HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. ta 
Then, following the same procedure as before, we have for the height 
of tide 
2 
h=3 = ty a [+3 cos . p® cos 3 (x—1) 
PHANG G 
+7); cos A (1—5 sin?A) . p® cos (x—J)] . (85) 
Now, cos \(5 sin? \—1) hasits maximum value ,"*.when cos\= 2/15: 
3/15 
that is to say, when \=58° 54’; thus we may write (35) 
f=2 * (<) val eos? A. 435 cos® 3 I. cos [8t+3(h—v) —3 (s—£)] 
c 
4 3../15cosd(1—5sin2d) $57 15(“) cos®$eos[t+ (b=) —(—8)] ](36) 
In this expression observe that there is the same ‘ general coefficient ’ 
outside [ |] as in the previous development ; that the spherical harmonics 
cos®A, 7% / 15 cos (5 sin? A—1) have the maximum values unity, the first 
at the equator and the second in latitude 58° 54’. The ‘ speeds’ of these 
two tides are respectively 3(y—c) or 43°°4761563 per mean solar hour, 
and y—o, or 14.°:4920521 per mean solar hour. 
The coefficient of the tide 8(y—o), which is comparable with those in 
the previous schedules [B], [C], [E], is 
a 
ps (=) cos® 3 J, 
5 2 
and the mean value of this function multiplied by cos 3 (v—£) is 00599; 
also the coefficient of the tide (y—c), likewise comparable with previous 
coefficients, is 
ef (*) cos® 4 J, 
and the mean value of this function multiplied by cos (v—£) is 00165. 
The expression for the tides is written in the form applicable to the 
equatorial belt bounded by latitudes 26° 34’ N. and S. (viz. where 
sin/=}/5). Outside of this belt, what may be called high tide, will 
correspond with low water. The distribution of land on the earth will 
probably, however, seriously disturb the latitude of evanescent tide. 
It must be noticed that the y—c tide is comparatively small in the 
oo belt, having at the equator only 2 of its value in latitude 
58° 54’, 
Referring to the schedule [E] of theoretical importance, we see that 
the ter-diurnal tide M; would come in last but four on the list, and the 
diurnal tide M, (with rigorous speed y—o) would only be about a half 
of the synodic fortnightly variational tide. 
It thus appears that the ter-diurnal tide is smaller than some of the 
tides not included in our approximation, and that the diurnal tide should 
certainly be negligeable. 
The value of the M, tide, however, is found with scarcely any trouble, 
from the numerical analysis of the tidal observations, and therefore it is 
proposed that it should still be evaluated. 
