v.] NORMAL VARIABILITY. 09 



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(3) Suppose that a row of compartments, whose upper 

 openings are situated like those in Fig. 7, page 63, arc 

 made first to converge towards some given point below, 

 but that before reaching it their sloping course is 

 checked and they are thenceforward allowed to drop 

 vertically as in Fig. 9. The effect of this will be to 

 compress the heap of shot laterally ; its outline will still 

 be a Curve of Frequency, but its Prob: Error will be 

 diminished. 



The foregoing three properties of the Law of Error are 

 well known to mathematicians and require no demon- 

 stration here, but two other properties that are not 

 familiar will be of use also ; proofs of them by Mr. J. 

 Hamilton Dickson are given in Appendix B. They are 

 as follows. I purposely select a different illustration to 

 that used in the Appendix, for the sake of presenting 

 the same general problem under more than one of its 

 applications. 



(4) Bullets are fired by a man who aims at the centre 

 of a target, which we will call its M, and we will suppose 

 the marks that the bullets make to be painted red, for 

 the sake of distinction. The system of lateral deviations 

 of these red marks from the centre M will be approxi- 

 mately Normal, whose Q we will call c. Then another 

 man takes aim, not at the centre of the target, but at 

 one or other of the red marks, selecting these at random. 

 We will suppose his shots to be painted green. The 

 lateral distance of any green shot from the red mark 

 at which it was aimed will have a Prob: Error that we 



