688 ME. WILLIAM PAEKES ON THE TIDES OF BOMBAY AND KITBEACHEE. 
the diurnal tide ceases to rise, and in the second it ceases to rise at the same time that 
diurnal tide ceases to fall, the times of actual high water (the combination of the two 
tides) will be the same as those of semidiurnal high water. Thus, though there is a 
diurnal inequality in height equal to the whole range of the diurnal wave, there is no 
inequality of time. If we now turn to the semidiurnal low waters, we find that the 
first, being between the two high waters in question, is coincident with diurnal half ebb , 
and the following one with diurnal half flood. Thus when the first semidiurnal tide 
ceases to fall, diurnal tide is still falling at its most rapid rate, and the actual combined 
tide continues to fall till the rate of fall of the diurnal tide is balanced by the rate of rise 
of the semidiurnal tide, and thus actual low water is retarded. When the second semi- 
diurnal tide ceases to fall, diurnal tide is rising, and the actual tide has therefore been 
on the rise since the moment when the rate of semidiurnal fall was equal to the rate of 
diurnal rise. In this case the actual low water has been accelerated. Thus, one having 
been retarded and the other accelerated, a - diurnal inequality in time is the result. The 
level of the diurnal tide, however, will have been the same at half flood and at half ebb, 
and will not therefore have affected the level of semidiurnal tide when at its lowest points. 
Hence in such case there is no diurnal inequality in height of low water. 
It appears, then, that when there is no diurnal inequality in high-water time , there is 
none in low-water height, and when there is none in high-water height there is none in 
low-water time. This will be seen to be almost universally the case in the diagrams. 
I now proceed to describe the mode adopted to compare the actual effects of diurnal 
tide with the changes in the positions of the sun and moon supposed to have produced 
them. 
The diagrams (of which Plate XXXVI. is a specimen) are laid down in the manner 
usually adopted in tidal investigations, and from them the amount of diurnal inequality 
in height and time at any given high water or low water may be ascertained by simple 
measurement. By a similar process of measurement the time and range of any pure 
semidiurnal tide may be ascertained. From these two elements (the time and range 
of semidiurnal tide, and the amount of diurnal inequality in time and height) the 
time and range of the diurnal tide producing those diurnal inequalities may be ascer- 
tained by the following process : — 
Let H be half range of semidiurnal tide. 
h be half diurnal inequality in height. 
t be half diurnal inequality in time. 
c be interval of time between semidiurnal and diurnal tide. 
D be half range of diurnal tide. 
[In reference to the expressions ( t and c) which denote values of time, 360 degrees is 
supposed to represent indifferently twenty-four hours, or the period of diurnal tide. 
Where the expression denotes a proportion of semidiurnal tide, double the value in 
degrees must be taken to represent the value in hours and minutes which it would 
denote if representing a proportion of diurnal tide.] 
