276 ESSAY ON PROBABILITIES. 



possible claims is one claim. But as these premiums 

 are payable at all periods of the year, they may be con- 

 sidered as, one with another, due at six months after 

 the valuation, at which time the present office age of 

 the parties may be considered to be their real age. 



(C.) All bonuses whicli have actually been added to 

 policies (if any) must be included in the claims ; and 

 the value of each claim must be carefully found, with 

 reference to the time after death at which it is paid. 

 (See Appendix the Second.) 



(A.) The principal of the assets must be deduced 

 entirely by means of the income it yields, and must be 

 ascertained from the income by means of the rate of 

 interest assumed. On this subject, which contains a dif- 

 ficulty of a peculiar character,' see the Sixth Appendix. 



(M.) Against the expenses of management may be 

 set, as far as they go, the incidental profits, when they 

 can be tolerably well ascertained. 



The profit being thus found, and that share of it 

 which belongs to the insured (if the office be not 

 mutual), it remains to inquire, What principle of division 

 should be adopted ? And, firstly, it may be doubted 

 whether the whole of the profit is immediately divisible, 

 consistently with prudence. To use an astronomical 

 phrase, the increase of the surplus is partly secular, and 

 partly periodic ; that is to say, instead of a steady and 

 uniform increase, there is a fluctuating rate of aug- 

 mentation, compounded of that permanent rate which 

 the largeness of the premiums necessarily gives, and 

 the alternate accelerations and retardations occasioned 

 by the departures of the incidents of the several years 

 from the average. The only way of obtaining the per- 

 manent part of the surplus is by estimating it on the 

 average of a considerable number of past years, regard 

 being had to the relative, not the absolute, surplus. 

 Let us suppose, for instance, that the present value of 

 all claims is ascertained to be one million, and the present 

 value of all premiums 700,000/,, the office possessing 

 besides (clear of charges of management) 500, OOO/. : 



