M. : " , , ºx. §§§ º º ºxx. 38888. ©ºº º § ©º ©ºººººº. 3& flºº º 4- i f | i ; { t f tºº IITUTITUTIII]TºllTºllTlºſ º (QA 4/4, 7 , S3, 5 CONTRIBUTIONS TO MATHEMATICS, COMPRISING CHIEFLY THE RECTIFICATION OF THE CIRCLE T0 607 PLACES OF DECIMALS, BY W I L L I A M S H AN KS, HOUGHTON-LE-SPRING, DURHAM, LONDON : G. BELL, 186, FLEET-STREET; MACMILLAN & Co., CAMBRIDGE; ANDREWS, DURHAM. 1853. PRINTED FOR THE AUTHOR, Durham : Printed by George Walker, No. 6, Sadler-Street. TO WILLIAM RUTHERFORD, ESQUIRE, L.L.D., F.R.A.S., ROYAL MILITARY ACADEMY, WOOLWICH. MY DEAR SIR, I know of no person to whom I can, with so great pleasure, so much propriety, and such deep gratitude, inscribe this small volume as to you, from whom I received my earliest lessons in numbers; and I earnestly wish it had been something more worthy of notice that the Pupil was presenting to the Master, than the present “ContRIBUTIONS To MATHEMATICs” can pretend to be. Still, I venture to indulge and to express the thought, that whatever proves the firm determination of any of Great Britain's Mathematicians not to allow themselves to be outstripped by their Continental neighbours, even in calculation, redounds, in its measure, to their own credit, and also affords pleasure and satisfaction to all who feel interested in excellence of this kind. You, Sir, have laboured long, ardently, and most successfully in the Study of Mathematics, and have evinced, in nearly every branch of that beautiful but abstruse science, such clearness and depth of thought as are rarely met with. This however is not all. We seldom indeed find profundity united with great facility of "computation;–but you happily combine both in a very eminent degree. I regret my inability adequately to convey to you the heart-felt sentiments of esteem, gratitude, and respect with which I am, My dear Sir, Your sincere and obliged Friend, THE AUTHOR, Houghton-le-Spring, Feb. 28, 1853. *mºnº º PR E E A C E . TowARDs the close of the year 1850, the Author first formed the design of rectifying the Circle to upwards of 300 places of decimals. He was fully aware, at that time, that the ac- complishment of his purpose would add little or nothing to his fame as a Mathematician, though it might as a Computer; nor would it be productive of anything in the shape of pecuniary recompense at all adequate to the labour of such lengthy computations. He was anxious to fill up scanty intervals of leisure with the achievement of something original, and which, at the same time, should not subject him either to great tension of thought, or to consult books. He is aware that works on nearly every branch of Mathematics are being published almost weekly, both in Europe and America; and that it has therefore become no easy task to ascertain what really is original matter, even in the pure science itself. Beautiful speculations, especially in both Plane and Curved vi Geometry, have, even of late years, been pushed to a very great extent in our own country, without much regard being paid, as to the probability of their ultimate and direct utility. The Doctrine of Impossible or Imaginary Quantities, which certainly long perplexed Mathematicians, has also lately re- ceived a proper share of attention from men of genius. The Integration of Quantities seems to merit farther labour and research ; and no doubt this important and abstruse branch will, by and by, obtain due consideration, and we shall have important simplifications of, and additions to, our already large stock of knowledge. Holding sentiments somewhat similar to the above, and having, as before stated, occasionally had spare moments from the duties of an arduous profession, the Writer entertains the hope, that Mathematicians will look with indulgence on his present “Contributions” to their favourite science, and also induce their Friends and Patrons of Mathematical Studies, to accord him their generous support, by purchasing copies of the work. Dr. Rutherford, of the Royal Military Academy, Woolwich, vii a distinguished Mathematician, has kindly co-operated with the Author in separately calculating and then collating the value of ºr to 441 places of decimals, so that accuracy is en- sured at least to that extent; and it is confidently hoped no error has crept into the remaining 86 places. It is proper to state, that the talented writer just mentioned lately sent a “Paper on determining the value of ºr,” to the Royal Society of London, an Abstract of which has just been published in the Proceedings of that Learned Body, wherein are given the values of tan "+, of tan 'ºr, and of ºr, to 441 places of decimals: also, the extension of the same, by the present writer, to 527 places. In the following pages, the ratio of the circumference of a circle to its diameter, is determined to the great extent of 527 places of decimals. The values, of the base of Napier's Logarithms, of the Napierian logarithms of 2, 3, 5, and 10, and of the Modulus of the Common System, are given to 137 places of decimals, except that of M, which extends only to 136. viii A few of the higher powers of 2, as far as 2.”, having been obtained in the calculation of tan "+, conclude the volume. It only remains to add, that Machin's formula, viz., + = 4 tan '#' – tan '##, was employed in finding ºr –and that the values of tan '#, and of tan -º are found and given separately ; as also the value of each term of the series em- ployed in determining these two arcs. Houghton-le-Spring, Feb. 28, 1853. Since the above date, and while the following sheets were in the Press, the Author has extended the values of tan --. and of tan '# to 609, and the value of ºr to 607 decimals; which extensions are given in the proper place. Should Mathe- maticians evince a wish to possess the eaſtended values of each term of the series used in finding these arcs, a few supple- mentary sheets might soon be furnished. April 30, 1853. LIST OF SUBS GRIBERS. No. of Copies. W. Whewell, D.D., Master of Trinity College, Cambridge - sº amº M. A. C., Houghton-le-Spring tº º sº - º W. Rutherford, Esq., L.L.D., F.R.A.S., Royal Military Academy, Woolwich - Rev. Temple Chevallier, B.D., Professor of Mathematics, University, Durham - Hon. & Rev. John Grey, M.A., Rector of Houghton-le-Spring - * Augustus De Morgan, Esq., Professor of Mathematics, University College, London e- * º s tº º sº Rev. P. Kelland, M.A., F.R.S.E., Professor of Mathematics, University, Edinburgh - sº q=º º º ass tº a G. B. Airy, Esq., F.R.S., Astronomer Royal, Royal Observatory, Greenwich - John Stephenson, Esq., Colt Crag, Northumberland * tºº tº Nathaniel Ellison, Esq., Morton House, Durham - * -8. * º S. Fenwick, Esq., F.R.A.S., Mathematical Master, Royal Military Academy, Woolwich - gº gº tº tºº e- * . Rev. Charles Whitley, M.A., Hon. Canon, & Vice-Master of University College, Durham º «º iº gº gºe gº tº Robert Rawson, Esq., Highland House, Portsea, Portsmouth gº gº R. Tatham, D.D., Master of St. John's College, Cambridge tºs & Sir J. F. W. Herschel, Bart., Master of the Mint, &c., &c., London - tº- 1 1 2 1 1 1. . . X No. of Copies. John Narrien, Esq., F.R.S., Professor of Mathematics, Royal Military College, Sandhurst - gº º * * * $º * > Rev. J. R. Young, M.A., Rector of Whitnash, Warwickshire º ſº James Laurie, Esq., Billiter-Street, London º gº sº tº W. Goodricke, Esq., Houghton-le-Spring º gº tºg tº Joseph Whitehead, Esq., Wash Brook Cottage, near Oldham, Lancashire gº H. W. Cookson, D.D., Master of St. Peter's College, Cambridge º tºº Rev. Bartholomew Price, M.A., Fellow and Tutor of Pembroke College, Oxford W. Finley, Esq., Durham - ſº tº gº º º Rev. Robert Walker, M.A., F.R.S., Reader in Experimental Philosophy, Oxford George Bell, Esq., Hexham - ſº ſº º * = tº Wilkinson Mathews, Esq., Q.C., 64, Brook-Street, Hanover Square, London - W. S. B. Woolhouse, Esq., F.R.A.S., Alwyne Lodge, Islington, London William Winship, Jun., Esq., Morpeth - ſº º #º sº Thomas Dixon Walker, Esq., Darlington º sº - sº Mr. George Andrews, Durham s gº º º gº TABLE OF CONTENTS, PAGE. Introductory Remarks and Historical Notices.......... ............. xiii—xvi Explanatory Remarks and Formulae.................................... l + terms of tan "+, to 530 decimal places ........................ 2—31 — terms of tan "+, to 530 52 - - - - - - - - - - - - - - - - - - - - - - - - 31–61 + terms of tan '#, to 530 25 - - - - - - - - - - - - - - - - - - - - - - - - 61–73 — terms of tan "ºr, to 530 23 - - - - - - - - - - - - - - - . . . . . . . . . 73–85 Value of tan "+, to 609 places of decimals ..................... Value of tan "; to 609...... ...................................... $ 86–87 Value of ºr, to 607 places .......................... .................. - Explanatory Remarks and Formulae.... ............................... 88 Value of s, the base of Napier's Logarithms, to 137 places | 89 Values of Nap. logs. of 2, 3, 5, and 10, to 137 places......... Value of M, the Modulus of the Common System of Logarithms, to 136 places of Decimals ............... : s e º sº a º 'º e s e g is a º ºr e s is e e | Powers of 2, as far as 27**, commencing with 2**, and proceed- 90–95 ing 2**, 2**, 2**, 2**, &c. .............................. ..... - *** * --- * - - - - INTRODUCTORY REMARKS AND HISTORICAL NOTICES. THE PROBLEM, “to find the ratio of the circumference of a circle to its diameter,” has engaged the attention of Mathe- maticians from very remote times. The Greek Geometers and Arithmeticians, chiefly from their clumsy scale of notation, could not be expected to make any considerable progress in ascertaining the ratio in question: and indeed we may remark, by the way, that even in the Geometry of Curve lines at large, they did not and could not proceed to any very great extent. Until the time of Newton and Leibnitz, the limits of Mathe- matics were but contracted ; and though since, and by, their very extraordinary labours, great additions indeed have been made to the previous stock of Mathematical knowledge, yet we must admit that not very much has lately been done, or perhaps remains to be done, towards extending the boundaries of that department of human knowledge and research. It would not be of any service to recapitulate in this place what is already duly recorded as matter of history respecting the various Mathematicians, and the different processes employed by them, who have applied themselves to the solution of this xiv striking and curious Problem. Nor can we well afford space even to glance at the ignorant, presumptuous, and abortive attempts made at different periods “to square the circle !” In later times, Mathematicians—and they alone are competent to deal with such enquiries—have pointed out satisfactorily how to find the value of ºr ultimately by means of infinite series of various degrees of convergency, as will be seen in what fol- lows: but no one, so far as we know, has hitherto been able— and we are of opinion that it can never be accomplished—to ascertain the limit, strictly speaking, of the ratio under con- sideration. In other words, the circumference and diameter of a circle are incommensurable.* We proceed, then, to take up the history of the Problem since the year 1831. Previous to 1831, the value of ºr, as the late Professor Thomson of the University of Glasgow writes, in his work on the Differential and Integral Calculus, had been calculated “to the extraordi- nary extent of 140 figures ſ” We may here be permitted to indulge a smile at the learned writer's words, now that the ratio has been found to 607 places of decimals | In the year 1841, Dr. Rutherford, Royal Military Academy, Woolwich, a distinguished Mathematician, presented a paper to the Royal Society of London, which was published in their transactions, in which he gave the value of ºr to 208 decimals. * For full and interesting particulars, the reader is here referred to the History of this curious Problem, written by the profound Mathematician Professor De Morgan, and which is given in the Penny Cyclopædia. XV The formula he employed is += 4 tan '#– tan’; + tan '#. Subsequently it was found that the last 56 figures were in- correct, an error having crept into the value of one of the terms of the series employed. But of this talented writer we shall have to speak afterwards. The Mathematician who seems next to have engaged in the solution of this Problem is M. Dase, about the year 1846, then a young man of great promise, who used the formula "++ tan "++ tan "+. He found the value of ºr # = tan correctly, as was afterwards shown by Dr. Clausen, to 200 places of decimals, and communicated his result to Professor Schum- acher of Altona. Somewhere about 1847, the eminent Mathematician Dr. Clausen, of Dorpat, above-mentioned, turned his attention to this subject, and employing Machin's formula, + = 4 tan "4 — tan '#, and also the formula: = 2 tan *, + tan '#, he calculated the value of r from each of these formulae, and found it correctly to 250 decimals. The values of the four arcs and of ºr are given in No. 589 of the “Astronomiche Nachrichten,” published in 1847. In the earlier portions of the year 1851, the Author of this Volume, not then aware of M. Dase's, or of Dr. Clausen's labours, employed Machin's formula, given above, and calcu- lated the value of ºr to 315 decimals. Dr. Rutherford, in the same year, verified the Author's results, using also Machin's xvi. formula; and moreover pushed his calculations to 350 places of decimals. During the latter part of 1851, and the early months of 1852, Dr. Rutherford and the present writer ex- tended the value of z, the former to 441 places, and the latter to 527 decimals. In the months of March and April, 1853, the Author still further extended the ratio in question; and the value of ºr, given in this Volume, is, it is presumed, more extensive than has hitherto been determined, consisting of no less than 607 decimals. The values of tan '#, and of tan tº are given to 609 places. These values, then, have been care- fully collated, as far as 441 decimals, with Dr. Rutherford's results, and may be pronounced free from errors, inasmuch as each party worked independently of the other. The Author, therefore, is alone responsible for the accuracy of the additional 166 and 168 respective places of decimals. Whether any other Mathematician will appear, possessing sufficient leisure, patience, and facility of computation, to calculate the value of ºr to a still greater extent, remains to be seen : all that the Author can say is, he takes leave of the subject for the present, and deems the farther extension of this ratio a work of considerable difficulty, notwithstanding the assertions of some writers, who have evidently had little or no experience in such matters. EXPLANATORY REMARKS AND FORMULAE. mºm-mº- FROM Machin's well known formula, viz. # = 4 tan – I tan T' l the 5 239 ° value of 7, given afterwards, has been determined. It may also as well be stated here, that from Newton's series we have, —l 1 l l I l I l tan 5 = 5 - 3.5 + 5 - 7.3; +-gº - II;IT-H, &c.; l } l l l I 239 F.339 T323.93 + 5.2395 T.2397 + 9,2399 T2 &c. And, tan T' The value of each term of the above series employed in finding the two arcs is given separately, so that its accuracy may readily be tested; and no difficulty can possibly arise to Mathematicians, for whose perusal chiefly the following pages are intended, in comprehending all that follows. + TERMS OF TAN -1 #. 25.52 5 49.549 73.57 3 97.597 l 121.512 1 2 000064 0.56888 888888 888888 888888 888888 888888 888888 63 015384 615384 615384 615384 615384 615384 77101 176470 588235 294117 647058 823529 99 864380 952380 952380 952380 952380 134217 728 185 127900 689655 1724.13 793.103 260301 048242 424242 424242 371 456631 005405 405405 536347 135500 487804 781 874935 307377 1 148877 455961 1699 47.1557 2 528336 3780 5 I45.51 as To 106th DECIMAL PLACE. 3 888888 888888 888888 888888 888888 888888 888888 888888 888888 8888 615384 615384 615384 615384 615384 615384 615384 615384 615384 6153 4I 1764 705882 352941 176470 588235 294117 647058 823529 411764 7058 952380 952380 952380 952380 952380 952380 952380 952380 952380 9523 448275 862068 965517 241379 310344 827586 206896 551724 13793] 0344 424242 424242 424242 424242 424242 424242 424242 424242 424242 4242 405405 405405 405405 405405 405405 405405 405405 405405 405405 4054 878048 780487 804878 048780 487804 878048 780487 804878 048780 4878 777777 777777 777777 777777 777777 777777 777777 777777 777777 7777 8612.24 489795 918367 346938 775510 204081 632653 061224 489795 9183 498300 377358 490566 037735 849056 603773 584905 660377 358490 5660 632909 752140 350877 192982 456140 350877 192982 456140 350877 1929 07.0506 907695 003278 688524 590163 934426 229508 196721 311475 4098 67592] 253449 092304 923076 923076 923076 923076 923076 923076 9230 8555 01.1744 329067 416115 942028 985.507 246376 811594 202898 5507 12 93.7990 364026 425243 002739 726027 397260 273972 602739 7260 19625 419149 588135 953022 337662 337662 337662 337662 3376 29 850020 2.37398 25.1227 312987 654320 987654 320987 6543 45512 501444 315451 283056 037647 058823 5294ll 7647 69 547.193 218279 790724 669900 224719 101.123 5955 106489 465744 978948 3784.19 288086 021505 3763 163 35'7036 111885 232151 63701 1 002061 8556 251019 920837 273148 811228 357500 1980 386 331611 498127 055694 233357 8288 595446 887446 654544 556249 5790 918 990594 430942 943102 7427 1 420115 380.112 089607 8032 2197 071067 413084 0874 3 402823 669209 3846 5275 6956II 1773 8 187244 9183 12717 1220 19 7701 307 + TERMS OF TAN – , 25.52 5 49.549 73.57 3 121.512 1 l 145.5 145 888888 888888 888888 888888 888888 888888 888888 888888 846153 846,153 846153 846153 846,153 846153 846,153 846153 823529 411764 705882 352941 176470 588235 294117 647058 809523 809523 809523 809523 809523 809523 809523 809523 827586 206896 551724 137931 034482 758620 689655 1724.13 424242 424242 424242 424242 424242 424242 424242 424242 054054 054054 054054 054054 054054 054054 054054 054054 048780 487804 878048 780487 804878 048780 487804 878048 777777 777777 777777 777777 777777 777777 777777 777777 673469 387755 102040 816326 530612 244897 959183 673469 377358 490566 037735 349056 603773 584905 660377 358490 824561 403508 771929 824561 403508 771929 824561 403508 360655 737704 918032 786885 245901 639344 262295 081967 769230 769230 769230 769230 769230 769230 769230 769230 246376 811594 202898 550724 637681 159420 289855 072463 273972 602739 726027 397.260 273972 602739 726027 397260 623376 623376 623376 623376 623376 623376 623376 623376 209876 543209 876543 209876 543209 876543. 209876 543209 058823 5294ll 764705 882352 941176 470588 235294 117647 056179 775280 898876 404494 382022 471910 112359 55056] 440860 215053 763440 860215 053763 440860 215053 763440 701030 927835 051546 39.1752 57.7319 587628 865979 381443 198019 80.1980 1980.19 801980 1980.19 80.1980 1980.19 80.1980 76.1904 76.1904 761904 761904 76.1904 761904 761904 76.1904 390018 348623 853211 009.174 311926 605504 587155 963302 131363 001769 911504 424778 761061 946902 654867 256637 126712 396843 760683 760683 760683 760683 760683 760683 443091 905460 2409.25 619834 710743 801652 892561 9834.71 346337 460743 176821 1456 405188 120094 175467 939760 62015.5 033759 639922 480620 985194 2.16751 785246 741223 808962 406015 037593 984962 338336 126491 421751 098587 827931 001.459 854014 598540 641830 945240 616451 403126 315261 577840 567375 886524 596485 496974 112297 044389 967563 606979 040220 689655 478942 178760 389.221 83.1639 587063 58897] 940519 001342 746 273303 375665 297285 378284 679474 581115 161633 1 163615 953283 935444 429685 376366 467372 337525 1815 529984 261991 202737 496686 604078 285286 28344274.17853 872.326 2.13206 948298 245856 FROM 106th To 212th DECIMAL PLACE. 5 888888 888888 888888 888888 888888 888888 888888 888888 888888 8888 846153 846,153 846,153 846153 846153 846153 846,153 846,153 846,153 8461 823529 411764 705882 352941 176470 588235 294117 647058 823529 4117 809523 809523 809523 809523 809523 809523 809523 809523 809523 8095 793.103 448275 862068 965517 241379 310344 827586 206896 551724 1379 424242 424242 424242 424242 424242 424242 424242 424242 424242 4242 054054 O54054 O54054 O54054 O54054 054054 O54054 054054 054054 O540 780487 804878 048780 487804 878048 780487 804878 048780 487804 8780 777777 777777 777777 777777 777777 777777 777777 777777 777777 7777 387755 102040 816326 530612 244897 959183 673469 387755 102040 8163 566037 735849 056603 773584 905660 377358 490566 037735 849056 6037 771929 824561 403508 771929 824561 403508 771929 824561 403508 7719 213114 754098 360655 737704 918032 786885 245901 639344 262295 08.19 769230 769230 769230 769230 769230 769230 769230 769230 769230 7692 7681 15 942028 985.507 246376 811594 202898 550724 637681 159420 2898 273972 602739 726027 397.260 273972 602739 726027 397.260 273972 6027 623376 623376 623376 623376 623376 623376 623376 623376 623376 6233 876543 209876 543209 876543 209876 543209 876543. 209876 543209 8765 058823 529411 764705 882352 941176 470588 235294 l 17647 058823 5294 797752 808988 764044. 943820 224719 101.123 595505 617977 528089 8876 860215 053763 440860 215053 763440 860215 053763 440860 215053 7634 298969 072164 948453 608247 422680 41237] 134020 618556 701030 9278 1980.19 80.1980 198019 80.1980 1980.19 80}980 198019 80.1980 1980.19 80.19 76.1904 761904 761904 76.1904 76.1904 76.1904 76.1904 761904 76.1904 7619 752293 577981 651376 146788 990825 688073 394.495 412844 036697 2477 16814] 592920 353982 300884 955752 212389 380530 973451 327433 6283 760683 760683 760683 760683 760683 760683 760683 760683 760683 7606 074380 165289 256198 347107 438016 528925 619834 710743 801652 8925 155038 75.9689 92.2480 620155 038759 689922 480620 155038 75.9689 92.24 406015 037593 984962 406015 037593 984962 406015 037593 984962 4060 145985 401.459 854014 598540 145985 40.1459 854014 598540 145985 4014 822695 035460 99.2907 80.1418 439716 312056 737588 652482 269503 5460 1724.13 793.103 448275 862068 965517 24.1379 310344 827586 206896 55.17 28.1879 194630 872483 221476 510067 114093 959731 543624 161073 8255 464052 287581 699346 405228 758169 934640 522875 816993 464052 2875 910012 738853 503184 713375 796.178 343949 044585 987.261 146496 8152 872724 193788 819875 776397 515527 950310 559006 211180 124223 6024 302414 628801 939393 939393 939393 939393 939393 939393 939393 93.93 + TERMs of TAN -1 # 25.52 5 49.549 73.57 3 97.597 l IEI5, a 1. l 145.51.45 888888 888888 888888 888888 888888 888888 888888 888888 538461 538461 538461 538461 538461 538461 538461 538461 647058 823529 411764 705882 352941 176470 588235 294117 238095 238095 238095 238095 238095 238095 238095 238095 310344 827586 206896 551724 137931 034482 758620 689655 424242 424242 424242 424242 424242 424242 424242 424242 540540 540540 540540 540540 540540 540540 540540 540540 487804 878048 780487 804878 048780 487804 878048 780487 777777 777777 777777 777777 777777 777777 777777 777777 265306 122448 979591 836734 693877 551020 408163. 265306 735849 056603 773584 905660 377358 490566 037735 849056 298245 614035 087719 298245 614035 087719 298245 614035 672131 147540 98.3606 557377 049180 327868 852459 016393 307692 307692 307692 307692 307692 307692 307692 307692 550724 637681 159420 289855 072463 7681.15 942028 985.507 397.260 273972 602739 726027 397.260 273972 602739 726027 766233 766233 766233 766233 766233 766233 766233 766233 432098 765432 098765 432098 765432 098765 432098 765432 117647 058823 529411 764705 882352 941176 470588 235294 404494 382022 471910 112359 550561 797752 808988 764044 408602 150537 634408 602150 5376.34 408602 150537 634408 350515 463917 525773 195876 288659 793814 432989 690721 801980 198019 801980 1980.19 801980 198019 801980 198019 047619 047619 047619 047619 047619 047619 047619 047619 064220 183486 238532 IIO091 743119 266055 045871 5596.33 185840 707964 601769 91.1504 424778 761061 946902 654867 837606 837606 837606 837606 837606 837606 837606 837606 619834 710743 80.1652 892561 983471 074380 165289 256198 806201 550387 596899 224806 201550 387596 899.224 806201 150375 939849 624060 150375 939849 624060 150375 939849 598540 145985 401459 854014 598540 145985 401459 854014 992.907 80.1418 439716 3.12056 737588 652482 269503 546099 241379 310344 827586 206896 551724 137931 034482 758620 033557 046979 865771 812080 536912 751677 852348 993288 816993 464052 287581 699346 405228 758169 934640 522875 866242 038216 560509 554140 127383 535031 847133 757961 844720 496894 409937 888.198 757763 975.155 2795.03 105590 939393 939393 939393 939393 939393 939393 939393 939393 FROM 212th To 318th DECIMAL PLACE. 7 888888 888888 888888 888888 888888 888888 888888 888888 888888 8888 538461 538461 538461 538461 538461 538461 538461 538461 538461 5384 647058 823529 411764 705882 352941 176470 588235 294117 647058 8235 238095 238095 238095 238095 238095 238095 238095 238095 238095 2380 172413 793.103 448275 862068 965517 241379 310344 827586 206896 55.17 424242 424242 424242 424242 424242 424242 424242 424242 424242 4242 540540 540540 540540 540540 540540 540540 540540 540540 540540 5405 804878 048780 487804 878048 780487 804878 048780 487804 878048 7804 777777 777777 777777 777777 777777 777777 777777 777777 777777 7777 122448 979591 836734 693877 551020 408163. 265306 122448 979591 8367 603773 584905 660377 358490 566037 735849 056603 773584 905660 3773 087719 298245 614035 087719 298245 614035 087719 298245 614035 0877 442622 950819 672131 147540 983606 557377 049180 327868 852459 Olć3 307692 307692 307692 307692 307692 307692 307692 307692 307692 3076 246376 811594 202898 550724 637681 159420 289855 072463 7681.15 9420 397.260 273972 602739 726027 397.260 273972 602739 726027 397.260 2739 766233 766233 766233 766233 766233 766233 766233 766233 766233 7662 098765 432098 765432 098765 432098 765432 098765 432098 765432 0987 117647 058823 5294.11 764705 882352 941176 470588 235294 117647 0588 943820 224719 101.123 595.505 617977 528089 887640 449438 202247 1910 602150 5376.34 408602 150537 634408 602150 5376.34 408602 150537 6344 649484 536082 474226 804123 711340 206185 567010 309278 350515 4639 801980 198019 801980 198019 801980 198019 801980 1980.19 801980 1980 047619 047619 047619 047619 047619 047619 047619 047619 047619 0476 027522 935779 816513 761467 8899.08 256880 733944 954.128 440366 9724 256637 16814] 592920 353982 300884 955752 212389 380530 973451 3274 837606 837606 837606 837606 837606 837606 837606 837606 837606 8376 347107 438016 528925 619834 710743 801652 892561 983471 074380 1652 550387 596899 224806 201550 387596 899224 806201 550387 596899 2248 624060 150375 939849 624060 150375 939849 624060 150375 939849 6240 598540 145985 401.459 854014 598540 145985 401459 854014 598540 1459 290780 141843 971631 205673 758865 248226 950354 609929 078014 1843 689655 1724.13 793.103 448275 862068 965517 241379 310344 827586 2068 590604 026845 637583 8926.17 449664 429.530 201342 28.1879 194630 8724 816993 464052 287581 699346 405228 758169 934640 522875 816993 4640 783439 490445 859872 61.1464 968152 866242 038216 560509 554140 1273 06211] 801242 236024 844720 496894 409937 888198 757763 975.155 2795 939393 939393 939393 939393 939393 939393 939393 939393 939393 93.93 + TERMs of TAN -4 #, -1 25.52 5 49.549 73.57 3 97.597 l 121.512 1 I 145.51 4.5 888888 888888 888888 888888 888888 888888 888888 888888 615384 615384 615384 615384 6.15384 6.15384 615384 615384 294117 647058 823529 411764 705882 352941 176470 588235 952380 952380 952380 952380 952380 952380 952380 952380 241379 310344 827586 206896 55.1724 137931 034482 758620 424242 424242 424242 424242 424242 424242 424242 424242 405405 405405 405405 405405 405405 405405 405405 405405 878048 780487 804878 048780 487804 878048 780487 804878 777777 777777 777777 777777 777777 777777 777777 777777 346938 775510 204081 632653 0612.24 489795 918367 346938 584905 660377 358490 566037 735849 056603 773584 905660 192982 456140 350877 192982 456140 350877 192982 456140 934426 229508 196721 311475 409836 065573 770491 803278 923076 923076 923076 923076 923076 923076 923076 923076 289855 072463 768115 942028 98.5507 246376 811594 202898 726027 397.260 27.3972 602739 726027 397.260 273972 602739 337662 337662 337662 337662 337662 337662 337662 337662 654320 987654 320987 654320 987654 320987 654320 987654 235294 117647 058823 5294.11 764705 882352 941176 470588 112359 550561 797752 808988 764044 943820 224719 101.123 086021 505376 344086 021505 376344 086021 505376 344086 175257 731958 7.62886 597.938 144329 896907 216494 845360 198019 801980 198019 801980 198019 801980 1980.19 80.1980 190476 190476 190476 190476 190476 190476 190476 190476 770642 201834 862385 321100 917431 192660 550458 7.15596 336283 185840 707964 601769 91.1504 424778 761061 946902 068376 068376 068376 068376 068376 068376 068376 068376 892561 983471 074380 165289 256198 347107 438016 5289.25 062015 503875 968992 248062 015503 875968 992248 062015 60.1503 759398 496240 60.1503 759398 496240 601503 759398 854014 598540 145985 401.459 854014 598540 145985 401459 971631 205673 758865 248226 950354 609929 078014 184397 965517 24.1379 310344 827586 206896 551724 137931 034482 832214 765100 671140 939597 315436 241610 738255 033557 522875 816993 464052 287581 699346 405228 758169 934640 885350 318471 337579 617834 394904 458598 726114 649681 031055 900621 118012 422360 248447 204968 944099 37888.1 939393 939393 939393 939393 939393 939393 939393 939393 FROM 318th To 424th DECIMAL PLACE. 9 888888 888888 888888 888888 888888 888888 888888 888888 888888 8888 615384 615384 615384 615384 615384 615384 615384 615384 615384 6153 294117 647058 823529 411764 705882 352941 176470 588235 294117 6470 952380 952380 952380 952380 952380 952380 952380 952380 952380 9523 689655 1724.13 793.103 448275 862068 965517 24 1379 310344 827586 2068 424242 424242 424242 424242 424242 424242 424242 424242 424242 4242 405405 405405 405405 405405 405405 405405 405405 405405 405405 4054 048780 487804 878048 780487 804878 048780 487804 878048 780487 8048 777777 777777 777777 777777 777777 777777 777777 777777 777777 7777 775510 204081 632653 061224 489795 918367 346938 775510 204081 6326 377358 490566 037735 849056 603773 584905 660377 358490 566037 7358 350877 192982 456140 350877 192982 456140 350877 192982 456140 3508 688524 590163 934426 229508 196721 311475 409836 065573 770491 8032 923076 923076 923076 923076 923076 923076 923076 923076 923076 9230 550724 637681 159420 289855 072463 768115 942028 98.5507 246376 8115 726027 397.260 273972 602739 726027 397.260 273972 602739 726027 3972 337662 337662 337662 337662 337662 337662 337662 337662 337662 3376 320987 654320 987654 320987 654320 987654 320987 654320 987654 3209 235294 117647 058823 529411 764705 882352 941176 470588 235294 1176 595.505 617977 528089 887640 449438 202247 191011 235955 056.179 7752 021505 376344 086021 505376 344086 021505 376344 086021 505376 3440 824742 26804] 237113 402061 855670 103092 783505 154639 175257 7319 1980.19 80.1980 198019 801980 1980.19 80.1980 198019 80.1980 198019 8019 190476 190476 190476 190476 190476 190476 190476 190476 190476 1904 330275 229357 798165 137614 678899 082568 807339 44954l 284403 6697 654867 256637 168141 592920 353982 300884 955752 212389 380530 9734 068376 068376 068376 068376 068376 068376 068376 068376 068376 0683 619834 710743 801652 89.2561 983471 074380 165289 256198 347107 4380 503875 968.992 248062 015503 875968 992248 062015 503875 968.992 2480 496240 601503 759398 496240 601503 759398 496240 601503 759398 4962 854014 598540 145985 401.459 854014 598.540 145985 401459 854014 5985 163120 567375 886524 822695 035460 99.2907 80.1418 439716 312056 7375 758620 689655 1724.13 793.103 448275 862068 965517 241379 310344 8275 046979 865771 812080 536912 751677 852348 993288 590604 026845 6375 522875 816993 464052 287581 699346 405228 758169 934640 522875 8169 528662 420382 165605 095541 401273 885350 318471 337579 617834 3949 987577 63975] 552795 031055 900621 118012 422360 248447 204968 9440 939393 939393 939393 939393 939393 939393 939393 939393 939393 9393 : 10 + TERMs of TAN T' #. 25.52 5 49.549 I 7 3. 5 7 3 97.597 l 121.512 1 l 145.51.45 888888 888888 888888 888888 888888 888888 888888 888888 846153 846153 846153 846153 846153 846153 846153 846153 588235 294117 647058 823529 411764 705882 352941 176470 809523 809523 809523 809523 809523 809523 809523 809523 965517 24.1379 310344 827586 206896 55.1724 137931 034482 424242 424242 424242 424242 424242 424242 424242 424242 054054 O54054 054054 054054 054054 054054 054054 054054 780487 804878 048780 487804 878048 780487 804878 048780 777777 777777 777777 777777 777777 777777 777777 777777 530612 244897 959183 673469 387755 102040 816326 530612 490566 037735 849056 603773 584905 660377 358490 566037 771929 824561 403508 771929 824561 403508 771929 824561 786885 245901 639344 262295 O81967 213114 754098 360655 769230 769230 769230 769230 769230 769230 769230 769230 942028 985.507 246376 811594 202898 550724 637681 159420 602739 726027 397.260 27.3972 602739 726027 397.260 273972 623376 623376 623376 623376 623376 623376 623376 623376 876543 209876 543209 876543 209876 543209 876543 209876 470588 235294 117647 058823 5294ll 764705 882352 941176 808988 764044 943820 224719 101.123 595.505 617977 528089 860215 053763 440860 215053 763440 860215 053763 440860 587628 865979 381443 298969 072164 948453 608247 422680 801980 198019 801980 1980.19 80.1980 1980.19 801980 1980.19 76.1904 761904 761904 76.1904 761904 76.1904 761904 76.1904 247706 422018 348623 853211 (09174 31.1926 605504 587155 513274 336283 185840 707964 601769 91.1504 424778 761061 760683 760683 760683 760683 760683 760683 760683 760683 165289 256198 347107 438016 528925 619834 710743 801652 620155 038759 689922 480620 155038 75.9689 92.2480 620155 406015 037593 984962 406015 037593 984962 406015 037593 401459 854014 598540 145985 401.459 854014 598540 145985 886524 822695 035460 99.2907 80.1418 439716 312056 737588 862068 965517 24.1379 310344 827586 206896 551724 137931 838926 174496 644295 302013 422818 791946 308724 832214 934640 522875 816993 464052 287581 699346 405228 758169 044585 98.726] 146496 815286 624203 821656 ().50955 414012 993788 819875 776397 515527 950310 559006 2.11180 124223 939393 939393 939393 939393 939393 939393 939393 939393 FROM 424th To 530th DECIMAL PLACE. 11 888888 888888 888888 888888 888888 888888 888888 888888 888888 8888 846153 846153 846153 846153 846153 846153 846153 846153 846,153 846] 588235 294117 647058 823529 411764 705882 352941 176470 588235 2941 809523 809523 809523 809523 809523 809523 809523 809523 809523 8095 758620 689655 1724.13 793.103 448275 862068 965517 241379 310344 8275 424242 424242 424242 424242 424242 424242 424242 424242 424242 4242 054054 054054 O54054 O54054 O54054 O54054 054054 054054 O54054 O540 487804 878048 780487 804878 048780 487804 878048 780487 804878 0487 777777 777777 777777 777777 777777 777777 777777 777777 777777 7777 244897 959183 673469 387755 102040 816326 530612 244897 959183 6734 735849 056603 773584 905660 377358 490566 037735 849056 603773 5849 403508 771929 824561 403508 771929 824561 403508 771929 824561 4035 737704 918032 786885 245901 639344 262295 081967 213114 754098 3606 769230 769230 769230 769230 769230 769230 769230 769230 769230 7692 289855 072463 7681.15 942028 98.5507 246376 811594 202898 550724 6376 602739 726027 397.260 273972 602739 726027 397.260 273972 602739 7260 623376 623376 623376 623376 623376 623376 623376 623376 623376 6233 543209 876543 209876 543209 876543. 209876 543209 876543 209876 5432 470588 235294 II7647 058823 5294ll 764705 882352 941176 470588 2352 887640 449438 202247 1910II. 235955 056179 775280 898876 404494 3820 215053 763440 860215 053763 440860 215053 763440 860215 053763 4408 41237] 134020 618556 701030 927835 051546 39.1752 577319 587628 8659 80.1980 1980.19 80.1980 1980.19 801980 1980.19 80.1980 1980.19 801980 1980 76.1904 761904 76.1904 76.1904 76.1904 76.1904 76.1904 76.1904 761904 7619 963302 752293 577981 651376 146788 990825 688073 394.495 412844 0366 946902 654867 256637 le614] 592920 353982 300884 955752 212389 3805 760683 760683 760683 760683 760683 760683 760683 760683 760683 7606 892561 983471 074380 165289 256198 347107 438016 528925 619834 7107 038759 689922 480620 155038 759689 92.2480 620155 038759 689922 4806 984962 406015 037593 984962 406015 037593 984962 406015 037593 9849 401459 854014 598.540 145985 40.1459 854014 598540 145985 401.459 8540 652482 269503 546099 290780 141843 971631 205673 758865 248226 9503 034482 758620 689655 1724.13 793.103 443275 862068 965517 241379 3103 765100 67.1140 939597 315436 241610 738255 033557 046979 865771 8120 934640 522875 816993 464052 287581 699346 405228 758169 934640 5228 738853 503184 713375 796.178 343949 044585 937261 146496 815286 6242 602484 472049 6894.40 99.3788 819875 776397 515527 950310 559006 2.111 939393 939393 939393 939393 939393 939393 939393 9393939393939393 —-A- 12 + TERMs of TAN -1 #, º 4427 744605 404365 645682 169434 028029 169.5 6 920590 412147 258211 517101 820584 10822 708621 934243 349988 326462 16 933652 3852.58 440423 849138 26508 030977 139699 171603 41 515223 117636 777538 1. I93.5 T53 65047 686377 064049 * 101 963073 874301 1598.94 332762 250 839.109 393661 618 l 217.52 17 l 241,524 i l 265.52 65 l 289.52 89 FROM 120th To 212th DECIMAL PLACE. 13 029963 535278 128473 372781 065088 757396 449704 142011 834319 5266 849998 278265 544543 001156 069364 161849 710982 658959 537572 2543 925912 313691 660467 398320 451977 401 129 943502 824858 757062 1468 421550 377719 544078 698161 35001 1 049723 756906 077348 066298 3425 840469 626969 662594 406437 770416 017297 29.7297 297.297 29.7297 2972 596490 894230 597990 094943 415767 424027 089947 089947 089947 0899 366173 983660 183071 669454 460564 394140 030010 362694 300518 1347 413422 713330 732307 271733 642321 940532 540311 001015 228426 3959 088584 631041 004213 051005 226089 850127 641078 1394.40 398009 9502 347744 823499 233107 097.157 089174 197540 492923 759656 800156 0975 377349 570823 482050 043674 007297 842759 776467 363603 671916 0344 029880 684021 048696 702040 397.126 950228 257602 115898 540224 8296 970620 1997.10 204485 695097 029342 584629 667235 902309 208398 6572 1524 883861 264176 458974 37868] 392513 04715.1 422195 845055 0045 2 396439 703746 723537 303734 674401 744948 767746 170892 4953 3767 328791 916246 608861 766300 369555 377975 496163 8484 5 924245 791236 535439 858159 538435 214980 644728 7314 9318 813632 797385 704553 256860 458430 990651 2863 14 662631 242974 143813 969273 865086 460712 2612 23077 186152 207468 794557 355111 744241 8393 36 330349 283796 497058 098326 119693 7461 57209 530255 591005 644056 8.10775 0434 90 110575 281958 128734 296486 3880 141967 312474 870431 170661 7440 223 719055 432097 705874 9748 352627 804844 644711 1189 555 937755 330165 1416 876655 637285 9788 1382 682485 5699 2 181242 2649 3441 6832 5 4315 85 14 + TERMs of TAN -1 #. l l69.51 69 l ºm-mm-m-m-m-m-m-m I93.5.19 3 –– 217,521 7 I 241.524 1 l 265.52 65 289.52 89 l 313.53 1 3 272189 349112 426035 502958 579881 656804 733727 810650 352601 156069 364161 849710 982658 959537 572254 335260 926553 672316 384.180 790960 45.1977 401 129 943502 824858 414364 640883 977900 552486 187845 303867 403314 917127 972972 972972 972972 97.2972 97.2972 97.2972 972972 972972 470899 470899 470899 470899 470899 470899 470899 470899 150259 067357 512953 367875 647668 393782 383419 6891.19 390862 944162 436548 223350 253807 106598 984771 573604 487562 189054 726368 159203 98.0099 50.2487 562189 054726 609756 097560 975609 756097 560975 609756 097560 975609 497607 655502 392344 497607 655502 392344 497607 655502 803755 868544 600938 967136 150234 741784 037558 685446 440325 898617 511520 737327 188940 092.165 898617 511520 873082 720144. 796330 090497 737556 56.1085 972850 678733 316536 542443 747555 555555 555555 555555 555555 555555 642768 354389 867900 087336 24454] 484716 157205 240174 767266 567918 662865 230008 583690 987.124 463519 313304 759262 603276 456023 274927 203375 527426 160337 552742 771524 94.7631 379386 406746 275500 082987 551867 219917 793815 102121 659836 291422 209648 297.273 469387 755102 889024 801285 267833 95914] 516089 084869 603212 85.1405 327338. 290438 071346 660273 999920 987713 091106 403.162 839749 830894 822300 704778 517179 642084 927078 910007 719545 230384 919352 222413 045694 499.114 273264 424704 842432 007880 032989 892407 847878 800086 151398 170655 195201 454,168 554401 441317 401217 47439] 213859 452878 32.1720 200387 817383 935459 131902 871798 454.133 498566 226170 856980 250536 582321 330501 137813 724060 525314 139294 800440 617960 988659 37656] 132043 697660 155248 552045 708569 396848 544773 6886.16 497841 988934 975458 969.535 407761 618148 660679 642913 526377 217809 530618 165751 239496 754,171 440070 642549 089469 613738 959477 733837 387815 070970 894.178 805108 508461 762137 780552 135351 227663 421002 409863 500890 988582 129665 673997 213 721807 353126 409051 115613 210164. 266077 531110 337528 291224 354976 106616 243516 375928 303673 533 143729 013805 431907 703101 579860 252247 84.2266 181356 825.742 269330 325776 637269 1330 833044 187482 917380 075829 389129 2 103125 696906 742234 973559 833766 3324 089247 390595 629745 444114 5 254656 395875 103722 216221 FROM 212th To 318th DECIMAL PLACE. 15 887573 964497 041420 118343 195266 272189 349112 426035 502958 5798 115606 936416 184971 098265 895953 757225 433526 O11560 693641 6184 757062 146892 655367 231638 418079 096045 197740 112994 350282 4858 O71823 204419 889502 762430 939226 519337 016574 5856.35 359116 0220 97.2972 97.2972 97.2972 97.2972 972972 97.2972 97.2972 97.2972 97.2972 97.29 470899 470899 470899 470899 470899 470899 470899 470899 470899 4708 | 170984 455958 549222 797927 461139 896373 056994 818652 849740 9326 060913 705583 756345 177664 974619 289340 101522 842639 593908 6294 368159 203980 099502 487562 189054 726368 159203 980099 50.2487 5621 756097 560975 609756 097560 975609 756097 560975 609756 097560 9756 392344 497607 655502 392344 497607 655502 392344 497607 655502 3923 009389 671361 502347 417840. 375586 854460 093896 713615 023474 1784 737327 188940 092.165 898617 511520 737327 188940 092.165 898617 5115 031674 208144 796380 090497 737556 56.1085 972850 678733 031674 2081 555555 555555 555555 555555 555555 555555 555555 555555 555555 5555 672489 O82969 432314 4.10480 349344 978165 938864 628820 960698 6899 721030 042918 454935 622317 596566 523605 150214 592274 678111 5879 616033 755274 261603 375527 426160 337552 74.2616 033755 274261 6033 01:2448 132780 082987 551867 219917 012448 132780 082987 551867 2199 040816 326530 612244 897959 183673 469387 755,102 040816 326530 6122 622489 959839 35.7429 718875 502008 032128 514056 224899 598393 5742 O55335 968379 446640 316205 533596 837944 664031 620553 359683 7944 782101 167315 175097 276264 591439 688715 953307 392996 108949 4163 196168 582375 478927 203065 134099 616858 237547 892720 306513 4099 684801 207547 16981] 320754 716981 132075 471698 113207 547169 81.13 654313 590007 434944 237918 215613 382899 628252 788104 0892.19 3308 003563 430656 187545 787545 787545 787545 787545 787545 787545 7875 706246 774391 735100 072202 166064 98.1949 458483 754512 635379 0613 467892 557.190 072658 350007 117437 722419 928825 622775 800711 7437 946354 963135 833883 042786 537543 859649 122807 017543 859649 1228 717230 234820 726436 853520 798135 363321 799307 958477 503650 5190 672678 659592 4.26975 782938 798693 030006 825938 566552 901023 8907 87250I 52.1062 683265 206218 995652 617146 354208 754208 754208 7542 736627 949245 212581 686465 100553 933965 674244 252491 694352 1594 155114 623017 562276 653574 431450 579588 845471 200104 918032 7868 727364 7.11767 095697 058274 900720 219685 564260 808885 602588 9967 080801 307071 877482 787941 249555 6424.17 29.2469 554453 396300 0638 165104 306922 9.70335 152618 930529 266453 383533 339914 417226 7100 0.43366 171041 966761 850434 293836 649358 084598 529937 709010 6460 943620 531893 683551 165804 255548 660009 570191 537861 464637 9934 160518 792330 044727 801234 705814 241043 176220 363524 88.7421 3123 566648 940217 064671 305449 159006 428277 733117 004202 280782 9.987 16 + TERMs of TAN -1 #, 169.51 69 l 193.5.19 3 l 217.52 1 7 l 241.524 l 265,525s ––- 289.52 89 l 313.53 1 3 816568 047337 278106 508875 739644 970414 201183 431952 97.1098 2.65895 95.3757 225433 5260ll 560693 641618 497.109 757062 146892 655367 231638 418079 096045 197740 112994 994475 138121 546961 325966 850828 729281 767955 801.104 7297.29 7297.29 7297.29 7297.29 7297.29 7297.29 729729 7297.29 994708 994708 994708 994708 994708 994708 994708 994708 424870 466321 243523 316062 176165 803108 808290 155440 4.16243 654822 335025 380710 659898 477157 360406 09.1370 890547 263681 592.039 800995 024875 621890 547263 681592 097560 975609 756097 560975 609756 097560 975609 756097 444976 O76555 023923 444976 076555 023923 444976 076555 037558 685446 009389 671361 502347 417840 375586 854460 207373 271889 400921 658986 1751.15 207373 271889 400921 447963 800904 97.7375 565610 859728 506787 330316 742081 555555 555555 555555 555555 555555 555555 555555 555555 563318 777292 576419 213973 799.126 637554 585152 838427 828326 180257 510729 613733 905579 399141 630901 287553 755274 261603 375527 426160 337552 742616 033755 274261 1701:24 481327 800829 875518 672199 170124 481327 800829 448979 591836 734693 877551 020408 163265 306122 448979 97.1887 550200 803212 85.1405 622489 959839 35.7429 718875 664031 620553 359683 794466 403162 055335 968379 446640 424,124 513618 677042 801556 420233 463035 019455 252918 616858 237547 892720 306513 409961 685823 75.4789 272030 207547 1698ll 320754 716981 132075 471698 113207 547169 550185 873605 947955 390334 572490 706319 702602 230483 457875 457875 457875 457875 457875 457875 457875 457875 718411 552346 570397 111913 357400 722021 660649 819494 722419 928325 622775 8007ll 743772 241992 882562 277580 0701.75 438596 4.91228 0701.75 438596 491228 0701.75 438596 311418 685121 107266 435986 159169 550173 010380 622837 849829 351535 836177 474402 730375 426621 160409 556313 087542 087542 087542 087542 087542 087542 087542 087542 684385 382059 800664 451827 242524 916943 52.1594 684385 85.2459 016393 442622 950819 672131 147540 983606 557377 637540 453074433656 957928 802588 996763 754045 307443 977635 782747 603833 865814 696485 623003 194888 178913 063091 482649 842271 293375 394321 766561 514195 583596 664024 922118 380062 305295 950.155 763.239 875389 408099 394.452 440615. 384615. 384615. 384615. 384615. 384615. 384615 300562 660392 462006 079027 355623 100303 951367 781155 351667 916469 761537 537537 53.7537 53.7537 537537 537537 FROM 318th To 424th DECIMAL PLACE. 17 662721 893491 124260 355029 585798 816568 047337 278106 508875 7396 826589 595375 722543 352601 156069 364161 849710 982658 959537. 5722 350282 485875 706214 689265 536723 163841 807909 6045.19 774011 2994 972375 690607 734806 629834 254143 646408 839779 005524 86.1878 4530 7297.29 7297.29 729729 7297.29 7297.29 7297.29 7297.29 7297.29 7297.29 7297 994708 994708 994708 994708 994708 994708 994708 99.4708 994708 9947 4.14507 772020 725388 601036 269430 051813 471502 590673 575129 5336 558375 634517 766497 461928 934010 152284 263959 390862 944162 4365 039800 995.024 875621 890547 263681 592039 800995 024875 621890 5472 560975 609756 097560 975609 756097 560975 609756 097560 975609 7560 023923 444976 076555 023923 444976 076555 023923 444976 076555 0239 093896 713615 023474 178403 755868 544600 938967 136150 234741 7840 658986 I75II5 207373 271889 400921 658986 1751.15 207373 271889 4009 447963 800904 977375 565610 859728 506787 330316 742081 447963 8009 555555 555555 555555 555555 555555 555555 555555 555555 555555 5555 947598 253275 109170 305676 855895 196506 550218 34061] 3537II 7903 648068 669527 896995 708154 506437 768240 343347 639484 978540 7725 603375 527426 160337 552742 616033 755274 261603 375527 426160 3375 875518 672199 1701.24 481327 800829 875518 672199 1701.24 481327 8008 591836 734693 877551 020408 163265 306122 448979 591836 734693 8775 502008 032128 514056 224899 598393 574297 188755 020080 321285 1405 316205 533596 837944 664031 620553 359683 794466 403162 055335 9683 287937 743190 661478 599221 789883 268482 490272 373540 856031 1284 651340 996.168 582375 478927 203065 134099 616858 237547 892720 3065 811320 754716 981132 075471 698113 207547 1698.II 320754 716981 1320 27.1375 464684 0.14869 888.475 836431 226765 799256 505576 208178 4386 457875 457875 457875 457875 457875 457875 457875 457875 457875 4578 584837 545.126 353790 613718 411552 346570 397III 913357 400722 0216 07.1174 377224 199288 256.227 758007 117437 722419 928825 622775 8007 491228 0701.75 438596 4.91228 0701.75 438596 491228 0701.75 438596 4912 370242 214532 87.1972 318339 100346 020761 245674 740484 429065 7439 993.174 061433 447098 976109 215017 064846 416382 252559 726962 4573 087542 087542 087542 087542 087542 087542 087542 087542 087542 0875 382059 800664 451827 242524 916943 52.1594 684385 382059 800664 4518 049180 327868 852459 Oló393 442622 950819 672131 147540 98.3606 5573 365695 792880 258899 676375 404530 744336 56.9579 288025 889967 6375 738019 169329 073482 428115 O15974 440894 568690 095846 645367 4121 21451 1 041009 463722 397476 340694 006309 148264 984227 129337 5394 688473 520249 221183 800623 052959 50.1557 632398 753894 080996 8847 384615. 384615. 384615. 384615. 384615. 384615. 384615. 384615. 384615. 3846 015.197 568389 057750 759878 419452 887537 993.920 97.2644 376899 6960 53.7537 53.7537 53.7537 53.7537 53.7537 53.7537 53.7537 53.7537 53.7537 5375 D 18 + TERMs of TAN -1 #. l 169.51 69 l 193.5 193 l 217.52 1 7 l 241.5241 l 265.52 65 l 289.52 89 l 313.53 1 3 449704 142011 834319 526627 218934 911242 603550 295857 543352 601.156 069364 161849 710982 658959 537572 254335 350282 485875 706214 689265 536723 163841 807909 604519 386740 331491 712707 182320 44.1988 950276 243093 922651 ||, 297.297 29.7297 297.297 297.297 297.297 29.7297 297.297 297.297 089947 0899.47 0899.47 089947 089947 089947 089947 089947 787564 766839 378238 341968 91.1917 098445 595854 922279 482233 502533 071065 989847 715736 040609 137055 837563 636815 920398 009950 248756 2.18905 472636 815920 398009 975609 756097 560975 609756 097560 975609 756097 560975 234449 760765 550239 234449 760765 550239 234449 760765 375586 854460 093896 713615 023474 178403 755868 544600 216589 86.1751 152073 7327.18 89.4009 216589 86.1751 152073 049773 755656 108597 285067 873303 167420 814479 638009 555555 555555 555555 555555 555555 555555 555555 555555 930.131 004366 812227 074235 807860 262008 7336.24 454148 32.1888 412017 167381 974248 927038 626609 442060 085836 527426 160337 552742 616033 755274 261603 375527 426160 298755 186721 99.1701 244813 278008298755 186721 991.701 510204 081632 653061 224489 795918 367346 938775 510204 622489 959839 35.7429 718875 502008 032128 514056 224899 794466 403162 055335 968379 446640 316205 533596 837944 046692 607003 891050 583657 587548 638132 2957.19 844357 134099 616858 237547 892720 306513 409961 685823 754789 754716 981132 075471 698113 207547 169811 320754716981 617100 371747 211895 910780 669144 981412 639405 204460 754578 754578 754578 754578 754578 754578 754578 754578 606498 194945 848375 451263 537906 137184 1155.23 465703 117437 722419 928325 622775 8007II 743772 241992 882562 280701 754385 964912 280701 754385 964912 280701 754385 446366 782006 9204.15 224913 494809 688581 314878 892.733 378839 590443 686006 825938 566552 901023 890.784 98.2935 420875 420875 420875 420875 420875 420875 420875 420875 272425 249169 435.215 946843 853820 598006 644518 272425 770491 803278 688524 590163 934426 229508 19672] 311475 404530 744336 569579 288025 889967 637540 453074433656 405750 7987.22 044728 434504 7.92332 268370 607028 753993 32.1766 561514 195583 596214 511041 009463 722397 476340 352024 922118 380062 305295 950155 763.239 875389 408099 153846 153846 153846 153846 153846 153846 153846 153846 486.322 188449 848024 316109 422492 401215 805471 124620 375.375 375.375 375375 3.75375 375.375 375375 375375 375375 FROM 424th To 530th DECIMAL PLACE. 19 988165 680473 372781 065088 757396 449704 142011 834319 526627 2189 2601.15 606936 416184 971098 265895 95.3757 225433 526011 560693 6416 77401] 299435 028248 587570 621468 926553 672316 384.180 790960 4519 933701 657458 563535 911602 209944 75138] 215469 613259 668508 2872 297.297 297.297 297.297 297.297 297.297 297.297 297.297 297.297 297.297 29.72 089947 089947 089947 0899.47 089947 089947 089947 089947 089947 0899 792746 113989 637305 699481 865284 97.4093 264248 704663. 212435 2331 45.1776 649746 192893 401015 228426 395939 086294 416243 654822 3350 950248 756218 905472 636815 920398 009950 248756 2.18905 472636 8159 609756 097560 975609 756097 560975 609756 097560.975609 756097 5609 550239 234449 760765 550239 234449 760765 550239 234449 760765 5502 938967 136150 234741 784037 558685 446009 389671 361502 347417 8403 732718 894009 216589 86.1751 152073 7327.18 894009 216589 86.1751 1520 049773 755656 108597 285067 873303 167420 814479 638009 049773 7556 555555 555555 555555 555555 555555 555555 555555 555555 555555 5555 471615 720524 O17467 248908 296943 231441 048034 934497 816593 8864 909871 244635 193133 047210 300429 184549 356223 175965 665236 0515 337552 742616 033755 274261 603375 527426 160337 552742 616033 7552 244813 278008 298755 186721 99.1701 244813 278008 298755 186721 99.17 08.1632 653061 224489 795918 367346 938775 510204 081632 65306] 2244 598393 574297 188755 020080 321285 140562 248995 983935 742971 8875 664031 620553 359683 794466 403162 055335 968379 446640 316205 5335 976653 696498 054474 70817] 206225 680933 852140 077821 011673 1517 272030 651340 996.168 582375 478927 203065 134099 616858 237547 8927 132075 471698 113207 547169 81.1320 754716 981132 075471 698113 2075 966542 750929 368029 739776 951672 862453 531598 513011 152416 3568 754578 754578 754578 754578 754578 754578 754578 754578 754578 7545 971119 133574 007220 216606 498.194 945848 375451 263537 906137 1841 277580 071174 377224 199288 256.227 758007 117437 722419 928825 6227 964912 280701 754385 964912 280701 754385 964912 280701 754385 9649 564013 840830 449826 98.96.19 377162 629757 785467 128027 681660 8996 153583 617747 440273 037542 662116 040955 631399 317406 143344 7098 420875 420875 420875 420875 420875 420875 420875 420875 420875 4208 249169 435.215 946843 853820 598.006 644518 272425 249169 435.215 9468 409836 065573 770491 803278 688524 590163 934426 229508 196721 3114 957928 802588 996763 754045 307443 365695 792880 258899 676375 4045 610223 642172 523961 661341 853035 143769 968051 118210 862619 8083 694006 309148 264984 227129 337539 432176 656151 419558 35962] 4511 688473 520249 221183 800623 052959 501557 632398 753894 080996 8847 153846 153846 153846 153846 153846 153846 153846 153846 153846 1538 060790 273556 231003 0395.13 677811 550151 975683 890.577 507598 7841 3.75375 3.75375 375375 375.375 375.375 375375 375.375 375375 375.375 3753 20 + TERMs of TAN -4 T52 I *H 8307 658539 235.178 822542 337.53 13 136332 798696 798888 20774 443985 417314 32 858146 360889 51977 305744 82 231883 l --- 1301.13 361.53 61 205 l 385.5385 I A09, 54 on I 433.543 3 FROM 238th To 318th DECIMAL PLACE. 21 44.1693 503131 595406 696948 199738 630934 677674 198041 065208 3121 899954 724741 608669 335164. 206654 835981 818117 894.215 788100 7634 416764 682022 663830 985476 132148 263415 975883 956878 504736 1964 276670 642133 170517 004882 472277 781780 531858 704711 16600l 7604 817484 682398 207258 970808 856579 376525 060195 438312 211657 4940 150344 300696 410385 041643 453339 484683 085025 205556 97.7975 1937 162480 544777 168392 276830 434.184 342143 077501 845976 2.16470 4139 899623 695.240 173404 009.257 800708 999660 333812 507030 783185. 2967 325868 239127 426182 297944 191207 626167 484.105 546081 588014 5805 515 797877 696601 656913 421583 080382 008300 578858 998846 0155 816520 353870 906813 914933 689077 909768 838688 230903 2130 1292 716738 726852 99.2528 839898 298674 993604 978322 5218 2 046857 464747 765153 8846.25 45.9747 720197 666479 9621 324] 296.139 549160 243683 622836 001531 212757 2022 5 133289 356883 962686 179864 766227 361391 3997 8130 509691 709409 917052 642229 228626 8083 12 87.9051 761031 963040 677901 107246 9420 20402 96.1999 699030 831849 237902 2460 32 325475 246466 924.154 127887 9233 51219 832932 900617 836468 0141 81 165624 944989 756034 3838 1286.31 128178 853124 0525 203 872771 626530 5043 323154 976004 7569 512 271537 0200 812132 O843 1287 6252 2 0416 32 22 + TERMS OF TAN –1 #, 337.5387 l 361.53 61 I 385,538 5 I 409,5409 I 433.5433 l 457.5457 481.54 81 119468 749750 430531 000593 471810 089020 77.1513 3531 15 073042 866715 147894 84.5500 05865] O.26392 96.1876 832844 536667 397646 60807] 569355 666.179 710144. 927536 231884 024138 224651 865.122 222081 043919 000573 065902 578796 028575 294007 494621 768410 226784 488300 056657 223796 047977 98.1305 477403 2.55951 815395 204142 834375 350140 353024 390645 212434 051910 802429 234738 521847 632132 427096 731200 100478 635365 434738 309934 205397 860800 238421 204582 712354 145048 925.240 886647 700747 838348 719605 265091 650491 619000 635081 668148 731374 052342 02900] 221279 062856 799464 773419 142545 228548 764017 322397 620831 169371 955961 777300 069361 635910 395313 021011 256077 O35534 673102 2.18959 589928 007411 041498 021976 717053 325074 265703 421508 686651 402705 823140 01401] 395.187 516512 78937] 434629 890601 963951 766168 429023 703690 916650 839.400 394856 663161 739332 324610 166070 114355 572246 028960 566411 004868 928520 757836 1974.77 902679 927247 289902 669381 257532 651616 145477 628870 331738 231278 377124 344571 538031 494.274 443184 817,159 159189 0.78688 97.9588 353925 151608 92.932I 678439 459742 874753 93.7993 279802 6666.28 953813 388922 052.194 912162 328850 441395 318565 996055 047121 102833 940126 807657 488.340 502723 115027 261305 747481 742999 691628 766408 408140 026904 083259 250670 601.184 819546 013497 119832 939333 365622 325549 074248 638.107 744249 737606 191402 7.92357 826443 256629 611896 200129 247243 057707 910565 598259 448054 986678 084863 124315 488366 603959 818098 191204 7907ll 342918 202374 560495 543839 531406 375889 723635 050803 978788 770067 017120 429459 273377 51344 015844 28.1281 451607 86.2808 865662 470897 402962 81 431384 428741 953602 024899 264476 656802 858725 129159 714304 329.970 659003 484473 287053 046096 204 877860 797578 035.178 668753 005368 882423 325008 802629 846605 912429 748904 039335 515 616502 100289 414538 450916 654526 818068 278384 693980 970020 238415 1298 024345 245734 815543 283671 2 059710 333713 644358 849713 3268 5792.59 226560 373143 5 187294 954.196 472283 8232 873.762 314240 13 067427 576431 FROM 318th To 424th DECIMAL PLACE. 23 727002 967.359 O50445 103857 566765 578635 014836 795.252 225519 2878 574780 058651 026392 96.1876 832844 574780 058651 026392 96.1876 8328 057971 014492 753623 188405 797101 449275 362318 840579 710144. 9275 561604 584527 220630 372492 836676 2.17765 042979 94.2693 4097.42 1203 033994 334277. 620396 600566 572237 960339 943342 776203 966005 6657 056022 408963 585.434 173669 467787 114845 938375 350140 056022 4089 96.3988 919667 590027 700831 024930 747922 437673 130193 905817 1745 876712 328767 123287 671232 876712 328767 123287 671232 876712 3287 801387 533875 338753 387533 875338 75.3387 533875 338753 387533 8753 523143 000536 193029 490616 621983 914209 115281 501340 482573 7265 076970 322924 986737 400530 503978 779840 848806 366047 745358 0901 530448 368763 224020 997375 328083 98.9501 312335 958005 249343 8320 657475 743702 852.107 436883 116883 116883 116883 116883 116883 1168 265226 234082 573153 979900 051413 881748 071979 434447 300771 2082 759544 724702 526701 096786 488020 356234 096692 111959 287531 8066 99.9788 417438 017503 248487 806911 000503 778337 531486 146095 71.78 89.0042 557612 859423 23.7065 933802 867500 049875 311720 698254 3640 106539 879765 344223 718392 349390 439308 118597 530864. 197530 8641 032188 356582 122110 163739 653404 413214 356139 000488 997555 0122 756974 973512 221163 94.4046 371014 982682 826815 150997 384987 8934 515566 928207 426560 539890 229836 850600 855664. 171347 192019 1846 423232 271388 361033 256988 633637 404148 980.738 477755 636215 0004 398020 4453.12 958117 628239 782455 572130 434713 942208 508697 7751 219838 354085 810749 46.3839 634154 008832 28.1341 7377.17 253580 2202 615454 265695 714781 75.1575 010450 076932 245907 42025] 198898 0541 583210 95.3581 862680 093358 103357 5281.76 884805 411122 997781 6855 068349 61.7003 955642 598460 943278 61.1300 909927 110982 896145 2357 187682 308965 748294 609926 907958 600872 211060 774313 504565 2136 196449 064151 411164 333546 253805 047937 240566 314635 437005 0120 459553 927169 285593 334342 648.187 049771 386564. 288830 980348 6631 748776 115287 554263 015423 920243 776747 646172 826683 281607 3451 0.96024 956823 206637 043637 4.79328 594901 427069 157420 551998 9398 226839 630.125 059778 958028 7892.57 532842 149016 35744] 964299 2568 869681 809562 501160 928666 894284 024742 930829 143219 481495 6047 675764 501543 119874 991883 4.49550 678080 691533 39.1520 236572 7575 39.9975 300995 320404 866653 789087 253570 590078 307066462295 6776 431669 981600 248707 968802 973330 210794 023023 59.2024 850569 6965 636152 192201 731033 826088 228388 195732 426969 317435 922319 5844 921843 873417 481683 603781 277025 008670 528350 364397 403426 8302 869785 903948 401293 446757 806229 501758 182193 471247 676528 2781 115727 338271 699193 033774 250618 820585 486627 996398 632127 2545 704071 908940 905499 397813 240088 008155 947263 406352 766850 8335 24 + TERMS OF TAN –1 #, I 337.5387 l 361.53 61 l 385.5385 l 409.5409 433.543 3 481.548 338278 93.1750 741839 7626 II 275964 39.1691 394658 753709 445747 800586 510263 9296.18 768328 445747 800586 510263 362318 840579 710144. 927536 231884 057971 014492 753623 438395 415472 779369 627507 163323 782234 957020 057306 223796 033994 334277 620396 600566 572237 960339 943342 635854 34.1736 694677 871148 459383 753501 400560 224089 152354 570637 119113 573.407 202216 066481 994459 833795 671232 876712 328767 123287 671232 876712 328767 123287 387533 875338 753.387 533875 338753 387533 875338 753387 415549 597855 227882 037533 512064 343163 538873 994638 856763 925729 442970 822281 167108 753315 649867 374005 2099.73 753280 839895 O13123 359580 052493 438320 209973 831 168 831.168 83] ]68 83] 168 831,168 831 168 831 168 83.11.68 262210 796915 167095 Ilj681 233933 161953 727506 426735 157760 814249 363867 684478 37.1501 272264 631043 256997 841309 823677 58.1863 97.9848 866498 740554 156171 284634 897755 610972 568.578 553615 960099 750623 441396 508728 975308 64.1975 308641 975308 64.1975 308641 975308 64.1975 249388 753056 234718 826405 867970 6601.46 699266 503667 624697 336561 74334] 404358 353510 895883 777239 709443 522781 774580 335731 414868 105515 587529 976019 184652 750593 824228 028503 562945 160470 588235 294] 17 647058 496011 93473] 934731 93473] 8748] 1 230004 618937 644341 193159 883798 96.3844 393592 245240 492949 551554 467120 591623 O15037 809446 240071 98.2746 627141 886236 805619 361841 071030 769825 767154 0.07464 031527 97.1776 738984 93.1402 728.199 247837 230263 130433 984.198 537129 47256.] 91.1916 935787 300024 785346 091655 607756 056638 34.7989 999642 2.74557 546716 276523 36817] 021377 672209 026128 823529 411764 705882 352941 93473] 934731 934731 93473] 801385 681293 302540 415704 677345 537757 437070 938215 181405 895691 609977 324263 9101.12 359550 56.1797 752808 000445 434298 440979 955.456 871280 176600 441501 103752 756784 910004 376367 614879 656516 618495 000433 8394.79 381662 465930 756800 688172 664537 22148] 135358 336272 268788 7288.18 180642 648827 60226] 256415 030606 101376 929742 467742 083824 644204 247012 985012 257695 1321.75 09274] 298563 245995 28.1332 3290.48 456068 588522 726131 607394 616048 435744 156111 071344 256854 620091 398027 987748 530592 507700 053200 286617 078593 434188 153163 389.199 066480 636.124 896985 843835 1781.72 222335 789970 1858.15 351492 3461 ll 4700.95 974337 360745 873355 691457 FROM 424th To 530th DECIMAL PLACE. 25 198813 056379 821958 456973 293768 545994 065281 899109 792284 8664. 9296.18 768328 445747 800586 510263 9296.18 768328 188405 797.101 449275 362318 840579 710144. 927536 590257 87.9656 160458 452722 063037 249.283 667621 776203 966005 665722 379603 399433 427762 039660 635854 34.1736 694677 871148 459383 753501 400560 0.13850 415512 465373 96.1218 836565 096952 908587 671232 876712 328767 123287 671232 876712 328767 533875 338753 387533 875338 75.3387 533875 338753 069705 093833 780160 857908 847184 936595 174262 305039 787798 408488 063660 477453 580901 856763 753280 839895 013123 359580 052493 4383.20 2099.73 831168 831.168 831.168 831]68 831.168 831168 831 168 218508 997.429 305912 596401 028277 634961 439588 455470 737.913 486005 089058 524173 027989 821882 760705 289672 544080 604534 005037 783375 314861 179551 122194 513715 710723 192019 950.124 688279 308641 975308 64.1975 30864] 975308 64.1975 30864] 481662 591687 041564 792176 039119 804400 977995 099273 607748 184019 370460 048426 15012] 065.375 278.177 458033 573141 486810 551558 752997 601918 266033 254156 769596 199524 940617 577.197 149643 176470 588235 294117 647058 823529 411764 705882 934731 934731 934731 934731 934731 934731 93473] 387990 762124 711316 397228 637413 394919 168591 102974 828375 286041 18993I 350ll 4 416475 972540 038548 752834 467120 181405 895691 609977 324263 988764 044943 820224 719101 123595 505617 977528 570155 902004 454342 984.409 7995.54 565701 559020 759381 898454 746.136 865342 163355 408388 520971 445747 800586 231884 057971 776504 297994 056657 223796 224089 635854 257617 723531 123287 671232 387533 875338 734584 450402 925729 442970 753280 839895 83] 168 83.11.68 688946 015424 951653 94.4020 460957 178841 301745 635910 975308 64.1975 110024 449877 302663 438256 465227 817745 705463 182897 352941 176470 934731 934731 224018 475750 O45766 590389 038548 752834 089887 640449 044543 429844 302428 256070 5102 0.144 2693 0339 3417 8559 8767 7533 1447 8222 013] 831] 1645 3562 3098 2244 3086 7506 6585 8033 8622 5882 9347 5773 0.160 4671 4382 0979 640] 649890 590809 628008 752735 229759 299.781 181619 256017 505470 4595 392624 728850 325379 609544 468546 637744 034707 158351 4099.78 3080 043010 752688 172043 010752 688172 043010 752688 172043 010752 6881 921108 742004 264392 324093 81663] 130063 965884 86.1407 249466 9509 778435 517970 401691 331923 890063 424947 145877 378435 517970 4016 588810 733752 620545 073375 262054 507337 526205 450733 752620 5450 822479 377031 185031 185031 18503] 185031 185031 185031 185031 1850 386624 701296 006597 938144 329896 907216 494845 360824 742268 0412 562282 251059 725360 163599 182004 089979 550102 249488 752556 2372 928528 863353 405941 4235.13 184584 178498 98580I 217038 539553 7525 252931 234542 078806 049486 654325 955.734 406438 631790 744466 8008 453782 696442 530660 811518 067440 159680 638722 554890 219560 8782 E 26 + TERMs of TAN -1 T; l , —— 20742 2.77.1.19 505.55 05 32 926836 52272 82 l 529.5529 l 553,555 3 I 577.55 l 601.56 01 FROM 355th To 424th DECIMAL PLACE. 27 341889 077311 301049 204588 687313 37534l 262984 804646 598768 1339 763120 326865 358607 559444 612297 346183 252928 274503 250396 4727 155672 290826 898924 074067 079322 134422 478832 718882 5642.24 4110 988366 297517 042008 968820 104949 144309 350039 895.349 436767 3411 131761 95.1250 107672 072589 266776994lll 655843 287910 620065 4394 209 212881 070647 153218 496024 352956 745669 163742 480557 8791 332209 489790 819676 188160 038670 101448 6996.17 284846 2544 527 546176 658.442 352580 973089 550420 011593 538592 6714 837786 553918 658544 285016 481878 208912 266237 8246 1330 547517 794660 667744 336712 069791 307613 9584 2 113251 250280 840869 723849 280674 516249 3039 3356 566648 897801 89.1437 516525 95.2965 7001 5 331660 297.272 74.7163 541979 233991 1122 8469 395028 773656 535551 065038 1244 13 454411 496689 986995 513563 5685 21374 6544.41 467136 862253 0524 33 959029 200503 148898 9046 53955 148663 417219 4721 85 729775 207315 2631 136223 284804 4637 216 466949 6653 343995 O167 546 6794 8688 13 28 + TERMs of TAN - #, l 505.55 05 529.5529 _l 553,555 3 } 577.557 | 601.56 0 1 625.562 5 l 649.56.49 171257 325912 388642 857335 502837 680848 265132 835489 941159 874104 788231 873140 917654 799304 765025 986897 866345 576221 190915 274926 873222 881225 251073 366790 926884 132396 445558 033380 386803 7550.11 430727 429438 330798 308165 678.195 327457 221220 660395 672659 304663 434503 1494.66 070303 511666 606361 lb 1033 344443 292945 772788 246967 016066 266445 746596 112240 582248 265342 254963 767302 500717 445568 329605 85.1687 430448 058033 372284 232962 300880 096531 807581 91.4097 428381 165929 823074 060282 737909 272049 796911 412903 128485 148055 311234 592489 138968 686726 396888 452328 456785 351824 694497 990099 545590 493068 898757 899326 831355 768354 44.1751 260460 223220 337593 330417 122854 916254 363303 813530 451553 420476 670295 695832 590790 488384 024884 856288 446236 050638 732279 086495 768279 701396 163712 940928 503556 356600 094382 466739 891330 279398 182648 739097 714177 882155 301380 178822 377612 939494 86.1084 864.138 350015 685067 913065 229519 720580 416789 033370 058934 214972 780554 714493 411096 054904 38.1501 060980 709111 201492 707179 015684 028084 550564 350645 441961 496092 973970 782257 424979 452773 516920 007898 051286 856829 105303 288034 283446 147313 745351 166599 98.7395 330840 262645 594972 417384 Ol?899 204845 900403 716404 265428 980303 514473 215794 998243 616022 709866 504264 808704 056176 349279 575400 544729 321633 984846 030756 21947 850942 84.1615 648330 09.1179 854075 509487 318914 34 885910 858244 144413 109241 809685 952533 963423 55453 232528 993628 574443 140651 481226 996890 88 149968 337823 259166 635060 536422 670078 140131 479457 486.507 969890 711371 266441 222 775420 782333 750910 213457 309584 354173 959908 320748 664886 259633 563 097430 097526 068651 408422 89.5298 394352 864053 893479 1423 5384.14 234694 295987 2 263536 430448 220883 3599 336820 065583 5 723662 104067 9102 103753 14 475236 23021 36 FROM 424th To 530th DECIMAL PLACE. 29 648.108 816256 372935 797438 639372 000063366336 633663 366336 6336 987496 403494 175146 035607 721847 96.1839 000392 927.308 447937 1316 896142 333479 683540 426766 859510 083781 913609 98.0506 822612 0857 030885 016687 272967 601513 133923 183514 058403 657779 497098 6460 399499 324540 890042 608061 365958 505292 519825 549915 000383 8771 461732 995.498 928163 694320 152294 596209 546370 526816 017417 7523 29525] 145021 208127 896981 529164 324.122 525555 673426 324110 8334 369078 237465 564635 195969 990931 115729 713519 006232 622965 7174 033253 538027 766542 86.9450 88.1207 1993.58 462383 033535 410020 2330 020749 300258 546131 263647 748978 0651.12 178911 052684 683224 1947 140231 120356 520729 415085 896314 707180 l 12113 881481 108003 3006 809927 653072 770284 291529 972498 335928 344367 510573 135748 95.97 657983 798282 927886 831323 110176 930448 968277 924812 454687 9600 472309 845717 631480 420589 505723 311576 411574 743820 240682 0608 97.1553 872610 523267 692247 467678 254216 179853 824263 266663 9854 758873 038506 292399 442620 462525 642479 618483 250960 457890 5444 559715 327287 890.489 154826 237079 302602 463225 1473.79 381817 1055 909918 26.3235 537339 443850 879242 996504 518817 661735 033489 0162 579636 417788 101110 282152 725279 185405 88.4476 346676 392857 3704 268969 226060 072246 032723 723573 III.435 398816 778938 47099] 1978 918283 134688 11.1868 649422 256364 843699 812558 530047 352483 1340 593472 857409 283654 854084 650648. 484709 173216 561602 927541 4672 926825 107623 646726 671727 638068 754016 846416 255122 520402 8922 865987 557222 9.70378 583360 360440 535400 018733 466905 963563 4141 86.1564 045448 684494 684896 548779 189350 106652 070228 932739 4272 340162 115679 509842 991882 638878 191848 725723 234100 383705 3260 167621 144380 915871 146167 721501 533809 046907 225107 732629 6005 635456 003332 927837 56092] 412443 443873 643613 876672 340904 8520 687739 473659 755,163 084408 025480 266660 861052 927861 005238 1839 065508 110158 449130 913038 530761 278774 95.5880 888003 839.588 3593 537348 302.173 205496 090360 312134 663050 545273 861200 512984 0239 679709 615742 723697 132099 141990 675139 984968 638889 031022 2321 899423 791085 755888 039168 632822 273958 074061 409854 941423 0975 | 514462 380558 260052 689805. 447396 ll0516 585.145 069695 292.126 6457 885056 380746 123211 615758 891906 374595 69.1893 260304 264339 6809 666937 850890 067013 900516 468712 463841 527661 404229 097757 3748 90.1300 893470 136439 381117 616326 211498 743384 509351 563064. 5386 538013 952293 689723 857049 544460 632676 907036 95.3253 461964 9099 926580 999965 534926 976386 370417 127045 693808 937912 875520 6406 7I1236 946969 990575 363445 654088 62.7055 900806 856211 095332 4467 068.189 179240 775130 875946 436276 337040 562888 260648 314066 8023 6.13477 658126 625089 296340 817650 520213 170641 125723 960846 2886 30 + TERMs of TAN -1 #, l 673,567 3 l 697.56 97 l 721.57 a 1 –– 745.5745 FROM 473rd To 530th DECIMAL PLACE. 31 58233 382593 252213 217805 056777 434051 762522 814652 265865 8096 92 622904 544186 090388 378855 447475 608475 457262 6551844672 147326 182382 176759 337286 308694 134477 387.100 303829 8029 234 345413 611123 79.1202 784178 033764 856293 408016 1356 37.2775 868385 764405 164370 767960 82.1890 417380 5307 592 9.98726 274843 694449 065417 893.232 398262 7998 943352 923520 153068 01:3090 007690 123505 2995 1500 752040 384700 002065 902962 305314 883] 2 387579 416305 644712 506548 59932] 4768 3798 574868 254960 840207 879859 005] 6 043623 184499 898425 1498.16 1459 96.15 85.1225 770549 683976 1649 15 300006 277675 415530 4541 24344 947.919 898426 6978 38 738188 733994 7530 61642 869494 3130 98 0932.93 5453 156102 0401 248 4222 3953 6 32 — TERMs of TAN -4 #, 3. 5 3 27.52 m 51.55 1 75.57 5 99.599 123.51 2 3 l •002666 666666 666666 666666 666666 666666 666666 666666 182857l 428571 428571 428571 428571 428571 428571 1861 818181. 818181. 818181 818181. 81818] 81818] 2 184533 333333 333333 333333 333333 333333 2759 410526 315789 473684 210526 315789 3 647220 869565 217391 304347 826086 4971 026962 96.2962 962962 96.2962 6 927.366 606451 612903 225806 98.17 068105 142857 142857 14 096302 920205 I28205 20456 030284 20465] 29 944.146 458580 44152 937523 65 506903 97705 146 147.5147 To 106th DECIMAL PLACE. 33 666666 666666 666666 666666 666666 666666 666666 666666 666666 6666 42857l 428571 428571 428571 42857l 42857l 428571 42857l 428571 4285 81818] 818181. 81818] 81818] 81818] 818181. 81818] 81818] 818181. 8181 333333 333333 333333 333333 333333 333333 333333 333333 333333 3333 473684 210526 315789 473684 210526 315789 473684 210526 315789 4736 956521 739130 434782 608695 652.173 913043 478260 869565 217391 3043 96.2962 96.2962 96.2962 96.2962 96.2962 96.2962 96.2962 96.2962 96.2962 96.29 451612 903225 806451 612903 225806 451612 903225 80645] 612903 2258 142857 142857 142857 142857 142857 142857 142857 142857 142857 1428 128205 128205 128205 128205 128205 128205 128205 128205 128205 1282 162790 697674 418604 651162 790697 674418 60465] 162790 697674 4186 425531 91.4893 617021 276595 744680 851063 829787 234042 553191 4893 240156 862745 098039 215686 274509 803921 568627 450980 392156 8627 670843 578181 818181 818181. 81818] 818181. 81818] 81818] 818181 8181 212254 817540 338983 050847 457627 118644 067796 610169 491525 4237 402730 743726 600126 984.126 984.126 984.126 984.126 984.126 984.126 984] 220259 630730 860317 802985 074626 865671 641791 044776 119402 98.50 332 561019 920397 550260 28.1690 140845 070422 535211 267605 6338 503719 09 1506 095489 460906 666666 666666 666666 666666 6666 765 142923 806727 325763 402531 645569 620253 164556 9620 1 165229 705652 654626 222820 240963 855421 686746 9879 1778 649481 731868 211061 96009] 954022 988505 7471 2 720747 339088 747856 92.1152 140659 340659 3406 4169 903290 224438 820712 8394.91 368421 0526 6 402275 758728 431320 690420 2291.71 7171 2’ 9845 829904 685276 90.4828 762760 2019 15 164418 395.253 585363 698879 4661 23388 724587 994.719 047434 6681 36 120325 9724.16 192198 4730 55849 915789 282179 5337 86 453853 384384 7722 133969 435795 6450 207 806025 6005 322638 0960 501 3656 7797 l2 134 — TERMs of TAN –1 #, 27.52 7 51.55 I 75.57 5 99.599 123.51 2 3 l 147.5147 666666 666666 666666 666666 666666 666666 666666 666666 || 714285 714285 714285 714285 714285 714285 714285 714285 || 818181. 818181. 81818.1 818181. 81818] 81818] 81818] 81818] 333333 333333 333333 333333 333333 333333 333333 333333 842105 263157 894736 84.2105 263157 894736 842105 263157 478260 869565 217391 304347 826086 956521 739130 434782 629629 629629 629629 629629 629629 629629 629629 629629 064516 12903.2 258064 516,129 O32258 064516 129032 258064 571428 571428 571428 571428 571428 571428 571428 571428 051282 051282 051282 ()5] 282 051282 051282 051282 051282 046511 627906 976744 186046 511627 906976 744186 04651.1 617021 276595 744680 851063 829787 234042 553.191 489361 450980 392156 862745 098039 215686 274509 80392.1 568627 81818] 81818] 818181 81818] 818181. 81818] 818181. 818181 288135 593220 338983 050847 457627 118644 067796 610169 26984] 26984] 26984] 26984.1 26984] 26984] 26984] 26984.1 746268 656716 417910 447761 194029 850746 268656 716417 028169 014084 507042 253521 126760 563380 28.1690 140845 666666 666666 666666 666666 666666 666666 666666 666666 253,164 5.56962 025316 45.5696 202531 645569 620253 164556 518072 289.156 626506 024096 385542 168674 698795 180722 264367 816091 954022 988505 747126 436781 60919.5 402298 593406 593406 593406 593406 593406 593406 593406 593406 315789 473684 210526 315789 473684 210526 315789 473684 717171 717171 717171 717171 717171 717171 717171 717171 417475 728155 339805 825242 718446 60194] 747572 815533 801869 158878 504672 897196 261682 242990 654205 607476 496400 720720 720720 720720 720720 720720 720720 720720 179424 006678 260869 5652.17 391304 347826 086956 52.1739 734058 941321 250420 168067 226890 756302 52.1008 403361 213858 250588 842000 650406 504065 0.40650 406504 065040 643556 592942 644756 738015 748031 496062 992.125 984251 731074 585493 785842 859306 601526 717557 251908 396.946 435564 690615 699981 575283 782693 925925 925925 925925 744273 971030 021519 395829 217964 474014 388489 208633 463356 129588 511026 474920 506420 106986 159440 559440 136459 971989 454770 903792 257223 598098 492743 401360 18903 942949 747812 994.149 483039 066160 746791 346013 29 465758 817155 300770 235581 304763 770557 579285 45959 170985 2485.19 440367 447569 694434 580375 71 7301.41 709492 167764 598028 5995.72 172743 112019 287.172 668008 101839 316519 571393 FROM 106th To 212th DECIMAL PLACE. 35 666666 666666 666666 666666 666666 666666 666666 666666 666666 6666 714285 714285 714285 714285 714285 714285 714285 714285 714285 7142 81818] 818181 81818] 81818] 818181 81818] 81818] 81818] 81818] 8181 333333 333333 333333 333333 333333 333333 333333 333333 333333 3333 894736 842105 263157 894736 842105 263157 894736 842105 263157 8947 608695 652.173 913043 478260 869565 217391 304347 826086 956521 7391 629629 629629 629629 629629 629629 629629 629629 629629 629629 6296 516129 O32258 064516 129032 258064 516129 O32258 064516 129032 2580 571428 571428 571428 571428 571428 571428 571428 571428 571428 57.14 051282 051282 ().51282 051282 051282 051282 051282 051282 ()51282 0512 627906 976744 186046 511627 906976 744186 046511 627906 976744 1860 702127 659574 468085 106382 9787.23 404255 319148 936,170 212765 9574 450980 392156 862745 098039 215686 274509 803921 568627 450980 3921 81818] 81818] 81818] 81818] 818181. 818181. 81818] 81818] 81818] 818] 491525 423728 813559 322033 898.305 084745 762711 864406 779661 0169 26984I 26984] 26984] 26984] 26984] 26984] 26984] 26984] 26984] 2698 910447 761194 029850 746268 656716 417910 447761 194029 850746 2686 070422 535211 267605 633802 816901 408450 704225 352112 676056 3380 666666 666666 666666 666666 666666 666666 666666 666666 666666 6666 96.2025 316455 696.202 531645 569620 253164. 556962 025316 45.5696 2025 89.1566 265060 240963 85542I 686746 987951 807228 915662 650602 4096 850574 712643 678160 919540 229885 057471 264367 81609) 954022 9885 593406 593406 593406 593406 593406 593406 593406 593406 593406 5934 210526 315789 473684 2105.26 315789 473684 210526 315789 473684 2105 717171 717171 717171 717171 717171 717171 717171 717171 717171 7171 98.0582 524271 844660 194174 757281 553398 058252 427.184 466019 4174 635514 018691 588785 046728 971962 616822 42.9906 542056 074766 3551 720720 720720 720720 720720 720720 720720 720720 720720 720720 7207 130434 782608 695652 173913 043478 260869 565217 391304 347826 0869 344537 815126 050420 168067 226890 756302 521008 403361 344537 8151 650406 504065 040650 406504 065040 650406 504065 0.40650 406504 0650 968503 937007 874015 748031 496062 992.125 984251 968503 937007 8740 564885 496.183 206106 870229 007633 587786 259541 984732 824427 4809 92.5925 925925 92.5925 925925 925925 925925 925925 925925 925925 92.59 093525 179856 115107 913669 064748 201438 848920 863309 352517 9856 559440 559440 559440 559440 559440 559440 559440 559440 559440 5594 544217 68.7074 829931 97.2789 115646 258503 401360 544217 68.7074 8299 245033 112582 781456 953642 384105 960264 900662 251655 629139 0728 140645 161290 322580 64516] 290322 580645 161290 322580 645161 2903 237200 503144 654088 050314 465408 805031 446540 880503 144654 0880 849449 962012 269938 650306 748466 257668 711656 44.1717 7914ll 0429 123328 961377 80.1197 604790 41916.1 676646 706586 826347 305389 2215 36 — TERMs of TAN -4 #, 123.51 2 3 l 147.5147 666666 666666 666666 666666 666666 666666 666666 666666 857142 857142 857142 857142 857142 857142 857142 857142 81818] 818181. 81818] 81818] 81818] 81818] 81818] 81818] 333333 333333 333333 333333 333333 333333 333333 333333 368421 052631 578947 368421 052631 578947 368421 052631 304347 826086 956521 739130 434782 608695 652.173 913043 296296 296296 296296 296296 296296 296296 296296 296296 645,161 290322 580645 161290 322580 645.161 290322 580645 285714 285714 2857.14 2857.14 2857.14 2857.14 285714 2857.14 820512 820512 820512 820512 820512 820512 820512 820512 465,116 279069 767441 860465 116279 069767 44.1860 465,116 468085 106382 9787.23 404255 319148 936,170 212765 957446 568627 450980 392156 862745 098039 215686 274509 803921 81818] 81818] 81818] 81818] 81818] 81818] 81818] 81818] 49.1525 423728 813559 322033 898.305 084745 7627ll 864406 412698 412698 412698 412698 412698 412698 412698 412698 567164 179104 477611 940298 507462 686567 1641.79 104477 281690 140845 070422 535211 267605 633802 816901 408450 |666666 666666 666666 666666 666666 666666 666666 666666 316455 696.202 531645 569620 253164 5.56962 025316 45.5696 385542 168674 698795 180722 89.1566 265060 240963 855421 O57471 264367 816091 954022 988505 747126 436781 609195 065934 065934 065934 065934 065934 065934 065934 065934 263157 894736 842105 263157 894736 842105 263157 894736 717171 717171 717171 717171 717171 717171 717171 717171 757281 553398 058252 427.184 466019 417475 728155 339805 401869 158878 504672 897196 261682 242990 654205 607476 207207 207207 207207 207207 207207 207207 207207 207207 565217 391304 347826 086956 52.1739 130434 782608 695652 260504 201680 672268 907563 025210 084033 613445 378151 406504 065040 650406 504065 0.40650 406504 065040 650406 157480 314960 62992] 259842 519685 039370 078740 157480 160305 343511 450381 679389 312977 099236 641221 374045 259259 259259 259259 259259 259259 259259 259259 259259 115107 913669 064748 201438 848920 863309 352517 985611 405594 405594 405594 405594 405594 405594 405594 405594 319727 891156 462585 034013 605442 176870 748299 319727 476821 192052 980.132 450331 125827 814569 536423 841059 225806 451612 903225 806451 612903 225806 451612 903225 503144 654088 050314. 465408 805031 446540 880503 144654 447852 760736 196319 018404 907975 4601.22 699386 503067 568862 275449 IO1796 407185 628.742 514970 059880 239520 FROM 212th To 318th DECIMAL PLACE. 37 666666 666666 666666 666666 666666 666666 666666 666666 666666 6666 857142 857142 857142 857142 857142 857142 857142 857142 857142 857.1 81818] 81818] 81818] 81818] 81818] 81818] 81818] 81818] 818181. 8181 333333 333333 333333 333333 333333 333333 333333 333333 333333 3333 578947 368421 052631 578947 368421 052631 578947 368421 052631 5789 478260 869565 217391 304347 826086 956521 739130 434782 608695 6521 296296 296.296 296296 296296 296.296 296296 296296 296296 296.296 2962 161290 322580 64516] 290322 580645 161290 322580 645 161 290322 5806 2857.14 2857.14 2857.14 2857.14 2857.14 2857.14 2857.14 2857.14 2857.14 2857 820512 820512 820512 820512 820512 820512 820512 820512 820512 8205 279069 767441 860465 lló279 069767 441860 465,116 279069 767441 8604 808510 638297 872340 425531 91.4893 617021 276595 744680 851063 8297 568627 450980 392156 862745 098039 215686 274509 80392.1 568627 4509 818181. 81818] 818181. 81818] 818181. 818181. 81818] 81818] 81818] 818] 779661 016949 152542 372881 355932 203389 830508 474576 27.1186 4406 412698 412698 412698 412698 412698 412698 412698 412698 412698 4126 611940 298507 462686 56.7164 179104 477611 940298 507462 686567 1641 704225 352112 676056 338028 169014 084507 042253 521126 760563 3802 666666 666666 666666 666666 666666 666666 666666 666666 666666 6666 202531 645569 620253 164556 962025 316455 696202 53.1645 569620 253] 686746 987951 807228 915662 650602 409638 554216 867469 879518 0722 402298 850574 712643 678160 919540 229885 057471 264367 816091 9540 065934 065934 065934 065934 065934 065934 065934 065934 065934 0659 84.2105 263157 894736 842105 263157 894736 842105 263157 894736 8421 717171 717171 717171 717171 717171 717171 717171 717171 717171 717] 825242 718446 601941 747572 815533 980582 524271 844660 194174 7572 635.514 018691 588785 046728 971962 616822 429.906 542056 074766 3551 207207 207207 207207 207207 207207 207207 207207 207207 207207 2072 173913 043478 260869 565217 391304 347826 086956 52.1739 130434 7826 260504 201680 672268 907563 025210 084033 613445 378151 260504 2016 504065 0.40650 406504 065040 650406 504065 0.40650 406504 065040 6504 3.14960 62992) 259842 519685 039370 078740 157480 314960 62992] 2598 801526 717557 251908 396946 564885 496.183 206106 870229 007633 5877 259259 259259 259259 259259 259259 259259 259259 259259 259259 2592 510791 366906 474820 143884 892086 330935 251798 56.1151 079136 6906 405594 405594 405594 405594 405594 405594 405594 405594 405594 4055 891156 462585 034013 605442 176870 748299 319727 891156 462585 0340 602649 006622 516556 291390 728476 821192 052980 132450 331.125 8278 806451 612903 225806 451612 903225 806451 612903 225806 451612 9032 088050 314465 408805 031446 540880 503144 654088 050314 465408 8050 484662 576687 llé564 417177 91.4110 429447 852760 736,196 319018 4049 958083 832335 329341 317365 269461 077844 311377 245508 982035 9281 —Terns of TAN — 4 5 * 27.527 51.55 1 75.57 5 99.599 I 123.51 2 3 l 147.5147 666666 666666 666666 666666 666666 666666 666666 666666 42857l 428571 428571 42857l 428571 428571 428571 428571 81818] 81818L 818181. 81818L 818181. 818181. 818181. 818181 333333 333333 333333 333333 333333 333333 333333 333333 473684 2105.26 315789 473684 210526 315789 473684 2105.26 739130 434782 608695 652.173 913043 478260 869565 217391 962962 96.2962 96.2962 96.2962 96.2962 96.2962 96.2962 96.2962 451612 903225 806451 612903 225806 451612 903225 806451 142857 142857 142857 142857 142857 142857 142857 142857 128205 128205 128205 128205 128205 128205 128205 128205 651162 790697 674418 604651 162790 697674 418604 651162 872340 425531 91.4893 617021 276595 744680 851063 829787 803921 568627 450980 392156 862745 098039 215686 274509 81818] 81818] 81818] 81818] 81818] 81818] 81818] 818181 779661 016949 152542 372881 355932 203389 8305.08 474576 984.126 984.126 984.126 984.126 984.126 984.126 984.126 984.126 791044 776119 402985 074626 865671 641791 044776 119402 816901 408450 704225 352112 676056 338028 169014 084507 666666 666666 666666 666666 666666 666666 666666 666666 645569 620253 164556 962025 316455 696202 531645 569620 89.1566 265060 240963 8554.21 686746 987951 807228 915662 229885 057471 264367 816091 954022 988505 747126 436781 340659 340659 340659 340659 340659 340659 340659 340659 O52631 578947 368421 052631 578947 368421 052631 578947 717171 717171 717171 717171 717171 717171 717171 717171 815533 98.0582 524271 844660 194174 757281 553398 058252 401869 158878 504672 897196 261682 242990 654205 607476 07.2072 07.2072 07.2072 07.2072 07.2072 07.2072 07.2072 07.2072 086956 52.1739 130434 782608 695652 173913 043478 260869 806722 689075 630252 100840 336134 453781 512605 042016 065040 650406 504065 040650 406504 065040 650406 504065 425196 850393 700787 401574 803149 606299 2.12598 425196 862595 419847 328244 274809 160305 343511 450381 679389 592592 592592 592592 592592 592592 592592 592592 592592 474820 143884 892086 330935 251798 56.1151 079136 690647 944055 94.4055 94.4055 94.4055 94.4055 94.4055 94.4055 94.4055 136054 421768 707482 993197 278911 564625 850340 136054 145695 364238 410596 026490 066225 165562 913907 284768 258064 516129 032258 064516 129032 258064 516129 032258 314465 408805 031446 540880 503144 654088 050314. 465408 O79754 601226 993865 030674 846625 76687] 165644 171779 437.125 748502 9940ll 976047 904.191 616766 46.7065 868263 FROM 318th To 424th DECIMAL PLACE. 39 666666 666666 666666 666666 42857l 428571 428571 428571 81818] 81818] 81818] 81818] 333333 333333 333333 333333 315789 473684 210526 315789 304347 826086 956521 739130 962962 96.2962 9.62962 96.2962 612903 225806 451612 903225 142857 142857 142857 142857 128205 128205 128205 128205 790697 674418 604651 162790 234042 553191 489361 702127 803921 568627 450980 392156 81818] 81818] 81818] 81818] 27.1186 440677 966101 694915 984.126 984.126 984.126 984 126 98.5074 626865 671641 791044 042253 521126 760563 380281 666666 666666 666666 666666 253,164 556962 02:5316 45.5696 650602 409638 554216 867469 60919.5 402298 850574 712643 340659 340659 340659 340659 368421 052631 578947 368421 717171 717171 717171 717171 427.184 466019 417475 728155 635.514 018691 588785 046728 07.2072 07.2072 07.2072 07.2072 565217 391.304 347826 086956 806722 689075 630252 100840 666666 666666 666666 428571 42857l 42857] 81818] 81818] 81818] 333333 333333 333333 473684 2105.26 315789 434782 608695 652.173 96.2962 96.2962 80645] 612903 142857 142857 142857 128205 128205 128205 697674 418604 651162 659574 468085 106382 962962 225806 215686 81818] 593220 984] 26 0.74626 422535 098039 81818] 288135 984 126 402985 845070 862745 81818] 254237 984 126 776119 690,140 666666 666666 645569 620253 072289 156626 919540 229885 340659 340659 578947 368421 666666 20253] 879518 678160 340659 05263] 717171 339805 971962 717171 717171 825242 718446 616822 42.9906 07.2072 07.2072 07.2072 521739 130434 782608 336134 453781 512605 504065 ()40650 406504 606299 212598 425196 801526 717557 251908 592592 592592 592592 179856 115107 913669 944055 94.4055 564625 850340 666666 666666 6666 42857] 81818] 333333 473684 913043 96.2962 451612 142857 128205 790697 978.723 274509 81818] 338983 984] 26 865671 211267 (366666 164556 506024 057471 340659 05263] 717171 60.194] 54.2056 07.2072 695652 042016 065040 850393 396.946 592592 064748 428571 81818] 333333 2105.26 478260 96.2962 90.3225 142857 128205 674418 404255 803921 8]818] 05.0847 984 126 641791 605633 666666 96.2025 096385 264367 340659 578947 717171 747572 074766 07.2072 1739.13 806722 650406 700787 564885 592592 201438 944055 94.4055 94.4055 136054 421768 707482 2781.45 695364 2384.10 5.96026 490066 032258 0645.16 129032 258064 5.16129 088050 314465 190184 049079 101796 407185 408805 ()31446 540880 75460I 226993 865030 628742 514970 059880 4285 818] 3333 3157 8695 96.29 8064 1428 1282 6046 3.191 5686 818] 4576 984] O447 8028 6666 3164 5421 8160 3406 3684 0.40650 406504 O65040 650406 850393 700787 401574 803149 312977 099236 641221 374045 592592 592592 592592 592592 482014 388489 208633 0935.25 944055 94.4055 94.4055 94.4055 421768 707482 993197 278911 211920 529801 324503 311258 064516 129032 258064 516129 805031 446540 880503 144654 141104 294478 527607 361963 473053 892215 568862 275449 717] 8.155 355] O720 ()434 6890 5040 4015 496] 5925 8489 9440 993] 2251 ()322 503] 6748 2395 G. 40 — TERMs of TAN –1 #. 51.55 1 99.599 T23.5 T2s I 147.514 7 666666 666666 666666 666666 666666 666666 666666 666666| 714285 714285 714285 714285 714285 714285 714285 714285 818,181 818181. 818181. 81818] 818181. 81818] 81818] 81818] 333333 333333 333333 333333 333333 333333 333333 333333 894736 842105 263157 894736 842105 263157 894736 842105 652.173 913043 478260 869565 217391 304347 826086 956521 629629 629629 629629 629629 629629 629629 629629 62.96.29 5,16129 O32258 064516 129032 258064 516129 O32258 064516 571428 571428 571428 571428 571428 571428 571428 571428 051282 051282 ()5]282 051282 051282 051282 051282 051282 511627 906976 744186 046511 627906 976744 186046 511627 489361 702127 659574 468085 106382 9787.23 404255 319148 274509 803921 568627 450980 392156 862745 098039 215686 818181. 81818] 818181. 81818] 81818] 81818] 81818] 81818] 27.1186 440677 966101 694915 254237 288135 593220 338983 26984] 26984] 26984] 26984] 26984] 26984] 26984] 26984] 761194 029850 746268 656716 417910 447761 194029 850746 169014 084507 042253 521126 760563 380281 690140 845070 666666 666666 666666 666666 666666 666666 666666 666666 556962 025316 45.5696 202531 645569 620253 164556 962025 686746 987951 807228 915662 650602 409638 554216 867469 919540 229885 057471. 264367 816091 954022 988505 747126 593406 593406 593406 593406 593406 593406 593406 593406 210526 315789 473684 210526 315789 473684 210526 315789 717171 717171 717171 717171 717171 717171 717171 717171 339805 825242 718446 601941 747572 815533 980582 524271 401869 158878 504672 897196 261682 242990 654205 607476 720720 720720 720720 720720 720720 720720 720720 720720 782608 695652 173913 043478 260869 565217 391304 347826 756302 521008 403361 344537 815126 050420 168067 226890 650406 504065 0.40650 406504 ()65040 650406 504065 0.40650 748031 496062 992.125 984251 968503 937007 874015 748031 832061 068702 290076 335877 862595 419847 328244 274809 | 92.5925 92.5925 92.5925 92.5925 92.5925 925925 92.5925 925925 208633 093525 179856 Il 5107 913669 064748 201438 848920 559440 559440 559440 559440 559440 559440 559440 559440 97.2789 115646 2.58503 40.1360 544217 687074 82993] 97.2789 655629 139072 847682 119205 298013 245033 112582 781456 580645 161290 322580 64516] 290322 580645 161290 322580 446540 880503 144654 088050 314465 408805 031446 540880 466257 66871] 65644I 717791 411042 944785 276073 619631 209580 838323 353293 413173 652694 610778 443113 772455 FROM 424th To 530th DECIMAL PLACE. 41 666666 666666 666666 666666 666666 666666 666666 666666 666666 6666 714285 714285 714285 714285 714285 714285 714285 714285 714285 7142 81818] 818181. 81818] 818181. 81818] 818181. 81818] 81818] 81818] 818] 333333 333333 333333 333333 333333 333333 333333 333333 333333 3333 263157 894736 842105 263157 894736 842105 263157 894736 842105 2631 739.130 434782 608695 652.173 913043 478260 869565 217391 304347 8260 629629 629629 629629 629629 629629 629629 629629 629629 629629 62.96 129032 258064 516129 O32258 0645.16 12903.2 258064 516,129 O32258 0645 571428 571428 571428 571428 571428 571428 571428 571428 571428 5714 051282 051282 051282 051282 051282 051282 051282 051282 051282 0512 906976 744186 046511 627906 976744 186046 511627 906976 744186 0.465 936,170 212765 957446 808510 638297 872340 425531 91.4893 617021 2765 274509 803921 568627 450980 392156 862745 098039 215686 274509 8039 81818] 81818] 818181. 818181. 818181. 81818] 81818] 81818] 81818] 8181 050847 457627 118644 067796 610169 49.1525 423728 813559 322033 8983 26984] 26984] 26984] 26984] 26984] 26984] 26984] 26984] 26984] 2698 268656 716417 910447 761194 029850 746268 656716 417910 44776] 1940 422535 211267 605633 802816 901408 450704 225352 112676 056338 0281 666666 666666 666666 666666 666666 666666 666666 666666 666666 6666 316455 696202 531645 569620 253164. 556962 025316 45.5696 202531 6455 879518 072289 156626 506024 096385 542168 674698 795180 722891 5662 436781 609195 402298 850574 712643 678160 9.19540 229885 057471 2643 593406 593406 593406 593406 593406 593406 593406 593406 593406 5934 473684 210526 315789 473684 2105.26 315789 473684 210526 315789 4736 717171 717171 717171 717171 717171 717171 717171 717171 717171 7171 84.4660 194174 757281 553398 058252 427.184 466019 417475 728155 3398 635.514 018691 588785 046728 971962 616822 42.9906 542056 074766 3551 720720 720720 720720 720720 720720 720720 720720 720720 720720 7207 086956 52.1739 130434 782608 695652 173913 043478 260869 5652.17 3913 756302 521008 403361 344537 815126 050420 168067 226890 756302 5210 406504 065040 650406 504065 0.40650 406504 065040 650406 504065 0406 496062 992.125 984251 968503 937007 874015 748031 496062 992.125 9842 160305 343511 450381 679389 312977 099236 641221 374045 801526 7175 925925 925925 92.5925 925925 92.5925 92.5925 925925 925925 925925 9259 863309 352517 985611 510791 366906 474820 143884 892086 330935 2517 559440 559440 559440 559440 559440 559440 559440 559440 559440 5594 115646 258503 401360 544217 68.7074 82993] 97.2789 115646 258503 4013 953642 384.105 960264 900662 251655 629.139 072847 682119 205298 0132 645161 290322 580645 161290 322580 645.161 290322 580645 161290 3225 503144 654088 050314. 465408 805031 446540 880503 144654 088050 3144 901840 490797 546012 269938 650306 748466 257668 71.1656 441717 7914 089820 359281 437.125 748502 9940ll 976047 904.191 616766 46.7065 8682 42 — TERMs of TAN -1 #, I H 175 038324 751677 7296.18 780499 263330 171.5 273659 918011 765867 563990 540562 428 071380 130136 552614 0634.15 669943 405843 011522 779605 1048 980904 977.720 715881 1 643220 349577 665121 I --- 2575 221224 774022 195.51 9 $ 4 037.532 774520 6332 760765 9 936621 15597 24 I - 3T9.52. To l I 267.52 67 29] .529 m FROM 121st To 212th DECIMAL PLACE. 43 270424 289464 796189 94.1520 467836 257309 94.1520 467836 25.7309 94.15 55521] 360489 128961 357531 428.571 428571 42857l 42857l 42857l 4285 405114 297100 206458 710503 401 117 318435 754189 944.134 078212 2905 257770 626965 516388 687293 378000 437.158 469945 355191 256830 6010 649302 006628 746006 409666 521396 141860 962566 844919 786096 2566 422981 524399 912674 372344 357189, 537830 601047 120418 848.167 5392 877471 093096 700581 093785 581720 305757 748880 410256 410256 4102 076069 200909 779751 664830 457796 466790 936772 114010 050251 2562 552671 036618 569822 034138 335062 868941 015932 355867 491625 6157 722954 142766 636287 334283 517542 166279 38.1845 289029 882904 7342 199595 461668 646018 665237 510431 326850 576925 436775 955910 9860 491230 620594 694580 911169 228760 565655 556998 930360 258431 2351 38.470 243531 893036 236682 384541 980066 600509 623890 611547 4901 60 448310 912893 81 1198 804966 562824. 28.4021 607947 13574] 1939 95013 027901 852475 047284 634667 910592 68242I 654352 5658 149 388449 064730 817909 843200 482186 698105 002358 7049 234953 067124 785150 210544 880417 94.1291 998335 6245 369 633277 150289 608699 434623 586384 6267.42 1514 581678 046017 575087 928657 613413 306507 2683 915 613053 812280 138407 538785 8100.95 4252 1 44.1634 5771.57 821158 161989 355.187 8474 2270 433122 300317 557324 92.1274 6801 3 576589 628951 85.1596 094856 6798 5635 508525 618430 803884 8236 8 881730 290562 680457 9578 14001 015424 827959 7477 22 075782 866201 4667 34814 854699 3858 54 916435 1159 86641 6788 136 7211 2157 3 44 — TERMs of TAN -1 #, l 171.517 195.51 95 219.52 19 l 243.52 4 3 I 267.52 67 l 291.52 91 204678 362573 099415 204678 362573 0994.15 204678 362573 714285 714285 714285 714285 714285 714285 714285 714285 027932 960893 854748 603351 955307 262569 832402 234636 928961 748633 879781 420765 027322 404371 584699 453551 844919 786096 256684 49.1978 609625 668449 197860 962566 670157 068062 82.7225 130890 052356 0.20942 408376 963350 564,102 564102 564,102 564,102 564,102 564,102 564,102 564,102 814070 351758 793969 849246 231155 778894 472361 809045 635467 980.295 566502 463054 187192 118226 600985 221674 995169 082125 603864 734299 516908 212560 386473 429951 094786 729857 819905 213270 142180 094786 729857 819905 110548 837209 302325 581395 348837 209302 325581 395.348 592612 003652 968036 529680 365296 803652 968036 529680 038.197 539220 089686 098654 708520 179372 197309 417040 942065 325471 338008 810572 687.224 669603 524229 074889 867219 732148 100389 458008 658008 658008 658008 658008 845237 976225 540161 293377 361702 127659 574468 085106 428610 081502 346456 488059 874008 368200 836820 083682 074557 615206 446490 884613 309036 299588 477366 255144 061455 012148 956544 11.1967 358925 317057 813765 182186 583325 446298 0.13018 431207 368526 88.1614 746007 968127 550559 464702 875615 796870 481879 217237 868556 850196 050319 028037 060900 583958 004.465 663014 027221 510404 049855 711806 914669 342973 354361 409014 270010 952828 043931 757616 211047 538799 712312 79.1314 28.1665 994.790 475056 707183 96.1790 994496 587590 774997 96849] 246.173 149938 853048 1271.48 482091 686255 924945 596796 864743 256437 179553 1941.79 015527 313053 593573 390905 342725 216698 493134 107935 977076 082659 1771.17 212585 512879 170360 003755 02.1338 234879 512370 132666 894334 002509 646487 385957 815483 843702 600247 698348 524528 790975 87.7093 574667 464267 42.1280 094680 255351 131772 95.1203 406414 676144 625562 321815 532457 154115 470682 932551 5378 312808 803923 6601.14 708088 209579 303106 187177 8 493179 315010 235147 959643 261120 534352 266708 13414 307651 231599 693497 674501 165294 128081 l 3.15.53 1 5 21 190347 578580 457166 617278 831047 143994 33479 420625 719593 767947 048686 043.136 52 903703 676059 692443 220351 85.5592 83610 501711 888835 029529 901648 132 160164 639456 913859 365693 208931 412516 586213 671403 FROM 212th TO 318th DECIMAL PLACE. 45 0994.15 204678 362573 0994.15 204678 362573 0994.15 204678 362573 0994 714285 714285 714285 714285 714285 714285 714285 714285 714285 7142 871508 379888 268156 424581 005586 592.178 770949 720670 391061 4525 912568 306010 928961 748633 879781 420765 027322 40437I 584699 4535 844919 786096 256684 49.1978 609625 668449 197860 962566 844919 7860 785340 314136 125654 450261 780104 712041 884816 753926 701570 6806 564,102 564,102 564,102 564,102 564,102 564,102 564,102 564,102 564,102 564] 226130 653266 331658 291457 286432 160804 020.100 502512 562814 0703 876847 290640 394088 669950 738916 256157 635467 980.295 566502 4630 690821 256038 647342 995.169 082125 603864 734.299 516908 212560 3864 213270 142180 094786 729857 819905 213270 142180 094786 729857 8199 837209 302325 58.1395 348837 209302 325581 395.348 837209 302325 5813 365296 803652 968036 529680 365296 803652 968036 529680 365296 8036 358744 394618 834080 717488 789237 668161 434977 578475 336322 8699 867841 409691 629955 94.7136 56.3876 651982 378854 625550 660792 95.15 658008 658008 658008 658008 658008 658008 658008 658008 658008 6580 382978 723404 255319 148936 170212 765957 446808 510638 297872 3404 008368 200836 820083 682008 368200 836820 083682 008368 200836 8200 032921 810699 588477 366255 144032 92.1810 699588 477366 255144 0329 234817 813765 182186 234817 813765 182186 234817 813765 182186 2348 490039 840637 450199 203187250.996 015936 254980 079681 274900 3984 0.7843] 372549 019607 843137 254901 960784 313725 490196 0.78431 3725 942084 942084 942084 942084 942084 942084 942084 942084 942084 9420 562007 604562 737642 585551 330798 479087 452471 482889 733840 3041 075876 002996 254681 647940 074906 367.04] 198501 872659 176029 96.25 336975 698260 073800 738007 380073 800738 007380 073800 738007 3800 057305 136955 511156 363636 363636 363636 363636 363636 363636 3636 759660 266.165 807974 583512 544802 86.7383 512544 802867 383512 5448 833141 7397.27 266490 034820 070671 378091 872791 519434 628975 2650 519123 507246 510474 796821 486160 278745 644599 303135 888501 7421 781344 266372 947070 824834 022084 002749 140893 470790 378006 8728 655334 894543 807607 309071 331256 550209 O84745 762711 864406 7796 732860 595.552 590893 614213 651064 726059 192936 454849 498327 7591 995871 288808 291615 457112 342609 469851 309300 002640 264026 4026 612027 356354 443842 915874 944832 889482 032295 598.180 065146 5798 695402 66.1856 724446 352541 086086 501335 413422 069446 386006 4308 0.74449 626554 O94939 950809 601410 909977 982545 1391.16 6873.70 4025 592518 879660 762582 601050 808900 034791 940135 431818 541725 5005 622033 503517 58.1588 923094 663569 233986 866273 204719 505212 6832 227116 412582 929.315 489772 034624 258654 814717 094777 367095 7000 481427 272831 007216 368169 935735 696.109 148637 643456 155644 9077 197814 220548 332243 050115 172531 240670 625089 905958 132477 7001 46 — TERMs of TAN -1 #, I 171.51 1 l 195.51 95 219.52 19 –– 243.52 4 3 l 267.52 67 I 291.52 9 I I 3.15.53 1 5 152046 783625 730994 152046 783625 730994 152046 783625 857142 857142 857142 857142 857142 857142 857142 857142 139664 804469 273743 016759 776536 312849 162011 173184 519125 683060 109289 617486 338797 814207 650273 224043 962566 844919 786096 256684. 491978 609625 668449 197860 282722 513089 005:235 602094 240837 696335 078534 031413 0.2564] 02564] 02:564] 025641 02564] 02564] 02564] 02564] 517587 939698 492462 31.1557 788944 723618 090452 261306 541871 921.182 266009 852216 748768 472906 403940 886699 734.299 516908 212560 386473 429951 690821 256038 647342 052132 701421 800947 86.7298 578.199 052132 70.1421 800947 95.3488 372093 023255 813953 488372 093023 255813 95.3488 529680 365296 803652 968036 529680 365296 803652 968036 551569 506726 457399 103139 013452 914798 206278 026.905 4.18502 202643 171806 167400 881057 268722 466960 352422 086580 086580 086.580 086.580 086.580 086.580 086.580 086580 255319 148936 170212 765957 446808 510638 297872 340425 836820 083682 008368 200836 820083 682008 368200 836820 218106 995884 773662 551440 329218 106995 88.4773 662551 178137 651821 862348 178137 063745 019920 318725 099601 490.196 07843] 372549 O19607 849420 849420 849420 849420 825095 057034 220532 31939] 651821 862348 178137 651821 5936.25 498007 968127 490039 843.137 254901 960784 313725 849420 849420 849420 849420 634980 988593 155893 536,121 468164 794007 490636 704119 850187 265917 602996 254681 738007 380073 800738 007380 073800 738007 380073 800738 363636 363636 363636 363636 363636 363636 363636 363636 028673 8351.25 448028 6.73835 176678 445229 68.1978 798586 602787 456445 993031 358885 522336 769759 450171 821305 I25448 028673 8351.25 448028 572438 162544 1696] 1 307420 0.17421 602787 456445 993031 84.1924 398625 42.9553 264604 610169 49.1525 423728 813559 322033 898305 084745 762711 97.3244 147157 190635 451505 O16722 408026 75.5852 842809 402640 264026 402640 264026 402640 264026 402640 264026 045602 605863 192182 410423 452768 72964l 693811 074918 681672 0257.23 472668 810289 389067 5241.15 755627 009646 396825 396825 396825 396825 396825 396825 396825 396825 732915 36050l 567898 I 19122 257053 291536 050156 739811 677789 721362 2291.02 167182 662538 699690 402476 780185 449932 360024 464831 80428] 345565 749235 474006 116207 651466 479186 600604 229607 250755 287009 063444 108761 288.131 989992 170816 955223 880597 0.14925 373.134 328358 FROM 318th To 424th DECIMAL PLACE. 47 730994 152046 783625 730994 152046 783625 730994 152046 783625 7309 857142 857142 857142 857142 857142 857142 857142 857142 857142 857.1 357541 899441 340782 122905 02.7932 960893 854748 603351 955307 2625 715846 994535 519125 683060 109289 617486 338797 814207 650273 2240 96.2566 844919 786096 256684 491978 609625 668449 197860 962566 8449 612565 445026 178010 471204 188481 675392 670157 068062 827225 1308 02564] 025641 025641 02564] 02564] 02:5641 025641 025641 02564] 0256 532663 316582 91.4572 864321 608040 201005 025.125 628140 703517 5879 507389 162561 576354 679802 955665 024630 541871 92.1182 266009 8522 995169 082125 603864 734.299 516908 212560 386473 429951 69082] 2560 867298 578.199 052132 70.1421 800947 86.7298 578199 052132 70.1421 8009 372093 023255 813953 488372 093023 255813 95.3488 372093 023255 8139 529680 365296 803652 968036 529680 365296 803652 968036 529680 3652 829596 412556 053811 659192 8251.12 107623 318385 650224 215246 6367 907488 986784 140969 162995 594.713 656387 665198 237885 462555 0660 | 086580 086580 086580 086580 086580 086580 086580 086580 086580 0865 531914 893617 021276 595744 680851 063829 787234 042553 191489 36.17 083682 008368 200836 820083 682008 368200 836820 083682 008368 2008 440329 218106 995884 773662 551440 329218 106995 88.4773 662551 4403 862348 178137 651821 862348 178137 651821 86.2348 178137 651821 8623 840637 450199 203187250.996 Olš936 254980 07968] 274900 398406 3745 490.196 078431 372549 019607 843137 254901 960784 313725 490.196 0784 849420 849420 849420 849420 849420 849420 849420 849420 849420 8494 673003 802281 36882] 292775 665399 239543 726235 74.1444 866920 1520 647940 074906 367041 19850I 872659 176029 962546 8164.79 400749 0636 007380 073800 738007 380073 800738 007380 073800 738007 380073 8007 363636 363636 363636 363636 363636 363636 363636 363636 363636 3636 6.73835 125448 028673 8351.25 448028 6.73835 125448 028673 835125 4480 494699 646643 109540 636042 402826 855123 674911 660777 385159 0106 358885 0.17421 602787 456445 993031 358885 0.17421 602787 456445 9930 810996 563573 883.161 512027 491408 934707 903780 068728 522336 7697 864.406 779661 016949 152542 372881 355932 203389 8305.08 474576 2711 364548 494983 277591 973244 147157 190635 45,1505 016722 408026 7558 402640 264026 402640 264026 402640 264026 402640 264026 402640 2640 566775 244299 674267 100977 198697 068403 908794 788273 615635 1791 302250 803858 520900 32.1543 408360 128617 363344 051446 945337 6205 396825 396825 396825 396825 396825 396825 396825 396825 396825 3968 912225 705329 153605 0.15673 981191 222570 532915 360501 56.7398 1191 7585.13 93.1888 544891 640866 873065 015479 876160 990712 074303 4055 95.1070 336391 437308 868501 529051 987767 584097 859327 217.125 3822 329305 135951 661631 419939 577039 274924 471299 093655 589123 8670 |208955 223880 597014 925373 134328 358208 955223 880597 014925 3731 H — TERMs of TAN -1 #, I 171.51 I 195.51 95 219.52 19 243.52 4 3 l 267.52 6 7 l 291.52 91 315.53 1 5 941520 467836 257309 94.1520 467836 25.7309 94.1520 467836 42857l 428571 42857l 42857l 428571 428571 428571 428571 698324 022346 368715 083798 882681 564245 810055 865921 437158 469945 355191 256830 601092 896174 863387 978142 197860 962566 844919 786096 256684 49.1978 609625 668449 900523 560209 424083 769633 507853 403141 36.1256 544502 410256 410256 410256 410256 410256 410256 410256 410256 396984 924623 115577 8894.47 236180 904522 613065 326633 167487 684.729 064039 408866 995073 891625 615763 546798 386473 429951 690821 256038 647342 99.5169 082125 603864 478672 98.5781 990521 327014 218009 478672 985781 990521 534883 720930 232558 139534 883720 930232 558.139 534883 96.8036 529680 365296 803652 968036 529680 365296 803652 713004 484304 932735 426008 968609 865470 852017 937219 792951 541850 220264 3.17180 616740 088105 726872 246696 800865 800865 800865 800865 800865 800865 800865 800865 021276 595744 680851 063829 787234 042553. 191489 361702 368200 836820 083682 008368 200836 820083 682008 368200 .29218.1 069958 847736 625514 40329.2 181069 958847 736625 481781 376518 218623 481781 376518 218623 481781 376518 0.19920 318725 09960I 5936.25 498007 968127 490039 840637 313725 490196 0.78431 372549 O19607 843137 254901 960784 208494 208494 208494 208494 208494 208494 208494 208494 912547 5285.17 110266 159695 817490 494.296 577946 768060 704119 850187 265917 602996 254681 647940 074906 367041 380073 800738 007380 073800 738007 380073 800738 007380 363636 363636 363636 363636 363636 363636 363636 363636 286738 351254 480286 738351 254480 286738 351254 480286 007067 137809 187279 151943 462897 526501 766784 452296 313588 8501.74 216027 874564 459930 313588 8501.74 216027 -594501 718213 058419 243986 254295 532646 048109 965635 864.406 779661 016949 152542 372881 355932 203389 830508 528428 093645 484949 832775 9.19732 441471 571906 3545.15 264026 402640 264026 402640 264026 402640 264026 402640 530944 625407 166123 77850l 628664 495.114 006514 65.7980 78778] 350482 315112 540192 926045 016077 170418 006430 253968 253968 253968 253968 253968 253968 253968 253968 222570 532915 360501 56.7398 119122 257053 291536 050156 727554 179566 563467 492260 061919 504643 96.2848 297213 629969 418960 244648 318042 813455 657492 354740 061162 694864 048338 368580 060422 960725 0755.28 700906 344410 343283 582089 552238 805970 149253 731343 283582 089552 FROM 424th To 530th DECIMAL PLACE. 49 257309 94.1520 467836 25.7309 94.1520 467836 257309 94.1520 467836 2573 42857l 428571 42857l 428571 428571 428571 42857l 428571 428571 4285 787709 497206 703910 614525 139664 804469 273743 016759 776536 3128 076502 732240 437158 469945 355191 256830 601092 896174 863387 9781 197860 962566 844919 786096 256684 491978 609625 668449 197860 96.25 617801 047120 418848 167539 267015 706806 282722 513089 005235 6020 410256 410256 410256 410256 410256 410256 410256 410256 410256 4102 165829 145728 643216 080402 010050 25.1256 281407 0351.75 879396 9849 029556 650246 305418 719211 822660 098522 167487 684.729 064039 4088 734.299 516908 212560 386473 429951 69082] 256038 647342 995,169 O321 327014 218009 478672 98.5781 99052] 327014 218009 478672 98.5781 9905 720930 232558 1395.34 883720 930232 558139 534883 720930 232558 1395 968036 529680 365296 803652 968036 529680 365296 803652 968036 5296 730941 704035 874439 46.1883 408071 748878 923766 816143. 497757 8475 035242 290748 898678 414096 916299 559471 365638 766519 823788 5462 800865 800865 800865 800865 800865 800865 800865 800865 800865 8008 127659 574468 085106 382978 723404 255319 148936 170212 765957 4468 836820 083682 008368 200836 820083 682008 368200 836820 083682 0083 514403 292.181 069958 847736 625514 403292 181069 958847 736625 5144 218623 481781 376518 218623 481781 376518 218623 481781 376518 2186 450199 203187250.996 015.936 254980 079681 274900 398406 374501 9920 313725 490.196 0.78431 372549 019607 843137 254901 960784 313725 4901 208494 208494 208494. 208494. 208494 208494. 208494 208494 208494 2084 836501 901140 684410 646387 832699 619771 863117 870722 433460 0760 198501 872659 176029 96.2546 8164.79 400749 063670 411985 018726 5917 073800 738007 380073 800738 007380 073800 738007 380073 800738 0073 363636 363636 363636 363636 363636 363636 363636 363636 363636 3636 73835] 254480 286738 351254 480286 738351 254480 286738 351254 4802 819787 985865 724381 625441 696.113 074204 946996 466431 O95406 3604 874564 459930 313588 850174 216027 874564 459930 313588 850174 2160 738831 615120 274914 089347 079037 800687 285223 367697 5945O1 7182 474576 271186 440677 966101 694915 254237 288135 593220 338983 0508 050167 224080 267558 528428 093645 484949 832775 9.19732 441471 57.19 264026 402640 264026 402640 264026 402640 264026 402640 264026 4026 456026 058631 921824 104234 527687 296416 9381.10 749185 667752 4429 868167 202572 347266 881028 938906 752411 575562 700964 630225 0803 253968 253968 253968 253968 253968 253968 253968 253968 253968 2539 739811 912225 705329 153605 015673 981191 222570 532915 360501 5673 622291 021671 826625 386996 904024 767801 857585 139318 885448 9164 0795.10 703363 914373 088685 015290 519877 675840 978593 27217] 2538 876132 930513 595166 163141 993957 7039274924.47 129909 365558 9123 238805 970149 253731 343283 582089 552238 805970 149253 731343 2835 || | — TERMs of TAN -1 #. == | 330 345832 1796.17 140200 ; : 339.533.9 522389 444239 721098 826 188262 244262 1 306836 818227 2067 379034 || 3 270950 l 363.5, 53. siſ l 387.53 8.7 4] 1.54 * 1 I 435.543 5 FROM 239th To 318th DECIMAL PLACE. 51 212725 747558 153115 286946 494786 067094 3936.72 708523 874805 3334 672289 744738 995.749 9992.17 608684 466363 825070 344248 114722 1411 07.1905 915308 105939 0997.10 578166 126902 422095 673213 035635 0418 960975 276821 022964 152103 017985 748873 835398 141076 261758 9304 131895 447085 8.10384 497655 833957 467032 4897.18 196045 150503 1093 672386 95.4356 392034 257366 764662 083123 327170 361936 918232 5508 85.1422 091092 513255 053656 836004 468045 581375 004561 698528 4649 191102 196050 426516 88974] 590981 883910 193116 246873 704181 2134 12964 46148] 188168 330775 353806 535208 172683 013100 173151 2000 20 521878 227.288 791256 395333 385491 465523 479030 870034 0868 32488 461573 544260 564214 248103 680420 353792 661007 9695 51 4386.50 386937 962418 118851 305670 514,105 848223 5906 81451 175599 781869 172669 850336 214188 744350 8822 128 988664 786150 724787 000438 179498 275372 1280 204291 920.734 723780 827208 795.253 402838 1589 323 590210 286580 023766 405911 278572 9165 512605 434855 962002 909363 607345 5110 812 108069 766890 170702. 598658 5169 1 286726 946550 362236 402754 8574 2038 919614 581971 582309 52.19 3 231127 98.1103 649476 5000 5120 91.7727 025736 6644 8 116714 56.1243 6032 12866 2.16678 0548 20 396650 6234 32337 2866 51 2724 813 l 52 — TERMs of TAN –1 #, 339.53 so I 363.53 63 l 387,5387 l 411.54 l I 435.543 5 l 459.5459 483.54 83 727700 409282 111514 920023 598820 058997 050147 492625 454.100 013708 439117 450998 894460 64,1399 416909 620991 186184 46711 1 017842 615726 536580 057636 887608 069164 137256 323692 706658 422279 918441 906689 458689 458689 389305 586341 93.1898 758788 5983.16 047816 329014 084507 805139 625551 649630 413635 074996 778593 759540 0557.10 510351 714052 112582 776059 482058 066527 890.510 963658 399007 117916 95.2226 125548 597676 237942 886645 255497 229970 611804 96.1817 647387 930287 211555 040601 180846 062230 694813 779800 893.214 638601 115970 077525 602295 305639 415347 990152 719092 160377 732637 419647 797787 859617 075042 994833 495062 291086 300410 107914 554633 128484 685642 34.1982 516707 426800 975929 951716 098292 467166 132269 436670 474614 693705 051571 089069 316133 957114 580081 893062 230503 592284 511089 273097 017124 826698 988507 798888 258971 624737 653661 675239 592267 420505 619439 859500 76988.7 164975 763072 202514 821230 177393 469344 99956] 194340 106250 556.196 631341 969426 847124 862839 993828 988442 224618 711343 540745 328200 139324 022433 261638 414319 999052 634950 794005 768982 538206 470527 197340 639396 440284 894867 797916 992435 104871 899805 77.1709 44956] 823578 172561 511517 076954 189063 64.7076 788.164 620504 598225 287370 467519 894046 253344 705994 623808 988558 535363 126488 008128 560537 174886 221860 353776 042939 103370 083705 807196 334380 375821 687495 250128 082291 311198 053709 018774 05159] 833729 971000 669669 729040 635252 788968 228475 816916 O18707 265779 519630 116116 205821 626793 782282 648006 289292 637331 453464 389044 448581 826225 017545 650886 2044 733114 501927 076710 185657 355265 503236 617454 3 243062 543262 315712 080643 046959 985373 325179 5144 071558 902472 265555 127977 726594 510086 8 160017 582087 690480 349547 764239 531505 12945 148911 54.1236 362881 490635 753244 20 537819 4099.73 633101 1947.18 617060 32586 101777 828728 928826 693421 51 705980 129457 428263 049229 82050 064566 826900 537339 130 210611 630288 229936 206653 447468 190774 327 995050 891396 520618 784556 FROM 318th To 424th DECIMAL PLACE. 53 368731 563421 828908 55457227.1386 430678 466076 696165. 191740 4129 253644 314868 804664 723032 069970 845481 049562 682215 743440 2332 265129 682997 118155 619596 541786 743515 850144 092219 020172 9106 458689 458689 458689 458689 458689 458689 458689 458689 458689 4586 042253 521126 760563 380281 690140 845070 422535 211267 605633 8028 306406 685236 768802 2284.12 256267 409470 752089 136490 250696 3788 402203 856749 311294 765840 220385 674931 129476 584022 038567 493] 800544 959128 065395 095367 847411 444141 689373 297002 724795 6403 437489 164420 485.175 202156 334231 805929 919137 466307 277628 0323 867854 116181 333333333333 333333 333333 333333 333333 333333 3333 275780 243983 400527 704485 488126 649076 517150 395778. 364116 0949 363457 005587 340820 052219 321148 825065 274151 436031 331592 6892 1946.38 569646 056647 169322 997416 020671 834625 322997 416020 6718 152242 762665 792425 258.125 94.5780 051150 895.140 664961 636828 6445 488354 539423 604353 775294 895168 810.126 582278 481012 658227 8481 726006 616714 074481 081669 13878] 320020 050125 313283 208020 0501 034035 440754 616042 552661 383568 729515 386600 496277 915632 7543 852889 302339 554241 828594 486634 214046 170813 955773 955773 95.57 707461 317551 541405 650313 335108 749878 800161 640019 464720 1946 710325 847138 366008 743025 653130 524129 928431 292275 847710 8433 810309 442392 601.133 722685 844949 113766 162941 475842 651940 0477 442002 911229 7399.52 245975 623145 281054 06344] 219776 370954 7532 095471 539977 330885 245152 403516 96657l 937681 819713 2.19315 8364 383509 1094.10 933903 621344 520004 832463 020760 613037 652137 9038 107079 696230 114436 827442 021105 736396 474710 612686 783367 6190 636798 468037 8381.76 874.787 926302 254197 111495 213180 933943 5623 112789 361724. 491597 145455 645687 211519 973027 345909 115774 2707 778838 355927 495122 246211 854500 364866 947107 118082 282732 1270 595228 880692 149322 64.1752 751038 444924 507407 031066 191682 0621 24.1246 411341 335065 826853 38.1945 383.168 91.7636 362447 510689 92.91 753132 0858.11 452052 130548 909067 660651 300592 678152 204330 6803 419029 5900.73 045206 019621 328550 365637 110831 8688.18 218096 8908 507535 796831 533430 168349 754775 567689 216213 499461 285944 2530 035913 441077 266500 592402 953156 620603 349007 122562 202702 4576 304643 082882 517532 704939 862874 734377 445650 130036 974475 6980 640566 865851 755142 640617 441118 548639 095738 401041 394782 0491 478975 839432 688996 151800 764403 464297 467915 059856 228001 9895 721850 826547 666492 928595 71 1767 414778 663415 204842 416618 0696 242589 136790 317600 267392 997512 442300 601903 326125 485154 8448 622044 804092 651461 629838 513007 76924l 760308 798490 91.7537 6518 980963 245460 603967 850923 511227 058423 325599 528.193 196005 3904 046420 678042 098899 021733 950956 985454 165374 072889 283196 2041 54 — TERMs of TAN Tº #, 339.53 39 l 363.53 63 l 387.53 8.7 l 411.54 11 l 435.543 5 459.545 9 483.54 83 793510 324483 775811 209439 528023 598820 058997 0501.47 361516 034985 422740 52478] 341107 871720 116618 075801 628242 074927 953890 489913 544668 587896 253602 305475 894586 894586 894586 894586 894586 894586 894586 894586 169014 084507 042253 521126 760563 380281 690140 845070 300835 654596 100278 551532 033426 183844 0.11142 061281 1294.76 584022 038567 493112 947658 402203 856749 311294 269754 768392 370572 207084 468664 850136 239782 016348 450134 770889 487870 619946 091644 204851 752021 563342 333333 333333 333333 333333 333333 333333 333333 333333 868073 878627 968337 730870 712401 055408 970976 253298 950391 644908 616,187 98.9556 135770 234986 945169 712793 346253 229974 160206 718346 253229 974160 206718 346253 O12787 723785 166240 409.207 161125 319693 094629 156010 0.12658 227848 10.1265 822784 8101.26 582278 481012 658227 25.3132 832080 20050] 253132 832080 200501. 253132 832080 424317 617866 004962 779156 327543 424317 617866 004962 739557 7395.57 7395.57 7395.57 7395.57 739557 739557 7395.57 472019 464720 194647 201946 47.2019 464720 194647 201946 734939 759036 144578 313253 012048 192771 084337 349397 326968 973747 016706 443914 081145 584725 536992 840095 104018 912529 550827 423.167 848699 763593 380614 657210 800299 765807 962529 274004 683840 7494.14 519906 323185 967126 600464 037122 969837 587.006 960556 844547 563805 770739 610353 287356 321839 080459 7701.14 942528 735632 300174 111090 674004 555808 656036 446469 248291 571753 859607 318951 760924 200451 467268 623024 830699 774266 763603 780017 165566 315600 178970 917225 950782 997762 225831 772557 579327 745075 204541 019955 654101 995565 780827 604850 719888 445935 925862 850.109 890.109 890109 234022 750536 669551 369909 894017 490533 507625 272331 24.2537 940.190 052116 886665 360315 694265 762004 319654 550805 293589 063791 452226 2.13488 05.5388 248557 800428 345706 075828 810506 295059 667572 650265 363268 200400 464703 419155 251771 784303 067295 753156 294690 018770 242490 969934 359063 353979 270002 38992.1 500592 827587 702874 213414 819239 722887 142261 966525 125958 704644 869.402 8361.23 464008 846936 031177 700303 348290 227693 063137 757005 92.1391 355791 308666 993205 858.185 311090 102623 032367 482528 97.9897 191216 340989 62.1256 950263 213100 756396 062216 759423 003157 201086 300160 391792 823307 633486 891880 86.2546 169633 639581 207359 936494 FROM 424th To 530th DECIMAL PLACE. 55 492625 368731 563421 828908 554572 27.1386 430678 466076 696165 1917 749271 137026 239067 055393 586005 830903 790087 463556 851311 9533 504322 766570 605187 319884 726224 783861 671469 740634 005763 6887 894586 894586 894586 894586 894586 894586 894586 894586 894586 8945 422535 211267 605633 802816 901408 450704 225352 ll 2676 056338 0281 337047 353760 445682 45.1253 481894 150417 827298 050139 275766 0167 765840 220385 67493] 1294.76 584022 038567 493112 947658 402203 8567 773841 96.1852 86.1035 422343 324250 681198 910081 743869 209809 2643 318059 299.191 374663 07.2776 280323 450134 770889 487870 619946 0916 333333 333333 333333 333333 333333 333333 333333 333333 333333 3333 153034 300791 556728 232189 97.3614 775725 593667 546174 142480 2110 733681 462140 992.167 101827 676240 208877 284595 300261 096605 7441 229974 160206 718346 253229 974160 206718 346253 229.974 160206 7.183 230179 028132 992327 365728 900255 754475 703324 808.184 143222 5063 848101 265822 784810 126582 278481 012658 227848 101265 822784 8101 200501. 253132 832080 200501. 253132 832080 200501. 253132 832080 2005 779156 327543 424317 617866 004962 779156 327543 424317 617866 0049 739557 739557 739557 7395.57 739557 739557 7395.57 739557 739557 7395 472019 464720 194647 201946 47.2019 464720 194647 201946 47.2019 4647 590361 445783 132530 120481 927.710 843373 493975 903614 457831 3253 465393 794749 40334] 288782 816229 116945 107398 568019 093078 7589 401891 252955 082742 316784 869976 359338 061.465 721040 189125 2955 0.11709 601873 536299 765807 962529 274004 683840 749414 519906 3231 104408 352668 213457 076566 125290 023201 856148 49.1879 350348 0278 183908 045977 011494 252873 563218 390804 597701 1494.25 287356 3218 986332 574031 890660 592255 125284 73804.1 002.277 904328 018223 2346 365688 487584 6501.12 866817 155756 207674 943566 591422 121896 1625 863534 675615 212527 964205 816554 809843 400447 427293 064876 9574 410199 556541 019955 654101 995565 410199 556541 019955 654101 9955 89.0109 890.109 890.109 890.109 890.109 890.109 890.109 890.109 890 109 8901 154684 095860 566448 801742 919389 978213 507625 272331 154684 0958 427645 788336 933045 356371 490280 777537 796976 241900 647948 1641 265524 625267 665952 890792 2.91220 556745 182012 847965 738758 0299 169851 380042 462845 010615 711252 653927 813163 481953 290870 4883 150669 473684 2105.26 315789 473684 210526 315789 473684 210526 3157 192723 400417 5365.34 446764 09.1858 037578 288100 208768 267223 3820 0.22410 979739 296066 252587 99.1718 426501 035.196 687370 600414 0786 940247 472700 498004 106776 180698 151950 718685 83.1622 176591 3757 466635 928372 155250 600407 331975 56008] 466395 112016 293279 0224 419536 543808 745788 211861 979797 979797 979797 979797 979797 9797 802862 270426 245544 417362 314004 008016 032064 128256 513026 0521 646866 412001 408179 806486 723800 200397 614314 115308 151093 4393 56 — TERMs of TAN -1 l T; , —— 826 41814] 507.55 on 1 311918 2082 3 I 531.55 3 1 I 555,555 5 l 579.557 9 FROM 357th To 424th DECIMAL PLACE. 57 638.473 687103 92.1659 159630 555,194 734086 574974 936989 864487 4088 584.143 Ill 262 189239 236615 053437 131053 407102 97391] 714634 1921 766280 379432 559157 130096 808675 126598 736438 150274 699452 2037 306742 610852 894853 074.133 332890 844516 989130 684076 736709 7275 5250 323258 226087 736123 824702 930319 860244 309980 98.9143 7165 8 336756 171695 61711] 173465 866057 099922 300642 489737 6004 13238 329.197 690667 322300 313405 384833 624263 468450 7471 21 022961 656743 908330 890.366 858345 709620 886435 1322 33387 115358 391067 775.959 469444 793928 451723 1697 53 025871 611558 852394 083695 118214 150822 7735 84220 98.2186 695303 400328 91 1003 116004 0856 133 775324 155709 128014 460731 233987 5259 212497 884280 492.193 256844 289470 0601 337 563723 150406 203241 64.1733 5409 536264 642958 655964 794537 0630 851 970353 398866 478.107 4408 1 353603 335557 708702 1700 2150 699143 244387 2527 3 417345 788920 2699 5430 238660 1299 8 6291.76 5283 13713 2362 21 7936 346 58 — TERMs of TAN -1 +, # l 507.55 07 I 53T353 555,555 5 – 579,55 7 9 I 603.5g of l 627.5627 1 651.56 5 1 858499 798783 886095 829818 889856 6492.17 228709 434471 449866 957019 126200 393223 383724 954430 225080 096072 194130 895.580 696.772 002799 028035 987422 800295 1951.19 835545 2097.45 584767 129345 484391 332665 966064 437843 540829 515759 412492 525094 088891 469527 047453 575352 97.1773 370282 3291.77 179781 781278 I48731 879000 586625 652339 358391 378643 996606 387943 453361 602109 930875 5.19468 836483 905.262 235400 965957 377.117 71218.1 593639 091051 32713] 781489 618689 245318 84882.1 545012 295814 940.278 678940 181304 524.212 076620 926.289 546409 610688 045676 259810 353253 231024 927700 490421 865370 97.01.45 087497 596846 798586 510395 268632 891958 651935 703580 852993 761948 432680 421382 999042 931094 686031 615344 900617 993668 354576 422565 631669 320434 368660 458093 178712 456009 834771 462082 313856 065790 757547 655264 930626 074392 193402 402351 047175 170271 718367 546609 006623 229377 738350 008160 092591 939.254 764453 420382 000219 219099 755655 228812 965322 768688 179396 181991 006632 472679 743998 623161 499012 257249 038212 512068 108678 806728 457143 808446 821291 054811 518883 362043 97.2416 653476 85.9122 357316 046328 620606 35.1251 813288 021500 666,194 493174 429302 861642 490423 813003 546028 742063 07736] 266407 976034 199640 284267 134046 346475 370247 819782 383849 115848 388243 835643 776814 043609 550516 161708 92.1122 190700 877438 296670 1 17737 476914 875 021404 969962 271317 278758 735533 158697 846981 I 390868 720960 437574 309887 283934 451397 262436 2210 915872 538087 435.195 684241 909462 90.4006 3 514606 168945 844969 681023 092146 868332 | 5587 264766 812142 629168 676.196 568633 8 882592 535180 77.1567 392881 072949 14122 055200 147939 835829 696.184 22 452955 795384 818989 375844 35699 848338 201840 52.1448 56 764424 480524 97.9392 90261 576360 995515 143 531157 986025 228247 4.10928 362 979190 577262 918 l FROM 424th To 530th DECIMAL PLACE. 59 ( 185190 923251 240105 134335 819556 833.138 619329 388560 157790 9270 882632 929.309 082986 249089 967156 2.12334 720250 489236 790606 6536 512988 040161 171080 096.227 681470 188192 630810 246213 592233 0097 503812 528217 905211 888245 263216 823574 31.7394 58.1200 154142 5818 170641 617444 420934 0.11380 494964 771033 070962 073537 722003 8240 910239 834735 251406 902430 214797 317875 522720 647.178 626880 0242 033837 126607 624790 934651 843987 037850 155632 312711 301352 5145 759679 902846 291286 023136 598517 105396 92.9892 009743 700040 4282 759989 398880 958117 515465 315265 919558 849298678219 555857 5781 601563 563273 655503 279089 O18946 381821 413538 92.2983 603213 5756 824967 163480 387846 254568 322741 609902 242128 121784 804669 9670 892.243 214630 631643 272308 526671 621519 031655 735993 078150 7207 643089 372284 717774 516592 553508 312975 731852 806660 993689 5453 785407 9845.48 459444 335904 712321 136640 290608 023778 738752 0506 154674 367498 010909 639456 542050 976953 12802.1 171965 306756 5538 985803 405062 155570 065966 882633 297213 473329 314764 914.194 5790 284727 006.740 932377 466136 331271 322114 241791 601321 111611 4839 063052 741901 493070 991396 629829 99.9095 449689 218794 725,160 9882 103243 538035 491146 157706 536959 315369 892597 088223 300772 2765 190207 280983 938385 931047 168672 108250 014868 785493 190507 4364 098616 397532 711784 883.128 587391 716086 159478 483139 877424 3702 832795 635398 583287 492998 704516 545346 443521 120459 162390 6547 840108 053029 97.1261 103619 125336 119067 696801 669868 077620 0951 090149 887924 014244 808966 019043 939875 379711 778279 99.0667 6032 419489 219987 705431 595729 540684 331197 307734 520345 445345 0345 428388 670839 281941 022081 6472.17 219510 278686 165181 596846 2419 969497 955936 365.156 499379 1255.25 003868 393424 975456 013693 7104 111189 237726 379496 873.160 639078 232916 718278 719115 456583 7186 054948 966413 445488 570150 549384 25.3604 507351 835637 495330 O135 059497 947762 978934 850529 497759 406363 996635 764459 O93700 4411 941680 554.313 1262.15 952566 200643 327872 828758 925885 187918 0232 442759 895.296 492754 706566 742333 574305 106215 231306 573725 0703 516241 591165 813132 417561 810681 984215 1471.42 102200 830.105 2485 917.102 506191 900572 993014 464475 200150 176196 394954 360005 3003 114110 179785 895177 520727 928442 425263 815770 051623 952313 6382 917476 037948 939.302 872694 474331 965327 838351 876706 508071 3141 434835 286013 033397 797.747 793118 016053 0067.25 440649 411024 8163 616935 762494 520878 759001 731452 384313 772231 763693 099887 8220 672519 800727 001908 772290 491372 628374 447394 990725 873093 6000 833552 194385 952565 3282.19 46.1680 397133 270011 060751 465098 9289 081579 958272 570642 400749 88.7863 494.100 868025 228985 375043 7435 460173 863087 136344 842876 423666 658600 453720 352495 340077 8639 60 — TERMs of TAN –1 #, I 675.56.1 ° I 699.56 99 I 723.5', 2 3 l 747.5147 FROM 474th To 530th DECIMAL PLACE. 61 2322 433569 496814 192330 832782 886.703 2.19921 650622 872588 3075 3 694003 321143 680895 018113 999289 601586 9151.43 84.7868 0344 5875 790934 246698 278693 527.157 874411 660358 143889 2003 9 346527 4.13311 196330 358495 601346 662390 74.1455 0831 14867 876892 491558 619869 838444 284010 564259 0556 23 65.1690 204803 837712 414522 854676 837524 9565 37626 150940 975490 037489 198017 740548 3944 59 859299 021887 607479 271577 614567 6092 95233 012078 952.165 336187 652759 3573 151 515588 275261 166565 816417 4421 241068 717792 919025 294087 7713 383 564135 125312 051371 9560 610307 304354 300116 0419 971 118967 918919 3593 1 545.288 075900 5294 2459 005.351 8003 3 913112 7113 6227 2738 9 9102 157 62 —1_1_ + TERMs of TAN 239 2 Tºg 25.2392 5 ‘004,184 100418 410041 841004 184100 418410 041841 004184 256472 314424 647365 705207 110882 995239 43 669315 244039 189749 849750 9265 821624 155095 2 171634 To 106th DECIMAL PLACE. 63 100418 410041 841004 184100 418410 041841 004.184 100418 410041 8410 795.983 130970 285940 838406 710850 935276 679625 652677 323781 8220 669149 755829 095479 748990 815827 076863 032232 548380 568606 8866 706714 424931 650304 018923 292878 006112 668284 847390 356820 3447 649910 958401 251023 219679 525542 528236 062922 977188 324769 4641 538 796524 135423 076341 975321 274864 130207 477093 742005 1822 1387.11 499836 853406 239112 405817 269585 125596 3247 36 649062 916865 436937 862057 588749 5669 9870 867649 291507 134389 7394 2 6982.11 201145 6677 746 2806 –1 l + TERMS OF TAN 239) l l l 25.2392 5 49.23949 75.3597; 041841 004.184 100418 410041 841004 184100 418410 041841 189053 275836 401771 021551 025640 430246 795106 737638 082963 667706 802354 108595 622837 057561 776273 597828 821519 875801 682004 578809 15956] 114088 58.1412 034972 732955 061617 594270 270867 066178 545649 072147 909775 787132 788863 162170 809010 452908 675354 266227 8897.21 718039 720350 609290 495947 360548 739205 218773 753267 149692 O84234 413607 006610 210850 766605 485510 415444 080226 3184ll 827881 191857 793653 399.222 706317 303084 7950.12 403678 044738 345780 861250 921034 742516 869742 900052 96.7530 133249 258828 827639 121920 201196 843390 2083 924322 522022 514129 777510 922082 592366 427604 586552 342435 007962 808664 794839 674440 166 201668 803033 645404 091452 47363 609332 586656 13 564325 FROM 106th To 212th DECIMAL PLACE. 65 004.184 100418 410041 841004 184100 418410 041841 004.184 100418 4100 335808 357386 545495 569466 345656 95.3541 462710 525538 407816 4321 521656 991641 00564] 288498 294328 779646 432527 082945 624038 9800 99.01.11 36.1608 135754 049268 470570 849483 070794. 198149 0.19791 2286 1994.71 532427 971439 708680 128879 843332 956085 390928 121162 7638 469402 829866 899384 896498 94.2939 060192 620940 872748 818452 3434 018955 208790 713257 488947 383020 326846 090637 946732 589376 2425 951531 968692 316072 729742 194813 179589 094707 311877 838925 2359 001803 020434 74.2246 518340 305081 613382 002086 793297 92.1684 31.45 473116 668941 428649 639365 603627 232249 368641 841462 690287 9957 939480 343394 045655 57.1482 510280 421295 163743 255983 303844 3208 957763. 129330 736,173 900047 210402 607534 902335 853342 926868 2993 037567 960637 831380 061299 093622 569026 914333 140058 273565 3794 295686 338099 939116 003.137 508460 78.1995 772776 086942 453978 4464 612783 116434 886172 62.1975 573870 376431 3657.25 435454 470975 1455 632956 476936 9.19751 663815 299394 588583 89.5428 731248 96.5887 4894 3901 423375 474509 4221.18 662956 846425 467141 688665. 16059] 1334 1 126408 045586 792619 968694 447910 373379 893324 6754 326 309990 542751 021243 603584 405107 7466 94813 657876 072742 480171 3741 27 623900 709038 0336 8067 8811 66 —1_1_ + TERMs of TAN 239 2 l 25.2392 5 l 49.23949 l 73.2397 3 I 97.23997 l 4.18410 041841 004.184 100418 410041 841004 184100 418410 681663 960042 ll 2076 890.322 553494 820072 719173 665090 223272 718888 761000 781751 549058 592961 388244 798645 381744 845896 060967 639454 813802 165320 557387 766982 983975 796570 792573 266774 79.1227 606348 280166 391833 864455' 535178 iO7608 234802 358623 682452 682005 088989 546733 031741 453773 338100 703809 320940 573018 808629 545054 750974 869624 903635 859154 673665 993601 178634 994839 054023 740677 708918 426551 180744 244976 174266 241869 314028 8909.16 174355 269790 252415 816438 020204 307605 587832 191876 514,102 511128 399368 952766 196849 295.040 685781 24015] 572562 956859 379421 702376 569997 266.182 784337 543422 609557 730.123 722326 282456 942251 525991 471367 056192 318404 9761.11 420704 178077 397588 502409 607449 186490 252090 169562 358548 994151 247713 568278 030986 756504 391598 730589 871753 583180 351205 460263 949531 378176 123710 895992 149853 052757 716786 293037 061422 851279 306402 484711 247169 84.1235 824739 093858 188458 737368 130977 859289 798057 536471 520030 29255] 254029 3928ll 061709 559822 229767 950177 220800 829672 249686 687998 053300 282071 465,197 521477 340912 835895 895965 234854 939097 050889 600055 527522 001554 23615 481721 043857 932688 486326 886565 064506 629124 6 926474 876O14 033786 349945 930251 230369 2035 316126 918.186 233776 700876 599088 013643 119952 176 616429 121.239 121 FROM 212th TO 318th DECIMAL PLACE. 67 041841 004.184 100418 410041 841004 184100 418410 041841 004.184 1004 468320 750658 563736 725380 360325 583791 477042 62.1968 366304 9267 543788 57.1419 50993] 123404 068339 936764 370264 484705 927492 9020 916388 374855 923285 624078 077596 117209 627052 787214 653628 7536 134656 246102 489834 708510 076821 572596 438277 926779 580802 0125 260985 027112 050289 905612. 337456 644075 580368 238355 747976 9474 814547 175271 878723 326613 331572 550032 198955 741176 581406 5768 383387 700078 030129 910683 270714 757455 506353 046922 573569 6506 789014 480.119 995408 713951 697537 543575 954.141 006966 629134 3515 580612 265575 46.1341 893266 953585 958390 711345 047259 874444 1403 086829 927895 903929 1223.17 179815 616207 434844 785655 252409 4234 453130 992806 717673 406606 086812 084902 723538 507965 193538 5162 900106 551235 424079 4599.11 952807 762754 94.2690 471767 88.9805 97.59 830893 136653 567305 117935 244398 132423 255405 702269 124954 7134 001895 118570 108340 254455 237362 760878 133657 589946 575445 3920 543666 238436 915670 448038 025085 629399 416247 677997 8333ll 6835 0.12027 461513 751612 222407 262280 416776 529524 44766] 952510 3342 464028 429359 043342 72040] 379948 679744 377336 528417 1241.18 0089 555054 290325 718242 651435 416512 613785 685675 419287 667293 6399 305852 089153 330500 937.189 314126 199894 996717 308471 47.4953 9987 303290 672829 818.186 703351 786678 25.1405 515959 903326 899929 4901 93424] 027268 335501 502911 435710 453082 263542 094877 287628 1824 226206 674.109 760176 62.1081 112389 644896 887935 932955 357067 9631 321617 063527 068649 453237 151859 175317 443636 440599 258894 7970 925496 618440 840869 139465 981684 736418 140596 959575 294898 9286 146397 459943 61759] 815087 041852 069616 469636 979573 490044 7878 747705 222289 647319 993472 477906 143203 307121 416883 063304 813] 52143 754536 608695 124573 311582 932098 831847 137805 363073 0098 15 415540 2446.24 412088 726447 915162 398.186 978199 7196 4563 097.277 795328 658994 058790 145363 9382 1 352286 196422 951728 638669 95.35 401 192096 186255 4026 119146 4391 –1 l + TERMs of TAN 239° I 25.2392 5 49.23949 l 73.2397 3 l 97.23997 l 121.239 12 1 l 145.2391.45 l 184100 418410 041841 004.184 100418 410041 841004 184100 377604 753878 307533 782827 31.1140 750659 818937 87.9406 281158 244843 981328 164208 916218 889404 086935 790057 723684 669157 695695 819664 880637 273404 134643 627933 158460 300699 238995 069903 606105 647573 483852 775.245 834463 960125 237990 538013 828287 434491 521242 970001 340291 200933 150197 117306 185303 783378 009462 913175 310423 291882 210229 337078 747455 183495 724188 389299 802.170 631904 184137 16760] 269,199 63303] 243313 637026 429339 050554 145211 319025 851130 539480 109083 29.4362 227335 310030 772401 516774 392893 543984 174700 342418 291722 394388 775159 767239 240802 345363 359708 006335 543622 253189 153345 075258 993897 756644 354933 1091.19 173191 040446 896656 764683 680738 434935 370519 932702 401782 804018 732066 148383 254304 694222 419871 983583 101838 38.1038 458048 084980 435837 996605 809345 347384 432976 239490 445147 831838 552840 802261 657828 099085 438466 667513 279919 583.187 914730 134401 773474 156681 966.038 423985 696035 715424 089] 16 384280 939429 900096 117459 264077 930181 278306 839.543 528545 882722 6301.44 524509 771474 173524 213064 682859 619681 56.1790 296084 896288 024264 167873 937459 585438 182393 859599 62298] 738659 172352 438188 445775 129549 468299 348596 152128 954245 725916 753751 9695.27 186505 234825 351630 743III 874528 918513 854773 153555 738620 796565 790636 194008 953112 115964 324228 220287 779899 052838 559798 270102 920611 287833 528362 764513 006631 101491 381243 393157 689206 916182 294172 735328 068646 958196 692647 323478 069398 646490 703367 342097 674080 063066 697418 360636 042772 124983 502201 736629 205744 161633 081304 417466 829699 649701 085457 976207 705143 686402 628802 549797 876602 583658 276287 159879 053207 695933 210288 576572 454736 187663 87.2262 904395 785.179 399573 608321 111380 354182 853815 196488 215366 134489 614288 791702 288696 105 382137 424072 99.1758 515616 644780 826898 31381 727985 876627 546469 013660 9 352686 137160 l 12871 2789 500800 169.2391 69 FROM 318th To 424th DECIMAL PLACE. 69 4.18410 041841 004.184 100418 410041 841004 184100 418410 041841 004] 026998 081645 598415 088971 451825 968019 436898 445077 036953 8450 116329 708304 043742 629036 122959 646479 859927 665075 324090 5052 058097 95972] 448731 746117 314224 334605 116361 lé6495 516664 4223 895655 604274 098255 993901 354602 907606 992.146 866659 354713 4761 735548 407822 035900 777641 747086 161097 777113 224197 20895] 1707 435621 509823 585349 077328 913649 036479 780603 634282 447981 3940 568031 687744 37375] 027420 255891 055274 690827 029194 944387 9927 646793 702697 332033 949882 809976 022400 616360 367271 707282 6230 044591 712545 149684 000397 913623 569730 710193 746287 601680 9203 931438 282447 544302 557189,276638 354952 435295 558710 095871 8769 1291.40 708290 563349 381197 650777 411655 970585 503708 654654 593] 462069 169434 831049 334711 784802 159426 031123 312809 99.1631 7094 01.1832 691383 186442 887703 308463 234440 510866 854676 843164 0482 954250 590558 878557 352208 945971 013238 137968 640573 566246 5951 378455 048250 611944 061169 181768 545524 301933 919273 767825 8359 970488 154736 641147 234264 894023 724871 759277 922254 52.3090 0735 626087 628779 233407 797366 967439 354074 445269 130612 386751 7265 583761 097165 835721 637331 186933 178334 151835 705855 728444 6829 363926 702670 463307 674752 316667 494637 351922 234867 039472 5058 192691 337150 811036 240986 601916 450342 656374 834776 338737 2921 617839 348523 729520 865292 751772 108868 665130 909743 670606 0365 0.53557 177668 530426 816358 172342 889479 959370 322872 712526 4697 295310 848648 135100 463572 810850 231648 624610 689766 800080 5698 398560 125673 267323 625938 412030 309465 023321 561992 457076 2592 668494 489365 603462 628148 309836 937570 986856 267129 297805 3921 798.432 675594 316343 323981 360328 945766 824263 490257 524810 3484 536020 945384 117718 849661 069058 703982 4580.17 292982 607222 7089 994441 972084 533927 180066 616166 110744 784559 523407 645871 8805 635361 274517 585675 430539 001483 463536 770330 003298 862601 8994 744693 661319 862283 933051 652385 859184 380.121 100009 248162 9033 603501 390634 224283 997054 270044 515920 328381 79874] 214387 0220 615565 659093 318585 827450 523031 618147 356584 945057 728282 5246 278744 635732 626712 963427 196656 004388 887045 674606 470.155 2585 915908960622 408856 246916 975987 714761 820089 122659 263047 5500 702247 525917 426908 283004 704114 103846 899016 886028 054905 7563 057457 946152 385637 158554 413689 413795 634636 785356 292992 8798 113277 584405 665454 79.1519 870965 672919 875278 211795 376358 5594 832587 188989 279129 624456 264698 609281 994085 017991 392898 4823 248 673724 3291.96 278692 853919 109812 604324 551291 3839 74321 090151 028451 2594.17 557657 818852 6938 22 226055 749074 424966 2285.13 1716 6650 710368 145084 1519 1 99.1209 854] 5 70 I + —1_*— I 25.2392 5 l 49.23949 l 73.2397 3 l 97.23997 I 121.2391 2 1 l 145.2391 4.5 841004 184100 418410 041841 004.184 100418 410041 841004 687.118 3097.27 499841 085557 454243 718916 532322 645544 916466 838050 687.997 516877 811673 538166 535234 607767 567360 254146 244672 634956 78.2637 178928 97.1852 050239 98.1972 25.1198 860216 503543 636703 315762 126138 809561 085025 009164 934881 990519 431147 564556 818629 676684 935063 814535 06.1790 557071 563447 547067 52.1681 92.1317 749469 81978] 232178 456690 228832 217687 4695.16 254.173 92.1334 455.194 188322 96.1807 070772 754805 992836 786968 781161 775607 29.3231 683267 071050 246002 968761 513359 579752 952278 36.1093 176169 189009 323356 990784 991325 562902 421750 764070 175295 502890 789831 766108 742961 787060 195112 001316 018914 322401 155162 083020 732598 142973 676854 017267 815106 549283 605855 006074 006613 872594 6721.11 433657 906906 729018 027013 500727 830941 937762 284542 392191 213045 106151 435787 958809 746496 963032 672642 927826 817118 258160 849490 110941 616466 485751 832840 592062 869560 136346 581281 635246 373062 510202 028720 808640 620275 759253 723763 914596 831079 306561 645225 868330 557230 807249 696743 570758 374834 261869 328928 885867 351932 440897 543148 99.1657 032683 992504 779789 780815 272619 1497.22 830421 866453 895.556 042194 184587 331221 614449 566055 997612 609327 778952 854465 273916 568507 400.150 215221 081658 605409 400506 675436 849110 160882 2064.25 402927 562754 903426 749906 140461 213057 174453 916746 230896 262838 84.4142 100.965 329123 092640 732219 826464 883199 561340 661308 598558 184936 566914 269001 104603 918988 897.470 237423 549418 569279 424190 043856 236628 956561 767038 392333 707935 488792 735942 122270 462698 088418 525159 628505 500488 534829 109525 485299 168319 209473 622259 98.4082 202021 160489 302952 570726 019684 39.1780 710928 542151 776060 644087 546124 264937 135633 801875 484247 112930 388420 067098 167216 766919 779674 72778] 150268 4894.65 562475 809592 029919 034150 012616 531153 289768 809152 193326 466508 576201 636255 013806 308673 193491 761940 125225 869129 153652 141986 280853 997396 640333 010780 328607 175124 640785 886938 798919 160208 086580 367765 499647 324330 934062 653157 404902 209397 438565 078650 22.1527 614121 850591 375.178 093565 156734 976758 989275 585.119 887724 320780 106437 823074 448615 360166 723608 28.1251 442711 675820 56.5231 828043 916878 382646 100281 167086 FROM 424th To 530th DECIMAL PLACE. 71 184100 418410 041841 004.184 100418 410041 841004 184100 418410 0418 326412 797690 276830 3297.52 816233 526954 204140 839275 226388 2520 064477 370639 104339 692765 265858 458431 569131 83.1937 370297 4618 076205 518530 233194 685698 937878 181522 311209 345890 804842 8356 282055 280162 043819 764007 089860 830591 299875 776348 603567 0510 130471 980569 112035 107382 825081 485642 132787 103603 934702 9476 324636 941425 090599 935693 289556 358500 850386 812308 169673 9405 836633 496351 395948 642248 150372 966929 477739 360989 196283 5600 876488 635935 470635 807618 944693 907259 976364 759348 860235 8927 764347 038981 457336 852737 695321 492152 929437 8351.71 778.255 8098 321841 3928.78 108060 660992 073444 464299 319743 197974 874775 8527 519266 154353 777310 649776 407957 673182 609308 600353 525715 1339 203651 055051 485819 437422 326633 754160 611268 542111 174953 4357 933771 978579 715972 675741 236981 271844 191258 660038 778156 8793 341168 575388 608743 569403 392138 5771.97 722815 690213 685254 7492 347793 367851 682356 738398 173634 634802 062093 397.296 843934 5992 576.050 003489 641673 642091 255155 352466 3.13358 658599 959990 4215 264652 789263. 313276 543908 887.220 916385 257005 385750 765200 4058 420535 771352 95.2684 626221 627668 774828 027205 538304 230873 5420 957958 210044 668632 224805 779028 192907 209298 3653I4 682925 5675 306249 611778 674744 374799 373738 520344 36.1780 110900 805383 87.32 810612 333344 895260 399502 844058 557900 190095 936260 773657 0.128 280269 549073 745.176 196849 222089 734545 419440 534430 462948 9287 213422 230744 702664 591863 575.253 184087 646081 896.186 267.114 1668 727754 151228 838468 146126 571735 590438 661117 750017 356732 5240 977880 847.194 609292 628115 904385 323449 053597 960762 579391 3791 819876 5521.16 122430 189069 323636 423943 201842 0684.74 916246 0613 230123 307408 837830 842406 863534 056213 956584 626930 962190 2712 037409 516893 022638 959287 089942 433000 065990 809472 681747 0862 171325 653163 257357 257028 317711 863334 367523 131631 144378 5850 799244 178747 509683 401086 893565 174945 502384 54.5500 929658 1026 774374 894.485 780652 6287.14 603656 173200 925113 446530 898849 62.23 149988 498550 888903 664141 240511 203297 268645 043.128 802437 7566 981116 586688 235656 948022 903172 119063 654435 286674 157567 5765 802898 798752 943517 045947 333739 263533 690004 226288 796646 3878 260422 036143 816598 565523 248479 34.1546 297629 292127 059663 2020 700452 502226 264526 785267 207414 654609 920751 228841 564700 7132 382497 155909 724065 898614 677154 589866 089160 090296 081660 7554 648039 827120 364392 364061 94.2640 446143 160812 324076 784613 9753 676652 015806 027503 452705 523651 753889 784684 335986 677000 5407 312140 845167 429317 479694 708300 908498 894598 759499 151029 7741 686545 357619 803903 827244 827574 214490 782266 984.191 201616 96.18 *— —r —1–1– 72 + TERMs of TAN 239, wº 301862 364999 027607 328599 46.1683 731845 995870 619895 169.239*** 039023 731722 871014 163190 256435 3354.12 164486 697774 - 964832 680960 745270 620356 087787 535012 220204 165961 1787 727634 683305 915403 645975 379265 543726 536063 94.2648 994249 915653 476418 160 818096 234011 508527 l - 193,2391.93 48266 tº, 1 217.2392 | 1 FROM 424th To 530th DECIMAL PLACE. 73 932688 158021 452639 685368 041674 861003 584337 276777 928044 8068 5435ll 480509 872128 094084 078920 116503 207875 783972 733567 2964 323.191 975265 773897 819313 350369 648247 323675 322586 047293 1625 300179 799.170 382252 035877 683114 879874 720169 166405 207204 0946 421026 332687 150656 476624 295.388 8794.17 797330 692223 336599 1020 96.7267 047217 015177 871705 195347 371683 687501 904963 727049 2112 351939 250894 76.1459 956985 988341 458696 624003 169201 347997 8582 492632 747737 343024 087588 728287 654078 722487 681422 560895 1969 4353 372725 358159 08.1927 125690 173865 57.1982 974920 6006 1 308206 927512 053908 475286 109283 297848 3067 393 271446 639499 222418 620752 3478 118268 065896 017777 9996 35 579165 7295 107 º, -----+------- ------- «>-<------- --------- - ------ - - --------------- - w 74 — TERMS OF TAN —1–4– *āş, rºar Hooooooo-uld 591781 03303 ºn 89230, 24%, 320% 3.239 3 207130 657784 694717 044358 353107 l 27.2392.7 625 50.4450 992.156 534929 140585 401882 34 f To 106th DECIMAL PLACE. 75 920706 922838 711051 0.49550 860456 565361 49.4844 302352 902425 903] 504117 774838 012668 41993] 103731 062768 1997.94 916876 363675 6532 277.333 160941 927840 356942 027239 372947 843998 290857 74.1262 3560 572368 816240 990308 822735 650056 088436 919830 637539 044104 7818 016237 966206 817495 701548 360914 304927 010909 500230 454650 3047 8612 325632 805329 801939 499709 443756 491259 986594 8806 2 248500 094939 031410 240775 524232 665049 6573 600 210207 188417 609928 216711 4321 162931 637564 678357 1890 44 814365 9242 124 M 76 l –1 — T -smºms-se ERMs of TAN 239? 3.2393 l 27.2392.7 I 51.2395 l l 75,2397 5 520281 75.1842 604203 360226 011693 545305 486601 065632 101281 103.187 917333 402164 097154 982286 102519 152410 861703 062037 380554 550367 525015 645469 534458 727107 542884 613082 620427 824045 476000 156736 848854 838391 371193 984548 080758 484615. 396070 69] 150 803634 967.427 681376 246905 74.1759 792589 026665 370979 973435 179771 603139 372749 98.9959 736065 414538 477266 569362 159304 549955 550537 846822 051549 422643 903446 747486 845864 555,139 664655 984709 311351 257509 592700 295037 506081 434561 277907 553011 692820 680656 701443 978475 504820 572391 981514 422356 565487 303770 060212 449348 954085 34930 177899 133497 922044 539267 145002 995.317 9 865903 779529 382304 583072 860173 2803 836973 366,198 136465 801072 517174 229 FROM 106th To 212th DECIMAL PLACE. 77 848637 128108 754039 1452.17 118072 069819 146548 798988 137369 7963 024230 818992 732051 828519 026857 093550 202220 633273 796457 2426 814920 312562 844693 403272 473401 199302 623645 646552 130183 9577 548524 327244 155279 453327 311601 824689 160763 899.236 796668 1924 838944 282650 266217 433605 898063 290353 475549 367917 639082 0039 457044 928621 718506 699419 026184. 538634 054516 643736 696033 6581 343330 612585 382276 759755 103159 553766 093129 312854 822358 7319 860674 140196 4997.20 833764 409859 799363 212605 129977 080039 6717 577089 266394 232967 357081 636340 934.253 97.2947 686922 337209 6904 93.1397 319552 758.149 865416 893480 431871 162039 126006 526909 1571 056906 338235 919081 554691 705361 047721 736803 396736 139201 6285 235202 129462 697097 698102 423904 338985 266837 663054 724976 0247 346350 708842 725419 735958 858458 905263 673954 876773 063735 4980 285644 563574 268752 225546 142491 122806 751783 998285 17388] 3016 347831 626,125 105459 600283 386711 263426 065390 135644 203667 8147 927.909 539383 562310 390627 607485 7697.15 222633 107483 780931 4615 66262 197374 11.1335 909268 565575 777644 932375 750987 7404 19 164199 532321 846748 806750 213671 882399 5416 5560 273643 580195 153162 132236 614] 1 617851 790183 264345 3466 471 950.150 5116 1379 — TERMS OF TAN 239? ] 27.2392.7 1 51.2395 l 1 75.2397 5 l 99.23999 1 878435 942473 240086 857630 296028 956319 864872 721068 006968 686322 018698 553157 711856 703874 482898 698422 401404 688698 265721 170859 046846 234751 009662 891379 172339 376274 92.1247 635229 673748 218026 235730 287215 150374 899072 552083 318740 305824 893296 056129 014058 453810 98.2153 246571 359024 230675 485295 008008 416996 225943 801122 499240 627163 424048 880792 38.1289 572733 730740 689451 977308 621665 160962 730211 94.7537 408949 978063 023951 052669 367215 156951 572070 799360 797611 494617 565844 084944 718745 250700 372102 289106 125236 368734 022321 89.3231 083480 102500 874831 752150 397753 930093 257363 283003 123574 839.574 616583 636742 98.2308 890555 014778 203043 909096 949.107 6.13683 643695 423437 889702 999708 110041 9932.14 683172 956262 001181 363995 6470.15 045.179 924211 918245 618100 519015 517547 6936.17 998555 187625 903072 410410 284023 240551 226668 804707 587000 028260 699149 404876 331183 904575 895.173 1501.76 210866 978341 069939 433801 914880 333119 403489 909429 735386 250625 340940 069413 715068 883750 928310 l 16517 637905 349591 342797 567068 209332 245032 517498 865642 238617 368256 7790.71 97.3791 909780 790384 875437 586131 950044 752981 75.4006 963372 937353 861970 365533 749865 404342 713621 210758 501525 926569 394387 726591 118 706856 538024 109877 654908 281195 34911 829789 476506 398403 10 284400 425048 3034 123.2391 2 3 FROM 212th TO 318th DECIMAL PLACE. 79 249330 613032 009150 752603 596119 588266 919349 09.1752 839533 6460 9604.13 212062 997328 524869 829964 465477 842668 28365] 27.1215 8.188 205880 171592 906884 411846 798322 992691 436364 761502 777977 875054 486337 211364 042298 322572 898962 466520 331504 95.1238 565339 951772 O06506 242874 18619.1 123564 96.1977 475,123 956532 436386 797553 606125 794241 336474 535859 853114 386376 692191 546845 044737 156587 318893 256873 198749 514480 978470 81.4410 315879 434641 112737 274514 048480 268304 231101 095862 817491 158495 114743 037455 176535 637162 976382 717144 933197 639176 359015 0.15092 084776 0834.18 725621 399045 504438 253522 773673 429667 332215 8111.78 206994 250150 379013 56.1931 592.139 792576 ll4788 651874 075900 528068 245853 588123 667908 096772 7956 718637 656582 986626 323991 1733 687671 078789 762751 790292 6968 162213 642273 638594 048994 93.10 217161 977014 98.7608 195866 5621 99.5758 842553 066037 156412 5241 763584 039898 504504 587954 2732 48.1546 577668 152835 590.402 2699 343748 975351 316090 816542 9928 849552 972328 826128 654265 3610 566370 932222 032909 539682 5660 815140 751747 896093 689556 4989 413006 516957 792685 294866 1169 650623 695053 466592 182028 4681 534654. 790282 69] 100 378961 6838 152212 070290 627486 958320 3937 580830 355760 591097 403290 0246 754282 780704 000724 743670 312914 953071 503755 351948 362847 6816 282482 898076 330295 943977 51] 171 006240 264820 79845] 346988 1826 959510 716107 854491 688570 712559 170196 381263 730.145 356805 4763 958.357 943527 629273 707908 520435 797977 033104 205877 600687 4127 214286 000519 102665 234999 599383 234095 545010 593060 34.1109 8834 95.2527 811893 198677 053320 008473 987864 399.241 736866 764457 2340 158740 317759 022926 697554 369559 429040 181142 200322 316452 4863 176363 687.225 746625 906376 366583 378446 350458 740520 618506 94.17 896416 859435 951241 89.1677 547242 387587 321956 192060 8512 265 181700 119815 611257 884843 145839 304531 8041 78542 157301 940558 896469 793585 3122 23 289119 640503 145.179 7986 6912 941 132 3251 2 0540 80 tººk –1 l- TERMs of TAN 239? 3.2393 27.2392.7 51.2395 1 75.2397 5 l 99.23999 l 123.2391 2 3 1 147.2391 74 l 268577 138007 728681 464732 784697 399.195 917682 5861.13 622990 513931 002087 142504 293233 551092 676.196 381839 063257 312505 993808 728.128 132911 22986] 338429 557704 265614 406728 055706 359068 94.2121 050967 308291 463579 828062 767794 968839 98.1347 249339 86.2835 963867 307992 623574 459.209 140801 789794 279793 842694 055503 797889 221363 426229 066256 851069 194020 641428 873502 601412 323417 579476 428.128 007072 0.13673 111691 20976] 282903 263101 372090 250940 022821 99.4833 965785 858106 240311 600769 614814 467400 678819 368132 377481 163811 071361 985349 875701 524369 796984 283363 430724 294.104 014494 023180 775825 169747 863415 558598 0.17610 820684 566528 055045 734524 477371 398352 066422 019507 29.1392 572465 153204 657775 963205 865318 925290 994439 889667 909925 130846 799381 221091 393491 620922 904.179 195777 364881 148022 788755 933407 289658 623258 559209 395636 711616 97.2560 250720 862228 031410 950753 646201 202894 969705 829571 880941 657681 04.1912 569577 680880 363360 696312 694373 35266l 88.1726 116047 740984 577883 452672 648910 497913 499715 645601 669464 804698 762908 517768 514415 190360 113859 226631 788714 267775 953862 724764 678365 351746 792900 423411 376834 190470 192081 762203 538881 524398 224756 803971 172583 450474 908556 884.285 55.1734 91301.4 523159 518300 136447 774489 489990 654880 858023 933684 604187 760174 513998 353469 86.1907 049854 949366 203146 55.9147 854315 859052 780490 974414 955391 839.742 331965 0291.77 318213 079742 064822 501940 160245 99.5352 194321 982772 758487 564146 372819 053234 463625 500941 972404 246674 99.1752 74.4632 813339 367467 401623 678838 026189 576974 755059 95.1255 353057 407997 810790 643982 195306 041056 706157 979063 289430 285472 453030 898053 119409 808646 703052 731671 141656 005405 019025 269340 153278 163759 803401 072921 893948 748697 861950 675407 6 108711 339530 850745 382439 731527 511177 934353 1818 347852 400413 645565 048709 590857 541706 600013 320329 088199 161 506953 777464 48.188 171.239171 FROM 318th To 424th DECIMAL PLACE. 81 595702 797045 113828 563832 918532 063758 460135 409046 400973 6164 546201 759649 086345 507345 171671 312101 479058 701.183 766253 5539 634204 021395 370809 961125 046074 611370 150953 461390 550009 3371 842941 306.202 011377 991.179 775710 141531 543993 175534 000270 4395 709087 750145 602879 639944 288461 546771 377582 460222 236645 4130 278546 340237 744.180 548778 855013 871247 674123 747512 114360 8860 614927 175733 997802 996320 956891 926771 377455 729.190 118871 2457 858129 953290 408751 337020 165561 064678 547670 470881 47721] 3003 930.252 993866 248345 970894 040036 6.78633 947094 933758 222503 2776 285420 490597 496439 424500 134318 019495 313383 903970 210175 189] 746230 742723 455817 502219 826602 419332 829187 916.111 944783 8516 719113 554515 618794 798321 798367 662592 892399 999086 547850 6281 655759 185227 816117 461493 815803 279418 136414 074231 250994 0507 320637 252382 149952 455464 730619 800249 048780 682774 938009 6438 111516 585008 411183 063300 675702 076486 386636 831362 894.139 7598 134962 480303 700411 887710 307892 793404 943219 230791 632160 3672 952979 125415 113264 843279 852697 641205 776756 268655 395980 3059 0.32212 370538 938.903 628383 142757 924.385 232913 457883 206727 3760 84004L 459255 520294 581135 840333 478317 260643 915899 354579 0343 550271 148223 459377 633553 590308 377884 275214 151884 127113 2497 917124 060675 743547 505039 612573 595141 929266 443346 246.149 5155 658845 503071 947.192 762867 280906 995903 081688 968814 804348 9856 603754 545072 877394 68.1924 808523 363747 626489 513769 542940 8315 293000 44760] 799002 222307 974534 466367 617278 204217 298332 0554 004509 417335 093606 347679 048149 598246 079801 050046 607293 9150 219908 4991 17 513941 355580 113783 207871 060745 970949 928649 0079 427232 899014 166419 181326 182645 699404 675059 608283 003278 6778 222948 475629 345523 802933 051878 733070 154708 398196 42.1521 5317 096.950 618472 433507 258622 062780 174012 072642 233188 608021 8702 623882 508187. 193153 95845] 662623 184774 82840l 588403 209222 6636 458266 684476 957515 992844 728449 070200 708054 773279 472646 9296 808312 487867 491302 554102 877864. 29.2716 992404 857339 702092 7943 457411 541131 852423 374.135 304995 044145 438818 573.222 681094 0039 052565 486.136 518830 96.1542 214910 538220 500564 685242 532280 1474 585689 482282 606854 1377.71 380887 361578 006043 884905 915905 5184 951221 08.1894 385450 343121 197103 398354 424708 872991 235750 6500 685754 602492 85733S 874665 748981 126348 090092 915579 956555 1066 122925 862661 O19745 832074 60223] 138463 390316 827894 863536 5865 14 387775 572664 898320 830179 793645 432942 869438 758208 5921 4298 694927 504530 078406 664402 934186 039252 4963 I 285152 132043 406366 268895 206409 7315 384 444870 375208 350068 06.17 115070 189281 8394 34 4611 82 l * * —1 ---sº- T ERMS OF T AN 239’ 3.2398 I 27.2392.7 l 51.2395 I I 75,2397 5 l 99.23999 l 123,2391 2 3 l 147.239147 808283 240864 037746 878.906 42.5780 38.5404 669726 895781 074329 520020 279350 5996.17 923323 8494.18 889181 766058 400545 64903] 390232 523904 839806 256674 099318 380.139 201888 827440 350485 438215 080779 601528 131599 743324 420237 827113 330409 982576 746354 528988 203210 492555 630597 888331 02001] 396495 312321 786854 340247 355326 277840 592.190 174189 387936 023262 564905 218543 898072 193506 447052 563378 890.185 714432 258479 206244 478174 669886 433579 354807 321129 201736 331897 405056 315847 482.150 532892 926562 932565 678562 524653 738694 083129 388732 026575 589807 847649 491079 014797 334600 040055 949039 247632 583904 337.137 956230 141571 641192 986330 967999 326489 780547 748307 575079 457284 382874 217825 643184 429,100 226874 979968 901947 257745 077137 789452 306555 527204 162900 022373 170270 886.164 499378 079505 782604 9584.79 773.259 36.1612 482260 98.5726 368965 431331 738815 140816 214908 6264.75 066593 847638 756077 949010 764169 394023 3.28782 624366 707503 150074 578139 864695 217276 5987.40 240686 503099 334.192 4.27892 096839 052903 952822 246810 885440 359107 306247 332882 882.917 419671 6454.18 573806 574468 899618 819430 178697 17593] 187339 304455 004.048 933053 662712 401527 897210 456016 970.746 7|11151 199041 792768 903090 756447 298.588 592352 388283 967800 295636 589408 240713 059529 220161 558105 241610 432121 766919 800000 248555 126953 448275 154907 848887 642896 570707 17004] 626818 35364] 268844 989205 041036 233818 872762 595499 7455ll 827706 087103 4943.15 221876 8.15574 549756 285283 338170 607302 117125 763888 271817 057345 745617 797379 773639 138133 480411 860305 443700 132784 788527 215369 923943 575428 828728 083150 118912 046213 367675 244888 609901 327224 541927 084959 723062 647946 135226 253244 609867 747323 642791 833673 119787 358904 391827 854.120 064249 641849 135033 888537 613273 257546 057077 826320 604711 207169 549097 916989 61320] 399494 612422 285559 365843 444096 744270 9586.10 876878 079202 348114 320003 887.215 857037 811026 388509 147317 101335 668.479 774413 783273 378713 741638 658725 839198 51930l 607285 322060 855117 600241 762955 030685 389138 134927 341295 632371 342225 1858.15 288293 848255 009708 005341 460088 260487 959297 337333 845474 816414 907851 840795 706586 44.2921 47.1994 120648. 442346 849631 602286 02.9613 996994 352926 114639 469218 592.796 354729 124380 FROM 424th To 530th DECIMAL PLACE. 83 709028 110504 708776 351026 792155 251824 548.133 733677 538911 0742 586713 498072 98.4044 857537 129862 375277 63062] 264394 121691 8769 560046 504623 097940 319763 364989 778836 514327 833874 959911 7864 583612 55.4252 288949 676485 724707 763695 145052 131650 365905 162177 247618 163230 824920 365644 O55163 771900 265904 766392 231450 2497.28 933994 4596 58.2650 98.1558 188160 219338 816239 8202 292.123 833777 114245. 494521 679518 3289 969373 162305 205597 513057 277.179 7891 159461 868083 877513 259916 62.5881 538858 959252 235035 568912 II.25 796768 726100 226271 814459 856607 7399.09 985359 009839 792977 0075 87.1546 312995 58349] 346398 783912 004258 145627 214777 486201 855364 433946 922251 522I 62 009022 850840 450306 365310 816855 758407 053824 379873 761823 926541 017708 133853 161890 196544 398230 6984.48 602323 633526 595262 579572 909010 57.2011 518921 303095 787721 975.984 500830 183486 072408 061329 189305 296065 500527 350785 596093 839798 99.2552 093496 689703 433732 749.985 121710 232923 3.14768 164509 688555 837367 122631 732998 576854 575218 882082 03540.] 406570 723568 217872 823163 7397.95 922985 256612 817145 659056 501526 059748 147727 872760 330597 245648 194773 122403 2.18079 374572 758826 868216 472659 806315 873394 486962 446871 543690 227544 766479 806114 869.163 561745 199092 198471 547565 860645 035745 859229 830154 398179 878988 661436 0992.45 85.2544 29.9706 739 137 864.588 286732 034842 570483 133177 0.78744 997414 489735 190659 100791 3455 901424 276097 308028 737637 368316 0006 355040 404373 132963 886995 77.1167 6099 434963 483109 626544 391715 612797 0423 251219 678802 226133 084857 816041 3038 512244 85.1591 848368 924989 248864 8270 275837 060929 339618 456,197 616451 4815 362262 300243 476419 752129 430663 2658 295.357 006720 655653 573886 424149 4763 97.2591 240774 394.109 810403 481780 5135 629869 212828 209859 442496 846962 i306 672955 35451.1 686119 131209 94.3247 7697 700088 508418 894095 184140 177156 8523 697284 935.716 060343 529516 879497 O234 984633 266693 532409 24.1253 579948 5379 078789 233055 025058 471202 413250 9781 075709 381.178 681391 284927 607604 6570 488242 287085 361511 837949 051237 8798 414358 917431 973839 202370 364960 1862 341421 096710 024259 326991 058708 0.267 661338 869807 114474 374.713 975.278 4693 776696 554922 159735 052310 151707 9758 149741 866798 529784 285683 480910 513] 607507 890501 257521 719356 775060 1360 34.2997 823579 423727 025.202 915923 5017 919237 7965.13 888303 439987 612005 4047 211262 000881 597808 989.912 615865 9163 471781 179530 327307 160337 422162 4154 689915 045051 788612 658499 297.707 154945 8892.19 417467 1343 757466 018589 372761 101921 616635 096042 07451] 275614 455939 3554.21 141186 4727 184877 916780 052431 646909 958790 876865 241018 892.434 708200 487.170 198830 6708 398812 749176 00:5807 7.15512 563241 6855 4978.75 929.282 737126 794088 O61151 0230 N * r— NVI, Jo Swaa]. - #8 6 I & 693"6I& I g 6 1693'96I #66968 I £9/I/I IIOEI6 98/3 693/80 &I6099 p66[8? /99:#86 6 66889? 9786/W 0376/L glóż38 £8889 I gº.609 I3&I93 #968/I 808099 8/8/99 QWI786 [88876 69//96 80I LWOI&g £1966I 6/6/IL 09930ſ. W899&I 998396 896908 &I98II] . , 1682'I/I &I636; 999906 836810 6780//, 78798; pg809& 98.6906 090390 —H FROM 424th To 530th DECIMAL PLACE. 85 783831 165860 867796 237217 86.7272 730377 272336 497233 560671 5895 672234 232342 483820 849290 881416 707208 522765 454037 231969 5190 537574 427174 502547 417954 380528 780023 640864 334989 763250 8204 220506 247024 808695 259178841603 9696.18 827306 232261 35.1379 4371 098020 169574 499008 706393 527455 568982 393065 448379 545673 8257 065635 703749 661576 850008 01.1126 735617 378064 892085 886032 1780 276980 258665 964844 665038 247489 539740 113402 851312 185770 3025 251 168189 409456 604968 194113 850415 560013 995686 423948 0077 75462 305521 257568 560263 288960 177869 75661 1 0381 22 681.102 345074. 495326 129340 690465 4606 6819 624222. 302795 776712 1061 2 051222 804943 3851 617 1853 86 —1 VALUE of TAN #. */ ... " •1973955 5984988 0758370 0497651 947.9029 3447585 1037878 41.12628 1180736 9136010 4456479 8367942 3935574 7565495 3186928 0664389 6806189 5284058 2593112 4251613 2973139 0488878 1553093 84290.57 9311695 9341928 5180636 4919697 2982251 4023246 6755492 1102670 4574378 8154748 3907997 4774413 5290970 5465,122 4383026 9756051 8377617 78.16424 5985563 6303434 7839296 + &c. I V 1—#– ALUE OF TAN 23.9% -0041840 7600207 4723864 5382149 5928545 274.1048 0653076 9454975 4506664 4486375 6052458 3947893 l 186505 8922128 3.198601 5454814 8059924 4983021 1460391 2539495 2760779 9102328 3097700 2064652 8276346 532969] 0481838 6543560 6551103 2510343 5262824 4512693 556.7049 9684445 2479043 4522355 3881423 7677083 65.15691 8252702 0022930 8954495 6516494 2122006 8523882 + &c. VALUE OF ºr, --- 3.1415926 5358979 3238462 6433832 79.50288 4197169 399375] 7982148 0865132 8230664 7093844 6095505 822.3172 5359408 8196442 8810975 6659334 4612847 5648233 7867831 6527120 1412737 2458700 6606315 5881748 8152092 0962829 2540917 1511609 4330572 7036575 9591953 092.1861 1738.193 2611793 8301.194 9129833 6733624 64 3086021, 3950160 9244807 970304] => *l b28/ 1445/10 084.0% 100% "8"|38 ſºlº boºl. 31.8% wºods; i. To 609 PLACEs of DECIMALs. 87 52.10151. 7688940 2410339 6997824 3785732 6978280 3728804 2163032 700522I 0747001 5645015 5600612 86.18552 6633257 933971] 3233537 82.17960 84.17664 83105.25 4730396 6572565 5194017 0856094 9527368 6737385 084008] 2367856 1580093 8985020 0752236 9683796 1392278 3541932 5572232 8413846 2337830 3370181 9264880 2827768 6119150 9856067 5901213 To 609 PLACES of DECIMALs. 3195082 7019612 887.1817 7834142 289.3273 7826058 1362290 8330928 00846.27 1962330 7733759 4763460 3318473 4145703 688.1558 8812733 9785334 6518045 7425481 3586746 4475197 7891959 1451232 2209446 3686276 6155208 3167964 2646574 3177283 9307086 3140193 8695.195 0370586 4.107708 5585540 0043585 4409344 9644014 2418724 9509228 3862395 4553335 7 To W07 PLACES of DECIMALs. (742) i– 0582097 4944592 3078.164 |0628620 8998628 0348253 4211706 1284811 1745028 4102701 |9385211 0555964 4622948 9549303 1909145 6485669 23.46034 (86.10454 3266482 1339360 7260249 1536436 7892.590 3600113/3053054 8820466 52.13841 4695,194 1051185 480.7446 2379 7495673 5188575 2724891 227.9381 %2/. 7230943 6285530 9662027 5569397 9869502 2247499 6206074 *Toº olºbal tº 9% ºbsº 44404% ſpoog (ºce/. º 24 44%. 42n //0, 4 %.9%.4%// Zac A.S. /26 xx/ %3/8- /37 xx/4 Z3 */…//4%a- .4%'.5%.4% ... / 23. _T EXPLANATORY REMARKS AND FORMULAE. FROM the Exponential Theorem, we readily find that s, the base of Napier's c 1 1 l I Logarithms = 1 + 1 + l2 + i.a5-F 12.54 + i.a. Tº -- &c. The above series the Author has summed to 137 places of decimals, as will be found below. The following series, given by Mr. J. R. Young, in his “Essay on the Com- putation of Logarithms,” were employed in obtaining the subjoined values of Napier's Logarithms of 2, 3, and 5:— l l l I Nap log 2 = 2 { (; + 3 + 4 ºr + # * *) I l l l 45 + 3495 ºf 5.49; t 747, † se) l l I l IöI F 3.IGIs it 5.IGIF + 7.15IF + sc)} * , l l ãi + 5.315 # 5.5IF + 7.5I; + se) + l l + 3495 °F 5.45; F 7.457 -F se) l l l l IGI -H 3TGIF F 5.IGIF + 7.IGIT + se)} l I l l ãi + šāis t 531; -- 75.7 F se) tº-l l l l 45 + 3495 H 549; H 7.45. H se) l l l l + 7 ( TGI + 5.IGIF + 5. TGIF + 7TGIT + se)} M, the Modulus of the Common System of Logarithms, was obtained as usual by dividing 1 by the Nap. log of 10. To 137 PLACES OF DECIMALs. VALUE OF s, THE BASE OF NAPIER's LoGARITHMS, 89 *—2-71828.18 2845904 5235360 2874.713 5266249 7757247 0.936999 595.7496 6967627 7240766 3035354 7594571 3821785 2516642 7427466 3919320 0305992 1817413 5966290 4357 &c. VALUES OF NAP. Logs. OF 2, 3, 5, AND 10, To 137 PLACES OF DECIMALs. Log 2–6931471 8055994 5309417 2321214 5817656 8075500 1343602 55254.12 0679523 5847083 2754439 2266635 5206804 5602137 0371911 8226310 4298719 4582110 0448886 1730 &c. Log. 3=1.0986122 8866810 9691395 2452369 2252570 4647490 5578227 4945.173 4693570 0667031 1626456 2261348 7915959 6453630 4663543 4230252 7148232 3776931 0688498 5614 &c. Log. 5=16094379 1243410 0374600 7593332 2618763 9525601 35.42685 1772191 2646780 8257554 5759268 0738412 2078288 5798574 2982618 5124170 8082338 1773353 3644800 7449 &c. Log. 10=2-3025850 9299404 5684017 9914546 8436420 7601.101 4886287 7297603 3326304 4104637 85.13707 3005047 7285093 1400711 3354530 3350481 2381057 6355463 4093686 9180 &c. VALUE of M, THE MODULUS OF THE COMMON SYSTEM OF LOGARITHMs, To l86 PLACES OF DECIMALs. M=-4342944 8190325 1827651 1289189 1660508 2294397 0.058036 66566.11 4454084 2952.103 2056138 9388912 2647096 695346] 1420043 3938056 4705613 4312230 2306044 292 &c. 90 POWERS OF 21 3 22 5 23 7 249 26 I 27 3 285 29 7 21 o 9 21 21 21 33 21 4.5 21 57 21 69 21 8 1 219 3 22 o 5 22 1 7 22 29 224 I 22 53 22 65 22 7 7 22 89 23 o 1 23 13 23 2 5 23 37 23.49 8.192 335544 32 137438 95.3472 562949 95.342] 312 230584 30092] 369395 2 944473 296573 929042 7392 386856 262276 681335 905976 32 158456 325028 528675 187087 900672 649037 107316 853453 566312 041152 512 265845 599,156 983.174 580761 412056 068915, 2 108890 3574.14 700308 308279 874378 165827 66592 446014 903970 612462 830714 365452 967230 119608 32 182687 704666 362864 775460 604089 535377 456991 567872 748288 838313 422294 120286 634350 736906 063837 462003 712 306499 108173 177771 671669 405430 06.1836 723747 824436 720435 125542 034707 733615 276715 788464 153328 322047 108889 280690 514220 174162 876888 173427 869549 172032 807104 958010 493707 210624 583337 114373 395836 055367 340864 637790 190801 098222 86.2718 293348 820473 429344 482784 62818] 556388 621521 298.319 353369 412955 676865 916659 500148 583703 165496 77.9375 1237.91 144740 111546 645244 279463 731260 859884 816587 480832 050705 592855 496895 058920 568683 443244 482088 208742 321488 079687 242833 6.11528 216133 864932 738352 939863 330300 854881 517440 994646 472819 573.284 310764 496.293 641680 200912 301594 695434 407407 195266 897217 253689 137681 875632 210293 678733 187250 166873 987.181 321100 187111 070794 496.258 953336 290809 113497 683515 85.1494 691226 366406 945974 256676 672365 4471.54 128886 279963 092772 225526 319680 285071 055534 765205 687.154 331.191 114674 930799 503575 580541 044765 104347 039828 249458 414056 23 61 469708 516554 766645 577896 119357 867405 475136 509781 663974 THE NUMBER 2. 2 25792 296.440 32 508621 9550.72 395315 527974 912 624321 240258 523955 2 049321 980009 891412 04992 882022 830120 515223 756472 32 156476 551217 363035 650651 062272 880927 953786 318994 025066 751066 112 127228 039870 876259 952667 341236 679475 2 652112 6256II 110916 076612 542970 543913 04.192 383053 314503 110312 249804 976007 347867 819704 32 862498 637620 473983 897520 118172 609686 658950 889472 186879 441969 346143 804424 240403 500927 655506 284327 7312 141458 194306 441805 022921 688692 739799 676953 740606 386995 2 POWERS OF 237 3 23 8.5 23 97 24 o 9 242 1 2433 244.5 24 57 24.69 24 81 24 93 25 0.5 25 1 7 25 29 25 4 1 25 53 25 65 25 7 7 25 8 9 26 o 1 26 13 26 2.5 263 7 26.49 | 26 6 1 267 3 26 85 26 97 | 27 o 9 192392 608380 832418 028706 250488 982489 282615 914406 569563 788040 123927 889584 245580 802002 872276 101594 785409 308.933 32278] 234760 863573 706989 896500 376484 291213 224103 652939 132211 193758 049719 790383 061606 554207 965680 936592 856243 541537 049632 97.1652 261409 O20340 446035 827429 116284 339174 221813 575529 665188 766273 134731 446696 27.4914 966030 065326 908548 405369 508613 186654 759860 005667 942051 700859 147575 372141 426839 350727 96.1253 7896.38 658321 589064 376671 906846 152429 128433 398058 172929 552235 994448 522880 768684 813044 624349 710063 1984.46 276319 445958 633261 149719 628532 994230 255733 641241 886083 594780 445064 656183 766925 1598.47 114436 104748 499452 676539 840422 070298 483172 870932 545473 378073 429049 853758 163107 186368 799942 58.7076 079339 706258 956588 175738 820099 343608 703536 660456 483666 362097 543683 668618 719826 207126 91.1421 249686 161229 757097 41915] 538928 306661 294840 814439 182918 143871 451639 708507 102884 470345 034408 120766 797594 289323 271729 746591 624604 509341 479053 326093 494660 802946 209068 121005 042039 294380 070262 698202 423679 202613 064886 767234 302363 665219 294978 076779 601.183 712739 829903 113776 198591 702481 572738 232230 202489 246448 487.379 339928 315402 730943 161336 452193 57992] 490939 595345 300430 H39234 637988 958594 318883 410818 490335 842688 858253 435056 570305 077.202 774402 3301.46 450712 536415 611653 563406 069991 233596 95.9622 256395 1944.27 986.211 854915 834533 299571 126268 956813 146612 76219.4 716377 031523 757735 258248 395043 333195 391910 664852 587394 955828 032112 131168 36.1778 542609 749276 160526 608323 619796 97.3907 161953 128926 560984 491052 95.3303 657516 987693 546688 405123 735360 016083 193792 475352 896732 269318 958159 276723 570738 682003 462587 676177 397.904 546501 27 2 1 110313 045262 039745 974574 564148 618275 912162 262.181 702247 THE NUMBER 2. 93 { 808341 276387 918563 337888 723688 546221 947680 252152 376113 23392 358965 868084 914435 429944 212228 285325 097698 312816 132559 806136 103832 419567 580952 752105 149328 705669 160017 228929 487896 496593 856929 759054 881 158 247262 269165 037842 087943 0.56969 518242 405004 837984293088 793224 180786 254499 99500l 192214 761347 146720 890899 0.13638 366449 1697.04 624450 049843 197952 488331 166247 791296 876912 351862 748975 799110 141747 404157738813 392204 456950 953152 007832 864122.981980 48.7315 514059 736743 009817965446 945567 110411 062408 475544 773419 207604 434558868169936321438647 068904 288424 37] 162 ; 171831 391925 074347 763953 124024 061220 612698 394231 965386 224281 678382 138132 510452 844115 199600 255475 962961 262277 413022 197465 263465.323779 076281 484949 585756 264642 954428 933028 828373 892081 087.153 966199 096448 962353 503257 659977 541340 909686 081019 46.1967 480498 264555 149905 494979 99.4934 337526 800933 236607 418785 571621 296120 8916.17894012 907438 059251 046509 776622 537143 987.345 701363 466891 117206 689387 686886 629069 228650 404504 591214 177216 799278 708038 601607 859973 196548 763266 756055 205685 08056I 326988 000984 828.126 112185 794450 213063 734340 632802 122486 089979 195342 852032 257600 455551 301406 807270 905585 923195 749370 302455 4784.12 432.192 999.131465938 130562 282581 629279 941409 789420 758857 639577 322260 847644 248448 258278 310945 435353 064001 449746 742828 089170 871197 475.195 084164 406590 796163 250320 615014 993816 265862 385324 388842 322399 064737 409395 901034 673313 239101 414671 424972 330288 696699 445654 656916 442888 56.1084.282189 102735 939449 415668 666486 2501.68 553401 474729 75007] 546201 219846 564806 407984 806578 857927 680688 898673 244049 305629 305324 019649 152944 704710 576774 700207 178009 817696 560762 595585 763460 718448 293046 151049 452246 917204 8601 12 437285 112883 591519 287135 102764 208317 034698 556403 372871 107022 606311982237 119086 300010538092 219726 657412 528702 821528 005436 057945 387924 323977 748484 316402 573200 038876 171756 675697 871026 ! 94 Powers of 2, CONTINUED 23 85 23 97 24.09 242 1 2433 244 5 24 57 2469 248 1 249 3 25 o 5 25 1 7 2529 2541 25 53 25 65 257 7 25 89 260 1 26 13 262 5 26 37 2649 26 6 1 267 3 26 85 Q 6 o º a T * * 27 09 32 436672 671660 8512 135122 846515 2 285746 31.7932 62592 722416 918252 035768 32 283101 96.97.16 033850 703872 432758 566795 687465 248305 9712 324579 089595 135857 65706] 258035 2 630547 595098 167647. 296332 291291 21792 922272 294952 209468 332577 706512 882860 032 553627 320124 249982 290238 285876 768194 691072 909965 750322 892792 746081 601895 124252 545463 0912 343219 713322 568879 087950 241362 428938 426216 821555 2 425382 794576 9242.12 874424 418862 050893 179378 410.109 00992 443036 792658 708157 593364 241965 896045 846273 396780 650463 278678 702730 068613 502419 935092 310203 786335 8332.13 544297 421346 796638 236104 090591 205413 810259 470883 157284 267744 157836 479030 215082 355061 577374 966822 792737 412236 360680 760649 82.1810 776097 732633 222092 786410 615905 244052 013334 602762 167013 693889 631286 567769 205313 788274 787963 704661 300913 836088 090171 929749 781582 664965 276773 531499 334295 033654 307261 681734 422425 510536 259569 777366 438502 127327 265848 042543 848384 194254 891156 519197808092 932.104 713532 913691 358225 960298 165966 803417 7.10263 422.194 864990 090662 860647 980329 353338 128780 002679 894.123 897731 016699 941135 277214 i27429 O31272 975482 890976 846331 485106 244402 958891 324746 906594 93.1209 410757 792144 116257 376299 517707 451961 272 1 718616 332941 283823 374646 391662 230019 021332 282452 972323 FROM THE 114th DIGIT, PAGE 93. 95 232 398272 214332 2112 301904 737075 2 651660 180306 00192 873320 009853 338386 432 033118 760359 274030 825472 245565 444243 158643 026113 3312 397836 059619 977801 834960 204595 2 870153 650020 342907 631599 699802 19392 511614 935048 332454 965903 237038 978629 632 055574 773957 96.9735 540339 658911 656466 97.2672 776363 427413 184403 677323 124290 214488 872006 4512 543598 459868 440331 746231 551709 271854 64.1973 84241.1 52 FINIS. —t GEORGE walkBR, PRINTER, 6, SADLER-STREET, DURHAM. • •） ~~~~ -…-…- |- ********************************** ~~*~*~*~~~~ ~~~~--~~~~ ~~~~.~~ …….-- … … -. ~~~~--~~~~~ ~~~~. ------.-.-.-.-.-.-...- .-.-.-.-...…..–.…. .---...,---, …...…-）. -- UTILATE GARD * : ****** ********** ---> *.*** - N tº : . . . . . . . 8 * f w • • • • * * *··i sº， º *** ！！！ ;º- · · * * * ， ！ fºr ºr rºº º r * 2: … . . . . ." º -, *...* a -s . . . . . e. * & iz º.º. （…）. ·' ’ ， ！· ** * · · · · * * · * * * * - , ： ; ºr º .~** - º * *•* • ** , ! * * * . ：：§ ¶ • ** ** • • • • • • … * * e * ... * * * · · · -- º :*（º. - x.º， ， ， ， , ， . . : :：：：:：::：::: • • • • • • • • • • • • • • • • • • • • • • • ， ſº rgſae！！！ … ~~~~ ！ ！ ！ • • • • • •sp ： . * （º.sz.： ， :, ：,- ſºlº， ， ， ， ， ， ， ， ， ）· • 5 ： № º.º…！！！！！！！！！！！！！！ ！！ ！ w:º ： •* -·• • • • • º ， ， ， ， ， ， ， ，~ ~ ~ ！， v ~ ~ ~ ~ ~ - • * * · * • • • • • • • • • • • • •~--~ £ €·S - • • • №tº-·** … »： ： ：-） **** •… . 3.：tº：}} （* 24;- ··; + （< * ≈ ≠ ≤ ≥ ± f,* * * * · * * tw-º : • • • • • • • • • • • • • • • • • • • • • ·， ， , • • • • • • • • • • • „… -: " " （ → ， ：. ~ · · · ， ， ， ， ，· - wº ： • + • • • •=~~~~ ~~ * * ， ， , º（ , * * · * ::：i';ºſ. ſă ț¢ £: * * *）（.*; ******* t » ~） **t º ‘. . . . º ， , ， ， , ， ， ， ， .， ， ， ， ，！（，，Lº.）?（.*）'）; •• • • • • ！ • .• • • • • • • • • • •$（'#'）:.*'， '（.** t : ^* * > º * † ºw 3. ！！！！！！!. ، ، ، , ， ， ， ， ， º * º * º ** ** ** ** ************, *** ·， ， ， ， e ºſae º: º ſº º: º: w … º., w. •• • • •* * º : ： ， :. （4* 4 : *************** * … sºwº ºwº， w，：---·- º ·§§§§-·--· ··--------|-· -- ¿;":::：：:::-· ~§ ø ± − × s. --' * * .- ~- ---~~ ~~ *…！！！！！！ & & （！-----· ،·- ·… ， - ，- -------|-····* ： * ！！！ ！！ !! ！！！|-*.-№º ºs-^ * ** **-- * ** • • • • • • • • ? .！ 8- -º ， ºr ae···∞ *（ <！--***= *（»）， º- • … • ¶ • • • • ► ► ► ►----- §§§§:∞ & …“· ··ſ'，ae ： ? …-…* * * ， ， ， ， ，··…--！ {{}}&&&&&&&&&-· …|-*** •·----* :·§§§: * ，-•