208 



THE PRINCIPLES OF SCIENCE. 



[CHAP 



Qaetelet also tested the theory in a rather more com- 

 plete manner, by placing 20 black and 20 white balls in an 

 urn and drawing a ball out time after time in an indifferent 

 manner, each ball being replaced before a new drawing was 

 made. He found, as might be expected, that the greater 

 the number of drawings made, the more nearly were the 

 white and black balls equal in number. At the ter- 

 mination of the experiment he had registered 2066 white 

 and 2030 black balls, the ratio being i 'O2. 1 



I have made a series of experiments in a third manner, 

 which seemed to me even more interesting, and capable 

 of more extensive trial Taking a handful of ten coins, 

 usually shillings, I threw them up time after time, and 

 registered the numbers of heads which appeared each 

 time. Now the probability of obtaining 10, 9, 8, 7, &c., 

 heads is proportional to the number of combinations of 

 10, 9, 8, 7, &c., things out of 10 things. Consequently 

 the results ought to approximate to the numbers in the 

 eleventh line of the Arithmetical Triangle. I made 

 altogether 2048 throws, in two sets of 1024 throws each, 

 and the numbers obtained are given in the following 

 table : 



The whole number of single throws of coins amounted 

 $0 IO X 2048, or 20,480 in all, one half of which or 

 20,240 should theoretically give head. The total number 



1 Letters on the Theory of Probabilities, translated by Dowries, 1849, 

 PP- 30, 37- 



