V VII] Introduction xlix 



It is, however, shorter to use (v) to calculate the differences. We have 

 T 5 (3-9) = + -002,5948, T, (3'9) = + '002,0092, T. (3-9) = - -000,8923, 



T U (3-9) = --001,1120, 

 r 6 (4-0) = + -001,9914, r, (4-0) = + -001,8116, T, (4'0) = - -000,4459, 



T U (4-0) = - -001,0974, 



1X6 = -0648,0741, 2x5 = -0004,5826, 3*5 = '0054,9909, 4*5 = '0000,9612 ; 

 whence S a r 6 (3'9) = '0001,2980, B z r 6 (4'0) = '0001,1720, 



S4 T6 (3'9) = - '0000,0501, S 4 T 6 (4'0) = - '0000,0256. 

 But 



# = 746, < = -254, 00 = '0315,8067, T ^0 (1 + 8)$ (I + <) = '0034,5727. 

 Thus 



T S (3-9746) = -746 (-001,9914) + -254 (-002,5948) 



- -0315,8067 {1-746 (-0001,1720) + 1*254 (-0001,2980)} 



+ -0034,5727 {2'746 (- '0000,0256) + 2*254 (- -0000,0501)} 

 = -0021,4466] 



- '0000,1160V = -0021,3300, 



- '0000,0006J 



or to seven figures r 5 (3'9746) = '002,1330. 



We will now take an illustration from the most difficult part of the table as 

 far as interpolation is concerned. 



Illustration (iii). Required the value of T M (3'94725). This lies between 

 Ti9(3'9) and ri 9 (4'0). The S 2 and 8 4 of these values cannot be found from the table, 

 because it does not proceed beyond the argument 4'0. Nor can they be found from 

 (v) because this would involve our knowing T&, T& and TZI. These might be found 

 by repeated applications of (vii), but this would involve the calculation from 

 (vii) of 12 additional tetrachoric functions, which would be very laborious. It seems 

 simpler to write our table for Ti 9 thus: 



h TIO A A 2 A 3 A 4 A 5 A 



4-0 +'000,5010 



+ 000,3266 

 3-9 +-000,8276 -'000,0334 



+ 000,2932 --000,0856 



3-8 +-001,1208 --000,1190 -'000,0101 



+ 000,1742 --000,0957 +'000,0211 



3-7 +'001,2950 -'000,2147 +'000,0110 +'000,0053 



-000,0405 -'000,0847 +'000'0264 



3-6 +'001,2545 --000,2994 +'000,0374 



- -000,3399 - -000,0473 

 3-5 +'000,9146 --000,3467 



- -000,6866 

 3'4 +'000,2280 



B. ii. g 



