CONDORCET. 397 



a? (c 4- c^ + c' + . . .), that is :j — 



xc 

 c 



The question now arises what is the value of xl Suppose that 

 during m + n past years the event hapjoened 771 times and did not 



7)1 



happen n times ; we mio^ht reasonably take for x, so that the 



rr > O -^771+71 



C 711/ 



whole value of the rio^ht would be -z . Condorcet how- 



\ — c m-\-7i 



ever prefers to employ Bayes's Theorem, and so he makes the 



whole value of the risfht 



1 



. 



x'^ii-xy-^^^dx 



1 — c 



/, 



that is 



x""' (1 - xy dx 



m+ 1 c 



m + 7i-\- 2 1 — c * 



Moreover Condorcet supposes that at the present moment the 

 event has just happened on which the right depends, so that he 

 adds unity to the result and obtains for the value of the whole right 



m + 1 c 



1 + 



7Jl + 71 -^ 2 1 — C * 



730. The investigation of the preceding Article goes over the 

 same ground as that on page 680 of the volume which contains the 

 memoir, but is we hope more intelligible. We proceed to make 

 two remarks. 



First. It is clear that Condorcet is quite wrong in giving this 

 method as applicable to the first case, namely that in which the 

 event must happen in a certain length of years. The method is 

 quite inapplicable to such an example as he mentions, namely 

 when the right would accrue on the next succession to the property, 

 that is, on the death of the present holder ; for the probability of 

 such an event would not be constant from year to year for ever as 

 this method assumes. The method would be applicable to the 

 example of the second case in which the right is to accrue upon 

 a sale, for that might without absurdity be supposed as likely to 

 happen in one year as in another for ever. 



