MATHEMATICS AND ACTUARIAL SCIENCE. 281 



unadjusted or ungraduated state, and the tables of assurances and 

 premiums on them formed the basis of our numerous life assurance 

 companies for a long period ; indeed, some of our existing companies' 

 premiums, and even some of their valuations, are still made by the 

 Carlisle table. 



In 1848 was formed the Institute of Actuaries, which is described 

 as a scientific and practical association amongst actuaries, and 

 Avhich had amongst its objects " the development and improvement 

 of the mathematical theories on which the practice of life insurance 

 is based, and the collection and arrangement of data connected wilh 



the subjects of the duration of life, health, and finance 



The improvement and diffusion of knowledge, and the establish- 

 ment of correct principles relating to subjects involving monetary 

 considerations, and the doctrine of probability." 



In 1863 the institute became convinced that the existing tables 

 of mortality were scarcely sufficiently reliable as bases and tests of 

 the stability of life insurance companies, and that at all events the 

 actual results of the experience of a selected twenty of the old 

 English and Scotch companies would be a valuable help to the 

 actuary. The institute consequently set on foot the collection, 

 classification, arrangement, and adjustment of the results of actually 

 assured lives in these companies. The work occupied ten years, 

 and was completed in 1873, embraced some 160,000 lives, and gave 

 as the result the Hm, Hy, H^j., H^ (j, tables of extremely extensive 

 use to-day. 



I notice that again, on June 3rd of this year, 1893, the institute 

 thinks the time has come when a fresh investigation into the 

 mortality amongst assured lives may usefully be entered into, and 

 has started again this arduous piece of work, so that in a few years 

 we may have the up to date experience to help us in our scientific 

 researches. 



Whether collected by the actuary or by others, for insurance or 

 other purposes, the question of adjustment or graduation of the 

 residts next claims the help of mathematics, and that of the higher, 

 if not highest, order; since, as they are to be used as a prediction 

 of the future, a basis for contracts to be completed thirty, fifty 

 years hence, a graduation or adjustment to make them what they 

 would have been if extended over a larger number of years, larger 

 and more varied area of country, or a larger population, or number 

 of lives, becomes not only allowable, but absolutely necessary. 

 With a view to graduation, and of saving the enormous labor 

 involved in the calculation of annuities, &,c., specially those on 

 several lives, various efforts have been made to put into a mathe- 

 matical formula the 



LAW OF MORTALITY. 

 All these efforts have a very distinct scientific basis, and have 

 produced increasingly useful results to the actuary and the cause 

 of science; but it will probably be necessary now only to refer to 



