102 BELL SYSTEM TECHNICAL JOURNAL 



10 (-364,176P + 6,208,146/ 8 +125 I 735 ) 778* 6 +303,753,831/ 4 



-672,186,949/ 2 -2,432,820,224)/2 7 3 13 5 3 7 1 ll 



11 (199,112 ( 985/ 11 + l ) 885 ) 396 ) 761/ 9 -31,857 ) 434,154/ 7 

 -287,542,736,226; 5 - 556,030,221, 167/ 3 + 487,855,454,7290/ 



2 13 3 14 5 3 7 2 11 



For any given value of P the corresponding value of t in (2) can be 

 found from tables of the probability integral. The value of a for 

 this value of P and for any value of c can then be determined by (1). 

 In this way values of a were calculated for every integral value of c 

 from 1 to 101 and for eleven particular values of P: 0.000001, 0.0001, 

 0.01, 0.1, 0.25, 0.5, 0.75, 0.9, 0.99, 0.9999, 0.999999. These results 

 are presented in Table II. The numerical values of the coefficients 

 <2i to Qi, corresponding to the particular values of P used in Table II, 

 are given in Table VII. 



From the information given in Table II, two sets of curves were 

 drawn, Figs. 1 and 2, the first for each integral value of c in the range 

 a = to a = 15 and P = 0.000001 to P = 0.999999, and the second for 

 every fifth integral value of c in the range a = to a = 200 and the same 

 range of P. From these curves any one of the variables (P, c, a) 

 may be found corresponding to assigned values of the other two, sub- 

 ject to the practical condition that c is to be an integer. 



Proof 



The well-known expressions for the summation of Poisson's ex- 

 ponential binomial limit are: 



e~ a da. (3) 



