ON THE STATISTICAL VIEW OF NATURE. 575 



destroying or augmenting each other. The repeated 

 measurement of a physical quantity, of the position of a 

 fixed star ; the arrangement of the bullet marks on a 

 target ; the grouping of the impressions made on the 

 sand by a stone let fall vertically from the same point 

 at a considerable height ; even the countings by a large 

 number of skilled persons of the same number or the 

 estimates of the same distance or height of an object, of 

 the weight of a heap of materials : all these statements 

 will show a certain regularity around the mean number 

 which we consider to be the most probable or correct 

 one. Small errors will be more frequent than large ones ; 

 very large ones will be practically absent ; and the mean 

 will be the result of a mutual destruction or compensa- 

 tion of many small sources of error acting both ways. 

 Mathematicians, from the time of Lagrange and 

 Bernoulli, have tried to put into a mathematical 

 formula this regularity in the distribution of error ; 

 and, since Laplace and Gauss approached the subject 

 from different points of view, they have arrived at 

 a definite analytical expression 1 for the distribution 

 of errors of increasing magnitude around a fictitious 

 centre or mean which is considered in every instance 

 to be the most probable quantity. Practical trials 

 on a very large scale have been made by Bessel, 

 Encke, Quetelet, Faye, and others, and they have in 

 every, case yielded a satisfactory approximation to the 

 figure given by the theoretical formula ; so that at 

 present little doubt as to its usefulness exists in the 

 minds of those who employ it for the purposes of 



This is the well-known "curve of Error." 



