98 



January 19, 1832. 

 JOHN BOSTOCK, M.D., Vice-President, in the Chair. 



A paper was read, entitled " On the theory of the Perturbations 

 of the Planets." By James Ivory, Esq. A.M. F.R.S., Instit. Reg. 

 Sc. Paris., & Reg. Sc. Gotting., Corresp. 



The methods hitherto employed by mathematicians for deter- 

 mining the variations which the elements of the orbit of a planet 

 undergo in consequence of perturbation, and for expressing these 

 variations analytically in the manner best adapted for computation, 

 are found to depend upon a theory in mechanics, of considerable in- 

 tricacy, known by the name of the Variation of the Arbitrary Con- 

 stants. In seeking the means for abridging the severe labour of the 

 calculations, we must separate the general principles on which they 

 are founded from the analytical processes by which they are carried 

 into effect ; and in some important problems great advantage is ob- 

 tained by adapting the investigation to the particular circumstance 

 of the case, and attending solely to the principles of the method in 

 deducing the solution. The author suggests the possibility of 

 simplifying physical astronomy by calling in the aid of only the 

 usual principles of Dynamics, and by setting aside every formula or 

 equation not absolutely necessary for arriving at the final results. 



The present paper contains a complete determination of the 

 variable elements of the elliptic orbit of a disturbed planet, deduced 

 from three differential equations, that follow readily from the 

 mechanical conditions of the problem. In applying these equations 

 the author observes, the procedure is the same whether a planet is 

 urged by the sole action of the constant force of the sun, or is be- 

 sides disturbed by the attraction of other bodies revolving round 

 the luminary ; the only difference being that, in the first case, the 

 elements of the orbit are all constant, whereas in the other case they 

 are all variable. The success of the method followed by the author 

 is derived from a new differential equation between the time and 

 the area described by the planet in its momentary plane, which 

 greatly shortens the investigation by rendering it unnecessary to 

 consider the projection of the orbit. But the solution given in the 

 present paper, although it makes no reference to the analytical 

 formulae of the theory of the Variations of the Arbitrary Constants, is 

 no iess an application of that method and an example of its utility, 

 and of the necessity of employing it in very complicated problems. 



January 26, 1S32. 



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

 in the Chair. 



The reading of a paper, entitled " Experimental Researches in 

 Voltaic Electricity," by the Rev. William Ritchie, LL.D. F.R.S. 

 Professor of Natural and Experimental Philosophy in the Royal In- 



