v.] NORMAL VARIABILITY. 07 



pitfalls, easily overlooked by the unwary, while they are 

 cantering gaily along upon their arithmetic. The Laws 

 of Error are beautiful in themselves and exceedingly 

 fascinating to inquirers, owing to the thoroughness and 

 simplicity with which they deal with masses of materials 

 that appear at first sight to be entanglements on the 

 largest scale, and of a hopelessly confused description. 

 I will mention five of the laws. 



(l) The following is a mechanical illustration of the 

 first of them. In the apparatus already described, let q 

 stand for the Prob: Error of any one of the shots 

 that are dispersed among the compartments BB at its 

 base. Now cut the apparatus in two parts, horizontally 

 through the rows of pins. Separate the parts and interpose 

 a row of vertical compartments A A, as in Fig. 8, p. 63, 

 where the bottom compartments, BB, corresponding to 

 those shown in Fig. 7, are reduced to half their depth, in 

 order to bring the whole figure within the same sized 

 outline as before. The compartments BB are still deep 

 enough for their purpose. It is clear that the inter- 

 polation of the AA compartments can have no ultimate 

 effect on the final dispersion of the shot into those at 

 BB. Now close the bottoms of all the AA compart- 

 ments ; then the shot that falls from the funnel will be 

 retained in them, and will be comparatively little dis- 

 persed. Let the Prob: Error of a shot in the AA com- 

 partments be called a. Next, open the bottom of any 

 one of the AA compartments ; then the shot it contains 

 will cascade downwards and disperse themselves among 

 the BB compartments on either side of the perpendicu- 



f 2 



