86 U. S. COAST AND GEODETIC SURVEY 
is shown the relation of yearly high water to yearly sea level at the same three stations 
used in Figure 42. 
The horizontal line associated with each of the diagrams of Figure 43 represents 
for each station the average height of high water above sea level for the 25 years repre- 
sented, this height in feet being given by the figures at the left of the horizontal line. 
The yearly values of high water minus sea level are seen to range themselves more or 
less closely along the sine-like curves associated with each diagram. 
From theoretical considerations of an astronomical character it can be shawn 
that there should be a periodic variation in the range of the tide, and thus of the rise 
of high water above sea level, with a period of 18.6 years. This is brought about by 
the change in the longitude of the moon’s node, which introduces a variation in the 
inclination of the lunar orbit to the earth’s Equator. The effect of this, however, is 
different on the daily and semidaily constituents of the tide. The sine-like curves of 
Figure 43 were drawn in conformity with the above theoretical considerations. 
In Figure 43 it is seen that the rise of high water at Boston and Los Angeles was 
least in 1931 and 1932, and greatest in 1941. The amplitude of this variation is differ- 
ent at the two places for two reasons: (1) this amplitude is a function of the range of 
the tide; (2) the variation depends on the relative ee of the daily and semi- 
daily idles. 
At Pensacola it is seen the phase of the variation in rise of yearly high water above 
sea level is opposite to that at Boston and Los Angeles, the greatest rise coming in 
1931 and 1932 and the least rise in 1941. At Pensacola it will be recalled that the tide 
is of the daily type while at Boston it is of the semidaily type and at Los Angeles it is 
of the mixed type. If we look into a nautical almanac we will find that in 1931 and 
1932 the moon had its greatest declination while in 1941 it had its least declination. 
Summarizing the variations of high water, it may be said that high water is sub- 
ject to periodic variations from day to day, month to month, and year to year, in a 
period of approximately 19 years. In addition it is also subject to the nonperiodic 
variations found in sea level. : 
Definition of Mean High Water 
In view of the variations to which the height of high water is subject, mean high- 
water at any place may be defined simply as the average height of the high waters at 
that place over a period of 19 years. 
In tides of the semidaily and mixed types no difficulties are encountered in the 
application of this simple definition. In applyimg this definition to tides which are 
predominantly of the daily type, however, the question whether or not to include 
secondary tides comes up. For where the tide is predominantly daily, there are 
periods every fortnight when two high and two low waters occur. The secondary 
tides in such cases are frequently difficult to detect on the tide record because of the 
disturbing effects of wind and weather. Moreover, on their first and last appearance 
each fortnight, they have small ranges and some arbitrary figure would have to be set 
for the range, below which the fluctuation on the record would not be considered as 
constituting a high or low water. 
In the practical work of tide tabulation, it is customary to tabulate the heights 
of high and low waters to the nearest tenth of a foot, except in special cases of tides of 
