[baker] DOCTRINE OF PROBABILITY 



25 



Probability required 

 .a (1 — Ï 



If 



\ a Sin C y \ x , y x 2 I dx dy Sin C 



{ \ a b Sin C } 



= i = -333 



i.e. in 10 locations of points line should cross sides 3-33- • times. 

 « 100 " « « « « « 33- 3- • " 



« 1000 " « « « « « 333 . . « 



In the experiment a smooth triangular board was used with 

 barriers at the edges. Fine shots were used for points, 5 being em- 

 ployed so as to give 10 combinations at each change in their positions, 

 which was effected by means of a whisk. Minute glass globes might 

 have been better than shot from their greater elasticity and therefore 

 less tendency to locate themselves near the sides. The board was of 

 course carefully levelled with a spirit level. 



In all 1000 events were produced. Taking any 10 consecutive 

 locations the widest possible divergences from the 3-33- • of theory 

 were observed, the number of times the joining line crossed the given 

 sides varying from to 8. Here are numbers selected from 10 consecu- 

 tive decades: — 



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

 Again 4, 3, 8, 4, 2, 5, 2, 2, 2, 4. 



Taking 100 consecutive events, a much closer relative agreement 

 was observed between experiment and the 33-3- • of theory in 

 the 1000 the intersections varying from 26 to 37. 



Taking 1000 consecutive throws, a wonderfully close agreement 

 was observed between the 333-3- • of theory and experiment, there 

 being by experiment 332 intersections. 



