Section III., 1914. [23] Tr^ns. R.S.C. 



Some Experiments in the Doctrine of Probability. 

 By Alfred Baker, M.A., F.R.S.C. 



(Read May 27, 1914) 



In what is known as local probability opportunities for treating 

 the problems experimentally sometimes occur, afford ng an amusing 

 relaxation to the student. It is not difficult, on the assumption 

 that all positions of certain movable bodies (or the occurrence of certain 

 geometrical forms) are equally likely, to devise problems in probabili- 

 ties respecting such, and to calculate the probability of particular 

 positions or of particular geometrical forms. Not often, however, 

 have such problems been treated experimentally, and the results 

 of experiment compared with the deductions of theory. In what 

 follows three problems in local probability are treated experimentally, 

 and the results compared with what theory affords. The first of 

 these three has several times been made the subject of experiment. 

 In the solution of the problem the geometrical constant ~ occurs. 

 If such result be equated to the numerical result as obtained by experi- 

 ments, we seem to have a means of determining the numerical value 

 of H". An account of the result obtained by certain experimenters 

 will be found in Ball's "Mathematical Recreations and Problems." 



Problem 1. An indefinite number of equidistant parallel lines 

 are drawn on a plane, and a rod whose length is equal to the perpen- 

 dicular distance between two consecutive lines is thrown at random 



2 

 on the plane. The probability of its falling on one of the lines is— 



/ Cos — — dx-f-2/Cos — r — dx ^ 



Probability required = — = — 



27ra Ï 



2 

 = o 141 en = -6366- • •. The length of the rod is 2a. 



i.e., in 10 throws the rod should cross a line 6-366 times. 

 100 " " " " " " 63-66 " 



1000 " " " " " " 636-6 " 



In the experiment a glass rod was employed to avoid the chance 

 of magnetization which might incline the rod, when free in the air, 

 to point north and south. A very fine rod was selected that it might 

 approximate as nearly as possible to a straight line. The drawing 

 board on which the lines were ruled was carefully levelled. In all 



