THE PROBABLE ERROR OF THE MEAN. 19 



A series of 26,602 casts of 12 dice each (Prof. Weldon's 

 experiment) is lately reported by Professor Karl Pearson of 

 University College, London, in the Philosophical Magazine, 

 vol. 50, p. 168; July, 1900. The total number of "fives" and 

 " sixes" thrown was 106,602. Thus the fact. 



The total number of dice thrown was 12 times 26,602 or 

 315,672; hence the actual ratio for the fives and sixes was 

 106,602 divided by 315,672 which 150.3377. 



But the fives and sixes mark one third of the six faces of 

 dice, and should therefore have occurred one third, that is 

 0.3333 times of all, for strictly even chances. 



The fives and sixes actually thrown exceed their theo- 

 retical probability (of the even chance) by o .0044, that is by 

 44 on 10,000. This corresponds to our " analytical excess" 

 in the following. 



False Science from False Facts and False Tools. 



Suppose one of our modern "exact scientists" proceeds 

 to establish the law of probability by throwing of dice, and 

 takes this mere fact of 0.3377 as the true probability, would 

 he not get up some very fine science ? 



He would, in that case, overlook the fundamental error 

 involved in the fact that dice, marked as they are, cannot 

 give a strictly even chance, but necessarily favor the high 

 throws, that is the fives and sixes. 



Why? Under the five depressions we have only two, 

 under the six small holes only one ; in other words, the best 

 of dice, by the method of making, are lightened at the faces 

 with five and six depressions in comparison to the opposite 

 faces, which thus are relatively " loaded" because a mere 



trifle of substance less has been removed. 



.*- 



Nature can not be Suppressed. 



Now, the force of gravity cannot be suppressed it points 

 out with unerring hand this trifling amount of matter. So 

 nature always points out what exact scientists overlook. 



And thus we would "falsely " condemn the true proba- 

 bility of an even chance if we tried to prove an abstract 



