SKILL IN TARGET-SHOOTING. 505 



of a would conform to that average. But the number of 

 shooters at each target being limited, never more than 

 six, and sometimes not more than two or three (owing 

 to our rejection of those scores where the arrows were not 

 all delivered), the distribution of the hits on each results 

 from the summation or superposition of several series of 

 numbers graduated according to the values of so many 

 different specified values of a as a modulus ; the inter- 

 mediate values being absent : and it by no means follows 

 that such a series of sums will follow the law of gradation 

 of either separately, or accommodate itself rigorously to 

 an average modulus ; any more than it would follow that 

 a curve whose ordinate is the sum of the ordinates of (say), 

 two concentric circles should itself be a circle. Suppose, 

 for instance, we were to ground our calculation of an 

 average modulus or value of a on a series of hits given 

 by summing up each separate column of Table I. This 

 would give the following series : Gold, 862 ; Red, 1337 ; 

 Blue, 1 121 ; Black, 1042; White, 910, on a total num- 

 ber of 10,000 shots. And from this deducing five several 

 values of a by the use of the formula of (3), after the 

 manner of those in Table III., we should obtain the 



series, 



a = 2771, 3-340, 3-931, 4-399, 4-809, 



which exhibits (only in a much more exaggerated form) 

 precisely the sort of dilatation in question. This being 

 then the tendency, in the case of each particular target, 

 a similar tendency will of course be exhibited by the 

 successive values resulting from a combination of any 

 number. 



