THE LA W OF ERROR. 



445 



minute sources of error, which will as often produce 

 excess as deficiency. Granting this assumption, the Law 

 of Error must be as it is usually taken to be, and there is 

 no more need to verify empirically than to test the truth 

 of one of Euclid's propositions mechanically, after we have 

 proved it theoretically. Nevertheless, it is an interesting 

 occupation to verify even the propositions of geometry in 

 an approximate manner, and it is still more Instructive to 

 inquire whether a large number of observations will be 

 found to justify our assumption of the Law of Error. 



Encke has given an excellent instance of the cor- 

 respondence of theory with experience, in the case of 

 certain observations of the difference of Right Ascension 

 of the sun and two stars, namely a Aquilas and a Canis 

 minoris. The observations were 470 in number, and were 

 made by Bradley and reduced by Bessel, who found the 

 probable error of the final result to be only about one- 

 fourth part of a second (o"'26^j). He then compared 



the number of errors of each magnitude from th part of 



10 r 



a second upwards, as actually given by the observations, 

 with what should occur according to the Law of Error. 

 The results were as follow &: 



s Encke, ' On the Method of Least Squares,' Taylor's ' Scientific Me- 

 moirs,' vol. ii. pp. 338, 339. 



