6 PRACTICAL ASTRONOMY. is called the Equation of the Center, and is known when n and e are known ; t being the time since perihelion passage. Assuming e to be constant and causing n t to vary from to 360, the resulting values of the second member of the equation will form a table of the equations of the center. The errors in these values arise from the small variations in the values of e ; these errors can be found by substituting in the second member of the above equation the actual values of e at the time, and the differences being tabulated will give a table by which the equations of the center may be corrected from time to time. 4. Equation of the Equinoxes in Longitude. Due to physical causes, the pole of the equator completes a revolution about the pole of the ecliptic in about 26,000 years. The plane of the equator conforming to this motion of the pole, its intersection with the plane of the ecliptic, called the line of the equinoxes, turns with a retrograde motion of about 50". 2 per annum about the sun as a fixed point. This motion is not however, perfectly uniform. The true pole describes once in 19 years around the moving mean place above re- ferred to, a small ellipse, whose transverse axis directed toward the pole of the ecliptic is 18".5 in angular measure, and whose conju- gate axis is 13". 74. The corresponding irregularity in the motion of the line of the equinoxes causes a slight oscillation of the true on either side of the moving mean equinox. Both are on the eclip- tic; and their distance apart at any time is called the Equation of the Equinoxes in Longitude, its projection on the equator the Equation of the Equinoxes in Right Ascension) and the intersection of the declination circle which projects the mean equinox with the equator, the Reduced Place of the Mean Equinox. The maximum Talue of the Equation of the Equinoxes in Longitude is 13" 74 ^-^ + sin 23 28' = 17".25. To illustrate, P, in Fig. 2, is the pole of the equator, VE the ciiptic, VM the equator, V the true, V 9 the mean, and V" the re- duced place of the mean vernal equinox. W is the equation of the equinoxes in longitude, and VV" in Right Ascension. The equation of the equinoxes in longitude is a function of the
