342 A Letter to William Morgan, Esq. F.R.S. 



the numbers of your table, if I have not mistaken their import ; 

 but the formula may readily be made to extend with equal 

 accuracy to ages somewhat above this limit, as well as to an 

 earlier period. We may take, for example, 105 for the age 

 at which the decremental quotient, indicating the rate of mor- 

 tality, becomes = 1, and make it 150 at 35 ; it must then be 

 \/ 150 at the intermediate age of 70; and supposing a 10 = 



— , — = 1 '074.2, b being =105, and c = 1, and the fluent 

 becomes =/- Tfifcjfi • ~p V being" 1 05 - *, or/- &^ : 



and log a = -031087, and for 10000 at birth,/= 9*218 ; which 

 gives, at 95, 11, instead of 26, and at 55, 7207, a number 

 nearer to the truth than the former. 



10. If, happily for the welfare of mankind, it should here- 

 after appear that any firm reliance ought to be placed on these 

 conclusions, or if the formula could be any otherwise modified 

 so as to serve for the purposes of calculation, it might be made 

 to afford essential assistance in determining the values of two 

 or more joint lives ; and by means of a proper table of fluents, 

 the labour would be little greater for combinations of lives 

 than for single ones, since the sums of the fluents would re- 

 present the products of the quantities to be combined; and a 

 single table might be computed, which would render the inte- 

 gration of the fluent of e a> diy a matter of little difficulty. But 

 such an improvement would at present be premature. 



While results like these, however, are fairly deducible from 

 the face of the evidence that you have laid before the public, 

 you must allow, my dear sir, that any government granting 

 annuities would be highly culpable in reckoning on values of 

 human life like those which are represented by the Northamp- 

 ton tables ; and that any private office has a right to expect, 

 beyond such a valuation, a fair percentage for the payment of 

 their unavoidable expenses. On the other hand, I do not see 

 how it is possible for any assurance office, not returning a 

 large share of their profits, to satisfy the public that their terms 

 are reasonable, without acting most improvidently for their own 

 interests. Such offices as the Equitable are exempt from these 

 objections ; and I have not the least doubt of the judgement and 

 integrity with which you have long conducted the business of 

 that Society, nor of the impropriety of calling on a private 

 body to adopt any other regulations than those which are ap- 

 proved by its members. But, as a man of science, it is natural 

 to hope that you will be ready to allow other men of science 

 to partake in the fruits of your researches, and that you will 



be 



