Tht method, according to Mr. Altenburger (J.I.A., xxxv, 332), was devised by Dr. Karup in 1878, and communicated by him to the Austrian Government in 1882, and to the Swiss Government in 1884; but, unless perhaps in Germany, of which I have no knowledge, it does not seem to have been published until comparatively recently, and no doubt it has been discovered independently by other actuaries. So far as I am aware, the first account of it in the English language is that given by the late Wm. D. Whiting, in 1894, in the Transactions of the Actuarial Society of America, vol. iii, p. 427. Mr. Whiting wrote at the suggestion of an unnamed member of the Council of the American Society, and he does not say to whom the authorship of the formula should be attributed. The first reference in the Institute Journal is to be found in a letter of Mr. Julius Altenburger, in J.I.A., xxxiv, 152, and therefore the formula sometimes goes by his name, but he himself says that the name of Dr. Karup should be attached to it.

In the present note, attention is directed mainly to Endowment Assurances, and Policies for the Whole of Life by Limited Payments; but the method is available for many other classes, and its very general applicability is elaborately worked out by Mr. Frederick Bell in his paper (J.I.A., xxxix, 17) read before the Institute, 19 December 1904. The principles of the method are therefore well known, but, in so far as they have yet been developed, there remains a certain amount of rigidity which it is the object of this note to remove. Elasticity may be introduced, which will render the formula more convenient under the presentday varying conditions of British companies.

The question whether the net premium method of valuation, now almost universally adopted by offices distributing their profits in the form of reversionary bonuses, should be regarded as a final and scientific method of ascertaining divisible profits or as merely a temporary expedient which must, in the words of Mr. Sorley, “inevitably disappear before the advance of true actuarial science”, is one which has frequently engaged the attention of actuaries. The importance of the subject is so great to all connected with the administration of Life offices that in the hope of provoking an interesting and useful discussion on the general question, I venture to submit the following notes on an alternative method of valuation, based on a suggestion by Mr. Manly (in the discussion on Mr. Warner's paper on the Net Premium Method of Valuation reported in the 37th volume of the Journal, p. 57), that in the valuation balance sheet the present value of the bonus at the rate to be declared at a given valuation should be treated as a liability for the future existence of the policies.

As the alternative method is, to some extent, based on the original principles of the net premium method, I propose, as briefly as possible, to summarize the modifications which have been introduced in the last 30 years in the principles and application of the net premium method.