HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 81 
the two terms become 
R cos (yt—4). 
But this is the form in which the results of harmonic analysis for the 
total K, tide is expressed in the first method. 
From (41) we have . 
k=f+(h, —}7r)—)’ oo wh hoheiet meal sees (42) 
In this formula h, —47 is V, for the solar K, tide, and »’ is a complex 
function of the longitude of the moon’s node, to be computed (as 
explained below) from the second of (40). 
We must now consider the coefficient f. 
If M, be the mean value of the lunar K, tide, then we know that its 
ratio to M should according to theory be given by 
eM sin I cos I : 
M, sin » cos w(1—# sin? 2) 
The ratio of M to S should also according to theory be given by 
M_ 7(1+$e?) sin I cos I 
S  7,(1+e,”) sin w cos w 
We must therefore put the coefficient 
Ss 2 9S y¥4 \ 
{1+ Ga +20r cos y} 
5, 
a a 
where i), “€uttactces een) 
Bo. (1+ 3e;*) . 1 
M, 7r(l+2e) (1—# sin) 
S__S, sin w cos w (1--3 sin? 7) 
M ~M. sin £ cos L 
f is clearly a complex function of the longitude of the moon’s node to be 
computed as shown below. 
The reversal of the process of reduction for the use of the instrument 
for prediction is obvious. 
In the case of the K, semi-diurnal tide, if we follow exactly the same 
process, and put 
Dif sin 2y 
ae cos 27+8;M 
{1+ (=)? i cos 2y}# 
f= 
ee 
M, Pan ae enn wee 
where Ce 
S, mein Cl + 3e,?) - 1 
M, r(i+ie?) (i—# sin®Z) 
tk S, sin? » (1—% sin?/) 
M, sin? 1 
1883, " 
