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round about the moon's axis, in the space of a month. But, 

 true it is, that the earth, considered exclusively as the centre 

 of the moon's orbit, supposed for the present a perfect circle, 

 moves not a hair's breadth from her central position, and, from 

 that immovability of the earth, it follows certainly and inevitably, 

 that any change of relation between the earth and the parts of 

 the moon's circunifercnce must be the effect solely and exclu- 

 sively of a movement of that circumference away from the earth 

 round about the moon's axis. 



When a globe, disk, or wheel makes a forward movement, 

 and changes place, turning round on its axis at the same time, no 

 part of its rotating circumference ewer falls behmd the perpendi- 

 cular line that connects its axis with the road, rail, or track 

 along which it moves. All the parts alike move forward, and 

 it is the perpendicular radius accompanying the axis, that moves 

 still forward, past them, leaving them behind in the spot they 

 occupy for the moment, and in which they are kept back, not by 

 virtue of a rotatory power inherent in the revolving body, but 

 by a foreign power or force acting from without, and which only 

 yields them gradually to the impulse of the forward-moving 

 power, to take their turn in the forward movement. It is ob- 

 vious, therefore, that if the same point of the moving body's 

 circumference remain always in one with the perpendicular 

 radius, (and it makes no diff'erence whether the line of motion 

 be a straight line or a circle, for in both cases ajike the radius- 

 vector, (in a perfect circle at least,) is invariably perpendicular 

 to the line of motion, and always as far forward as the axis it- 

 self,) that point so remaining in one with the radius will always 

 be on the same side of the body and its axis, and there will not, 

 as there can not, be any rotation. The extrinsic force that re- 

 tards the successive points of the circumference has no effect 

 upon the perpendicular radius-vector ; it never keeps it back, 

 and consequently it does not keep back or retard that point of 

 the circumference, whatever it may be, that is always in one 

 with the radius. That point, so far from rotating backwards, is 

 constantly moving forwards; and this is true in all circum- 

 stances ; the infallible, and I may say, the only infallible sign 

 of rotation being, that the several points of the wheel's circum- 

 ference in succession pass the radius-vector, and cross the line 

 of motion itself, 90° distant from the radius on either side. 

 And this happens, when a body revolving in an orbit presents 

 the same point of its circumference invariably to the same fixed 

 point of the plane in which it moves ; for in such a case that 

 seemingly invariable point of circumference will be found to 

 diverge from the radius on one side and return to it on the other, 

 K^ to cross the orbit of the axis twice, once in going out and once 



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