PART II.— TABLES. 



EXPLANATION OF TABLES. 



Table 1. Astronomical constants and formulas.— There are given 

 in this table some fundamental astronomical constants and formulas, 

 which are used in the computation of other tables which follow, 

 with references to the authorities from which they were obtained. 

 The form and degree of precision is for the most part identical with 

 that of the original source. 



It wiU be noted that T is the time expressed in Julian centuries 

 reckoned forward from Greenwich mean noon on December 31, 

 1899 (Gregorian calendar), which corresponds to December 19, 1899, 

 by the Julian calendar. (See p. 11 for an explanation of these cal- 

 endars.) By the Julian calendar the date corresponding to an inte- 

 gral value of T will always be December 19 of a year ending with 

 the figures 99 A. D. or 02 B. C. ; for example, by the Julian calendar, 

 T= -1 on December 19, 1799; -2 on December 19, 1699, etc. The 

 Gregorian calendar was first introduced in 1582. By this calendar, 

 T= -3 on December 29, 1599; -2 on December 29, 1699; -1 on 

 December 30, 1799; on December 31, 1899; +1 on January 1, 

 2000; +2 on January 1, 2100; -1-3 on January 2, 2200; etc. 



In the formulas for the true longitude and distance of the moon 

 the notation has been changed in order to be in accord with the 

 notation of the present volume, and the terms not used here have 

 been omitted. The terms containing fc^ were for the reduction to 

 the ecliptic and have been omitted here because it is desired to repre- 

 sent the position of the moon in its orbit rather than in the ecliptic. 

 The longitude in the orbit is referred to an origin ( T ' of fig. 6) selected 

 so that the longitude of the moon's nodes will be identical in either 

 the ecliptic or the moon's orbit. 



Table 2. Astronomical quantities and relations. — The values com- 

 piled in this table for convenience of reference are based upon Table 1. 



The mean longitudes of the lunar and solar elements and also the 

 rate of change in these elements are derived from formulas of Table 1 . 

 The rate of change, although computed for the epoch January 1, 

 1900, will apply without material error to all modern times, since the 

 variations m the rates for all the elements are very small. 



The inchnation of the earth's orbit to the ecliptic changes about 

 0.013 of a degree in a century. The value computed for epoch 

 January 1, 1900, may therefore be used without material error for 

 all modern times. The inclination of the moon's orbit to the ecliptic 

 is regarded as an absolute constant. 



The eccentricity of the earth's orbit changes about 0.000042 per 

 century. The value as computed for the epoch January 1, 1900, may 

 therefore be used as a constant. The mean value of the eccentricity 

 of the moon's orbit is also used as a constant. 



The mean radius of the earth is taken as the cube root of the 

 product of the polar radius and the square of the equatorial radius, 

 this being the radius of a sphere having the same volume as that of 



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