CHAPTER XV. 



LAGRANGE. 



555. Lagrange was born at Turin in 1736, and died at 

 Paris in 1813. His contributions to our subject will be found to 

 satisfy the expectations which would be formed from his great 

 name in mathematics. 



556. His first memoir, relating to the Theory of Probability, 

 is entitled Memoire sur VutiliU de la methode de prendr^e le milieic 

 entre les resultats de plusieurs observations ; dans lequel on examine 

 les avantages de cette methode par le calcul des prohahilites ; et ou 

 Von resoud differens prohlenies relatifs a cette matiere. 



This memoir is published in the fifth volume of the Miscellanea 

 Taurinensia, which is for the years 1770 — 1773 : the date of 

 publication is not given. The memoir occupies pages 167 — 232 

 of the mathematical portion of the volume. 



The memoir at the time of its appearance must have been 

 extremely valuable and interesting, as being devoted to a most 

 important subject ; and even now it may be read with ad- 

 vantasfe. 



"O" 



557. The memoir is divided into the discussion of ten pro- 

 blems ; by a mistake no problem is numbered 9, so that the last 

 two are 10 and 11. 



The first problem is as follows : it is supposed that at every 

 observation there are a cases in which no error is made, h cases 

 in which an error equal to 1 is made, and h cases in which an 



