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Ninth Meeting. S&ptember 13, 1870. 



Mr. J. T. Thomson, F.R.G.S., Yice President, in the chair. 



The following new members were elected : — Wm. Mason, H, J. Abel, 

 and W. Downie Stuart. 



1. The non-mathematical portion of a paper, " On Central Forces, — 

 especially as regards Force varying directly as the distance," by 

 R. Wilding, was read. 



(abstract.) 



In nature, all forces tend towards certain points, or " centimes of 

 foi'ce," these centres being the affected particles themselves. These 

 attractive forces are found to depend principally on the mutual distances 

 apart of the particles ; and the nature of this dependence on the distance 

 is denominated the law oi force. 



The particular " law of force " by which a moving body is actuated 

 may be ascertained from the nature of the curve in which it moves, and 

 this last is a matter to be determined by observation. 



When two material particles move in obedience to their mutual 

 attractions, whatever the law of force may be, it may be shown that (1) 

 they move in a plane which is invariable, (2) their common centre of 

 gravity moves with uniform velocity in a straight line (this velocity may 

 be zero), and (3) the lines joining the bodies and their common centre of 

 gravity sweeps out equal areas in equal times. But, in the case of more 

 than two bodies in motion attracting each other, it is generally found 

 that neither moves continually in the same orbit, but is disturbed by the 

 attraction of the others, and compelled to vary its course considerably. 



This is the case in the solar system. Neither the earth nor any of 

 the other planets move in fixed orbits, but are continually perturbed in 

 their motions, but certain peculiarities in its present constitution 

 effectually prevent any injury to its stability. 



The particular law of force proposed for consideration by the 

 author, is that each particle attracts proportionally to its mass and 

 distance from the attracted particle. It is shown that the members of a 

 system of material particles actuated by this law would move in 

 permanent undisturbed orbits, that is, there would be no perturbation. 

 The orbits would be ellipses, relatively to the principal heavy central 

 body which would be in the common centre of the ellipses, and the mean 

 angular motions would be all equal, that is, all would complete their 

 revolutions in equal times. 



