60 



stitutiones^ ^c. Leidce et Amstelodami, 1728: parsi. cap. 7, p. 385. 

 The noted particle zfnever occupied a more important place than 

 here. Give all that he requires, and the conclusion of his argu- 

 ment would be correct. Refuse, and it fcills to the ground at 

 once. The moon does not rotate on her axis, nor do her parti- 

 cles move in parallel lines ; they move in concentric ellipses. 

 Another illustration substantially the same as this, is to show that 

 a body moving along the diagonal of a square or parallelogram, 

 would reach the end of the diagonal without turning round on 

 its axis. So it would most certainly ; but the propounders of 

 that illustration, as well as M. Gravesande, forget, or overlook 

 the fact, that the moon or other body revolving in an orbit has a 

 certain thickness, and that the molecules of its mass describe diffe- 

 rent orbits of different dimensions in proportion to their distance 

 from the orbit's centre, and that at every angle of the rhombus 

 or four squares, which they make use of to illustrate the moon's 

 orbital revolution and rotation, the point of the circumference a, 

 in one with the radius-vector at starting, is carried ^0° away from 

 the radius, and that at each of these angles the direction of the 

 line of motion is also changed 90° ; and that these four changes of 

 90° each, make up a complete rotation of « round the axis, dur- 

 ing the orbital revolution. In fact, the only substantial differ- 

 ence between the case of revolution in a circle, and revolution 

 along the four sides of a square or a rhombus, is that in the former 

 case, the rotation is performed gradually and imperceptibly, 

 and in the latter only four times, to the amount of 90° at once. 

 It is true, that in the latter case the rotation is effected by means 

 of the axis being four times drawn back, away from the advanced 

 point a; but the result is not the less precisely the same; for 

 round about the axis a proceeds, and tbis is proved irrefragably 

 by its assuming every varying degree of angular distance in its 

 progress away from and back again to, the radius-vector facing 

 the centre of the square. If the body were to stop at any angle, 

 or in the middle of any side of the square, and turn once round 

 on its axis, from east to west, while the square was carried past 

 it in the same direction, it would exhibit all the phenomena of 

 parallelism^ associated with unquestionable rotation. 



In the article Moon, in the Penny Cyclopaedia, the author 

 proceeds in the usual manner. '« The discovery of the telescope, 

 and the examination of the moon which followed, soon shewed 

 that the planet always turns the same face towards the earth, or 

 very nearly. From hence it immediately follows that the moon 

 must revolve round an axis in the same time as that axis revolves 

 round the earth. If any one should walk round a circle, with- 

 out turning himself round, that is, keeping his face always in the 

 same direction, he would present alternately his front and back 



