Ixxxii Tables for Statiti<-i<in* and Bioinetrici>n<* [Ll\ 



The function H (r, v) is introduced because, as a rule, its logarithms have far 

 smaller differences and it is thus capable of more exact determination from a table 

 of double entry. Its physical relation to the curve may be expressed as follows; 

 let the origin be transferred to the mean, then if y, be the ordinate at the mean, 



r,") 



where a is the standard-deviation of the curve 



a 



.(xcii). 



Vr 1 cos <f> 

 The distance of the mean from the origin is given by 



/*,' = tan <f> (xciii). 



When r is fairly large : 



- (xciv). 



/ 



Hence --A/ -*/ ~' ? ( xcv )' 



// (/, v) V ,- - 1 V 2ir 



/l-4co.s a <4 

 where q = . / - J- , 



and thus the evaluation if $ be > 60 may be made by aid of Table II*. 



Illustration. In the curve fitted to the statures of St Louis School Girls, 

 aged 8 (p. Ixxx), we have 



N~ 2192, a =14-9917, 



r = 30-8023, v = 4'56967. 

 Find y,. 



We have tan <f> = vfr = '148,3548. 



Hence <f> = 8 3 26''31315 = 8'43855. 



Turning to the Tables, p. 136, we see the large differences of \ogF(r, v) at 

 this value of <f>, and accordingly settle to work with log H(r, v). 

 We have for log H (r, v), 



r = 30 r = 31 



<f> = 8 -388,2032 -388,5583, 



<j> = 9 -388,2278 :{,S8,5822, 



log H(r, v) = '388,2032 + ('4386) [24] - i ("4386) x ('5614) [28] 

 = 388,2137. 



For a fuller dincnssion of these integrals see Phil. Train. Vol. 186, A, pp. 876881, B. A. 7'nni. 

 Report, Liverpool, 1896, Preliminary Bcport of Committee..., and the /*./(. Trant. Report, Dover, 1899, 

 already cited. 



