29 



the ** hinge" of the proposition is used as a substitute, and the 

 effect of that hinge is to hold A fast, and keep him from rotating 

 round about C, as he naturally would were he free to obey the 

 impulse of the centrifugal moving power. It is indeed an ab- 

 surdity to talk of bringincj back what never goes away. The 

 correct expression in the moon's case would be, that her inlierent 

 power of turning round on her axis, if she really possess such a 

 power, in a direction contrary to that of the impulse given to 

 her parts by the centrifugal power, neutralizes that influence so 

 far as to keep the same point of her circumference continually in 

 one with the radius-vector, and so to make her revolve in her 

 orbit continually, without turning round on her axis^ to a greater 

 extent than that indicated by her libration in longitude, which 

 is a real oscillation on her axis, occasioned by the ellipticity of 

 her orbit, and her varying velocity in the different parts of that 

 orbit. 



The same thing may be proved by an experiment on a great 

 scale, performing continually between earth and heaven. The 

 earth's centre is not the centre of the moon's orbit ; but the two 

 bodies together have a common centre of gravity situate at a 

 certain distance between their axes, and round that centre of 

 gravity both axes revolve. The distance between the earth's 

 proper centre or axis and that centre of gravity is the measure 

 of the radius-vector which connects the earth's axis with that 

 centre of revolution, and is just a prolongation of the moon's 

 radius- vector, as if the two radii-vectores together, however dif- 

 ferent in length, formed but one inflexible rod revolving on a 

 pivot at the centre of the system. But, if it be true that the 

 moon's radius- vector revolves about the moon's axis, and revolve 

 about that axis it must, of the point of the moon's circumference 

 that is always in one with it, so revolve, as alleged, then the 

 earth's radius-vector must also revolve round the earth's axis; 

 and both radii forming virtually one inflexible rod, must, like 

 the double rod, AB, DE, simultaneously perform three dis- 

 tinct revolutions ; 1, round the common centre of gravity ; 2, 

 round the earth's axis ; 3, round the moon's axis ; all at oncey 

 which is perfectly impossible. 



The preceding argument and illustrations respecting the rod 

 AB apply precisely to the case of a globe revolving in close 

 contact with the centre of its orbit; the diameter of such a globe 

 being represented by the rod AB ; and whatever is true or 

 false respecting the rotation and revolution of that rod, is equally 

 true or false respecting the revolution of the globe whose dia- 

 meter it represents. The effects and changes produced by the 

 revolution and rotation in immediate contact with the centre of 

 its orbit are not in any respect different in kind from the effects 



