It is not to be expected, at this period of time, that anything new remains to be discovered in the Doctrine of Annuities, especially by one not conversant with analysis; yet a useful application may occasionally be found of the results of former investigations, the more so should such have remained in comparative neglect.

The announcement of the relation which subsists between an annuity payable yearly, and when it is payable half-yearly, quarterly, monthly, &c., the rate of interest continuing the same, is due to the illustrious De Moivre, and was made by him in the second edition of his treatise of Annuities on Lives, published in 1743. It was reproduced in the subsequent editions of the same work, and is to be found, with some errors of the press corrected, in that appended to the third edition of his Doctrine of Chances, 1756.

Although I have not strictly followed De Moivre, having computed my factors before I found they were described in his work, I here transcribe his rules with the demonstration of them, remarking that, the notation he employs being at variance with that to which we are now accustomed, and likely, therefore, to cause embarrassment to the student, I have substituted the modern notation throughout.

The rapid growth of Accident Assurance, the passing of the Employers' Liability Act, and the periodically recurring discussions respecting schemes for a National Accident Fund, have created a demand for statistics on the subject of accidents, which cannot be said to have been satisfied.

The Tables given in this paper are believed to be unique as regards this country. The object of their compilation was to show the Rates of Fatal Accidents in various occupations. They are based upon a comparison of the male population in each occupation in England and Wales, as enumerated at the Census of 1871, with the average of the number of the violent deaths occurring to male persons following that occupation in England and Wales during the three years, 1870, 1871 and 1872. For the extraction of the particulars relating to these deaths from the records of the General Register Office, special permission was obtained by Dr. Farr; and it is with his cordial approval that the facts are now laid before the members of the Institute.

The Census of 1871 was taken on the 3rd April of that year. The population enumerated was therefore slightly in excess of the mean population to which the average of the deaths for the years 1870, 1871 and 1872 would have reference. The difference would, however, be slight; and for the present purpose it was thought that the population as enumerated might be considered suitable.