15 



be distant from its first position by the whole length of the moon's 

 diameter, as shown at S. At S., a will again turn round 

 the third quarter of 90°, and get into the position shown at E. 

 At E., a will turn round its fourth quarter of 90°, and get into 

 the position shown at N. In these quarter points a could get 

 into the several positions it occupies in no other way than by the 

 moon's retro-rotating, or turning round on her axis backwards, 

 in the direction from east to west ; and if this retro-rotation were 

 to happen 360 times, instead of only four, as in the diagram, why 

 should not a turning away of her circumference to the extent of 

 one degree of the circle of rotation be allowed to happen at each 

 of these 360 points, as well as a turning away to the extent of 

 90° at each of the cardinal quarter points, and with the same 

 result, namely, a remaining always looking south ? 



With respect to a revolving body, all the results of her orbital 

 revolution, and self-rotation during that revolution, would be most 

 precisely the same ; if, instead of revolving, she were to stand 

 still, and the orbit, supposed a solid ring or disk, to revolve or 

 turn round on its own centre, till every point of its circumference 

 in succession were past the moon's axis or centre. Suppose this 

 revolution to be made from east to west, being the direction con- 

 trary to that which the moon takes in her usual progress; that 

 the moon herself were at the same time to remain constantly at 

 the point N (Fig. 1) during the orbit's revolution, and to keep 

 her point a constantly fixed on the radius looking to the earth ; 

 the result would be that the orbit would complete its revolution 

 without producing the smallest change in the moon's relations to 

 the orbit itself, to the radius-vector, and to the earth at the inner 

 end of the radius, in other words, without causing or requiring 

 her to turn round on her axis. But precisely the same result 

 would follow the moon's ow^n revolution in her orbit ; the same 

 face always looking to the earth, in one with the radius, and 90* 

 distant on either side from the line of motion ; what should make 

 rotation necessary in this case, namely, to produce results that 

 can be shown so distinctly and undeniably to be produced with- 

 out it ? Again, suppose the moon to remain constantly at N, 

 and, w hile the orbit revolves from east to west, to turn round on 

 her own axis also from east to west exactly once during the orbit's 

 progress past her. Well, when the orbit's point W reaches 

 north, the moon's own point a will have turned round to b ; when 

 the orbit's point S reaches N, a will have turned round to 

 c; when the orbit's point E. reaches N, a will have turned 

 round to d ; and when the orbit's point N returns to the moon 

 on the other side, a will have returned to its first position in one 

 with the radius. But, the effect of this revolution of the orbit is 



