358 
EEV. S. HAITGHTON ON THE TIDES OF THE 
From this Table we find : — • 
Mean Lunitidal Interval of 44 Half-Floods 
„ „ 43 Half-Ebbs 
h m s 
20 45 19 
2 54 24 
Keducing the Lunitjdal Intervals found from Tables V III. and IX. to the phase of 
High Water, we have 
Mean Lunitidal Interval =i m . 
From High Waters 23 48 58 
„ Low Waters 23 43 1 
„ Half-Floods 23 45 19 
„ Half-Ebbs 23 54 46 
Mean 23 48 1 
h m 
i m = 23 48 
or - 0 11 
We may calculate the ratio of the Solar and Lunar Semidiurnal Tides from 
Tables VIII. and IX. by the following method :■=— 
Let M"=M^~ycos>, 
S"= S (^)’cosV, 
where P, p are the parallax of the Moon and Sun, taken at an interval before the 
observation equal to the age of the respective Tides ; and P m , p m are the mean values 
of same. 
Then if the Semidiurnal Tide be 
T=M"cos2 (m— ^J+S" cos2(s— i s ), . . . . 
we may write (20) thus, 
T=Acos2(m— B), . . 
where 
A=\/M" 2 -|-S" 2 +2M" S" cos 2 . 
M" sin 2 i m + S" sin 2 [m — s + * j 
an M" cos2^” ^ -l-S ,, cos 2 (m — s + 
( 20 ) 
( 21 ) 
( 22 ) 
(23) 
The Maximum and Minimum values of A are M"+S" and M" — S", as used in finding 
(18); and the Maximum and Minimum values of B are found by differentiating (23), 
which gives, as the equation of condition, 
S ,, -FM / ' cos 2 {m— s— i m — i t )=Q. 
(24) 
