THE PRIME RESULTANT 119 



times our own distance. An observer, therefore, sta- 

 tioned at the Centrum would require a telescope of no 

 less than 300 diameters to see the sun as more than a 

 mere point of light. 



It being out of the question to attempt to draw the 

 figures to scale I have been compelled, in order to exhibit 

 the earth's relations to the general scheme, to magnify 

 the proportions, both of herself and of her orbit, count- 

 less thousands of diameters. Note, that in all the posi- 

 tions in which she is shown, her axis persistently points 

 to the Vertex, the latter, as already explained, being a 

 blank point in the line of the Prime Resultant. The con- 

 sequence of this arrangement is, that in our circling of 

 the sun's orbit with him, the Vertex is projected in the 

 line of our sight against the celestial sphere, on which it 

 consequently describes the so-called precessional circle, 

 of radius 23%, around the pole of the ecliptic. 



Turning our attention more particularly to Figure 4, 

 it will be observed that our winter solstice occurs when 

 the earth is farthest within, and our summer solstice 

 when she is farthest iviihout, the line of the solar orbit; 

 also, that the vernal equinox occurs when the planet 

 crosses the sun's path in front of him. 



Thus at one point, say A, the sun at vernal equinox 

 would be projected upon the sky in a certain direction, 

 while at B it would be projected one quadrant to the west. 

 To an observer on the earth, therefore, viewing the sun at 

 the time of the vernal equinox in successive years, the 

 path of that body will seem to be toward 270, right as- 

 cension. Again, the declination of the sun will likewise 

 suffer a change in journeying the quadrant from A to B, a 

 change which can be resolved into two factors, namely; 

 first, an uprighting of the axis to the extent of 23% in 

 one direction; and, second, a tilting of the axis to the 

 same amount in a new direction at right angles to the for- 

 mer. The net effect upon the apparent movement of the 

 sun in declination, then, will be, not the sum of 23% plus 

 23>^ but the hypothenuse of the right angled triangle 

 two of whose sides are equal to 23j^ traced on the celes- 



