442 



THE PRINCIPLES OF SCIENCE. 



hypothesis of one thousand distinct causes f ; but mathe- 

 maticians have generally proceeded on the hypothesis of 

 infinity, and then, by some of the beautiful devices of 

 analysis, have substituted a general law of easy treatment. 

 In mathematical works upon the subject, it is shown that 

 the standard Law of Error is expressed in the formula 



y=Y<-" \ 



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

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

 for each series of observations, and expressing the general 

 amount of the tendency to error, but varying between 

 one series of observations and another, while e is the 



peculiar constant, 2*71828 the base of the Naperian 



logarithms. To show the close correspondence of this 

 general law with the special law which might be derived 

 from the supposition of any moderate number of causes 

 of error, I have in the accompanying figure drawn a 



-3 -I -2 



curved line representing accurately the variation of y 

 when x in the above formula is taken equal to o, ^, i, |, 2, 

 &c., positive or negative, the arbitrary quantities Y and c 



f * Letters on the Theory of Probabilities/ Letter XV. and Appendix, 

 note pp. 256-266. 



