VIII IX] /iifroductio,' l\\ii 



4951 

 Interpolating linearly, r= -00 + -05 x r-: -0380, which is in good agreement 



with the value 0379 found by d vi i.ping the full tetrachoric equation and 

 solving it. 



Let us now use the appropriate central difference finial formula (ybis). We 

 require the values of the following eight S a 's and 8 /a 's for the two tables of r*: 



S* Zi t0 



$'*!,! 

 8* 2-2,0 



S*i 



8'% o 



We need only compute the second and third lines of (7 bis), as we have already 

 obtained the values of the first. Calling this remainder R, we have : 



OqfiQl77fi i.fi-4^1 'a..^fiQ 



0369,1776 .U 4531 + 5469 



. , _ 



+ 1-3312 -4531 + -5469 



the upper line in the curled brackets referring to r = - 00, and the lower to r = OS. 

 These give: 



(- '000,1 159 

 " I- '000,1040 ' 



which must be taken away from the hyperbolic formula values of djN, i.e. -126,0388 

 and -132,5363 respectively. 



Thus we get 



d/N= -125,9229 for r = O'OO, 



and -132,4323 for r = 0'05. 



* It is extremely easy to obtain by the machine the central differences of any table entry. To get 

 S 2 for any entry, add the entries to right and left of the given entry, place the entry itself on the 

 machine and subtract it twice; the result on the slide is the &*. To get <5"- for any entry, add the entries 

 above and below it and subtract twice the given entry. The discovery of either 5 1 or 5^ is thus a single 

 continuous operation, and one of great simplicity and rapidity. 



