115 



When, however, the author remarks in conclusion, all the lines of 

 curvature issuing from the umbilic are equally close to the oscu- 

 lating sphere, then these successive differentiations will either at 

 length exhaust the coefficients, and thus no determinate equation 

 will arise ; or else they will conduct to an equation whose roots are 

 all imaginary : and one or other of these circumstances must always 

 take place at the vertex of a surface of revolution. 



The Society adjourned over the Christmas Recess to meet again 

 on the 10th January next. 



January 10, 1839. 



JOHN WILLIAM LUBBOCK, Esq., V.P. and Treas.. 

 in the Chair. 



William James Frodsham, and John Hilton, Esquires, were seve- 

 rally elected Fellows of the Society. 



A paper was read, entitled, On the Laws of Mortality." By 

 Charles Jellicoe, Esq. Communicated by P. M. Roget, M.D., 

 Sec. R.S. 



The author, considering that the variations and discrepancies in 

 the annual decrements of life which are exhibited in the tables of 

 mortality hitherto published would probably disappear, and that 

 these decrements would follow a perfectly regular and uniform law, 

 if the observations on which they are founded were sufficiently nu- 

 merous, endeavours to arrive at an approximation to such a law, by 

 proper interpolations in the series of the numbers of persons living 

 at every tenth year of human life. The method he proposes, for 

 the attainment of this object, is that of taking, by proper formulae, 

 the successive orders of differences, until the last order either disap- 

 pears, or may be assumed equal to zero. With the aid of such dif- 

 ferences, of which, by applying these formulae, he gives the calcula- 

 tion, he constructs tables of the annual decrements founded princi- 

 pally on the results of the experience of the Equitable Assurance 

 Society. 



January 17, 1839. 



JOHN FORBES ROYLE, M.D., V.P., in the Chair. 



Beriah Botfield, and Peter Hardy, Esquires, were severally elected 

 Fellows of the Society. 



A paper was read, entitled, " On the state of the Interior of the 

 Earth." By W.Hopkins, Esq. A.M., F.R.S., Second Memoir. "On 

 the Phenomena of Precession and Nutation, assuming the Fluidity of 

 the Interior of the Earth." 



