6 U. S. COAST AND GEODETIC SURVEY 
as the ‘‘age of diurnal inequality” or “diurnal age.’ Like the phase and parallax ages, 
the diurnal age varies from place to place, being generally about one day, but in some 
places it may have a negative value. 
It is to be observed that although the three variations in the rise and fall of the 
tide described above are noted the world over, they are not everywhere exhibited in 
equal measure. In many regions the principal variation is that related to the moon’s 
phase; in other regions it is that depending on the moon’s distance or parallax; in still 
other regions the principal variation is that related to the moon’s declination. 
The month of the moon’s phases (synodic month) is approximately 29% days in 
length; the month of the moon’s distance (anomalistic month) is approximately 27% 
days in length; the month of the moon’s declination (tropic month) is approximately 
2714 days in length. It follows, therefore, that very considerable variation in the range 
of the tide occurs at any given place in consequence of the changing relations of the 
three variations to each other. 
How great these variations may be is illustrated by the following examples. At 
Boston, the range of tide has an average value of 9.4 feet; yet within a fortnight the 
tide will vary in range from less than 6 feet to more than 12 feet. In Los Angeles 
Harbor, the mean range of tide is 3.8 feet; but within a week there may be individual 
ranges from less than a foot to more than 6 feet. At Seattle, the mean range is 7.6 
feet; individual ranges within a single day, however, may vary from less than 5 feet to 
more than 15 feet. 
The range of tide is also subject to other periodic variations. But the three 
discussed above are the principal variations. 
Mean Values 
Since the rise and fall of the tide varies from day to day, any tidal characteristics 
derived from a short series of observations may differ considerably from the average 
or mean values. In other words, to derive values that will represent averages, the 
results from short series of observations must be corrected to mean values. 
The principal tidal variations are those connected with the moon’s phase, parallax 
and declination, the periods of which are approximately 29% days, and 27% days, 
and 27'; days, respectively. It follows, therefore, that in a period of 29 days the phasé 
variation will have almost completed a full cycle, while the other variations will have 
gone through a full cycle and but very little more. Hence, for tidal character- 
istics dependent primarily on the phase variation, tide observations covering 29 days 
or multiples, constitute a satisfactory period for determining approximate mean values 
of these characteristics. Such are the lunitidal intervals, mean range, mean high 
water and mean low water. For characteristics dependent primarily on the declination 
of the moon, as for example, higher high water or lower low water, observations coy- 
ering 27 days or multiples, constitute the more satisfactory period. 
As will be seen in the detailed discussion of the various tidal datum planes, the 
values determined from two different 29-day or 27-day periods may differ very con- 
siderably. This is due to the fact that these periods are not exact synodic periods for 
the different variations, and to the further fact that variations having periods greater 
than a month are not taken into account. Furthermore, meteorological conditions, 
which change from month to month, leave their impress on the tides. For accurate 
