POISSON'S PROBABILITY SUMMATION 617 



suniinaiA' (if ihc data used is gi\en in Tabic I and llu- oLst-rNt-d distri- 

 butions are given in full in Table II. 



The distributions shown in the first group are taken from the work 

 of Rutherford and Geiger, Whitaker, Holm, and Greenwood and 

 White. Rutherford and Geiger observed the collision with a small 

 screen of an a particle emitted from a small bar of polonium placed 

 at a short distance from the screen. The number of such collisions 

 in each of 2608 eighth-minute intervals was recorded, the distance 

 between bar and screen being gradually decreased so as to compensate 

 for the decay of the radioactive substance. From this record two 

 frequency-distributions were calculated, that of the number of par- 

 ticles striking the screen in an eighth-minute interval, and in a quarter- 

 minute interval.'^ These are distributions (al) and (a2), respectively. 

 Distributions (a3) and (a4) are based on a count of the number of 

 death notices in the London Times on each day for three consecutive 

 years. ^* The distribution of deaths of men over 85 years of age (a3) 

 and that of deaths of w^omen over 80 (a4) are show^n here. The next 

 (a5) is a frequency-distribution of the number of telephone lines 

 simultaneously in use, from measurements on a group of 100 sub- 

 scribers.'^ The last distribution of this group (a6) was obtained 

 from a count of the number of bacilli in each of 1,000 phagocytes, or 

 white blood cells, in the same solution and as far as possible under 

 the same conditions, and is typical of a large number of distributions 

 of the number of tubercle bacilli ingested per cell.'^ 



The first two examples in the second group are due to "Student" 

 and the remaining seven are new. Distributions (bl) and (b2) show 

 the results obtained from two different solutions of yeast cells by 

 counting the number of cells per square of a haemacytometer slide 

 on which the solution had been spread as uniformly as possible after 

 it had been thoroughly shaken to break up any clumps of cells. '^ 

 The next example (b3) w^as obtained from the records of the "lost and 

 found" offtce of the Telephone and Telegraph Building, 195 Broadway, 

 New York City. The number of lost articles found in the building 



15 "The Probability Variations in the Distribution of a Particles," by Ernest 

 Rutherford and Hans Geiger, Phil. Mag., Vol. 20, pp. 698-707, October, 1910. 



" "On the Poisson Law of Small Numbers," by Lucy Whitaker, Biometrika, 

 Vol. 10, pp. 36-71, 1914. Six other similar distributions are given. 



1* "Calculation of Blocking Factors of Automatic Exchanges," bv Ragnar Holm, 

 P. 0. E. E. J., Vol. 15, pp. 22-38, April, 1922. 



1^ "A Biometric Study of Phagocytosis with Special Reference to the 'Opsonic 

 Index'," by M. Greenwood and J. D. C. White, Biometrika, \'o\. 6, pp. 376-401, 

 1908-1909. Fourteen other distributions are given. 



" "On the Error of Counting with a Haemacytometer," by "Student," Biometrika, 

 Vol. 5, pp. 351-360, 1906-1907. Two other distributions are given. 



