cciv Tables for Statisticians and Biometricians [XXXVIII XLI 



With the usual notation, if the curve be 



/_ #\ w i/., x\ m z 



2/ = 2/o(l+- (l--) 

 \ eii/ \ a 2 / 



with origin at the mode, we have 



r = mi + m% + 2 = m/ -f m 2 ' , 



, and m/ = mi + 1, m z ' = m 2 + 1, 

 ?- 2 (r + l) 



and b z = ^ -', but e = 



Thus /, 2 = / u 2 {4(r+l) + J/3 1 (r+2) 2 j, 



and i&, (r+2) 2 + 4(r + 2)- 



But & = '186,171, /*, = 66-810,601, 



and accordingly we have the quadratic for r + 2, 



0465,4275 (r + 2) 2 + 4 (r + 2) - 9'987,074 = 0, 

 whence r + 2 = 2-428,165, 



and r = -428,165. 



But == -043,731. 



Hence to find w/ and w 2 ' we have 



w' 2 = -428,165m' + -043,731, 



yielding m^ = -168,250, 7W 2 ' = -259,914 ; 



and accordingly mi = -'831,750 and w 2 =- '740,086, 



= 10-583,167, a 2 = ^ 2 6 = 9-416,833. 



mi + m 2 

 Thus the required curve is 



( r \ --881,750 / r \ -'740,086 



1 + 15^167) I 1 - (FJltfSs) 



7/0 being determined in the usual way from the complete B-function. 

 Now the value of r, if found from /3i and {3 Z , is 



but by compelling the curve to have the range 20, we have found r = '428,165, 

 instead of -366,152. In doing this we neglected the value of /3 2 . If we find /3 2 from 

 the above equation, substituting the value r '428,165 and /9i = '186,171, we have 

 /9 2 = 1 '447,590, while the observation value is 1'413,846. This alteration is not 

 statistically of any great importance. 



But we have only made the range = 20, we have not made its terminal start at 



* In Biometrika, Vol. XX A . pp. 342 343, the equations for r at foot of first and top of second page 

 are erroneous, but the numerical value of r is correct. 



