Up to the period in which he lived--the latter half of the seventeenth century--the town of Breslau, in Silesia, was the only place which recorded the ages of its dead; and from these Halley drew a table of the probabilities of the duration of human life at every age. This was in 1693, and was the first table of the sort ever published.[8] In it he taught, with great clearness and exactness, the conditions needful for the formation of rates of mortality; the manner of forming them with complete geometrical precision; of deducing a corresponding table of the present state and annual movement of the population; of reading in them the probability of survivorship of any person taken at random in a given society; of, in truth, concluding upon the probable duration of the co-existence of several individuals from the sole knowledge of their age. He also first developed the true method of calculating life annuities, taking for his guide the rate of mortality during five successive years in Breslau. That the tables of Dr. Halley were very much wanted may be assumed, as in 1692 annuities were granted on single lives at 14 per cent., or only 7 years’ purchase; and that the State took very little trouble to apply these tables is as true, for we read that, soon after they were published, annuities were estimated on 1 life at 9 years’ purchase, on 2 lives at 11 years’, and on 3 lives at 12 years’ purchase. Some allowance must, of course, be made for the difficulty of raising money and the difference of interest; still the price paid was out of all proper proportion. But the most singular circumstance connected with government annuities at this period is, that, when life annuities were changed into annuities for 99 years, the owner of a life annuity might secure an annuity for 99 years, by paying only 4-1/2 years’ extra purchase. Thus, by the payment of 15-1/2 years’ purchase, a certain annuity of 99 years could be procured. FOOTNOTE: [8] The following figures will give some idea of the chances of life as estimated by Dr. Halley:-- Out of 1000 born, 661 will be living at 10 years of age. ” ” 628 ” 15 ” ” ” 598 ” 20 ” ” ” 567 ” 25 ” ” ” 531 ” 30 ” ” ” 490 ” 35 ” ” ” 445 ” 40 ” ” ” 397 ” 45 ” ” ” 346 ” 50 ” ” ” 292 ” 55 ” ” ” 242 ” 60 ” ” ” 192 ” 65 ” ” ” 142 ” 70 ” ” ” 88 ” 75 ” ” ” 41 ” 80 ” ” ” 19 ” 84 ” CHAP. IV.