21 



the centre of E, just as if they were integrant particles of E*8 

 own mass, turning round about their (K's) own axis. The 

 radius-vector is, in all cases and circumstances without exception, 

 virtually an integrant or integral part of the orbit and its centre, 

 and can no more change its relation to that centre by revolving 

 or rotating about the axis of a planet or satellite than the orbit^a 

 centre itself can. Such a revolution or rotation of the orbit's 

 centre is absolutely impossible ; and for the radius-vector it is 

 equally so. The axis, moreover, of a planet or satellite, is, like 

 the radius-vector, only an imaginary line incapable of any move- 

 ment independent of the mass of which it forms a part. There- 

 fore, it cannot be said in any case that the axis itself rotates while 

 the body does not In the case, however, of a common wheel, 

 with a separate axle, that might be said ; but I have shown al- 

 ready that it would be said without ground. 



This same diagram will serve very well to show the nature 

 and the cause of that pai-allelism which has been mistaken for the 

 effect and sign of non-rotation. Each of the disks has a diameter 

 of one inch, and a circumference of three inches, or thereabouts ; 

 consequently the orbit described round E's centre by .the inner- 

 most point of M's diametric breadth a, measures three inches 

 also ; while the orbits described by M's central axis and the 

 outermost point of her diametric breadth b, measure respectively 

 six inches and nine. These several orbits are described by the 

 revolving body equally in all the three cases of revolution just 

 spoken otj showing most plainly that, whether the revolving body 

 turn round on its axis or not, it is not in the least degree affected 

 in respect of rotation or non-rotation, by the great difference of 

 dimensions that exists between the orbits of its outermost and in- 

 nermost points of circumference, whether these be always the same 

 points, or a series of points changing continually. It might appear, 

 indeed, that if the outermost point travel so much faster than the 

 innermost point, it would push the latter round the axis ; but this 

 is prevented by the axis itself moving forward always in line with 

 the two points a and Z>, and the effect of that forward movement 

 of the axis is that it (the axis) and b virtually revolve about a, 

 instead of a's partaking with Z» in a rotation round the axis* 

 Strictly speaking, they, along with a, revolve in one line round 

 about the centre of the orbit, just as if they were all three points 

 in the lineal extension of the radius-vector. This is really the 

 case when the body revolves without rotating ; but, when it does 

 rotate, the points of circumference change places continually, 

 while the radius-vector alone, or the points in its length, describe 

 the two orbits corresponding to the outermost and innermost 

 points of circumference, the axis itself remaining always on the 

 radius, in line between them. If the three points cr, by and c 

 (axis) were to move along w ith equal degrees of velocity, it is 



