\ \ XVIII XLI] I,,!,;,,!,,,!;,,,, rxr j 



(ii) lleselectsf/ from TableXXXVIII togiveuHnearlyan posHible ,'(i.-. 



(iii) Hi takes {'mm Table XLI the values of (he A"s eonvs|>onding to thi- 

 valur of'y and adds them n to the moments found in (i). 



(iv) Dividing by N the computer obtains the iiiomeiit-cocfficientH of the whole 

 system in corrected form about the division between the first and second subranges 



The moment-coefficients must now be referred to the mean by the usual 

 formulae*. Special cases may arise, which need detailed consideration. 



The formulae as given above apply to /-curves asyrnptoting to the vertical at 

 one terminal and to the horizontal at the second. But at the second terminal 

 there may be also abruptness, and this will now be considered. 



Suppose there to be p subranges, and let K\ t Kt, K 3 ' and K{ be the values 

 found for KI, K%, K 3 and /f 4 , when we write n p , 7?p_i, n p _, n p _s, n^ for n t , n t , ti 3 , 

 n t and n 5 respectively, and change all the signs. We then have in working units: 



" = (N- ni - n p ) ( V3 " f - 

 + 

 " = (N- m - n y ) W - $ v? + ^) + K< + Kt' + 4,(p-2) AV 



2fK 1 '+(p-'2?n p ...... (vi). 



Here, for example in N^", the first term (N u\ - n p )(v 3 "' - { v\") represents 

 the frequency of the observed data excluding the first and last subrange fr&jueticies 

 about the division between the^first and second subranges. K 3 represents the 

 moment of the first subrange frequency about the same point, and 



represents the moment of the last subrange transferred to the same point (#= 1) 

 again. 



If there be high contact at the second terminal, then 

 n p = np_! = n p _ 2 = w p _3 = N p _4 = 

 and all the K"s vanish. This corresponds to the case of /-curves in formulae (iv). 



If there be non-asymptotic abruptness at the second terminal, then we must 

 put q= If. Such cases arise with limited range /-curves. 



* Mean = value of variate at division of first and second subranges + /*^,'", 



the last three moments in working units. 



+ The taking of q = l for the case of non-asymptotic abruptness differs to some extent frum using 

 the non-asymptotic abruptness-coefficients of Pairman and Pearson (Iliometrika, Vol. xii. p. 240). In 

 the latter method we should find the crude moments for the p - 1 subranges (excluding the first) and 

 add the terms in the usual abruptness-coefficients fr, , 6 t , 6 3 , 6 4 and & 5 . In the present method we find 

 the crude moments on p - 2 subranges, and deduce the corrected moment for the pih subrange from the 

 auxiliary curve itself. 



