RELATIONS OF TIME AND SPACE. 



143 



For this purpose, suppose two spheres to be situated as in Fig'ure 

 1, the one at A, the other at B, 

 having a meridian on the one paral- 

 lel to a meridian on the other, and 

 that the angular ^locity of rota- 

 tion is the same in both. The au- 

 dience will perceive that the me- 

 ridian will continue parallel, and be 

 so found at the end of the rotation. 

 If, instead of this, we suppose that 

 the sphere A, while it revolved, 

 was also transferred to the place of 

 B, then the meridian on A, when 

 it arrives at B, would be found at 

 the completion of its rotation to be 

 parallel to its first position. Noon 

 at any place occurs when the plane 



of that meridian passes through the sun in the direction of C. If, 

 after one rotation, the earth were transferred to B, then the meridian 

 already shown in the figure must be in a direction parallel to its 

 former position. But noon will not have occurred. To accomplish 

 this the earth must have revolved as much more as the direction of 

 noon has meanwhile changed ; that is, until the meridian reaches the 

 line in the figure passing from B to the sun. Now, if the earth's due 

 eastern motion in its orbit* were 

 equable, the solar days would be 

 equal, for the excess above a whole 

 rotation (already described) would 

 in every case be the same. This 

 cannot be the case, especially be- 

 cause of two reasons : The first is 

 found in the oblique position of the 

 orbit itself. The earth does not move 

 due east, but eastward, insomuch that 

 if the direction of the circle passing- 

 through A, in Figure 2, represent a 

 due eastern direction, the circle 

 through B would represent that in 

 which the earth is actually moving. 

 It will be perceived on either supposition that a quarter revolution 

 eastward would be accomplished in 

 the same time, or the position as re- 

 gards a due eastern motion would be 

 the same at four points, these being 

 the equinoctial and solstitial points. 

 This is artificially registered on Figure 

 5, in which the first curve A is made 

 to intersect the horizontal line at the 

 times of the equinoxes and solstices. 



Now, in passing from the equinox 

 to the solstice, the due eastern motion, as in Figure 3, E B, is less 



