SIR G. B. AIRY ON THE TIDES AT MALTA. 
135 
same lunar hour every day, and with a coefficient periodical in a month. The solar 
diurnal tide, if sufficiently important to be considered, would have a coefficient 
varying slowly, and the epoch of its daily tide would advance on the moon’s, gaining 
2tt in a month (approximately). So that putting M and S for certain coefficients 
depending on the moon and sun, the first nearly constant and the latter not varying 
much in the lunation, and R and r for certain angles, both periodical in a lunation 
(nearly), we should have for approximate height at any time — 
M sin R cos (moon’s hour angle — A) 
+ S cos (sun’s hour angle — A), 
or M sin R cos (moon’s hour angle— A) 
+ S cos (moon’s hour angle +? — A), 
or (M sin R+S cos r) cos (moon’s hour angle — A) 
— S sin r sin (moon’s hour angle — A). 
Each of the factors, it is to be remarked, is periodical in a lunation. 
It will be remembered that p is the factor of the sine of tidal angle measured 
from the tidal zero of each day, and that q is the factor of the cosine of the same 
angle. Now if we connect the expression p sin 6-\-q cos 0 into the form B. cos (0— A), 
where 0 is the tidal angle from the zero of tidal time, we obtain 
inch. 
h. 
m. 
I. 
+ 0-25 
cos 
(0- 
-11 
51), 
II. 
+ 0-90 
cos 
(0- 
- 3 
45), 
III. 
+ 0-55 
cos 
(0- 
- 2 
33), 
IV. 
+ 0-21 
cos 
(0- 
-20 
21), 
y. 
+ 0-38 
cos 
(0- 
-16 
19), 
VI. 
+ 0-41 
cos 
(0- 
-13 
44), 
VII. 
+ 0-47 
cos 
(0- 
-15 
38), 
VIII. 
+ 0-21 
cos 
(0- 
-11 
38). 
And if instead of 0 we introduce (f>, the tidal angle from the moon’s transit, where 0— 
<f ) — London retard of high water on moon’s transit + 16 m , 
we obtain for the diurnal tide 
inch. 
h. 
m. 
inch. 
h. 
m. 
[. 
+ 0 - 25 COS ((f) — 
2 
16) 
II. 
-j-0'90 cos (</>— 
17 
51) = 
— 0’90 COS ((f)- 
-5 
51) 
III. 
-hO'54 cos ((f)— 
15 
47) = 
— 0*54 cos ((f)- 
-3 
47) 
IV. 
— (- 0 "2 1 cos ((f)— 
9 
36) = 
— 0'21 cos ((f)- 
-2 
24) 
V. 
+ 0'38 cos ((f)— 
6 
53) 
VI. 
+ 0'41 cos ((f)— 
3 
59) 
VII. 
+ 0*46 cos (c f> — 
5 
5) 
VIII. 
+ 0'21 cos ((f)— 
0 
40) 
