322 
REV. S. HAUGHTON ON THE TIDES OE THE 
The hours of High Water corresponding to these values, and nearest to the time of 
the Moon’s declination vanishing, were : — 
1st June .... 
15th „ . . . . 
28th „ . . . . 
Mean 
h m 
8 32 
8 00 
6 40 
7 44 
Hence, using the mean value of 2 cr during the observations (45° 50'), we obtain 
±0-299=Ssin 45° 50' cos (s-i s ); 
but 
h. m 
s= 7 44 
i s =- 4 11 
s—i s = 11 55 
which corresponds to 180°, or the cosine equal to unity. Hence we have 
or, finally, 
0-299 =S sin 45° 50', 
c 0-299 ft. 
b — sin 45° 50' 
=0-417 ft.=5-00 inches. 
B. Semidiurnal Tide (Heights). 
If the preceding Table be plotted to scale, it is easy to separate the Semidiurnal Tide 
from the Diurnal Tide just discussed ; but it is not possible, from observations made at 
the Solstice only, to separate the Solar and Lunar Tide and determine their coefficients. 
The general expression for the Semidiurnal Tide is 
T=S' cos 2(s— f s )+M' cos 2 (to— i m ), (3*) 
where 
S', M'= Solar and Lunar Coefficients, not corrected for declination or parallax, 
s, m= Hour-angles of Sun and Moon, 
i s , v=true Soli tidal and Luni tidal Intervals. 
This expression may be thrown into the form 
T=A cos 2 (to— B), (4) 
where 
A=n/M' 2 +S' 2 +2M'S' cos 2(m^Ts—i~^I s j, 
tan 2B — ^ s * n s i n 2 ( m ~ s + Q 
M'cos 2 i m + S' cos 2 (m — s + i s ) 
( 5 ) 
