and back again on her other side, presenting tliem all in their 

 turn on every side of her axis, and making them all in succes- 

 sion pass her radius-vector, thereby exhibiting to the earth a 

 complete '* vicissitude of succession," and all the signs of rotation, 

 or whirling round on an axis, all this would or might be pro- 

 duced without rotation, or turning, or whirling round ! It is 

 also stated, that not only the middle point of that side of the 

 moon which is always looking to the earth, but also the radius- 

 vector and the earth itself, or at least " its visual ray," which is 

 the same thing, revolve (that is, move in an orbit, or describe 

 a circle,) round about the moon's centre, while that very centre 

 itself is revolving about the earth ! Paradoxical as such doctrine 

 seems, and well calculated as it is to startle and surprise, and pro- 

 voke to scrutiny, it has nevertheless kept its ground for two centu- 

 ries, and received the solemn sanction of the great minds of whose 

 achievements astronomy so proudly boasts. But how will unscien- 

 tific readers be amazed to be told that all these paradoxes are 

 founded on no less monstrous an assumption, than that it is the 

 property of the centre of a circle not only to change its place con- 

 tinually within the circle, but even to rotate or go round about the 

 axis of a body moving along the circle's circumference, yet with- 

 out going out of the circle^ which one would think an indispensable 

 requisite to enable it to perform that rotation ! Without this fun- 

 damental proposition to rest on, the doctrines of the moon's rota- 

 tion, and of the sidereal day's being the true measure of the earth's 

 rotation cannot subsist a moment. This will be best accomplish- 

 ed, perhaps, by stating the simple truth, which must at once re- 

 ceive the assent of those who examine the question, even though 

 they be told at the same time that the opposite error has been 

 expressly affirmed by Galileo and La Place, sanctioned by New- 

 ton, and tacitly at least, perhaps inadvertently, admitted by all 

 other astronomers, as an established truth in their science. 



The centre of a circle, considered in relation to the circle 

 itself, is a fixed point, which remains invariably in the same place, 

 equidistant from every point of the whole circumference ; and, 

 consequently, every radius, or straight line drawn from the centre 

 to the circumference, will be invariably of the same length, and 

 cut or touch the circumference at right angles. 



From this it follows obviously that every point of the circum- 

 ference, and all the points together, whether limited in number, 

 or infinitely numerous, will bear precisely the same relation to 

 the centre. Each of them will occupy the intersection of two lines 

 crossing at right angles, or per})endicular to each other, namely, 

 the radius that connects it with the centre, and the circumfer- 

 ence itself, of which it forms a part. 



The centre of a circle is, by the necessity of its nature as such, 



3 



