The mode in which the Property and Income Tax of this country is levied, has created so much dissatisfaction, and is so universally acknowledged to be inequitable, that I am induced to call the attention of the Members of this Institute to the subject, with a view to arrive at some elucidation of the principles upon which direct taxation should be based: being satisfied that there is no tribunal before which the consideration of such a matter could be more properly brought, or where its peculiar features could be more thoroughly and efficiently investigated.

We now pass to the traces of the early practice of LIFE INSURANCE, a subject which has in general been but very slightly noticed.

The estimation of the value of human life in its rudest approximation—that is, of the term of years which, on the average of a sufficient number of observations, would be observed to fall to the share of each of a given number of individuals born under certain circumstances, and continuing in certain climates or ranks—was to all appearance a subject the consideration of which, not only the speculations of the remoter ages had no impelling cause to enter upon, but one which, if pursued, would have led not only to scepticism, but even to persecution, for entering on a tacitly admitted forbidden ground.

Before I proceed to the more immediate object of this paper, viz., to the Consideration of some leading Problems in the Theory of Probabilities, I would premise a few observations with reference to the doctrine of Life Contingencies.

In my work on Notation, p. 13, I have asserted a fact which is of such essential importance in the elucidation of the doctrine, that it can scarcely be too often repeated, or too strongly impressed upon the mind of a student, viz,, that curtate expectations of life are the values of annuities which do not bear interest; and this is universally true, whether they be the expectations of single lives, of joint lives, of the longest of two or more lives, or of a life or lives after another or others,—in short, however remote or complicated the contingencies may be in which they are involved; and the values of annuities, or those series in which interest is involved, are invariably in the same form of expression as their corresponding curtate expectations, as thus employing the notation explained in the work already alluded to.

The chief, perhaps the sole, applications of the Theory delivered in Part I., are to Church Livings and Copyhold Estates. Of these applications we shall treat in order.

The principle on which the valuation of the rights of presentation to Church livings is subjected to treatment by this theory is, that the worth of the living is greater than that of the services to be performed by the holder of it. It is conceived, therefore, that the patron, in presenting a clerk to a benefice, is entitled to consider that, in addition to affording the clerk an opportunity for the exercise of his vocation, he is conferring upon him also an annuity due for his life, whose amount is the excess of the value of the benefice over that of the clerk's services. The law sanctions the arrangements that arise from this mode of viewing the subject, and permits the open purchase and sale of the right of presentation, whether for ever or for any number of times; save and except during the "mortal sickness" of an incumbent, or during the period between his death and the appointment of his successor; the purchase of a right of presentation in these circumstances being held to be simony, and the guilty party consequently being amenable to law.