326 
REV. S. HAUGfHTON ON THE TIDES OE THE 
Having corrected the curve of Lunitidal Intervals for the Diurnal Inequality, the 
remainder is the acceleration or retardation on the time of the Semidiurnal Tide. 
We have, by equation (5), 
tan 2B— sin + s f sin 2 (m — s + i s ) 
M/ cos2z m + S' cos 2 (m— s + i])' 
Differentiating this expression so as to obtain for B a maximum value, we find, as 
the equation of condition, 
0=M' cos 2 (m^s — + S' (10) 
Substituting in (5) we obtain 
tan 2B= 
-t/M' 2 — S' 2 sin 2 i m + S' cos 2 i„, 
and assuming 
VM' 2 — S' 2 cos 2z m — S' sin 2 i„ 
S' 
M' 
=sin 25, 
we find, after reduction, 
and, finally, 
and 
tan 2B=tan 2 (« m +0) ; 
2(B-C)=25 
~=sin2(B— C). 
( 11 ) 
( 12 ) 
On examining the Lunitidal Curve, corrected for Diurnal Inequality, we find the fol- 
lowing ranges from Springs to Neaps : — 
High. Water. 
Low Water. 
h m 
h m 
+1 0 
7 18 
-1 6 
5 30 
2~~6 
1 48 
or mean maximum range 
2B=l h 57 m . 
Although we have not found the value of i m , we may take as an approximation to it 
the Moon’s mean Hour- Angle at High Water, already given in the Table, 
i m = + 0 h 7 m . 
Hence we have 
2B-2C=l h 57 m — 0 h 14 m , 
or 
^=sin (l h 43 m )=sin (24° 55')=0-421 (13) 
Collecting together the partial results obtained at this most interesting Tidal Station, 
we obtain: — - 
