clxxiv Tables for Statisticians and Biometricians [XXXI~ A , L 



But equation (xxxix) gives us 



2043,6117 #--3103,6160 



o-6 



e = 



3-9995,5095 E - 47887,8552 ' 

 and substituting the above value for E we have 



3102,7069 --3103,6160 . 0000fisn 

 6-0723,0539 - 4-7387,8552 



Thus Pi 2 +e = -3550,9347 and jS = '591,822. 



Accordingly formula (xxxvii) gave a very workable approximation. 

 Let us take a very small sample in our next illustration. 



Illustration (ii). Supposing n = 5, and r = '6, what is p, the most likely value 

 of p ? We apply first formula (xxxvii) and have 



A _ -192 _ -0384 -040,2432 

 p= ~4~ "16 64 



= -550,2288. 



We will therefore take as our first approximation 



p 1 p r = -330,1373. 



Now with such a small sample as n = 5, it is not possible to use equations (xxxviii) 

 and (xxxix). We must proceed to the equations from which that method was 

 deduced, and must obtain the first five .E"s. These are given by 



4-T ........................... (xli), 



&n-l 



and if e be the correction on px 2 , 



Now pi 4 =-1089,9064, 1 -pi 4 = '8910,0936, ?- 2 - Pl 4 = -2510,0936. 



Let = cos- 1 (- p! 2 ), and therefore cos ( v -0) = -330,1374, 



which gives us TT- = 1-234,3472, and cos- 1 (- pi 2 ) = 1 '907, 245 4, 

 angles being in circular measure. Thus by (xl), 



# 2 = -330,1373+ -= 



V-891,0093 x 1-907,2454 



= '885,5966. 

 Our successive equations from (xli) are 



1-7820,1872 #3 = '990,4119 + l/# 2 , 

 2-6730,2808^4 = 1-650,6865 + 2/E 3 , 

 3-5640,3744^5 = 2-310,9611 + 



