[ 198 ] 



XVI. Note on the Paper by Prof. E. Rutherford, F.R.S., and 

 H. Geiger, Ph.D,, on " The Probability Variations in 

 Distribution of a Particles." By E. C. Snow, M.A* 



IN the Phil. Mag. for October last Prof. Rutherford and 

 Dr. Geiger contributed a paper with the above title, a 

 mathematical note by Mr. Bateman being appended. The 

 latter showed that if x is the true average number of a. 

 particles falling on a screen from a constant source in a 

 given interval, the probability that n a particles are observed 



x n 

 in the same interval is given by — -. .e~ x (p. 705). The figures 



found by the experimenters were compared with those 

 obtained from the above expression, and the conclusion 

 reached was that " on the whole, theory and experiment are 

 in excellent accord/' but no numerical measure of the agree- 

 ment was attempted. 



As the distribution of the figures is of a general form often 

 reached in many branches of statistics, it is of interest to 

 compare the numbers given in the paper with those derived 

 from fitting an ideal frequency curve to the experimental 

 results, and also to obtain a measure of the " goodness of fit " 

 of the latter with the theoretical values. 



The theory of ideal frequency curves has been developed 

 by Prof. Karl Pearson f, and the notation used here is that 

 devised by him. 



Taking the figures given by the experiments for -J minute 

 intervals (p. 701, last row but one) the following statistical 

 constants are found : — 



/*i=Q. 



fi 2 = 3-6114. ft= -2451. 



/x 3 = 3*3979. /3 2 = 3-5265. 



^ = 45-9922. 



A reference to Rhind's Tables J shows that the distribution 

 lies just within the area of Pearson's Type IV., but is quite 

 close to Type V. The equation of the first of these is of the 

 form 



y=y (x' 2 + a?)- m e- rtan ~ */«? 



and of the second 



y=y Q X~P. et x . 



* Communicated by the Author. 



t Phil. Trans, vol. clxxxvi. A. pp. 343-414. 



% ' Biometrika,' vol. vii. July and October 1909, p. 131. 



