MR. WILLIAM PARKES ON THE TIDES OE BOMBAY AND KURRACHEE. 689 
Then the general equation to the tidal curve being, Height at any time = Half range 
multiplied by cosine of interval between that time and high water, we have for total 
height of water at time t, 
H cos 2 t (semidiurnal tide)-j-D cos c—t (diurnal tide), 
and this is a maximum when 
0= — 2H sin2i(-f D sine— t, 
or 
D 2 sin 2 1 
H sin c — t ’ 
also the half diurnal inequality being 
A=H— (H cos 2£+D cos c—t), 
|j = l — (cos 2£ + jj cos c — t) 
2 sin 2 1 
. COS c — t 
sin c—t 
c °s2 1 
2 sm 2 1 ’ 
whence c, and by substitution in (A) I) also may be found. 
Then, by taking the successive corresponding values of H, h, and t, we may deduce 
the corresponding values of c and D, and thus obtain a series of heights and times of 
diurnal tides. 
If we next apply the same system to the successive low waters, we obtain by inde- 
pendent means a second series which ought to correspond with the first. This process 
was tried, but it was found that there was a decided discrepancy between the two series 
of diurnal tides ; and the values of diurnal inequality upon which the results were based 
were, moreover, not sufficiently sharply defined to give confidence in their correctness. 
A process in some respects the reverse of this was therefore tried, viz. the assumption 
of a hypothetical diurnal tide, and its combination with the semidiurnal tide by means 
of an inversion of the formulae given above. There were at the same time some data for 
determining the approximate values of the local constants which would enter into the 
expressions for diurnal tide. As has been before stated, whenever there is no diurnal 
inequality in time, the time of diurnal tide corresponds with that of actual tide, and the 
range is equal to the difference in height between two consecutive tides. Thus a simple 
inspection of the diagram gives four values for diurnal tide in each month, two when 
diurnal inequality in time vanishes at high water, and two when it vanishes at low water. 
But besides this, diurnal inequality in time of low water is sometimes for several con- 
secutive days so small that a series of diurnal tides, in which the times are those of semi- 
diurnal low water, and the ranges the total amount of diurnal inequality in height of 
low water, could not be far from the truth. 
= 1 — cos 2 1— 
1 - 
cotan c—t=— 
(A) 
(B) 
