6 
REV. S. HAUGHTON ON THE TIDES OE TH K 
where 
M = Lunar Coefficient, 
S = Solar Coefficient, 
p,p m = Lunar parallax, Lunar mean parallax, 
P, P ; „ = Solar parallax, Solar mean parallax, 
[jl = Lunar declination, for a period preceding the time of observation by an 
interval called the Age of the Lunar Tide — 
c t = Solar declination, for a period preceding the time of observation by an 
interval called the Age of the Solar Tide — 
s = Sun’s hour angle, 
m = Moon’s hour angle, 
i a = Solitidal interval, 
i m = Lunitidal interval. 
In order to compare (15) with (14), we must transform (15) into a function of 
s and u. This may be accomplished as follows : — 
Writing 
m=s+m — s 
we have 
m — i m — s + m — s — i m 
from which (15) becomes 
M' cos (m — f m )+S’ (cos s—i) 
= {M' cos m— s— f m +S' cos cos s 
{ — M' sinm— s— f (ll +S' sinfjsins 
From which we obtain, by comparison with (14) 
(16) 
A!=M' cos S' cos i s 
(17) 
(18) 
B!= — M' sin m — s — f m +S' sin i' s 
Having thus got rid of s, we must transform (17) and (18) (which are now functions 
of m— s, and of the Moon’s declination, and parallax) into functions of u. This may 
be thus effected — 
1°. We have 
p a 1 + e cos v 
( 19 ) 
where 
r = Moon’s distance 
a — Moon’s mean distance 
e = Eccentricity of Moon’s orbit 
v = True anomaly, measured from perigee ; 
