CONDORCET. 395 



e + 1 ' 

 The result, that the first probability is — ■ -^ and the second 



6 + ^+1 

 ' _i_ 1 



is -7 =- , is we presume obtained by Bayes's Theorem. 



After supposing that q is infinite it is perplexing to be told 

 that e = q = l. Condorcet should have proceeded thus. Sup- 

 pose e = q, then 



ee + eq 2e' 2x , e' 



—. = -. = Y>^here x= - . 



ee + eq e -\- e 1 + x e 



The followinsf then is the result which Condorcet considers 



himself to have obtained. Let us suppose we have observed in 



a certain series that a certain law holds during so many terms 



as form the fraction x of the whole series, then the comparative 



2x 

 probability that the whole series is subject to this law is ^j . 



JL ^p JO 



It is however obvious that this result has been obtained by 

 means of several most arbitrary hypotheses. 



725. The remainder of this part of Condorcet's memoir is dif- 

 ficult, but the meaning can be discovered by patience. There is 

 nothing that appears self-contradictory excej^t perhaps on page 727. 

 In the last line Condorcet takes for the limits of a certain integra- 

 tion b and 1 — a + Z> ; it would seem that the latter limit should -be 

 1 — a, for otherwise his Article vil. is only a repetition of his 

 Article VI. 



726. The third part of Condorcet's memoir is entitled Svr 

 devaluation des Droits eventuels. It is published in the Hist, cle 

 V Acad.... Paris, for 1782 ; it occupies pages 674 — 691. 



This part commences thus : 



La destruction du Goiivernement feodal a laiss'e snbsister en Europe 

 un grand nomhre de droits eventuels, mais on pent les reduire a deux 

 classes principales j les uns se payeut lorsque les proprietes viennent a 

 changer par vente, les autres se payent aux mutations par succession, 

 soit directe ou collaterale, soit collaterale seulement. 



Condorcet then proposes to determine the sum of money which 

 should be paid down in order to free any proj)erty from such feudal 

 rights over it. 



