588 LAPLACE. 



1016. Laplace gives some remarks on his pages 343 — 348 

 relative to another method of treating errors, namely, that which 

 consists in making the sum of the 2n^^ powers of the errors a 

 minimum, n being supposed indefinitely great. He explains this 

 method for the case of one unknown quantity, and he refers to the 

 Mecanique Celeste, Livre ill. for the case in which there is more 

 than one unknown quantity. The section intended of Livre IIL 

 must be the 39th, in which Laplace gives some rules as in 

 the present place, but without connecting his rules with the con- 

 sideration of infinite powers of the errors. Another method is given 

 in the next section of the Mecanique Celeste which Dr Bowditch 

 in a note on the passage ascribes to Boscovich : Laplace takes up 

 this method in the second Supplement to the Theorie...des Proh., 

 where he calls it the method of situation. 



1017. Laplace gives on his pages 346 — 348 some account of 

 the history of the methods of treating the results of observations. 

 Cotes first proposed a rule for the case in which a single element 

 was to be determined. His rule amounts to taking 



7i = 72 = "- =7s = l 

 in Art. 1007, so that 



S3, 



Laplace says that the rule was however not employed by mathe- 

 maticians until Euler employed it in his first memoir on Jupiter 

 and Saturn, and Mayer in his investigations on the libration of 

 the moon. Legendre suggested the method of least squares as 

 convenient when any number of unknown quantities had to be 

 found ; Gauss had however previously used this method himself 

 and communicated it to astronomers. Gauss was also the first 

 who endeavoured to justify the method by the Theory of Proba- 

 bihty. 



We have seen that Daniel Bernoulli, Euler, and Lagrange had 

 studied the subject : see Arts. 424, 427, 5oQ. Lambert and Bos- 

 covich also suggested rules on the subject ; see the article Milieu of 

 the Encyclopedie Methodique and Dr Bowditch's translation of the 

 Mecanique Celeste, Yol. ii. pages 434, 435. 



