cxlii Tables for Statisticians and Biometricians [XXV 



(ii) Find the value of P. 60 (\, 3'25). 



Here, even using the B x 's, we must go as far as A 7 to be accurate to the seventh 

 figure. Our scheme is as follows : 



A A 2 A 3 A 4 A 5 A 6 A 7 



5. M (i 3 ) 1-013,5197, 

 5.(i,8-5) -949,2072, -'064,3125, 

 ^ -so (4, 4 ) '893,9850, --055,2222, -009,0903, 

 5.)(i4-5) -846,1813, -'047,8037, '007,4185, -'001,6718, 

 ^50 (i, 5 ) -804,4742, -'041,7071, '006,0966, - '001,3219, '000,3499, 

 -6 .50 (*, 5-5) '767,8131, -'036,6611, '005,0460, --001,0506, -000,2713, --000,0786, 

 .tt(i,6 ) -735,3579, -'032,4552, '004,2059, --000,8401, '000,2105, -'000,0608, -000,0178, 

 ^.6o(*,6-5) -706,4329, -'028,9250, -003,5302, -'000,6757, -000,1644, -'000,0461, '000,0147, - '000,0031. 



Substituting these results in the forward difference formula, we have 

 B .50 (i 3-25) = 1-013,5197 - 1 (-064,3125) - (-009,0903) - T V ('001,6718) 



- ^ (-000,3499) - ^ (-000,0786) - rfh (-000-0178) 



-*M* (-000,0031) 

 = 1-013,5197 - -032,1562(5) - -001,1362(9) - -000,1044(8) 



- -000,0136(7)- -000,0021(5) - -000,0003(7) 



-000,0000(5) 

 = "980,1064, and again B (, 3-25) = 1-021,58087. 



Hence 7. 50 (i 3'25) = -959,4016(7), 



and thus P.go (i 3'25) = -979,7008(3), 



which is the correct value to seven figures. 



(iii) Find the value of P.w (J, 3'25). 



Now P.io(^, 3'25) is easy to find; we have the following series of differences for 

 B.(i,2): 



q U. 10 (4,) A A'-' A3 A^ 



3 -591,5567, 



3-5 -582,0941, - "009,4626, 



4 -572,9144, --009,1797, +'000,2829, 



4-5 -564,0073, --008,9071, +'000,2726, -'000,0103, 



5 -555,3632, -'008,6441, +'000,2630, -'000,0096, +-000,0007. 



Hence .10 (i 3'25) = '591,5567 - -004,73130 - -000,03536 



- -000,00064 - -000,00003 

 = '591,5567 - -004,7673 

 = -586,7894. 



And /.io (i 3-25) = 5. 10 (J, 3'25)/5 (i 3-25) 



= 574,3935. 



