Vtlb\ ee MAA os X07 ee Fe ree Or ee en eed Gornell University Library Sthaca, New York BOUGHT WITH THE INCOME OF THE SAGE ENDOWMENT FUND THE GIFT OF HENRY W. SAGE 1891 MATHEMATICS Date Due APR 1 411958 JUL 2 0 1960 MAR 2 ol1961 Mie |g 4ne SS Esso Pr E100 G _ ornell University Libra Tables of the logari DEPARTMENT OF APPLIED STATISTICS (COMPUTING SECTION) UNIVERSITY OF LONDON, UNIVERSITY COLLEGE TRACTS FOR COMPUTERS Epirep sy KARL PEARSON, F.R.S. No. IV Tables of the Logarithms of the Complete [-function to Twelve Figures a ) . Onginally computed by Or A. M. LEGENDRE, Membre de l’Académie royale des Sciences, F.R.S. CAMBRIDGE UNIVERSITY PRESS G, F. CLAY, MANAGER LONDON: FETTER LANE, E.C. 4 ALSO H. K. LEWIS & CO., LTD., 136, Gower Street, London, W.C. 1 WILLIAM WESLEY & SON, 28, Essex Street, London, W.C, 2 Chicago : University of Chicago Press (Agent for the United States and Canada) — Bombay, Calcutta, Madras : Macmillan & Co., Limited Tokyo : The Maruzen-Kabushiki-Kaisha 1921 Price Three Shillings and Nunepence net Vv EM The Cambridge University Press, Petter Lane, London, £.U. 4, and their Agents, are now the sole Agents for the sale of the following publications of the Biometric and Galton Laboratories, University of London: Eugenics Laboratory Spcteneas MEMOIR SERIES. I. The Inheritance of Ability. By Epaar Scuuster, D.Se., Formerly Galton Research Fellow, and Eruen M. Exuprrton, Galton Scholar. Price 4s. net. II. A First Study of the Statistics of Insanity and the Inheritance of the Insane Diathesis. By Davin Heron, D.Sc., Formerly Galton Re- search Fellow. Price 3s. net. III. , The Promise of Youth and the Performance of Manhood. 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Darwinism, Medical Progress and Eugenics. | The Cavendish Lecture, 1912, By Karu Pzar- son, F.R.S. va Ws 4 AI DEPARTMENT OF APPLIED STATISTICS (COMPUTING SECTION) UNIVERSITY OF LONDON, UNIVERSITY COLLEGE TRACTS FOR COMPUTERS Epirep By KARL PEARSON, F.R.S. No. IV Tables of the Logarithms of the Complete [-function to Twelve Figures Originally computed by A. M. LEGENDRE, Membre de I’Académie royale des Sciences, F.R.S. CAMBRIDGE UNIVERSITY PRESS Cc. F. CLAY, MANAGER LONDON: FETTER LANE, E.C. 4 ALSO H. K. LEWIS & CO., LTD., 136, Gower Street, London, W.C. 1 WILLIAM WESLEY & SON, 28, Essex Street, London, W.C. 2 Chicago : University of Chicago Press (Agent for the United States and Canada) Bombay, Calcutta, Madras : Macmillan & Co., Limited Tokyo : The Maruzen-Kabushiki-Kaisha 192] wn f EM pb s21999 Ces tables ont été enfin construites apres une multitude de recherches entreprises dans la vue de découvrier les méthodes et les formules les plus propres a diminuer la longueur et la difficulté des calculs. Legendre: Traité des Fonctions Elliptiques, Tom. L., p. 3. LEGENDRE’S TABLE OF THE COMPLETE T-FUNCTION This table was originally published in Tom. II. (pp. 490-499) of Legendre’s Tratté des Fonctions Elliptiques, avec des Tables pour en faciliter le calcul numérique, Paris, 1825. That work, full of most exciting and valuable material, much of which is now neglected, has become very scarce and very costly. There must be numerous mathematicians who have been seeking all their lives for a copy they could afford to purchase. It contains numerous tables of which many others than that of the I’-function are of essential value to the computer. There are all sorts of tables to 10 or more significant figures even of familiar functions which are not to be found easily elsewhere, and deserve republication. Should this reprint show that there is an adequate demand for such tables, I hope to be able to issue other facsimiles of Legendre’s creative energy. Those whose arduous labours have been shortened by Legendre’s earlier computing work, and who possibly have looked upon him as a mathematician sans phrase, may be helped by our frontispiece to realise the humour of the situation when they see the real Legendre in the flesh. The scientific friendship will undoubtedly become a personal one in the case of any computer who is a humanist. One of the many reasons for this reissue of Legendre’s [-function table is that the Tables of the Incomplete I-function ie. of the integral I,(p) = Le a?~* da/T (p), prepared by the computing section need as a companion volume a table of the complete T-functions. It is true that such a table adequate for most purposes is already provided in the Tables for Statisticians (Table XX XI) issued by the Cambridge University Press. This table, however, only gives the logarithms of the complete F-function to seven decimal places, Legendre’s table provides twelve decimal places. We have found for many purposes especially in the construction of tables of other functions that it is needful to work with at least ten figures, and so to use the original Legendre table in association with Vega’s original table of logarithms to ten places. If, however, for any special purpose we need the full range of Legendre’s values (i.e. twelve figures), then they can only be used in associa- tion with Briggs’ Arithmetica logarithmica, a work sadly needing re-editing. Legendre’s Table for the complete I'-function is here reissued preserving his first, second and third forward differences. These suffice to show that the fourth differences are of no importance to 12 figure computation. Accordingly it is adequate and, perhaps, more convenient in the case of any one having a machine to enter the table by Everett’s central difference formula: Ug = Huy + Ou, — 2Op {(h + 1) Buy + (8 +1) dy}. In order to realise what we are doing we must note that Legendre prints as “ Diff. 1,” up — % and places this on a line with u. In the same way his Diff. IT. is Up — Uy — (Uy — Uy) = Up + Uy — 24, 4 LEGENDRE'S TABLE OF THE COMPLETE I'-FUNCTION and this is placed again in parallel with w. But this is the value of 8u,. In other words the central difference of each function value must be read off in Legendre’s column “II” of differences, in the line above that of the function value. Thus we need to work only with column IT. reading as central difference the column shifted up one line. For example: Find log PF (1:078,3649). We have 6 = 3649, $= 6351. Up = 9°982,541,524,262, Su, = 640,746, U, = 9°982,343,916,451, 8u, = 639,894. Accordingly up = 9982 + 6351 x 541,524,262 +3649 x 343,916,451 — (03862467 {1°6351 x 640,746 + 13649 x 639,894} = 9-982 + 469,417,171(8) — 074,200(9) or log I. (1:078,3649) = 9°892,469,342,971. The whole of the work done is exhibited above except what is done on the machine. If the reader prefers to work by forward differences, he must bear in mind that Legendre used differences of the Newtonian sign, or, if D!, D", D™ represent his printed differences, his forward difference formula is Ug = Uy — OD'u, — 40 (1 — 0) D8 u, — 46 (1 — 6) (2 — 8) Du. In our case 6 = 3649, u, = 9'982,541,524,262, D'uy) = 197,607,811, D u,= 639,894, 40(1— 90) = ‘115,873,995, Dy, = 851, 10 (1 — 6) (2 — 0) = 063,155,189(7), Up = 9°982,541,524,362 — 72,107,090(2) — 74,147(1) us 53(7) or log T' (1:078,3649) = 9:982,469,342,971 as before. There is very little to choose between the labour involved in the two processes, but the use of central differences would have saved Legendre two of his difference columns, or the, printing of 12,000 figures. LEGENDRE : Tables of the Gamma. Function. Log. Ta. Diff. I. Il. Ill. WL] 9: .998 755 Soo 253)2 010.000 - 000 000/250 324 55 ji9 oe ae 44r £2RR Bog G11 21 00 O' 9-999 251 68 313 28 oi 77 8667/2 ey: iy. iN "213 713 qi2 2 qu 6 6} 710 709 201 700 191 343 232, 1039 1038) 1034 1031 1030 1024 : 9. 988 339 858 790 985 a 980 052 06 765 894 sy baa 2i5 40d 215 8978 738 215 214 158 214 550 489 212 564 38 664 58olg11 gigit 58|g08 1/661 850|g04 1|660 946|g02 660 044/902 28 4 ‘ioe 040/246 060 042! on 998/245 352 89 ; 319 103/244 646 92 672 330]243 o41 eh 35 659]243 239 5bq oO 3|705 704 703 709 149 g 122 102 084 070 285° 4 2 s 2j242 534 S19 a 67 042 958 555j241 832 461 : Bsn 126 8 nh 241 131 413 240 431 393 9- 298 Bic 24 308 29 732 334 S9- -998 079 830 034 303|69 9: 998 840-796 Bbs) 6g ay ae th 641 229/69 g: 995 127 871 9 337 264 946 183 Fe23 236 252 129 702 7o1 700 es 694 693 056 048 o4o 036 034 036 Z 038 29 5 046 054 065 1025 1020 1018 1014 1014 10081 . 0! 1008 1004 1002 052 536 oat 904 ” i209 ee 159 56)209 273 702 9. 999 Soh ee 618 140 s-98 % 042 038 5 985 065 e 284 348 93 19- a 145 S 20h 053 971 41203 fod : 659 142|898} 658 244|896 657 348/893) f 654 4851893 655 562/887 654 675|888 963 465/653 787/836 a 8|652 go1|880 652 021|882\8 651 139/878 650 261|876 3851873 64 are 647 641|871 sea 7110|866 6 294 421 193 23) oat 1874 ass 5233, j : 9-99 953 532 953 232 796 B34 619 860/235 559 064 6 068 796|234 866 984 yee 234 1 5 Be 692 4169" 9 2 34/688 080 125) 97 138) 97 163 38 ee ou 645 865] le 22853 861 aid 315/85o0)4 Gha 456l8se 720 . S19]232 108 471 048 231 421 26216 2 > oak 66/230 735 064 7 470 oe 230 ofg 813 96 _ 420 889/229 365 528 68 86 218] 2 685 251 684 285 683 323 9- 9-8 739 a oils 6 197 346 641 601|855 ey dai 851 8 055 361/228 682 205 393 156 227 9 843 110 : 3 313] ae 845|\20 63 886|225 353 fof 49416 430 ies 392/225 279 947/67 5 198 445224 Go2 3eal6 ‘0 596 095|223 925 608 256 650 397/223: re 4oo 4og|222 545 220 825 189]221 gor 390 99|221 228 495 Re ay 220 556 534 138 oe 219 885 503 253 264]219 215 for 039 037 866/218 546 226 gt Gholar7 8 989 f95 666 ; a a7 4o3 022/2 a6 544 oacl66 9.988 37 858 790/215 878 738 678 “3 102 195 330 Re g18 682 362] 957}. 681 405 356 aa 449 495 a1 ¢ 66 eu 942 1. 645 “910 674 768 g88 674 9 672 671 got 671 031 eae 668 252 66 666 664 ; se 61 - sat ge 3 reat 635 664|838 634 826|83 633 987/836)f 633 151/833 632 318/830 6/631 488/831 630 657/828 31/29 829/824 005/822 ea 359)81 26 5401816) a8 724/815, a gogibr4 By 458 833 171 677 695 978 631 ah, Ae af tof o| 935 1. 93dlr-egtlg. g3o}1 . 092 929]: .093\9. 92711 : 094/19. 923i. caf. 92241 .096 022 2923 Boh8 88 a j14[60 97 =H 800 oA8 grat I. °9 9:97 895 582 035 Belt: ‘0999. 958 25 o19 766 graft. me: 978 340 673 962 183 923 330 401843 51812 7|623 2 31809 dail to LEGENDRE: Tables of the Gamma Function Log Fra. Diff. 1. HW. | UL a. Log. Ta. Diff, I. I. 1.100]9.978 340 673 962/183 723 330/621 667] 806]1.150/9.96g goo 696 012/153 5go 056/583 652 I 9-978 156 950 6321183 101 663/620 861) So4fr.151 ae 747 105 a 153 006 404/582 935)715) 1.10219.977 973 848 g69}182 480 802/620 057] So1f1.152/9.969 594 99 52]152 423 469/582 223/91 1.103/9.977 io 368 167]181 860 745/619 256] 799]1.153/9.969 hat 676 083/151 841 246/581 508)q11 re 9-977 G09 507 422/181 241 48q/618 457} 7991 154/9.969 289 834 837|151 259 7381580 799 H+ 10919.977 428 265 933]160 623 032/617 658] 79541. 155/9.969 138 595 ogg|150_ 678 941/580 0go}708, 1.106/9.977 247 642 901/180 005 3741616 863] 794]1.156/9.968 987 896 158/150 098 851|579 382|708 I. 9-977 067 634 bay 179 388 511/616 069) 79241. 159719.968 B34 797 309 49 519 46g 578 694|903 I. $/9..976 888 249 016/198 772 442/615 279] 791]1.158/9.968 688 277 838/148 g4o 795/597 97 1.109]9.976 739 476 594)178 159 165/614 76 7891 .15919.968 539 337 043/148 362 824/597 268 1. 9-976 531 319 4ogl177 542 679/613 699 _787}1.160}9-968 390 974 219/147 785 556 576 569/700 1.111/9-976 353 776 730/176 928 o80|612 g1a| 78441. 161]9.968 243° 1868 663/147 208 989/575 867\69 1.11219.976 176. bin 750/176 316 268 612 28 78311 .162/9.968 095 g79 694 46 633 122/575 169 I. 9-976 000 531 682/175 703 940/611 345] 780]1.163/9.967 949 346 552/146 057 953/544 472/694 1.114/9.975 824 a 742| (75 092 595/610 565] 77941. 16419.967 803 288 5g9]145 483 481/573 74 1-115/9-975 649 739 149/174 482 030|609 786] _776}1-165/9.967 657 805 118}144 gog 703/573 0 I. 9-975 475 253 117/173 872 244/609 008] 775f1.166}9.967-512 8q5 415/144 336 618/572 392/6 1.11919.975 301 380 873/173 263 236 bob 233 ae 1.167]/9.967 368 558 797]143 764 226/571 703/68 1.118/9.975 128 117 639/192 655 003/607 461| 772f1.168]9.967 224 794 571/143 192 523/571 014/68 Te 9-974 955 462 634]172 047. 542 Got 689} 77041.169]9.967 081 bee 048|142 621 509/570 326/68 I. 9-974 783 415 092]171 440 853/605 919 be mmpalg pee 938 980 539 142 051 183 569 642/684 1.12119.974 611 974 239/170 834 934|605 151| 766f1.171/9.y0 796 929 356|141 481 541/568 958/684 I. 9-974 441 139 30 ae 229 783/604 385 63 1.172/9.966 685 447 815/140 912 583/568 294/65 I. 9-974 270 gog 522/169 625 398/603 622] 76441.173 9.966 514 535 232/140 344 309/567 595/680 1.124]9.974 101 284 124 7 021 776/602 858} 75of1.174]9.966 374 190 923]139 776 714/566 915/678)k 1,125/9.973 932 262 34€/168 418 918/602 ogg] 75941-175/9.966 234 414 209|139 209 799|966 237/699)5 I. 9-973 763 843 430]167 816 Br9|601 340} 758¢1.176 9-966 095 204 410]138 643 562/565 560/673§ 1.129/9.973. 596 026 611/169 215 ee Boo 582} 755 rety 9-965 956 560 848}138 078 002/564 884|67 I. 9-973 428 811 132/166 614 897/599 824] 75341. 178/9.965 ars 482 846]137 513 115/564 212/691 I. 9-973 262 196 235/166 015 070/599 074] 752]1.179/9.965 680 969 731]136 948 903/563 541 671 I. 9-973 096 181 165 165 415 996/598 322 49 ne 9.965 544 020 858 136 385 362/562 870/66 1.13119.972 930 765 169/164 817 674/597 573] 7491 .18119.965 Go7 635 466]135 822 492/562 204164 E I, 9-972 595 947 495/164 220 101 5g 824) 74791. 182/9.965 271 812 974]135 260 288/561 534/6654h t.133/9.972 G01 729 394/163 623 277/596 079} 743§1.183/9.965 136 562 686/134 698 754/560 869/665;8 I. 9.972 438 104 117/163 027 200/595 334] 744f1.184]9.965 001 853 932/134 137 885/560 2041669} f I. 9-972 275 076 917/162 431 866/594 590 7411 -185)9.964 867 716 0491133 597 681/559 542/66118 te 9-972 112 645 051/161 837 276/593 84] 73qf1.186)9.964 734 138 366]133 018 139/558 8816601 f {. 9-971 50 807 7751161 243 427/593 110} 73BH1.187/9.964 bor 120 229/132 459 258/558 221/650] I. 9-971 789 564 348)160 650 317/592 379) 736)1.188/9.964 468 660 969[131 gor 039/557 562/654|| 1. 9-97: 628 914 031]160 057 945/591 636] 735f1.189/9.964 336 75g 932/131 343 475/550 905}65 L. 9-971 468 856 086/159 466 309/590 gor} 73241.19019.964 205 4715 450}130 786 570/556 249/652 I. -971 309 389 777/158 875 G08|5q0 169} 730f1.191 19.964 074 629 884]130 230 321/555 5971654, 1.14 Aeon Be 51h 36, 158 285 239/589 439} 731f1-192/9.963 944 399 566/129 674 724/554 943/652 i, 9-970 992 229 130/157 695 800/588 708] 726]1.193/9.963 814 724 Sh2]129 119 7811554 291/64 1. 9.970 Ba, 533 3301157 1097 092/587 982} 72641 .194/9.963 685. 605 0614128 565 490/553 643164 i, 9.970 677 426 238 156 51g 110/587 256] 72491.195)9.963 557 039 571/128 017 847/552 994/475 1. -970 520 go7 128/155 931 854/586 532] 724]: .196/9.963 429 027 724/127 458 853/552 347164516 Ls ee 364 oe 2741155 345 322/585 808} 720f1.197/9.963 301 568 841/126 go6 506/551 210 1.14819.970 209 629 aha 154 759 514/585 088} 718bt.198]9.963 174 662 365/126 354 804/551 059/642 I. 9.970 054 870 438/154 174 426/584 370} 718}1.19919.963 048 309 5611125 803 747/550 415/64 1,15019.969 goo 696 012/153 5go 056/583 652} 7191. 200/9.g62 g22 503 814]125 253 332/549 775/64o18 as 73 rae PETE PS _ 3 is LEGENDRE : Tables of the Gamma Function. 3. a Log. Pa. DEL | th (Mi) Log. Pa. Die | mm fanf 1.200]9.962 922 503 814/125 253 3321549 775} 642t1.250]9.957 321 083 716] 98 521 gt4|51g9 419/505 | 1.201 Hee as 250 482/124 703 557 a9 133} 639f) .25119.957 222 561 boo 98 002 ‘07 518 84 595 1.20219. 962 he 546 925/124 154 424154 496 639}1 .25219.957 124 559 305} 97 483 3 518 270}572] 1.203!9.962 548 392 So1}123 605 928/547 85g] 637]1.253}9.959 027 075 650 a 965 385/517 698]572) 5 1.20419.962 424 786 573/123 058 069/547 222/ 632}1.254/9.956 930 110 265) 96 447 689/517 126/571/F 1.205/g9.962 301 728 504/122 510 847/546 590} 635}1.255]9.956 833 662 578! 95 930 561/516 555/570) 8 1.206/9.962-179 217 657]121 964 2571545 955] 630f1.256|9.950 737 732 017 95 414 006/515 985/565/— I 207/9-962 abt 253 foo|121 ¥r8 3021545 305 630f1 .257 5 086 bia 318 o11 oe 898 021/515 ta 568] 1.20819.961 93° 835 og8}120 872 979 a Soe 630} .258}9.956 547 419 990} 94 382 601/514 852/566 T 4 0 H1r.209/9.961 814 g62 121/120 328 282 61 694 @33 839]119 784. 217/543 439} 627 -21119.961 574 849 622/119 240 778/542 812) 625 : ee God 844 ce 69 966 542 184| 621 -21319.961 336 gto 878/118 128 779/541 566] 624 -214/g.961 218 955 999 117 614 213/540 942] 620 .215]g.g61 ror 140 886/117 073 291/540 322] 620 -216}g9.960 94 067 615/116 532 949 a O07 -259]9.956 453 037 389] 93 867 749/514 286/563 .260/9.956 359 169 640} 93 353 463/513 7231563)8 .261/9.956 265 816 177] 92 839 740/513 160/56:|f .26219.956 192 976 439 os 308 Bg 512 599/561 .263}9.956 080 649 859] gt 813 981/512 038]561 -26419.955 988 835 876} o1 301 943511 477/554 .26519.955 897 533 933] go 790 406/510 920/554 .266]9.955 806 743 467| 90 279 546/510 363/558 .267/9.955 716 463 g21| 89 ts 183|509 805/553 .268/9.955 626 694 738] 89 259 376)509 252/553 .26919.955 539 435 360] 88 750 126/508 699/553 -270}9.955 448 685 234] 88 241 427/508 140/554 — . . 539 702} 616 534 666]115 993 247/539 086} 618) -218]9.960 9751 541 4rgl115 454 261 538 468] 616 é36 087 258/114 915 693/537 852] 6i2 .22019.960 52a1 1791 565/114 397 841/537 240] 613 -221|9.960 406 793 724/113 840 601/536 629] 612 222 Ee ie O33 ne 113 303 974536 aie .22319.960 199 649 149|112 767 959/535 405 G09 -224/9.960 066 881 19° 112 232 554/534 796] Gobf1.27419.955 098 766 191] 86 212 151505 947 54 636|111 697 758/534 190] 60741.27519.955 o12 554 ofo] 85 706 204/505 398 543 .271|9.955 360 443 804] 87 733 281/507 592/540 «2:9219.955 a 710. Bob 87 225 689/507 043/54 .29319.955 185 484 837 sd 718 646/506 495)548 22919. 31 787 310|110 629 985/532 978] Go241.277/9.954 841 647 030] 84 695 953/504 308/542 alo See CG i 325}110 0 : on 532 376} 604 on 3 ose ‘Sa a 077 ms B45 503 766 aaah |r-22919.959 511 060 318}109 564 631/531 772] 600 299 9-954 672 759 432| 83 687 879 503 2231643 -230|/9.959 for 495 687|109 032 859/531 172} 6boof1.280]9.954 589 071 553] 63 184 696 .23119.959 292 462 828}108 501 687/530 592] 598} -23219.959 183 961 1411107 971 115/529 974 291 .23319.959 075 g90 026/107 441 141}529 397) 5o 234 a ose 68 548 8851106 gir 764/528 781} 505 »23519.958 861 637 124|106 382 983/528: 186} 5o2 )-¢ 502 680/83o/5 —_—_——_— .28119 28219 9 954 505 886 897| 82 681 976/502 141/539 .954 423 204 921] 82 196 B35 501 6021538 9-954 341 025 086] 81 678 233/501 064 638) -954 259 346 853) 81 197 160/500 526/§36)| 954 178 169 684} 80 6n6 643\499 9901535 283 284 .285 .23619.958 755 254 138]105 854 997/527 594] 593 : .237|9.958 big 399 341}105 329 203 7 oor] 591 .238]9.958 544 072 138 - 800 202/526 410] 58oh1. .239|9.958 439 271 936/104 273 792/525 821} 58 -240\9.958 334 998 144/103 747 971|525 232} 58 219 Poo .28619.954 097 493 041| 80 176 653/499 455)532 285 a ops 014 306 388] 79 677 198 138 923/534) 288 9.953 9 639 190| 7 178 2751498 389|532 ' 289]9.953 56 460 915 8 679 886497 857|5201% -29019-953_779 781 029] 78 182 029/497 328/531 -24119.958 231 250 173)103 222 739}524 646} 586 -242/9.958 128 027 434}102 698 093/524 060) 585); -243}9.958 025 329 341|102 194 033/523 475| 583 -244)9.957 923 155 308)101 650 558/522 892| 582 .24519.957 821 504 750|101 124 666/522 310] 582 -291}9.953 701 599 000] 47 684 701/496 797/528 ap 5953 623 o14 299 71 184 a4 496 269}526 .293|9.953 546 726. 3 76691 635|495 7431528) -294|9,953 470 034 760} 76 195 8g2}495 215}625 .295|9.953 393 838 868] 75 700 677/494 Sgolfo3 ee ee ee . . I 1 I I I I I I L I I I I I I I 1 I I I I I I I I 1 190] bo} i .226|9.959 842 950 878)111 163 568/533 583] Go5f1.276)9.954 926 847 836} 85 200 806/504 853/545 I I I I I I I I I I I I T I I I I I I I I I I I Bir .246|9.957 720 377 084|100 605 356/521 728) 577}1.296|9.953 318 138 191| 75 205 987(494 167}525 Bir .24 oe be 771 728|100 083 6281521 151 5b, a 6 uss 242 932 ah 74 711 820/493 642|520 1246 9-957 519 688 100] gg 562 477/520 570] 57741.298|9.953 168 220 384] 74 218 198)493 122]523 1.249|9.957 420 125 623 99 041 907/519 993) 576}1.299|9.953 094 002 206] 73 725 o56}4g2 299 318k 1.250|9:957 321 083 716] 9 : 521 914/519 417| 57591 .300\9.953 020 277 150] 73 232 457|492 o81{519)f 4, LEGENDRE : Tables of the Gamma Function. Log. ra. Diff. I. II. Log. Ta. Diff. 1. 993 020 297 150 +952 947 044 693 "oe +952 802 055 503 Be 52 930 2 7 732 a Os one 186 oe ap 253 254 2, 965 513 2 18 6 166 759 ata 034 141 52 874 304 317 73 232 45 72 740 re 72 248 814 492 081 4g1 562 491 043 71 72 771/490 525 71 267 246/490 o12 79 777 234/489 495 85 739|488 ds 906 758488 i 9 798 ze 10 289 822 3209/4 68 334 aides . +952 +992 ‘oe -952 - iS 856 ins » 2 -902 241 258 -902 193 Be 312 ee 106 489 795 -952 039 614 198 -951 973 224 015 St go7 318 742 51 Bi 897 874 0 god 9 “9 ‘9 ei) ‘63 gro b 8 a7 847 Hie 486 429) 50 485 aoe 71485 4i4 361 5 17 ed 875 5 66 3go 1 f 65 905 273 65 420 868 64 936 64 453 63 168 283 I I 333 I i 536 655 1 585 048 379 522 041 986 459 oe 996 391 472 905 909 216 .9d -95 63 006 386 62 62 61 89}479 907 61 479 410 9-9/9 ob 514 go2 269 8 B53 4 ale 805 182 ; 9 799 338 9-949 709 960 a 2 deed 335 58 43 244 474 777 3128/4 6/48 a 25114 47 Se B44 “ue 17 9034 31 5141.356/9-949 663 048 Ate 616 600 9-949 570 617 9-949 525 ogg 9-949 480 043 156 924 839 020 811 ‘ 449 ie 18 819 45 055 ac 44 592. 065 3 391 322 3 37 655 9 ot 4g 9 261 50 POO OS rie) 9- 949 435 451 746 365 206 807 7°9 44 129 381 43 665 1 : 205 3 2 944 os 2 383 5 256 WO hS Oo 19-219 422 19 17 59 9 13 —s -949 096 333 Ode ob 888 453 581 634 156 692 Choose 8 o14, 5 354 fo po 324 3 859 7 891 8 =~ ee Eh 702 DAN ESN 1 822 8 33 362 2 off jo 444 5 4 39 985 904 ree 070 rie Bar i38 612 9 diss 156 oe 37 699 897 214 221 062 154 (a8 607 ogg 448 51035 299 4 6 584 is ae 393 120 B60 63 634 899 803 372 612 746 585 831 ai 825 434) 60 604 342 60 125 485 13 22 29 ee 030 i 934 58 6 691 09 Bld 7 44o 58 214 705 oe | 59 938 241/475 Bi 2 41149 274 262 267/495 2 9786 7811475 003] 4 56 311 778/474 515 690 274 053 et ae 9° 2) 183 8 469 .767 a 55 837 263 55 364 232|4 8} 54 889 685 54 416 61 53 944 03 oad 586 102 476 991 485 ee Bee 48 821 835 8 784 po 3 47 803 ge 469 3:38 G5 15 S90 _ 223 9.948 640 1 165 092 605 193 570 675 536 60g 502 996 So oa OS oS ebsile 805}3 799 ay 4i4 223 092 576 928 605 265 S23) Be Sys 244 048 788 648 36 333 5 89 38 35 428 13 2. tN SU. eee 34 065 623 33 613 340 33 161 499 i~ 031| 48441. 38 Beeeek i 46g 834 ‘8 8 ded Be 865 8 373 056 948 341 698 36: 415 823 201 362 351 2¢ 309 350 256 821 ef 204 763 323 53 471 93114 53 000 a 4 52 52 52 on ke 495|4 51 588 306 668 189] 4 “948 310 9 8 280 I 8 250 31 948 220 he -948 191 | a 525 904 363 464 845 253 41 559] 28 32 410 100 32 259 141 31 808 621]4 31 358 541 30 go8 899 30 459 694 30 o10 925 29 562 bg 2 29 114 694 7-228 ae 6 ae cor 226 8 oS 951 B14 4 191 153 1? 0 51 118 5921469 240| 475 50 649 os 468 465 50 182 si! 468 292 4g 712 29 49 244 477 467 818 467 349 .948 162 9 a8 13 974 3 8 10 0" .948 079 653 -948 052 971 Oopoe lo 4 331 i 105]2 Au 8 21 3 is 88, 26 436 ca 4/4 gi2 oA 409 003/404 39 39 527 798|457 652452 LEGENDRE : Tables of the Gamma Function. 5. ds Log. Ia.. Diff I. Tl. Log. Fe. Dif.d. | UL Ill. 1.4u0 8 Ba ng 411} 26 436 388/444 898 9.947 267 707 452] 4 702 338 jah 382] 39a 1.401 9-945 026 335 023] 25 gg1 510/444 449 9.947 263 a 114] 4 297 a 423 ggo| 390 1.40219.948 o00 343 513} 25 547 0611444 ae 9.947 258 427 158 43H 2 66]423 Goo} 3a} 1.4039 -947 of 4 796 452] 25 103 038/443 9.947 254 873 192 3 30 366 423 210} 390 L. 4o49- 947 949 9 O98 fui 414) 24 one ae 443/443 168} 425f1.45419.947 251 i 826] 3 007 156/422 820} 388 1-408]9.947 925 033 971] 24 216 275/442 143 Af -455}9-947 248 435 67a} 2 584 336)422 432] 388 1.406]9.947 goo 817 ae 593 | Bis G42 319 . 9-947 245 851 334] 2 16% go4|422 044] 38o) Le “407 9-947 Bn of otf 1 of 23 331 213/441 896 9 947 243 689 430] 1 939 Baldo 655] 386 1..408}9.947 ee 22 889 9 aes 4721 . 9-947 241 949 570] 1 318 205]421 270] 389 1 -hoglo. 947 830 22 shoe 44 of 1919-947 240 - rey 365 896 935]420 893 385) 1.4r6l9.947 808 308 89 22 006 796/440 630 119.947 239 "3h 430] 46 052|420 498] 385 1.411|9.947 786 368 21 566 es 4h4o 209 119.947 239 258 378|— 55 454/420 113) 383) 1.412/9.947 764 802 21 125 954 439 78 219.949 239 202 824 + 364 559 #9 730) 384 1.413|9.947 743 696 - 20 686 170]4 38 of a 9-947 239 567 383] 784 28 346] 383 1.414 9-947 722 ggo ee 20 246 80114 i 9-947 240 551 672] 1 203 eee 8 963 S| oe 1.415|9.947 702 743 19 807 849 Bs 24 Aik 9-947 241 555 Box! 1 6a2 se8l 418 380) 1..416]9.947 682 936 obo 19 369 315/438 116 .947 243 1 of 2 041 179/418 201] 381 1.41719.947 663 566 + 18.931 199/437 700 eae 245 a 284 2 559 abo 417 820] 382 1.4189. oF 644 635 36 18 4g3 499/439 985 19-947 247 658 464] 2 877 200/417 438] 348 1.419|9.947 626 142 037| 18 056 214/436 ih 919.947 240 545 664] 3 aah 638 417 960} 398 1.42019.947 608 085 823) 17, 1619 343 436 4 Wh 19-947 253 850 302] 3 911 698 416 682] 378) 1..422|9.947 599 466 480 ie 182, 886/436 ais 9-947 257 562 000 j ue 380/416 304) 37 1.4221. on ae 283 S94 746 8431435 633] 7219-947 261 Ggo 380 44 6841415, 34 1.42319.947 556 536 v6 311 2101435 2191 . 9-947 266 235 064} 4 es 610/415 %e 394 1.42419.947 54o 025 35 875 99 434; 809 7419.947 271 195 674 t 306 168/415 174) 396 1.42519.947 524 349 eee 15 441 182)434 foo} 4u 7519-947 276 571 832) 5 791 332 414 798) 375 1..42619.947 508 go8 368] 15 006 782 7519-947 28% 363 164] 6 206 130\414 423] 374) a 9-947 493 gor 586] 14 a 793 33 9 959 119-947 288 569 294] 6 620 553/414 4a) 394 1 ..428]9..947 ie 33 328 ie 14 139 212/433 oe 819.947 295 189 847] 7 034 602/413 675) 372) 1-42919.947 13 706 0391432 9 919-947 302 224 449 7 448 299/413 303} 371 1.430 Hee is, 83 542} 13 293 2 2721432 462 _4o- | .480}9-947 ae 692 726] 9 861 580/412 932] 374 1. 431|y.947 438 210 270] 12 840 gt2{43r 9-947 317 534 306}8 29% 512/412 558] 37¢ 1.43219.947 425 ano abs 12 408 959/431 er 19-947 325 808 818) 8 Gbq 0 o}4r2, 188} 370 1 .43319.947 f2 of 1 Ar0]43i. vig 9-947 334 495 888} 9 099 a8 4ir 818} 390)% 1.434|9.947 400 982 ae 1 265|430 942 9-947 343 bas 146] g 511 o76]411 448} 309; 1.43519.947 389 436 7a6| 11 ae 523/430 338 519.947 353 106 222] 9 922 524 4ir o80| 368} 1,436/9.947 378 321 201] ro 685 1851429 936 -947 363 028 746l10 333 Go4|410 712] 379] 2-43 9-947 367 636 016] 10 255 249 foe 33 x 2 373 362 35 Lo 944 ag 2 306) 1.43 9-947 357 386 767] 9 2 73 bee se 135 9-947 364 106 666) 11. 154 658/499 99 976 1 .439/9-947 34 555 353 Q 396 42 8919.947 395 261 324l11 564 634 ae 1.44019.947 338 158 dnd by 844 (da8 _4oc 9-947 406 825 g58)11_ 974 244 ae aid 365 1.44019.947 329 19a 630] 8 539 508/42 33 -947 418 600 202/12 383 488/408 89 1.442 nate 320 651 122] 8 me $72 fa 238 aoe 431 183 my 12 792 367/408 51, 1.443]/9.947 312 539 550] 7. er Boils 143 9-947 443 976 057113 200 881/408 150) 363) 1.444 oe 304 855 516 jab 945 19-947 457 ed 938|13 609 081/407 789] 36 1.445|9.949 297 ie i d S30 830 ut Be 4 9-947 40 785 969]14 016 818 sue aot |F-448|9-947 290 558 7 425. 954)" 9-947 464 Bo2 789]! faq aia}ion 063) ; zi 3947 abd Jog 6 9n7 i 25 562 9.947 ae a 831 305}4 o i 1.44819.949 a8 3 aly BB 299 8 169 9.947 5 49 2 334 15 238 004/406 ; 144g a ee 12 834 564 5 129 538 \ed 38 9-947 52g 296 338}15 644 345}405 g79} 35: 1.450/9.947. 207. 707 452} 4 702 338 9-947 544 g40 683/16: 050 324/405 620} | LEGENDRE : Tables of the Gamma Function. Log. Ta. Diff. 1. Il. u.| ; | Log. La. Diff. I. Wi. 9-949 544 g4o 683) 16 050 324/405 620} 35oft 8 83 I 35 903 111 331 9-947 560 gg1 007} 16 455 944)405 261 3Beft a. a3 893 i Has 36 oa 497 327 9-947 577 446 951] 16 861 205[404 goa] 35741 552l9. “948 9 : 636 055 = 679 3a (3 332 9-947 594 308 156] 17 266 109/404 3 5| 3584 9.948 315 607/37 067 280 32818 9-947 611 574 263! 15 670 652/404 189] 35611 .55419.948 9 3 382 883 37 454 676 32¢ 9-947 629 244 915} 18 074 83g9)403 831) 356]1 9.949 on 837 563/37 841 a 303 9-947 647 319 454) 18 478 age 4o3 475} 35641556 058 679 307)/38 228 483 32 9.947 665 iz 424] 18 880 145 408 ve 35411 ae, 99 os 096 7 4 a 038 614 | 3a 9-947 684 680 569} 19 285 264)402 765) 355f1 9.949 135 3-139 000 982 329 9-947 703 g65 833] 19 688 o2q|402 410] 353h1 9-949 174 53 es 39 386 441 324 9-947 723 653 862! 20 ogo 439/402 057] 3531 .560/9. “Blo 213 gto 410/39 772 193 327 9-947 743 744 201} 20 492 496 He aah 35241 .56119.949 253 682 583)40 157 281 323 9-947 764 236 797| 20 894 200/401 - me 35441 9.949 293 839 864]40 542 062 323) 9-947 785 130 997| 21 295 552 Hse of 34gft 9-949 334 38 926}40 926 520 326 9-949 806 426 549} 21 696 550}400 3515 9.949 305 308 346 41 310 655 321 oo $23 123 e99| 22 097 199/400 ah 35o0h1 9-949 416 619 101]41 694 464 323 9-947 850 220 298} 22 497 499 399 948] 350hr 49 458 313 565/42 077 952 321 9-947 872 pe 22 897 445)399 598} 34041 ee 500 391, 517 E ie, ve 322 9-947 895 615 240} 23 297 043 38 249| 348% .56819.949 542 852 634 42 3 He 322) 9.947 918 gta 283, 23 696 29213 or 34741 .569|9.949 585 696 595/43 226 483 319) 9'9.947 942 608 575) 24 095 193 398 348h1 9.949 628 923 078/43 608 683 319 9.947 966 703 768] 24 493 749 398 a 349 49 672 531 761/43 990 564 “320 9-94) ggi 191 515| 24 691 953/397 859} 345) . Be 76 8 522 305 44 Ae 126 320 9-94 016 °9 468] 25 289 812/397 514] 346 9.949 760 894 451|44 763 368 317 9-948 041 379 280} 25 687 326]3 333 168} 344 9-949 805 647 819]45 134 290 319 2-08 0674 ote 606 26 084 4941396 824) 344 9.949 850 782 109/45 514 895 318) 9.94 en 151 100] 26 481 318)39 6 480| 344 4g 896 297 604|45 895 183 “319 9-948 ne 632 418] 26 8797 408 306 136} 345 ete se fe Be ie ie 153 316 .3)9.948 146 510 216] 297 273 934 395 791| 341 9.949 988 iby 340|46 654 806 315 919.948 173 784 150 = 669 725/395 450} 341 9.950 035 122 146/47 034 143 319 9-948 201 453 875) 2 065 175/395 109] 342 0/9.950 082 156 289]47 413 105 313) 9.948 ae 519 050| 28 460 284/394 767 342 960 129 569 454 i 870 31 9.948 2 ar 0 9 334] 28 855 051/394 425] 340 G50 ie 36, 4 i A 262 Ee, 9-948 28 34 385) 29 249 476/394 085] 339 9.950 225 531 586/48 548 340 315 9.948 316 083 861] 29 643 561/393 746] 339 9.950 274 079 926/48 926 104 311 19.948 3 345 727 422) 30 037 307}393 407] 339 9.950 323 006 030]/49 303 553 311 9-948 375 764 729] 30 430 714/393 068] 338 9.950 372 309 583/49 680 6o1 313 719.948 406 195 443] 30 823 782/392 730! 337 Q. ge 421 990 274/59 057 518 312 9.948 an o1g 225] 31 216 512/392 393) 334 9.950 472 047 792/50 434 032 310) Ait 9.948 468 235 737} 31 608 g05}3g2 056) 336 g.g50 522 481 824|/50 8160 234 309) iz 9.948 499 844 642| 32 000 961/391 720] 334 9. .950 573 292 058)51 186 12 311 Bit 9-948 531 845 603} 32 $92 681}391 383] 334 9.950 624 478 184|51 561 709 310 Bir. 9. 948 564 238 284) 32 784 064/391 049) 336 9.950 676 03g 893}51 936 a 304 BY! -543/9.948 597 022 348! 33 195 113/390 713) 334 3 a. 950 7247 oft 74 52 311 308) H11.544\9.948 630 1 1a 461) 33 565 826)390 379} 332 9.950 780 28 52 686 ! 369) fit .945/9- -948 663 763 287] 33 956 205/390 044) 338 9-950 832 a qu ab 53 060 ois 308) Bit .546!9.948 697 719 492) 34 346 252/389 712] 33:f1.59619.950 886 036 360]53 434 982 “305 Bi) 94719. 948 732 065 744) 34 735 964 2 381) 33281 9. oe 939 471 343453 808 713 36 I. 9-948 766 801 708! 35 125 345}38g ofg} 332 9.950 ou 360 056 54 182 138 306) I. 9.948 Sor ¥ 7 063| 35 514 3941388 917) 331 9. gor 047 462 194{54 555 256 305) 1 9.948 837 441 44q| 35 ‘i 111/388 386] 33: 9 91 102 017 hbo 54 928 068 305 LEGENDRE : Tables of the Gamma Function. Log. la. Diff, I. II. IT. a. Log Ya, Dill. I. Il. 19. Gor to2 o17 450 156 949 518 ae 246 093 g18 870 304 963 516 380 379 815 434 oi 376 fod 32 581 855 155 BB ad by 9-991 9. on g: 9 rt e207" 3 9: 98 d Q. got .go! 2 abt glQ- 951 & 9.951 6 923} 5 8 068 foo 598 3308 Us 2 qt 6 484 5bo = 188 549 By Sag 232 615 5h a 58 639 AN 372 5oy 342 202 371 899 341 594 a0 383 369 {81 371 <3 0|379 989] | 340 685| 302 370 082) 9 G94 36g 781 —- § 298 855 428 372 064 586 445 611 597) 519 516 118 95 2a 73 5 38 8 ‘9 7 .954 818 1 9.954 894 392 23! 954 970 436 180 .g05 046 835 412 73 18 93 548 99 73 go4 a3 74 261 809 74 618 798 74 975 505 75 331 92 75 688 oof 76 043 76 399 2 76 764 840 58}357 833 nee 550 a 268 356 98 356 07 356 foal: a 356 14] 355 869 5|355 589 355 308 Br o31 .gor 738 eee 945 9.951 85 2-251 &i5 oft 3 a 51 goq 998 oe ip ob 964 G 964 a3. 660 Ba 025 3 7 Shr "19° oe 086 a 4o7 9.952 147 468 960 9.952 209 055 go3 271 009 938 ‘59 008 95 59 378 23 5 4 62 ee 600 60 483 881 60 851 866 61 5 369 179 368 281 367 985 365 687 61 He ot 593367 3gu Gi 964 245366 62 on 830 08 330 768 396 018 o 52 45g 071 62 522 4g1 081 586 ie 143 52 680 426 525 952 914 Ope 934 52 BB 066 60 a ‘a gto 645 fo2 62. 684 331 63 ofS 536 63 41g 446 63 785 ob62 64 150 382 64 515 4og et 880 re 65 244 58 65 608 33h 65 972 593 pee *e 366 38 365 gto 365 616) 365 320) 365 oe 36 36 Ve 364 14 363 Be 363 567 os i a : a si 99° 9355 9 2 Bei; 591} 6 i ot 746 o12 3 ohh 191 128 66 336 160 - 436 ages A2i és 425 116 67 om = 363 2 362 238 362 ae 362 406] 2 362 115 368 880} - 018/368 582) 3 ‘oS 3 © DOOCO peers 367}9.955 Sgr .955 123 590 552 . 955 200 700 423 955 =e O68 355 984 045 Sass 434 254 443 Q. oF ie 684 662 565 527 9g 955 670 799 762 9.905 a 38. ogo 9-955 830 327 238 8 165 046]77 819 99179 g4o 77 109 871 77 464 623 78 193 29 78 529 219 78 880 865 19 234 235 19 ee 328 80 292 693 0993 148): 21 M6 370) 093} | 820 545 : 271 9-955 gic 619 91 55 ggi 264 9: oe 99 ae 56 042 261 a "356 153 3 610 541 9.956 335 310 699 ggt 9.956 317 361 2 399 764 212 a 35 iB fn 067 O56 268 Gab 286 80 644 964 80 gg6 opr 81 348 81 400 fs 82 051 314 82 402 221 82 752 855 83 103 219 83 453 310 380/99 956 6 649 973 596/83 803 132 9.956 732 876 728 ae os 819 m0 ae 413 956 got 531 382 4l9. 966 386 382 364 o7r 582 ogo 84 5o1 ol 84 850 289 85 199 726 85 58 201 84 ee Bir .G Bir. L. I. Fi 1. fr .G pr .6 1.6 I. ie 1.6 I. Bir .6 ait. Eng 1.610 I. I. ia is I. I. I. Te Us ir. I. I. Es t. 1.6 I. I. I. I. I. I. Tes I I 9}9-993 og — tte oe @ © © eo 8 8 ee ee lo, oe 311 .993 380 108 237 9-953 448 619 353 492 759 9-993 586 727 012 tg . 953 656 322 233 953 726 28 132 53 796 5: ie Sy a by 19. 833. 3988 307 03, 9-954 009 702 179 Boa a3 fo 7 4 182 5 226 ong 38 9-95) 234 9-9 9-954 298 875 ce 958 650) 68 14 cau 68 ae 46 68 873 004 Gg bh 255 69 (595 221 6g 955 899 yo 316 ae 70 676 395 71 036 4 71_395 94 7 754 & 92 113 g63 72 472 645 72 831 043 73 189 158 361 82 361 53 361 251 360 ee 360 360 391 391| 286 360 105 35g 81 359 534 359 a5o 358 96d 358 82 358 3 358 a 354 833 157 130 291 ie 026 609 1,04 ie 863 070 Cs 802 408 85 8g6 G08 86 244 349 86 592 022 86 939 428 87 286 569 ie 089 067 oe 722 Soc 702 55k 1 854 oe g5o 942 701 ine 031 719 58 121 083 .998 210 58 300 9: a 9: % 9 99 9s 2 9.9 9-9 9-9 9- ‘oF 9. 9 9: 9 9: = 9 95 9-9 9-9 9-958 391 245 195 oot 6549 : ee x a 633 442 g80 049 38 8 326 Bas 88 672 ie 89 018 2 ee 363 833 35/89 119 140 345 551 345 021 345 286) 265 8. LEGENDRE : Tables of the Gamma Function. Diff. J. II. fa. Log. Ta. Diff. 1. Il. 391 245 692 3 3g61344 234] 2618 .95019.963 345 058 894 107 641 803/331 602 481 989 088 i 630 343 973] 260fr. st ae 363 45a qoo 6997/1 of gt 8 405} 331 » 573 076 918 431 6031343 712] 26281 .q52lg. os 560 é a4 o82)1 2/331 11 958 664 508 301 975 3151343 450| 260}1.753!9. oe 668 ee 844]108 ést 7/330 872 .958 956 283 636 118 765}343 190 I. 5alg. 7 ay 721,108 966 i 330 62 | 705}9.958 me 8 402 for 61 955 342 929 1.75919. 983 3 bag 581 470]109 299 $48 |330 383/243 . =e g4o 864 er 92 804 884/342 669 1.756/9.963 995 878 848] 109 629 = 330 145)241 9-959 033 66g 24 sr 64 342 i solr. 7 ae, 364 re 596 614]10g9 957 g11)32g god) 2. 9.959 126 816 7 3 4g 964)342 154 d. 89. 364 215 464 5x6 110 287 815/329 663 9.959 220 306 Bi 9 93 832 115/341 892 1.759/9.964 325 752 340|110 617 478)}329 423 }1019.959 314 138 872! 94 174 007/341 635) 261]1. 1.760 2 36h 436 36g 818}110~946 go1)329 182 9.959 408 312 3 4 515 6421341 394 1.961 oe 547 316 Itt 276 083/328 941 9-959 502 828 Sat 3) 85 ey: 341 ef: ) 783} 688 592 4:9 611 605 oa 328 702 9-959 597 685 53 1 g 134134> 864 é a 197 826}111 933 726/328 463 9.959 ga 883 691 9; 295 8/340 6o4 fr. 2 131 552)112 26a 189/328 223 519.959 788 422 bel 35 95 89 se 340 347] 255]. 112 590 412/329 985 9.999 55; 302 271 219 949/340 992 112 918 397/327 947 9-959 980 522 aie 9% 560 oft 33g 836} 2 . 113 246 14 3249 B36 aan 077 082 261] 96 899 8 330 581| 255fr. 113 593 652/327 291 e g60 173 982 138] 97 239 (56 339 326 ‘ 113 goo 923/327 033 019.960 291 221 506 21 578 784/339 070] 252f1. afi 229 956/320 796/23 noes 368 800 380 gi7 854/338 818 : y 114 554 752/326 559 9.960 sr 718. mail 256 672/338 562 Ht. : 114 881 311/326 324 - gbo sea 274 906 28 596 234/338 311} 25491.973/9.¢ 4 28 115 209 see 326 087 0 140} 98 933 543 338 057 . ‘ 9 494 923]115 533 722/325 85, oe. 593 685] 99 271 602/337 802 . 028 345 115 859 73 325 617 0 861 775 B87 99 ae Goh 337 552 ~a7bl9. ie 250 888 218/116 185 190/325 380 961 384 9h 3 300] -777|9-966 367 073 408|116 510 570/325 146 6 331 62, 12 2 : 2356/3 oh 7789. i {83 583 978/116 835 6 324 g12 161 615 903/160 621 303]3 +779|9-966 600 419 6 94 117 160 628/324 678 262 237, S06 100 958 .og9 336 Bs .780/9.966 717 580 322 a i 306]324 443 363 i we Tol 644|336 295 ei 66.835 065 628]1 49} 324 7 eh 489 of Q Lot 6a ae 336 046 25 ae 68 952 875 394/1 33 26 ib 0/323 9 120 B88l101 g66 984/335 5 . 783)9. “98 7 071 009 33 118 455 8} 323 of 868 084 im 102 302 778/335 i RBS: -967 18g 467 2 f 118 781 a 323 bi 779 390 650}102 638 324/335 ag6 85]9-967 308 248 954/119 105 194/323 an 873 028 974 102 973 620 334 046 BB 6 42 35 Br 119 428 475/323 o 976 002 te 103 38 666}3 : -248]t 784 a 967 94 as 626 an “St Aas 322 Bu : 079 311 260/103 643 465 334 i 788/19. 98 eee 34 148]120 3 339|322 586 1-739 +962 182 954 725]103 978.016/334 304] 248]1. 780/09. 98 1. The .962 286 aaa acs 104.312 320/334 056 1.790 to a a °Q ° ee FEES s S CSOOOOS a rae) Ow 22 oO (0 7 ) 7 786 608 487]120 925]322 355}2 7 997 005 hia 120 Bs 280]322 124 391 245 o61}104 646 He 6}333 807 “791 i9 968 027 724 6gafi21 oft fof 321 Bod 230 3 9-96 962 98 8g1 434/104 980 183)333 563 +7929 968 148 766 096} 121 363 298|321 oo 871. 626 105 313 746/333 318 ; 3! 968 270 129 3g4} 121 gpa 321 434 706 185 366}105 647 064|333 068 7949-968 391 814 356} 122 96]321 206 8i1 832 430}105:980 132/332 822 79°,9 968 513 820 752}122 3aq ae 320 976 917 812 562/106 312 954/332 579 7989 Si 636 148 354 122 648 578/320 748 024 125 516/106 645 533/332 335 : 284.9 38 968 758 796 932/122 969 326/320 : 130 7971 049/106 977 868/332 089] 2 9.968 881 766 258]123 289 846/320 291 107 309 957/331 846 8 969 005 056 ro4 123 610 137/320 otf , 00,9. 69 128 666 aqt| 123 g30 201/319 836 9-903 237 748 917 9. 963 345 058 BoA 4j107 641 0313 331 6o2 LEGENDRE : Tables of the Gamma Function. Log. ra. Diff. I, Il. II. Log. Ta. Dif. 1. I. .800 801 802 .803}9.969 -804 .805 . 806 .807 .808 809 810 811 812 813 814 815 9.969 128 666 24X 9.969 252 596 442 9-969 395 B46 479 39 Sot 416 126 .969 626 305 155 66 751 513 341 9-989 877 ofo 9-970 002 886 9-979 129 090 9-979 259 533 9.970 382 333 g-970 5og 452 9.970 638 838 9-970 764 641 9-979 892 711 9-971 021 099 123 930 201 124 250 039 124 569 647 124 02 125 208 18 125 529 116 125 845 Bar 126 164 29 126 482 Bee 126 800 582 127 118 386 127 435 gb6 127 753 322 18 o7o 455 128 387 364 128 319 836 319 610 319 382 319 154 318 930 318 705 318 478 318 253 318 030 317 804 317 580 317 356 317.133 316 gog 316 686 316 463 226 228 225 22, 22 227 235 233 226 224 224 223 224 223 223 222 9-975 712 596 5o9 9.975 852 me 480 9-975 992 205 21 9.976 132 472 596 9-976 273 048 4o7 9.976 413 932 438 9-976 555 124.477 9.976 696.624 313 9.976 838 431 = 9.976 980 546 534 9-977 122 968, 499 .977 265 697 41 ee 408 733 oe 9-977 552 075 290 9-977 695 723 822 839 b:8 493 139 649 881 139 958 939 140 267 379 t4o 545 811 140 884 031 14t 192 039 1141 499 836 14t a 422 142 114 9 142 far oe 142 728 920 143 035 667 143 342 204 ie 648 532 143 954 651 144 oot ee 308 850 308 642 308 432 308 220 308 008 ao7 997 307 586 307 399 307 166 306 955 306 747 306 53 306 326 306 119 305 gio 305 9703 -84t 842 843 845 .816 819 818 819 .820 821 .822 .823 824 -825 826 829 828 .829 .830 831 . 832 .833 834 ,835 .836 837 838 839 840 , £971 149 803 Bast 278 823 9-971 408 160 9-971 537 813 9-971 667 781 7 798 obo ee 928 665 9-972 059 ore .972 190 80g oe 322 353 .972 454 212 Sone 586 385 Go2 9-972 718 872 59 9-972 851 673 410 9-972 984 a dee -973' 118 215 boo Meee 251 956 S42 9-973 386 o10 425 9-973 520 397 031 9.973 655 056 142, -973 79° 047 gan 925 351 9-974 060 {38 521 294 864 O1o 510 143 689 927, 638 $42 o15 342 309 699 2 a 255 186 465 9-974 9-974 SOO 3st EN oe = © cr LD ew <2 Or 704 050 129 020 S12 12g 336 754 129 652 973 129 968 ie 130 284 146 130 599 500 130 aa 633 131 229 546 131 544 238 131 858 911 132 172 964 132 486 S59 132 800 811 133 114 406 133 427 784 133 740 942 134 053 883 134 366 606 134 679 111 134 ggt 400 135 303 473 1135 615 329 135 926 967 136 238 390 136 549 598 136 860 5g0 139 rat 368 134 481 931 139 792 270 138 102 316: 241 316 019 315 797 315 596 315 354 315 133 314 913 314 oe 314 473 314 253, 314 033 313 814 313 595 313 378 313 158 222 222 221 222 221 220 221 219 220 220 219 219 2179 220 217 819.979 738 51 9-977 3 32 9-977 983 939 0 ae 128 22 i 9.978 273 a 097 978 418 554 102 978 564 036 225 978 709 823 978 bse gt4 979 002 311 979 149 o1t 979 290 015 979 443 324 979 590 935 220 882 002 375 794 053 947 87 06 ae +979 967 009 oF 9.060 035 591 388 Q- 9: 9: 9. 9. 9. 9: 9- co 144 566 264 144 891 © 145 197 145 482 123 145 486 g95 146 ogt 662 146 396 120 146 700 393 147 004 19 147 308 259 611 8q4 g15 324 218 548 -521 56 824 38 5a 38 305 495 308 286 305 078 304 872 304 667 304, 458 304 253 304 046 303 840 303 635 303 430 303 224 303 021 302) 815 302 612 312 ght 312 Be 0 312 312 289 312 073 31r 854 311 640 423 311 311 208 310 992 310 478 310 Bhs 310 348 310 134 30g 920 218 218 216 216 219 214 217 ad 216 214) 215 215 214 214 213 .980 184 415 +992 3.080 333 Bho. 468 9.980 te O72°171 9.980 632 793 778 9.980 782 739 386 80 933 072 791 ee 283 00 ae 9.981 234 648 183 9.981 385 885 764 9.981 537 428 333 -981 689 269 688 eer Bi, he 628 9.98: 993 853 950 82 146 596 455 92. AAO ot 9.982 299 638 941 126 gg6 fag Jo 731 604 150 033 698 150 335 405 150 637 150 938 151 239 151 540 151 841 152 141 152 442 152 742 153 042 486 153 342 264 000 3g2 581 560 355 g4o 322 505 ee et ee Pe ee me Dk) am De Pk ent dm dk) dg ented) nt | et — . .846 84 ‘3i8 849 .850 DOGSCS HOSS .975 157 089 878 75 299 502 211 75 434 224 251 5 573 255 785 95 712 596 Sq9 IS ~ . WDOoS gg . At 138 412 333 138 422 o40 139 031 53 139 340 814 309 707 30g 494 4|309 280 30g 06 308 856} 213 214 213 211 21 eo oo CoN 319.982 452 981 208 9.982 606 623 056 9.982 760 564 285 9.982 914 804 So 9-983 069 344 086 53 fr B18 153 g41 229 154 240 4og 154 ee 392 154 838 173 302 407 302 204 302 001 301 797 301 R33 301 392 301 19 300 98 300 786 300 585 300 382 300 183 299 981 agg 781 299 581 299 381 299 ‘180 298 983 298° 781 298 585 Il. ai4 210 212 212, 211 aur 209 QUI 211 208 210 2009, 2098 269) 2071 al 209 208) 206 205) 209) 205 207) 206) 205) 205 206 203) 206) 203} non) 203 203) 204 202) 203} 203 201 202 201 203) 199 202 206. 200 200 207 19] 202 196} RPE 201 139 649 881 10. LEGENDRE : Tables of the Gamma Function. Log. Ta. Dif. I. lI. qt. Log. fa. Diff. 1, ii, — et woe wpowo mdm met matte tr ~ 8 « « be « « @ w foe oe oe ko Mw Ke PAB Cn +Qoo -go1 -Qo2 -go3 1.905 ae eeeee. a SST OOOGO OOK 83 069 344 085 = 383 oe fc 259 -983 39g 319 01 9.983 53h oh oe 9-983 690 484 9.983 846 318 B08 84 002 847 9 rl 984 159 74 23 9-984 316 398 709 9-984 473 620 003 9-984 63 br 138 300 84 78 88 953 4o1 Q. 9-984 ban 265 110 9.985 105 473 232 9.985 264 197 570 9-985 = my 929 Fag 114 9.985 oe as 929 9-985 got 953 180 9.986 062 135 672 2.08% 222 613 211 9-9 05 814 16 9. 388 i 469 954 9-987 029 ¢ 419 820 )-987 191 663 571 334 201 a6 517 031 g61 7 680 156 215 ; 843 573 586 38 007 283 882 -988 171 286 g11 2: 988 335 582 484 .988 500 ae 4o7 a. 388 665 oSo 492 9-988 830 222 548 9-988 995 686 384 9-989 161 441 810 9-989 327 488 638 9.989 493 826 676 ara bees OO} 9-989 660 455 737 -989 827 345 630 . 989 994 586 168 g-ggo 162 087 162)1 9-999 329 878 424)16 9:99° ion 969 765 Q. ggo 6 > 330 9-99° 834 gg1 34 9-991 003 942 388 9.99! ia 182 192 154 838 1953 155 136 758 155 435 142 BB 333 329 156 031 319 156 156 329 108 108 31156 626 700 00 156 g24 096 157 221 204 157 518 2979/2 157 815 to1 158 111 70 158 408 io 158 704 338 159 000 35 159 2g6 188 159 Sot 815 159 ae 251 160 182 492 160 477 539 160 772 391 161 067 050 161 361 20 161 655 9 161 949 eh 162 243 751 162 534 a 162 830 945 163 124 254 163 4197 391 163 710 206 164 003 029 164 295 os 164 5Bq 164 86s 285 165 172 056 165 463 836 165 755 426 166 046 828 166 338 038 166 629 061 166 gtg 893 167 210 538 7 500 994 2 Br 168 081 341 168 391 22 s 168 950 45 168 950 454 i6g 239 1 ea 169 5B 298 298 2.98 297 297 297, 297 297 2b 296 2095 295 295 ao 295 294 294 294 294 294 293 293 293 293 293 292 292 292 oj 3]292 2g1 291 291 2g1 2g1 2gt 290 832 290 290 290 290 269 O 83 28 585 384 184 988 291 992 396 198 003 > 804 2968 608 296 413 296 216 021 826 630 436 241 047 852 465 272 079 885 694]_1: 500 309 119 925 733 544 350 162 97! 780] _1¢ 5go} 16 4o2 210 023 832 290 645 456 268 079 Sb 33 142 9°7 65g at eo _186 201 197 199 197 19 AGO 519-992 193 182 342 911 S12 528 682 635 853 030 023 914 508 192 098 gobi 634 872 9-99! 9-99! 9-991 9-991 9-991 169 528 16 819 83 ij7o 106 653 170 395 238 170 683 636 170 971 849 “198 195 15 ‘9 194 1gI 919-992. 5 ; Me 491 666 50 194 686 355. 9.992 365 946 228 9.992 537 493 gia -992 999 329 31 Ste bee ‘5 156 053 862 28% 226 45g ES 399 543 6 572 814 5h 746 392 oo2 20 215 810 ae: 80341 4 2 9-994 163 9-994 44 i co 994 dis te 063 9-994 793 723 969 9-994 9 2 aba 148 9.995 14 125 418 9: «995 321 253 794)" 9-992 9. )-993 9 992 9-993 9-993 9- 29° 9-993 9 4 9-994 294 363 959 1 345 res z= 206 16: 6 383 995 ei -998 562 113 113 3 740 514 058 a9 rae 29 290 97277 415 te 456 9 14 636 wee 3) 484)1 60 816 66 ei aaa BS sa seeks 7 s Bs 8 028 611 786|1 uy 171 259 873 17t 549 714 171 835 391 172 122 843 172 4to 131 192 69) 234 172 984 153 4j173 290 iio 173 5 5by id 84 As 74 ee 995 a 701 814 174 G87 451 175 272 gob 175 558 199 175 843 270 176 128 179 76 a9 gos 178 697 454 Tae ohh e 981 821 alee 266 006 550 o10 833 836 178 119 481 1978 4oo 945 178 684 232 178 969 335 7179 250 266 199 533 o12 ee 8:5 583 097 973 180 380 187 180 662 221 180_944 079] 6/288 05 238 He 288 585 288 398 288 211 288 026 287 8411184 oe boy 287 472 287 288 287 103 286 oF 286 919 ? 286 i 0/286 368 286 185 3/286 0021783 285 8i9 285. 63 285 455 285 273 285 091/185 284 gog 284 729 284 546 284 367 284 185/718) 284 a 283 826] ;% 283 645 4041199 997 242 338 BiB 9 3 540 094 a 721 561 903 340 o 085 iho 284 ie 181 225 758 181 507 260 51182 386 & 182 069 a8 182 380 706 267 7190 990 450 422 633 334 816 529 oe +000 000 000 000 SWOO OD POOOOO POO OOD POO OOO [OO © SESS RSLEe 2 ool te 631 500 182 gt2 11 391183 toa 56: 283 28 ae 4" 282 282 3go 281 858 281 326 280 4 280 183 492 82 183 aes 920 283 282 be 81 282 034 281 502 280 280 bg 280 o 283 28 282 Fs 282 21 281 679 86}281 14 on 280 279 ov6 LECTURE SERIES (continued). x. 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Price 5s. net, On Torsional Vibrations in Axles and Shafting. By Karz Prarson, F.R.S. Issued. Price 6s. net. i. It. IV. Vv. An Experimental, Study of the Stresses in Masonry Dams. By Karu Pearson, F.R.S., and A. F. Campsent Ponuarp, assisted by C. W. Wueen, B.Sc. Eng., and L. F. RicHarpson, B.A. Issued. Price 7s. net. On a Practical Theory of Elliptic and Pseudo- elliptic Arches, with special reference to the ideal Masonry Arch. By Karu Pearson, F.R.S., W. D. Reynoups, B.Se. Hng., and W.F. Sranton, B.Sc. Eng. Issued. Price 48. net. VI. VII. On the Torsion resulting from Flexure in Prisms with Cross-Sections of Uni-axial Sym- metry only. By AnpREw W. Youne, HE. M. Ex- DERTON and Karn Pearson, F.R.S. Issued. Price 7s. 6d. net. Questions of the Day and of the Fray. I. The Influence of Parental Alcoholism on the Physique and Ability of the Offspring. A Reply to the Cambridge Economists. By Karn Prar- son, F.R.S.. Price 1s. net. Mental Defect, Mal-Nutrition, and the Teacher’s Appreciation of Intelligence. A Re- ply to Criticisms of the Memoir on ‘ The Infiu- ence of Defective Physique and Unfavourable Home Environment on the Intelligence of School Children.’ By Davin. Heron, D.Sc. Price 1s. net. s Tl. Ill. An Attempt to correct some of the Misstate- ments. made by Sir Vicror Horsury, F.R.S., F.R.C.S., and Mary D. Srurer, M.D., in their Criticisms of the Memoir: ‘A First Study of the Influence of Parental Alcoholism,’ &c. By Karu Pearson, F.R.S. Price 1s. net. The Fight against Tuberculosis and the Death- rate from Phthisis. By Karu Pearson, F.R.S. [Out of print. Social Problems: Their Treatment, Past, Present and Future. By Kart Prarson, F.R.S. Price 1s. net. Tracts for I. The Digamma and Trigamma Functions (to assist the summation of series in products of inverse linear factors). By HLeANoR Parrman, M.A. Price 3s. net. II. On the Construction of Tables and on Inter- polation, Part I. Uni-variate Tables. By Karu Prarson, F.R.S. Price 3s. 9d. net. VI. | Eugenics and Public Health. Lecture to the York Congress of the Royal Sanitary Institute. By Karu Pearson, F.R.S. Price 1s. net. VII. Mendelism and the Problem of Mental Defect. ‘I. A Criticism of Recent American Work. By Davip Heron, D.Sc. (Double Number.) Price 2s. net. VIII. Mendelism and the Problem of Mental Defect. Il. The Continuity of Mental Defect. By Karn Pearson, F.R.S., and Gustav A. JAEDERHOLM, Ph.D. Price 1s. net. TX. Mendelism and the Problem of Mental Defect. III. On the Graduated Character of Mental Defect, and on the need for standardizing Judgments as to the Grade of Social Inefficiency which shallinvolve Segregation. By Karn Pzar- son, F.R.S.. (Double Number.) Price 2s. net. The Science of Man; Its Present Needs and Future Prospects. Being the Address to Section H, British Association; 1920. By Karu Prarson, F.R.S. Price 1s. 6d. net. Computers. On the Construction of Tables and on Inter- polation. Part Il. Bi-variate Tables. By Karu Prarson, F.R.S. Price 3s. 9d. net. | III. IV. Facsimile Reissue of Legendre’s I-Function Tables. Price 3s. 9d. net.