444 ON THE CALCULATION OF THE [54 



The general equation for finding I n is 



( - I)"- 1 (2n + l}l n =- (C?I t + C 3 n I 3 + &c.) 



,, i . 



Hence putting n = 32, the equation for finding / is 

 P B = 65 / = (C '"/, + Cf-I 3 + &c. + CfJ 31 ) 



/ 4 + &c. 



of the products P r n = C"I r for n 32, and calculation of the quantities 



/., and B.^. 



P r r 



6099 25587 71040 7 



2 73 95824 31465 88000 9 



7 52052 11742 87069 31200 ji 



14292 18243 52720 81535 36160 13 



181 02208 01083 62555 55851 98784 15 



I 45956 33740 16156 32779 21049 55360 17 



707 20034 04420 28331 06379 22168 88480 19 



I 9II22 29427 92298 81501 97313 85143 24OOO 21 



260 61036 46811 76525 19023 36205 50468 48000 23 



15554 89989 86905 19795 "5515 5095 1 74607 85920 25 



3 26957 75316 75298 38464 45063 81824 21193 67520 27 



16 61488 53356 44144 55275 75671 54091 08961 07520 29 



8 95482 61960 15233 01854 18130 16189 66511 72000 31 



28 99746 33490 63992 38881 71047 04677 31614 73984 Sum 



4 53632 15585 96100 8 



14991 65046 74768 61360 10 



344 04340 75247 90249 64000 12 



5 36521 41705 40998 03634 45360 14 



5456 55799 32924 09847 00119 61290 16 



34 38319 oini 06135 63711 54717 15840 18 



I2 575 34 2 9 r '77 2 4 63047 26474 10262 50016 20 



24 49639 24021 61449 84035 26184 70163 48400 22 



2257 65747 79208 93849 11233 52764 25664 03700 24 



82742 14563 16036 20888 25426 35887 94710 49840 26 



9 11013 3 OI 7 92694 23112 48336 95819 28170 55080 28 



17 67611 84070 36444 68422 26180 95706 47598 17136 30 



27 63649 29648 26477 79222 58362 41320 15644 68122 Sum 



814 19505 34163 85807 FS, 



27 63649 29648 26477 79222 59176 60825 49808 53929 



28 99746 33490 63992 38881 71047 04677 31614 73984 



65 ) I 36097 03842 37514 59659 11870 43851 81806 20055 P& 



2093 80059 11346 37840 90951 85290 02797 01847 Ijj 



Also = !- 



-I +^ 



~~ -* '!> I K 



Hence the numerator of B.^ is 10 67838 30147 86652 98863 85444 97914 26479 42017 

 and the denominator is 510 



