121 



been frequently excited to give shocks, and in whom a small fish 

 found in its stomach after death, appeared to be totally undigested. 

 The secretion of mucus was also either suppressed or considerably 

 diminished. From the circumstance that the branchiae are supplied 

 with twigs of the electrical nerves, the author conceives there may 

 be some connexion between the electrical and the respiratory func- 

 tions ; and that the evolved electricity may be employed in decom- 

 posing water, and in thus supplying the system with air, in situations 

 where the animal has not access to that of the atmosphere. The 

 author considers the mucous system of the torpedo as performing 

 important offices in its economy, in consequence of its connexions 

 with the electrical nerves. Contrary to the statement of Mr. Hunter, 

 he finds that the electrical organs are very scantily supplied with 

 blood-vessels. He concludes by some remarks on the peculiar 

 characters of the electricity of the Torpedo, the purposes it appears 

 to serve, and the varieties exhibited by different individuals, ac- 

 cording to the age, the sex, and other circumstances. 



The Meetings of the Society were then adjourned over Easter to 

 the third of May. 



May 3, 1832. 



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



The following Report, drawn up by the Rev. William Whewell, 

 M.A. F.R.S., the Rev. George Peacock, M.A. F.R.S., and the Rev. 

 Henry Coddington, M.A. F.R.S., on Mr. Lubbock's Paper, read 

 before the Royal Society Feb. 9, 1832, and entitled, "Researches 

 in Physical Astronomy," was read. 



Report. 



The method of the variation of parameters as applied to the in- 

 vestigation of the perturbations of the solar system has been suc- 

 cessively developed in modern times. This method gives the vari- 

 ations of the elements of the elliptical orbit in terms of the differentials 

 of a certain function R of these elements, and of the disturbing forces. 

 Euler, Lagrange (1783), Lagrange and Laplace (1808) obtained the 

 formulae for da, de, dra - , dp, dq where p = tan <p sin 0, q = tan <p sin 0. 

 Poisson first gave the expression for dz. Pontecoulant, p. 330, has 

 introduced di and dv instead of dp and dq; but those develop- 

 ments gave expressions neglecting the square of the disturbing force. 

 Mr. Lubbock has published (in a Paper in the Phil. Trans. April 1830,) 

 expressions which include the effect of any power of the disturbing 

 force. This method has been principally applied to the secular in- 

 equalities ; but it is susceptible of being applied with no less strictness 

 to periodical inequalities, all of which may be represented by certain 

 changes in the elements of the elliptical orbit. 



But the same problems may also be approximately solved di- 

 rectly; for we obtain a differential equation involving the radius 

 vector and the time. In this equation there occurs the same func- 



