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 320 A N N U I T I E S. fuited to this populous city, pitches upon 1280 perfons It may not be improper in this place to obferve, that all born in the fame year, and records the number re- however perfeft tables of this fort may be in themfelves, maining alive each year, till none were in life. and however well adapted to any particular climate, yet the conclufions deduced from them muff always be unDr Halley’s table on the bills of mortality at Breflaw. certain, being nothing more than probabilities, or conjedtures drawn from the ufual period of human life. And the practice of buying and felling annuities on lives, by rules founded on fuch principles,- may be juflly conlidered as a fort of lottery or chance-work, in which the parties concerned mult often be deceived. But as eftimates and computations of this kind'are now become faftiionable, we fiiall here give fome brief account of fuch as appear molt material. From the above tables the probability of the continuance or extindtion of human life is eltimated as follows. 1. The probability that a perfon of a given age lhall live a certain number of years, is meafured by the proportion which the number of perfons living at the propofed age has to the- difference between the faid number and the number of perfons living at the given age. Thus, if it be demanded, what chance a perfon of 40 years has to live feven years longer ? from 445, the number of perfons living at 40 years of age in Dr Halley’s table, fubtradt 377, the number of perfons living at 47 years of age, and the remainder 68, is the number of perfons that died during thefe 7 years; and the probability or chance that the perfon in the queltion fhall live thefe 7 years is as 377 to 68, or nearly as 5-! to 1. But, by Mr Simpfon’s table, the chance is fome>thing lefs than that of 4 to 1. 2. If the year to which a perfon of a given age has an equal chance of arriving hefore''he dies, be required, Mr Simpfon’s table on the bills of mortality at London. it may be found thus : Find half the number of perfons living at the given age in the tables, and in the column of age you have the year required. ’ Thus, if the quellion be put with refpedt to a perfon of 30 years of age,, the number of that age in Dr Hal ley’s table is 531, the half whereof is 265, which is found in the table' between 57 and 58 years ; fo that a perfon of 30 years.has an equal chance of living between 27 and 28 years longer. 3. By the tables, the premium of infurance upon lives may in fome meafure be regulated. Thus, The chance that a perfon of 25 years has to live another year, is, by Dr Halley’s table, as 80 to 1 ; but the chance that a perfon of 50 years has to live a year longer is only 3010 1. And, confequently, the premium for infuring the former ought to be to the premium for infuring the latter for one year, as 30 to 80, or as 3 to 8. Puob. I. To find the value of an annuity of 11. for the life of a fmgle perfon of any given age. Monf. de Moivre, by obfervihg the decreale of the probabilities of life, as exhibited in the table, compofed an algebraic theorem or canon, for computing the value of an annuity for life; which canon I lhall here lay down by way of Rule. Find the complement of life; and, by the tables, find the value of 11. annpity for the years denoted by the faid complement; multiply this value amount by the