59 



tal force, or the earth's attraction of gravitation, were to act upon 

 the moon's centre only, leaving her circumference, and all the 

 other molecules of her mass between that and the centre, free to 

 obey the impulse of the centrifugal or tangential force, which 

 would, in that case, carry them all forward with the same velo- 

 city as the centre itself, and consequently all once round about 

 that centre during the period of each orbital revolution. The 

 changes, then, that would happen to his " remarkable spot S," 

 would be really the effects, the signs, and the evidence of the 

 moon's rotation, or turning round on her axis. Mr B., in com- 

 mon with other astronomers, has overlooked the very important 

 difference that exists between the moon moving under the anta- 

 gonist centrifugal and centripetal forces and an artificial body 

 of the same form, a globe or a disk, which may be made to move 

 in an orbit under the influence of the tangential force alone, per- 

 fectly free from any centripetal attraction. Such a body may be 

 made to shuffle in a certain way round its orbit, presenting every 

 point of its circumference to the centre of that orbit, apparently 

 without rotating ; but, even in that case, a real retro-rotation or 

 backward -turning of the shuffling body on its own axis can easily 

 be proved ; and loithout rotation, either backwards or forward, 

 the presentation of every point of its circumference to the cen- 

 tre of its orbit, or to a spectator within the periphery of the or- 

 bit, is perfectly impossible. On the other hand, were this arti- 

 ficial moving body to be subjected to a centripetal force, in the 

 shape of a string, or other material vinculum, connecting any 

 one point, or by two strings, or other material vincula, connect- 

 ing any two diametrically opposite points of its circumference 

 with the centre of its orbit, it would then, in every orbital revo- 

 lution, necessarily and inevitably present, like the moon, the 

 same face continually to that centre, without requiring any 

 '' quarter," or complete " rotation, in a direction contrary to that 

 of its revolution." 



Gravesande's illustration is this : *' The effect of the moon's 

 motion round her axis is, that she turns continually the same face 

 to the earth. Suppose the moon in N (fig. 9); the face looking 

 to the earth is m n i If the moon were not to rotate on her 

 axis, and her individual particles were to move forward in paral- 

 lel lines, the line mi would coincide with the line In, in the 

 moon's position B, and the hemisphere mn i would coincide 

 with I m n. But, seeing that while the moon describes the quar- 

 ter of her orbit, she also accomplishes the fourth part of her ro- 

 tation, the face which should coincide with Imn is in 772,71,1,* 

 that is, again looking to the earth T. In the same manner is it 

 proved that the same face m n i is seen by a spectator on the 

 earth in the positions P and E." Philosophi<E Neictmiance In- 



