THE PRIME RESULTANT 73 



But there is another way to measure this change, namely, 

 by the length of arc described, and this amounts to 50.2" 

 per annum. This circle of revolution can be and has been 

 mapped upon the celestial sphere, or at least a consider- 

 able arc of it has been, from data which have come down 

 to us through the past 3,000 or 4,000 years. Imagine the 

 axis of the earth extended northwardly to the farthest 

 sky, then the point of it, which now lies near the pole star, 

 does not rest permanently in one spot, but travels anti- 

 clockwise around a central point, called by astronomers 

 the pole of the ecliptic, but which is not marked by any 

 star. The radius of that circle (mark the extraordinary 

 coincidence) is 23^>, which is just exactly the inclination 

 of the earth's axis! What is even more remarkable is, 

 that in all my reading I have never found this curious 

 fact alluded to, just as though coincidences such as this 

 were quite the normal thing. Nor has any astronomer, 

 as far as I am aware, ever attempted to investigate the 

 marvel ! Yet its cosmic significance is crucial. 



Newton, groping in the dark, as I have already de- 

 scribed, undertook to explain the fact, but not the coin- 

 cidence. The phenomenon is known as the precession of 

 the equinoxes. Newton's explanation may be thus 

 stated: The equatorial radius of the earth exceeds the 

 polar by about 13 miles, consequently there is a great 

 ring of excess matter belting the planet and rotating 

 obliquely with respect to the ecliptic. If this belt were 

 in the form of a satellite, he reasoned, it would rotate 

 around the earth agreeably to the same principles of ro- 

 tation as the moon, and its orbit should therefore have 

 nodes and exhibit a precessional movement of those 

 nodes. But the ring, he went on, is not a satellite, but, 

 on the contrary, is firmly affixed to the planet, conse- 

 quently its natural nodal motion of rotation, being unable 

 to express itself otherwise, must react upon the earth it- 

 self and cause a wobbling of that body's axis, technically 

 called nutation. The tendency of the nodes to regress he 

 found to arise from the fact, in the case of the moon, that 

 that body is continually shifting from one side of the 

 ecliptic to the other, and that the sun's attraction upon it 



