XVII.] 



THE LAW OF ERROR. 



381 



treatment. In mathematical works upon the subject, it is 

 sliown that the standard Law of Error is expressed in the 

 tbrinula 



in which x is the amount of the error, Y the maximum 

 ordinate of the curve of error, and c a number constant 

 for each series of observations, and expressing the amount 

 of the tendency to error, varying between one series of 

 observations and another. The letter e is the mathematical 

 constant, the sum of ratios between the numbers of permu- 

 tations and combinations, previously referred to (p. 330). 



To show the close correspondence of this general 

 law with the special law which might be derived 

 I'rom the supposition of a moderate number of causes 

 of error, I have in the accompanying figure drawn a 



_» 



curved line representing accurately the variation of y 

 when a; in the above formula is taken equal o, -, i, - 2, 



2 2 1 



&c., positive or negative, the arbitrary quantites Y and e, 

 l)eing each assumed equal to unity, in order to simplify 

 the calculations. In the same figure are inserted eleven 

 dots, whose heights above the base line are proportional 

 to the number? in the eleventh line of the Arithmotical 

 Triangle, thus representing tlie comparative probabihtios 

 of errors of various amounts arising from ten equal causes 



