384 



THE PRINCIPLES OF SCIENCE. 



[CHAP. 



of one of Euclid's propositions mechanically. Neverthe- 

 less, it is an interesting occupation to verify even the pro- 

 positions of geometry, and it is still more instructive to 

 try whether a large number of observations will justify our 

 assumption of the Law of Error. 



Encke has given an excellent instance of the correspond- 

 ence of theory with experience, in the case of observations 

 of the differences of Eight Ascension of the sun and two 

 stars, namely a Aquilse and a Canis minoris. The obser- 

 vations 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'2637). He then compared the numbers of errors of 

 each magnitude fromo'i second upwards, as actually given 

 by the observations, with what should occur according to 

 the Law of Error. 



The results were as follow : l 



The reader will remark that the correspondence is very 

 close, except as regards larger errors, which are excessive 

 in practice. It is one objection, indeed, to the theory of 

 error, that, being expressed in a continuous mathematical 

 function, it contemplates the existence of errors of every 

 magnitude, such as could not practically occur ; yet in this 

 case the theory seems to under-estimate the number of 

 large errors. 



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

 Memoirs, vol. ii. pp. 338, 339. 



