436 Royal Society. 



LXIX. Proceedings qf' Learned Societies. 



ROYAL SOCIETY. 



1834. A PAPER was read, entitled/' On a C 

 April 10. — ■*"*■ Dynamics, by which the Study of i 



General Method in 

 the Motions of all 

 free Systems of attracting or repelling Points is reduced to the Search 

 and Differentiation of one central Relation, or characteristic Func- 

 tion." By William Rowan Hamilton, Esq., Andrews Professor of Astro- 

 nomy in the University of Dublin, and Royal Astronomer of Ireland. 

 Communicated by Captain 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 

 laws of attraction or repulsion, and with one predominant mass ; 

 10th, the rigorous transition from the theory of binary to that of mul- 

 tiple systems, by means of the disturbing part of the whole charac- 

 teristic function, and approximate expressions for the perturbations. 



A paper was also read, entitled, " Observations on the Motions of 

 Shingle Beaches." By Henry R. Palmer, Esq., F.R.S. 



The reading of a paper, entitled, " On some Elementary Laws of 

 Electricity." By W. Snow Harris, Esq., F.R.S. — was commenced. 



April 17. — The reading of Mr. Harris's paper was resumed in con- 

 tinuation. 



April 24. — The reading of Mr. Harris's paper was concluded. 



For the purpose of determining several questions relative to the 

 forces exerted by bodies in different states of electricity, the author 

 contrived an electroscope of peculiar construction, and also an elec- 

 trometer, both of which he minutely describes ; and in order to ob- 

 tain a unit of measure, in estimating the quantity of electrical accumu- 

 lation, instead of transmitting the electricity evolved by the machine 

 immediately from its conductor to the battery to be charged, he inter- 

 poses between them a coated. jar, furnished with a discharging elec- 

 trometer, so that the quantity of charges that have passed through it 

 may be estimated by the number of explosions occurring in the pro- 



