ON THE MNARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 59 
before, let 2u, 2% be the lags of M,, S,; and 2«, generically, the lag of 
the K tide. 
Let 6=f[+h—s—r,+é. 
Then 0 might be defined as the mean moon’s hour-angle, the mean 
moon coinciding with the true, not at Aries, but at the intersection. 
Let the argument of the K tide be written generically 2/0+u—«]. 
Then 
hj=M, cos 2(0—p) +S cos 2[64+s—h+v,—£—2]+K, cos 2[9+u—«] ' 
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If we write 
6o=S—Mo+s, 
and ‘ 
FH cos 2(u—¢)=M,+ 8 cos 2[s—h—f, +p] 
HT sin 2(u—o)=S sin 2[s—h—f, +p], 
the first two terms of (55) are united into 
Fhieo08 200 po of) Sa ae eo (BB 
with fortnightly inequality of time and height defined by 
; S sin 2(s—h—f,+,) 
M,+Scos2(s—h—Cotp)tr .. « » (57) 
H=/[M.2+58?+2MS cos2(s—h—Z,+p)]) 
tan 2(u—¢)= 
The amount of the fortnightly inequality depends to a small extent 
on the longitude of the moon’s node, since ¢, and M, are both functions 
of that longitude. 
For the K tide we have 
K, cos 2(0+u—«)=K, cos 2(u—« +9) cos 2(0—9) 
—K, sin2(u—«+ ) sin 2(0—¢@). 
Hence 
éH= K, cos 2(u—«+¢) ) 
(58) 
oo = — 
dork : Poinawiite.; Medtie 
ayy Ma AUK +9) | 
It is easy to find from the Nautical Almanac (see Moon’s Libration) 
the exact time of mean moon’s transit on any day, and then the successive 
additions of 125420601 or 12 25™ 145-16 give the successive upper and 
lower transits. The successive values of 2(s—h) may be easily found by 
successively adding 12°-618036 to the initial value at the time of the first 
transit of the mean moon, and ¢ may be obtained from the table of the 
fortnightly inequality for each value of 2(s—h). 
The function wu is slowly varying, e.g., for the K, tide 21=2(s—£) 
+2(7,—v"’), and the increment of argument for each 125-420601 may be 
easily computed once for all, and added to the initial value. 
In the case of the diurnal tides it will probably be most convenient to 
apply corrections for each independently, following the same lines as those 
sketched out in § 5. 
The corrections for the over tides M,, S,, &c., and for the terdiurnal 
