12 U. S. COAST AND GEODETIC SURVEY 
waters of a day, the lower is called “lower low water” and the higher “higher low water.” 
The diurnal inequality in the tide depends primarily on the declination of the moon, 
which varies from zero to its maximum north or south declination in half a fortnight. 
Hence, the diurnal inequality in the tide likewise varies within a fortnight, being generally 
least when the moon is close to the equator and greatest when the moon is near its 
fortnightly maximum north or south declination. 
The existence of diurnal inequality in tides and its variation within a fortnight 
find ready explanation in the existence of semidaily and daily constituents in the tide 
brought about, respectively, by the semidaily and daily tide-producing forces. This 
becomes evident from a consideration of the tide resulting from the combination of 
daily and semidaily constituent tides. 
The Combination of Daily and Semidaily Constituent Tides 
The daily and semidaily tide-producing forces of sun and moon bring about 
constituent tides of like periods in the waters of the sea. The relative ranges and times 
of these constituent tides at any particular place, however, depend not only on the rela- 
tive magnitudes and phases of the corresponding tide-producing forces, but also on local 
hydrographic features. Hence, the relative ranges and times of the daily and semidaily 
constituents of the tide are different at different places. 
Suppose that at a certain place the daily and semidaily constituents of the tide 
have equal ranges. The rise and fall of each of these constituent tides may be repre- 
sented as in Figure 3, the semidaily constituent by the dotted curve and the daily 
constituent by the dashed curve. The height of the resultant tide at any moment is 
then clearly the sum of the heights of the two constituent tides at that moment. In 
Figure 3, the resultant tide is indicated by the heavy full-line curve. 
Now, the times of the two constituent tides may have different relations to each 
other depending on local hydrographic features. In Figure 3, three different cases are 
considered. In the upper diagram the two constituent tides have such time relations 
that their low waters occur at the same instant; in the middle diagram the high waters 
of the constituent tides occur at the same time; and in the lower diagram the two 
constituents are at sea level at the same time. In each case the resultant tide exhibits 
considerable diurnal inequality, but there are profound differences with regard to the 
phase of the tide which exhibits the inequality. 
When the time relations are as pictured in the upper diagram,the diurnal inequality 
in the height of the tide is exhibited wholly in the low waters. The middle diagram 
shows that with the ranges of the two constituents exactly the same as before, but with 
different time relations, the inequality in height is featured wholly in the high waters. 
Finally, the lower diagram shows that with the ranges of the two constituents still the 
same, but with time relations different than in the two preceding cases, the height 
inequality is featured in equal degree in both the high and low waters. 
Without going into a detailed consideration of the matter, it is clear that the two 
upper diagrams of Figure 3 represent the limiting cases of the combination of daily 
and semidaily constituent tides of the same range. When the low waters of the two 
constituents occur at the same time, the inequality in height of the resultant tide is 
wholly in the low waters as represented by the upper diagram. As the times of the 
low waters of the constituent tides begin to differ, the inequality will begin to appear 
