MR. WILLIAM PARSES ON THE TIDES OF BOMBAY AND KURRACHEE. 691 
ascertaining the character of the correction required. We have now a series of observed 
heights of high water and low water, and a corresponding series of calculated heights. 
In order to ascertain whether the differences between these followed any regular law, 
they were set off as ordinates from a horizontal line, and a continuous line drawn through 
their extremities. This continuous line assumed a form obviously, though roughly, ap- 
proximating to the curves of a series of diurnal lunar tides having a maximum half-range 
of about 12 inches at Bombay and 6 inches at Kurrachee*. It made its high water and 
low water nine hours at Bombay and ten hours at Kurrachee after the moon’s transit, 
high water at full and change being at night in the summer, and in the morning in the 
winter. It had evident periods of disappearance twice in a month, two days at Bombay 
and three days at Kurrachee before the moon crossed the equator ; and, like the first- 
described diurnal tide, it reappeared after vanishing with the times of high and low 
water reversed. There seemed to be some evidence of solar influence upon this tide, 
but of too uncertain a character to justify its being taken into account. 
The incorporation of this empirical tide with the first diurnal tide effected a materially 
closer coincidence with the observed heights and times, but it cannot be taken as a final 
solution of the problem. A more perfect series of observations at Bombay may probably 
suggest some form of the correction more consistent with known physical causes. 
The combination of the two diurnal tides may be effected by the following formulae, 
similar to those given in page 690. 
Let a be interval between the two tides. 
D be half-range of first tide. 
d be half-range of second tide. 
8 be interval between the times of first and combined diurnal tides. 
Then height of diurnal tide at time 6 
=D cos 8-\-d cos a — 8 ; (A) 
and this is a maximum when 
D 
-j + COSa 
cotan 8 = — , 
sin « 
whence 6 may be found, and the half-range by substitution in (A). 
For the purposes of practical computation tables and diagrams were formed from the 
various formulae above given, and under the authority of the Secretary of State for 
India, tide tables for Bombay and Kurrachee for the year 1867 were published. The 
times and heights given in these tables were compared with observation for four months 
at Bombay and eight months at Kurrachee. The diagrams give in a graphic form the 
result of the comparison, the small black dots showing the observed, and the redf ones 
the calculated times and heights. It should be stated that the calculated heights are 
* This result is modified, so far as Bombay is concerned, by the process described in the Postscript, 
t In Plate XXXVI. small circles. 
5 B 
MDCCCLXVIII. 
