It has been represented to me that, in view of the influential position occupied by M. Violeine, the quasi official and authoritative character of his book, and the currency likely to be thereby imparted to the erroneous principles employed by him in the treatment of problems of the class to which the first of those I have discussed belongs;—I say it has been represented to me that in these circumstances it might be well to be a little more explicit as to his manner of proceeding. In my discussion of the problem in question I did enough, I believe, to shew that M. Violeine's solution is certainly erroneous. I admit however that I did not succeed to my own satisfaction (nor apparently to that of others) in precisely hitting the blot in it, and, as it were, reducing it to its elements. I think that from the consideration I have since given to the matter, I am now able to point out the fallacy by which it is vitiated, and I therefore willingly accede to the suggestion that has been made to me.

There has been no more valuable improvement in the science of Assurance calculations than that effected by the invention of the Commutation or D and N System of calculation;—a method which, as is now universally known through the writings of Baily, Professor De Morgan and Mr. Gray, we owe, in this country, to the genius of Mr. George Barrett, of Petworth, Sussex. It appeared at first in an incomplete and rather inconvenient form, but various important modifications and extensions of the principle of the method were some time afterwards made; and it was practically applied to the calculation of Life Contingencies by the late eminent actuary Mr. Griffith Davies, with whose name it is now generally associated.

This is a serious proposal to alter our numeral system and to count by twelves. Thus 10 would be twelve, 11 thirteen, &c., two new symbols being invented for ten and eleven. The names of numbers must of course be changed. There are persons who think such changes practicable. I thought this proposal absurd when I first saw it, and I think so still: but the one I shall presently describe beats it so completely in that point, that I have not a smile left for this one.

In this paper, Mr. Henry describes an instrument by the aid of which he has actually obtained the values (to four figures) of many thousand products, being the D values in the various tables he has published. The principle of the instrument, which he claims as entirely his own invention, may be briefly described as follows:—

Let ABC be a right-angled triangle, of which AB is the base and AC the hypothenuse, and from any point D in the hypothenuse let fall DE perpendicular to AB; then from the similar triangles ADE, ABC, we have

Although the general principles upon which the business of Insurance is based, must be the same wherever it is carried on; yet its particular developments must of necessity vary in countries under different laws, and with a public opinion differently educated. An investigation therefore of the book before us, with the view of pointing out those points wherein the practice of our Trans-Atlantic Brethren differs from ours, may not be without advantage to the interests of Insurance in this country.