228 



Mr. Gompertz on the Law of Mortality. 



[Hay 12, 



solved by the rules which apply to ordinary algebraical equations ; for there 

 are certain functions of the symbols of partial differentiation which com- 

 bine with certain functions of the independent variables according to the 

 laws of combination of common algebraical quantities. In the first part of 

 this memoir I have investigated the nature of these symbols, and applied 

 them to the solution of partial differential equations. In the second part I 

 have applied the calculus of symbols to the solution of functional equa- 

 tions. For this purpose I have worked out some cases of symbolical 

 division on a modified type, so that the symbols may embrace a greater 

 range. I have then shown how certain functional equations may be 

 expressed in a symbolical form, and have solved them by methods analo- 

 gous to those already explained. 



The Society then adjourned to Thursday, May 12th. 



May 12, 1864. 



Major-General SABINE, President, in the Chair. 



In accordance with the Statutes, the names of the Candidates recom- 

 mended by the Council for election into the Society were read, as follows : — 



Sir Henry Barkly, K.C.B. 



William Brinton, M.D. 



T. Spencer Cobbold, M.D. 



Alexander John Ellis, Esq. 



John Evans, Esq. 



William Henry Flower, Esq. 



Thomas Grubb, Esq. 



Sir J. Charles Dalrymple Hay, Bart. 



William Jenner, M.D. 



Sir Charles Locock, Bart., M.D. 



William Sanders, Esq. 



Col. WiUiam James Smythe, R.A. 



Lieut. -Col. Alexander Strange. 



Robert Warington, Esq. 



Nicholas Wood, Esq. 



The following communications were read : — 



I. Second Part of the Supplement to the two Papers on Mortality 

 published in the Philosophical Transactions in 1820 and 1825.'' 

 By Benjamin Gompertz, F.B.S. Received March 30, 1864. 



(Abstract.) 



The objects of this paper are various ; but the subject appears to the 

 author more especially important in consequence of the state of compe tition 

 among assurance estabhshments, which he holds to be injurious to the interest 

 of those valuable establishments, and to those of the assuring population. 



The author's purpose in this paper is greatly to extend the modes of cal- 

 culating valuations, and to improve the methods of calculation hitherto 

 used by actuaries, which are in many cases very laborious, and in some 

 almost impracticable. This part commences with observations on the inge- 



