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(3) Suppose that a row of compartments, `vhose upper openings are situated like those in Fig. 7, page 63, are 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 demonstration 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 areas 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 approximately 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