[baker] DOCTRINE OF PROBABILITY 27 



(1). c = 25. 



In 10 locations of points dis. bet. them shd. exceed 25, 5-625 times 



100 " " " " " " 56-25 " 



1000 " " " " " " 562-5 " 



(2). c = 50. 



In 10 locations of points dis. bet. them shd. exceed 50, 2-5 " 



100 " " " " " " 25 " 



1000 " " " " " " 250 " 



(3). c = 75. 



In 10 locations of points dis. bet. them shd. exceed 75, -625 " 

 100 " " " " " " 6-25 " 



1000 " " " " " " 62-5 



In the experiment it was not practicable to take points at random 

 on a line. The object however, was attained by having a rectangular 

 board constructed with barriers along the edges, and lines rued on 

 it parallel to one of the sides, "points on a line;" then meant the same 

 as points on this board estimating distances only at right angles to 

 the ruled lines. The ruled lines enabled one quickly to determine 

 those distances. As before 5 shots were used giving after each dis- 

 turbance 10 combinations. In all 1000 events were produced. 



Taking any 10 consecutive events, the widest possible divergences 

 from the 5.625 2-5 and -625 of theory were observed, the number 

 of times the distance between the points exceeded 25, 50 and 75 

 varying r rom to 8, from to 6 and from to 6 respectively. Here 

 are numbers selected from 10 consecutive decades: — 



c = 25. ... 6, 7, 6, 6, 6, 8, 6, 8, 3, 0. 

 c = 50. ... 5, 0, 1, 6, 0, 2, 6, 0, 1, 1. 

 c = 75. .. 0, 0, 0, 0, 3, 2,0, 0, 1, 2. 



Taking 100 consecutive events a much closer agreement between 

 experiment and the 56-25, 25, and 6-25 of theory was observed, in 

 the 1000 the number of times the distances exceeded 25, 50 and 75 

 varying from 55 to 63, from 16 to 33, and from 2 to 10 respectively. 



Taking 1000 consecutive events a remarkably close agreement 

 between experiment and the 562-5, 250 and 62 • 5 of theory was observed 

 there being by experiment 577, 253 and 66 occasions on which the 

 distance between the points exceeded 25, 50 and 75 respectively. 



Now some one may ask what does all this prove? That the 

 theoretical solutions of the problems were correct? Not at all. 

 Here the mathematician in all confidence and truth can say: If the 

 facts do not agree with the theory so much the worse for the facts. 

 Any one with sufficient knowledge of mathematics would be absolutely 



