11 



to the corresponding point of the horizon, she could only accom- 

 plish that feat by means of a rotation, or turning round on her 

 axis once, during the period of her orbital revolution ? In such 

 a case, one of two things must happen ; either the point of the 

 revolving body that diverges from the radius-vector westward 

 turns round on the body's axis 90° in each quadrant, or the centre 

 of the orbit, carrying the inner end of the radius-vector along 

 with it, turns round about the body's axis to that extent in the 

 contrary direction. But the centre is a fixed spot, which, by 

 the necessity of its nature as a centre, is incapable of movhig 

 from its place ; the radius-vector, proceeding from that centre, is 

 by its nature just as incapable as the centre itself of turning 

 backwards by its inner end; while, on the contrary, not only is 

 there no incapability of movement on the part of the planet, but 

 there has been a real and visible movement of the parts of its 

 circumference, past and away from the radius-vector and the 

 centre and across the orbit; therefore, it follows inevitably, that 

 the divergence to be accounted for is and can only be the effect 

 of the last mentioned movement of the planet, and of a real and 

 actual rotation, or turning round, of the body on its axis. 



From these premises it follows inevitably that whensoever, and 

 to whatsoever extent there happens a change of relations between 

 the parts and points of circumference of a body revolving in an 

 orbit, or circular path, on the one side, and the radius-vector or 

 other radius, or radii of the circle and its centre, on the other, 

 that change must be the result, solely and exclusively, of a rotary 

 movement of the revolving body on its own axis. For example, 

 suppose a disk to be placed at the north point of an orbit, and 

 to turn once round on its own axis at that point, every point of 

 its circumference in succession would be seen to pass the radius- 

 vector, till they had all completed a rot«ition about the axis, the 

 point that first diverged from the radius on the one side being the 

 last to return to it on the other. But if, instead of completing 

 the rotation at N, the planet were to rotate to the amount of 

 just one degree of its orbit, the result would necessarily be pre- 

 cisely the same, so far as respects the radius-vector, and tlie in- 

 variable centre which the radius everywhere represents ; and that, 

 whether the rotation be from west to east, or from east to west 

 If a cord were attached to the circumference of the disk and to 

 the centre of the orbit, it would be carried round about the axis 

 precisely in the same way, whether the rotation were performed 

 all at once at N, or only gradually during the revolution ; 

 and such perfect sameness of effect can only be reasonably 

 ascribed to sameness of cause. When, therefore, the planet 

 moves one degree, and each point of her circumference at the 

 same time diverges one degree from the radius, that divergence 



