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perfectly true that at the end of the first quadrant of c's, or the 

 middle orbit, a and b would be perpendicularly in line with it, or 

 parallel to the meridian N S ; and a rotation backwards (from 

 west to east) would bring a back again to the radius. But, in 

 fact, the moon does not move in this manner ; the same point of 

 her circumference remains constantly in one with the radius, 

 always on its own orbit, at the same distance from the centre ; 

 and as the three points of her mass really do revolve under this 

 condition, the result is that, when a finishes its quadrant, c and 

 b would be 90° behind it, unless a rotation or forward move- 

 ment to that extent hiinc/ them into their proper places upon the 

 radius, in line with a. This is effected gradually by their mov- 

 ing faster than «, in proportion to the greater dimensions of their 

 respective orbits, so that they remain in line with a upon the 

 radius, all the way round, without disturbing «'s or their own 

 relations to the radius and the centre ; or, in other words, with- 

 out the body's rotating on its axis. The cause of the moon's not 

 rotating backwards, from east to west, or preserving her parallel- 

 ism^ as she naturally would, were she to revolve with her circum- 

 ference yVee, and her axis alone subjected to the centripetal force, 

 we shall consider by and by. 



Take a stick or rod of any kind, and attach it by one end to a 

 fixed point on a floor or a table, and then to one side of its outer 

 end attach a disk of any size or substance by a nail or pin stuck 

 through its centre. Make the rod revolve from west to east round 

 the point to which it is attached, and at the same time keep the 

 disk continually turning round on its axis. Turn it round and 

 round, backwards or forwards, its relations to the radius and the 

 centre will remain unaffected by the revolution of its axis in 

 its orbit, though the relation of that axis to every object outside 

 of the orbit will be continually changing ; and this happens be- 

 cause the revolution of the axis carries forward the wiiole mass 

 simultaneously with, and in the line of, the radius-vector, with- 

 out changing its relations to the points of its own circumference. 

 If the same point remain always in one with the radius, it will, 

 of course, never change its relation to the axis. If the whole 

 circumference pass the radius once in an orbital revolution, it 

 will change its relations to the axis once also, and onh/ once ; 

 but, if that change and passing of the radius once be made in the 

 direction from east to west, the parts of the mass will preserve 

 their so-called parallelism, by virtue of the forward motion of the 

 axis in the contrary direction, which afix^cts the relation of the 

 circumference to extra-orbital objects, but not at all to the axis 

 itself^ or to the radius-vector and the centre. The same thing 

 will appear still more clearly, if possible, by a variation of this 

 experiment, Make a large disk, and fix it to a table or floor by 

 a pin through its centre, to serve as an axis of revolution. Near 



