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is the infallible sign of the planet's rotation, and the invariably 

 perpendicular radius-vector is the fixed point where the rotation 

 begins and ends. If the rotation be made in the same direction 

 as the orbital revolution, or from west to east, to the extent of 

 one degree of circumference for each degree of the orbit, the 

 planet will, in every complete orbital revolution, inevitably bring 

 every point of its circumference in succession once to the radius- 

 vector, and there present it directly to the centre ; and from this 

 undeniable fact it follows inevitably that if the same point of cir- 

 cumference remains continually in one with the radius- vector, and 

 directed to the centre, that permanence of its relation to these 

 members of the orbit, which are in themselves invariable in their 

 relations to the planet's axis, must be, and is, the certain token of 

 the planet's non-roiation. 



But, as astronomers say, if the moon were not to r^otate on her 

 axis, she would carry every point of her circumference in turn 

 past the radius-vector, backwards, or from east to west, and pre- 

 sent them all in turn to the earth in or near the centre of her 

 orbit, and, at the same time, keep all her parts perfectly parallel 

 to a fixed straight line drawn across the plane of her orbit, and 

 that permanent parallelism is a proof of her non-rotation. The 

 moon would, indeed, if she were perfectly /^-e^ in her movements, 

 under the single condition of keeping her axis within the limits of 

 a definite orbit, exhibit these phenomena, and preserve that per- 

 fect parallelism ; but, horresco ref evens, that would most certainly 

 be the effect of her rotation on her axis backwards, or in a di- 

 rection contrary to that of her revolution, namely, from east 

 to west, while she revolves from west to east. And to keep in 

 countenance this paradox, it is assumed, not tacitly or inadvert- 

 ently, but directly and expressly, that, in this case of retro-rota- 

 tion, or so-called parallelism, it is the radius- vector, nay, the centre 

 of the orbit itself^ that moves in the opposite direction from the 

 point a of the moon's circumference ! But I have endeavoured to 

 show already, that the radius-vector and the centre are perfectly 

 incapable, by their very nature as such, of making the smallest 

 change in their relations to the moving body ; and that, what- 

 ever change takes place in the relations of the moving body's 

 circumference, is, and must be, solely and exclusively the 

 effect of the rotary movement of the planet, or satellite on 

 its own axis. And the parallelism which has been assumed, 

 and so triumphantly referred to as the token of non-rotation, 

 would be occasioned by so very simple a process as this. When 

 the planet turns round on its axis from east to west, the axis 

 itself, while it preserves the same invariable relations to the 

 radius-vector and the centre, is continually changing its place 

 on the orbit, and of course its relations to every surround- 



