TYPE AND VARIABILITY 



443 



calculation in assuming the circles to represent the deviation of 

 each, when only a limited number of shots had been fired. 



It is this deviation and not our probable error that is to be 

 taken as expressing error in marksmanship, for with an infinite 

 number of shots our E would disappear, but the error in marks- 

 manship or the deviation of A or B would never disappear. With 

 infinity it would have an exact and fixed value,with E = o. 



It is obvious that the deviations above alluded to are devia- 

 tions from an " ideal " (the center of the target) which is compar- 

 able to the selection type in practi- 

 cal breeding. It is obvious, too, 

 that these heavy circles represent 

 the means of all the shots fired by 

 the two marksmen, but they do not 

 represent their distribution. That 

 is to say, A, for example, might 

 have put most of his shots, or all 

 of them for that matter, at a uni- 

 form distance from the bull's-eye, 

 none hitting the center and none 

 going wild; in other words, his 

 shooting might have been very 

 uniform, but neither very good 

 nor very bad, owing either to bad 

 marksmanship or to a badly sighted 

 gun. Now it is conceivable that 

 another marksman, C, should succeed in making an average 

 identical with that of A, but in a very different manner, some 

 of the shots hitting the bull's-eye and some going wild. These 

 two men, then, do shooting of an entirely different class the one 

 from the other, that is, make a very different distribution even 

 though they win the same mean. If now, from this mean (repre- 

 sented by the heavy circles), we calculate standard deviation 

 with respect to all the shots fired, we then have a conception of 

 deviation corresponding exactly to that of the ordinary standard 

 deviation ; namely, deviation from the mean of all the variates. 

 Thus we illustrate both deviation from mean and deviation from 

 an ideal, together with the probable error involved. 



eB 



FIG. 44. Let the heavy lines A and 

 B represent the calculated marks- 

 manship of A and B respectively ; 

 then the light lines peA and peB 

 will represent the probable errors 

 in the assumption that lines A and 

 B represent truly the marksman- 

 ship of A and B 



