24 THE ROYAL SOCIETY OF CANADA 



3,800 throws were made. Taking any 10 consecutive throws the 

 widest possible divergences from the 6-366 of theory were observed, 

 the incidences on the ruled lines varying from 3 to 10. Here are 

 numbers selected from ten consecutive decades : — 



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

 Again 6, 7, 4, 7, 7, 9, 5, 4, 4, 6. 



Taking 100 consecutive throws a much closer relative agreement 

 between experiment and the 63-66 of theory was observed. In 

 the first 1000 the incidences (for 100) on the ruled lines varied from 

 59 to 74; in the second 1000 from 59 to 71; in the third 1000 from 55 

 to 75. 



Taking 1000 consecutive throws a wonderfully close agreement 

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

 the first 1000 there were 633 incidences on the lines. 



And finally taking the entire number of throws (3800) while 

 theory gave 2419 incidences on the lines, experiment gave 2423 — a 



2423 

 marvellously close agreement. These 2423 incidences give ^» no as 



the probability that in a given throw the rod shall cross a line. Theory 



2 

 gave— Equating these results we have ^ = 3- 1366 — not so very 



remote from the well known number 3-14159. 



Problem 2. Two points are taken at random in a triangle. The 

 chance that the line joining them shall cut two particular sides is 1/3. 



