30 



and changes that are or would be produced by the revolution 

 and rotation of a globe at the far end of a radius- vector, of any 

 conceivable length, even to the orbits of Herschel and Leverrier, 

 or beyond them ; for the radius-vector is the instrument and 

 accompaniment of the revolution, virtually a part of the orbit 

 itself, representing the corresponding point of the centre's own 

 circumference, at the point of the orbit where the globe may 

 happen to be for the time, and the index of the globe's rotation, 

 or turning round on its own axis, every point of tlie globe's cir- 

 cumference inevitably passing the radius-vector once in every 

 complete rotation. Metaphysically considered, indeed, the centre 

 of an orbit is an imaginary point, without length, breadth, and 

 thickness; but considered physically, it is a certain portion of 

 space, with a certain definite circumference, however small, di- 

 visible into any number of parts or degrees like the orbit itself; 

 so that the orbit is virtually the centre itself expanded to those 

 limits, as, on the other hand, the centre is virtually the orbit 

 itself contracted to the smallest conceivable limits; consequently, 

 whatever could be truly predicated concerning any point of the 

 orbit, or concerning a body moving along the orbit, could be 

 just as truly predicated concerning the same or a similar event 

 at any point of the centre itself. 



The principle, and the fact of retro-rotation, may be beauti- 

 fully and perfectly illustrated by the movements of a magnetic 

 needle in a compass-box. Fix the box, containing the needle, to 

 the outer end of a rod or radius-vector that shall describe a circle 

 round its other end fixed in the centre, in such a way that the 

 two ends of the needle shall be pointing directly to the north and 

 south points of the card fixed immovably in the bottom of the 

 box. Then make the radius revolve from west to east, carrying 

 of course the box along with it. As it revolves, the card will be 

 seen to carry its point N, in the same direction away to the left 

 of the needle's north point, and so on round the whole circum- 

 ference, every one of its points in succession passing the needle, 

 which will seem to stand still, and remain invariably pointing in 

 the same direction, or maintaining an invariable parallelism, as 

 if it were facing the sun or other stationary spectator outside of 

 the orbit. Now, in this case, one of three things happens, — \st^ 

 the hoyijlxed, though it be to the radius, turns round on its own 

 axis ; or, 2c?, the radius itself, carrying the box along with it, turns 

 round on its own centre of gravity or the pivot in the box ; or, 3o?, 

 the needle, which is movable on its pivot, turns round on that pivot, 

 while the box and the radius revolve without rotating. To prove 

 which of them it is that rotates, just Jix the needle in line with 

 the radius, in the direction NS, so that it shall not move on its 

 pivot ; then make the rod revolve, and box and needle alike will 



