10 



revolves round about the moving axis, at the very time that axis 

 is revolving about the centre itself. 



The axis of a revolving body remains constantly at the same 

 distance from the centre of its orbit, and the radius-vector is al- 

 ways the shortest straight line between that axis and that centre. 

 But the radiuS'Vector has only one movement, 'd\\v3i\s forwards 

 with the moving axis which it connects with the immovable 

 centre, its different parts moving with different degrees of velo- 

 city proportional to their distance from the centre. It never 

 turns back its inner end any more than the centre itself to which 

 it is attached turns back from its central position, and conse- 

 quently every change that takes place in the relation of the parts 

 of the moon's mass or circumference to that radius can only be 

 the effect of movement in the moon itself or its parts. The re- 

 lation of the radius-vector to the moon's axis is invariable; and 

 if the same point of the moon's circumference be always inter- 

 sected by the radius, the relative position of that point not only 

 to the radius, but also to the axis of the moon and to the centre 

 of the orbit, must be just as invariable as the invariable and im- 

 movable centre itself. It will always keep the same relative 

 place on the shortest straight line between the axis and the centre, 

 being itself the nearest point of the revolving body to that centre ; 

 and there is only one way in which its relative position can be 

 changed, namely, by its diverging from the radius- vector, either 

 to the right hand or to the left. In either case the moon's mass 

 will oscillate, or turn on its axis, to the extent of the divergence, 

 and if the divergence be continued in either direction till every 

 point of the circumference in succession shall have passed the 

 radius-vector, the body will have performed a complete rotation 

 on its own axis, whatever may be the phenomena or appearances 

 which it may present in other respects. The passing of all its 

 points across the radius-vector is the surest, as it is indeed the 

 most perfectly incontrovertible sign and proof of its rotation. 



The radius-vector certainly does not cross the orbit with it ; 

 the inner end of the radius- vector, which, I may say again, is no- 

 thing else than the shortest straight line betwixt the moon's axis 

 and the centre of the earth, certainly does not revolve in the oppo- 

 site direction roundabout on its outer end at the moon'saxis, unless 

 it were true, what is, however, positively and perfectly impossible, 

 that the fixed centre itself revolves about the moon and her axis. 

 How, then, is it possible to avoid the conclusion that, if the moon 

 were to revolve with all the points of her circumference in succession 

 parsing the radius -vector and. crossing the orhit, though she might 

 at the sametime keep the same face constantly looking to the 

 same fixed point outside ; or, in other words, supposing her to 

 move in or on a horizontal plane with the north, south, east, and 

 west quarter points of her circumference always directed, each 



