13 



ing object, outside of the orbit, all round the compass ; and, as the 

 rotiition is performed in precisely the same proportion as the 

 orbital revolution, degree for degree, but in opposite directions, 

 the result is apparently, though not really, to neutralize the rota- 

 tion, and so to keep the parts of its mass always directed to the 

 same points of the compass, always parallel to themselves, and to 

 a fixed straight line drawn in the plane of the orbit 



A planet, moon, or other round body revolving in an orbit 

 has a certain definite breadth or thickness, and the orbits or 

 circles described by the different parts of its mass are conse- 

 quently of diiferent dimensions, proportional to their radial 

 or diametric distances from the orbit's centre. The innermost 

 point of circumference c, will describe an orbit less than the orbit 

 described by the body's central axis c, by the amount of the 

 measure of one circumference of the body, while c will, in its 

 turn, describe an orbit also one circumference less than the orbit 

 described by the outermost point of circumference b. Thus, 

 when the body revolves without rotating, 6 will be found to travel 

 the measure of two circumferences, and c one circumference, 

 more than a. When, therefore, a diverges from the radius-vec- 

 tor to the left, and turns round about the axis from east to west, 

 returning to the radius-vector from the right, it travels, by vir- 

 tue of such rotation, just the measure of one circumference more 

 than the length of its own proper orbit, and consequently through 

 a measured space, or along a measured line, precisely equal to 

 the dimensions of c's orbit ; and in no other way, and by no 

 other means than rotation round c, could it accomplish such a 

 feat. In the meantime, however, Z>, and the succeeding points 

 of circumference, which all take the outmost place in their turn, 

 have travelled the measure of one circumference more than c, 

 and consequently more than a likewise; and that additional 

 length of the outermost point's journey, has the effect of making 

 both a and c, as well as b itself, preserve the parallelism referred 

 to, while not the less a's rotation on the axis is a real and actual 

 event ; there being the measure of two circumferences travelled 

 by the outermost point to be met by only one circumference in 

 excess on «'s part, and consequently there being that space 

 available for the purpose of keeping a always in the same paral- 

 lelism, and apparently without rotation ; but such an appearance 

 can deceive c-nly those who neglect to inquire into, or who loil" 

 fully overlook, its cause. All the three points, a, i, and c, will 

 be found in this case to have travelled precisely the same mea- 

 sured length of space in the same time, and rotation on the axis 

 c, is the indispensable means of producing such an equality in 

 the rate of movement. If, on the contrary, there be no rota- 

 tion, the point a will remain constantly in one with the radius, 



