THE LAW OF EQUILIBRIUM 155 



tex) to project itself upon the celestial sphere in the 

 shape of a minute precessional circle approximately 2 40' 

 in diameter, corresponding as to period and direction of 

 rotation precisely with the precessional circle described 

 by the gravitational pole. 



In nature, however, nothing is absolutely fixed, but 

 only relatively, and the so-called invariable plane is by no 

 means an exception to the general rule. The charting of 

 the precessional circle (see Flammarion's Popular 

 Astronomy, p. 40), shows that its center is not stationary, 

 but is heading, apparently, for the space between 

 Hercules and Lyra. This phenomenon I attribute to a 

 rotation of the Gravisphere, not, however, around a sta- 

 tionary axis, but because of its revolution in an enormous 

 orbit (spiral, of course) whose definite curvature, period 

 and velocity of description remain to be ascertained. If 

 I may venture upon a rough approximation, I should 

 judge the radius of the curve to be not less than ten light 

 years and the period upward of 2,000,000 years, with a 

 maximum limit of, say, 20 and 10,000,000 respectively. 



THE KOTATION OF THE APSIDES 



Another radical reform in mathematical astronomy 

 made necessary by the discovery of the spiral as opposed 

 to the rectilinear conception of the sun's path, concerns 

 the problem of the rotations of the lines of apsides. As- 

 tronomers recognize three kinds of years, namely, (1) 

 the tropical year, from vernal equinox to vernal equinox, 



(2) the sidereal year, from the time the sun leaves a 

 given star's meridian until he returns to it again, and, 



(3) the anomalistic year, from one perihelion place to the 

 next. Of these, the first is 365 d. 5 h. 48 m. 45.98 s. long, 

 the second 20 m. 23 s. longer, and the third longer still 

 by 4 m. 39 s. Now, we have previously seen that the 

 reason for the sidereal year being longer than the tropical 

 year is because, while the earth is rolling forward in her 

 orbit, the system as a whole is slipping backward, around 

 a circle, the completion of which requires 26,000 years. 

 The result of this arrangement is to cause the earth an 



