196 PROCEEDINGS OF THE CANADIAN INSTITUTE. 



between experiment and the 333.33.... of theory was observed, 

 there being by experiment 332 intersections. 



III. The third problem was : Two points are taken at random on 

 a given line of length, a : to determine the chance that the distance 

 between them shall exced a given length c. This chance is by the 



(a c\2 

 I , i. e., if a = 00, we have, ac- 

 cording as c ^ 25, 50 or 75, — probabilitv required = — 1, -l-„ 

 ^ ^ • ^ 100 100 



3 . So that 

 100 



(1) In 10 trials distance bet. points shd. exceed 25, 5'625 times, 



u ]oo " " <' " '•' " " 56-25 " 



" 1000 " " " " " " " 562-5 " 



(2) In 10 " " " " " " 50, 2-5 



<< 100 " " " " " " " "^5 " 



u 1000 " " " " " " <' 250 " 



(3) In 10 " " " " " " 75, -625 times. 

 " 100 " " " " " " " 6"25 " 



" 1000 '• " " " " " " 62-5 " 



For the experiment a perfectly level i-ectangular board with an 

 elevated rim about it had been used. Paper divided into 100 equal 

 spaces by lines drawn parallel to two sides of the board, was pasted 

 down on it. Five small shots were placed on the board, so that 

 after each agitation (effected as before) there were furnished 10 sets 

 of two points each, located on a line, which was any line running 

 the length of the board. The ruled lines running across the board 

 assisted in immediately locating the points on such (any) line 

 extending along the board. 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 from to 8, to 6 and to 6 respectively. The following 

 are numbers selected from ten 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. 



Considering 100 consecutive events a much closer agreement 



