XXV] /iiti'iH/Hi-titm r\li 



Illustrations. 



(i) Find the value of P. K (|, 3'2:. . 



(a) Let us work first with l x (\ t q) - 2P* ( J, 7) - 1 : 



q /.(4, q) A A' A 8 A A A A' A 



3 -792,9688, 



3-5 -829,5293, -036,f><;<)f>, 



4 -858,8867, <):!! ),:r.7 I, --007,2031, 



4-5 -882,6932, -023,8065, -'005,5509, -001,6522, 



5 -902,1454, -019,4522, -'004,3543, -001,1966, -'000,4566, 



5-5 -918,1358, -015,9904, --003,4618, -000,8925, -'000,3041, '000,1515, 



6 -931,3460, -013,2092, --002,7812, '000,6806, --000,2119, "000,0922, -"000,0593, 



6'5 -942,3012, '010,9562, -'002,2530, 000,5282, --000,1524, 000,0595, -000,0327, O00,026, 



7 '951,4197, '009,1185, -'001,8377, '000,4153, - 000,1129, '000,0395, -000,0200, 000,0127, -'000,0139. 



Here we must go as far as A 8 . 

 / .25 (i 3-25) = -792,9688 + \ ('036,5605) - (- -007,2031) + -fa (-001,6522) 



- -nb (~ -000,4556) -I- ^ (-000,1515) - ^ (- -000,0593) 



+ rift (-000,0266) - s^fo (- -000,0139) 

 = -792,9688 + "018,2803 +-000,9004 + '000,1033 + '000,0178 +'000,0042 



+ -000,001 2 + -000,0004 + '000,0002 

 = -792,9688 + '019-3078 = -812,2766, 

 and P. 25 (i 3-25) = -906,1383, which is accurate to the last figure. 



The process is somewhat lengthy and can be shortened by using B x ( , q). 



(b) Starting from the I x (\, q)'s, multiply them by their respective B(,q)'8 and 

 we obtain the following series : 



q B x (\,q) A A- A 3 A 4 A* 



3 -845,8334, 



3-5 -814,3885, -'031,4449, 



4 -785,2678, --029,1207, -002,3242, 



4-5 -758,2593, -'027,0085, -002,1122, -'000,2120, 



5 -733,1721, --025,0872, -001,9213, -'000,1909, +'000,0211, 



5-5 -709,8349, -'023,3372, -001,7500, --000,1713, +-000,0196, --000,0015. 



The differencing here is briefer and more effective. 



5.25 (, 3'25) = -845,8334 - -015,7224(5) - -000,2905(3) - -000,0132(5) 



- -000,0008(2) - -000,0000(4) 

 = -845,8334 - -016,0271 = -829,8063. 

 But B (\, 3-25) = 1-021,58087, hence 



/.2s(i 3-25) = B. K (l 3-25)/5(i 3-25) = -812,27668 

 and P.25 (i 3-25) = { 1 + /. (|, 3'25)} = -906,1383, 



the correct value, as before. 



