410 LECTURE XLIII. 



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 mathemati- 

 cally the effects of gravity in each 'particular motion, but we may in some 

 measure illustrate the subject, by considering in what manner astronoTners. 

 have proceeded in their explanations and calculations, and we may entV , 

 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 ; <Cnd 

 in order to determine the effects of their attraction, we must suppos^ the 

 actions of an infinite number of such points to be combined. It was sltajvn 

 by Newton, that all the matter of a spherical body, or of a spherical sur- 

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

 as collected in the centre of the sphere. The steps of the demonstration 

 are these : a particle of matter, placed at the summit 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, whatever 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 of 

 the opposite and equal actions of the infinite number of minute surfaces, 

 terminating the opposite pyramids into which the sphere may be divided ; 

 it is also demonstrable, by the assistance of a fluxional calculation, that a 

 point, placed without the surface, is attracted by it, precisely in the same 

 manner, as if the whole matter which it contains were collected in the 

 centre ; consequently the same is true of a solid sphere, which may be 

 supposed to consist of an infinite number of such hollow spheres. If, 

 however, the point were placed within a solid sphere it would be urged 

 towards the centre, by a force which is simply proportional to its distance 

 from that centre. This proposition tends very much to facilitate all calcu- 

 lations of the attractions of the celestial bodies, since all of them are so 

 nearly spherical, that their action on any distant bodies is the same as if 

 the whole of the matter of which they consist were condensed into their 

 respective centres; but if the force of gravity varied according to any 

 other law than that which is found to prevail, this simplification would no 

 longer be admissible, even with respect to a sphere. 



It can scarcely be doubted that the power of gravitation extends from 

 one fixed star to another, although its effects may in this case be much too 

 inconsiderable to be perceived by us. It may possibly influence the pro- 

 gressive motions of some of the stars ; and if, as Dr. Herschel supposes, 

 there are double and triple stars revolving round a common centre, they 

 must be retained in their orbits by the force of gravity. Dr. Herschel 

 also imagines that the motion of our sun is in some measure derived from 

 the same cause, being directed nearly towards a point in which two strata 

 of the milky way meet ; the attraction of the stars, other things being 

 equal, must, however, be proportional to their brightness, and that part of 

 the heavens, to which the sun is probably moving appears to afford less 

 light than almost any other part, nor does the hemisphere, of which it is 



