398 CONDORCET. 



Secondly. We see no advantage in applying Bayes's Theorem. 

 Condorcet is very fond of it; and throughout this memoir as well 

 as in his other writings on the subject indulges to excess in signs 

 of integration. In the above example if m and n are very large 

 numbers no practical change is made in the result by using Bayes's 

 Theorem ; if m + w is a small number our knowledge of the past 

 would be insufficient to justify any confidence in our anticipations 

 of the future. 



731. From what we have said it may be expected that when 

 Condorcet comes to his second case he should be obscure, and this 

 is the fact. He gives on his page 685 the modifications which his 

 three methods now require. The second method is really un- 

 altered, for we merely suppose that observation gives m and n in- 

 stead of m and n. The modification of the third method seems 

 unsound ; the modification of the first method is divided into two 

 parts, of which only the former appears intelligible. 



But we leave these to students of the original memoir. 



732. We may add that on pages 687 — 690 Condorcet gives an 

 investigation of the total value arising from two different rights. 

 It is difficult to see any use whatever in this investigation, as the 

 natural method would be to calculate each separately. Some idea 

 of the unpractical character of the result may be gathered from the 

 fact that we have to calculate a fraction the numerator and deno- 

 minator of which involve n + n + 7i' + n" — 2 successive integra- 

 tions. This complexity arises from an extravagant extension and 

 abuse of Bayes's Theorem. 



733. The fourth part of Condorcet's memoir is intitled Re- 

 flexions SUV la methode de determiner la Prohahilite des Mnemens 

 futurs, d'apres I' Observation des evenemens passes. The fourth and 

 fifth parts appeared in the Hist de V A cad.... Paris, for 1783 ; they 

 occupy pages 539 — 559. This volume was published in 1786, 

 that is after Condorcet's Fssai which is referred to on page 54? 1. 



734. Suppose that in m -f n trials an event has happened m 

 times and failed n times ; required the probability that in the next 



