TABLES 
EXPLANATION OF TABLES 
Table 1. Fundamental astronomical data.—This table includes 
fundamental constants and formulas with references which form the 
basis for the computation of other tables contained in this volume. 
Because of the smallness of the solar and lunar parallax no distinction 
is made between the parallax and its sine. The eccentricity of the 
earth’s orbit and the obliquity of the ecliptic are given for epoch 
January 1, 1900. The former changes about 0.000042 per century 
and the latter about 0.013 of a degree in a century. The values given 
may therefore be considered as applicable to the present century. 
The formulas for longitude of both sun and moon are the same as 
used in the previous edition of this book and are from the work of 
Simon Newcomb. In a later work by Earnest W. Brown, slightly 
different values are obtained for the elements of the moon’s orbit but 
the differences may be considered negligible in so far as the tidal work 
of the present century is concerned. In these formulas it will be noted 
that J is the number of Julian centuries reckoned from Greenwich 
mean noon on December 31, 1899, of the Gregorian calendar which 
corresponds to December 19, 1899, by the Julian calendar. In the 
application of these formulas to early dates special care must be taken 
to make suitable allowances for the particular calendar in use at the 
time. See page 4 for information in regard to calendars. 
Table 1 includes the numerical values of the mean longitude of the 
solar and lunar elements for the beginning of the century years 
1600 to 2000 and also the rate of change in these longitudes as of 
January 1, 1900. As the variations in these rates are very small, 
they are applicable without material error for all modern times. 
This table includes also the principal astronomical periods depending 
on the solar and lunar elements with formulas showing how they are 
derived. In these formulas the longitude symbol is used to represent 
its own rate of change according to the unit in which the period is 
expressed. 
Table 2. Harmonic constituents —This table includes the arguments, 
speeds, and coefficients of the constituent harmonic terms obtained 
in the development of the tide-producing forces of the moon and sun. 
They are grouped with reference to the formulas of the text from 
which they are derived, the long-period constituents first, followed 
by the diurnal, semidiurnal, and terdiurnal terms. The reference 
numbers in the first column correspond to the numbered terms of the 
formulas of the text, the letter A indicating a term in the lunar 
development and the letter B a term in the solar development. In 
the second column the usual symbols are given for the principal 
constituents, parentheses being used when the term only partially 
represents the constituent. 
For an explanation of the constituent argument (E) see page 22. 
The argument consists of two parts—the VY which contains the 
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