EPHEMERIS. 5 The value of n derived from these equations is evidently the earth's mean motion from a fixed point. Its mean motion from the moving mean vernal equinox (or mean motion in longitude) is evidently given by 360 '" 360 - 50."2' These observations repeated at different times will determine the changes that take place in n, e, and l p from the last two the variations in the eccentricity and the rate of motion of perihelion can be found. Having in this manner found the elements of the earth's place and motion, the corresponding mean longitude of the sun at any instant can be obtained by adding to that of the earth 180. ]j _|_ n ' T -j- 180 will then give for any instant the mean longi- tude of the sun's mean place. The difference between the longi- tudes of the sun's true and mean places at any instant is the Equation of the Center for that instant. From the preceding elements let it be required to construct the Tables of the Sun. 1. The Table of Epochs. Take mean midnight, December 31 January 1, 1890, as the epoch. To the mean longitude of the sun's mean place at that epoch, add the product of the sun's mean motion n' ', by the number of mean solar days after the epoch, subtracting 360 when this sum is greater than 360. These longitudes with their corresponding times being tabulated, form the table of epochs, from which the mean longitude of the mean place of the sun can be found by inspection for any day, hour, minute or second. 2. The Table of Longitudes of Perigee. The longitude of peri- helion increased by 180 is the corresponding longitude of perigee. Hence the former being found, and its rate of change determined, the addition of 180 to each longitude of perihelion will give the longitude of perigee, and these values being tabulated form the table of longitudes of perigee. 3. The Table of Equations of the Center. The difference be- tween the true and mean anomalies at any instant, given by the first of Eqs. (650), Mechanics, n t = 2 e sin nt + e* sin 2 nt + etc., (13)
