THE LATITUDE-VARIATION TIDE. 
107 
where 
W+:U") 
Y pj ^pj ~b ^pj j - ’ 
a fi = ff vi + ff pj” J 
( 6 ) 
<=(—) - £ Q k smp(2£+ 1)- 
m 
m 
(A") = 
v sm N m v fi Y 
^ Cl N m v sin ft 
r Pj " = “ cos p — . ^ c r w r sm v ft 
<r Pj " = — sm p — . ^ s r w r cos v ft 
w r = (—■)* 
2 sm Nmv p v sin v p v 
Nmv sin ft sm — P sin ^ ft + p 
the summations with respect to k being from k — 0 to 
k = m —1. The probable errors are to be computed by 
the usual formulae. These forms are adapted to the treat¬ 
ment of the observations one section of N superposed j- 
periods at a time. The quantities e r implied in c r and s r must 
be taken for the middle of the section, and to this epoch the 
resulting values of r Pj and ^ Pj relate. We then have for the 
same epoch the final values 
/ vP(N + l) . , \P(N + 1)(?. 
c pj — ( ) rpj • ^pj 5 s pj — ( ) Pj 
% = V C pj 2 + s pj 2 , Sj = ian 1 ( s Pj -5- Cpj), 
for substitution in the forms (4). 
Let e n e 2 , . . e 2rj or e lt £ 2 , . . e 2s + 1) according as the 
number of consecutive periods or sections from which the e’s 
