700 Prof. E. Rutherford and Dr. H. Geiger on the 



examined. The length of tape corresponding to half-minute 

 marks was subdivided into four equal parts by means of a 

 celluloid film marked with five parallel lines at equal distances. 

 By slanting the film at different angles, the outside lines 

 were made to pass through the time-marks, and the number 

 of scintillations between the lines corresponding to 1/8 minute 

 intervals were counted through the film. By this method 

 correction was made for slow variations in the speed of the 

 motor during the long interval required by the observations. 

 In an experiment of this kind the probability variations 

 are independent of the imperfections of the zinc sulphide 

 screen. The main source of error is the possibility of missing 

 some of the scintillations. The following example is an illus- 

 tration of the result obtained. The numbers, given in the 

 horizontal lines, correspond to the number of scintillations 

 for successive intervals of 7'5 seconds. 



Total per minute. 



1st minute: 3 7 4 4 2 3 2 25 



2nd „ 5254 3 542 30 



3rd „ 5 4 13 3 15 2 24 



4th „ 82223426 31 



5th „ 7 4 2 6 4 510 4 42 



Average for 5 minutes . . . 30*4 

 True average 31*0 



The length of tape was about 14 cms. for one minute 

 interval. The average number of particles deduced from 

 counting 10,000 scintillations was 31*0 per minute. It will 

 be seen that for the 1/8 minute intervals the number of 

 scintillations varied between and 10 ; for one minute 

 intervals between 25 and 42. 



The distribution of a particles according to the law of 

 probability was kindly worked out for us by Mr. Bateman. 

 The mathematical theory is appended as a note to this paper. 

 Mr. Bateman has shown that if x be the true average number 

 of particles for any given interval falling on the screen from 

 a constant source, the probability that n a particles are 



observed in the same interval is given by ^e~ z . n is here 



a whole number, which may have all positive values from 

 to co . The value of x is determined by counting a large 

 number of scintillations and dividing by the number of 

 intervals involved. The probability for n a particles in the 

 given interval can then at once be calculated from the theory. 

 The following table contains the results of an examination of 

 the groups of a particles occurring in 1/8 minute interval. 



