8 



out carrying the points of her circumference in succession past 

 her radius-vector, and across the line of motion described by her 

 axis, and, consequently, keeping the same face continually look- 

 ing to the earth, and very nearly the same visible points of her 

 circumference continually in one with her radius-vector ; and no 

 logic can evade the conclusion, deduced from the very nature and 

 circumstances of all rotation, that she revolves in her orbit with- 

 out turning round on her axis. 



The radius-vector of a planet, or other body moving round an 

 orbit, may be considered in two points of view : either as a con- 

 stituent and substantive part of the orbit itself, or of its centre, 

 or as a constituent and substantive part of a body revolving in 

 contact with the centre of its orbit. In the former case, the ra- 

 dius-vector is virtually a rod attached by a hinge or ligature to 

 the centre of the orbit, or, more correctly still, it is virtually a 

 line drawn on the surface of a disk co-extensive with the orbit, 

 and consequently capable of making no more than one revolution 

 round only one of its ends at once ; and the end round which 

 only it is possible for it to revolve is the one attached to the cen- 

 tre of the orbit, and no more movable from its place than the 

 centre itself is. And, in performing that single revolution of 

 which alone it is capable, each of the points of which every ra- 

 dius is composed moves with different degrees of velocity, pro- 

 portional to its distance from the centre, and all these points 

 moving together describe a series of concentric circles, increasing 

 in dimensions as they go outwards. Consequently, all the points 

 move through unequal spaces in equal times ; and the result is, 

 that, while the innermost points describe an invisible circle round 

 an invisible point, all the other points describe always increasing 

 circles round that point as well as the centre ; whereas, on the 

 contrary, according to the astronomical doctrine I am combating, 

 each of these points describes a circle, not round the centre itself) 

 hut round the outer end of the radius of which it forms a part, 

 while that outer end, and that only, by itself, describes a single 

 circle round the centre of the orbit. 



In the other point of view, the radius-vector may be considered 

 as a part of the revolving body, and to represent by its inner 

 end the circumference of a circle as large as the orbit itself, but 

 only half within the orbit, and having the axis of the revolving 

 body for its centre. But it is obvious that the radius-vector so 

 circumstanced, so long as it remains attached to the orbit's cen- 

 tre, can no more revolve about its outer end, or the axis of the 

 revolving body, than any of the radii of the solid disk we have 

 been considering, or than the centre itself; and, consequently, 

 the point of the revolving body's circumference that remains al- 

 ways in one with the radius, can no more revolve about the axis 



