446 



THE PRINCIPLES OF SCIENCE. 



The reader will remark that the correspondence is 

 remarkably 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 possible exist 

 ence of errors of every magnitude, such indeed as could 

 not practically occur ; yet in this case the theory seems to 

 under-estimate the number of large errors. 



Another excellent comparison of the law with observa 

 tion has been made by Quetelet, who has investigated the 

 errors of 487 determinations in time of the Right Ascen- 



o 



sion 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 proportionately increased in number, so 

 that their sum may be one thousand, give the following 

 results as compared with what theory would lead us to 

 expect h : 



In this instance the correspondence is also satisfactory, 

 but the divergence between theory and fact is in the 

 opposite direction to that discovered in the former com- 



11 Quetelet, Letters on tlie Theory of Probabilities, translated by 

 Dowries, Letter XIX. p. 88. See also Galton s Hereditary Genius, 

 P- 379- 



