Probable in a Correlated System of Variables. 173 



distribution calculated from tables of the area of the normal 

 curve*. 



Belt. 



1 



2 



Observed 

 Frequency. 



Normal 

 Distribution. 



e. 



e 2 

 in 



1 



4 



10 



89 



190 



212 



204 



193 



79 



16 



2 



1 



6 



27 



67 



162 



242 



240 



157 



70 



26 



2 





 - 2 



-17 

 +22 

 + 28 

 -30 

 -36 

 +36 

 + 9 

 -10 

 







•667 

 10704 

 7224 

 48S9 

 3-7)9 

 5400 

 8-255 

 1-157 

 3-846 







3 



4 



5 



6 



7 



8 



9 



10 



11 





1000 



1000 



X 2=45-8U 



Hence we deduce: P = '000,00155. 



In other words, if shots are distributed on a target according 

 to the normal law, then such a distribution as that cited by 

 Mr. Merriman could only be expected to occur, on an average, 

 some 15 or 16 times in 10,000,000 trials. Now surely it is 

 very unfortunate to cite such an illustration as the foundation 

 of those axioms from which the normal curve must flow ! 

 For if the normal curve flows from the axioms, then the data 

 ought to be a probable system of deviations from the normal 

 curve. But this they certainly are not. Now it appears to 

 me that, if the earlier writers on probability had not pro- 

 ceeded so entirely from the mathematical standpoint, but had 

 endeavoured first to classify experience in deviations from 

 the average, and then to obtain some measure of the actual 

 goodness of fit provided by the normal curve, that curve 

 would never have obtained its present position in the theorv 

 of errors. Even today there are those who regard it as a sort 

 of fetish ; and while admitting it to be at fault as a means of 

 generally describing the distribution of variation of a quantity 

 x from its mean, assert that there must be some unknown 

 quantity z of which x is an unknown function, and that z 

 really obeys the normal law ! This might he reasonable if 

 there were but few exceptions to this universal law of error ; 

 but the difficulty is to find even the few variables which obey 

 it, and these few are not those usually cited as illustrations by 

 the writers on the subject ! 



* I owe the work of this illustration to the kindness of Air W R 

 Macdonell, M.A., LL.l). 



