The Probabilities of Life, calculated from Forty-fix Years Obfervation on the Bills of Mortality at Northampton: viz. from 1735 to 1780. TABLE IV. The Expectation of Life at every Age, according to the Bills of Mortality for both London and Northampton. TABLE V. Showing the Number of Years Purchase an Annuity on a fingle Life is worth according to the Probabilities of Life, at London and Northampton, from the Age of 6 to 75 Years; at 3, 4, and 5 per Cent. 3 per cent. 4 per cent. 5 per cent. 3 per cent. 4 per cent. 15 per cent. Lan. North. Lon. North Lon. North Lon. North Lon North. Lon. North 6/18.8 20.73/16.2|17.48|14.1|15.04||41|13.0 14.62[11.4|13.02|10.2|11.70 718 9 20.85 16.3 17.61 14.2 15.1742 12.8 14.39 11.2 12.84 10.1 11.55 8 19.0 20.89 16.4 17.6614.3 15.2343 12.6 14.16 11.1 12.66 10.0 11.41 919.020 81 16.4|17.63|14.3|15.21||44|12.5 13.93|11.0|12.47| 9.9 11.26 10 19.0 20.66 16.417.5214.3 15.14 45 12.3 13.69|10.8|12.28| 9.8[11.11 11 19.0 20.48 16.417.39 14-3 15 04|46|12.1 13.45 10.7 12.09 9.7 10.95 12 18.9 20.28 16.3 17.25 14.2 14.94||47|11.9 13.20 10.5 11.89 9.5 10.78 1318.7 20.08 16.217.10 14.114.8348 11,8 12.95 10.4 11.68 9.4 10.62 14 18.5 19.87 16.0|16.95|14.0|14.71||49|11.6|12.69|10.2|11.47| 9.310.44 15 18.3 19.66 15.8 16.79 13.9 14.59 50 11.4 12.44 10.1 11.26 9.2 10.27 16 18.1 19.44 15.6 16.62 13.7 14.46 51 11.2 12.18 9.9 11.06 9.0 10.10 17 17.9 19.22 15.4 16.46 13 514-335211.0 11.93| 9.8|10.85 8.9 9.93 18117.6 19.01 15.216.31|13 414.22 53 10.7 11.67 9.6 12.64 8.81 9.75 19 17.4 18.82 15.0 16.17 13.2 14.11 54 10.5 11.41 9.4 10.42 8.6 9.57 20 17.2 18.64 14 8 16.03 13.014.01 55 10.3 11.15 9.3|10.20 8.5 9.38 21 17.0 18.47 14.7 15 9112.9 13.92 56 10.1|10.83 9.1 9.98 8.4 9.19 22 16.8 18.31 14.5 15.80 12 713.8357 9.9 10.61| 8.9 9.75 8.2 9.00 23 16 5 18.15 14.3 15.68 12.6 13.75 58 9.6 10.34 8.7 9.52 8.1 8.80 24 16.3 17.98 14.1 15.56 12.4 13.66 59 9.4 10.06 8.6 9.28 8.0 8.60 25 16 117.81 14.0 15.44 123 13.5760 9.2 9.78| 8.4) 9.04| 7.9 8.39 26 15.9 17.64 13.8 15.31 12.1 13 47 61 8.9 9.49 8.2 8.80 7.7 8.18 27 15.6 17.47 13.6 15.18 12.0 13.3862 8.7 9.21 8.1 8.55 7.6 7.97 28 15.4 17.29 13.4 15.05 11.8 13.28 63 8.5 8.91 7.9 8.29 7.4 7.74 |29|15.2 17.11 13.2 14.92 11.7 13.1864 8.3 8.61 7.7| 8.03] 7.3| 7.51 30 15.0 16.92 13.114.78 11.6 13.0765 8.0 8.30 7.5 7.76| 7.1 7.28| 31 14.8 16.73 12.914.64 11.4 12.9766 7.8 7.99 7.3 7.49 6.9 7.03| 32 14.6 16.54 12.7 14.50 11.3 12.867 7.6 7.68 7.1 7.21 6.7 6.79 33 14.4 16.34 12.6|14.35|11.2|12.74|68| 7.4 7.37 6.9| 6.93| 6.6| 6.54| |34|14.2|16.14|12.4 14.20 11.0 12.62 69 7.1 7.05 6.7 6.65 6.4 6.28 35 14.1 15.94 12.3 14.04 10.9 12.50 70 6.9 6.73 6.5 6.36 6.2 6.02 36 13.9 15.73 12.1 13.88 10.8 12.3871 6.7 6.42 6.3 6.08 6.0 5.76 |3713.7 15.5211.9|13.72|10.6|12.25||72| 6.5| 6.10] 6.1| 5.79 5.8 5.50 38 13.5 15.30 11.8113.55 10.5 12.1273 6.2 5.791 5.9 5.5 5.6 5.24) 39 13.3 15.08 11.6 13.38 10.4 11.98 74 5.9 5.49 5.6 5.23 5.4 4.99 40 13.2 14.85 11.5 13.20 10.311.8475 5.6 5.20 5.4 4.96| 5.2| 4.74) THE USE OF THE TABLES. Table I. Shows the probability of life, according to Dr. Halley's computation: the firft column fhows the ages; the second column, the number of perfons living at thofe ages; and the third column, the decrement of life, or the number of perfons that died each year: thus, oppofite age 1, is 1000 in the second column, and 145 in the third column; which fhows, that of 1000 perfons born in the fame year, 145 died before the expiration of the year; and of 855, the remainder of the persons living, 57 died the fecond year, and so on. But the calculations according to this table differ from thofe made from the tables of the probabilities of life in London, partly owing to the different fituations of these two' places. Breflaw being an inland town not much frequented by strangers or foreigners, and London being a mercantile port, and crowded with traffickers and travellers from all parts of the world; and partly owing to the difference of climate, difference of food, and different manners of life, between the inhabitants of these two places, which is always found to occafion a different proportion in the deaths at the fame ages. Thefe confiderations induced Mr. Simpfon to compofe a table of the probability of life, calculated from the bills of mortality of London, and which table will confe quently much better anfwer the purpose of calculating the value of an annuity for a life at London, than the other table of Dr. Halley. This table may be seen page 51. It must, however, be observed, that Dr. Halley's table is "better adapted for the ufe of all Europe in general than any other particular table. Table III. Shows the probability of life at all ages, from 46 years obfervation on the bills of mortality at Northampton: viz. from from the year 1735 to 1780 inclufive. This table is juftly reckoned to be the most correct of any extant, as it is taken from a large manufacturing town, and which confists generally of the fame perfons: and alfo that the table is conftructed from a larger number of persons born than any other table, being 11650, which affords an opportunity of obferv. ing the decrement of life to a greater exactness. Table IV. Shows the expectation of life, or the number of years which any perfon may be fuppofed to have a fair chance of living, according to an equality of chance at every age, according to the bills of mortality for both London and Northampton. Thus, against age 2 stands 32.5 in the second column, under London; and 37.79 in the third column, under Northampton; which fhows, that a child of the age of two years has an equal chance of living 32.5 years, according to the London tables, or 32 years 6 months; and according to the Northampton tables 37.79 years, or 37 years and upwards of 9 months. Table V. Shows the value of an annuity for a fingle life, according to the probabilities of life at London and Northampton, from the age of 6 to 75 years inclufive, at 3, 4, and 5 per cent. Thus, fuppofe, it were required to find the number of years purchase which an annuity is worth to a person of the age of 30: here in the second column, and oppofite the age 30, stands 15.0, which shows that an annuity for a person of 30 years of age in London, and at 3 per cent. is worth 15 years purchase; and an annuity for a Northampton life, at the fame rate of intereft, is worth 16.92 years purchase; and for a London life, at 4 per cent. an annuity is worth 13.1 years purchase; and for a Northampton life, at the fame rate and intereft, |