515 



LECTURE XLIII. 



ON THE LAWS OF GRAVITATION. 



At was first systematically demonstrated by Sir Isaac Newton, that all the 

 motions of the heavenly bodies, which have been described, may be deduced 

 from the eflfects of the same force of gravitation which causes a heavy body 

 to fall to the earth ; he has shown that in consequence of this universal 

 property of matter, all bodies attract each other with forces decreasing as the 

 squares of the distances increase; and of later years the same theory has been 

 still more accurately applied to the most complicated phenomena. We are at 

 present to take a general view of the operation of this law, in the same order 

 in which the affections of the celestial bodies have been enumerated. It will 

 not be possible to investigate mathematically the effects of gravity in each 

 particular motion, but we may in some measure illustrate the subject, by 

 considering in what manner astronomers have proceeded in their explanations 

 and calculations, and we may enter sufficiently into the principles of the 

 theory, to understand the possibility of its applications. 



The bodies which exist in nature are never single gravitating points; and 

 in order to determine the effects of their attraction, we must suppose the ac- 

 tions of an infinite number of such points to be combined. It was shown by 

 Newton, that all the matter of a spherical body, or of a spherical surface, 

 may be considered, in estimating its attractive force on other matter, as' 

 collected in the centre of the sphere. Tlie steps of the demonstration arc 

 these: a particle of matter, placed at the summi^t of a given cone or pyramid, 

 is attracted by a thin surface, composed also of attractive matter, occupying 

 the base of the cone, with equal force, whateve r may be the length of the 

 cone, provided that its angular position remain unaltered : hence it is easily 

 inferred that if a gravitating point be placed any where within a hollow 

 sphere, it will remain in equilibrium, in consequence ot the opposite and 



