228 
THE REV. W. WHEWELL ON THE PROGRESS OF THE 
will be greater for high water or for low water, according as the time of the maximum 
of the diurnal wave is nearer to the time of high or of low water. 
Hence by taking the diurnal inequality of high and of low water at any place, and 
by combining these effects, we may determine the time of the arrival of the diurnal 
portion of the tide, and also its magnitude ; and may thus separate this tide wave 
from the semidiurnal wave which brings every tide. And the time and magnitude of 
the diurnal wave being thus determined at a series of places along any coast, we trace 
its progress nearly in the same manner as we do that of the tide itself. 
This is what I have done in the Tables subjoined at the end of this memoir. The 
heights of high water, for example, observed in June 1835 (from the 9th to the 28th) 
were laid down as ordinates, and a line was drawn connecting them. This line, when 
the diurnal inequality was manifest, was a zigzag line, such as is represented for 
Plymouth and for Singapore, in the figures to the Seventh Series of these Researches, 
and for several places in America and Europe in the Sixth Series. The line of mean 
heights was then drawn, cutting off all the diurnal inequalities. The same was done 
for low water; and the diurnal inequalities of the high and low waters, thus cut off, 
were tabulated in order. In general they were, of course, alternately two additive 
and two subtractive sums. These sums were laid down as ordinates at certain in- 
tervals, which intervals represent half tides (six lunar hours) ; and the curve drawn 
through the extremities of these ordinates is the diurnal wave according to its 
changes from day to day at the same place. The assemblage of the circumstances 
of such waves at different places gives the progress of the wave along the coast. 
The forms of the curves thus representing the diurnal wave being determined for a 
sufficient number of places, it is easy to see what relations among these forms would 
indicate the different modes of propagation of the diurnal inequality which may be 
supposed. In all cases this inequality, depending as it does upon the moon’s decli- 
nation north and south, would increase from nothing to a maximum, and decrease 
to nothing again in about a fortnight ; after which the inequality becomes negative, 
increases to a negative maximum, and decreases to nothing again in another fort- 
night, and so on. The epochs at which the inequality vanishes correspond to the 
times when the moon crosses the equator, but occur after those times at intervals 
varying from a few hours to four or five days, and perhaps more. It appeared to ine, 
from the cases which I considered in my last memoir, that the epoch gradually in- 
creases as we proceed along the coast in the direction of the progress of the semi- 
diurnal tide wave ; and that this increase of epoch goes on much more rapidly than 
the increase of epoch for the inequalities due to the moon’s parallax and declination; 
so that the diurnal inequality is propagated much more slowly than the other in- 
equalities, and employs, for example, two days or more to make its way from the 
coasts of Spain to those of England ; or, as I have before expressed it, the diurnal in- 
equality creeps along the coast from day to day. Another mode in which we might 
explain different modifications of the diurnal inequality which the observations at 
