° 
THE 
PHILOSOPHICAL MAGAZINE 
AND JOURNAL. 
I. An algebraical Expression of the Values of Lives, with 
a Mode of finding the correct Value of any Number of joint 
Lives. By A CorrEsPoNxDENT. 
To Mr. Tilloch. 
Sir, —Tue bills of mortality for the year 1815, published in 
the newspapers of yesterday, have suggested to me the following 
calculations, which perhaps, from their novelty, you may think 
worthy a place in your Magazine. 
I am, sir, 
Your very obedient servant, 
London, Jan. 2, 1816. A.B. C.D. 
ee 
In making calculations from the registers of the duration of 
lives, it has not been usual to attempt to represent the results 
of a whole table by a single formula, although such a simplifi- 
cation would afford great advantages in the solution of a variety 
of problems. As an instance of this mode of treating the sub- 
ject, we may take the bills of mortality for the year now elapsed, 
and by reducing the numbers into the form of a diagram, and 
observing the different flexures of the curve resulting from them, 
we may ascertain the nature of the ‘terms proper to constitute 
the required expression; and calling the age a, the annual 
deaths will appear to be : <= + :000401a —-0000042 x, 
without any very material error: at least with incomparably 
greater accuracy than is obtained by the rough approximation of 
supposing an equal annual mortality in a given number of per- 
Vol. 47. No. 213. Jan, 1816. A2 sons 
