290 ESSAY ON PROBABILITIES. 



for every 100?. guaranteed; the present value of all 

 the claims is 1,000,000?., that of all the premiums 

 700,000?., and the value of the assets of the office 

 600,000?. The surplus is therefore 300,000?.,, and, 

 going upon real tables, the office begins to pay 130?. for 

 every 100?. guaranteed; and this it would be able to 

 do in favour of all who are insured at the time of the 

 preceding valuation. But part of this dividend does 

 not, and, by hypothesis, cannot, arise from the pre- 

 miums: it is therefore paid entirely out of surplus, 

 and will gradually disappear. The dividend will be 

 reduced to 125?., about which it will fluctuate, being 

 sometimes a little less and sometimes a little more. An 

 increase of business in such an office would make the 

 surplus disappear more rapidly, since each new comer 

 brings in an equivalent to 125?. and those of the new 

 comers who die receive 130/. A diminution of busi- 

 ness would produce a contrary effect ; and a total ces- 

 sation of new comers would allow the dividend to re- 

 main at 130?. As far as any danger from fluctuations 

 of mortality is concerned, I do not see any objection to 

 such a division as the preceding : but when it is re- 

 membered that the possible diminution of the rate of 

 interest must also be provided for, I think it would be 

 prudent to reserve a small proportion of the surplus 

 for accumulation. 



There are two ways in which this reserve may be 

 made ; firstly, by employing a table of less than the 

 real mortality in the valuation of the claims and pre- 

 miums ; secondly, by calculating the surplus from a 

 real table, and dividing as upon the supposition that a 

 given fraction of this surplus, say one eighth or one 

 tenth, should be expunged in the calculation. The 

 latter plan is the best of the two, in every respect but 

 one, as follows. The mutual insurance office must be a 

 republic, and many of its members have very little in- 

 formation upon the questions which are, from time to 

 time, submitted to them. They are easily dazzled by 

 the appearance of surplus, and are quick to believe that 



