v.] NORMAL VARIABILITY. 65 



accidents befall each shot in its career. In rare cases, 

 a long run of luck continues to favour the course of 

 a particular shot towards either outside place, but in 

 the large majority of instances the number of accidents 

 that cause Deviation to the right, balance in a greater 

 or less degree those that cause Deviation to the left. 

 Therefore most of the shot finds its way into the com- 

 partments that are situated near to a perpendicular line 

 drawn from the outlet of the funnel, and the Frequency 

 with which shots stray to different distances to the right 

 or left of that line diminishes in a much faster ratio 

 than those distances increase. This illustrates and 

 explains the reason why mediocrity is so common. 



If a larger quantity of shot is put inside the apparatus, 

 the resulting curve will be more humped, but one half 

 of the shot will still fall within the same distance as 

 before, reckoning to the right and left of the perpen- 

 dicular line that passes through the mouth of the 

 funnel. This distance, which does not vary with the 

 quantity of the shot, is the " Prob : Error," or " Prob : 

 Deviation," of any single shot, and has the same value 

 as our Q. But a Scheme of Frequency is unsuitable 

 for finding the values of either M or Q. To do so, we 

 must divide its strangely shaped area into four equal 

 parts by vertical lines, which is hardly to be effected 

 except by a tedious process of " Trial and Error." On 

 the other hand M and Q can be derived from Schemes 

 of Distribution with no more trouble than is needed to 

 divide a line into four equal parts. 



