is necessary that to enable her to do so, and bring continually 

 the same point back to the radius- vector, she must rotate, or turn 

 round once on her axis during each revolution in her orbit, in a 

 direction contrary to that of her revolution. In opposition to this, 

 I have seen reason to believe, and shall endeavour to prove, that 

 the alleged presentation of every part of the circumference, witli- 

 out rotation or turning round, is impossible ; that the shuffling 

 kind of progression to which is ascribed this impossible effect, 

 is a real retro-rotation or turning round on the axis back- 

 wards, in a direction really contrary to that of the moon's revo- 

 lution, namely, from east to west ; that the rotation which they 

 ascribe to the moon is not *' contrary to," but in the same direc- 

 tion with^ that of her revolution, namely, from west to east ; and 

 that, were she to rotate once in that direction during each orbi- 

 tal revolution, the inevitable result of such a rotation. would be 

 the presentation, not of the same point continually, but of every 

 part of her circumference in succession to the centre of her or- 

 bit. I admit, however, that if the moon were indeed to move 

 freely in space, she would move in the manner they allege, and 

 which I call retro-rotation ; and that, as she does not, there must 

 be some power acting against her freedom, and producing the 

 effect of kcepiny the same face continually looking to the earth ; 

 but that, whatever may be the nature of that power, its effect is 

 not to cause but to prevent the moon from rotating " in a direction 

 contrary to that of her revolution ;" in short, to keep her from 

 rotating at all. She does, indeed, turn roundabout in presence 

 of the sun, and without turning round about in some way or other, 

 neither the moon nor any other body revolving in an orbit could 

 present every part of its circumference as the moon does to the 

 sun or other fixed object, or stationary spectator, outside, or in- 

 deed to any other body or spectator whatever ; but so far is the 

 moon's turning round from being a revolution of her circumfer- 

 ence round about her axis, that, on the contrary, it is the axis 

 itself, carrying the whole mass of her body forward along with it, 

 that virtually revolves about a pivot on the radius-vector, close 

 to the innermost point of circumference, or that point itself, as 

 its centre of revolution. To the sun or other spectator outside, 

 the effect of this kind of revolution is the same as would be the 

 effect of the moon's turning once round on her axis, while re- 

 maining at a fixed point of the orbit ; but, with respect to the 

 earth or the centre of the orbit, the presentation of every point 

 of the revolving body's circumference without actual rotation or 

 turning round on the axis is impossible, so long as the axis it- 

 self revolves at a fixed distance from the centre of its orbit If, 

 however, the body were to remain at a fixed point, and turn round 

 with its whole mass, including the axis, about that point, as its 



