PROBABILITY THEORY AND TELEPHONE ENGINEERING 51 



tive in the lower range of R and positive in the upper range; and the 

 magnitude of pb,o{R' > R) always increases with increasing b. Since 

 the value of R at which pb.o{R' > R) changes sign depends somewhat 

 on b it will be denoted by Rt,. Fig. 4 shows that Ri is equal to about 

 1.24; and that Ri, when 1 > 6 > 0, is greater than Ri but only slightly 

 greater except when b is very nearly zero. (See also Figs. 8 and 9.) 



9 .6 .7 .6 5 4 3 .2 .1 .05 .02 .01 -OOS^PblR' > R) 



1.8 2.0 2.2 2.4 2.6 2.8 3.0 



Fig. 7 



Since the curves of pbiR' > R) in Fig. 2 cross each other (though 

 somewhat diffusely) in the neighborhood of i? = 1.2, it is unnecessary 

 in approximate work to evaluate b when we are concerned only with 

 values of R in this neighborhood ; likewise when R is in the neighbor- 

 hood of 0. Except in these two neighborhoods, however, a fairly 

 accurate evaluation of b is necessary; for Fig. 2 shows that, in the 

 upper i?-range, pb{R' > R) depends very greatly on b, while even in 

 the lower i?-range the dependence on b is considerable. Thus the 

 error resulting from assuming a value for b (in order to avoid the con- 

 siderable labor of its actual evaluation) would usually be large. Quan- 

 titatively these facts are indicated more clearly and accurately by 

 Figs. 6 and 7. 



The computations underlying the graphs have proved to be so 

 difficult and laborious that it has been deemed advisable to preserve 

 the fundamental results in tabular form herewith (Table I), chiefly 



