TIDAL DATUM PLANES 129 
of mean high water, mean low water, lower low water, and higher high water are ap- 
proximations, and where accurate determinations are desired these must be derived 
from the observations as outlined in the previous sections. For the plane of spring 
low water and for the Indian tide plane, however, the determination by means of the 
harmonic constants is to be preferred. 
Spring Low Water 
Spring low water has been used as a datum for hydrographic charts and for the 
- prediction of tides. This datum may be defined as the average of the low waters that 
come at the time of spring tides. Spring tides are those that occur about the times of 
new and full moon, when the tide-producing forces of sun and moon conspire and bring 
about a greater rise and fall than usual. At most places there is a lag between full or 
new moon and the greatest rise and fall of the tide, this lag being known as the phase 
age of the tide. On the Atlantic and Pacific coasts of the United States the phase age 
of the tide is about one day; that is, spring tides come about one day after full and new 
moon. : 
It is obvious that there must be considerable variation in the height of spring low 
water from one fortnight to another. In the first place, it will vary in response to 
changes in sea level; and, in the second place, it will vary in response to changes in the 
positions of sun and moon as regards parallax and declination. It should be noted in 
passing that the two low waters coming nearest, one before and the other after, the time 
given by adding the phase age to the time of new and full moon are taken as constituting 
the spring low waters of any given new or full moon. 
For all practical purposes it is sufficient to determine the plane of spring low water 
approximately, especially if its relation to mean sea, level or half-tide level is given. 
This relation is given when spring low water is determined through harmonic constants, 
and this method therefore furnishes a convenient means for deriving the datum. As 
an approximate formula for the plane of spring low water, we may take it to be MLW-5S, 
in which MLW is mean low water and 8, the principal solar semidiurnal constituent. 
When it is necessary to determine spring low water and harmonic constants are not 
at hand, it may be derived by comparison with the spring low water at some other place 
in the same general region. If R and SpLW represent, respectively, the mean range 
and spring low water at the comparison station and the same abbreviations, with sub- 
script 1, the like quantities at the station for which spring low water is desired, then we 
have SpLW,= . SpLW. In both cases SpLW represents the distance of spring low 
water below half-tide level. 
Indian Tide Plane 
In predicting the heights of high and low water for tide tables it is obviously desir- 
able to refer these heights to a plane such that no negative heights will be necessary; 
that is, the datum with regard to which the predictions are given should be so low that 
no low water will fall below it. But it is manifestly even more desirable that the plane 
used in the tide predictions for any given port should be the same as that used on the 
949995—51——10 
