690 ME. WILLIAM PAEKES ON THE TIDES OF BOMBAY AND KUEEACHEE. 
A series of trials based on these data led to the following results : — 
1st. That the diurnal tide was referable to the transit of the moon immediately ante- 
rior to it, and not to one a day and a half anterior, as in the case of semidiurnal tide. 
2nd. That the time of high or low water of solar or lunar diurnal tide was about three 
hours at Kurrachee, and two hours at Bombay after the transit of the sun or moon*. 
3rd. That the amount of diurnal tide (being proportional to the declination and the 
cube of the parallax combined) was for the half-range at Kurrachee about of an 
inch for each degree of the sun’s, and for each degree of the moon’s declination when 
at the mean distance from the earth. At Bombay the range was taken to be -§• more. 
A series of diurnal tides was then calculated from the following expressions : — 
Let M be moon’s declination. 
S be sun’s declination. 
P be moon’s parallax (sun’s parallax neglected). 
MP 3 
L=-jTyg- (57 being the mean value of moon’s parallax). 
T=moon’s hour-angle. 
C= proportion of half-range for each degree of sun’s declination. 
Then the height of diurnal tide at any time t (measured from the time of high water of 
solar-diurnal tide) is 
(3LcosT— £+Scostf)xC (A) 
This is a maximum when 
0 = 3L sinT— t— S sin t , 
S sin £=3L (sin T cos t — sin t cos T), 
s 
=sin T cotan t— cos T, 
S 
-y + COS T 
cotan t—' ^ — , 
sin I 
whence t may be found, and thence by substitution in (A) the range of the diurnal tide. 
The application of the daily successive values of S, L, and T in these formulae gave a 
series of hypothetical diurnal tides, and these were combined, by inverted forms of 
the expressions at p. 689, with the actual semidiurnal tides, so as to obtain the values 
of diurnal inequalities which they would produce. 
These hypothetical diurnal inequalities were then compared with the actual ones. As 
had been anticipated, the assumed values for the constants which gave a coincidence in 
high-water time and low-water height did not give a coincidence in high-water height 
and low-water time. This result is indeed identical with that w T hich was obtained when 
the series of diurnal tides, deduced from the high-water observations, was compared with 
those deduced from the low-water, but in its present form it offers greater facility for 
* It has since been found that the times are nearly the same at both ports (see Postscript). 
