49^ ON THE ESTIMATION OF 



ing to the statement given by myself in my review 

 of M. Quetelet's work on Probabilities,'"" to run as fol- 

 lows: In the gold (out of 500 hits), 107; in the red 

 annulus, 106; in the blue, 101; in the black, 97; and 

 in the white, 89; supposing the target (terminating with 

 the white) to receive half the entire number (1000) of 

 arrows discharged ; which in the case observed was 

 not far from the truth. Whereas by the actual record 

 of that day's shooting, handed to me afterwards, the 

 proportional numbers corresponding to a total of 500 

 hits were: Gold, 31; red, 89; blue, 121; black, 140; 

 white, 119. This discordance with observation, being 

 far too great to be attributable to ordinary casualty (the 

 whole number of arrows discharged on the day in ques- 

 tion being upwards of 7000), led me, of course, to 

 re-examine the reasoning on which the first expectation 

 had been grounded. And so enlightened, I was at no 

 loss to discover its fallacy, affording, as it does, a good 

 example of the necessity of close attention to the word- 

 ing of all reasonings on questions of probability. It 

 was, in fact, traceable to the wording of a proposition 

 perfectly true, and, as applied to the case where it was 

 employed in another inquiry, correctly applicable, viz.,t 

 " Suppose a ball dropped from a given height, with the 

 intention that it shall fall on a given mark. Fall as it 

 may, its deviation from the mark is error; and the prob- 

 ability of that error .... decreases in geometrical 



* Essays from the Edinburgh and Quarterly Reviews, &c., &c. 

 Longman, 1857. P. 401. 



t Essays, &c., c. Pp. 398, 399. 



