694 ME. WILLIAM PAEKES ON THE TIDES OF BOMBAY AND KDEEACHEE. 
POSTSCRIPT. 
Since receiving the observations made at Bombay and Kurrachee in the year 1867 the 
author has subjected them to another process for obtaining the actual times and heights 
of diurnal tide, which has been more successful than that described in the paper. 
The only data made use of were the diurnal inequalities in height at high and low 
water, the range of semidiurnal tide and the diurnal inequality in time, which were 
necessary to the previous process, being now altogether disregarded. 
The diurnal inequalities in height were obtained from the diagrams by measuring the 
widths between the lines joining alternate tides where they were crossed by the vertical 
lines representing noon on successive days. The two daily values thus obtained are 
respectively the sine and cosine of an angle which represents the difference in time 
between semidiurnal and diurnal tide. Dividing the low-water by the high-water value 
gives the cotangent of that angle, and thence the angle itself. Thus the time of actual 
diurnal tide (first in relation to the time of semidiurnal low water, and then in relation 
to solar time) was obtained. 
The actual range of diurnal tide was obtained by adding together the squares of the 
high-water and low-water values (sine and cosine), and taking the square root of the sum. 
With these two series of results as ordinates, curves were drawn representing times 
and ranges of actual diurnal tide, which were thus presented in a convenient form for 
comparison with the diurnal tide which had been previously calculated. 
The comparison confirmed the previous conclusion that the tide based on the simple 
declination theory was insufficient ; and the empirical correction which had been adopted 
seemed to provide an approximation to the required addition to it, both in time and 
height. But it appeared that a better coincidence in time would have been obtained 
by assuming the diurnal tide at Kurrachee to be forty minutes earlier. This supposition 
was tested by treating the observations of 1865 in a similar manner, and also by recal- 
culating a portion of the tides of 1867 with the earlier diurnal tide. In both cases the 
supposition was confirmed, a better agreement being obtained. 
On treating the Bombay observations in the same manner, a fair general coincidence 
with the calculated diurnal tides was found to exist ; but it was further found, on com- 
paring together the Kurrachee and Bombay curves of actual diurnal tide (thus for the 
first time recorded for the same period), that the times were nearly identical at the two 
ports, and the range at Bombay about one-tenth greater than that at Kurrachee. 
The tables for the four months over which the Bombay observations extend were 
recalculated with the diurnal tides which had been calculated for Kurrachee (but made 
forty minutes earlier, and increased in range by one-tenth), and the result was quite as 
good as that shown by the original tables. This fact would seem to point to the possi- 
bility that the diurnal tide is a vertical undulation, acting simultaneously, or nearly so, 
over a large area. 
