304 PROFESSOE K. PEARSON AND MR. L. N. G. FILON 



x= 14-9917 tan 0, 



y - 235-323 cos 82 ' 8023 tfe- 4 ' 56967 ', 



the axis of x being positive towards divarfs and the origin 2'224l on the positive side 

 of the mean. The unit of x is 2 cms. of height, and all the constants except the 

 mean height are given in two-centimetre units. 

 We have the following values of the constants : 



* 

 p. 2 = 770739, Mean height = 118'27l centims., 



p, = 2-38064, a- = 277622, 



^ = 192-17419, yi = modal frequency = 324'18 ; 



y., = mean frequency = 3237G, 



d -135,606, Sk. = skewness = '04885, 



r= 30-8023, m= 16'4011, 



v 4-56967, ft- 14-9917. 



It will be seen at once that the skewness is small, that the mean and mode are 

 close together, and the mean and modal frequencies are almost identical. Our 

 problem is : Are these differences significant or not ? 



Let n = 2192, the total population ; then the values of a, r, v given above were 

 assumed to be absolutely exact, and A calculated with its constituents to 9 places 

 of figures, as it depends on the differences of vei-y small quantities. We shall 

 indicate one or two stages in the arithmetical work 



A _ | -131,108,064 -017,214,971 '008,837,638 '063,438,906 



017,214,971 -010,392,042 - '003,264,669 '008,837,638 



- '008,837,638 - '003,264,669 '001,144,775 - '004,422,657 j 



063.438,906 '008,837,638 '004,422,657 '030,799,043 I 



The evaluation of this determinant and its minors was then carried out by means 

 of the Brunsviga, and we found 



A_ "104,824,.472 A^ _ 1200-842,528 



/7 : 10 1S 1* ~~ 10 12 



A,, 670-195,695,496 A 1S 5059-387,378 



n* 10 1 - n" 



AH _ 4606-123,523 Ay _ 1762-570,609 



w :1 = 10 12 n 3 ' 10 1S 



AS., _ 76025-131,845 A^ _ 18675-261,289 



w 3 = 10 12 w s = 10 1S 



A M _ 4828-382,384 Ay _ 3833-460,555 



?i s " 10 12 n x ~ 10 l 



Ay 15979-332,581 

 n s ~ 10 1 



