108 U. §. COAST AND GEODETIC SURVEY 
lower low water goes through a fortnightly cycle, being lowest about the time of maxi- 
mum north or south declination and highest about the time when the moon is on the 
Equator. The effects of the phase and parallax cycles of the moon are also reflected 
in lower low water, but the declinational effect is the principal one. 
The difference in the morning and afternoon tides of a day, which is known as © 
diurnal inequality, arises from the existence of daily and semidaily constituents in the 
tide. The greater the daily constituents in relation to the semidaily, the greater the 
diurnal inequality until the tide becomes daily in type. Hence Table 4, which gives 
the ratio of K, +0; to M2 at a number of stations on the coasts of the United States, 
gives also a criterion for determining the existence: of inequality at those stations. 
It must be noted, however, that the magnitude of the diurnal inequality depends 
also on the senenlinnles of the daily and semidaily tides, and these are not given in Table 
4. Thus from that table the ratios of K,+0, to M2 in Los Angeles and Seattle do not 
differ much. But because the magnitudes of the daily and semidaily tides at Seattle 
are more than twice those at Los Angeles, the inequality at Seattle is more than twice 
that at Los Angeles. 
In the consideration of diurnal inequality (page 11) it was found that ie may be of 
three kinds. It may exist principally in the high waters, principally in the low waters, » 
or equally in the high and low waters, depending on the phase relations of the daily andl . 
semidaily constituents. It happens that on the Atlantic coast the inequality is princi- 
pally in the high waters. This, in conjunction with the small ratios of the diurnal to 
the semidiurnal constituents, makes the use of the plane of lower low water of little 
advantage on the Atlantic coast, and the plane of mean low water is used on that coast — 
almost without exception. For this reason the examples given in connection with 
lower low water will be confined to the Pacific coast, where the diurnal inequality in 
the low waters is considerable and where the datum of lower low water is of practical © 
importance. 
At Los Angeles for the month shown in Figure 44 the difference between the 
highest and lowest lower low waters was 1.5 feet. At Seattle for the same month this 
difference was 4.0 feet while at Ketchikan, Alaska, for the same month the difference 
was 6.2 feet. In part the variation in lower low water from day to day arises from 
disturbing effects of changing meteorological conditions; but in regions of large range 
of tide, as for example Seattle and Ketchikan the variation is primarily of a periodic — 
character, depending on the changes in the moon’s declination, phase and parallax. 
Monthly Lower Low Water 
The declinational cycle of the moon has a period of 27% days, the phase cycle has 
a period of 29% days, and the parallax cycle a period of 27% days. Hence in a period 
of a month the daily variations in lower low water should very largely be eliminated, 
and we may expect monthly values to show considerably less variation than daily 
values. In Figure 50 are shown the monthly lower low waters at Los Angeles, Seattle 
and Ketchikan for the two year period 1946-1947. 
From one month to the next Figure 50 shows variations of as much as 0.4 foot at 
Los Angeles, 1.1 feet at Seattle and 1.0 foot at Ketchikan. Within the two year peric4 
