I I I I 



\ \\lll 



By using ten-figure tables such as Table II for * ;uid then comparing 



the results with Table III the reader will judge the degree of accuracy often 

 quite sufficient for practical purposes of the latter table. 



Further Applications of Tables II and III. (Illustrations of Camp's Method.) 

 (c) To sum the first t + 1 terms of a binomial (p + q) n t where p + q 1. 



then, if S t+ i = M O 4- ui + . . . + u t = sum of first t + 1 terms, find, if = n t, 



Then approximately S t+1 = WH- - a + $>> , 



where is the ratio of tail to ordinate of normal curve with dichotomic 



ordinate at %i from its mean, and 



1 (, 3 #i 2 15 10#i 2 + .Tt 4 ) . 



y (vi). 



Since we are really concerned only with cases in which n and t are relatively 

 large numbers, u t must be evaluated by logarithmic calculation; we therefore replace 



_ n .' t t by r . _ -ixp/a TT anc * use E. S. Pearson's Tables of the T-functionf; 



for p n ~ t q t the ordinary logarithm tables to seven figures are often not sufficiently 

 accurate, and we must use Vega's or Peters' ten-figure tables. 



Illustration (iii). To find the sum of the first 261 terms of the binomial ( + f) 450 - 

 Here p = $, q = $, = 260, s = n-= 



26 1 



i? _ /260 192 

 ~V 191259' 

 1 p _ log 260 + log 192 - log 191 - log 259 



5 Z lOg e Jt - ; - 



o- 2 log M e 



003,94145 ^ n ^ KK 

 = ^29448 = >0 9 ' 0755 ' 



thus - = -095,2655, \ = -009,0755, ^ = 0000,8236, 



<r a <r 



loioQ -165.11929 



Thus ^ = 3-990,964, x? = 15-927,794, and xf = 253*694,622. 



Iog 10 e = -434,2944,819, and l/log, = 2-302,5850,930. 



t Tracts for Computers, No. vin. Cambridge University Press. 



B. IL 



