516 LECTURE XLIir. 



equal actions of the infinite number of minute surfaces, terminating the oppo- 

 site 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 iii 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 in- 

 finite 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 propo- 

 sition tends very much to facilitate all calculations 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 gra- 

 vity 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 in- 

 considerable to be perceived by us. It may possibly influence the progres- 

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

 ave 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 the centre, abound so 

 much in bright stars as the opposite hemisphere. If Sirius is a million times 

 as far from the sun as the earth, and if he should descend towards the sun 

 by means of their mutual gravitation only, he would move, on a rough esti- 

 mate, but about 40 feet in the first year, and in 1000 years only 8000 miles. 

 It has been conjectured that the mutual gravitation of the stars of a nebula 

 is sometimes the cause of the peculiar form of the aggregate, which some- 

 what resembles that of a drop of a liquid, held together by its cohesion: hut 



