ENCYCLOPEDIE METHODIQUE. 443 



The following is the method given in the article Milieu. Let 

 the numerical results of discordant observations be set off as 

 abscissae from a fixed point ; draw ordinates to represent the pro- 

 babilities of the various observations ; trace a curve through the 

 extremities of these ordinates and take the abscissa of the centre 

 of gravity of the area of the curve as the correct value of the 

 element sought. The probabilities are to be represented by the 

 ordinates of a certain semi-ellipse or semicircle. The article says 

 that to determine analytically the centre of the semicircle would 

 be very difficult, because we arrive at an equation which is almost 

 unmanageable ; accordingly a method of approximation is pro- 

 posed. First take for the centre the point corresponding to the 

 mean of all the observations; and determine the centre of gravity 

 of the area corresponding to the observations ; take this point 

 as a new centre of a semicircle, and repeat the operation ; and 

 so on, until the centre of gravity obtained corresponds with 

 the centre of the respective semicircle. The magnitude of the 

 radius of the semicircle must be assigned arbitrarily by the cal- 

 culator. 



This is ingenious, but of course there is no evidence that w^e 

 thus obtain a result which is specially trustworthy. 



The other memoir which is noticed, in this article Milieu is 

 that by Lagrange, published in the Miscellanea Taurinensia ; see 

 Art. boQ. It is strange that the memoirs by Daniel Bernoulli 

 and Lagrange should be asserted to be unprinted in 1785, when 

 Daniel Bernoulli had published a memoir with the same title in 

 the Acta Acad....Petrop. for 1777, and Lagrange's memoir was 

 published in the Miscellanea Taurinensia for 1770 — 1773. The 

 date of publication of the last volume is not given, but that it 

 was prior to 1777 w^e may infer from a memoir by Euler; see 

 Art. 447. 



826. We will now notice the portions of the Encyclopedie 

 Methodique which relate to games of chance. The three volumes 

 which we have mentioned in Ai't. 817 contain articles on various 

 games ; they do not give mathematical investigations, with a slight 

 exception in the case of Bassette : see Art. 467. The commence- 

 ment of the article Breland is amusing: il se joue a tant de 



