PROCEEDINGS 



OF 



THE ROYAL SOCIETY. 



1833-1834. No. 16. 



April 10, 1834. 



JOHN WILLIAM LUBBOCK, Esq., M.A., V P. and Treasurer, 

 in the Chair. 



The Right Hon. Edwin Viscount Adare 3 Charles Ansell, Esq.; 

 Felix Booth, Esq. ; Lieut. Alexander Burnes, E.I.C. ; Francis Cor- 

 baux, Esq. • Sir William Browne Folkes, Bart., M.P. ; James William 

 Freshfield, Esq. ; John Davies Gilbert, Esq., M.A.; Edward Griffith, 

 Esq.; Edmund Halswell, Esq., M.A. ; William Charles Henry, M.D.; 

 Robert Hudson, Esq. ; Rev. William Forster Lloyd, M.A. ; John Phil- 

 lips, Esq.; Captain Walter Nugent Smee, E.I.C.; William Spence, 

 Esq.; Henry Sykes Thornton, Esq., M.A.j John Warburton, M.D.; 

 and Horace Hayman Wilson, Esq., were elected Fellows of the So- 

 ciety. 



A paper was read, entitled, " On a General Method in Dynamics, 

 by which the Study of the Motions of all free Systems of attracting 

 or repelling Points is reduced to the Search and Differenciation of one 

 central Relation, or characteristic Function." By William Rowan Ha- 

 milton, Esq., Andrews Professor of Astronomy in the University of 

 Dublin, and Royal Astronomer of Ireland. Communicated by Cap- 

 tain Beaufort, R.N., F.R.S. 



After some introductory remarks illustrative of the scope and de- 

 sign of this paper, the object of which is sufficiently pointed out in its 

 title, the author considers, 1st, the integration of the equations of mo- 

 tion of a system, the characteristic function of such motion, and the 

 law of varying action ; 2nd, the verification of the foregoing integrals ; 

 3rd, the introduction of relative or polar co-ordinates, or other marks 

 of position of a system ; 4th, the separation of the relative motion of a 

 system from the motion of its centre of gravity, the characteristic func- 

 tion for such relative motion, and the law of its variation ; 5th, the 

 systems of two points in general, and the characteristic function of 

 the motion of any binary system ; 6th, the undisturbed motion of a 

 planet or comet about the sun, and the dependence of the character- 

 istic function of elliptic or parabolic motion on the chord and the sum 

 of the radii; 7th, the systems of three points in general, and their 

 characteristic functions ; 8th, a general method of improving an ap- 

 proximate expression for the characteristic function of motion of a 

 system, in any dynamical problem ; 9th, the application of the fore- 

 going method to the case of a ternary or multiple system, with any 



x 



