832 



masses and mutual distances. After proving that any number of 

 spheres may move so that the central force shall vary directly as the 

 distance, he shows that only certain values of <p are possible for an 

 infinite number of spheres, giving the criterion of possibility ; and 

 thence that the only possible law of central force for an infinite 

 number of spheres is that in which the force varies directly as the 

 distance. 



The author then enters upon some general considerations on the 

 physical impossibility of an universal law, rigorously exact and ex- 

 pressed by equations involving differentials of no higher order than 

 the second, and on the amount of disturbance by extraneous agen- 

 cies. Having shown how all equations expressed by rectangular 

 coordinates may be transformed into others involving only the mu- 

 tual distances of the spheres at m equal intervals of time, he gives 

 an equation of diff'erences defining the motion of n points, such that 

 the distances and their differentials of every order not exceeding m 

 may have any assigned values. 



After deducing a general formula for transforming equations of 

 differences not exceeding the mth order into equations between the 

 distances at m equal intervals of time, the author applies it to the 

 last equation, and shows that the equations so found are possible for 

 any number of moving points and for every value of m; and that 

 the most general law, by which the motion of n equal spheres can 

 be determined, so that all move according to the same law at all 

 times, may be found by taking a proper value of m. He then shows 

 that these equations give a method of unlimited approximation to 

 any unknown law ; and suggests the mode of extending the solution 

 of the problem to solids of any figure and mass. Finally, he gives 

 the mth diff'erential of the distance between any pair of points mo- 

 ving according to this law, in terms of the differentials of lower 

 orders including the distances. 



June 21, 1849. 



The EARL OF ROSSE, President, in the Chair. 



The following Gentlemen were admitted into the Society : — 

 Sir Robert Kane, M.D.; Thomas Andrews, M.D.; John Scott 

 Russell, Esq. 



The Right Rev. The Lord Bishop of Manchester was elected into 

 the Society. 



The following papers were read : — 



1. " On the Anatomy and Affinities of the Family of Medusae." By 

 Henry Huxley, Esq. Communicated by the Bishop of Norwich, F.R.S. 



The author commences by remarking that no class of animals has 

 been so much investigated with so little satisfactory and comprehen- 

 sive result as the family of Medusm (including under that name the 

 Medusae, Monostomatcs and the Rhizostomidce), and proposes in this 



