TIDAL DATUM PLANES 105 
From the 50 years of observations at Seattle, 1899-1948, three slightly overlapping 
19 year series may be formed; 1899-1917, 1915-1933 and 1930-1948. The direct 
averages of low water on the tide staff for these 19 year periods are, in feet, respectively, 
0.240, 0.259 and 0.359. The difference between the first and second of these primary 
determinations of mean low water is 0.019 foot and between the first and third, 0.119 
foot. Referred to the respective 19 year sea levels, mean low water for each of the 
three series is, in feet, below sea level, respectively, 3.804, 3.796 and 3.803. The 
greatest difference between any two of these three values is 0.008, which is so small 
as to be scarcely significant. 
It appears therefore that primary determinations of mean low water with respect 
to sea level are in practical agreement. Sea level at many places, however, is subject 
to a slow change. Hence, for precise purposes, the datum of mean low water must be 
specified with regard to the 19 year series used. 
Secondary Determination 
The procedures for deriving secondary determinations of mean low water are in 
all respects similar to the ones used for deriving mean high water, which have already 
been discussed. Both methods, comparison of simultaneous observations and cor- 
rection by tabular values may be used, the former generally being the more satisfactory. 
Hither method of deriving a secondary determination of mean low water involves 
two separate corrections, the first correction being the derivation of mean low water 
below sea level for the period of observations, and the second correction being the deri- 
vation of mean sea level from the sea level of the period of observations. But as in 
the case of mean high water it is more convenient to use half-tide level instead of sea 
level. 
Hence the examples used to illustrate the derivation of mean high water from a 
day, month or year of observations are also examples for the derivation of mean low 
water. For mean high water is derived as half the mean range above mean half-tide 
level and mean low water is derived as half the mean range below mean half-tide level. 
Thus after deriving the mean half-tide level and the mean range of tide, both mean 
high water and mean low water are determined. 
The accuracy with which mean low water can be derived from a short series of ob- 
servations is thus exactly the same as that with which mean high water can be derived. 
In general it may be said that when corrected to a mean value, a year of tide observa- 
tions will determine the fall of low water below half-tide level correct within 0.05 foot, 
a month within 0.1 foot and a day within 0.5 foot. 
It must be noted that mean low water is determined with respect to half-tide level 
which is itself subject to variations. Hence the accuracy with which the plane of 
mean low water can be determined depends also on the accuracy with which the plane 
of half-tide level is determined. The degree of accuracy in deriving mean low water 
noted above for observations covering various periods of time refers only to the fall of 
low water below half-tide level. 
949995—51——8 
