TIDAL DATUM PLANES La 
Diurnal Inequality 
Diurnal inequality, or difference between corresponding morning and afternoon 
tides arises primarily from the fact that the moon’s orbit is inclined to the plane of the 
equator. This gives rise to daily and semidaily tide-producing forces, and as a result 
morning and afternoon tides differ in greater or lesser degree. 
Diurnal inequality is thus a feature of all tides which have two high and two low 
watersa day. But the magnitude of the diurnal inequality is not the same at all places. 
In fact, the distinction between the semidaily and mixed types of tide is based on this 
difference in magnitude of diurnal inequality. In general, it may be said that in the 
semidaily type of tide the diurnal inequality is relatively small, while in the mixed type 
of tide it is relatively large. This statement is obviously only of a qualitative character 
and does not serve as a definite criterion for separating the mixed type from the semi- 
daily type. In the detailed discussion of the different types of tide, however, it will be 
found that quantitative criteria can be formulated to separate these two types of tide. 
In Figure 2 the tide curve for San Francisco was taken to illustrate the mixed type 
of tide. On glancing at that curve it will be seen that the morning low waters were 
lower than the afternoon low waters, and the morning high waters were lower than the 
afternoon high waters. In other words, the tide at San Francisco exhibits inequality 
in both high and low waters. It will be noted, however, that the inequality in the low 
waters is greater than in the high waters. : 
On investigation, it is found that the diurnal inequality in the tide at different 
places varies not only in magnitude, but also in the proportion in which it is exhibited 
by the high and the low waters. In some places the inequality is featured principally 
by the high waters; at other places the inequality is exhibited principally in the low 
waters; and at still other places the inequality appears in approximately equal degree 
in both high and low waters. This matter, however, it is more convenient to consider 
in connection with the detailed discussion of the different types of tide. 
It is to be noted that the diurnal inequality in tides is featured not only in the 
heights but also in the times of the tide. Where there is considerable inequality in the 
heights of the tide, there will also be considerable inequality in the times, and this is 
evidenced by differences in the morning and afternoon lunitidal intervals and, therefore, 
by differences in the durations of rise and fall as between morning and afternoon tides. 
Thus, for the last day shown in Figure 2, the duration of rise of tide at Hampton Roads 
was 5.9 hours for the morning tide and 6.3 hours for the afternoon tide, or a difference 
of 0.4 hour. At San Francisco, for the same day, the durations were 7.4 hours and 
5.9 hours, or a difference of 1.5 hours. 
For any particular day, the difference between the heights of the two high waters 
or the two low waters would appear to be the natural measure of the magnitudes of the 
respective inequalities. For certain reasons, however, it is more convenient to use 
half these differences as the measure of the inequality. That is, the high water ine- 
quality is taken as half the difference between the two high waters of a day, and the low 
water inequality is taken as half the difference of the two low waters of a day. Tech- 
nically, these are known as the diurnal high water inequality and diurnal low water 
inequality, and are abbreviated as DHQ and DLA, respectively. 
To distinguish the two tides of a day, definite names have been given to each of 
the two high and two low waters. Of the two high waters, the higher is called the 
“higher high water” and the lower the “lower high water.’ Likewise, of the two low 
