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THE PRINCIPLES OF SCIENCE. 



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 

 to 10x2048 or 20,480 in all, one half of which or 

 10,240 should theoretically give head. The total number 

 of heads obtained was actually 10,353, or 5222 in the 

 first series, and 5131 in the second. The coincidence 

 with theory is pretty close, but considering the large 

 number of throws there is some reason to suspect a 

 tendency in favour of heads. 



The special interest of this trial consists in the ex- 

 hibition, in a practical form, of the results of Bernoulli's 

 theorem, and the law of error or divergence from the 



