The formula for the law of mortality which I am about to explain and apply to a practical case, is not a merely empirical formula. but is based on a presumed property of the causes of death. The value of the formula is however a question which is in a great measure independent of the correctness of my hypothesis; for it is well known that even a false hypothesis may be of great service. While I shall certainly be very much interested to learn the opinion entertained by actuaries as to the theoretical part of the subject, yet the practical application of the formula is the point to which I attach most importance, and to which I would by preference invite criticism.

The honour I have received by the invitation of the President and members for organising the Fourth Session of the International Statistical Congress, to be held daring the week commencing the 16th July instant, which the state of my health prevents me having the satisfaction to attend, induces me to offer to the notice of the distinguished members some observations which, I think, may be considered of some importance in connexion with the objects of the Congress; having for many years paid attention to the subject of vital statistics, and to the mode of rendering the information derivable from its pursuit interesting, beneficially and scientifically, to the public, who may gain consoling pecuniary advantage from it, and to the student, who may enjoy the contemplation of the paths of science; because the services which have been obtained by the public from Assurance Societies, and from the proper management of Friendly Societies, have been obtained by the attentive and philanthropic study of the subject, and the mode of pursuing that study depends on statistical inquiries, and, I may say, on deep mathematical reflection,—a reflection which, whilst it may and has been of important service to society at large, may offer many new views in philosophical and mathematical branches of enquiry even quite unconnected with statistics or its objects.

I have recently tad occasion for a special purpose to apply the formula to a case which, I think, presents points of sufficient interest to justify me in laying it before the readers of the Journal of the Institute of Actuaries.

The chief difficulties encountered in the construction of the following Table have arisen, first, from the extreme paucity of the data for adult ages,—the whole number of deaths observed above the age of 14 being 27 only,—and secondly, from the want (hitherto) of a simple and satisfactory method of adapting the law of mortality prevailing in adult life to the observations for infancy and childhood. I proceed to explain the mode in which these difficulties have (as I venture to think) been overcome.

The Insurance Times of New York having reprinted the greater part of Mr. Sprague's paper On the proper method of estimating the liability of a Life Insurance Company under its policies, and Mr. Makeham's letter which appeared in the same number of this Journal, the Hon. Elizur Wright has thought it desirable to explain the aim of the American Insurance Law in a letter to that periodical, from which we make the following extract. We do this not only on account of the general interest with which Mr. Wright's views will be read, but still more because he corrects a misconception as to the object and purpose of the American Life Insurance legislation.—Ed. J. I. A.

We have received through the courtesy of Mr. William Barnes, late Superintendent of the Insurance Department of New York, and now “Consulting Counsel and Actuary,” a pamphlet of 63 pages, purporting to be a report on the condition and prospects of the above Insurance Company for the year 1870, but which may with perhaps greater propriety be called a review of the general position of Life Insurance in America, England, Germany, and France.