INTRODUCTION 



(1) Transition from Frequencies to Ordinates and Ordinates to Frequencies. 

 (Biometrika, Vol. xvn. pp. 311 818, and Lecture Notes.) 



Actually groat accuracy in these transit ions is not possible, unless we have 

 graduated the data l>y a curve or surface of known mathematical form. Still 

 useful approximations can often be obtained by applying fairly simple graduation 

 formulae. 



(i) Cell Frequencies from Ordinates in the case of a Bivariate Frequency 

 Surface. 



The Lagrangian interpolation formula which corresponds to the midpanel 

 central difference formula up to and including second order differences takes the 

 following form* : 



#)(!- y 2 ) *-i,o + 

 + x) (1 + y)*i.i + 

 - gpy (1 + a) (1 - y) ^.x - 



- y 2 ) 



-#)(l + y)*_ M 



(1) 



Here the units of the x and y variates are both supposed to be unity ; if they are 

 not, but are h and k respectively, the modifications required are indicated below. 

 This surface passes through the tops of all nine ordinates of the cell scheme : 

 -a -y 



CENTRAL CELL ORDINATES. 



CELL FREQUENCIES. 



Corresponding to the cell ordinates z, we have the nine cell frequencies/. If 

 we note the following integrals : 



} 



K. Pearson, 



or Computers, No. in. pp. 2628. Cambridge University Press. 



