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centre of the universe. Suppose then the earth to remain at a 

 tixed point of space, while the sphere of the heavens turns round 

 about it, and to turn round on its own axis 360 times during the 

 period of the revolution of the stars in the ecliptic ; the sun all 

 the time remaining in the centre of the orbit, in one with N 

 outside, or, as it were, straight south of N, north. Commenc- 

 ing its revolution at N (fig. 5,) and moving from east to west, or 

 to the right hand, while the earth at the same time turns round 

 on its axis from west to east, the star will continue to move al- 

 ways further and further away from N, to the extent of one de- 

 gree, during each of the earth's rotations. But the earth is fix. 

 ed in the same point of space, and, so long as it is so, its rota- 

 tion can only be complete when the same point of its circum- 

 ference a returns to the fixed point N ; and the opposite point 

 ^, 180° distant, again faces the sun, and is in one with the ra-' 

 dius-vector, or straight line that connects N and S. In making 

 this return, a will every day, or in every turn, be in one with the 

 off-moving star four minutes sooner than it reaches N ; conse- 

 quently, its rotation will then be incomplete to the extent of one 

 degree of its own circumference. On the second day, a will 

 point to the star 8 minutes before it reaches N ; on the third 

 day, 12 minutes; and so on through the whole series of the 

 earth's 360 rotations or days, during which it will have seen the 

 star 361 times, the sidereal day being 1- 360th part shorter than 

 the solar day, which measures the earth's complete rotation. It 

 is, however, perfectly obvious and undeniable that in this case 

 the difference is occasioned by the star's moving away from N, 

 and not by N's moving away from the star; consequently, the 

 star, by so moving away from N to an always increasing angular 

 distance, presents itself to the earth's point a four minutes of 

 time sooner in each rotation, or every day. It is, on the other 

 hand, just as perfectly obvious and undeniable that the rotation 

 is incomplete till a return to N ; and that being so, either N 

 itself or a straight line drawn between it and the sun, must and 

 can be the only true index of the rotations. Now, just reverse 

 the process, and let the star stand still at N, while the earth re- 

 volves from west to east, rotating as before, and carrying of 

 course its radius-vector NS along with it, which radius will re- 

 volve round S, as its pivot of rotation. When the earth com- 

 pletes her first quarter, the star, remaining at N, will be in pre- 

 cisely the same relation of place to the earth, as it was, when it 

 (the star) had reached its own first quarter of rotation, while the 

 earth was remaining at N ; and so on throughout the whole re- 

 volution of the earth in her orbit, which is precisely the converse 

 of that of the stars, their mutual relations being precisely the 



