200 Probability Variations in Distribution of a. Particles. 



For the " goodness of fit " * of the experimental values with 

 the curve we find % 2 = 9*6270 and P = *474. For the 

 theoretical values and the experimental values the figures are 

 ^ 2 = 13*9826 and P = '173. In the latter case, therefore, in 

 one trial out of six a random sampling would lead to a system 

 of numbers diverging more widely from the theory than do 

 the actually observed figures. The fit may be considered 

 fair. In the former case the corresponding probability is. 

 one in two, or three times as good. But this is obtained by 

 the use of extra constants and must not be taken as con- 

 troverting the authors' conclusions that "as far as the 

 experiments have gone, there is no evidence that the variation 

 in number of a particles from interval to interval is greater 

 than would be expected in a random distribution." 



In the case of the J minute intervals the "goodness of fit''' 

 of the two rows of figures (the one obtained from experiment 

 and the other from theory) given at the bottom of p. 703 of 

 the paper can also be ascertained. Here % 2 = 14*9953 and 

 P = *31, the observations at the end o£ the range being clubbed 

 together, as before. 



Judging from the figures given, therefore, the agreement 

 between theory and experiment in the case of the \ minute 

 intervals is better than in the £ minute intervals, a conclusion 

 opposite to that of the authors of the paper. This, however, 

 can be accounted for by the very poor agreement between 

 experiment and theory in the case of 8 particles per interval 

 in the latter experiments. Here theory gave 68 while ex- 

 periment only showed 45, and this discrepancy contributed 

 no less than 7*78 to the total value (13*98) of x 2 - 



The ideal frequency distribution could also be obtained 

 from the figures given for the \ minute interval experiments. 

 For these, & = -2283 and ^ 2 = 3*6429, and the distribution 

 has passed over into a true Type IV. curve, instead of being 

 on the border-line between Type TV. and Type V. as in the 

 case of the J minute interval experiment. 



The Sir John Cass Technical Institute, 

 London, E.C. 



March, 1911. 



* See Pearson, Phil. Mao-, vol. 1. pp. 157-175, July 1900. Also 

 "Tables for Testing the Goodness of Fit of Theory to Observation,"' 

 W. Palin Elderton, • Biometrika,' vol. i. pp. 155-163. 



