XVII.] 



THE LAW OF ERROR. 



385 



Another comparison of the law with observation was made 

 by Quetelet, who investigated the errors of 487 determi- 

 nations in time of the Right Ascension of the Pole-Star 

 made at Greenwich during the four years 1836-39. These 

 observations, although carefully corrected for all known 

 causes of error, as well as for nutation, precession, &c., 

 are yet of course found to differ, and being classified as 

 regards intervals of one-half second of time, and then pro- 

 portionately increased in number, so that their sum may 

 be one thousand, give the following results as compared 

 with what Quetelet's theory would lead us to expect : l 



In this instance also the correspondence is satisfactory, 

 but the divergence between theory and fact is in the opposite 

 direction to that discovered in the former comparison, the 

 larger errors being less frequent than theory would indi- 

 cate. It will be noticed that Quetelet's theoretical results 

 are not symmetrical 



The Probable Mean Result. 



One immediate result of the Law of Error, as thus 

 stated, is that the mean result is the most probable one ; 

 and when there is only a single variable this mean is 

 found by the familiar arithmetical process. An unfor- 

 tunate error has crept into several works which allude 

 to this subject. Mill, in treating of the " Elimination of 

 Chance," remarks in a note z that " the mean is spoken of 



1 Quetelet, Letters on the Theory of Probabilities, translated by 

 Downes, Letter XIX. p. 88. See also Gallon's Hereditary Genius, 

 P- 379- 



8 System of Logic, bk. iii. chap. 1 7, 3. 5tli ed. vol. ii. p. 56. 



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