610 



BELL SYSTEM TECHNICAL JOURNAL 



TABLE I 



A^ = number of samples 

 aiV = total number of occurrences 

 a = average number of occurrences per sample 



Series 



Alpha particles 



Alpha particles 



Deaths of aged 



Deaths of aged 



Telephone lines in use 



Bacilli 



\'east cells 



Veast cells 



Lost articles 



Number 12 



Fires 



Incorrect reports 



Cutoffs 



Double connections 



Calls for wrong number 



Deaths from kick of horse 



Number 12 



Calls from group of two coin-box telephones. 

 Calls from group of four coin-box telephones 

 Calls from group of two coin-box telephones. 

 Calls from group of six coin-box telephones. . 



Cutoffs 



Double connections 



Calls for wrong number 



Connections to wrong number 



Party lines 



"Lost and found" advertisements 



Number 12 



Number 12 



Comets 



Particles in emulsion 



Particles in emulsion 



N 



aN 



a 



a 1 

 a 2 

 a 3 

 a 4 

 a 5 

 a 6 

 1 

 2 

 3 

 4 

 5 

 6 

 7 



9 

 1 

 2 

 c 3 

 c 4 

 c 5 

 c 6 

 c 7 

 c 8 

 c 9 

 clO 

 ell 

 cl2 



2608 



1304 



1096 



1096 



>1000 



1000 



400 



400 



423 



500 



364 



506 



506 



506 



506 



200 



250 



145 



140 



141 



138 



267 



267 



267 



267 



300 



209 



100 



50 



100 



50 



50 



10097 



10094 



903 



2364 



>4315 



1927 



720 



1872 



439 



421 



9487 



138 



1057 



1760 



2520 



122 



251 



172 



384 



212 



468 



557 



906 



1351 



2334 



1981 



7051 



421 



421 



258 



46 



106 



3.87 

 7.74 

 0,82 

 2.16 

 4.32 

 1.93 

 1.80 

 4.68 

 1.04 

 0.84 



26.1 

 0.27 

 2.09 

 3.48 

 4.98 

 0.61 

 1.00 

 1.19 

 2.74 

 1.5C 

 3.39 

 2.09 

 3.39 

 5.06 

 8.74 

 6.60 



33.7 

 4.21 

 8.42 

 2.58 

 0.92 

 2.12 



for the probability P are the values of the observed relative frequency 

 F, which are calculated as indicated in Table II, and the observed 

 distribution is represented by an irregular series of dots, as in Fig. 4. 

 A third set of curves, Fig. 5, supplementary to Figs. 1 and 2, has 

 now been drawn using a logarithmic scale for a. This chart shows the 

 individual c curves up as far as a = 30 and it shows more clearly than 

 does Fig. 1 the range 0.1 ^a ^2. It may also be used as a background 

 in the same way as Figs. 1 and 2, with the additional advantage of 

 making the distances of the plotted points from the vertical line 

 proportional to the percentage deviations rather than proportional 

 to the absolute values of the deviations, so that the fit of a distribution 

 having a small average can be compared directly by eye with that of 

 a distribution ha\ing a large a\-erage, since it is more often the relative 

 than the absolute value of the deviation which is significant. 



