XXXVIII XLI] 



cxev 



Our value of w' is -0583,3164; hence by linear interpolation between 9 = 0*4 

 .UK! 0'5 we have 



q = -43747 for n' = '0583,3164. 



We now require KI and K z for this value of q from Table XLI (p. 230) 

 q = 0-4, K l = - 47-801 6,2629 *, 

 q = 0-5, KI = - 46-6546,2486 ; 

 A\=- 47 -37 18,4485. 



7 = 0-4, #2 = + 37-9368,8590, 

 7 = 05, K 2 = + 36-1452,9770; 



#, = 37-2655,7780. 

 Both these results arc by linear interpolation. 



We now require the AY and K at the abrupt but non-asymptotic terminal. 



Here we take 



n, = /i 12 = 6-94 ^ 



hence for q = -43747, 



hence for q = -43747, 



n lo = 8-29 

 NO =8-74 



- and we put 7 = 



and A" t to get 



We work these out from our Table XLI, reversing the signs of 

 AYundtf,'. We find ^' = + 4-0542,3379, 



K t ' = - 2-31 80,3042. 



We see from these results that the non-asymptotic abruptness towards the end 

 of the first year of life will raise the mean age at death and lower the variability. 



We have now to find v\" and vz" or the raw moments about x= 1 of the whole 

 system without the frequencies of the first and last subranges, i.e. i = 63'99 and 

 w p = w ia = 6'94. We can arrange this for a continuous process on the machine : 



x 2 



Frequencies 



22-59 



18-58 



15-96 



13-30 



11-51 



10-61 



9-30 



8-74 



8-29 



7-51 



Totals 126-39 



x 

 0-5 

 1-5 

 2-5 

 3-5 

 4-5 

 5-5 

 6-5 

 7-5 

 8-5 

 9-5 



503-575 



0-25 



2-25 



6-25 



l'2-2. r > 



20-2') 



30-^:. 



42'25 



56-25 



72-25 



90-25 



3025-4375 



We can now turn to formulae (vi) and insert the above results there in the first 

 two values. Numerically we have 



197-32/*!'" = 503-575 - 47-3718,4485 + 4-0542,3379 + 69'4 = 529-6573,8894. 



* The render may be reminded that for A', and A'., the absolute values w, , ,, n 3 , n t , w s are to be oned. 



662 



