DOCTRINE OF PROBABILITY. 195 



rod had been used. In all, 3,800 throws had been made. Taking 

 any 10 consecutive throws, the widest possible divergences from the 

 6 •366 of theory were observed, the incidents on the ruled lines 

 varying from 3 to 10. The following are numbers selected from ten 

 consecutive decades : 



3, 4, 8, 8, 8, 7, 10, 5, 4, 6, 

 And again, 6, 7, 4, 7, 7, 9, 5, 4, 4, 6, 



When any 100 consecutive throws were considered, a much closer 

 relative agreement between experiment and the 63'66 of theory was 

 observed, in the first 1,000 throws the incidences on the ruled lines 

 varying from 59 to 74 ; in the second 1,000 from 59 to 71 ; in the 

 third 1,000 from 55 to 75. 



Taking 1,000 consecutive throws, a wonderfully close agreement 

 between experiment and the 636'6 of theory was observed. Thus 

 in the first 1,000 there were 633 incidences on the lines. 



And finally for the entii-e number of throws (3,800) while theory 

 gave 2,419 incidences on the lines, experiment gave 2,423. 



II. The second problem was : Two points being taken at random 

 in any triangle : to determine the chance that the line joining them 

 shall cut two particular sides of the triangle. This chance is by the 



theory shewn to be J = "333 ; i.e., in 10 locations of the 



points, the line should cross the sides 3 times ; in 100 locations 33 

 times ; in 1,000 locations 333 times, etc. For the experiment, a 

 perfectly level triangular board with elevated rim about it had 

 been used. For points, five small shots were placed on the board, 

 so that after each agitation of them (which was effected by means of 

 a whisk) by joining them two at a time, 10 lines were obtained. In 

 all, 1,000 events were produced. 



Taking any 10 consecutive events the widest possible divergences 

 from the 3-33.... of theory were observed, the number of times 

 the joining line crossed the sides varying from to 8. The following 

 are numbers selected from 10 consecutive decades : 



3, 2, 7, 5, 4, 1, 5, 4, 0, 4. 

 And again, 4, 3, 8, 4, 2, 5, 2, 2, 2, 4. 



Considei'ing 100 consecutive events, a much closer relative agree- 

 ment between experiment and the 33'33.. of theory was observed, 

 in the 1,000 the intei'sections varying from 26 to 37. 



Taking 1,000 consecutive events, a remarkably close agreement 



