — 2 2T cosp (2k + 1) £ 
pj v ' m k k r v 1 ' m 
h" = — Sc ammv P' 
~ ' T mv sin /S r 
0/ = — cosp - . Zc,v t sinvp T 
S„" = —sin p^ . Ss t v r cos v p, 
p 2 sm mv ft r sin v r v 
*’ r = C-) -T7-. /-3y.» 
m v sin /5 r sin \v ft, — P ~J sin [v p r -f p -J 
the summations with respect to k being taken from k = 0 to 
k = m — 1. The probable errors are to be computed by the 
usual formulae. These forms are adapted to the treatment of 
the observations one ^‘-period at a time; the quantities 
e r implied in c r and s r must be taken for the middle of the 
period, and to this epoch the resulting values of C vj and 
relate. We then have for the same epoch the final values 
