40 



which causes its particles to revolve in different orbits propor- 

 tional to their radial distance from the orbit's centre ; and, if the 

 orbit described by the body's innermost point of circumference, 

 a, be exactly equal to 360 measures of the body's circumference, 

 it is obvious that the return of a to the radius-vector will be the 

 measure and indicator of each rotation ; yet, in every such rota- 

 tion, any given star will appear on the same meridian sooner than 

 at the preceding transit, and these daily gainings, or losses rather, 

 of the star will amount to one sidereal day in the course of the 

 year. From this it follows most obviously, that the transit of 

 the star is not, and cannot be, the measure of rotation, inas- 

 much as the measure it gives is 4 minutes of time, or 1° of space, 

 shorter than the measure of the revolving body's real circumfe- 

 rence, which, as already supposed, measures exactly one degree 

 of the inner verge of the orbit. The centre of the orbit never 

 ^changes its place in the slightest degree ; the radius-vector is 

 equally invariable in its relation to the revolving body ; it never 

 falls ha^k a hair's-breadth ; its whole length moves constantly for- 

 ward, and forward only, turning round on the centre, and the 

 centre only, and not at all round about the revolving body's axis; 

 consequently, its relation to the orbit's centre, and to the body's 

 axis, is precisely the same at every degree of the orbit's circum- 

 ference. When, therefore, a, in rotating, turns away from the 

 radius, the radius moves forward just one measure of the body's 

 circumference, and meets a again at the end of the first degree 

 of the orbit ; and the same thing is repeated in every one of the 

 360° of which the orbit consists. If the body were to stand at 

 any point of its orbit, and turn just once round on its axis, it is 

 most obvious that the return of the same point a to the radius^ 

 vector would be unanimously acknowledged to be the comple- 

 tion of just one rotation ; but, what should make a difference, 

 when the rotation is performed, not all at once at the same point, 

 but only gradually, minute for minute, as it were, during the 

 body's progress in the orbit? No reasonable answer but the 

 true one can be given to this question, and that true answer is, 

 that there is not, and cannot be any difference ; and that in a 

 perfect orbit, with a revolving body describing equal areas in 

 equal times, which, in that case, would be with perfectly uniform 

 velocity, the radius-vector indicating the transit of the sun within 

 the orbit, and not the transit of the star outside, would be the 

 true measure of rotation. 



The phenomenal relations of the heavens and the earth are 

 the same, whether we ascribe them to the earth's orbital move- 

 ment round the circuit of the heavens, from west to east, or to 

 the circumvolution of the heavenly sphere itself, in the opposite 

 direction, or from cast to west, round the earth at rest in the 



