44 Mr. Morgan on. Survivorships. 



chase required, and consequently the value of a given sum is 



= Sx^x V— 3C + 3CC — CCC, as before. But the rules 



derived from the foregoing solution are in general more simple 

 than those derived from the two problems just mentioned, and 

 are therefore to be preferred to them. 



The foregoing problems, together with those which have 

 been investigated in my former papers, comprehend, as far as 

 I can perceive, all the different cases of survivorship between 

 three lives. The great number of contingencies on which these 

 reversions depend, must necessarily render the solutions intri- 

 cate, and consequently the general rules complicated and la- 

 borious. It would not, however, be a difficult task to abridge 

 these rules very considerably, without destroying their accuracy 

 in any great degree ; but this would be foreign to my purpose 

 in these papers, which has uniformly been confined to the inves- 

 tigation of the correct values of the different reversions. Nor 

 do I think that such an abridgement is necessary, as the opera- 

 tions of even the longest of the present rules, may be completed 

 in very nearly as short a time as the inaccurate approximations 

 which have hitherto been employed for the same purpose. 



It may not be improper to observe, that the solutions in these 

 papers are not only the first which have ever been deduced, in 

 the case of two and three lives, from just principles and the 

 real probabilities of life ; but that, as to many of the problems, 

 not even an attempt has ever been made to approximate to the 

 value of the reversion. 



Being now possessed of correct solutions of all the cases in 

 which two and three lives are involved in the survivorship, we 

 are possessed of all that is really useful, and therefore I feel the 



