UJ 01 MU ^ z 3 01 m OL UJ Q s U. ^ j < 2 u u li !> C CM I 5E U- r O m Lb a* * m >- B UI t W H z K CO t (D z UJ J UJ LU U. O cc CL > u 'TY OF CALIFORNIA, OF CIVIL ENGINEER! NO u*.EY. CAUFOKNIA National Tube Company BOOK OF STANDARDS AND USEFUL INFORMATION CONTAINING TABLES OF SIZES AND OTHER USEFUL INFORMATION PERTAINING TO TUBULAR GOODS THE ENGINEERING DATA FOR THIS BOOK EDITED BY PROF. REID T. STEWART 1872 Price, $1.00 1902 Engineering Library COPYRIGHT, 1902, BY NATIONAL TUBE COMPANY PITTSBURGH, PA. CENTRAL BUREAU OF ENGRAVING NEW YORK National Tube Company MANUFACTURERS OF BLACK AND GALVANIZED WROUGHT MERCHANT PIPE Of All Kinds in Sizes from }i to 30 inches. BOILER TUBES OF MILD STEEL AND CHARCOAL IRON For Stationary, Locomotive and Marine Work. CASING, TUBING AND DRIVE PIPE FOR WELL PURPOSES. GAS AND OIL LINE PIPE. CYLINDERS, Lapwelded and Seamless, tested 100 Ibs. to 3,700 Ibs., for Com- pressed Air, Carbonic Acid Gas, Anhydrous Ammonia, Etc., Etc., Etc. WATER AND GAS MAINS, CONVERSE AND MATHESON LEAD JOINT PIPE FOR MAINS. Seamless Tubes, Shrapnel, Projectiles and Miscellaneous Forgings, 800375 National Tube Company WORKS AT MCKEESPORT . . . PENNSYLVANIA PITTSBURGH MIDDLETOWN . PHILADELPHIA . CHESTER OIL CITY ELLWOOD CITY CHRISTY PARK . VERSAILLES WHEELING . ' . . WEST VIRGINIA YOUNGSTOWN OHIO WARREN SYRACUSE NEW YORK COHOES NEW CASTLE .... DELAWARE GENERAL OFFICE FRICK BUILDING, PITTSBURGH, PA. LOCAL SALES OFFICES HAVEMEYER BUILDING . . NEW YORK CITY, N. Y. 420 CALIFORNIA STREET . . SAN FRANCISCO, CAL. 267 SOUTH FOURTH STREET . . PHILADELPHIA, PA. WESTERN UNION BUILDING . . . CHICAGO, ILL. THE FRICK BUILDING .... PITTSBURGH, PA. NATIONAL TUBE WORKS .... ST. LOUIS, MO. FOREIGN OFFICE DOCK HOUSE, BILLITER STREET, LONDON, E. C., ENG. TELEGRAPHIC ADDRESS, TUBULIFORM, LONDON ^PREFACE In the following tables of Standard dimen- sions of Tubular Goods, it has been our aim to group together in one book all of the dimensions and data pertaining to standards as manufac- tured by National Tube Co. at this date, with the object of making this book a practical and valuable aid to all users of 'Pipes, Tubes, etc. The use of Tubular Goods has become so ex- tensive that a great variety of articles necessary for different purposes has to be manufactured, and a large amount of data has accumulated on the subject, and we trust that our effort to put this before the public in a compact form will prove of *balue. We have also taken up certain subjects closely related to the use of pipes, tubes, etc., and furnished such general information and engineering data pertaining to same, as, we think, *h>ill be useful and appropriate in a book of this kind, vjith the idea of popularizing such information that would lead to the intelligent application of tubular goods for purposes where engineering skill and judgment should be exercised. This data was prepared for publication by Prof. c fyid T. Stewart and is largely compiled from modern welt-known engineering authorities on the subjects. TABLES OF STANDARD DIMENSIONS OF Tubular Goods AS MANUFACTURED BY THE NATIONAL TUBE Co. NATIONAL TUBE COMPANY. -I THOO ^ ~ - ~ CSt-iaGO-<*OOC5CSCOTHl O5C1COCOC31O1O - 03 O5 OC300OCO O 5D i> O5 TH dCQiOJ 5*^l3S H TH TH d CO -* 10 CO i> 05 TH d ^ 10 OS CQ 10 00 - TH d ^ 10 OS CQ 10 TH-tlT IT lTH(?5C^C t-OSdCOOlCOTHOCDCOOSCOCOOt^THlOOSCOt^THL HTHddCO^lOiOt^OSOd-rhiOt^OCOt^OCOCDC THTHTHTHTHC t> 00 O TH C s oST) v$ z rt^ i<9 :! o . ~f O5pi-ICOOOOOCOt^OCO g ^M '"' g3 IQ>< J> CO C V4 ^3J T-fT-l-rH^-iTHT-lT-IC^C^C^COCOCOCOCO^U < h c x^.5 OiOOOlOOdiOiOOOOOCOOOiOOOO .5 .S lOCCGOOCOCOOiOOOOOOlCOlOCOCOCOCOJ>i> co ^ -^ 10 10 co' t> 06 os o oi . TH TH TH C<* W CO CO T* "* iO CO t> 00 05 O GO an 4 NATIONAL TUBE COMPANY f= NATIONAL TUBE CO.-Standard Double Extra Strong Pipe. fe- ll ^^xx er cent, above and 5 per cent, below standard in weight per foot, oser than T V inch. Shipped plain ends unless otherwise ordered. Nom.Wgt. per ft. Ibs. *.3SS8SB3SS-S8 -33aS; 8 Sg SP TRANSVERSE AREAS. 11 lllSllilEISilil ..^..-jgcgjH Internal. THO?^iCt>OS^OO^t^ External. siiiiiiiiiiiiii THooosTHC3ioooTH External. ||S2|S|||||KS|| GQCO^0OI>050W^Ct-jOCO^ 1.1 isgiifiiiiciggi DIAMETER. Internal. iiiigigiggg 1 Allow variation of 5 p Cannot cut to length cl THTHTH(MCOC0^^10CO External. Slslilsiilillll o 2 *.^^^^.. NATIONAL TUBE COMPANY. w vj l>T-lCOt ftoo^oSS^o -lO^COC?Ci-^ f^ -M CO 3* ?? w 10 ' :D1> " GOC: '^^^2i5^^^^^;^o^2^ I ^ -^ ^- -M, *, '"'^i^^^H^i^H^H^^cQcqicQCNl^c^ -rHOi^OlCO-r-it-^O5THT-l?Dt-OOCOOC-i Nominal rcoooo-do> Inside 1 Diameter. Actual Outside Diameter. Npminal Thickness. Nom'l Weight per foot in Pounds. Number of Threads per inch of Screw. 2 3 4 5 2.375 2.875 3.5 4. 4.5 5. 5.563 .154 .204 .217 .226 .237 .246 .259 3.609 5.739 7.536 9.001 10.665 12.49 14.502 8 8 8 8 8 8 6.625 7.625 8.625 9.625 10.75 12.75 .28 .301 .322 .344 .366 .375 18.76 23.271 28.177 33.701 40.065 49.98 8 8 8 8 8 8 NATIONAL TUBE COMPANY. 3|S* .2- ^ i fl -< "^ i-cy Q 1 || S * SyQ a .2- 3 Jll l=g r^ i pfi 1 " 1 i a a|SS "t j5 ^> 5 oJ oi\ s "u'o" ^i[]Q ja 1 || - ^ O< ^ E "S'S "" f|jjj 1 c .2* 2* 8^ 3 gfi|S a 111** 8 II s li * oS H ^ (X) 1 O _e c w S 55 " oo "o 1 c c. NATIONAL TUBE COMPANY. Tubes. CO. NATION ^Jcr d* LENGT OF TUBE PER SQUARE FT. Nearest B.W.G. :>OCOT ICDIO^COCDOO i> i> 00 CD 3 T-i TH rH 07 CJ CO CO CO TJH ^' 1C CO t> O T T- OC^t^CDOJCOt S-i IC?COCDOOC TH TH T-l T-lT-l O? CO CO D SrH rHC^CO liSl8lS55 ^H rH T-l T-l Oi CO COCOCOCOCOCO(MC?C^T-lT-lT-IOOO50OOO OO5C9^ NATIONAL TUBE COMPANY. 1 W om. pe Ib TUB FT. LE PE DIA Nearest B.W.G. 10COOOOCOOOOOOOOO Ot>OOK300OC*00000 SaSSSSS !5 CO i> O OJ * H O5 (M CO CO CO CDlOOf-it-OSC-O^-i-lTHCOOSt^C OlOCOOO-rHOOlOOOTH Oi-iTHT-lO)CO^^JOt>OOO5OCOCOOO iCOC CJCOlClOi T-i05CO^oi>CST-(C01CI>Oi IT IT- IT lTHT-lT-!THCQOiC^WO5 and inch. 5 per cent, th closer th NATIONAL TUBE COMPANY. g ^ -r-l Olfr WO>COCOCOCOCO^-*CD *JL ^co w o< " 5 p o^*Oic^j>ooocoo5ot^ i :5c<5^HCO5i;bo3i>coT-t t--^T-lO^OCX)Ot)00505CB050SOOOCQTHT-lWC5 i>GO OO 00 O5 O OS O Oi CO CO ^ 1O i> 2 a "3 ^ 3g 3g 3* 1 ! p2 iS ^i ^r ^ rr! ri rr! SP ? ^ 22 92 99 ^ fe . ; -. , . . ."".- W w w o W " S -3 wt-o^oocoeococRaa^^^oiowwott.^0 S W 1 PQ s M ^* 15 ! ^ p as f 3 SSSwooSoowSSSIsoSpoopGoasSo W .O T-lT-lT-lT-li-lTHCCOOO^OOO0 OCOCOT-lOOOO5CO standard in weight per foot. LENGTH OF TUBE PER SQUARE FT. u 5 M T^COCOOXM-r-l-r-i-i-l h 3 C0 N W |SgS|g|||||| 000*0* Internal. ?D O5 TH ?D O3 C5 J> O TH-r-lC^CQCOlOT-l-rHT-lO^ External. OOO5OiO?O-r-iOO ^CO"^CO-rHOOi-H?OOOOOQO T-lTHOJ05CO^0^t'-r-ICO TH T-l W C -^ ft * 1 1 ii rt o ^ ^ !* M o S 1 3 -a ^ OJ 1 1 3 5 . CIRCUMFERENCE. Internal. COCD^T-lOOCO^ C5lOt>lOC3OOOCOiOOlOCO WCOC0^1OOCDOOC<-^100 External. II11I15I111I co^^iojoot-oseo^cot- THICKNESS. B.W.G. COCOCOCOCOC005W000505 g Q lOlOKSlOiOHSIOGS^f^OOOC 1 DIAMETER. Internal lOC^iOlOlOiOOi^-CiO^^"^ i-iTH-r-tT-'i-icQe'ico^^ic 4J X H ^-S^^^^^^X^^:^ 14 NATIONAL TUBE COMPANY. I NATIONAL TUBE CCX-Bedstead Tubing. IH! 0> w, ^^ COCO-rHCOlOlO^O 22P$THTHTHo;jcoooio^ioo3 CO O5 IO Ci t- O T- (JOi i t> W TH C^CO^iOCOi>OOGOTHTHT*T* ' TH TH TH OJ Lap-Welded Tuyere Pipe. Threads per Inch. ^^ . III! O 1 ^ w, O ^SP* CQ CO W CO TRANSVERSE AREAS. 3 OO OOCDC^COt-OOiO-OOiOi COO5COt>OiOCOOO?^-i-iO OOi-iTHTHOiOJOiCOCO^i> TRANSVERSE AREAS. 1 S Cr^OJ>THOOO5 OJ-rHOOCOT-'CJCJi^CDiOT-HC^ t>TH^OOi-HC*COI>COlO-i-iC CIRCUMFERENCE. 1 Internal. TH CO CO O cico T-iTHi-iWCQOiOiCOOO^lO External. 1-H JO CO TH rH THICK- NESS. si THO) THICKNESS. llglllllllil DIAMETER. Internal. 1O o o? 38 j DIAMETER. Internal. r-l?Oi-i^"^Oi^^C?O? COOI>OOl^OCOOOt>CO-i-i?O C^CO-*iOOI>OOOOOi-HCOl> External. o T ( CO CO ^HrHrHrH External. c o oo o 10 o DoSSt^^OOOOWCoSo | Nominal. THT? ^ ,_, ,_ ^ rH CJ 4 : T) NATIONAL TUBE COMPANY. 15 STANDARD DIMENSIONS OF COUPLINGS FOR STEAM, GAS AND WATER PIPE, BLACK AND GALVANIZED. Size of Pipe. Nominal Inside Diameter Inside Diameter of Coupling Outside Diameter ' of Coupling Length of Coupling Thread per Inch of Screw. Average Weight of Coupling in Pounds. Inches. Inches. Inches. Inches. # H if H 27 .031 X M If If 18 .046 H If II 1 18 .078 % II 1 1A 14 .124 X II If* i* 14 .250 1 Hi 1& i lltf .455 IX IK iJi 2^ UK .562 iK ix 3A 2^ UK .800 2 % 2^ 2^ UK 1.250 2K SB A 2^ 8 1.757 3 3X 8H 3^ 8 2.625 3K SB 4yV 3^ 8 4.000 4 4U 5 3^ 8 4.125 4K 4^ 5K 3^ 8 4.875 5 5A 6A 4^ 8 8.437 6 6H -T 5 ^ 4^ 8 10.625 7 7^ 8 T 5 ^ 4^ 8 11.270 8 8^ ^ 4^ 8 15.150 9 9iV 10^ 5^ 8 17.820 10 io T v Utt 6^ 8 27.700 11 HM 12H 6^ 8 33.250 12 12 T V 18# 6^ 8 43.187 13 13H 15 T V 6^ 8 49.280 14 14ff 16^ 6^ 8 63.270 15 15H 17^ 6^ 8 66.000 ( - 16 NATIONAL TUBE COMPANY. STANDARD DIMENSIONS OF COUPLINGS FOR REGULAR CASING. Size of Casing. Nominal Inside Diameter Inside Diameter of Coupling Outside Diameter of . Coupling Length of Coupling .Thread per Inch of Screw. Average Weight of Coupling in Lbs. Inches. Inches. Inches. Inches. llf \7/ & 2 rV 2^ 14 .90 2 %~$? 2|| 2$ 14 1.31 2^ 3^1. g2 9 2$ 14 1.50 2/^ 2^T 3 5 2fy 14 1.62 2% 2H 3fff 2$ 14 1.75 3 8* 3|^ 3/4 14 2.62 3^ 41 4 3/^ 14 2.87 319 4j/ 31^ 14 3.06 3^ 3! 7 4K 3/^ 14 2.25 4 4 ' 4f| 3^ 14 3.62 4X 4i^ 5 3^ 14 3.93 4/^5 444 5A 35*6 14 4.06 5^ 1 sf! 5|| 4^ 14 4.93 5.68 5$ aft 4/^ u&lly 2 5.93 6.37 6^ 6.L5. 7 S 4/^ 14 & 11 ji 7.93 65*6 651 7|| 4f^ 14 & ll/^ 9.68 7X 7!! 4^ 14 & 11^ 9.93 735 8 83 51^ 11^ 14.00 8// 3^1 93/ 51^ ll/^ 15.37 8$A 8?6 yj>/ 5/^ 11 /^ 15.93 9^6 9a/ 1086 11 /^ 24.60 10* 10/ H>| 6/^ 11^ 26.00 1Q26 \~\_7/. gi^$ 11^ 27.83 11^ lifl \%7/ 6/^ 11^ 29.75 125^ ^2al 14 6/^ 11 M 35.00 13^ 13f| 15 6/^ H>^ 42.50 14 /^ 16 1/ gr^ UK 50.00 # 15* 17/8 6JS UK 52.50 NATIONAL TUBE COMPANY. 17 STANDARD DIMENSIONS OF COUPLINGS FOR LINE PIPE. Size of Pipe, Nominal Inside Diameter Inside Diameter of Coupling Outside Diameter of Coupling Length of Coupling Thread per Inch of Screw. Average Weight of Coupling in Pounds. Inches. Inches. Inches. Inches. X H fi IT B ^ 18 .06 H II u Itt 18 .17 % If 1* lit 14 .29 X if 1/8 2A 14 .41 \ Hi 1# 2A UK .64 w IK 2M 3 UK 1.10 w in A HI UK 1.18 2 a* 2^ 3^ UK 2.50 2K 3tt 3 T V 3^ 8 3.12 3 3& 4A 3^ 8 3.85 3K 3^ 4H 4 T \ 8 5.00 4 4& 5 T 3 ff 4A 8 6.50 4K 4ff 5^ 4 T 3 ^ 8 7.70 5 5X Z& 5^ 8 11.21 6 6 T B TT ftt 5^ 8 12.00 7 7 8H 6^ 8 14.75 8 8tt 9 T V 5^ 8 23.25 9 m 10^ 6>g 8 26.48 10 IOH HH 6^ 8 29.50 11 11% 12ii 6^ 8 34.75 12 12 T V 13^ 6^ 8 39.50 18 13H 15 T V 6^ 8 46.00 14 14|| 16 T V 6^ 8 59.75 15 15H 17k 6^ 8 62.25 \i 18 NATIONAL TUBE COMPANY. STANDARD DIMENSIONS OF COUPLINGS FOR DRIVE PIPE. Size of Pipe Nominal Inside Diameter Inside Diameter of Coupling Outside Diameter of Coupling Length of Coupling Thread per Inch of Screw. Average Weight of Coupling in Pounds. Inches. Inches Inches. Inches. 2 i i ll^i* 1.10 l/^ !% 2 3 9 5 gi| l\% 1.18 2 JJC 2% 3'M \\\4> 2.50 gs? 3 15 3i 8 3.12 3" 3J4 ^ts 3% 8 3.85 3&j 3i 5 423 4^3 8 5.00 4 4J4 5^ 4-3 s 8 6.50 4^4 4% 5% 43 8 7.70 5 517 gi 5/^ 8 11.21 g_s 71 3 51^ 8 12.00 7 7* 1 41 gix 8 14.75 8 gi i 9 ? 6V^ 8 23.25 9 9j| y& 8 2648 10 10% nil giz 8 29.50 11 11% gi^ 8 34.75 12 12 7 jt 13% giz 8 39.50 13 isle 15rs gi^ 8 46.00 14 14 2 ? jg^ gi^ 8 59.75 15 15f! 17W 6^ 8 62.25 STANDARD DIMENSIONS OF COUPLINGS FOR TUBING. Size of Tube Nominal Inside Diameter Inside Diameter of Coupling Outside Diameter of Coupling Length of Coupling Thread per Inch of Screw. Average Weight of Coupling in Pounds. Inches. Inches. Inches. Inches. 1.10 ji7 J23 2_9 2ri 11/4 1.18 2 2 2% 39i 11^ 2.50 0?9 s2 3% llifj 3.12 3 g 3 7^ 41 3^ H/^j 3.85 gix sii 423 4 ^ 8 5.00 4 4v gj 5 8 6.50 423 gK/ 8 7.70 5 5J4 6 T I 8 11 21 6 rfl 8 12.00 1 ; n NATIONAL TUBE COMPANY. 19 SPECIAL LIGHT LAP- WELDED PIPE FITTED WITH CAST IRON LUGGED FLANGES. Shrunk on, Beaded and Expanded, and Finished with Bolts, Nuts and Gaskets, Complete. 1A11 quotations based on random lengths, 16 to 18 feet. Suitable for water at pressure not exceeding 80 Ibs per square inch. For compressed air. For gas, and for exhaust steam. (See illustration, page 25.) Q "O }O^X3 c - - oja 's^og 8*Id W* adi >>xp $ $ ? $ $ f .xxx, xxxx^ lii^^g^^g HHHMHHHP ^^^^^^^^ saStreijj JO JlT?d jo itiSpM 22J2S883SS S}[og jo azig a"^^^^^^^^ stnog jo qjSuaq 5 ^ ^ ^ ^ ^ ^! Cr)Tl-j salon liog jo aj^uaQ r N 5P^P x iP > i' :> 'i! :i ' v ?' s ? ) |s * * f 3 aSuB[^;ui salon aiog jo Jtaquin^ aSuBi^ jo ojiH jo ssau^oiitx " ^1 oS! eS ^!^!^^ C-r-r-lr-l aanssajj 9JBS Ss&ssssss adirf jo ^ax inw SI 1 1 1 1 1 1 adjd jo ssainpittx Sl^SS * 05 ^^ adij jo Q 'Ol^xa geo-*oot-Qooo* NATIONAL TUBE COMPANY. duinj jo }00 r~< jo a JO 9ZT S jo JO 9J1U9O ui S9IOH ; jo aaqui pus 'Id j jo }oo 9dij jo gdtj jo '6 P* X 3 O- . ' ' opiqx JO 9dlJ JO ^00 j 9dlJ JO J9d ?HSi jo ^59^ IUH fdfd jo | g j NATIONAL TUBE COMPANY. 8 Q 2 H o 3 II to J-. cc rr ^ P N eo" c 5 J S o w lg S s fe 5 a I 9di WITH CONVERSE PATENT LOCK JOINT. (Cast Iron Hub.) SILVERTIN. SIZE. APPROXIMATE WEIGHT. 0. D. Inches. Nearest B'g'm Wire Gauge. Plain Ends, per foot. Ibs. Hub. Ibs. Lead, one side. Ibs. Complete, per foot. Ibs. 2 13 1.91 5 1 2.00 3 12 3.33 9 2 3.94 4 11 4.89 14 2^ 5.81 5 10 6.85 19 3 8.02 6 10 8.26 21 4 9.65 7 9 10.65 32 5/2 12.74 8 9 12.21 35 7 14.54 9 8^ 14.58 37^ ?K 17.08 10 8^ 16.18 41 8 18.90 12 7 22.35 58 10 26.13 14 7 25.25 73 12 30.00 15 W 30.00 85 15 36.40 16 5 39.60 132 17# 46.25 18 X 47.00 149 30 56.25 20 65.15 217 38 78.50 22 u 78.50 280 50 96.00 24 y% 93.50 342 58^ 114.50 26 H 102.00 380 70 138.00 28 X 110.00 430 85 151.00 30 ft 136.60 475 100 168.60 NATIONAL TUBE COMPANY. WEIGHTS OF FITTINGS. Converse Joint, As a matter of convenience and to give an idea of the average weight of Converse Patent Lock Joint Fittings, we submit the following list of a few standard patterns. All ends are Converse L/ock Bells, except where other- wise stated. Bell connections for cast iron pipe are indicated by an asterisk (*) ; bell connections for threaded pipe, by a single dagger (f). REDUCING TEES. Size. Weight Ibs. Size. Weight Ibs. Size. Weight Ibs. 3x2x2 34 6x5x5 81 14x14x10 3x2x3 30 6x6x5 97 14x14x12 3x3x2 36 7x4x7 16xl6x 4 330 3x4x3 35 7x7x4 'si 16xl6x 6 355 4x2x4 43 7x5x7 16xl6x 8 4x3x2 39 7x7x5 16x16x10 4x4x2 35 7x6x7 16x16x12 4x3x4 36 7x7x6 16x16x14 4x4x3 37 7x6x6 18xl8x 6 4x3x3 40 8x4x8 107 18x18x10 4x4x6 55 8x8x4 91 18x18x12 5x3x5 8x5x8 117 18x18x16 5x5x3 57 8x8x5 118 20x20x 6 5x4x5 8x6x5 100 20x20x 8 640 5x5x4 60 8x6x8 103 20x20x10 5x5x6 70 8x8x6 97 20x20x12 6x3x3 60 8x6x6 87 20x20x14 6x3x6 60 10x10x4 118 20x20x16 6x4x5 76 10x10x5 24x24x 6 6x4x6 68 10x6x10 24x24x 8 6x6x3 59 10x10x6 iii 24x24x10 6x6x4 70 10x10x8 136 24x24x12 6x5x4 79 12x12x4 161 24x24x14 6x4x4 58 12x12x6 156 24x24x16 6x5x6 12x12x8 160 NATIONAL TUBE COMPANY. 29 CONVERSE JOINT FITTINGS. CROSSES. SIZE. Weight' Ibf. SIZE. Weight Ibs. SIZE. Weight Ibs. 2x2x2x2 3x3x3x3 4x4x4x4 5x5x5x5 6x6x6x6 21 39 57 71 104 8x 8x 8x 8 10x10x10x10 12x12x12x12 14x14x14x14 16x16x16x16 156 205 306 18x18x18x18 20x20x20x20 22x22x22x22 24x24x24x24 REDUCING CROSSES. SIZE. Weight Ibf. SIZE. Weight Ibs. SIZE. Weight Ibs 3x3x2x2 3x2x3x2 4x4x2x2 4x4x3x3 4x3x4x3 5x5x3x3 5x3x5x3 5x5x4x4 5x4x5x4 5x5x5x4 6x6x4x4 6x6x3x3 6x3x6x3 6x6x5x5 6x5x6x5 '39 46 60 50 71 'i\ 77 67 120 102 6x 4x 6x 4 6x 6x 6x 3 8x 8x 4x 4 8x 4x 8x 8 8x 6x 8x 6 8x 6x 4x 4 8x 8x 6x 6 8x 8x 5x 5 lOxlOx 4x 4 lOx 4xlOx 4 lOxlOx 5x 5 lOx SxlOx 5 lOxlOx 6x 6 lOx 6xlOx 6 lOxlOx 8x 8 78 103 98 131 129 132 118 127 125 123 162 166 i98 lOx 8xlOx 8 12xl2x 6x 6 12x 6xl2x 6 12xl2x 8x 8 12x 8xl2x 8 12x10x12x10 14x14x12x12 16x16x10x10 16x16x12x12 18xl8x 6x 6 18x18x10x10 18x18x12x12 20x20x 6x 6 20x20x10x10 20x20x16x16 218 166 261 646 MISCELLANEOUS CROSSES. SIZE. Weight Ibf. SIZE. Weight Ibf. SIZE. Weight Ibs. 4x4x6x4 6x5x6x4 6x4x4x4 6x4x6x3 92 110 90 93 6x6x6x4 6x6x6x3 8x6x8x5 8x4x8x8 105 103 126 131 8x6x8x4 8x4x6x6 136 Some of the weights in these tables of Converse Joint Fittings are not given ; the reason being that there are not Standard pat- terns for the sizes where weights are omitted, and the patterns of some other sizes are made adaptable for same. This would cause a variation in weights, and for this reason it is thought best to give no fixed weights for fittings so manufactured. ' 30 NATIONAL TUBE COMPANY. TEES, SIZE. Weight, Ibf. SIZE. Weight, Ibf. SIZE. Weight, Ibf. 2x2x2 3x3x3 4x4x4 5x5x5 6x6x6 7x7x7 17 29 45 56 70 84 8x 8x 8 9x 9x 9 10x10x10 12x12x12 13x13x13 14x14x14 127 178 192 359 15x15x15 16x16x16 18x18x18 20x20x20 22x22x22 24x24x24 957 MISCELLANEOUS TEES. SIZE. Weight, Ibf. SIZE. Weight, Ibf. SIZE. Weight, Ibs. 6x 5x 4 lOx 4x10 lOx 5x10 lOx 6x 6 79 iio lOx 8x10 10x10x12 lOx 8x 8 12x 6x12 135 182 12x 8x12 12x 8x 8 14x12x14 16x 8x16 282 600 REDUCERS. SIZE. Weight, Ibf. SIZE. Weight, Ibf. SIZE. Weight, Ibf. 3 to 2 4 to 2 4 to 3 5 to 3 5 to 4 6 to 2 6 to 3 6 to 4 6 to 5 7 to 5 8 to 3 8 to 4 27 22 27 39 36 55 36 40 46 52 60 53 8 to 5 8 to 6 10 to 4 10 to 5 10 to 6 10 to 8 12 to 5 12 to 6 12 to 8 12 to 10 13 to 12 14 to 13 70 63 90 94 94 107 154 154 138 '90 88 16 fco 6 16 to 8 16 to 10 16 to 12 18 to 16 20 to 12 20 to 18 20 to 16 24 to 12 24 to 18 24 to 20 295 256 256 442 395 505 608 ) NATIONAL TUBE COMPANY. 31 ELLS. Wt. wt. Wt. SIZE. SIZE. SIZE. Ibs. Ibs. Ibs. 2x2x90 12 7x 7x45 14xl4x22i 6 2x2x60 7x 7x30 14x14x10 2x2x45 '9 7x 7x224 39 15x15x90 2x2x30 8 7x 7x10 15x15x60 2x2x224 8x 8x90 95 15x15x45 2x2x10 8x 8x60 71 15x15x30 3x3x90 25 8x 8x45 69 15x15x224 3x3x60 8x 8x30 15x15x10 3x3x45 12 8x 8x224 64 16x16x90 420 3x3x30 8x 8x10 50 16x16x60 3x3x224 13 10x10x90 148 16x16x45 265 3x3x10 10x10x60 16x16x30 4x4x90 32 10x10x45 93 16x16x224 4x4x60 25 10x10x30 16x16x10 4x4x45 4x4x30 23 17 10x10x224 10x10x10 18x18x90 18x18x60 4x4x224 12x12x90 205 18x18x45 4x4x10 12x12x60 18x18x30 5x5x90 41 12x12x45 132 18x18x224 5x5x60 12x12x30 108 18x18x10 5x5x45 32 12x12x224 112 20x20x90 840 5x5x30 12x12x10 95 20x20x60 5x5x224 13x13x90 230 20x20x45 5x5x10 13x13x60 20x20x30 620 6x6x90 57 13x13x45 20x20x224- 365 6x6x60 48 13x13x30 20x20x10 6x6x45 6x6x30 41 39 13x13x224 13x13x10 24x24x90 24x24x60 1143 6x6x224 30 14x14x90 247 24x24x45 6x6x10 30 14x14x60 24x24x30 7x7x90 72 14x14x45 163 24x24x224 550 7x7x60 14x14x30 24x24x10 Y'S. SIZE. wt. SIZE. Wt. SIZE. Wt. Ibs. Ibs. Ibs. 3x3x3 33 6x6x6 123 12x12x12 350 4x4x4 70 8x8x8 180 18x18x18 1145 5x5x5 95 10x10x10 262 20x20x20 2400 32 NATIONAL TUBE COMPANY. PLUGS. SIZE. Wt. Ibs. SIZE. Wt. Ibs. SIZE. Wt. Ibs. 2 1 6 10 10 25 3 3 7 14 12 30 4 5 8 19 14 40 5 9 9 22 16 54 MISCELLANEOUS. CROSSES. TEES. ELLS. SIZE. Wt. Ibs. SIZE. Wt. Ibs. SIZE. Wt. Ibs. 3x3xlfxlf 22 2x 2 x ff 11 6x 4fx90 70 4x4x2fx2f 4x4x6*x6* 56 124 2x 2 xlif 3x 3 xl f 11 22 6x 5fx90 12xl2fx60 65 180 4x4x4 x2f 6x6x8*x8* 75 184 3x 2fx3 4x 4 x2 f 43 44 REDUCERS. 6x6x4x2f 83 5x 3 x2 f 40 SIZE. Wt. ibs 6x 6 x2 f 97 4 to 2f 17 10x10 x4i-- 163 12 to 12* 247 10x10 x7 165 16 to 16* 450 4x 4 x4 49 8 to 8 * 61 2x 2 x2 f 16 8* to 6 62 6x 6 x6 * 115 6* to 6 46 Fittings on the above Miscellaneous List may vary in weight 15 per cent. All combinations of Converse and threaded pipe, and Converse and cast-iron pipe connections will be uncertain weights, as patterns are changed for each requirement. NATIONAL TUBE COMPANY. SPECIAL Steel Lap- Welded Pipe FITTED WITH MATHESON PATENT JOINT. 0. D. Thick- ness Nearest B. W. G. Approximate Weights. Lead Space. Size of Rings. Per Foot Complete. Pounds of Lead in Joint. 2 13 1.91 # X A*# 3 12 3.40 1 % A*tf 4 io# 5.25 1^ A X*^ 5 9^ 7.30 2 A X*x 6 9^ 8.75 3^ T 3 ir Ail 7 9 10.75 4 A A^i 8 8K 13.00 5 A ^xl 9 8^ 14.65 6X -^ #*1 10 8 17.08 7/8 A T 7 ^l 12 6 25.12 11^ ^ KxlX 14 5K - 31.00 13^ X ^xiy 15 4K 35.42 15 X ^xlX 16 3K 42.00 16 X >^xlX 18 1* 56.00 26^ N ^xlX 20 0^ 67.00 30 H ^xlX . |j^ 34 NATIONAL TUBE COMPANY. WEIGHT OF FITTINGS. Matheson Joint, Heavy-faced figures indicate openings tapped for Standard Pipe. TEES. SIZE. Wgt. Ibs. SIZE. ^ Wgt. Ibs. 2 x 2 x 2 11 6x6x4 96 3 x 3 x 3 19 6x6x3 93 3 x 3 x 4 35 6x4x4 100 4 x 4 x 4 35 6x3x6 90 4 x 4 x 4 39 7x7x7 4 x 4 x 8 35 7x7x6 lis 4 x 4 x 3 35 8x8x8 159 4 x 4 x 2 37 8x8x6 173 4 x 4 x 2 36 8x8x4 172 4 x 4 x 1 34 8x6x8 176 4 x 4 x 6 98 9x9x9 4 x 3 x 4 35 10 x 10 x 10 256 5 x 5 x 5 41 10 x 10 x 8 270 5 x 5 x 4 58 10 x 10 x 6 268 5 x 5 x 4 58 10 x 10 x 4 285 5 x 3 x 5 56 11 x 11 x 11 353 6 x 6 x 6 91 12 x 12 x 12 ELBOWS. SIZE. Degree. Wgt Ibs. SIZE. Degree Wgt. Ibs. 2x2 90 9 8x8 30 60 3x3 45 11 8x8 45 77 3x3 90 18 8x8 90 137 4x4 45 22 9x9 45 4x4 90 33 9x9 90 4x3 90 32 10 x 10 13 66 5x5 45 36 10 x 10 16 78 5x5 90 45 10 x 10 18 79 6x6 30 29 10 x 10 25 90 6x6 45 45 10 x 10 28 98 6x6 45 45 10 x 10 30 98 6x6 90 79 10 x 10 36 110 7x7 45 57 10 x 10 45 126 7x7 90 100 10 x 10 90 235 n 1 NATIONAL TUBE COMPANY. 35 ELBOWS. SIZE. Degree Weight. Ibs. SIZE. Degree Weight ' Ibs. 11 x 11 45 160 12 x 12 45 11 x 11 60 192 12 x 12 90 372 11 X 11 90 255 CROSSES. SIZE. Weight. SIZE. Weight. Ibs. Ibs. 2x2 x 2 x 2 13 6x4 x 3x 3 125 3x3 x 3x 3 28 7x7 x 7x 7 135 4x4 x 4x 4 42 7x7 x 6x 6 153 4x4 x 4x 3 43 8x8 x 8x 8 200 4x4 x 3 x 3 46 8x8 x * x 4 229 4x4 x 2x 2 45 8x8 x 8x 6 230 4x4 x 2x 2 43 8x8 x 4x 4 209 4x3 x 3x 3 45 8x8 x 14 x 16 1190 5x5 x 5 x 5 66 8x6 x 8x 6 220 5x5 x 5 x 4 69 8x6 x g x 4 235 5x5 x 4x 4: 74 8x6 x 3 x 3 238 5x4 x 5 x 5 72 8x4 x 4x 4 218 6x6 x 6x 6 108 9x9 x 9x 9 6x6 x 4x 4 117 10 x 10 x 10 x 10 337 6x6 x 4x 3 120 10 x 10 x 10 x 8 339 6x4 x 4x 4 127 12 x 12x12 x 12 Heavy faced figures indicate openings tapped for Standard Pipe. ' 36 NATIONAL TUBE COMPANY. REDUCERS. SIZE. Weight Lbs. SIZE. Weight Lbs. SIZE. Weight Lbl 3x2 6x4 21 9x8 4x3 11 6x3 9x7 4x3 14 6x3 25 9x6 4x2 12 7x6 10 x 9 5x5 19 7x5 10 x 8 50 5x4 17 8x7 10 x 6 46 5x3 8x6 39 10 x 4 52 6x5 8x4 43 12 xlO 75 6x4 22 PLUGS. SIZE. Weight Lbs. SIZE. Weight Lbs. SIZE. Weight Lbf. 2 1 6 7 10 23 3 2 7 13 12 4 3 8 15 14 58 5 5 9 16 88 Heavy-faced figures indicate openings tapped for Standard Pipe. Some of the weights in these tables of Matheson Joint Fittings are not given ; the reason being that there are not Standard patterns for sizes where weights are omitted and the patterns of some other size are made adaptable for same. This would cause a variation in weights, and for this reason it is thought best to give no fixed weights for fittings so manufactured. $n n? NATIONAL TUBE COMPANY. PLAIN UPSET. UPSET TUBES are becoming very generally used for Marine Boiler work ; in many cases the ordinary, as well as the Stay Tubes, are thickened or upset on ends, greater durability and strength being claimed for same. The difficulties encountered in upsetting ends of tubes are not generally appreciated, and upsets are often asked for that are either very difficult or practically impossible to make. As a guide for ordering such tubes a set of tables has been prepared showing the practicable limits that should be observed in tubes of this kind. If a greater diameter is required for upset end than that shown on table giving maximum upset this can be accomplished by expanding the end after upsetting as is shown in the cut below. The tables are all based on an upset 2^ inches long which is the usual length for Boiler Stay Tubes. If shorter length will answer a heavier upset than those shown on maximum table can be secured. UPSET AND SWELLED. NATIONAL TUBE COMPANY. TIONAL TUBE COMPANY. ING ORDINARY UPSET FOR TUB tpuj jo iB u ! ssqn jo ssaujp ipuj JOUOUDBJJ P UB '0 'A '9 3 - ^__ -^^^^^^^ ^ QOOC^^IOOOOOCOOC OOOSOSOSO5OSO5OOOC O5O5O5O5O5O5OOOO-1 IT-IT- I 5j 3 cOCOlOQOTHCCi>C?-i> OS OS O O O O -i-H T-I TH C3 C4 lOlOtOlO _ OOCQi>WO OOOiOiOO isg&ss II^sIss lOJ>OCOlOOO-r-lOOt-O3l>T-l?C>-r-l OS OS O O O O i-H TH T-H O? CO CO ^ OC4OOOOSOOOO(7?CO-i-HO t- i> i> t- 00 00 00 00 OS OS O O rH -r-H CO CO CO CO gQ CO CO CO CO CO TJH T)H TH ^' tOt^OCOlOOO-rHCOt-Cit-THCO-i-l -* -<* 10 to to to o o ?o t- i> oo oo os OC?lOOOOCOCDOOC^t-GOCOlOGO-rHCOt^O?t^fH?OT-( OS O5 O O O O T-I I-H -I-H Oi Oi CO CO -^ ^^oo'co'oo'ooco'eo'eo'co'co'co'eo'co OOJlOOOOCOOaOO?i>CQ?O-rHD t>t>J>l>OOQOQOOOOSOSOC>THTH OOOOO5 gC<)r^TH?O-rH 05 O O O O TH TH TH CO 1C ^ NATIONAL TUBE COMPANY. FFICULT) FOR TUB COMP BLE UPSET NA TABLE SHOWING o => ^ 33 $ 1Q 1Q 1Q 1Q >O IQ 1Q 3 5 3 >O IB I I ^ N i> OO GO OO Oi OJ Oi O O T-I -i-l ' C 5TH-?H^Ho5o5coo ~fti OIEU1I03Q ui saqnx JOS P UB -o -A -a ui ssqnx jo ssaujpiqj, O OS 00 i> CD JO T ^n NATIONAL TUBE COMPANY. PIPE BENDS. The attached table gives the advisable radius and the greatest and least radii to which standard thickness pipe may be bent. If the radius must be reduced from the minimum given in the table, the thickness of the pipe must be increased. For such bends it is best to submit sketch. When the radius is greater than the maximum given in the list, the bend is apt to look like a series of kinks, owing to the Bender having to take short heats, unless the radius is so great that the pipe may be bent cold. With offset bends try to make according to Drawing F.-26i, rather than Drawings F.-257 or 262. The straight length between the bends is of advantage to the pipe Bender. With the welded flanges there must be a short straight length of pipe adjacent to each flange. On sizes under 4 inches this should equal, at least, one and a half diam- eters. On sizes over 4 inches it should equal, at least, one diameter of the pipe. In all cases it is better if equal to two diameters of straight pipe. BENT TUBES. These are more difficult to bend than standard weight pipe. Try not to vary from the advisable radius given in the table. With tubes it is frequently necessary to in- crease the thickness over that of standard boiler tubes in order to bend them. 42 NATIONAL TUBE COMPANY. TABLE OF RADH FOR PIPE BENDS. Pipe Size. Minimum Radius. Maximum Radius. Advisable Radius. Inches. Inches. Inches. Inches. 2K 10 25 15 3 12 30 18 3K 14 35 21 4 16 40 24 *K 18 45 27 5 20 50 30 6 24 60 36 7 28 70 42 8 32 80 48 9 36 90 54 10 40 100 60 11 44 110 66 12 48 120 72 14 o. d. 60 140 84 15 " 68* 145 90 16 " 76 150 100 18 " 90 165 125 20 " 120 180 150 22 " 132 198 165 24 " 144 216 180 NATIONAL TUBE COMPANY. 43 STOCK PIPE BENDS AMERICAN OR ENGLISH STANDARD THREADS AND COUPLINGS. Irt * -A * Pipe Size. Radius "R." Centre To Face "A." Inches. Inches, l/^ Inches. 2 H 1 2 | 3 ?* 3 8 10 4 10^ m 5 14# 18^ 1 : NATIONAL TUBE COMPANY. OFFSET BEND, No. F. 257. ANGLE BEND, No. F. 260. OFFSET BEND, No. F. 261. 1800 BEND, No. F. 258. go" BEND, No. F. 259. DIMENSIONS National Trolley Poles DEFLECTIONS UNDER STATED LOADS If & 46 NATIONAL TUBE COMPANY. S Length of Pole, 34 feet. End of Pole 6 feet in ground. TABLE OF DEFLECTIONS MEASURED AT FREE END. TOP LINE GIVES LOADS IN POUNDS APPLIED 18" FROM END. I ^ TH GO* OS CO OS co Z> GO 00 i l> J> GO J> 00 i co co i> s 5 t> 00 s CO TH IO 10 co' co TH CO CO 10 CO t^ i> GO* i CftCOi^tHlOCOCO^S T* IO 10 CD CO *> J> OO OS 1 CO 10 00 CD "^H TH -rtl CO CO CO CO CO CD CO CO ThlT^^lOlOCOCOi>00 I CO CO i> IO OO O CO CO* ^ OO O OS ^ CO CO CO J> TH JO O OO i 5.* f SCO IO CO CO OS > TH -^ 00 "^ CO CO TjJ rjl -HH 10 CO CO CO CO CO TH CO TH CO CO 00 TH CO CO TH CO* CO' CO CO* CO rjl i 3 s 3 IO GO GO CO TH T^ t> OO O CO Tf > TH TH CO CO CO CO g 55 CO i> M* ^1 TH O t> 00 05 TH CO CO C5 O O O O TH TH TH TH g ? W oo HO.HX CO TH TH TH GO OO CO CO CO O O *Q 'O 8 2 : - g g - MIDDLE. 10'-10 ff XDIHX COOOTHOOTHGOOOO H^-r^rHCOCOCOCOCOCO OOOOOOOGJO -a-o SCO O CO O co: ocoo- GO GO OO GO OO BUTT. 17-8' HHX o o o l> CO 10 CO 10 CO o o o o o o Q O CO . '.. ' - 5 8 . *,..'i OS OS W*!M ill t^ i>- OS OS IO IO O CO CO CO CO OS aaquzuN TH CO CO T^ 10 CD i> GO OS NATIONAL TUBE COMPANY. END. FR DE i> T}< to OS 00 T^ 00 CO OS - W CO CO CO OWCO?OiCOOJOCOOJOO COlXNlOO^OOrfiOOOlOCOCOTHlOOOCO -i oa co o? oj co O O O O O O O >. .. - O O O O W O IO v. CO OJ - OJ - - CO W ^ -COl CT^ 48 NATIONAL TUBE COMPANY. Length of Pole, 33 feet. End of Pole 6 feet in ground. TABLE OF DEFLECTIONS MEASURED AT FREE END. TOP LINE GIVES LOADS IN POUNDS APPLIED 18" FROM END. 1 t- 06 II co I 1O i> 1O 05 10 CD e^ 06 1 co co i> j> 1 05 05 05 CO CO TH 10 TH 1O CO CO J> g is 1 SCO CO TH 10 00 CO 10 10 10 CO co co CO *> 1 TH CO CO CO TH OO TH IO TH TH 10 lO TH CO CO CO CO OS 1O O5 O5 CD to co co z> oo I 8 8. 3 2 S S $ S 5 innri CO CO l> 1O CO CO CO O5 TH TH 1 S 3 TH CO CO CO CO CO t- O5 1O O5 I CO O i> CO CO TH CO CO CO 1O OO O5 TH i> CO CO* CO CO O* O Q'0 8 . . ^ 50 05* 05* WIJ* l 1 1 s/l 1 I 1 i jaqumN cococococococococo ! ^ NATIONAL TUBE COMPANY. gro E FREE END. < H W T-H! t>00 I" ils 1O CO CD 1> l> OO CO CO ? W ^ 00 DOOOCOOO5OOOOOOOIO COOOOlOOOTHCOCOOCDCOrHOO 07 CO CO CO CO O O O O O O T 33 feet h o - o- ^ 10 CQ1C tOlQ^lC^r^ ^ ^ OO ^ OJ - ~ COW- OO O O ^ OO J>^ 00 <* OO , ^ OO ^ O IO -^ 1-1 lO OOOOOOOO OO O O O O* O s : ; : ^rr: 60 NATIONAL TUBE COMPANY. 3 Length of Pole, 32 feet. End of Pole 6 feet in ground. TABLE OF DEFLECTIONS MEASURED AT FREE END. TOP LINE GIVES LOADS IN POUNDS APPLIED 18" FROM END. | ! * 1 8 00 1 HH O CD 00 CO J> CO Z> Z> 1 CD CO i> 1 t^ O ^ 10 co co' CO I 1O *> CO TH -* OO 10 10 10 CD' CD 1 OO CO OO 1O 00 TH 8 10 8 8 CD CD 1 m OS OO CO - TH t> CD to 10' co CD' t^ 1 CO 1O OO ^f CO OO co' co' co os TH 1C OS CO t> 1O TH -^ 10' 10' co OO O O2 OS co' CO CO CO TH OS CO* -rj" ^ TjJ 10 00 CO "^ 1O co' co co" 8 O CO 1O OS OO 1O OO CO I TH CO ^f t OO OS os o CO CO xt< CO OO CO CO CO CO CO CO 1 rJH CO OS TH CO CO OS CO 1O CD i> OS CO g ? a oo HO ,* CO CO - O o* o o o o Q'O 8 5 : ! : 8 8 : 1 T Q o SDIHJ, C- CO o o CO CO o 00 TH OO O 00 CO CO CO CO CO O O Q-0 8 5 - 00 00* = 8 S 8 5 OO OO OO H o *0,HX O f 10 CO 10 CO CO CO CO CO O O a o CO . OS OS ^SPM CO CO OS 3 OO CO 00 TH OO o o os os ac> uaquiuN 10 10 10 CD to S co CO nf NATIONAL TUBE COMPANY. END. FR MEASURED DE BLE ^ 1-1 CD COOS t- 1C C CO TH O? 00 CO OOCOOIC ~i5 ic co co 10 10 tC CD J> 00 OS CO ^ T* 10 10 CD CO i> Z> 00 OS COCOOO-rHCOeOC^C^CO-rH^OOOOWCOCJ T-H COt-OS (MTt< CO TH 1005 r^OO^OOSJ> > " ?"^i>OS(MOOSO7)OD O'O'OO'OO'OT CO O OO oooooo^ o ,. - O O O O 1C O lO - - O - - 10 o 10 10 10 * I - COW- CQ- - COO?- O?(M(M( OO O OO OOOO cro 8: : : - S-- 5 CO *>CO CO 1C CO 1C 1C O CO t-t 1C CO "H CO T ^OOt^"^OO"^O CO CJ CO CO O3 CO oooooooo oo ooooo - 2 0= * c- : 8: : - 8- - SOOl>OOJ>t-l>COC 52 NATIONAL TUBE COMPANY. fl Length of Pole, 31 feet. End of Pole 6 feet in ground. TABLE OF DEFLECTIONS MEASURED AT FREE END. Q 8 o S k Q M J Cu a. 1 to S S 8 o H g PL, 1 9 s II i CO* t- II OJ CO* o I a 8 a 10* CO* CO I 1O 1O CO I- JH T oo oi H IO 1O CO* ^ 05 TH 10 ^ ^H 10* IO 10 1 S S J 8 IO IO 1 ^ S o^ CO* CO CO "^ ^ 10 10 10 co 1 CD CO O OD 05 05 ^ CO oi co co co S S g S 8 CO ^ "^ 10 10 1 l__l_l_l T-I CO -rH IO -^ CO CO 05 05 00 1 S " TH oi oi oi g 8 S 5 88 oj oi co co co I ^ s g s 05 00 10 10 O5 i-H CO IO O5 TH oi oa o CQ 1 cS ^ ol O) IO CD O ^ CO <*< IO t- O5 Q fc S XO.HX co oS - w do d r i i * s d d *Q 'O o ^ , o? : 8 g 8 : MIDDLE. o 1 O5 HH* 1 1 5 S OO TH OO O OO OJ CO Oi CO O? o o o O O O 'Q 'O o - " S 00* 00 : 8 S 8 : 00 OO 00 BUTT. 2 'XDIHJ, d d d d CO IO O? IO O) ^ W CO 00 CO d d d d d Q'O 'CO 0? : s = S - 05 05 VI** CO W ^ 8OO O5 ^dn O^ O5 00 O5 00 jaqumN ^oooooooooooooooo NATIONAL TUBE COMPANY. n gro FREE ECTIONS ME TA ooooooooo TH-rHi-lT-lr-l-i-lTHC o oo S: : S = 88S8fgS: = 8: : DDLE. 'XOIHJ, - " cow" c* - - cow- ^2 wci" o ooo oooo'o Q ^ O5DO5O. ^ O^ gt o'o'o'oo'o'o'o oo o'o'o'oo s 2 8= : : : 8- s : Sc : 00 OO l> l> CO O* 633 & 64 NATIONAL TUBE COMPANY. Length of Pole, 30 feet. End of Pole 6 feet in ground. TABLE OF DEFLECTIONS MEASURED AT FREE END. * O || O TH CO CO CO II CO co' t> -^ CO CO TH 10 10 CO CD I ? 1 s ^ $ g 10 1O CO* I 1 I O CO O5 "* OO O5 1O O5 "^H 10 10 10 Cu O Pu O 8 g . g . 3 "^ ^' 10 10 * 10 I 1 I s - g ol g g 10 10 I OS 00 O5 O? CO CO "* TjJ CO 00 CO 00 1 CD TH Tfrl O5 J> 1 -* 1O 1O 1O CD 1 M O TH OO co 10 i> i> I> O5 O5 1O O *! i> O5 Oi -* ^' ^ 10 10 U TH co ac> o w 05 05 CO CO* O O5 O 00 00 10 00 TH . -* CO CO ^' ^' 10 > o w T ~ l OO CO TH O TH CO 10 i> 05* 05 05 05* O5 TH Tt< i> O5 T}< O5 TH ?O i> oo o TH TH TH 05" 05 O5 O5 O5 O5 CO O EH CO 2 - * .- S ' 2 IO TH 1O "^ ^ - O5 O O5 1O ?f K fc- *0,HX CO Ctt 2 W o o o - O5 O5 ~ - O O Q '0 I - = = 2 S ! : MIDDLE. 9'-6" SOIHJ, O O O O a-o O O5 00 00 : 8 1 8 : OO OO 00 [D so PQ *-i ,HX O O O CO 1O O5 1O O5 ^f CO CO CO CO o o o o o a o .. s = 05 05* WPM -^ CO O5 O I 1 1 1 aaqmuN 1O CD i> OO o o o o 05 O TH 05 CO NATIONAL TUBE COMPANY. 2 M .s FREE END. MEASURED DEFL TA 1O CO TH CO 588S TH^CDlOOSt>OSlOOOOSlOOOCCOO5001O 05 C? CO CO CO CO -* " 10 JO CO CO *> 00 OS 1-1 i 05 GQ 05 CQ CO CO CO ^ 1C 1C CO CO I> -r-l T-! -rH -r-l -rH -r-l -r H c coiocoio COCO IO CO TH CO TH CO TH OSCOO5OS O -^ 00 t- rf< OO -^ OO ^ -^00^ O 1O "^ TH 1O ooo'o'o'o'o'o' oo o'o'o'o'o ^ -^ 06 oc 56 NATIONAL TUBE COMPANY. a g So a 1 1 1 i V "8 TABLE OF DEFLECTIONS MEASURED AT FREE END. Q 6 g 05 i> II O 00 05 Q 1 10 JO D* 00 c "^ CO OS T^ CD 10 10 JO Q O 3 * CO O5 CD O5 CO 05 CD TH 10 10 JO < 1 ol 8g S 10 JO 13 O5 i~s~~8"~i JO JO B 1 OS CO "^ TH "^ i> OS O5 CO CO CO -rJH JO O JO 10 CO "* JO JO 1 S TH CO JO J> CO CO CO' CO r^ -rj ^ JO JO s i 05* 05 CO* CO ^ OS CD JO i-l JO OO -i-t JO O5 5 05 05* 05 05* 05* S S, S S 5? *3 S iriinrEiJLO g s JO J> JO i> g 1 S 8 Ss P W t- -.O.HX o o o O a -o O^ , 05.. O050^ MIDDLE. 9'-2" ,0,HX O O 0^ CO CO 0* o o o o o a-o 00 - g - 00 00 00 fi ^ g 2 .- O O O CO JO O5 JO O5 O O O a - o 05 8- OS OS *mSl9A^ JO OS O OS ^ O5 O5 O 00 O5 "^ OS i> uaqnmx CO CO CO CO .O CD J> OO OS CO CO CO CO CO NATIONAL TUBE COMPANY. END. DE TA . |3S g a I .i.0 S8S3B __ OOOOTH-rH TH TH TH TH TH O OO <* 00 ,. U3 TH 10 CO, 00 CO , COCJ- Ci- - COW- CO COifflCOJO 1C OOOOOOOO OO OOOOO \~. = 8: r 8= 2 8- : 8: 8: = fr* go so- >i> t> COCOCOlCl 58 NATIONAL TUBE COMPANY. ^ Length of Pole, 28 feet. End of Pole 6 feet in ground. TABLE OF DEFLECTIONS MEASURED AT FREE END. TOP LINE GIVES LOADS IN POUNDS APPLIED 18" FROM END. 1 o co no CO t- 10 10* II CO CD 10 i 1 % S TH 1O 1 3> CO TH 10 10* 1 C<* OO J> CD CO CO OS CO TH TH TH 10 3$ OO O? OO TH OS CO 1O OS 1 1O CD O CO CO OS O* 1O CO* CO* TH* TH 00 lO 00 CO TH 1O 8 8 O O O? TH i> TH d d d d d -a-o - - - - OS* d WSPAV OJ TH TH 00 CO C5 TH O 10 TH CD 10 aaqmnN Iboiococococococo NATIONAL TUBE COMPANY. be . ti s DE TA T-l 1C1C I I T-t | 1C TH I CO^-^ 1C COCOCOTft^lClCCO WWCOCOCO^^TftlClCCO 1 ; co co co co ^' ^ 10 10 o OOOOO-r C<* ^ ^ OOCOOOOO. . O CD: r c- ooicoicoo^ - o- - 1C CO 1C 1C 1C ^ 1C "*' ^ o* - : cow- c- - cow- o - ww- O OO O OO O OO hglsSISS: :8: S > t> CD CO 1C CD 1C 1C < CO W CO CO W CO W - CO W - CO W CO CO W o'o'o'o'o'oo'o o'o o'o'oo'o - -O. .W,. ^0^ i i> CO CO 60 NATIONAL TUBE COMPANY. Length of Pole, 27 feet. End of Pole 6 feet in ground. TABI,E OF DEFLECTIONS MEASURED AT FREE END. TOP LINE GIVES LOADS IN POUNDS APPLIED 18" FROM END. | 3 8 II 8 1 CO CO 1 3 s 3 1 |3T3 1 CO* CO CO* T|* 1 CO CO* CO CO TH Tp 1 00 O CO O Tt< 00 00 TH CO CO 00 TH 1 1111^1^3 o g [JJJJsfTl cococococococococo I THrH-rHCOCOCOCOCOCO "^iOCOOCOOSCOTHOO ' ^ W co x COCO- CO- COCO" - 00 0* O O Q'O ::- g 8 s MIDDLE. 8'-6" ..O.HX 1>CO COTHCOTHO-rH oo oo'o'ooo a-o =::: g ^ TH NDIHJ. iOCOO*>COlOCOOCO o'o'oo'ooo'o'o 'Q 'O 2 . 05 OS *.aM || | S.I I 1 1 i ' U " IU " 1M COTHW5COi>OOOSOTH ooooooooooooooosos NATIONAL TUBE COMPANY. o .q ^H I O? 00 00 CO 5J>CODOOO?OO -GC^lOi>i-lt--rHlO * CQ CO* CO* CO ^ T to 10 5 T-I g 00 r-J W O6 ^ acoeoeo^^ioiogo S-i-iOOCO^OOOOCOOlCOWWO -0000050T-IO)COIOOOOOW10 O O O O O O O r T It lO 5OT-HO? OOOOOooOOOOOOO s : = : 1O CO 10 to t OO O 00 O OO : 5 : : O^ODJ>^OO^OO^ Tj^OO 0>0^^-iiO Tt< CO O5 CO CO CO CO s s CO* CO I CD CO TH CO rt< CD 00 CJ 04 tO rj< O5 OO O O5 C5 "* t- CO OJ CO CO CO ^ I ^1^111111 1 O? CD O5 T$< t- 00 05 TH T-H T-I T-I CJ C3 OJ C? CX* CO 1 ^ O5 T-t CQ 1C OO T-I o? oi cxi cxj 1 ^ g 9 S "* ^ 05 CD 00 05 T-H CO T-I T-I T-I O? O* d 9 g i '3IOIHX CXi T-I O T-< OO CQ CO C? O? o o* o OO O o> WC<COCOTt*OO OOOCOOOOO CQOO5COt>THC OOOOTH-rH-rHTHT-lT TH TH o* oa O5TH OOOOOOOOOT OOOOOOOOOOOOOOOOr O->^ , CO.. OOCOOOOO O - OO1OO1OO1O- - O- CO IQ CO It 00 . -rri OO W5 ^ ^ TH O CO, OO CO >. 01 - CO O? Oi - - CO O5 - CNJ ~ Ct Ct ~ O OO O OO O OO Iz 8Ss S- = = r CO t>CO* COlCCo'lO IQ ^c^ c8cococ5co c5 - cow- cowcoco^ o'oooo'o'oo o'o o'oo'o'o ^ 64 NATIONAL TUBE COMPANY. f Length of Pole, 25 feet. End of Pole 6 feet in ground. TABLE OF DEFLECTIONS MEASURED AT FREE END. TOP LINE GIVES LOADS IN POUNDS APPLIED 18" FROM END. 1 CO OO CO CO C CO | JO OS *> TH CO JO 1 co" co co 3 CO 1 CO ^ OS i> OS O co co' co CO C^ CO CO* 1 CO CO ^H JO *> 00 CO* CO* CO CO OO OO 1 i-HO5COCOOi>C5CO CO CO CO CO CO CO CO CO 1 OCOOOOCOCOCOCD-^i THCOCOCOOOOCOJOO CO CO CO CO CO CO CO CO ^ I 00 TH ^ ^ JO CO O -^ CO JO i> OS CO CO 1-1 CO CO CO CO CO CO CO CO & 00 8 OO CO JO TH JO CO O CO "* CO 00 CO TH-rHTHCococo'cococo 1 H/l JO CO CO t> ^ 00 OS CO 00 OS TH CO "tf OO TH TH CO CO CO* CO I $ S 5 CO OS "* JO -^ CO JO CO OO OS TH ^ | JO CO 00 O TH TH O TH CO CO 00 CO CO ^ JO CO J> O Q co fc J W co ,0,HX TH OO CO CO " O OO O O 00 a -o 8 : = i> ^ CO CO - O CO MIDDLE. 7'-10" 30.HX t- CO CO O O TH S TH- 00 8 SO CO CO CO CO CO CO o* o o o o o a*o 8 - - 00 O CO O ; o co o - 00 . OO OO 00 T3 .O.HX JO CO O CO CO O CO JO JO t- CO JO CO JO CO CO O t TH i> TH ^ ^ CO CO CO CO o o o o o o o o o cro - - - - - OS* OS* VU*AL COTHOOSOOOOi>J>*CO jaqumN cococococococococo NATIONAL TUBE COMPANY. p I H H H w Q Q ^ COTK SO -rH *& tO T_| T^H ,-( J>-r-llOOO ! CO CO CO CDCOTtOOO5 ooooo'o'oooo'o'ooo'ooo CO O CO ~ 51OOIO" " O- CD 1O 1O to ^ 1O ^ OO O 00 O OO 3 , OCOOCO 3 ~ O tO O 10 - ggi }> CD CO 1O CD 1O H H CQ OOOOOOOO OO OOOQO cro t> CO CO* 66 NATIONAL TUBE COMPANY. pj Length of Pole, 24 feet. End of Pole 6 feet in ground. TABLE OF DEFLECTIONS MEASURED AT FREE END. TOP LINE GIVES LOADS IN POUNDS APPLIED 18" FROM END. i 1O CO OO II O 10 00 CO CO 1 O ^f CO 00 00 O CO -* CO CO CO CO 1 1O CO OO O CO 1 1 1 I 1 CO CO CO CO CO CO CO 1 CO CO CO CO CO CO CO CO 1 OS CO ^ CD TH CO CO CO CO 00 O CO i> CO CO* CO CO CO 10 ^* 00 i> OS O TH CO OO OO CO -rH JO i> O -^ CO CO -CO CO 1 OO TH -^ CO CO 10 i> 00 OS TH g g TH- THTHi-lTHCOCOCOCOCO 1 S g 8' S 3 CO CO CO 10 O CO "* i> CO CO CO CO IS 2 2 * 2 TH 1O TH TH TH TH CO CO i TH CO CO 55 10 CD 00 O 1 i> T^ CO OS OO CO CO 10 J> i' ? w =,O:HX TH 00 CO CO CO - CO 00 O CO CO - - Q 'O o co co o CO O - MIDDLE. 7-6" mx t- CO CO TH CO O TH 00 <* * co co 00 O O TH 00 00 CO CO CO CO O a-o 00 00 8 8 = OO OO OO E 2 w HO.HX 1 1 S 1 II ! o o o o o 0000 a'o CO 8^ OS* OS -^fM ^ CO OS CO CO TH O 00 OO OS CO CD OO 00 TH W5 g qu,n N CD CD CO CD CD CO CO CO CO CO CO CO CO CO NATIONAL TUBE COMPANY. be . FREE END. TIONS MEASURED DE TA T-H I 0303 03 CO 21 ? C 03 O CO CO CO OOOOOOOOr OO'OOOOOOOOOOT I ooooo o'o'oo'oo'o'o'oo'o'o' 30IHJL d'O = :: - - o A bi) DDLE. ^fOO 1C 1 ilO^CO OOCO^ CO(M- CJ- - COC3- CJ- C3C5- O OOOOO O x^ OO O -^ 00 ^ OO ^ CO CQCOCOC? CC 0? - co oi co co w o'o'o'o'o'o'o'o o'o o'o'o'o'o Q'O QO 00 SEAMLESS TUBULAR GOODS NATIONAL TUBE COMPANY. SEAMLESS DRAWN TUBING. In submitting the following information on the subject of Seamless Tubing, together with the accompanying tables, etc., we call attention to the rapid strides made in the demand and in process of manufacture of this grade of Tubes in the last few years. These Tubes are becom- ing generally used for high grade Boiler work, where high steam pressures are required , especially for Marine Boilers, the Navy Department of all first-class Naval powers having extensively adopted the same. In both I/ocomotive and Stationary Boilers the use of this Tubing is becoming recognized as a high grade quality. The extending use of compressed air and other gases under high pressures has developed a good demand for these tubes for storage tanks, high pressure bottles, transmis- sion lines, etc. The absence of all laps or seams, together with uniformity of size, gauge and quality, recommends this grade of material as very superior where unquestion- ed uniformity and strength are required, in connection with the lightest weight available for the purpose. Seamless Tubes with varying thicknesses of walls are also being used quite extensively for Mechanical and Engineering purposes ; for bushings, collars, hollow shafts, spindles, axles, etc., in the construction of different classes of machinery. Different grades of steel can be used, giving a wide range of ductility and tensile strength, which allows a selection of material suited and adaptable to the require- ments demanded. The method of manufacture of Seam- less Tubes is such that the possibilities of physical de- fects in material are reduced to a minimum. NATIONAL TUBE COMPANY. Extract from Proceedings of Niagara Falls Society of American Mechanical Engineers. December, 1808. What Constitutes a Seamless Tube? 41 Henry Souther said, in the discussion of this question, that the scientific and technical designation of a tube, ' whether seamed or seamless, depended solely upon the tube itself, and not upon the process followed in its manufacture. Referring to the dictionary you will find that the word "seamless" means without seam, which conveys no light upon the subject. Turning to the word "seam" it is found that it is defined as a joint, suture, or line of union, and here in the last term we find the key. A tube jointed in any way cannot be seamless. If, in the primary stages of its manufacture, it be lap, butt or lock- jointed, it cannot by any subsequent operation be deprived of the seam, and therefore cannot be con- sidered, when completed, as being seamless A strictly seamless tube may be made by any one of three opera- tions. First, a billet may be, by successive steps, punched into the form of a tube with extremely thick sides ; and these may then, by the ordinary drawing pro- cesses, be reduced to a tube with thin walls. Next, the billet may be bored, or the blank may be cast with a hole in it, and in either case then drawn to the required di- mensions. Thirdly, the tube may be made by the cup- ping process, which consists in taking a disk of the metal, forming it into a cup shape, gradually elongating the cup and reducing it in diameter, and finally by this means producing a tube. Each and all of these processes yield a tube which is absolutely seamless and about which there is and can be no dispute. In all tubes formed with a seam the edges have first been separated, then united, either by lap or butt weld, or by some lock-joint system, and in these the joint cannot be eliminated by any after processes. The Custom House of the United States recognizes the difference between a seam and a seamless tube. A seamless tube is one in which the walls have never been separated from the time the metal was in a molten condition to the time of the completion of the tube." NATIONAL TUBE COMPANY. COLD DRAWN TUBES. The Weight Sheet for Seamless Cold Drawn Tubes, as given on following page, is applicable for Tubes intended for many different purposes. The sizes from ^ inch to \y 2 inch diameter and from 16 to 23 gauge inclusive are generally classified as Bicycle Tubing, on account of their very general use in Bicycle construction. They are used, however, for many other different purposes. These Tubes are manufactured from Open Hearth Steel of analysis best suited for the purpose. They have a fine finish and are drawn accurate to size and gauge. These tubes are admirably adapted for all construction requir- ing a maximum strength and minimum weight. They have great rigidity and are suited for high transverse strains. Tubes for boiler purposes, from i inch to 4 inches, and and from 13 to 6 gauge inclusive, are made of mild Open Hearth Steel, of analysis best suited to give toughness and ductility. The process of manufacture is such that only material free from laps, seams, cracks and all physical imperfections can be used. This insures a high uniformity of quality and reduces the possibility of acci- dent, due to imperfections of material, laps and welds, to a minimum. Tubes of thicknesses other than those given above are generally termed " Mechanical Tubes, " and are used in the construction of many classes of machinery for bush- ings, hollow shafts and spindles, axles, collars, rings, ferrules, pump barrels, etc., etc. Often a considerable saving in machine work is effected by the use of these tubes in place of parts heretofore made by boring and turning round bars, the tubes admitting of a lighter and stronger construction than by using the former material. NATIONAL TUBE COMPANY. 1 1 OH .9 csaooo-^ojcoi-iosocsfNioa i-; O Tf OV Tf< 05 C O J> 1C 1-1 ec ec Tt rji <* 10 10 o od oi r-J ec ji cc cd t' ** 10 id so t~ od o i-' s w co eo eo *' -*' ^ 10* SKiS llllllil 74 NATIONAL TUBE COMPANY. Table showing Weight per Foot in Pounds of Various Diameters and Thicknesses of HOT FINISHED TUBES. :| THICKNESS OF WALL. || M * H A M A M H H 1 2 4.60 5.54 6.40 7.18 7.88 ix 4.93 5.96 6.90 7.76 8.54 M 5.26 6.37 7.40 8.34 9.20 32 5.59 6.78 7.89 8.92 9.86 LX 5.92 7.19 8.38 9.49 10.52 % 6.25 7.61 8.88 10.07 11.18 3X 6.58 8.02 9.38 10.65 11.84 H 6.91 8.43 9.87 11.23 12.50 3 7.24 8.84 10.36 11.80 13.16 14.43 15.62 7.57 9.26 10.86 12.38 13.82 15.18 16.45 ixf 7.90 9.67 11.36 12.96 14.48 15.92 17.28 % 8.23 10.08 11.85 13.54 15.14 16.66 18.10 ix 8.56 10.49 12 36 14.11 15.80 17.40 18.92 KX 8.89 10.91 12.84 14.69 16.46 18.15 19.75 % 9.22 11.32 13.34 15.27 17.12 18.89 20.58 % 9.55 11.73 13.83 15.85 17.78 19.63 21.40 4 9.88 12.14 14.32 16.42 18.44 20.37 22.22 25.68 28.80 10.21 12.56 14.82 17.00 19.10 21.12 23.05 26.67 29.96 M 10.54 12.97 15.32 17.58 19.76 21.86 23.88 27.66 31.12 32 10.87 13.38 15.81 18.16 20.42 22.60 24.70 28.65 32.27 12 11.20 13.79 16.30 18.73 21.08 23.34 25.52 29.64 33.42 % 11.53 14.21 16.80 19.31 21.74 24.09 26.35 30.63 34.58 ax 11.86 14.62 17.30 19.89 22.40 24.83 27.18 31.62 35.74 % 12.19 15.03 17.79 20.47 23.06 25.57 28.00 32.61 36.89 5 12.52 15.44 18.28 21.04 23.74 26.31 2S.82 33.60 38.04 42.16 12.85 15.86 18.78 21.62 24.40 27.06 29.65 34.59 39.20 43.48 y. 13.18 16.27 19.28 22.20 25.06 27.80 30.48 35.58 40.36 44.80 32 13.51 16.68 19.77 22.78 25.72 28.54 31.30 36.57 41 51 46.12 i 13.85 17.10 20. 7 23.36 26.39 29.29 32.13 37.57 42.67 47.45 % 14.18 17.52 20.77 23.94 27.05 30.04 32.96 38.56 43.83 48.77 ax 14.51 17.93 21.27 24.52 27.71 30.78 33.79 39.55 44.99 50.09 il 14.85 18.35 21.77 25.11 28.38 31.53 34.62 40.55 46.15 51.42 6 15.18 18.77 22.27 25.69 29.05 32.28 35.45 41.55 47.31 52.75 15.51 19.18 22.77 26.27 29.71 33.03 36.28 42.54 48.47 54.07 1? 15.84 19.59 23.26 26.85 30.37 33.77 37.11 43.53 49. 3 55.39 3| 16.17 20.01 23.76 27.43 81 04 34.52 37.94 44.53 .50.79 56.72 1^ 16.50 20.42 24.26 28.01 31.70 35.27 38.77 45.53 51.95 58.05 sx 16.83 20.83 24.75 28.59 32-36 36.01 39.60 46.52 53.11 59.37 ax 17.17 21.25 25.25 29.17 33.01 36.76 40.43 47.52 54.28 60.70 K 17.60 21.67 25.75 29.75 33.67 37.51 41.26 48.52 55.44 62.03 NATIONAL TUBE COMPANY. 75 Table showing Weight per Foot in Pounds of Various Diameters and Thicknesses of HOT FINISHED TUBES. (CONTINUED.) -Ss THICKNESS OF WALL. 11 5 14 i 5 s % T 7 * w A % % % 1 7 17.83 22.08 26.25 30.33 34.33 38.25 42.09 49.51 66.60 63.36 & 18.17 22.50 26.75 30.92 35.00 38 99 42.92 50.51 57.79 64.69 18.50 22.92 27.25 31.49 35.67 39.74 43.75 51.51 58.95 66.02 % 18.83 23.33 27.75 32.07 36.33 40.49 44.58 52.50 60.11 67.35 L^ 19.16 23.74 28.24 32.66 36.99 41.23 45.41 53.49 61.27 68.67 % 19.49 24.16 28.74 33.24 37.66 41.98 46.24 54.49 62.43 70.00 ax 19.82 24.57 29.24 33.82 38.32 42.73 47.07 55.49 63.57 71.33 % 20.15 24.98 29.73 34.40 38.98 43.47 47.90 56.48 64.73 72.65 8 20.48 25.39 30.22 34.97 39.64 44.21 48.72 57.47 65.89 73.97 % 20.80 25.80 30.71 35.54 40.29 44.95 49.54 58.46 67.04 75.29 21.12 26.20 31.20 36.11 40.94 45.68 50.36 59.44 68.19 76.61 % 21.44 26.61 31.68 36.68 41.59 46.41 51.17 60.42 69.34 77.92 U 21.77 27.02 32.17 37.25 42.25 47.15 51.99 61.41 70.49 79.24 22.10 27.44 32.66 37.82 42.90 47.89 52.81 62.39 71.64 80 56 M 22.43 27.85 33.15 88.39 43.55 48.62 53.63 63.37 72.79 81.87 9 22.76 28.26 33.64 38.96 44.20 49.36 54.44 64.35 73.93 83.18 9 23.08 28.67 34.13 39.53 44.85 50.09 55.25 65.33 75.07 84.49 i^ 23.41 29.08 34.63 40.11 45.51 50.83 fi6.07 66.31 76 22 85.80 N 23.74 29.48 35.12 40.69 46.17 51.57 56.89 67.29 77.37 87.11 s2 24.07 29.88 35.61 41.26 46.83 52.31 57.71 68.27 78.51 88.42 H 24.40 30.29 36.10 41.83 47.48 53.05 5S.53 69.25 79.65 89.73 g 24-73 30.71 36.60 42.41 48.14 53.79 59.36 70.24 80.80 91.04 9 25.06 31.12 37.10 42.99 48.80 54.53 60.18 71.23 81.95 92.35 9 25.39 31 53 37.59 43.57 49.46 55.27 61.00 72.22 83.10 93.66 10 25.72 31.94 38.08 44.14 50.12 56.01 61.82 73.20 84.25 94.97 % 26.04 32.35 38.57 44.71 50.77 56.75 62.64 74.18 85.40 96.28 p 26.36 32.75 39.06 45.28 51.42 57.48 63.46 75.16 86.54 97.59 26.68 33.15 39.54 45.85 52 07 58.21 64.27 76.14 87.68 98 90 1^ 27.01 33.56 40.03 46.42 52.73 58.95 65.09 77.13 88.83 100.21 I 27.34 33.97 40.52 46.99 53.37 59.69 65.91 78.11 89.98 101.52 y 27.67 34.38 41.01 47.56 54.02 60.42 66.73 79.09 91.13 102.83 8 28.00 34.79 41.50 48.13 54.68 61.15 67.54 80.07 92.27 104.14 11 28.32 35.20 41.99 48.70 55.33 61.88 68.35 81.05 93.41 105.45 1^ 28.65 35.61 42.49 49.28 55.99 62.62 69.17 82 03 94.56 106.76 N 28.98 3R.02 42.98 49.8? 56.65 63.36 69.99 83.01 95.71 108.07 G 29.31 36.43 43.47 50.44 57.31 64.10 70.81 83.99 96.85 109.38 L< 29.64 36.84 43.96 51.01 57.96 64.84 71.63 84.97| 97.99 110.69 p 29.97 37.26 44.46 51.59 58.60 65.58 72.46 85.961 99.14 112.00 iS 30.30 37.67 44.96 52.17 59.26 66.32 73.28 86.95 100.29 113.31 | 30.63 38.08 45.45 52.74 59.92 67.06 74.10 87.94 101.44 114.62 76 NATIONAL TUBE COMPANY. Table showing Weight per Foot in Pounds of Various Diameters and Thicknesses of HOT FINISHED TUBES. (CONTINUED.) S| THICKNESS OF WALL. y X A ft H * * H * 1 12 30.96 38.49 45.94 53.31 60.58 67.80 74.92 88.92 102.59 115.93 31.28 38.90 46.43 53.88 61.23 68.54 75.74 89.90 103.73117.24 /4 31.60 39.30 46.92 54.45 61.88 69.27 76.56 90.88 104.87118.55 ax 31.92 39.70 47.40 55.02 62.53 70.00 77.37 91.86 106.01 119.86 IX 32.25 40.11 47.89 55.59 63.19 70.74 78.19 92.85 107.16 121.17 % 32.58 40.52 48 38 56 16 63.84 71.48 79.01 93.83 108.31 122.48 a^ 32.92 40.94 48.88 56.74 64.50 72.22 79.84 94.82 109.47,123.80 % 33.26 41.36 49.38 57.32 65.16 72.96 80.66 95.81 110.62125.12 13 33.60 41.79 49.89 57.91 65.83 73.71 81.49 96.81 111.78126.45 ix 33.94 42.21 50.40 58.50 66.50 74.46 82.32 97.80 112.94 127.77 IX 34.28 42.64 50.91 59.10 67.18 75.22 83.16 98.80 114.11 129.10 % 34.62 43.06 51.42 59.69 67.86 75.98 84.00 99.80 115.28130.43 IX 34.96 43.49 51.93 60.29 68.54 76.75 84.85 100.81 116.45 131.77 % 35.28 43.89 52.42 60.86 69.20 77.49 85.68ll01.80 117.60133.08 ft 35.59 44.29 52.90 61.43 69.85 78.28 86.50,102.79 118.75 134.39 % 35.90 44.68 53.38 61.99 70.50 78.96 87.32103.78 119.90 135.70 14 36.20 45.07 53.85 62.55 71.14 79.69 88.13104.76 121.05 137.01 36.52 45.45 54.32 63.10 71.78 80.41 88.94 105.74 122.20 138.32 IX 36.85 45.86 54.79 63.66 72.42 81.14 89.75 106.72 123.35 139.64 sx 37.19 46.28 55.29 64.22 73.07 81.87 90.57 107.71 124.51 140.97 /^ 37.54 46.71 55.80 64.81 73.72 82.61 91.39108.70 125.67 142.30 fix 37.90 47.15 56.32 65.41 74.40 83.35 92.22'109.70 126.84 143.64 ax 38.25 47.59 56.84 66.01 75.08 84.11 93. 04)110.69 128.00 144.97 fl 38.60 48.03 57.37 66.62 75.77 84.88 93.89 111.69 129.17 146.31 15 38.94 48.46 57.89 67.23 76.46 85.65 94.74 112.68 130.33 147.64 ix 39 27 48.88 58.40 67.83 77.15 86.42 95.59 113.69 131.49 148.97 IX 39.60 49.29 58.90 68.42 77.83 87.19 96.44 114.70 132.64 150.29 a| 39.92 49.70 59.39 69.00 78.50 87.95 97.29 115.71 133.81 151.61 ix. 40.24 50.10 59.88 69.57 79.16 88.70 98.13 116.72 134.98 152.92 RX 40.56 50.50 60.36 70.14 79.81 89.44 98.96 117.73 136.15154.25 | M 40.88 50.90 60.84 70.70 80.46 90 17 99.78 118.73 137.32 155.58 fl 41.20 51.30 61.32 71.26 81.12 90.90 100.59 119.72 138.49 156.91 16 41.52 51.70 61.80 71.82 81.76 91.62 101.40 120.70 139.65 158.24 ix 41.84 52.10 62.28 72.38 82.40 92.34 102.20J121.67 140.80 159.57 M 42.14 52.48 62.74 72.92 83.02 93.04 102.98 122.62 141.92 160.87 % 42.45 52.87 63.21 73.47 83.65 93.75 103.77 L28.57 143.04 162.17 IX 42 76 53.26 63.68 74.02 84.28 94.45 104.56 124.52 144.16 163.46 sx 43.13 53.71 64.21 74.63 84.97 95.23 105.41 125.53 145.33 164.80 M 43.47 54.11 64.69 75.19 85.61 95.95 106.21 126.49 146.45 166.09 % 43.82 54.55 65.19 75.77 86.27 96. 69 107.03 127.47 147.59 167.39 17 44.19 55.00 65.73 76.37 86.95 97.45 107.87 128.47 148.75 168.71 NATIONAL TUBE COMPANY. 3 I I 11 OOOOOOOOl-lTHTHTHl-HT-l-HT-lr-lTH "SSSS 3 82S5?SSSS38 O O O O i- -4 i-4 r4 T-I TH I-H' TH" i-i TH TH' O C* O O O O i-i i-< i-1 1-4 i-4 i-I i-4 ,-4 TH* TH* 0* CJ 01 S* 00 3 O TH W 00 TP O it t- O5 O -TH 0* CO - t- ad oo" oo" oo* os os o os o o ^ JH issiiSs QO ao" GO os" as os' o o o ** ** ~ ff* oi o* m eo n H5 NATIONAL TUBE COMPANY. ges of Weight Per Foot in Lbs. of Vario COLD-DRAWN TU rest Fracti of 1 Inch. eoeocoeoeocoeosoeoTi ec'eocoec^ "& >odeo: HB iQOjQjQOO5Oococ 3 0' OS OS 0> O O O O O JH ^j j4 rn 0* CJ J 2* 32 ^ TH T-J oj oj w oi w w w o -^ if ^ jot so 05 sceo 5 SB 91 NATIONAL TUBE COMPANY. >0 tO >0 >0 to U3 to to to O 50 D 5 O O O 10 wi d so to to o > c- oo x QO co oo oo' 06 oo" o> os os o os* os os' o' 00 Os' OS* OS 03 05 OS Os' O O O O O O O -j TH NATIONAL TUBE COMPANY. ! 1 >**- sg; g J^s 3 <| .5^8 1^" fiq I 8 Ho co' CD' co CD co' co co' CD' CD CD co' co' co t> i> i- 1- ^ 88 > &S$8 > 38$&3$3S co* co' co' t> t- J> i> t- z> i> t-' t-' t- 1> oo' oo' oo' B z>t-"t-"z>i>o6o6o6o6oo'oo"cpoDa6ooo6cs ng 06 06 06 os os oj os os os os os os o o o o o HB os" o o" o o o d p o - ^ sisSssSi X *. 4 '-9'S R* " SS'35S3g'S^sy55e''5S 8S38SSS&S8S M^5S?i5<^^^gS^S m B S8 88 ~" nm'tf. 82 NATIONAL TUBE COMPANY. TABLE OF LENGTHS AND WEIGHTS OF WORKING BARRELS. f /Working Barrel ^^j ' A i m >| 1 iTT5 P Itli L J b i r * i^^psypl^^ j r^^gi 2*' Working Barrel fc^^l . JJ W ^^^ ffe j >~* Threads ^ | | > o ^ K > ^ T 1 perl " * irT 1 U K T f riiF^^^^^^S"^ 5 ^^ L^L^^r . * J J W J * Threads ^ 1 ^ " J ra iki 1 *T T L1F 7 1 I / W\4^^w^v\^ ; k i . 4 Length 2 Inch Barrel in Feet. Weight in Ibs. 2J/2 Inch Barrel 3 Inch Barrel Weight in Ibs. Weight in Ibs. 5 32 to 37 6 35 " 40 7 38 " 43 8 41 " 46 9 44 " 49 37 to 43 47 to 55 43 " 49 54 " 62 49 " 55 61 " 69 55 " 61 68 " 76 61 " 67 75 " 83 NATIONAL TUBE COMPANY. ILLUSTRATIONS Standard and Special Seamless Cylinders. [5 inch Standard Seamless Cylinder. (See Table, page 84.) 8 inch Standard Seamless Cylinder. (See Table, page 85.) TENSILE STRENGTH or MATERIAL '= 90.000 LBS. 8 inch Special Seamless Cylinder. (See Table, page 86.) 84 NATIONAL TUBE COMPANY. Table of Weights and Capacities of 5 inch Standard Seamless Cylinders. Outside Diameter, 5^ B inches. Thickness of Wall, inch. (See illustration, page 83.) Tested to 3700 Ibs. per square inch Hydrostatic Pressure. Length over all in inches. Average Weight in IDS. Capacity in Cubic inches. Capacity in Cubic feet. Capacity Gallons. Capacity in Ibs. Liquid Carbonic Acid Gas. 36 39.00 653 0.3779 2.83 15. 39.47 663 0.3839 2.87 15.2 37 39.94 673 0.3900 2.92 15.4 37^3 40.41 683 0.3961 2.96 15.6 38 40.88 694 0.4022 3.01 15.8 38)4 41.35 704 0.4083 3.05 16. 39 41.82 714 0.4143 3.10 16.2 39^2 42.29 725 0.4204 3.14 16.4 40 42.76 735 0.4265 3.19 16.6 40^ 43.23 745 0.4326 3.23 16.8 41 43.71 756 0.4387 3.28 17. 44.18 766 0.4447 3.32 17.2 42 44.65 776 0.4508 3.37 17.4 42^ 45.12 786 0.4569 3.41 17.6 43 45.59 797 0.4630 3.46 17.8 46.06 807 0.4691 3.50 18. 44 46.53 817 0.4751 3.55 18.2 44^ 47.00 828 0.4812 3.59 18.4 45 47.47 838 0.4873 3.64 18.6 45^ 47.94 848 0.4934 3.68 18.8 46 48.42 859 0.4995 3.73 19. 46^ 48.89 869 0.5055 3.77 19.2 47 49.36 879 0.5116 3.81 19.4 47^ 49.83 889 0.5177 3.85 19.6 48 50.30 900 0.5238 3.90 19.8 48U 50.77 910 0.5299 3.94 20. 49 51.24 920 0.5359 3.99 20.2 49^ 51.71 931 0.5420 4.03 20.4 50 . 52.18 941 0.5481 4.08 20.6 50U 52.65 951 0.5542 4.12 20.8 51 53.13 962 0.5603 4.17 21. 53.60 972 0.5663 4.21 21.2 52 54.07 982 0.5724 4.26 21.4 54.54 992 0.5785 4.30 21.6 53 55.01 1003 0.5846 4.35 21.8 53^ 55.48 1013 0.5907 4.39 22. 54 55.95 1023 0.5967 4.44 22.2 54^ 56.42 1034 0.6028 4.48 22.4 55 56.89 1044 0.6089 4.53 22.6 57.36 1054 0.6150 4.57 22.8 56 57.84 1065 0.6211 4.62 23. 56^ 58.31 1075 0.6271 4.66 23.2 58.78 1085 0.6832 4.71 23.4 57^ 59.25 1095 0.6393 4 75 23.6 58 59.72 1106 0.6454 4.80 23.8 58^ 60.19 1116 0.6515 4.84 24. 59 60.66 1126 0.6575 4.89 24.2 59^ 61.13 1137 0.6636 4.93 24.4 60 61.60 1147 0.6697 4.97 24.6 NATIONAL TUBE COMPANY. 85 Table of Weights and Capacities of 8 inch Standard Seamless Cylinders* Outside Diameter, 8 T 9 a inches. Thickness of Wall, & inch. (See illustration, page 83.) Tested to 3700 Ibs. per square inch Hydrostatic Pressure. Length over all in inches. Average WeigKt in Ibs. Capacity in. Cubic inches. Capacity in Cubic feet. % p u ad s ty Gallons. Capacity in Ibs. Liquid Carbonic Acid Gas. 36 69.4 1781 1.0307 7.71 37. 36^ 70.25 1806 1.0454 7.82 37.5 37 71.1 1832 .0601 7.94 38. 37^ 71.95 1857 .0783 8.05 38.5 38 72.8 1883 .0895 8.16 39. 38^ 73.65 1908 .1042 8.27 39.5 39 74.5 1934 .1189 8.38 40. 39U 75.35 1952 .1336 8.49 40.5 40 76.2 1985 .1483 8.60 41. 40}^ 77.05 2010 .1630 8.71 41.5 41 77.9 2036 .1778 8.82 42. 41>^ 78.75 2061 .1925 8.93 42.5 42 79.7 2087 .2072 9.04 43. 42^ 80 55 2112 .2219 9.15 43.5 43 81.4 2138 .2368 9.26 44. 43^ 82.25 2163 .2515 9.37 44.5 44 83.1 2189 .2662 9.48 45. 44^ 83.95 2214 .2809 9.59 45.5 45 84.8 2240 2956 9.70 46. 45^ 85.65 2265 .3103 9.81 46.5 ' 46 86.5 2291 .3251 9.92 47. 46^ 87.35 2316 .3398 10.03 47.5 47 88.2 2342 .3545 10.14 48. 47^ 89.05 2367 3692 10.25 48.5 48 89.9 2393 .3839 10.36 49. 48J^ 90.75 2418 .3966 10.47 49.5 49 91.6 2444 .4113 10.58 50. 49^ 92.45 2469 .4260 10.69 50.5 50 93.3 2495 .4407 10.80 51. 50^ 94.1 2520 .4554 10.91 51.5 51 95. 2546 .4702 11.02 52. 51H 95.85 2571 .4849 11.13 52.5 52 96.7 2597 .4996 11.24 53. 52\4 97.55 2622 .5143 11.35 53.5 53 98.4 2648 .5290 11.46 54. 53^ 99.25 2673 .5437 11.57 54.5 54 100.1 2699 .5585 11.68 55. 54^3 100.95 2724 .5732 11.79 55.5 55 101.8 2750 .5879 11.90 56. 55^ 102.65 2775 .6026 12.01 56.5 56 103.5 2801 .6174 12.12 57. 56^ 104.35 2826 .6321 12.23 57.5 57 105.2 2852 .6468 12.34 58. 57}^ 106.05 2877 .6615 12.45 58.5 58 106.9 2903 .6762 12.56 59. 58J^ 107.75 2928 ; .6909 12.67 59.5 59 108.6 2954 i .7056 12.78 60. 59J^ 109.45 2979 1.7203 12.89 60.5 60 110.5 3005 1.7303 13.00 61. , J 86 NATIONAL TUBE COMPANY. Table of Weights and Capacities of 8 inch Special Seamless Cylinders for Holding Carbonic Gas. Outside Diameter, 8 inches. Thickness of Wall, & inch. (See illustration, pae 83.) Tested to 3000 Ibs. per square inch Hydrostatic Pressure. Length over all in inches. Average Weight in IBs. Capacity in Cubic inches. Capacity in Cubic feet. <&* Gallons. Capacity in Ibs. Liquid Carbonic Acid Gas. 36 74.2 1459 [8443 ~~6731 30. 36^ 75.0 1482 .8573 6.41 30.4 37 75.8 1504 .8703 6.51 30.9 37!^ 76.6 1526 .8833 6.60 31.3 38 77.4 1549 .8963 6.70 31.8 38^ 78.2 1571 .9093 6.80 32.2 39 79.0 1594 .9223 6.89 32.7 39^ 79.8 1616 .9353 6.99 33.1 40 80.6 1639 .9483 7.09 33.6 40^ 81.4 1661 .9613 7.19 34. 41 82.2 1684 .9744 7.28 34.5 41^ 83.0 1706 .9874 7.38 34.9 42 83.8 1729 1.0004 7.48 35.4 W 84.6 1751 1.0134 7.58 35.8 43 85.4 1773 1.0264 7.68 36.3 43^ 86.2 1796 1.0394 7.77 36.7 44 87.0 1818 1.0524 7.87 37.2 44^ 87.8 1841 1.0654 7.96 37.6 45 8S.6 1863 1.0784 8.06 38.1 45^ 89.4 1886 1.0914 8.16 38.5 46 90.2 1908 1.1045 8.26 39. 46J^ 91.0 1931 1.1175 8.35 39.4 47 91.8 1953 1.1305 8.45 39.9 47^ 92.6 1976 1.1435 8.55 40.3 48 93.4 1998 1.1565 8.65 40.8 48^ 94.2 2020 1.1695 8.74 41.2 49 95.0 204:1 1.1825 8.84 41.7 49^ 95.8 2067 1.1955 8.94 42.1 50 96.6 2090 1.2085 9.04 42.6 50^ 97.4 2112 1.2215 9.13 43.0 51 98.2 2135 1.2346 9.23 43.5 51^ 99.0 2157 1.2476 9.33 43.9 52 99.8 2180 1.2606 9.42 44.3 52^ 100.6 2202 1.2736 9.52 44.8 53 101.4 2225 1.2866 9.62 45.2 531^ 102.2 2247 1.2996 9.72 45.7 54 103.0 2269 1.3126 9.81 46.1 54^ 103.8 2292 1 3256 9.91 46.6 55 104.6 2314 1.3386 10.01 47.0 55^ 105.4 2337 1.3516 10.11 47.5 56 106.2 2359 1.3647 10.20 47 9 56^ 107.0 2381 1.3777 10.30 48.4 57 107.8 2403 1.3907 10.40 48.8 57^ 108.6 2426 1.4037 10.49 49.3 58 109.4 2449 1.4167 10.59 49.7 58^ 110.2 2471 1.4297 10.69 50 2 59 111.0 2493 1.4427 10.79 50.6 59^ 111.8 2516 1.4558 10.88 51.1 60 112.6 2538 1.4687 10.98 51.5 NATIONALITUBE COMPANY. Table of Weights and Capacities of Seamless Cylinders of various diameters. Tested 3700 Ibs. per square inch Hydrostatic Pressure. 14 15 16 17 19 20 21 22 24 25 27 28 30 33 43 46 50 53 56 66 70 74 79 85 90 94 98 103 6.8 7.2 7.8 8.2 8.7 9.2 9.6 10. 10.6 11. 11.8 12. 12.6 15. 16. 17. 18. 20.5 21.2 21.7 22.4 26. 26.7 27.5 28.1 32.5 33. 34. 85.2 39.4 40.5 <*H C-U o o u .5 .57 .6 .67 .7 .76 .78 .91 .98 1. 1.05 1.3 .4 .43 .5 .7 .8 .8* .88 2.1 2.22 2.3 2.4 2.7 2.8 2.9 3. 3.3 3.4 219 251 358 397 438 471 526 573 622 673 724 778 834 891 950 1010 1072 1136 1200 1267 1336 1406 1477 1550 1623 1699 1775 1854 1H riT3 C3 *1| 84.8 99.5 115.4 132.5 150.7 169.9 190.8 212.6 235.5 259.7 285. 311.5 461.7 495.4 603. 641.4 680.9 721.5 763.3 806.4 850.5 895.9 942.5 990. 1039. 8.29 9.62 11.04 12.56 14.18 15.90 17.72 19.63 21.64 23.75 25.96 28.27 30.68 33.18 35.78 38.48 41.28 44.17 47.17 50.26 53.45 56.74 60.13 63.61 67.20 70.88 74.66 78.54 88 NATIONAL TUBE COMPANY. Table of Weights and Capacities of Seamless Cylinders of various diameters. (CONTINUED.) s l| bb VM C^ O O bo *o o bo .S^6i oM o bo E v 11 5 a j> }l m m Si li 11 11??. u 109 41.2 3.47 1932 1140.3 95.03 i(! 114 42.7 3.62 2012 1192.8 99.40 IJL| |l 119 47. 3.9 2093 1245.6 103.87 11% [2V, /'s 125 48. 4. 2176 129U.8 108.43 12 :/; -'s 132 49. 4.05 2261 1356. 113.10 13 ! 's 137 50. 4.1 2347 1414.3 117.86 12}/ 13,-,. 13 143 55. 4.5 2433 1472.4 122.72 12% I8 fi 1 ; : j 150 56.4 4.7 2521 1532. 127.68 13 ''! - 162 57.4 4.8 2610 1592. 132.73 |.j 'T - 1 ' 168 58.5 4.9 2700 1664.7 137.89 13/ 4 ) I4 : ' ; s 1 ? (T 174 64.5 5.4 2790 1717.2 143.14 13% 1 4"'s 7^ 180 65.5 5.5 2883 1781.9 148.49 14 1 1 ' S 7^ 187 66.2 5.55 2976 1846.8 153.94 l5 l /6 jr 193 67.2 5.6 3074 1913.7 159.48 wi2 i r. ~ J f; 200 74. 6.1 3173 1981.2 165.13 14% |JJU M 209 75.6 6.2 3265 2050.4 170.87 15 JglB Li 220 76.6 6:3 3357 2120.4 176.71 IfiJJg 3 | 227 77.6 6.45 3452 2191.8 182.65 15Vi 1 r, 1 ' ., V^> 235 84.3 7. 3548 2263.2 188.69 15% 10>i y 244 85.7 7.1 3650 2337.9 194 83 16 ]Z 255 87. 7.2 3753 2412. 201.06 16^ 17H 1/1 263 88.7 7.4 3855 2487.6 207.39 wB 17* lj_ 272 95.5 8. 3957 2565.6 213.82 16% 'l7 282 96.7 8.1 4058 2646.6 220.35 17 18ft \i 291 98.3 8.2 4160 2722.8 226.98 1 S'''' 17 299 99.7 8.3 4274 2804.4 233.71 WH S-V'. J 9 (J 309 107. 8.6 4389 2886. 240.53 17% - 320 108.7 9.06 4484 2968.8 247.45 18 !''' s A 331 110.2 9.2 4580 3052.8 254.47 1 '>C 9 340 111.5 9.3 4686 3139. 261.59 18V6 IflH ' ^i 350 119.6 9.9 4793 3225.6 268.80 ' jga/ 19 361 121.3 10.1 4900 3313,4 276.12 19 ._<)].:" n 373 122.6 10.2 5008 3402. 283.53 20 ^'-i i' ii 382 126.5 10.5 5117 3492. 291.04 191^ ](p',' 5^ 392 132.7 11. 5226 3583.2 298.65 19% 21 " K2 403 134.4 11.2 5336 3676.2 306.35 20 21 M % 415 136.4 11.4 5446 3769.2 314.16 NATIONAL TUBE COMPANY. Table of Weights and Capacities of 5 inch Standard Lap-Welded Cylinders (Class B). Outside Diameter, 5 T 9 B inches. Thickness of Wall, Y inch. Tested to 3700 Ibs. per square inch Hydrostatic Pressure. Length over all in inches. Average Weight in Ibs. Capacity in Cubic inches. Capacity in Cubic feet. Capacity in u. s: Gallons. Capacity in Ibs. Liquid Carbonic Acid Gas. 36 49.14 618. 6T3576~ 2.68 14. 49.67 628. 0.3636 2.72 14.2 37 50.20 638. 0.3696 2.77 14.4 37^ 50.73 648. 0.3756 2.81 14.6 38 51.26 658. 0.3816 2.86 14.8 51.79 668. 0.3876 2.90 15. 39 3 52.32 679. 0.3930 2.95 15.2 39^ 52.85 689. 0.3996 2.99 15.4 40 53.38 699. 0.4056 3.04 15.6 40^ 53.91 709. 0.4116 3.08 15.8 41 54.44 719. 0.4176 3.13 16. 41^6 54.97 730. 0.4236 3.17 16.2 42 55.50 740. 0.4296 3.22 16.4 42^ 56.03 750. 0.4356 3.26 16.6 43 56.56 760. 0.4416 3.31 16.8 43^ 57.09 770. 0.4476 3.35 17. 44 57.62 781. 0.4536 3.40 17.2 44^ 58.15 791. 0.4596 3.44 17.4 45 58.68 801. 0.4656 3.49 17.6 45^ 59.21 811. 0.4716 3.53 17.8 46 59.74 821. 0.4776 3.58 18. 60.27 831. 0.4836 3.62 18.2 47 60.80 842. 4896 3.67 18.4 47^ 61.33 852. 0.4956 3.71 18.6 48 61.86 862. 0.5016 3.76 18.8 48^ 62.39 872. 0.5076 3.80 19. 49 62.92 882. 0.5136 3.85 19.2 49^ 63.45 892. 0.5196 3.89 19.4 50 63.98 903. 0.5256 3.94 19.6 50V*> 64.51 913. 0.5316 3.98 19.8 51'"" 65 04 923. 0.5376 4.03 20. 51 V^ 65.57 933. 0.5436 4.07 20.2 52 66.10 943. 0.5496 .12 20.4 52^ 66.63 954. 0.5556 .16 20.6 53 67.16 964. 0.5616 .21 20.8 53^ 67.69 974. C.5676 .26 21. 54 68.22 984. 0.5736 .31 21.2 68.75 994. 0.5796 4.35 21.4 55 69.28 1005. 0.5856 4.40 21.6 55^ 69.81 1015. 0.5916 4.44 21.8 56 70.34 1025. 0.5976 4.48 22. 56^ 70.87 1035. 0.6036 4.52 22.2 57 71.40 1045. 0.6096 4 57 22.4 57^ 71.93 1055. 0.6156 4.61 22.6 58 72.46 1066. 0.6216 4.66 22.8 58^ 72.99 1076. 0.6276 4.70 23. 59 73.52 1086. 0.6336 4.73 23.2 59H 74.05 1096. 0.6396 4.76 23.4 60 74.58 1106. 0.6456 4.80 23.6 NATIONAL TUBE COMPANY. Illustrations of Various Hydraulic Forgings, Various Styles of Valve Protecting Caps used on Carbonic Acid Gas Cylinders. These Caps are made of light material in various sizes, suitable for the Valves of Cylinders. Boiler Shells. Seamless Floats For Feed Water Regulators. These Shells are made in var- ious sizes from 6" Diameter, by i foot long, to 24" Diameter, x 3 feet long. They are made from Steel of 55,000 to 60,000 Tensile Strength. These Floats are made from Steel of High Tensile Strength, so as to make them as light as possible. They are subjected to a Hydros- tatic Collapsing Test of sco Ibs. per square inch. Shrapnel Forging. These jShrapnels are made of a' Special Grade of Steel, and Forged from a Solid Billet. Shrapnel^Forging. These Shrapnels are made of a Special Grade of Steel, and Forged from a Solid Billet. Shrapnel Forging. These Shrapnels are made of a Special Grade of Steel, and Forged from a Solid Billet. NATIONAL TUBE COMPANY. Illustrations of Various Hydraulic Forgings. Projectile Forging. Made from Special Grade of Steel, and Forged from a Solid Billet. Bushing Forging for Axle Bearings* Separator Tubular Forging. These are made from High Grade Steel, and forged from a Solid Billet. These Tubulars are made from High Grade Steel of 85,000 to 90,000 Tensile Strength. Separator Bowl Forging. These Bowls are made from High Grade Steel of 85,000 to 90, coo Tensile Strength. Separator Bowl Forging. Separator Bowl Forging. These Bowls are made from High Grade Steel of 85,000 to 90,000 Tensile Strength. These Bowls are made from High Grade Steel of 85,000 to 90,000 Tensile Strength. USEFUL INFORMATION RELATING CHIEFLY TO TUBULAR CONSTRUCTION COMPILED BY NATIONAL TUBE CO. NATIONAL TUBE COMPANY WATER. Water is composed of two gases, hydrogen and oxygen, in the ratio of two volumes of former to one of the latter. It is never found pure in nature, owing to the readiness with which it absorbs impurities from the air and soil. Water boils under atmospheric pressure (14.7 Ib.) at 212, passing off as steam. Its greatest density is at 39.1F., when it weighs 62.425 Ibs. per cubic ft. Weight of Water per Cubic Foot at Different Temperatures. N jl N j| 2'S M -O O 5'S jrl OJ . 3 '^ ,o rdrCi >i G 8,2 II , II OJ H fl v- G 0,2 || a 1| II $% |l *j II la s || Is ft ex ft a ft 32 62.42 140 61.37 240 59.10 350 55.52 460 51.26 40 62.42 150 61.18 250 58.81 360 55.16 470 50.85 50 62.41 160 60.98 260 58.52 370 54.79 480 50.44 60 62.37 170 60.77 270 58.21 380 54.41 490 50.05 70 62.31 180 60.55 280 57.90 390 54.03 500 49.61 80 62.23 190 60.32 290 57.59 400 53.64 510 49.20 90 62.13 200 60.07 300 57.26 410 53.26 520 48 78 100 62 02 210 59.82 310 56.93 420 52.86 530 48.36 110 61.89 212 59.71 320 56.58 430 52.47 540 47.94 120 61.74 220 59.64 330 56.24 440 52.07 550 47.52 130 61.56 230 59.37 340 55.88 450 51.66 560 47.10 One ft. of water column at 39.1F = 62.425 Ibs. on the square ft. = 0.0295 atmospheric pressure " " " " " " =0.8826 in. mercury column at 32. F. " ' " " " " =773.3 ft. of air column at 32".F. and atmospheric pressure. One Ib. pressure on sq. ft. = 0.01602 ft. water column at 39.1F. " u " " " in - 2.307 " ' " " 39.1F. One atmospheric pressure = 29.92 in. mercury column 33.9 ft. water column. One inch of mercury column at 32F. = 1.133 ft water column. One foot of air column at 32F. and 1 atmospheric pressure = 0.001293 ft. water column. NATIONAL TUBE COMPANY. BOILER INCRUSTATION AND CORROSION. Water, from natural sources, as a rule contains more or less carbon dioxide, which holds in solution carbonates of lime and magnesia. On boiling the water, the carbon dioxide is driven out and the lime and magnesium in so- lution are thrown down in the form of a white or grayish mud, that may be easily removed from the boiler by thorough washing. The presence of other impurities, such as organic matter or sulphate of lime, is likely to make the deposit hard and adhering. Sulphate of lime is more soluble in cold than in hot water, and is entirely thrown down at a temperature of 280 Fahrenheit. It forms a hard and adhering scale and has a bad effect upon scales and deposits, composed chief- ly of carbonates. The evident treatment of water containing sulphate of lime is to heat the feed water, before entering the boiler, to a temperature of at least 280 Fahrenheit. This should be done in such a manner as to give time for the deposi- tion of the sulphate of lime when thrown out of solution. A deposition may arise from the settling of clay and other matter held in suspension in the water. In water otherwise free from impurities this matter commonly de- posits in the form of a soft mud that may be easily re- moved from the boiler. In conjunction, however, with other impurities, as, for example, sulphate of lime, it may form an adhesive scale, in which case it is usually best to free the feed water from suspended matter by filtration. In some cases chemical treatment, either internally or externally, should be resorted to. This is especially the case with feed waters containing much free acid, in which case the free acid should be neutralized by chem- ical treatment, preferably before entering the boiler. NATIONAL TUBE COMPANY. If more than 100 parts per 100,000 of total solid residue be present in the water, it will ordinarily cause trouble from scale, and should be condemned for use in the boiler unless a better supply be unattainable. Scale re- duces the efficiency of the heating surface by detracting from the conducting quality of the metal and is apt to cause overheating or burning of the metal, or even bulg- ing of the plates that are subjected to the intense heat of the furnace. Grease, owing to its adhesive nature, may , by collecting impurities contained in the water, become sufficiently heavy to sink. In this condition it is apt to attach itself to a plate or pipe near the furnace and may, owing to its non-conducting qualities, cause serious over- heating, resulting in burning, bulging or even blowing out. If water contains more than 5 parts per 100,000 of free sulphuric or nitric acid, serious corrosion will ensue not only in boiler plates, but also in tubes, pipes, cylinders and other parts with which the steam comes in contact. Animal and vegetable oils and greases decompose into fatty acids when subjected to the temperature of high pressure steam. Because of this their presence in a high pressure steam engine or boiler will cause serious corro- sion. Experiments have shown that pure water, into which air has been forced, on boiling causes corrosion. Highly heated surfaces in contact with water contain- ing common salt corrode and pit rapidly. The sides of the furnace, the tube plates and the hottest tubes suffer most. It is clear then that feed- water, free from solids, com- bined or in suspension, organic matter, acids of all kinds, and air, would be best for the life of boilers. NATIONAL TUBE COMPANY. TROUBLESOME SUBSTANCE. TABULAR VIEW. TROUBLE. REMEDY OR PALLIATION. Sediment, mud, clay, Incrustation. Filtration ; blowing etc. Readily soluble salts. Bicarbonatesof lime, j magnesia, iron. \ off. Blowing off. Heating feed. Addi- tion of caustic soda, lime, or magnesia, etc. {Addition of carbon- ate soda, barium chloride, etc. Chloride and sul- , phate of magne- Corrosion. Carbonate of soda in ) p . . ( Addition of barium large amounts. f J img< "j chloride, etc. Acid (in mine waters). Corrosion. Alkali. Dissolved carbonic / acid and oxygen, l" Grease (fromconden- j sed water). j Organic matter (sew- ) age). f Heating feed. Addi- tion of caustic soda, slacked lime, etc. {Slacked lime and filt- ering. Carbonate of soda. Substitute mineral oil. Precipitate with al- um or ferric chlo- ride and filter. Organic matter. Corrosion, Ditto. NATIONAL TUBE COMPANY. Analyses in Parts per J00,000 of Water giving Bad Results in Steam-boilers. (A. K. Hunt.) 1 * ' In column headed A/ hd find 0.10, which is the * L/+54d value nearest to 0.136, and look along this line until column headed " 2 " is reached, then read 62 as the value of coefficient ra. Then v = 62x0.136 = 8.432 ft. per sec., the required velocity. To find the discharge in cu. ft. per sec., multiply this velocity by area of cross section of pipe in sq. ft. Thus, 3. 1416 x (I) 2 x 8.432 = 26.49 cu. ft. per sec. Since there are 7.48 gal. in a cu. ft., the discharge in gal. per sec. = 26.49x7. 48 = 198.2. The above formula is only an approximation, since the flow is modified by bends, joints, incrustations, etc. Wrought Iron and Steel Pipes are smoother than cast iron ones, thereby presenting less friction and less en- couragement for deposits ; and, being in longer lengths, the number of joints is reduced, thus lessening the undesirable effects of eddy currents. To find the head in feet necessary to give a stated dis- charge in cu. ft., use the formula.* ,.0.000704 Q 2 (L+54d) d 5 In which h = total head in feet, L = total length of line in feet, d = diameter of pipe in feet, Q = quantity of water in cu. ft. per second. Example. Given the diameter of pipe, ^=0.5 ft.; the length of pipe, L 20 ft. ; and the quantity of water to be discharged, #- = 3.07 cu. ft. per sec.; to find the neces- sary head. NATIONAL TUBE COMPANY. Substituting these values in the above formula,* we get : 0.000704 x 9.4 x (20+27) (0.5)' = 0.000704^9.4x47 The following formula* is simpler and can be used when 54 d in relation to L is so small as to be negligible. 0.000704 Q 8 x L d^ If the pipe, instead of being straight, has easy curves (say with radius not less than 5 diameters of the pipe) either horizontal or vertical, the discharge will not be materially diminished, so long as the total heads, and total actual lengths of pipe remain the same, but it is ad- visable to make the radius as much more than 5 diameters as can conveniently be done. To find the diameter of a pipe ^bf given length to de- liver a given quantity of water under a given head, use the following : = 0.234 fi In which d diameter of pipe in feet, Q cu. ft. per second delivered, L length of line in feet, h head in feet. Example. Given the head, h 700 feet ; the length of pipe, L 3000 feet; the quantity to be delivered, Q-4 cu. ft. per. sec. ; required the diameter of pipe necesssary. Substituting these values in the above formula,* we get: d=0.234 A/ 16x3000=0.234 4/68.57=0.545 ft.=6.54 in. NATIONAL TUBE COMPANY. The diameter of a pipe may also be found by using the following formula : * = 125 In which D = diameter of pipe in inches, q = gallons per second, " L = length of line in feet, h = head in feet. If, in formula v = m.\/ x we substitute V Iy-}-54d average value for m, we get : dxh The following table, calculated by the above formula shows the velocities and discharges through a pipe one mile long and one foot in diameter, under different heads. But they will be very nearly the same for any greater lengths ; and also quite approximate for shorter ones not less than 1000 or even 500 diameters long, provided that in all cases they have the same RATE; OF HEAD ; that is, if the given pipe of one foot diameter is 2 or 3 miles long, it must have 2 or 3 times as much head as the pipe in the table in order to have very nearly the same velocity and discharge. * When solving examples by the use of these formulas use the table of Fifth Powers and Fifth Roots. Solutions may also be easily effected by the use of logarithms. NATIONAL TUBE COMPANY. 105 The velocities and discharges through a straight, smooth pipe one foot in diameter, and one mile or 5280 diameters in length* Head in feet per 100 feet. Head in feet per mile. Velocity in feet per second. Discharge in cubic feet per second. Discharge in cubic feet per 24 hours. .0019 .1 .208 .1633 14,114 .0038 .2 .293 .2301 19,880 .0057 .3 .359 .2819 24,360 .0076 .4 .415 .3267 28,229 .0095 .5 .464 .3638 31,435 .0114 .6 .508 .3989 34,464 .0132 .7 .549 .4311 37,247 .0151 .8 .585 .4602 39,760 .0170 .9 .623 .4901 42,343 .0189 1. .656 .5144 44,431 .0237 .25 .735 .5753 49,701 .0284 .5 .805 .6322 54,604 .0331 .75 .871 .6832 59,011 .0379 2. .928 .7276 62,870 .0426 .25 .984 .7696 66,484 .0473 .5 1.04 .8168 70,572 .0521 .75 1.08 .8482 73,284 .0568 3. 1 13 .8914 76,982 .0758 4. 1.31 1.028 88,862 .0947 5. 1.47 1.150 99,403 .1136 6. 1.61 1.264 109,209 .1325 7. 1.74 1.366 118,022 .1514 8. 1.86 1.455 125,740 .1703 9. 1.96 1.539 132,969 .1894 10. 2.08 1.633 141,145 .2273 12. 2.27 1.782 153,964 .2652 14. 2.45 1.924 166,233 .3030 16. 2.62 2.057 177,724 .3409 18. 2.78 2.183 188,611 .3', 88 20. 2.93 2.301 198,806 .4735 25. 3.28 2.572 222,156 .5682 30. 3.59 2.819 243,604 .6629 35. 3.88 3.047 263,260 .7576 40. 4.15 3.267 282,288 .8523 45. 4.40 3-451 298,209 .9470 50. 4.64 3.638 314,352 1.136 60. 5.08 3.989 344,649 1.326 70. 5.49 4.311 372,470 1.515 80. 5.85 4.602 397,613 E ^ P i 106 NATIONAL TUBE COMPANY. The velocities and discharges through a straight, smooth pipe one foot in diameter, and one mile or 5280 diameters in length. Head in feet per Head in feet Velocity in feet per Discharge in cubic feet Discharge in cubic feet 100 feet. per mile. second. per second. per 24 hours. 1.704 90. 6.23 4.900 423,435 1.894 100. 6.56 5.144 444,312 2.083 110. 6.87 5.395 466,128 2.272 120. 7.18 5.639 487,209 2.462 130. 7.47 5.866 506,822 2.652 140. 7.76 6.094 526,521 2.841 150. 8.05 6.322 546,048 3.030 160. 8.30 6.534 564,576 3.219 170. 8.55 6.715 580,176 3.408 180. 8.80 6.903 596,418 3.596 190. 9.04 7.100 613,440 3.788 200. 9.28 7.276 628,704 4.261 225. 9.84 7.696 664,848 4.735 250. 10.4 8.168 705,728 5.208 275. 10.8 8.482 732,844 5.682 300. 11.3 8.914 769,824 6.629 350. 12.3 9.621 831,168 7.576 400. 13.1 10.28 888,624 8.532 450. 13.9 10.91 943,056 9.47 500. 14.7 11.50 994,032 10.41 550. 15.4 12.09 1,044,576 11.36 600. 16.1 12.64 1,092,096 12.30 650. 16.7 13.11 1,132,704 13.25 700. 17.4 13.66 1,180,224 14.20 750. 18.0 14.13 1,220,832 15.15 800. 18.6 14.55 1,257,408 16.09 850. 19.1 15.00 1,296,000 17.04 900. 19.6 15.39 1,329,696 17.99 950. 20.3 15.94 1,377,216 18.94 1000. 20.8 16.33 1,411,456 22.73 1200. 22.7 17.82 1,539,648 26.52 1400. 24.5 19.24 1,662,336 30.30 1600. 26.2 20.57 1,777,248 34.08 1800. 27.8 21.83 1,886,112 37.87 2000. 29.3 23.01 1,988,064 47.35 2500. 32.8 25.72 2,221,560 56.81 3000. 35.9 28.19 2,436,040 NATIONAL TUBE COMPANY. 107 Head is the vertical distance from the surface of the water in the reservoir to the center of gravity of the lower end of the pipe when the discharge is into the air ; or to the level surface of the lower reservoir when the discharge is under water. To reduce cubic feet to U. S. Gallons, multiply by 7.48. To find either the area of pipe, the mean velocity, or the quantity discharged, when the other two are given, use the ischarge in cubic feet per second, Area in square feet = Mea n velocity in feet per second. Mean velocity in _ Discharge in cubic feet per second, feet per second. . Area in square feet. Discharge in cubic feet Area in Mean velocity in per second. square f eet A feet per second. [The terms may be in inches instead of feet ; and in minutes or hours instead of seconds.] For the diameter of a long pipe required to deliver either more or less water than that of a J foot diameter, and under the same rate of inclination, or of head in feet per mile, see table on next page. The use of this table is not sufficiently correct for pipes less than about 1,000 (or at furthest 500) diameters long. ~ 108 NATIONAL TUBE COMPANY. S, & rtO n 3 a rt a; I* 'ft jM* 'ft *0 oj O a; !- rt ^j rt .2 *|f|| S P I s 3 Q ^tS W Q P 'O'S 1 .0833 .0020 12^ 1.042 1.106 \iL .1250 .0055 13 2 1.083 1.221 2 .1667 .0113 14 1.167 1.470 2^ .2083 .0198 15 1.250 1.746 3 .2500 .0310 16 1.333 2.053 3j^ .2917 .0458 17 1.417 2.388 4 .3333 .0643 18 1.5 2.754 4j .3750 .0857 19 1.583 3.153 5 .4167 .1119 20 1.667 3.585 55^ .4583 .1422 21 1.75 4.051 6 .5 .1767 22 1.833 4.551 6^ .5417 .2159 23 1.917 5.084 7 .5833 .2600 24 2. 5.649 7K .6250 .3090 245-6 2.052 6.000 8 .6667 .3631 26 2.167 6.912 8^ .7083 .4220 28 2.333 8.319 9 .75 .4871 30 2.5 9.822 Q/4 .7917 .5575 30^ 2.521 10. 10 .8333 .6337 32 2.667 11.6 10^ .8750 .7157 34 2.833 13.5 11 .9167 .8044 36 3. 15.5 11 tf .9583 .8987" 38 3.167 17.8 12 1. 1. 40 3.333 20.2 To find the discharge from a pipe (not less than 1,000, or at least 500 times its own diameter in length) when the head is given, take from the first table the discharge through a pipe one ft. in diameter for the given head, and divide the required discharge by this tabular one; then look for the quotient in the column of the second table, headed "Ratio of Discharge," and opposite it, in columns 1 and 2, will be found the required diameter. . NATIONAL TUBE COMPANY. From this table we see that a 14 inch pipe will deliver nearly 1J^ times as much as a 12 inch pipe, and a 16 inch one fully twice as much as a 12 inch, all having the same length and head. EXAMPLE. Having given the head from a reservoir to a certain point of delivery, as 20 ft. in a distance of 1,860 ft., what must be the diameter of a pipe to deliver 6 cubic feet of water per second ? We find that a fall of 20 ft. in 1,860, is equal to a fall of 1.075 ft. in 100; or 1,860: 20 = 100: 1.075. Then we see by the first table that with a fall of 1.075 ft. in 100, a long pipe of 1 ft. diameter discharges about 3.8 cubic feet per second. But we want 6 1.58 times as much as the 1 ft. pipe can deliver ; then by the second table, we see that the pipe to do this, under the same rate of head, must be about 14^ in. in diameter. In practice we should adopt at least 15 in. NATIONAL TUBE COMPANY. 13 1 8 I I 5 . ' vi T-I -i-I T-I i ot oi so" so 3d J33J Ut puooas J3d J33J UI frpopA lg8.9t:s988S88si8 ' r4 i-H r-< 8Sl88S8S88^S ' i-i r-i (N OJ CO *" -rh to tS^8S99^8&9 ' i-t IN CO rf to I> OS TH' CO iad joaj ui ^JPOPA ' B"S ^Icaslsesss 't-H'r-ioico*TjJiot>oo *j [3JSSSS2fefegS88 1-1 i> 06 ggfes ! ?.^? NATIONAL TUBE COMPANY. EXAMPLE. Given 120 feet head and 600 feet length of 18 inch pipe, discharging 3500 gallons per minute : To find effective head: Look in column headed "18 inch Pipe," and opposite 3500 in. first column read "4.7 ft." (which is the loss of head by friction for an 18 in. pipe 1000 ft. long), and multiplying this by 600/1000, or 0.6, we get 2.82 ft., the loss of head. The effective head re- quired then equals 120 ft. less 2.8 ft. or 117.2 ft. Flow of Water in Pipes for a Velocity of JOO Ft. per Minute. Diameter in Inches. Area in Square Feet. Flow in Cubic Feet perMinute. Flow in U. S. Gallons per Minute. Flow in U.S. Gallons per Hour. % .00077 0.077 .57 34 i/ .00136 0.136 1.02 61 X .00307 0.307 2.30 138 1 .00545 0.545 4.08 245 1% .00852 0.852 6.38 383 *# .01227 1.227 9.18 551 W .01670 1.670 12.50 750 2 .02182 2.182 16.32 979 ' &A .0341 3.41 25.50 1,530 3 .0491 4.91 36.72 2,203 4 .0873 8.73 65.28 3,917 5 .136 13.6 102.00 6,120 6 .196 19.6 146.88 8,813 7 .267 26.7 199.92 11,995 8 .349 34.9 261.12 15,667 9 .442 44.2 330.48 19,829 . 10 .545 54.5 408.00 24,480 11 .660 66.0 493.68 29,621 12 .785 78.5 587.52 35,251 To find the quantity in gallons a pipe will deliver, the velocity of flow being 100 ft. per minute : Square the di- ameter in inches and multiply by 4.08. 8* ' IB NATIONAL TUBE COMPANY. 118 Flow of Water in House-service Pipes. (Thomson Meter Co.) Condition of Discharge. 2-g 3-3 SST ij Z Discharge in Cubic Feet per Minute from the Pipe. Nominal Diameters of Iron or Lead Ser- vice-pipe in Inches. M % 4 1 1^ 2 3 4 6 Through 35 feet of service- ES no pressure. 30 40 50 60 75 100 130 1.10 1.27 1.42 1.56 1.74 2.01 2.29 .92 2.22 2.48 2.71 3.03 3.50 3.99 3.01 3.48 3 89 4.26 4.77 5.50 6.28 6.13 7.08 7.92 8.67 9.70 11.20 12.77 16.58 19.14 21.40 23.44 26.21 30.27 34.51 33.34 38.50 43.04 47.15 52.71 60.87 69.40 88.16 101.80 13.82 24.68 139.39 160.96 183.52 173.85 200.75 224.44 245.87 274.89 317.41 361.91 444.63 513.42 574.02 628.81 703.03 811.79 925.58 Through 100 feet of service- pipe, no back pressure. 80 40 50 GO 75 100 130 0.66 0.77 0.86 0.94 1.05 1.22 1.39 0.55 0.66 0.75 0.83 0.94 1.10 1.26 1.16 1.34 1.50 1.65 1.84 2.13 2.42 1.84 2.12 2.37 2.60 2.91 3.36 3.83 3.78 4.36 4.88 5.34 5.97 6.90 7.86 10.40 12.01 13.43 14.71 16.45 18.99 21.66 21.30 24.59 27.50 30.12 33.68 38.89 44.34 58.19 67.19 75.13 82.30 92.01 106.24 121.14 118.13 136.41 152.51 167.06 186.78 215.68 245.91 317.23 366.30 409.54 448.63 501.58 579.18 660.36 Through 100 feet of service- pipe, and 15 feet vertical rise. 30 40 50 60 75 100 130 0.90 1.15 1.31 1.45 1.64 1.92 2.20 1.52 1.81 2.06 2.29 2.59 3.02 3.48 3.11 3.72 4.24 4.70 5.32 6.21 7.14 8.57 10.24 11.67 12.94 14.64 17.10 19.66 17.55 20.95 23.87 26.48 29.96 35.00 40.23 47.90 57.20 65.18 72.28 81.79 95.55 109.82 97.17 116.01 132.20 146.61 165.90 193.82 222.75 260.56 311.09 354.49 393.13 444.85 519.72 597.31 Through 100 feet o service- pipe, and 30 feet vertical rise. 3C 4C 6C 7 IOC 13( 0.44 0.55 0.65 0.73 0.84 1.00 1.15 0.77 0.97 1.14 1.28 1.47 1.74 2.02 1.22 1.53 1.79 2.02 2 32 2.75 3.19 2.50 3.15 3.69 4.15 4.77 5.65 6.55 6.80 8.68 10.16 11.45 13.15 15.58 18.07 14.11 17.79 20.82 23.47 26.95 31.93 37.02 38.63 48.68 56.98 64.22 73.76 87.38 101.33 78.54 98.98 115.87 130.59 149.99 177.67 206.04 211.54 266.59 312.08 351.73 403.98 478.55 554.96 ~ir i m n NATIONAL TUBE COMPANY. J5 O g 1 Is igsss; COt-3-*SO }39d UI p*9H spunoj ut aanssajj ' S ^^SSI11 So J99J UT P B9 H 8 SiSllfl spunoj ui 9jnss9ij ' Tt 3698 2100 2362 2505 2769 2975 3180 3598 to 10 1139 2 122 26 IS 2875 3 in:; 3332 3562 4027 1 192 1961 5139 -.'93 1 3180 3137 3090 3912 1 15(1 1970 5191 6012 0539 3221 3490 3771 10 IS 1325 4880 5147 6015 65X1 7 I.V.I 7737 .5507 3S06 1105 1106 4708 531 592 1 6510 715S 7782 8405 4426 4773 5122 5472 6176 6880 7591 8303 9022 9742 10468 11197 6442 5839 6236 7034 7833 8640 9447 10260 11076 11898 12725 14385 9742 10740 11738 12744 13750 14763 15776 17821 19880 21956 H_ 118 NATIONAL TUBE COMPANY. Contents in Cubic Feet and U. S. Gallons of Pipes and Cylinders of Various Diameters and One Foot in Length. 1 gallon=231 cubic inches. 1 cubic foot=7.4805 gallons. For 1 Foot in For 1 Foot in For 1 Foot in 'H Length. V u* Length. . Length. 1 Cubic ft. U.S. * "5 G a Cubic Ft. U.S. Gals. a is CubicTt. U.S. Gals. P in Sq. ft 231 Cu. In. Q a so Area in Sq. Ft. 231 Cu. In. S~ also Area inSq. Ft. 231 ' Cu. In. M .0003 .0025 6M .2485 1.859 19 1.969 14.73 j^ .0005 .004 7 .2673 1.999 2.074 15.51 2 .0008 .0057 7^4 .2867 2.145 20 2.182 16.32 TS .001 .0078 71^3 .3068 2.295 20^ 2.292 17 15 (2 .0014 .0102 7% .3276 2.45 21 2.405 17.99 1% .0017 .0129 8 .3491 2.611 21/4 2.521 18.86 IB .0021 .0159 8*4 .3712 2.777 22 2.640 19.75 11 .0026 .0193 giz .3941 2.948 22J4 2.761 20.66 a^ .0031 .0230 834 .4176 3.125 23 2.885 21.58 n .0036 .0269 9 .4418 3.305 23J4 3.012 22.53 7i-iocoi-iTj<,- o os :>}.: il 286.13 317.92 349.71 381.50 413.30 445.09 476.88 508.67 540.40 134.65 168.31 202.97 235.63 269.30 302.96 186.68 370.28 103.94 187.60 171.27 504.93 538.59 572.26 505.92 1-. 2 -' I ;; :;. :j< ( 41 1< .V 5( (i( 6! 9i 12.13 7.66 3.19 18.73 J4.26 9.79 5.32 (0.85 J6.39 1.92 7.45 2.98 8.51 K4.05 9.58 5.11 149.61 187.01 224.41 261.82 299.22 336.62 374.03 111.43 148.83 186.23 523.64 561.04 598.441 ;: fcVHl 373.25 ?10. 65 748.05 157.09 196.36 235.63 274.90 314.18 353.45 392.72 432.00 471.27 510.54 549.81 589.08 128.86 >07 C,:{ -00.90 746.17 ?85.45 324.73 164.57 205.71 246.86 288.00 329.14 370.28 411.43 452.57 493.71 534.85 575.99 617.14 VS8.S6 199.42 740.56 781.71 BS8.86 804.00 905.14 172.05 215.06 258.07 301.09 344.10 387.11 430.13 473.14 516.15 559.16 602.18 645.19 688.20 731.21 774.23 817.24 800.20 903.26 946.27 989.29 EXAMPLE. To find number of gallons in a rectangular tank that is 7.5 ft. by 10 ft., the water being 4 ft. deep : Look in extreme left hand column for 7.5 and opposite to this in column headed " 10 " read 561.04, which being multiplied by 4, the depth of water in the tank, gives 2244.2 the number of gallons required. NATIONAL TUBE COMPANY. . Diameters in Inches. (Ellis.) given below, varying with the form of nozzle or d for a good form of tapering smooth nozzle or N oret cal o cent., 64 Theoretical Discharge of Circular Orifi OTE. The actual discharge will be less than the t through which the water flows. For a ring nozzle t 82 per cent., can be assumed as the actual dischar In NATIONAL TUBE COMPANY. WATER-POWER. (Kent's Pocket Book.) Power of a Fall of "Water Efficiency. The gross power of a fall of water is the product of the weight of water discharged in a unit of time into the total head, i. e. , the difference of vertical elevation of the upper surface of the water at the points where the fall in question begins and ends. The term " head " used in connection with water- wheels is the difference in height from the surface of the water . in the wheel-pit to the surface in the pen-stock when the wheel is running. If Q cubic feet of water discharged per second, D = weight of a cubic foot of water = 62.36 Ibs. at 60 F., H = total head in feet ; then DQH =. gross power in foot-pounds per second, and DQH -f- 550 = 0.1134 QH= gross horse power. If Q' is taken in cubic feet per minute, H. P. = A water-wheel or motor of any kind cannot utilize the whole of the head H, since there are losses of head at both the entrance to and the exit from the wheel. There are also losses of energy due to friction of the water in its passage through the wheel. The ratio of the power de- veloped by the wheel to the gross power of the fall is the efficiency of the wheel. For 75$ efficiency, net horse- power = 0.00142g'//= 706 NATIONAL TUBE COMPANY. Horse-power of "Water Flowing in a Tube* The head due to the velocity is ; the head due to the pressure is - ; 2^-' w* the head due to actual height above the datum plane is h feet. The total head is the sum of these 4- h + - Kg W in feet, in which v velocity in feet per second, f pressure in Ibs. per sq. ft., w = weight of 1 cu. ft. of water 62.4 Ibs. If p = pressure in Ibs. per sq. in., L = 2.309/. In hydraulic transmission the velocity and the height above datum are usually small compared with the pressure-head. The work or energy of a given quan- tity of water under pressure = its volume in cubic feet X its pressure in Ibs. per sq. ft.; or if Q = quantity in cubic feet per second, and/ = pressure in Ibs. per square inch, W= 144/0, and the H. P. = - 0.2618/0. 550 Formula for Computing Power of Jet Water-Wheels of the Pelton Type. (F. K. Blue). Let HP = horse-power delivered by the water-wheel ; d = diameter of nozzle ; w = weight of one cu. ft. of water, or 62.5 Ibs. ; E = efficiency of the water-wheel ; q quantity of water in cubic feet per minute ; c coefficient of discharge from the nozzle, which may be ordinarily taken as 0.9 ; li effective head (actual head less friction head) in feet ; then HP = wE ^ h = 0.00189 E q h = 0.00436 E q p. = 33,000 0.00496 E c d 2 |/1T s= 0.0174 E c d 2 |/"p". q = 529 HP = 2.62 c d 8 V"hT= 4 c d 2 4/~p~. NATIONAL TUBE COMPANY. 127 The Pclton Water-wheel. Mr. Ross E. Browne (En^g News, Feb. 20, 1892) thus outlines the principles upon which this water-wheel is constructed : The function of a water-wheel, operated by a jet of water escaping from a nozzle, is to convert the energy of the jet, due to its velocity, into useful work. In order to utilize this energy fully the wheel-bucket, after catching the jet, must bring it to rest before discharging it, with- out inducing turbulence or agitation of the particles. This cannot be fully effected, and unavoidable difficul- ties necessitate the loss of a portion of the energy. The principal losses occur as follows : First, in sharp or an- gular diversion of the jet in entering, or in its course through the bucket, causing impact, or the conversion of a portion of the energy into heat instead of useful work. Second, in the so-called frictional resistance offered to the motion of the water by the wetted surfaces of the buckets, causing also the conversion of a portion of the energy into heat instead of useful work. Third, in the velocity of the water, as it leaves the bucket, representing energy which has not been converted into work Hence, in seeking a high efficiency : 1. The bucket- surface at the entrance should be approximately parallel to the relative course of the jet, and the bucket should be curved in such a manner as to avoid sharp angular de- flection of the stream. If, for example, a jet strikes a surface at an angle and is sharply deflected, a portion of the water is backed, the smoothness of the stream is dis- turbed, and there results considerable loss by im- pact and otherwise. The entrance and deflection in the Pelton bucket are such as to avoid these losses in the main. F>- 134. FIG. 135. 2. The number of buckets should be small, and the path of the jet in the bucket short ; in other words, the total wetted surface should be small, as the loss by fric- tion will be proportional to this. 128 NATIONAL TUBE COMPANY. 3. The discharge end of the bucket should be as nearly tangential to the wheel periphery as compatible with the clearance of the bucket which follows ; and great differences of velocity in the parts of the escaping water should be avoided. In order to bring the water to rest at the discharge end of the bucket, it is shown, mathe- matically, that the velocity of the bucket should be one half the velocity of the jet. A bucket, such as shown in Fig. 135, will cause the heaping of more or less dead or turbulent water at the point indicated by dark shading. This dead water is subsequently thrown from the wheel with considerable velocity, and represents a large loss of energy. The in- troduction of the wedge in the Pelton bucket (see Fig. 134) is an efficient means of avoiding this loss. A wheel of the form of the Pelton conforms closely in construction to each of these requirements. In a test made by the proprietors of the Idaho mine, near Grass Valley, Cal., the dimensions and results were as follows : Main supply-pipe, 22 in. diameter, 6900 ft. long, with the head of 386} feet above centre of nozzle. The loss by friction in the pipe was 1.8 ft., reducing the effective head to 384.7 ft. The Pelton wheel used in the test was 6 ft. in diameter and the nozzle was 1.89 in. di- ameter. The work done was measured by a Prony brake, and the mean of 13 tests showed a useful effect of 87.3$. NATIONAL TUBE COMPANY. FIG. 136. Miners' Inch Measurements. (Pelton Water Wheel Co.) The cut, Fig. 136, shows the form of measuring-box ordinarily used, and the following table gives the dis- charge in cubic feet per minute of a miner's inch of water, as measured under the various heads and different lengths and heights of apertures used in California. Length of Openings 2 Inches High. Openings 4 Inches High. Opening Head to Head to Head to Head to Head to Head to in Centre Centre Centre Centre, Centre, Centre, inches. 5 inches. 6 inches. 7 inches. 5 inches. 6 inches. 7 inches. Cu ft. Cu ft. Cu. ft. Cu. ft. Cu. ft. Cu. ft. 4 1.348 1.473 1.589 1.320 1.450 1.570 6 1.355 1.480 1.596 1.336 1.470 1.595 8 1.359 1.484 .600 1.344 1.481 1.608 10 1.361 1.485 .602 1.349 1.487 1.615 12 1.363 1.487 .604 1.352 1.491 1.620 14 .364 1.488 .604 1.354 1.494 1.623 16 .365 1.489 .605 1.356 1.496 1.626 18 .365 1.489 .606 1.357 1.498 1.628 20 .365 .490 606 1.359 1.499 1.630 22 .366 .490 .607 1.359 1.500 1.631 24 .366 .490 .607 1.360 1.501 1.632 26 .366 .490 .607 1.361 1.502 1.633 28 .367 .491 .607 1.361 1.503 1.634 30 .367 .491 .608 1.362 1.503 1.635 40 .367 .492 .608 1.363 1.505 1.637 50 .368 .493 .609 1.364 1.507 1.639 60 .368 .493 .609 1.365 1.508 1.640 70 .368 1.493 .609 1.365 1.508 1.641 80 .368 1.493 .609 1.366 1.509 1.641 90 .369 1.493 1.610 1.366 1.509 1.641 100 1.369 1.494 1.610 1.366 1.509 1.642 NATIONAL TUBE COMPANY. PUMPS AND PUMPING ENGINES. (Kent's Pocket Book.) Theoretical Capacity of a Pump. Let Q cu. ft. per min.; G' = Anier. gals, per min. = 7.48050'; d = diam. of pump in inches ; / = stroke in inches ; A 7 ^ = number of single strokes per min. Capacity in cu. ft. per min. Q = *- = 0.0004545AW ; 4 144 12 Capacity in gals, per min. Diameter required for a given capacity per min. If v piston speed in feet per min., d - 13.54 A/&- -4.95 A/ ' r v r v If the piston speed is 100 feet per min. : Nl = 1200, and d = 1.354 i/^T = 0.495 \f~G\ G' = 4.0&/ 2 per min. The actual capacity will be from 60# to 95$ of the theo- retical, according to the tightness of the piston, valves, suction-pipe, etc. Theoretical Horse-power required to raise Water to a given Height. Let Q = cu. ft. per min.; G' = gals, per min.; W wt. in Ibs.; P pressure in Ibs. per sq. ft.; p = pressure in Ibs. per sq. in.; H height of lift in ft.; W= 62.36<2', P = 144^, p = 0.433 H, H= 2.309/, G' = 7.48050'. Hp Q'P Q'HxmxAZZ^Q'H__ G'H . 33,000 33,000 529.2 3958.7 ' HP = WH - g'X62.36x2.309^ _ Q'p = G'p 33,000 33,000 229.2 1714.5 ' NATIONAL TUBE COMPANY. For the actual horse -power required an allowance must be made for the friction, slips, etc., of engine, pump, valves, and passages. Depth of Suction* Theoretically a perfect pump will lift water from a depth of nearly 34 feet, corresponding to a perfect vacuum (14.7 Ibs. X 2.309 = 33.95 feet); but since a perfect vacuum cannot be obtained, on account of valve-leakage, air contained in the water, and the vapor of the water itself, the actual height is generally less than 30 feet. In pumping hot water, the water must flow into the pump by gravity. The following table shows the theoretical maximum depth of suction for different temperatures, leakage not considered : fi ^3 - b ^ 2:2--' 'p^b &l - fe ;-2 'fl^b ^1 . ex QooS cx J^ftij 3"o . ? 0) J^O.^ ||S .J3|> H <|jj| ^a So H <|^s |o 101.4 1 27.88 31.6 183.0 8 13.63 15.5 126.2 2 25.85 29.3 188.4 9 11.59 13.2 144.7 3 23.81 27.0 193.2 10 9.55 10.9 153.3 4 21.77 24.7 197.6 11 7.51 8.5 162.5 5 19.74 22.4 201.9 12 5.48 6.2 170.3 6 17.70 20.1 205.8 13 3.44 3.9 177.0 7 15.66 17.8 209.6 14 1.40 1.6 STEAM AND STEAM APPARATUS. NATIONAL TUBE COMPANY. STEAM. Under the ordinary atmospheric pressure of 14.7 pounds per square inch, water boils at 212 Fahr., passing off as steam, the temperature at which it boils varying with a variation in the pressure. Dry steam is steam not containing any free moisture. It may be either saturated or superheated. Wet steam is steam containing free moisture in the form of spray or mist, and has the same temperature as dry saturated steam of the same pressure. Saturated steam is steam in its normal state, that is, steam whose temperature is that due its pressure; by which is meant steam at the same temperature as that of the water from which it was generated and upon which it rests. Superheated steam is steam at a temperature above that due to its pressure. A British thermal unit is the quantity of heat required to raise one pound of water at 39. 1 Fahr. through one degree of temperature. The total heat of the water is the number of British thermal units needed to raise one pound of water from 32F. to the boiling point, under the given pressure. The latent heat of steam is the number of British thermal units required to convert one pound of water, at the boil- ing point, into steam of the same temperature. The total heat of saturated steam is the number of heat units required to raise a pound of water from 32 F. to the boiling point, at the given pressure, plus the number required to evaporate the water at that temperature. The specific heat of steam is the quantity of heat required to raise the temperature of one pound of steam through one degree of temperature. In British units and near the saturation temperature it equals, at constant pres- sure, 0.48. NATIONAL TUBE COMPANY. 136 The specific gravity of steam at any temperature and pressure, as compared with air of same temperature and pressure, is approximately 0.622. One cubic inch of water evaporated into steam at 212F. becomes 1646 cubic in., that is, nearly one cu. ft. Water in contact with saturated steam has the same temperature as the steam itself. Water introduced into superheated steam will be vaporized until the steam be- comes saturated, and its temperature becomes that due its pressure. Cold water, or water at a lower temperature than that of the steam, introduced into saturated steam, will condense some of it, thus lowering both the temper- ature and pressure of the rest until the temperature again equals that due its pressure. 136 NATIONAL TUBE COMPANY. PROPERTIES OF SATURATED STEAM. Sew % sS .^ u US "$ Bri .S c Sou l'h 5?| E'l^ M| * ^ _o leSfa Item 3 ffi ffl II *CQ |-S !! ffi'3 h ^0 1 101.99 70.0 1043.0 1113.1 0.00299 334.5 2 126.27 94.4 1026.1 1120.5 0.00576 173.6 3 141.62 109.8 1015.3 1125.1 0.00844 118.5 4 153.09 121.4 1007.2 1128.6 0.01107 90.33 5 162.34 130.7 1000.8 1131.5 0.01366 73.21 6 170.14 138.6 995.2 1133 8 0.01622 61.65 7 176.90 145.4 990.5 1135.9 0.01874 53.39 8 182.92 151.5 986.2 1137.7 0.02125 47.06 9 188.33 156.9 982.5 1139.4 0.02374 42.12 10 193.25 161.9 979.0 1140.9 0.02621 38.15 15 213.03 181.8 965.1 1146.9 0.03826 26.14 20 227.95 196.9 954.6 1151.5 0.05023 19.91 25 240.04 209.1 946.0 1155.1 0.06199 16.13 30 250.27 219.4 938.9 1158.3 0.07360 13.59 35 259.19 228.4 932.6 1161.0 0.08508 11.75 40 267.13 236.4 927.0 1163.4 0.09644 10.37 45 274.29 243.6 922.0 1165.6 0.1077 9.285 60 280.85 250.2 917.4 1167.6 0.1188 8.418 55 286.89 256.3 913.1 1169.4 0.1299 7.698 60 292.51 261.9 909.3 1171.2 0.1409 7.097 65 297.77 267.2 905.5 1172.7 0.1519 6.583 70 302.71 272.2 902.1 1174.3 0.1628 6.143 75 307.38 276.9 898.8 1175.7 0.1736 5.760 80 311.80 281.4 895.6 1177.0 0.1843 5.426 85 316.02 285.8 892.5 1178.3 0.1951 5.126 90 320.04 290.0 889.6 1179.6 0.2058 4.859 95 323.89 294.0 886.7 1180.7 0.2165 4.619 100 327.58 297.9 884.0 1181.9 0.2271 4.403 105 331.13 301.6 881.3 1182.9 0.2378 4.205 110 334.56 305.2 878.8 1184.0 0.2484 4.026 115 337.86 308.7 876.3 1185.0 0.2589 3.862 120 341.05 312.0 874.0 1186 0.2695 3.711 125 344.13 315.2 871.7 1186.9 0.2800 3.571 130 347.12 318.4 869.4 1187.8 0.2904 3.444 140 352.85 324.4 865.1 1189.5 0.3113 3.212 150 358.26 330.0 861.2 1191.2 0.3321 3.011 160 363.40 335.4 857.4 1192.8 0.3530 2.833 170 368.29 340.5 853.8 1194.3 0.3737 2.676 180 372.97 345.4 850.3 1195.7 0.3945 2.535 190 377.44 350.1 847.0 1197.1 0.4153 2.408 200 381.73 354.6 843.8 1198.4 0.4359 2.294 225 391.79 365.1 836.3 1201.4 0.4876 2.051 250 400.99 374.7 829.5 1204.2 0.5393 1.854 275 409.50 383.6 823.2 1206.8 0.5913 691 300 417.42 391.9 817.4 1209.3 0.644 .553 325 424.82 399.6 811.9 1211.5 0.696 .437 350 431.90 406.9 806.8 1213.7 0.748 .337 375 438.40 414.2 801.5 1215.7 0.800 .250 400 445.15 421.4 796.3 1217.7 0.853 1.172 500 466.57 444.3 779.9 1224.2 1.065 0.939 The absolute pressures given in column one may be converted into gauge pressures by subtracting the constant 14.7 : Thus, 115 Ibs., absolute = 115 14.7 = 100.3 Ibs. gauge. > NATIONAL TUBE COMPANY. 137 FACTORS OF EVAPORATION* ill oT a STEAM* PRESSURE IN POUNDS PER SQUARE INCH, GAUGE. HI 0. 5. 15. 25. 35. 45. 55. 65. 75. 85. Dgrs. 32 1.187 1.192 1.199 1.204 1.209 1.212 1.216 1.218 1.221 1.223 35 1.184 1.189 1.196 1.201 1.206 1.209 1.213 1.215 1.218 .220 40 1.179 .184 1.191 1.196 1.201 1.204 1.208 1.219 1.213 .215 45 1.173 .178 1.185 1.190 1.195 1.198 1.202 1.204 1.207 .209 50 1.168 .173 1.180 1.185 1.190 1.193 1.197 1.199 1.202 .204 55 1.163 .168 1.175 1.180 .185 1.188 1.192 1.194 1.197 .199 60 1.158 .163 1.170 1.175 .180 1.183 1.187 1.189 1.192 .194 65 1.153 .158 1.165 1.170 .175 1.178 1.182 1.184 1.187 .189 70 1.148 .153 1.160 1.165 .170 1.173 1.177 1.179 1.182 .184 75 1.143 .148 1.155 1.160 .165 1.168 1.172 1.174 1.177 .179 80 1.137 .142 1.149 1.154 .159 1.162 1.166 1.168 1.171 .173 85 1.132 .137 1.144 1.149 .154 1.157 1.161 1.163 1.166 .168 90 1.127 .132 1.139 1.144 .149 1.152 1.156 1.158 1.161 .163 95 1.122 .127 1.134 1.139 .144 1.147 1.151 1.153 1.156 .158 100 1.117 .122 1.129 1.134 .139 1.142 1.146 1.148 1.151 .153 105 1.111 .116 1.123 1.128 .133 1.136 1.140 1.142 1.145 .147 110 1.106 .111 1.118 1.123 .128 1.131 1.135 1.137 1.140 .142 115 1.101 .106 1.113 1.118 .123 1.126 1.130 1.132 1.135 .137 120 1.096 .101 1.108 1.113 .118 1.121 1.125 1.127 1.130 .132 125 1.091 .096 1.103 1.108 .113 1.116 1.120 1.122 1.125 .127 130 1.085 .090 1.097 1.102 .107 1.110 1.114 1.116 1.119 .121 135 1.080 .085 1.092 1.097 .102 1.105 1.109 1.111 .114 .116 140 1.075 .080 1.087 1.092 .097 1.100 1.104 1.106 .109 .111 145 1.070 .075 1.082 1.087 .092 1.095 1.099 1.101 .104 .106 150 1.065 .070 1.077 1.082 .087 1.090 1.094 1.096 .099 .101 155 1.059 .064 1.071 1.076 .081 1.084 1.088 1.090 .094 .095 160 1.054 .059 1.066 1.071 .076 1.079 1.083 1.085 .088 .090 165 1.049 1.054 1.061 1.066 .071 1.074 1.078 1.080 .083 .085 170 1.044 1.049 1.056 1.061 .066 1.069 1.073 1.075 .078 .080 175 1.039 1.044 1.051 1.056 .061 1.064 1.068 1.070 .073 .075 180 1.033 1.038 1.045 1.050 .055 1.058 1.062 1.064 .067 .069 185 1.028 1.033 1.040 1.045 .050 1.053 1.057 1.059 .062 .064 190 1.023 1.028 1.035 1.040 .045 1.048 1.052 1.054 .057 .059 195 1.018 1.023 1.030 1.035 .040 1.043 1.047 1.049 .052 .054 200 1.013 1.018 1.025 1.030 1.035 1.038 1.042 1.044 .047 1.049 205 1.007 1.012 1.019 1.024 1.029 1.032 1.036 1.038 1.041 1.043 210 1.002 1.007 1.014 1.019 1.024 1.027 1.031 1.033 1.036 1.038 212 1.000 1.005 1.012 1.017 1.022 1.025 1.029 1.031 1.084 1.036 ^ n r 138 NATIONAL TUBE COMPANY. FACTORS OF EVAPORATION. ill STEAM PRESSURE IN POUNDS PER SQUARE INCH, GAUGE. ^ a ||| 95. 105. 115. 125. 135. 145. 155. 165. 175. 185. Dgrs. 32 1.226 1.228 .230 1.231 1.233 1.235 1.236 1.238 1.239 1.240 35 1.223 1.225 .227 1.228 1.230 1.232 1.233 1.235 1.236 1.237 40 1.218 1.220 .222 1.223 1.225 1.227 1.228 1.230 1.231 1.232 45 1.212 1.214 .216 1.217 1.219 1.221 1.222 1.224 1.225 1 226 50 1.207 1.209 .211 1.212 1.214 1.216 1.217 1.219 1.220 1.221 55 1.202 1.204 .206 1.207 1.209 1.211 1.212 1.214 1.215 1.216 60 1.197 1.199 .201 1.202 1.204 1.206 1.207 1.209 1.210 1.211 65 1.192 1.194 .196 1.197 1.199 1.201 1.202 1.204 1.205 1.206 70 1.187 1.189 .191 1.192 1.194 1.196 1.197 1.199 1.200 1.201 75 1.182 1.184 .186 1.187 1.189 1.191 1.192 1.194 1.195 1.196 80 1.176 1.178 .180 1.181 1.183 1.185 1.186 1.188 1.189 1.190 85 1.171 1.173 .175 1.176 1.178 1.180 1.181 1.183 1.184 1.185 90 1.166 1.168 .170 1.171 1.173 1.175 1.176 1.178 1.179 1.180 95 1.161 1.163 .165 1.166 1.168 1.170 1.171 1.173 1.174 1.175 100 1.156 1.158 .160 1.161 1.163 1.165 1.166 1.168 1.169 1.170 105 1.150 1.152 .154 1.155 1.157 1.159 1.160 1.162 1.163 1.164 110 1.145 1.147 .149 1.150 1.152 1.154 1.155 1.157 1.158 1.159 115 1.140 1.142 1.144 1.145 1.147 1.149 1.150 1.152 1.153 1.154 120 1.135 1.137 1.139 1.140 1.142 1.144 1.145 1.147 1.148 1.149 125 1.130 1.132 1.134 1.135 1.137 1.139 1.140 1.142 1.143 1.144 130 1.124 1.126 1.128 1.129 1.131 1.133 1.134 1.136 1.137 1.138 135 1.119 1.121 1.123 1.124 1.126 1.128 1.129 1.131 1.132 1.133 140 1.114 1.116 1.118 1.119 1.121 1.123 1.124 1.126 1.127 1.128 145 1.109 1.111 1.113 1.114 1.116 1.118 1.119 1.121 1.122 1.123 150 1.104 1.106 1.108 1.109 1.111 1.118 1.114 1.116 1.117 1.118 155 1.098 1.100 1.102 1.103 1.105 1.107 1.108 1.110 1.111 1.112 160 1.093 1.095 1.097 1.098 1.100 1.102 1.103 1.105 1.106 1.107 165 1.088 1.090 1.092 1.093 1.095 1.097 1.098 1.100 1.101 1.102 170 1.083 1.085 1.087 1.088 1.090 1.092 1.093 1.095 1.096 1.097 176 1 078 1.080 1.082 1.083 1.085 1.087 1.088 1.090 1.091 1.092 180 1.072 1.074 1.076 1.077 1.079 1.081 1.082 1.084 1.085 1.086 185 1.067 1.069 1.071 1.073 1.074 1.076 1.077 1.079 1.080 1.081 190 1.062 1.064 .066 1.067 1.069 1.071 1.072 1.074 1.075 1.076 195 1.057 1.059 .061 1.062 1.064 1.066 1.066 1.069 1.070 1.071 200 1.052 1.054 .056 1.057 1.059 1.061 1.062 1.064 1.065 1.066 205 1.046 1.048 .050 1.051 1.053 1.055 1.056 1.058 1.059 1.060 210 1.041 1.043 .045 1.046 1.048 1.050 1.051 1.053 1.054 1.055 212 1.039 1.041 .043 1.044 1.046 1.048 1.049 1.051 1.052 1.053 NATIONAL TUBE COMPANY. Explanation of Table of Properties of Saturated Steam: The first column shows the absolute pressure of steam as it rises freely from water of the same temperature, and is equal to 14.7 Ibs. -j- the pressure shown by the steam gauge. The second column shows the temperatures in degrees Fahrenheit at which water vaporizes under the pressures opposite in column one. The third column shows the number of British thermal units required to raise one pound of water from 32F. to the boiling temperatures opposite in column two. The fourth column shows the number of heat units that are absorbed, or changed from sensible to latent heat, when one pound of water at the boiling point changes to steam of the same temperature. The fifth column shows the number of heat units ab- sorbed when one pound of water at 32F. has its temper- ature raised to the boiling point and is then changed to steam at constant pressure and temperature. This column gives the total heat of formation of steam from water at 32F. The sixth column shows the weights in pounds per cubic ft. of saturated steam at the corresponding pres- sures and temperatures given in columns one and two. The seventh column shows volumes in cubic ft. of one pound of steam. Explanation of Table of Factors of Evaporation : The fac- tors in this table were obtained, for the various feed- water temperatures and steam pressures given, by sub- tracting the heat above 32F. in one pound of feed-water from the total heat above 32 in one pound of steam, and then dividing the remainder thus obtained by 965.7, the latent heat of steam at atmospheric pressure. 140 NATIONAL TUBE COMPANY. Example: Given the boiler pressure =. 105 Ibs. per square in. guage, and the feed-water temperature =55F. ; to find the factor of evaporation. Look in the column or steam pressures headed 105 and opposite to 55 degrees in the first column, read 1.204, the factor required. It will therefore require 1.204 times as many heat units to evap- orate a certain weight of water from a feed-water tem- perature of 55F. into steam under 105 pounds guage as would be required to evaporate the same weight of water from a temperature of 212F. into steam under one at- mospheric pressure, that is, from and at 2J2F. This table is useful in rating boilers and in preparing reports of tests. FLOW OF STEAM FROM ORIFICES. The flow of steam from a vessel of one pressure into that of another pressure becomes greater the greater the difference in pressure between the two vessels, until the lower is 0.58 the absolute pressure of the higher. Any further reduction of the pressure in the second vessel, even down to a vacuum, fails to enhance the flow of the steam between the two. In flowing through the best shaped nozzle the steam expands to the external pressure and also to the volume corresponding to this pressure, so long as it is not less than 58 per cent, of the internal pressure. For an external pressure of 58 per cent, or less, the ratio of expansion becomes constant and is 1.624. NATIONAL TUBE COMPANY. OUTFLOW OF STEAM INTO THE ATMOSPHERE. (D. K. CLARK.) Velocity Actual Initial Pressure. External Pressure. Expan- sion in nozzle. of out- flow at constant velocity of out- flow ex- Discharge density. panded . Lbs. per sq. in. Lbs. per sq. in. Ratio. Ft. per Ft. per Lbs. per sq. in. per absolute. absolute. sec. sec. minute. 25.37 14.7 1.624 863 1401 22.81 30 14.7 1.624 867 1408 26.84 40 14.7 1.624 874 1419 35.18 45 14.7 1.624 877 1424 39.78 50 14.7 1.624 880 1429 44.06 60 14.7 1.624 885 1437 52.59 70 14.7 1.624 889 1444 61.07 75 14.7 1.624 891 1447 65.30 90 14.7 1.624 895 1454 77.94 100 14.7 1.624 898 1459 86.34 115 14.7 1.624 902 1466 98.76 135 14.7 1.624 906 1472 115.61 155 14.7 1.624 910 1478 132.21 165 14.7 1.624 912 1481 140.46 215 14.7 1.624 919 1493 181.58 The weight of steam discharged from a cylindrical nozzle or a short pipe may be approximately found, when the pressure of the atmosphere receiving the steam is less than 58 per cent, of the initial pressure, by the fol- lowing formula (Napier's Rule): Wap-r-^\ in which W flow in pounds per second, a = area of orifice in square inches; and p = absolute initial pressure per square inch of the steam. For a circular opening in a thin pla'te multiply the dis- charge as obtained from the above formula by 0.65. NATIONAL TUBE COMPANY. FLOW OF STEAM IN PIPES. (KENT'S POCKET BOOK). A formula commonly used for velocity of flow of steam in pipes is the same as Downing's for the flow of water in smooth cast iron pipes, viz. : V= 604/5 D, ' L in which V velocity in feet per second, Z,= length, and D = diameter of pipe in feet, //'height in feet of a col- umn of steam, of the pressure of the steam at the en- trance, which would produce a pressure equal to the difference of pressures at the two ends of the pipe. (For derivation of the coefficient 50, see Briggs on " Warming Buildings by Steam," Proc. Inst. C. E., 1882.) If Q quantity in cubic ft. per minute, d = diameter in inches, L and //being in feet, the formula reduces to Q =4.723 \/^ d > 5 H=0.448 ~^> d =0.537 \/^' If P! = pressure in pounds per sq. in. of the steam at the entrance to the pipe, p 2 = the pressure at the exit, then 144 (p\p*) difference in pressure per sq. ft. Let w density or weight per cu. ft. of steam at the pressure p lt then the height of column equivalent to the difference in pressures is If W= weight of steam flowing in pounds per minute Qw and d is taken in inches, L being in feet: W = 56.68 |/jy (Pi-Pa) d5 ; Q= 56.68 |/S*~P"> d< . d = 0.199 !/ W * L . = 0.199 Pi Pa d 8 Velocity in feet per minute V = Qn-0.7854 ^ = 10390 J pt ~ p } d ' ; j) NATIONAL TUBE COMPANY. For a velocity of 6000 feet per minute, d= For a velocity of 6000 feet per minute, a steam pressure of 100 pounds gauge, or W=0.264, and a length of 100 feet. Pi Pa d That is, a pipe 1 inch diameter, 100 feet long, carrying steam of 100 pounds gauge pressure at 6000 feet velocity per minute, would have a loss of pressure of 8.8 pounds per sq. inch, while steam traveling at the same velocity in a pipe 8.8 inches diameter would lose only 1 pound pressure. G. H. Babcock in "Steam," gives the formula ) w (Pi p 8 ) d 6 W=87|/L /I + 3.6 \ One of the most widely accepted formulae for flow of water is D'Arcy's, which is Using D'Arcy's coefficients, and modifying his formula to make it apply to steam, to the form a = c i or w = c j .-. we obtain for, Diam. in. 1 2 3 456 78 Value of c, 45.3 52.7 56.1 57.8 58.4 59.5 60.1 60.7 Diam. in. 9 10 12 14 16 18 20 24 Value of c, 61.2 61.8 62.1 62.3 62.6 62.7 62.9 63.2 In the absence of direct experiments these coefficients are probably as accurate as any that may be derived from formulae for flow of water. Loss of pressure in Ibs. per sq. in.=p l p s = Q w ** . c 3 d 6 NATIONAL TUBE COMPANY. RESISTANCE TO FLOW BY BENDS, VALVES, ETC Mr. Briggs states that in " Warming Buildings by Steam," that the resistance at the entrance to a pipe con- sists of two parts, namely: the head ^ , which is neces- sary to create the velocity of flow, and the head v* 0.505 - which overcomes the resistance to entrance *K offered by the mouth of the pipe* The total loss of head at entrance then equals the sum of these, or 1.505-^, in which V velocity of flow of steam in the pipe, in feet per second, and g = acceleration due to gravity, or 32.2. The Babcock & Wilcox Co. state in " Steam " that the resistance at the opening, and that at a globe valve, are each about the same as that caused by an additional length of straight pipe, as computed by the formula, r . 114 X diameter of pipe Additional length of pipe = t + (3 . 6 ^ diamet P er ^ - from which has been computed the following table: Diameter in inches 2 2* 3 3| 4 5 6 7 Additional length, feet 7 10 13 16 20 28 36 44 Diameter in inches 8 10 12 15 18 20 22 24 Additional length, feet 53 70 88 115 143 162 181 200 The resistance to flow at a right-angled elbow is about equal to % that of a globe valve. The above values are to be considered as being only approximations to the truth. NATIONAL TUBE COMPANY. Example. Find the discharge from a steam pipe when the given length = 120 feet and the diameter = 8 inches; the pipe containing 6 right-angled elbows and two globe valves, the pressure at the two ends being respectively 105 and 103 Ibs. per sq. in. gauge. The resistance to entrance, from the above table, for 8 inch pipe = 53 feet; the resistance of 6 elbows = 6 X 53 X % = 212 feet; the resistance of two globe valves = 2 X 53 = 106 feet; making a total resistance=53-{-212 + 106 = 371 feet of additional length of pipe. Therefore, the steam would encounter the same resistance flowing through a straight 8-inch pipe, whose length equals 120 -f- 371, or 491 feet, as it would in flowing through the given pipe with its various resistances. Then in the formula W = 0/1 i P) L = 491 feet; p^ = 105 Ibs. per sq. in.; p% = 103 Ibs. per sq. in. ; d 8 inches; , for an 8-inch pipe = 60.7; and w, from table of Properties of Saturated Steam, = 0.27 Substituting in formula we get W = 60.7 ,/ 0.27 (105-103)8? = m r 491 The pipe, then, under the stated conditions, would dis- charge approximately 364 pounds of steam per minute, or 21,800 Ibs. per hour; which, on the basis of 30 Ibs. per horse-power hour, would have a capacity of 728 boiler horse-power. Since one pound of steam at 104 Ibs. gauge has a volume of 3.7 cu. ft., the pipe would dis- charge 1,350 cu.ft. per minute, or 81,000 cu. ft. per hour. NATIONAL TUBE COMPANY i eo^^^"883gir3' S l TH i SScScSSka S9SS28;. M 06 o t^ TH w eo ''^ ^< S! S^SS^Sli " 'S2ssag^^~~ *!O -.-.2!2SS5S5SxS2gSSSSSfe?22S525?S22??5 W ^ ~ 5 D-i o^ ^On w - J^c -P" w S^ a rt&H w 9 ^ a Pi |j .2^ |j 2 H jgJ .2 2| rjffi^ i|j H| o-2 fl si 5|2 feo 1-S.9 o3o ri"" 1 Q m^S rt' rt Q CQ (D ft rt"" a & 8 5 W o, IK 423 6 1221 12 2290 22 3949 2 2 494 7 1420 14 2645 24 4264 3 692 8 1580 16 2961 26 4617 4 869 9 1738 18 3315 28 4932 5 1067 10 1935 20 3632' 30 5288 CONDENSATION OF STEAM IN BARE IRON PIPES. Steam pressure 100 Ibs. gauge, surrounding air at 62 F. Steam temperature = 338 Fahr. 1*1 3&J Condensed . per Hour ot Length. 3minal ter of Pipe inches. Condensed . per Hour ot Length. & Ip Condensed . per Hour ot Length. ominal ter of Pipe Inches. ||| rt -rH |3. CTj"" $3* 3*2 ^|- H |3? Q c/5.Sa Q 55.Sft Q c/5.Sa Q w.2o, VA 0.48 6 1.39 12 2.61 22 4.51 2 2 0.56 7 1.62 14 3.02 24 4.87 3 0.79 8 1.80 16 3.38 26 5.27 4 0.99 9 1.98 18 3.78 28 5.63 5 1.22 10 2.21 20 4.15 30 6.04 i n . NATIONAL TUBE COMPANY. CONDENSATION OF STEAM IN COVERED IRON PIPES. Corresponding to a percentage of that in a bare pipe varying from 15 per cent, for a 30-inch pipe to 19 for a 1% inch pipe, which approximates to what may be ex- pected in practice from the application of the best com- mercial pipe coverings. Steam pressure =100 Ibs. gauge, surrounding air at 62 F. Steam temperature = 338 Fahr. & US* & Sfl ?1 -g^; & S5 ^{ IE* Sjgbo c,2 ^ c t o*> fy c'oj * ^J fcj " ^J c'oj 'c^J sp *s.s 53! |ii P! |P 6^0 C to O in which ^ = the mean effective pressure in Ibs. per sq. in., as ob- tained from the indicator card, / length of stroke in feet, a area of piston in sq. inches and n number of working strokes per minute. If the engine has more than one cylinder compute the power of each and take NATIONAL TUBE COMPANY. the sum. If great accuracy is desired the area of cross- section of piston rod should be deducted from the piston area for the crank end, and the powers of the two ends computed separately, since the mean effective pressures of the two ends will not ordinarily be found to be exactly the same. For single acting engines substitute for n the number of working strokes only. Net or brake horse-power of an engine is the horse- power delivered by the engine from its shaft, by belt or otherwise. It may be obtained from the indicated horse- power by multiplying by the mechanical efficiency: For example, an engine indicating 300 H.P., with a mechan- ical efficiency of 88 per cent., would have a net or brake horse-power = 300 X 0.88 = 264. The unit of evaporation is the number of B.T.U. neces- sary to convert one pound of water at 212F. into steam of the same temperature, and is therefore equal to 965.7 B.T.U. , the latent heat of one pound of steam at atmos- pheric pressure. Boiler Horse-power. A Committee of the American So- ciety of Mechanical Engineers recommended the unit of boiler power known as the "Centennial Standard, " and this is now generally accepted. They advised that the commercial horse-power be taken as an evaporation of 30 pounds of water per hour from a feed water temperature of 100Fahr. into steam at 70 pounds per square inch gauge pressure. This is equivalent to 34} units of evaporation, that is, to 34^ pounds of water evaporated from a feed water temperature of 212 Fahr. into steam at the same temperature. This "Centennial Standard " unit is equivalent to 33,305 British thermal units per hour. It was the opinion of this Committee that a boiler rated at any stated power should be capable of developing that power with easy firing, moderate draught, and ordi- nary fuel, while exhibiting good economy; and, at times, when maximum economy is not the most important ob- ject to be attained, at least one-third more than its rated power to meet emergencies. NATIONAL TUBE COMPANY. Example. A battery of boilers evaporate 20,000 Ibs. of feed- water per hour, the temperature of feed-water beijig 40F., and the gauge pressure 100 Ibs. per sq. in. Find the equivalent evaporation from and at 2J2F.j also the commercial horse-power. The factor of evaporation, from 4OF. and at 100 Ibs. gauge, is (see table of factors of evaporation) 1.219. Therefore the equivalent evaporation from and at 212 = 20,000 X 1.219 = 24,380 Ibs. per hr. Since one commercial horse-power is equivalent to the evaporation of 34.5 Ibs. of water per hour, from and at 212, the commercial horse-power = 24,380-5-34.5 = 707. In the above example the steam is assumed to be dry and saturated. In case it is not a correction must be made. 1. Assume that the steam contains 2 per cent, of mois- ture. Of the 20,000 Ibs. of feed-water, then, 98 per cent, or 19,600 Ibs. will be evaporated and the remaining 400 Ibs. will pass from the boiler as water at the temperature of the steam. Each pound of this water will carry away from the boiler an amount of heat necessary to raise its temperature from 40F., the temperature of the feed- water, to 337, the temperature of the steam, or 296 B.T.U. per Ib. of entrained water. Had the entrained water been evaporated each pound would have carried away an additional amount equal to its latent heat at boiler pres- sure, or 876 B.T.U. per Ib., or 876 X 400 = 350,400 B.T.U. per hour, for the total amount of entrained water. Un- der the assumed conditions, then, the boiler imparts 350,400 heat units less to the feed-water per hour than would have been the case had there been no entrained water; that is, its capacity is less by 350,400-^33,305 (the heat equivalent of a boiler H.P.) = 10.5 horse-power. The actual commercial horse-power of the boiler then =707 10.5 = 696.5. 2. Assume that the steam is superheated 20 degrees; that is, to a temperature of 337 -f 20 = 357 F. Then the additional heat imparted to each pound of feed- water over that necessary to generate dry saturated steam is 20 X 0.48 (the specific heat of steam) = 9.6 heat units per Ib., or 9.6 X 20,000 = 192,000 per hr., or 192.000-^-33,305 = 5.8 horse-power. The actual horse-power of boiler then = 707 + 5.8 = 712.8. x-ri , p^ 154 NATIONAL TUBE COMPANY. Horse-power per Pound Mean Effective Pressure* T?nrtnii1* Ar6a in SC 3- in - X piston-Speed 33,000 SPEED OF PISTON IN FEET PER MINUTE. J> ., 6* rt^- . c ">, 100 200 300 400 500 600 700 800 900 u 4 .0381 .0762 .1142 .1523 .1904 .2285 .2666 .3046 "73427 4V< .0482 .0964 .1446 .1928 .2410 .2892 .3374 .3856 .4338 5 .0595 .1190 .1785 .2380 .2975 .3570 .4165 .4760 .5355 5V( .0720 .1440 .2160 .2880 .3600 .4320 .5040 .5760 .6480 6 .0857 .1714 .2570 .3427 .4284 .5141 .5998 .6854 .7711 .1006 .2011 .3017 .4022 .5028 .6033 .7039 .8044 .9050 7 .1166 .233-2 .3499 .4665 .5831 .6997 .8163 .9330 1.0496 .1339 .2678 .4016 .5355 .6694 .8033 .9371 1.0710 1.2049 8 .1523 .3046 .4570 .6093 .7616 .9139 1.0662 1.2186 1.3709 .1720 .3439 .5159 .6878 .8598 .0317 1.2037 1.3756 1.5476 9 .1928 .3856 .5783 .7711 .9639 .1567 1.3495 1.5422 1.7350 .2148 .4296 .6444 .8592 1.0740 .2888 1.5036 1.7184 1.9532 10 .2380 .4760 .7140 .9520 1.1900 .4280 1.6660 1.9040 2.1420 11 .2880 .5760 .8639 1.1519 1.4399 .7279 2.0159 2.3038 2.5818 12 .3427 .6854 1.0282 1.3709 1.7136 2.0563 2.3990 2.7418 3.0845 13 .4022 .8044 1.2067 1.6089 2.0111 2.4133 2.8155 3.2178 3.6200 14 .4665 .9330 1 3994 1 8659 2 3324 9, 7989 3 2654 3.7318 4 1983 15 .5355 1.0710 1.6065 2.1420 2.6775 3.2130 3.7485 4.2840 4.8195 16 .6093 1.2186 1.8278 2.4371 3.0464 3.6557 4.2650 4.8742 5.4835 17 .6878 1.2756 1.9635 2.6513 3.3391 4.0269 4.6147 5.4026 6.1904 18 .7711 1.5422 2.3134 3.0845 3.8556 4.6267 5.3978 6.1690 6.9401 19 .8592 1.7184 2.5775 3.4367 4.2959 5.1551 6.0143 6.8734 7.7326 20 .9520 1.9040 2.8560 3.8080 4.7600 5.7120 6.6640 7.6160 8.5680 21 1.0496 2.0992 3.1488 4.1983 5.2479 6.2975 7.3471 8.3966 9.4462 22 1.1519 2.3038 3.4558 4.6077 5.7596 6.9115 8.0634 9.2154 10.367 23 1.2590 2.5180 3.7771 5.0361 6.2951 7.5541 8.8131 10.072 11.331 24 1.3709 2.7418 4.1126 5.4835 6.8544 8.2253 9.5962 10.967 12.338 25 1.4875 2.9750 4.4625 5.9500 7.4375 8.9250 10.413 11.900 13.388 26 1.6089 3.2178 4.8266 6.4355 8.0444 9.6534 11.262 12.871 14.480 27 1.7350 3.4700 5.2051 6.9401 8.6751 10.410 12.145 13.880 15.615 28 1.8659 3.7318 5.5978 7.4637 9.3296 11.196 13.061 14.927 16.793 29 2.0016 4.0032 6.0047 8.0063 10.008 12.009 14.011 16.013 18.014 30 2.1420 4.2840 6.4260 8.5680 10.710 12.852 14.994 17.130 19.278 32 -i.4371 4.8742 7.3114 9.7485 12.186 14.623 17.060 14.497 21.934 34 2.7513 6.5026 8.2538 1.005 13.756 16.508 19.259 22.010 24.762 36 3.0845 6.1690 9.2534 12.338 15.422 18.507 21.591 24.676 27.760 38 3.4367 6.8734 10.310 13.747 17.184 20.620 24.057 27.494 30.930 40 3.8080 7.6160 11.424 15.232 9.040 22.848 26.656 30.464 34.272 42 4.1983 8.3866 12.585 16.783 20.982 25.180 29.378 33.577 37.775 44 4.6077 9.2154 3.823 8.431 23.038 27.646 32.254 36.861 41.469 46 5.0361 0.072 5.108 20.144 25.180 30.216 35.253 40.289 45.325 48 5.4835 0.967 6.451 21.934 27.418 32.901 38.385 43.868 49.352 50 5.9500 1.900 7.850 23.800 29.750 35.700 41.650 47.600 53.550 52 6.4355 2.871 9.307 25.742 32.178 38.613 45.049 51.484 57.920 54 6.9401 3.880 20.820 27.760 34.700 41.640 48.581 55.521 62.461 56 7.4637 4.927 22.391 29.855 37.318 44.782 52.246 59.709 67.173 58 8.0063 6.013 24.019 32.025 0.032 48.038 56.044 64.051 72.057 60 8.5680 7.136 25.704 34.272 42.840 1.408 9.976 68.544 77.112 NATIONAL TUBE COMPANY. plan _ The indicated horse-power of an engine equals^g QQQ aX I n Xp ^area of piston X piston speed ^ i n ^hichp = 33,000 33,000 mean effective pressure in Ibs. per sq. in.; /= length of stroke in f t. ; a effective area of piston in sq. in. ; and n number of impulse strokes per minute. The piston speed for a single acting, double acting or a multiple cylinder engine the length of stroke in ft. X number of impulse strokes per minute. FEED-WATER HEATERS.-(KENT). Percentage of Saving for Each Degree of Increase in Tem- perature of Feed-water Heated by Waste Steam. Initial Temp. of Feed. 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 Pressure of Steam in Boiler, Ibs. per sq. in. above Atmosphere. 20 40 60 .1018 1050 1062 0847 ,0853 ,0867 ,0875 .0899 ,0907 ,0915 .0924 ,0932 ,0941 ,0950 100 120 140 160 180 ,0844 ,0850 ,0857 ,0864 ,0872 ,0879 .0887 ,0911 ,0920 ,0955 ,0965 .0974 ,0984 ,0994 ,1004 ,1012 ,1024 .1035 ,0877 ,0884 0892 ,0900 0908 0917 ,0925 ,0934 ,0943 ,0952 ,0961 ,0971 ,0980 ,0990 ,1000 ,1010 ,1020 .1031 .0852 .0850 .0867 .0864 .0874 .0872 .08831.0879 .0890 .0887 .0898 .0895 .0906 .0903 .0914 .0923 .0931 .0940 .0912 .0920 0893 0901 .0875 NATIONAL TUBE COMPANY. An approximate rule for the conditions of ordinary practice is: A saving of \% is made by each increase of 11 in the temperature of the feed-water. This corresponds to 0.0909 per cent, for each degree. The calculation of saving is made as follows : Let total heat of 1 Ib. of steam at the boiler-pressure =H\ total heat of 1 Ib. of feed-water before entering the heater == Aj, and after passing through the heater = h% ; then ^2^1 the saving made by the heater is TT / Example. Given boiler pressure 100 Ibs. gauge; feed water temperature, original = 60F. and final ^209F. ; to find the percentage of saving resulting from heating the feed-water. From the table of properties of saturated steam we find #=1185 B.T.U.; h =60 32 = 28 B.T.U.; >& 2 =209 32=177 B.T.U. Then the saving by heater = ^"f 1 = ~ f. = 12.9 rl n. HoO do per cent. To solve by table look in column of steam pressures headed " 100" and opposite to 60 in first column read 0.0864, which multiplied by (20960 = 149) the increase of temperature of feed-water, gives 12.9 per cent., as before. NATIONAL TUBE COMPANY. 157 Safe Working Pressures in Cylindrical Shells of Boilers, Tanks, Pipes, etc., in Pounds per Square Inch. (KENTS POCKET BOOK). Longitudinal seams double-riveted. (Calculated from formula P = 14 000 X thickness -*- diameter.) $ o .; DIAMETER IN INCHES. 21 30 36 38 40 42 44 46 48 50 52 |S| 1 36.5 29.2 24.3 23.0 21.9 20.8 19.9 19.0 18.2 17.5 16.8 2 72.9 58.3 48.6 46.1 43.8 41.7 39.8 38.0 36.5 35.0 33.7 3 09.4 87.5 72.9 69.1 65.6 62.5 59.7 57.1 54.7 52.5 50.5 4 45.8 116.7 97.2 92.1 87.5 83.3 79.5 76.1 72.9 70.0 67.3 5 82.3 145.8 121.5 115.1 109.4 104.2 99.4 95.1 91.1 87.5 84.1 6 7 18.7 255.2 175.0 204.1 145.8 170.1 138.2 161.2 131.3 153.1 125.0 145.9 119.3 139.2 114.1 133.2 109.4 127.6 105.0 122.5 101.0 117.8 8 291.7 233.3 194.4 184.2 175.0 166.7 159.1 152.2 145.8 140.0 134.6 9 28.1 262.5 218.8 207.2 196.9 187.5 179.0 171.2 164.1 157.5 151.4 10 364.6 291.7 243.1 230.3 218.8 208.3 198.9 190.2 182.3 175.0 168.3 11 401.0 320.8 267.4 253.3 240.6 229.2 218.7 209.2 200.5 192.5 185.1 12 437.5 350.0 291.7 276.3 262.5 250.0 238.6 228.3 218.7 210.0 201.9 13 473.9 379.2 316.0 299.3 284.4 270.9 258.5 247.3 237.0 227.5 218.8 14 410.4 408.3 340.3 322.4 306.3 291.7 278.4 266.3 255.2 245.0 235.6 15 546.9 437.5 364.6 345.4 328.1 812.5 298.3 285.3 273.4 266.5 252.4 16 583.3 466.7 388.9 368.4 350.0 333.3 318.2 304.4 291.7 280.0269.2 |1| DIAMETER IN INCHES. IS 1 " 1 fl 54 60 66 72 78 84 90 96 102 108 120 h.2 rt t 16.2 1476 IsTs 1272 1172 Io74 977 Ti ~87~6 ~87l 7~3 2 32.4 29.2 26.5 24.3 22.4 20.8 19 '.4 18.2 17.2 16.2 14 '.6 3 48.6 43.7 39.8 36.5 33.7 31.3 29.2 27.3 25.7 24.3 21.9 4 64.8 58.3 53.0 48.6 44.9 41.7 38.9 36.5 34.3 32.4 29.2 5 81.0 72.9 66.3 60.8 56.1 52.1 48.6 45.6 42.9 40.5 36.5 6 97.2 87.5 79.5 72.9 67.3 62.5 58.3 54.7 51.5 48.6 43.8 7 113.4 102.1 92.8 85.1 78.5 72.9 68.1 63.8 60.0 56.7 51.0 8 129.6 116.7 106.1 97.2 89.7 83.3 77.8 72.9 68.6 64.8 58.3 9 145.8 131.2 119.3 109.4 101.0 93.8 87.5 82.0 77.2 72.9 65.6 10 162.0 145.8 132.6 121.5 112.2 104.2 97.2 91.1 85.8 81.0 72.9 11 178.2 160.4 145.8 133.7 123.4 114.6 106.9 100.3 94.4 89.1 80.2 12 194.4 175.C 159.1 145.8 134.6 125.0 116.7 109.4 102.9 97.2 87.6 13 210.7 189.6 172.4 158. C 145.8 135.4 126.4 118. S llt.fi 105.3 94.8 14 226. S 204. S 185.6 170.1 157.1 145.8 136.1 127.6 120.1 113.4 102.1 15 243.1 218. r 198. J 182.1 168.2 156. S 145.8 136.7 128.7 121. C 109.4 16 259.2 233. 1 212.1 194.4 179. J 166.7 155.6 145.8 137.2 129.6 116.7 ,. NATIONAL TUBE COMPANY. The preceding table has been computed for externally- fired boilers, with longitudinal seams double-riveted and having an efficiency of 0.7. A factor of safety of 5.5 has been assumed for steel of 55,000 Ibs. tensile strength. SIZES OF CHIMNEYS FOR STEAM BOILERS. BY WILLIAM KENT, M. E. The accompanying tabe of sizes of chimneys for various horse powers of boilers is based on the following data: . 1. The draught power of the chimney varies as the square root of the height* 2. The retarding of the ascending gases by friction may be considered as equivalent to a diminution of the area of the chimney, or to a lining of the chimney by a layer of gas which has no velocity. The thickness of this lining is assumed to be two inches for all chimneys, or the diminution of area equal to the perimeter X two inches (neglecting the overlapping of the corners of the lining). Expressed algebraically, let D diameter, A area, E= effective area. For square chimneys, E = D 9 3% = ^ ~ . ^ For round chimneys, E= n( D* ^ \= ^4 0.592 |/^ For simplifying calculations, the coefficient of |/ A may be taken as 0.6 for both square and round chimneys, and the formula becomes E = A 0.6 V~A- 3. The power varies directly as this effective area E. 4. A chimney 80 feet high, 42 inches diameter, has been found to be sufficient to cause a rate of combustion NATIONAL TUBE COMPANY. of 120 pounds of coal per hour per square foot of area of chimney, or if the grate area is to the chimney area as 8 to 1, a combustion of 15 pounds of coal per square foot of grate per hour. This is fair practice for a boiler of modern type, in which flues, or tubes are of moderate diameter, gas passages circuitous, and heating surface extensive in proportion to rate of combustion, so as to cool the chimney gases to 400 or 500 Fahr. and produce high economy. 5. A chimney should be proportioned so as to be capa- ble of giving sufficient draught to cause the boiler to de- velop much more than' its rated power, in case of emerg- encies, or to cause the combustion of 5 pounds of fuel per rated horse-power of boiler per hour. Conditions 4 and 5 being assumed, the 80 feet X 42 in- ches chimney, 9.62 square feet area, will cause the com- bustion of 9.62 X 120 = 1154.4 pounds of coal per hour, or at 5 pounds of coal per horse-power per hour, is rightly proportioned for 231 horse-power of boilers. The power of the chimney varying directly as the ef- fective area, JS, and as the square root of the height, h, the formula for horse-power of boiler for a given size of chimney will take the form, HP. = CE \/ h, in which C is a constant. For the 80' X 42" chimney ,**&& t \/ A =7.76 square feet. V~h= 8.944 feet. Substituting these values in the formula it becomes 231 = Cx 7.76 X 8.944, whence C- 3.33, NATIONAL TUBE COMPANY. and the formula for horse-power is HP. = 3.33 E \/~7T, or, HP. = 3.33 (,40.6 If the horse-power of boiler is given, to find the size of chimney, the height being assumed, 0.3 HP. For round chimneys, diameter of chimney = Diam. of ^ + 4". For square chimneys, side of chimney |/ E -f- 4". In the formulae and table no account has been taken of the difference which is believed by some authorities to exist in the efficiencies of round and square chimneys of equal area, nor of the differences of friction and of rate of cooling of the gases in -iron and in brick chimneys. Should experimental data of these differences, or of the effect of infiltration of air into brick chimneys, be ob- tained in future, the formulae and table may be corrected accordingly. NATIONAL TUBE COMPANY. ivalent quare imney. ofSquare inches S FOR ST (KENT.) (Assuming 1 H SIZE OF Equ S Chi ide J II p5 I**) > w<. SJSSSS y -bs AIR. NATIONAL TUBE COMPANY. AIR. Air consists of a mechanical mixture of the two gases oxygen and nitrogen in the ratio of 20.7 parts of the former to 79.3 of the latter by volume, and 23 of the for- mer to 77 of the latter by weight. In its natural state it contains small quantities of various substances, such as moisture, carbon dioxide, CO 2 , the lately discovered ele- ment argon, etc. The weight of dry air at 32 F. and atmospheric pressure (14.7 Ibs. per sq. in.) is 0.0807 Ibs. per cu. ft.; from which the volume of one pound=12.4 cu. ft. At other tem- peratures and pressures its weight in Ibs. per cu. ft. is ^~459^+t' * n wl " c k ^reading of barometer in inches and ^temperature F. The absolute zero of temperature, on the Fahr. scale is 492 below 32, or 460F. The absolute temperature then is obtained by adding 460 to the temperature as read from the Fahr. scale. Thus 60F. = 60 + 460 =520 absolute; and 20F.= 20-f460=440 absolute. Mechanical equivalent of heat. Heat energy and me- chanical energy are mutually convertible, that is, a unit of heat requires for its production, and produces by its disappearance, a definite amount of mechanical energy, namely, 778 foot-pounds of work for each British ther- mal unit. Boyle's law states that the product of the pressure and volume of a portion of gas is constant so long as the temperature is constant, that \s,pv=.c, in which p= pres- sure in Ibs. per sq. ft. and z/=:volume in cu. ft. For air at 32F,, this constant quantity is 26,200 foot-pounds, or pv=2Q,2QQ ft. Ibs. Charles' and Gay Lussac's law states that when the pres- sure is constant all gases expand alike for the same in- crease of temperature. The amount of this expansion NATIONAL TUBE COMPANY. between 32 and 212F, is 0.365 of the original volume: and for each degree it equals 0.365-^180=0.00203. Simi- liarly, when the volume remains constant the pressure varies in the above ratio. Combining Boyle's and diaries' laws we see that the pro- duct of the pressure and volume of a portion of gas is proportional to the absolute temperature. Thus, -j~ , in which p and ^^absolute pressures (that is pres- sures above a vacuum) in Ibs. per sq. ft.; v and v^ vol- umes in cu. ft.; T and 7\=absolute temperatures. Transforming the above equation and substituting 32 for 7\ and 26,200 for p^, we get =53.2 T. The specific heat of a gas is the quantity of heat, in heat units, necessary to raise the temperature of one pound of the gas through one degree of temperature. The specific heat of air at constant pressure is c p =0.238 and at constant volume is c v =0.169 British thermal unit. Adiabatic expansion or compression of a gas means that the gas is expanded or compressed without transmission of heat to or from the gas. This would be the case were the expansion or compression to take place in an abso- lutely non-conducting cylinder, in which case the tem- perature, pressure and volume would vary as indicated by the following formulae. v 2 /PA0.71. p. /vAl.41. T_,_/vA0.41. vI = VpV Pi-^v,' Ti-Vv./ v 2 _/TA2.46. p,_/T,\3.46. T^/pAO.Sg. v 1 \T,/ Pi7^T 1 / T x V pi y in which p lf Vj and T x =initial absolute pressure, vol- ume and absolute temperature and p 2 , v 2 and T 2 =final absolute pressure, volume and absolute temperature of the gas. D 166 NATIONAL TUBE COMPANY. Table for Adiabitic Compression or Expansion of Air. (PROC., INST. M. E., Jan. 1881, p. 123.) Absolute Pressure. Absolute Temperature. Volume. p a P 1 T 2 Ti V, V 2 ? " P 2 T, T7 "v; "vT 1.2 8.33 1.054 .948 1.138 8.79 1.4 7.14 1.102 .907 1.270 .788 1.6 .625 1.146 .873 1.396 .716 1.8 .556 1.186 .843 1.518 .659 2.0 .500 1.222 .818 1.636 .611 2.2 .454 1.257 .796 1.750 .571 2.4 .417 1.289 .776 1.862 .537 2.6 .385 1.319 .758 1.971 .507 2.8 .357 1.348 .742 2.077 .481 3.0 .333 1.375 .727 . 2.182 .458 3.2 .312 1.401 .714 2.284 .438 3.4 .294 1.426 .701 2.384 .419 3.6 .278 1.450 .690 2.483 .403 3.8 .263 1.473 .679 2.580 .388 4.0 .250 1.495 .669 2.676 .374 4.2 .238 1.516 .660 2.770 .361 4.4 .227 1.537 .651 2.863 .349 4.6 .217 1.557 .642 2.955 .338 4.8 .208 1.576 .635 3.046 .328 5.0 .200 1.595 .627 3.135 .319 6.0 .167 1.681 .595 3.569 .280 7.0 .143 1.758 .569 3.981 .251 8.0 .125 1.828 .547 4.377 .228 9.0 .111 1.891 .529 4.759 .210 10.0 .100 1.950 .513 5.129 .195 "Work of adiabatic compression of air. If air is compressed from a volume v t and pressure p l to a volume v 2 and pressure p a , in a non-conducting cylinder without clear- ance, the work involved in delivering one pound is as follows: Work of compression = 2.46 p t Vj [(v^) ' 41 " 1 ] = NATIONAL TUBE COMPANY. 167 Work of expulsion = p a v 3 = p^ (?) - 29 . Total work is the sum of the work of compression and expulsion less the work, p^, of the atmosphere done on the piston during admission, or Total work = 3.46 p lVl [(P?) ' 29 -!]. The mean effective pressure equals the total work -f- the initial volume, v x , or Isothermal expansion or compression of a gas means that the gas is expanded or compressed with the addition or rejection of sufficient heat to maintain the temperature constant. In this case, the temperature being constant, the pressure and volume will vary according to Boyle's law, namely pv=C, in which /^absolute pressure in Ibs. per sq. ft., v=. vol- ume in cu. ft., and C=a constant depending upon the temperature. For a temperature of 32 F. this constant is 26,200 ft. Ibs., and for isothermals corresponding to other temperatures it may be found from the formula 0=53.2 7", in which Z=the absolute temperature of the isothermal. Work of isothermal compression of air. If air is com- pressed from a volume Vj and pressure pj to a volume v a and pressure p 3 , in a cylinder without clearance, in such manner as to keep the temperature constant, the work involved in delivering one pound is as follows: Work of compression = PiV t log Xi. Work of expulsion = p a v a = pjV^ The total work then is the sum of the work of com- pression and expulsion less the work, p^, of the atmos- phere done on the piston during admission, or Total work = p x v x log e Xi + p^ p^ = p^ ^r* 168 NATIONAL TUBE COMPANY. In this formula Naperian, or hyperbolic, logarithms must be used. These may be obtained from the common logarithms by multiplying by the constant 2.303. The mean effective pressure equals the total work -f- the initial volume, v 1? or p x log ^i. Volumes Mean Pressures per Stroke, Temperatures, etc., in the Operation of Air-compression from from J Atmosphere and 60 Fahr. (F. RICHARDS, Am. Mach., March 30, 1893.) i z , A S.^aj _T3 V 5! ^-^ < ^ g a ^h s a < h G 1 2 3 4 5 6 7 1 1 1 60 1 1.068 .9363 .950 .96 .97 71 2 1.136 .8803 .910 1.87 1.91 80 3 1.204 .8305 .876 2.72 2.80 89 4 1.272 .7861 .840 3.53 3.67 98 5 1.340 .7462 .810 4.30 4.50 106 10 1.680 .5952 .690 7.62 8.27 145 15 2.020 .4950 .606 10.33 11.51 178 20 2.360 .4237 .543 12.62 14.40 207 25 2.700 .3703 .494 14.59 17.01 234 30 3.040 .3289 .453 16.34 19.40 252 35 3.381 .2957 .420 17.92 21.60 281 40 3.721 .2687 .393 19.32 23.66 302 45 4.061 .2462 .370 20.57 25.59 321 50 4.401 .2272 .350 21.69 27.39 339 55 4.741 .2109 .331 22.76 29.11 357 60 5.081 .1968 .314 23.78 30.75 375 65 5.423 .1844 .301 24.75 32.32 389 70 5.762 .1735 .288 25.67 33.83 405 75 6.102 .1639 .276 26.55 35.27 420 ! |&P-i $&& J Q 1000 28.88 14.20 97. 3. 1.8 2000 27.80 13.67 93. 7. 3.5 3000 26.76 13.16 90. 10. 5.2 4000 25.76 12.67 87. 13. 6.9 5000 24.79 12.20 84. 16. 8.5 6000 23.86 11.73 81. 19. 10.1 7000 22.97 11.30 78. 22. 11.6 8000 22 11 10.87 76. 24. 13.1 9000 21.29 10.46 73. 27! 14.6 10000 20.49 10.07 70. 30. 16.1 11000 19.72 9.70 68. 32. 17.6 12000 18.98 9.34 65. 35. 19.1 13000 18.27 8.98 63. 37. 20.6 14000 17.59 8.65 60. 40. 22.1 15000 16.93 8.32 58. 42. 23.5 180 NATIONAL TUBE COMPANY. Horse-power Required to Compress JOO Cubic Feet Free Air, from Atmospheric to Various Pressures. Gauge Pressure, Pounds. One-Stage jCompression, D. H. P. Gauge Pressure, Pounds. Two-Stage Compression, D. H. P. Four-Stage Compression, D H. P. 10 3.60 60 11.70 10.80 15 5.03 80 13.70 12.50 20 6.28 100 15.40 14.20 25 7.42 200 21.20 18.75 30 8.47 300 24.50 21.80 35 9.42 400 27.70 24.00 40 10.30 500 29.75 25.90 45 11.14 600 31.70 27.50 50 11.90 700 33.50 28.90 55 12.67 800 34.90 30.00 60 13.41 900 36.30 31.00 70 14.72 1000 37.80 31.80 80 15.94 1200 39.70 33.30 90 17.06 1600 43.00 35.65 100 18.15 2000 45.50 37.80 2500 39.06 3000 40.15 D. H. P., delivered horse-power at compressor cylinder. Capacity of Air Compressors. To ascertain the capacity of an air compressor in cubic feet of free air per minute, the common practice is to multiply the area of the intake cylinder by the feet of piston travel per minute. The free air capacity of the compressor divided by the number of atmospheres will give the volume of compressed air per minute. To ascertain the number of atmospheres at any given press- ure, add 14.7 Ibs. to the gauge pressure, divide this sum by 14.7 and the result will be the number of atmospheres. The above method of calculation, however, is only theoretical and these results are never obtained in actual practice even with compressors of the very best design. NATIONAL TUBE COMPANY. Allowances should be made for losses of various kinds, the principal loss being due to clearance spaces, but in machines of poor design and construction other consider- able losses occur through imperfect cooling, leakages past the piston and through the discharge valves, insufficient area and improper working of inlet valves, etc. We have seen compressors where the total loss was fully 25 to 30 per cent., whereas, 3 to 10 per cent, should be the maximum according to the size in compressors of proper design and construction. "Weights of Air , Vapor of Water, and Saturated Mixtures of Air and Vapor at Different Temperatures, under the Ordinary Atmospheric Pressure of 29.92 inches of Mercury. .0776 .0761 .0747 .0707 MIXTURES OF AIR SATURATED WITH VAPOR .044 .074 .118 .181 .267 .388 .556 .785 1.092 1.501 2.036 2.731 3.621 4.753 6.165 7.930 10.099 12.758 15.960 24.450 29.877 29.849 29.740 29.654 29.533 29.365 29.136 28.420 27.885 27.190 26.300 25.169 23.756 21.991 19.822 17.163 13.961 10.093 5.471 0.000 Weight of Cubic Foot of the Mixture of Air and Vapor. .0659 .0631 .000202 .000304 .086379 .084130 .080504 .077227 .075581 .073921 .072267 .070717 .067046 .065042 .063039 .060873 .058416 .055715 .049336 .045642 .041445 .00092 .00155 .00245 .00379 .00561 .00819 .01179 .01680 .02361 .03289 .04547 .06253 .08584 .11771 .16170 .22465 .31713 .46338 .71300 1.22643 182 NATIONAL TUBE COMPANY. FLOW OF AIR THROUGH AN ORIFICE FROM A RESERVOIR INTO THE ATMOSPHERE, In Cubic Feet of Free Air per Minute for Varying Diameters of Orifice and Gauge Pressures* Diam. of Orifice,! Inches. Receiver Gauge Pressure. 2 Ibs. 5 Ibs. 10 Ibs. 15 Ibs. 20 Ibs. 25 Ibs. 30 Ibs. 35 Ibs. 40 Ibs. 1 2 0.038 0.153 0.647 2.435 9.74 21.95 39. 61. 87.6 119.5 156. 242. 350. 625. 0.060 0.242 0.965 3.86 15.4 34.6 61.6 96.5 133. 189. 247. 384. 550. 985. 0.084 0.342 1.36 5.45 21.8 49. 87. 136. 196. 267. 350. 543. 780. 0.103 0.418 1.67 6.65 26.7 60. 107. 167. 240. 326. 427. 665. 960. 0.119 0.485 1.93 so!s 69. 123. 193. 277. 378. 494. 770. 0.133 0.54 2.16 8.6 34.5 77. 138. 216. 310. 422. 550. 860. 0.156 0.632 2.52 10. 40. 90. 161. 252. 362. 493. 645. 1000. 0.173 0.71 2.80 11.2 44.7 100. 179. 280. 400. 550. 715. 0.19 0.77 3.07 12.3 49. 110. 196. 307. 442. 601. 785. 45 Ibs. 50 Ibs. 60 Ibs. 70 Ibs. 80 Ibs. 90 Ibs. 100 Ibs. 125 Ibs. 150 Ibs. , 1 0.208 0.843 3.36 13.4 53.8 121. 215. 336. 482. 658. 860. 0.225 0.914 3.64 14.50 58.2 130. 232. 364. 522. 710. 930. 0.26 1.05 4.2 16.8 67. 151. 268. 420. 604. 622. 0.295 1.19 4.76 19.0 76. 171. 304. 476. 685. 930. 0.33 1.33 5.32 21.2 85. 191. 340. 532. 765. 1004. 0.364 1.47 5.87 23.50 94. 211. 376. 587. 843. 0.40 1.61 6.45 25.8 103. 231. 412. 645. 925. 0.486 1.97 7.85 31.4 125. 282. 502. 785. 0.57 2.33 9.25 37.2 148. 334. 596. 925. The above table was computed with the aid of Fliegner's equa- tions and have given results that approximate very closely to the conditions of actual practice. These equations are : Yorp^Zpa, G= 0.530 F ^J_; A>s/a, =1.060 pJ&yf&Li in which G = flow of air through the orifice in Ibs. per sec., F= area of orifice in square inches, pi = pressure in reservoir in Ibs. per sq. in., pa = pressure of atmosphere, 7\ = absolute temperature, Fahrenheit, of air in reservoir. ! NATIONAL TUBE COMPANY. FLOW OF AIR THROUGH PIPES.* The following new and original tables are based upon D'Arcy's formula adapted to the flow of elastic fluids, namely : Discharge in cubic ) = ^ feet per minute J r / X W-L As it is most convenient in the case of compressed air installations to deal with its equivalent volume of free air, i. e., air at atmospheric pressure, these tables have been specially calculated with this end in view. Table L Gives the theoretical volume of equivalent free air in cubic feet that will flow per minute at various pressures through straight pipes of various diameters, each 100 feet long, no re- duction of the final pressure being allowed for. The formula by which it is calculated is : Theoretical discharge ) c V d* /i of free air \~ 10 ^ Table II. Is a table of multipliers to be used in connec- tion with FI, as found by Table I., by which may be obtained the theoretical dis- charge of equivalent free air from pipes of various lengths up to 60,000 feet. It is calculated from Multiplier for length of pipe *Copyright 1899, by the Ingersoll-Sergeant Drill Co., New York, and is reprinted, by permission, from their catalogue of air compressors. 184 NATIONAL TUBE COMPANY. Table HI. Is a table of Multipliers to be used in con- nection with F t and M\ as found by Tables I. and II. , to obtain the real volume of discharge of equivalent free air, for reductions of the terminal pressure varying from 1 to 50 pounds. It is calculated from Multiplier for ) f% real discharge j f^ The notation used in above formulas is d actual diameter of pipe in inches. /^length of pipe in feet. c=o. co-efficient, (D'Arcy's) varying with the diameter of the pipe. z/ 1 =density of the air at initial gauge pressure. p and p 2 ~imtial and terminal gauge pressures. /! and/ 2 =factors to reduce compressed air at initial and terminal pressures p t and.p 2 to their corresponding volumes of free air. Tables are also added showing the increase in the length of pipe to be allowed for on account of the fric- tion caused by globe valves, elbows and tees. Several examples are worked out to show the method of using the tables for the solution of problems likely to be met with by the Engineer. NATIONAL TUBE COMPANY. 185 o* o O5 O O -r-c O *OgCOg7-.-OOOTTf.^-T HI o> -S il aj w| tt llii Ti'>0*0t-OOC30QOCT>0>OrHOtMOt : .g e oo TH eo ec < t- o ' 186 NATIONAL TUBE COMPANY. TABLE IL MULTIPLIERS FOR LENGTH OF PIPE. Length, Multipler Length, Multipler feet. Mi. feet. MX, 100 1.0 6000 0.129 200 0.707 7000 0.119 300 0.577 8000 0.112 400 0.500 9000 0.105 500 0.447 10000 0.100 600 0.408 12000 0.0912 750 0.365 15000 0.0817 1000 0.316 20000 0.0707 1250 0.283 25000 0.0632 1500 0.258 30000 0.0577 2000 0.224 35000 0.0534 2500 0.200 40000 0.0500 3000 0.183 45000 0.0471 3500 0.169 50000 0.0447 4000 0.158 55000 0.0426 5000 0.141 60000 0.0408 NATIONAL TUBE COMPANY. n4 i i? 8 8 81 eo" eo" co eo" eo" eo" co" eo" eo eo co co' co' eo' eo co' co' eo" eo" co eo co eo eo co eo co eo co eo eo s 53 e*d si si si si si si si si si si si si si l ~ I si si si si si si si si si si si si si si oi si si si si si si si si si si a* 50 si si st si si si si si si si si si si si si si si si si si si si si si si si si st o | gsg8gSq2SSSS^?3S8S5353ISS8|IS! co l_ d d o o d o' o' o d o o o d d d o o o o o o d o d o o I NATIONAL TUBE COMPANY. The formulas by which these tables have been calcu- lated show that the following factors enter into their composition : The diameter of the pipe ........ =d. The length of the pipe .......... =/. The initial and final pressures, [ , , or the reduction of pressure i l 2 The equivalent free air dis- charged . . . . ................ F. It being often required to find any one of these factors when the others are known, the following examples are given to show the method of procedure in each case. The simple statement of the formula, adapted to the tables becomes Free ai and by this all problems involving any of the above fac- tors may be solved, as shown in the examples. EXAMPLE 1. To find the volume of free air dis- charged. BXAMPI^E 2. To find the reduction of pressure. ' ' 3. To find a suitable diameter of pipe. " 4. To find the length of pipe which may be used. Example I Given a 3-inch pipe, 10,000 feet long, initial pressure 1,100 Ibs., terminal pressure 1,050 Ibs.; to find the volume of equivalent free air discharged. By Table I. Under 3" pipe and opposite 1,100 Ibs. we find 7^=2,906. By Table II. For 10,000 feet of pipe, Af ~Q.l. " " III. Under 50 Ibs. reduction and opposite 1,100 Ibs., J/ r =6.75. Then as shown ^=^tX^iX^r = 2,906x0.1X6.75 = l,961 cubic feet free air. NATIONAL TUBE COMPANY. 189 Example 2. Given a 4-inch pipe, 600 feet long, initial pressure 60 Ibs., required to discharge 1,200 cubic feet free air. What will be the reduction of pressure and the terminal pressure ? By Table I. Under 4" pipe and opposite 60 Ibs. , we find 7^=1,535. By Table II. For 600 feet, ^=0.408. Given F=1,2QO. By transposing the formula F 1,200 Mr = = = 1.9. ft X MI 1,535X0.408 Now by Table III., opposite 60 Ibs. pressure, and under 4 Ibs. reduction, we find M T 1.8Q, so that the terminal pressure will be slightly less than 604=56 pounds. Example 3. It is required to discharge 1000 cubic feet of free air from a pipe 2,500 feet long. The initial pres- sure is 100 Ibs. and the terminal pressure must not be less than 90 Ibs. What diameter of pipe should be used? Here we have given /^=1000. By Table II ^=0.200 for 2,500 feet. " " III Mr= 2.88 for p = 100 Ibs., and A=90 Ibs. By transposing the formula we get F 1,000 Ft= = = 1,736. M l ^M r 0.200X2.88 By Table I. looking along the line of 100 Ibs. pressure we see that the value of Ft for a 3}^-inch pipe is 1,370, and for a 4-inch pipe 1,904, so that this latter size of pipe would have to be used. Example 4, It is required to transmit 4,000 cubic feet of free air through a 6-inch pipe, the initial pressure being 200 Ibs. How far can it be carried with a reduc- tion of pressure of 10 Ibs. ? 190 NATIONAL TUBE COMPANY. Here we have given 7^=4,000. By Table I .F t =7,489 for 200 Ibs. pressure and 6" pipe. By Table III M r =3M for 200 Ibs. pressure and 10 Ibs. reduction . Then by transposing the formula : F 4,000 MI- = =0. 177 . F t xM r 7,489x3.01 Now by Table II. we see that this is an intermediate value of Mi between 3000 and 3500 feet, so that the dis- tance sought is approximately 3250 feet. GLOBE VALVES, TEES AND ELBOWS. The reduction of pressure produced by globe valves is the same as that caused by the following additional lengths of straight pipe, as calculated by the formula : 114 X diameter of pipe Additional length of pipe= l-f(3.6-f-diameter) Diameter of pipe. ) 1 lj 2 2j- 3 3j 4 5 6 inches. Addition'l length, j 2 4 7 10 13 16 20 28 36 feet. 7 8 10 12 15 18 20 22 24 ins. 44 53 70 88 115 143 162 181 200 ft. The reduction of pressure produced by elbows and tees is equal to f of that caused by globe valves. These additional lengths of pipe for globe valves, elbows and tees must be added in each case to the actual lengths of straight pipe. Thus, a 6-inch pipe, 500 feet long, with one globe valve, 2 elbows and three tees, would be equivalent to a straight pipe 500+36-f (2x24) +(3X24)=656 feet long, and 'this is the length which must be used in the tables as the value of MI. NATIONAL TUBE COMPANY. 191 GENERAL EXAMPLE* How much free air will a 6-inch pipe, 8,000 feet long, discharge under the following conditions, namely : Initial pressure 150 Ibs., terminal pressure 135 Ibs., with 2 globe valves, 3 elbows and 1 tee ? The equivalent length of straight pipe must first be found as follows : 8,000-f (2 X36)+ (3x24)+24=8, 168 feet. Now we have By Table I., /^ t =6,558 for 6 inch pipe and 150 Ibs. pressure. By Table II., ^/i=0.112 for 8000 feet, making by interpolation say 0.110 for 8,168 feet. By Table III., M r =3A2 forlSO Ibs. pressure and 14 Ibs. reduction, and 3.61 for 150 Ibs. pressure and 16 Ibs. reduction, so that by interpolation M r would be 3.51 for 15 Ibs. reduction of pres- sure. Then by the formula : Free air discharged =F=F t xMiXM T . ^6,558X0.11X3.51. =2,532 cubic feet equivalent free air per minute. FORMULA FOR FLOW OF AIR ESf PIPES. Mr. Richards, in Am. Mack., Dec. 27, 1894, published a new formula, viz. : V*L = 10,000^ B ' L JS* 10,000/!> in which V= actual volume of compressed air delivered, in cubic feet per minute (not the volume of free air, as NATIONAL TUBE COMPANY. in the other formula), Z,=length of pipe in feet, d in- ternal diameter of pipe in inches, p head or additional pressure in pounds per square inch required to maintain the flow, and a is a coefficient varying with the diameter of the pipe. Its value for different nominal diameters of wrought-iron pipe is given by Mr. Richards as follows : Diam. , Value Diam., Value Diam., Value Inches. of a. Inches. of a. Inches. of a. 1 .35 3^ .79 12 1.26 IM .44 4 .84 16 1.34 IK .50 5 .93 20 1.4 a .56 6 1. 24 1.45 2^ .65 8 1.125 3 .73 10 1.2 The following values of the fifth power of d and of d s a are given by Mr. Richards to facilitate calculations : Fifth Powers of d. Value of d s a. 1" .... 1 5" 6" 8" 10" 12" 16" 20" 3,125 7,776 32,768 100,000 248,&32 . 1,048,576 . . 3,200,000 . . 7,962,624 1"... 2" . . '. $':. 8 H" .35 1.34 3.80 18.08 63.47 177.4 413.2 . 860.2 5"... 2,918.75 6'... 7,776 8".. i 36,864 10" ... 120,000 12"... 313,528 16"... 1,405,091 20"... 4,480,000 24"... 11, 545,805 2"..!' .. 3.05 .. 7.59 32 g :: .. 97.65 .. 243 .. 525 . 1024 GAS. a ^ NATIONAL TUBE COMPANY. FLOW OF GAS IN PIPES. If d = diameter of pipe in inches ; Q = quantity of gas delivered in cu. ft. per hour ; / = length of pipe in yards ; h = pressure in inches of water column ; s ~ specific gravity of the gas, air being one ; then Q = 1000 Q=l3Wd*A/?^, r Si (Moles worth). (King's Treatise on Coal Gas.) Q '=1290 y- >(J - P< Gm > Am - Gas-light Jour., 1894). Mr. Gill's formula is said to be based on experimental data, and to make allowance for obstructions by tar, etc., that tend to check the flow of gas through the pipe. An experiment made by Mr. Klegg, in London, on a 4 inch pipe, 6 miles long, gave a discharge that cor- responds very closely with that computed by the use of Molesworth's formula. Maximum Supply of Gas through Pipes in cu. ft. per Hour, Specific Gravity being 0.45. Formula Q= tOOO|/ d *h + si. (MOLESWORTH.) LENGTH OF PIPE = 10 YARDS. Diameter of Pipe in Inches. Pressure by the Water-gauge in Inches. 0..1 0.2 0.3 0.4 0.5 0.6 0.7 34 70 192 394 689 1082 2231 0.8 0.9 1.0 1 4 2 13 26 73 149 260 411 843 18 37 103 211 368 581 1192 22 46 126 258 451 711 1460 26 53 145 298 521 821 1686 29 59 162 333 582 918 1886 31 64 187 365 638 1006 2066 36 74 205 422 737 1162 2385 38 79 218 447 781 1232 2530 41 83 230 471 823 1299 2667 NATIONAL TUBE COMPANY. Maximum Supply of Gas through Pipes, etc. (CONTINUED.) LENGTH OF PIPE _= 100 YARDS. Pressure by the Water-gauge in Inches. 735 1039 1270 1470 1080 1508 2133 2613 301^ 0.5 19 51 105 184 290 596 1042 1643 2416 3373 129 225 356 730 1276 2012 2958 4131. 1.0 26 73 149 260 411 843 1473 3416 3820 4184 4770 5333 5842 581 1193 42 115 236 412 649 LENGTH OF PIPE = 1000 YARDS. Diameter of Pipe in Inches. Pressure by the Water-gauge in Inches. 0.5 0.75 41 113 231 403 636 1306 2282 3600 1.0 47 130 267 466 735 1508 2635 4157 1.5 2.0 2.5 3.0 1* y 4 5 6 33 92 189 329 520 1067 1863 2939 58 159 327 571 900 1847 3227 5091 67 184 377 659 1039 2133 3727 5879 75 205 422 737 1162 2385 4167 6573 82 226 462 807 1273 2613 4564 7200 LENGTH OF PIPE = 5000 YARDS. s J u* 5 * Pressure by the Water-gauge in Inches. 1.0 1.5 2.0 2.5 3.0 2 3 4 5 6 7 8 9 10 12 119 329 675 1179 1859 2733 3816 5123 6667 10516 146 402 826 1443 2277 3347 4674 6274 8165 12880 169 465 955 1667 2629 3865 5397 7245 9428 14872 189 520 1067 1863 2939 4321 6034 8100 10541 16628 207 569 1168 2041 3220 4734 6610 8873 11547 18215 Where there is apt to be trouble from frost no pipe less than % inch should be used, and in extremely cold climates the smallest size should not be less than one inch. To provide for the resistance due to bends, one rule is to allow a pressure of 0.204 inch of water column for each right angled elbow. 1% NATIONAL TUBE COMPANY. Services for Burners* The following table is the standard of the principal gas works. It governs the size of pipe used by gas fitters for consumers, and will be found of value. Every service should have a T so placed as to permit of easily clearing the service pipe should any obstruction occur in it. Size Threads Weight Length Number of of Pipe. per Inch. per Foot. allowed. Burners. Feet. I/ 27 .243 2 1 M^ 18 .422 6 1 a/ 14 .561 20 3 l/ 14 -.845 30 6 3 UK 1.126 50 20 1 UK 1.670 70 35 l/ UK 2.258 100 60 IK 2.694 150 100 2 8 2 3.367 200 200 %y 8 5.773 300 300 3 8 7.547 450 450 4 8 10.728 600 750 TABLE OF AQUEOUS VAPOR Contained in 1000 Cubic Feet of Gas at Indicated Temperature Temp. Degrees Volume, Aqueous Vapor. Temp Degrees Volume, Aqueous Vapor. Temp. Degrees Volume, Aqueous Vapor. 40 9.33 54 15.33 68 24.06 41 9.73 55 15. 8( > 69 24.83 42 10.13 56 16.40 70 25.66 43 10.53 57 16.93 71 26.53 44 - 10.93 58 17.53 72 27.40 45 11.33 59 18.10 73 28.30 46 11.73 60 18. 6( 1 74 29.23 47 12.13 61 19.23 75 30.20 48 12.53 62 19. 8( ) 76 31.20 49 12.93 63 20.50 77 32.20 50 13.33 64 21.20 78 33.23 51 13.80 65 21.90 79 34.23 52 14.26 66 22.60 80 35.33 53 14.80 67 23. 3( ) 81 36.43 ^ M s NATIONAL TUBE COMPANY. 197 1 TABLE OF THE WEIGHTS OF GAS-HOLDERS. 1 In Pounds for every One-tenth of an Inch maximum Pressure, and for Diameter from 20 to 200 Feet. i S .o'og |j oooJ <~% ,0*0 Sg 20 164 53 1149 86 3026 119 5793 21 181 54 1193 87 3097 120 5891 22 198 55 1238 88 3168 121 5990 23 217 56 1283 89 3241 122 6089 24 236 57 1329 90 3314 123 6189 25 256 58 1376 91 3388 124 6290 26 277 59 1424 92 3463 125 6392 27 298 60 1473 93 3538 126 6495 28 321 61 1522 94 3615 127 6598 29 344 62 1573 95 3692 128 6703 30 368 63 1624 96 3770 129 6808 31 393 64 1676 97 3849 130 6914 32 419 65 1729 98 3929 131 7021 33 446 66 1782 99 4010 132 7128 34 473 67 1837 100 4091 133 7237 35 501 68 1892 101 4173 134 7346 36 530 69 1948 102 4256 135 7456 37 560 70 2005 103 4340 136 7567 38 591 71 2062 104 4425 137 7678 39 622 72 2121 105 4510 138 7791 40 655 73 2180 106 4597 139 7904 41 688 74 2240 107 4684 140 8018 42 723 75 2301 108 4772 141 8133 43 757 76 2363 109 4861 142 8249 44 792 -77 2426 110 4950 143 8366 45 828 78 2489 111 5041. 144 8483 46 866 79 2553 112 5132 145 8601 47 904 80 2618 113 5224 146 8720 48 943 81 2684 114 5317 147 8840 149 982 82 2751 115 5410 148 8961 50 1023 83 2818 116 5505 149 9083 51 1064 84 2887 117 5600 150 9205 52 1106 85 2956 118 5696 200 16364 - NATIONAL TUBE COMPANY. Example. Find the weight of a gas-holder 80 feet in diameter, the maximum pressure being 3.2 inches water column, or 32/10ths. In preceding table, opposite 80 in column of diameters read 2618, the weight for l/10th inch pressure. There- fore the weight required = 2618 X 32 = 83,776 Ibs. IRON AND STEEL. NATIONAL TUBE COMPANY. IRON AND STEEL. Wrought Iron is the product of the puddling process. It is made in a reverberatory furnace by melting pig iron on a hearth of iron oxide, over which passes a reducing flame which causes the carbon to unite with the oxide during the mixing which the puddler gives it, and further causes a large portion of the impurities to enter the surrounding slag. As the impurities carbon, manganese, phosphorus, sulphur, silicon leave the molten iron, the melting point rises so that the iron becomes first viscous, then pasty. When it has been worked into a ball the puddler carries it, still at a welding heat, to the hammer or squeezer where the greater part of the slag which permeated it is expelled from the mass. The roughly shapen slab is then rolled into muck bar, which, when piled, rolled and re-rolled becomes the wrought iron of commerce. Steel is the malleable product of either the cementation process, the crucible, the converter or the open hearth furnace. Cementation is the earliest process that we know of for making steel, and was founded upon the fact that wrought iron if packed in charcoal and heated to a high temperature, while excluded from air, absorbs carbon. The process consisted in packing bars of wrought iron, of about ^ inch thickness, in charcoal, and then sealing up the vessel and keeping it at a yellow heat until the carbon had penetrated to the centres of the bars and converted them into steel. The carbon penetrates the bar at the rate of about } inch in 24 hours, and while the point of saturation of iron by carbon is about 1.50%, yet the average content of carbon by this process in the finished bars, is about 1% or lower. The use of steel made by this process was always limited because of the fact that it contained the old seams and slag [marks which everywhere crossed and NATIONAL TUBE COMPANY. 201 recrossed the iron, causing great trouble in the manu- facture of cutting tools. But by melting this steel (called also blister steel, because its surface was covered with blisters) in a covered crucible, the seams and fibres of slag all disappeared, and a homogeneous ingot was the result. But this was a long way to a steel ingot, and the pursuit of cheapness gave rise to the direct method of melting iron in a crucible, made for the purpose, together with the requisite carbon and other ingredients necessary for imparting hardness, toughness, etc. The molten iron absorbs the carbon very quickly and gives a product which approaches closely the merit of that produced by the older method. Up to the middle of the nineteenth century these two processes were the principal ones, yet they were too expensive for a product of general use, except for tools. About 1856, Sir Henry Bessemer completed his experi- ments and gave to the world his famous process. In this process the pig iron is melted and poured into a bottle shaped vessel. Air is then blown into it from the bottom, burning out, first the silicon, then the manganese and carbon, (the first two elements entering the slag, the last one going out of the mouth of the converter as gas) but not reducing either the phosphorus or sulphur. When the carbon is burned out a fact recognized by the color of the flame the vessel contains practically pure wrought iron, which becomes steel on the addition of sufficient carbon and manganese to give the requisite hardness and toughness to the cast. When the iron is melted in a Converter which has a silicon lining the process is called the Acid Bessemer, and the principal fuel to keep the bath liquid is silicon. If the iron is high in phosphorus and melted in a vessel lined with dolomite or magnesite the process is called the Basic Bessemer and phosphorus is the principal element of fuel. Following the introduction of Sir Henry Bessemer's process, William Siemans invented the regenerative 202 NATIONAL TUBE COMPANY. furnace, a furnace in which the heat of the waste gases passes through chambers checkered off with fire brick, which so obstruct the passage of the gases to the chimney as to make them give up their heat. The air and fuel gas entering the furnace is then passed through this hot checker work and highly heated, thus returning to the furnace a large part of the heat carried out before by the gases passing to the stack. In a furnace of similar con- struction Open Hearth Steel is made. Pig iron, steel scrap, wrought iron, and iron ore charged together, or separately, (all, one or any two of them) are rendered steet by burning out their impurities with an oxidizing flame. If the metal is melted on a hearth lined with sand, the carbon, manganese and silicon are burned out and the sulphur and phosphorus remain as before. This is the Acid Open Hearth Process. But if, on the other hand, the bottom is made of dolomite or magnesite, and lime is added to hold the phosphorus in the slag formed (as in the case of Basic Bessemer) the phosphorus, silicon, car- bon and manganese are burned out, and sulphur remains as before. This is the Basic Open Hearth process. We have, then, steel made by the following processes: 1st. Cementation. 2d. Crucible. 3rd. Bessemer, ] j> f Converter. 4th. Open Hearth, j R ^: [ Furnace. Standard Specifications for Special Open-Hearth Plate and Rivet Steel, as adopted by the Association of American Steel Manufacturers. Testing and Inspection (1). All tests and inspections shall be made at place of manufacture prior to shipment. Test Pieces (2). The tensile strength, limit of elasticity and ductility, shall be determined from a standard test NATIONAL TUBE COMPANY 203 piece cut from the finished material. The standard shape of the test piece for sheared plates shall be as shown by the following sketch : Piece to be of same thickness as the plate. On tests cut from other material the test piece may be either the same as for plates, or it may be planed or turned parallel throughout its entire length. The elon- gation shall be measured on an original length of 8 inches, except when the thickness of the finished material is 5-16 inch or less, in which case the elongation shall be measured in a length equal to sixteen times the thickness; and except in rounds of % inch or less in diameter, in which case the elongation shall be measured in a length equal to eight times the diameter of section tested. Four test pieces shall be taken from each melt^>f finished material ; two for tension and two for bending. Annealed Test Pieces (3). Material which is to be used without annealing or further treatment is to be tested in the condition in which it conies from the rolls. When material is to be annealed or otherwise treated before use, the specimen representing such material is to be similarly treated before testing. Marking (4). Every finished piece of steel shall be stamped with the melt number. Rivet steel may be shipped in bundles securely wired together, with the melt number on a metal tag attached. Finish (5). All plates shall be free from surface de- fects and have a workmanlike finish. NATIONAL TUBE COMPANY. Chemical Properties (6). Extra soft and [Maximum Phosphorous, .04 % Fire Box Steel. J " Sulphur. .04 % Flange or boiler ) " Phosphorous, .06 % Steel. J " Sulphur, .04 % Boiler Rivet ) " Phosphorous, .04 % Steel. f " Sulphur, .04 % Physical Properties (7). Steel shall be of four grades EXTRA SOFT, FIRE Box, FLANGE or BOILER, and BOILER RIVET STEEI*. Extra Soft Steel (8). Ultimate strength, 45,000 to 55,000 pounds per square inch. Elastic limit, not less than one-half the ultimate strength. Elongation, 28 per cent. Cold and Quench bends, 180 degrees flat on itself, without fracture on outside of bent portion. Fire Box Steel (9). Ultimate strength, 52,000 to 62,000 pounds per square inch. Elastic limit, not less than one-half the ultimate strength. Elongation 26 per cent. Cold and Quench bends, 180 degrees, flat on itself, without fracture on outside of bent portion. Flange or Boiler Steel (10). Ultimate strength, 52,000 to 62,000 pounds per square inch. Elastic fimit, not less than one-half the ultimate strength. Elongation, 25 per cent. Cold and Quench bends, 180 degrees flat on itself, without fracture on outside of bent portion. Boiler Rivet Steel (11). Steel for boiler rivets shall be made of the extra soft quality specified in paragraph No. 8. Variation When Ordered to Gauge (12). For all plates ordered to gauge, there will be permitted an average excess of weight over that corresponding to the dimen- sions on the order equal in amount to that specified in the following table, provided no plate shall be rejected for light gauge measuring .01" or less, below the ordered thickness. NATIONAL TUBE COMPANY. Table of Allowances for Overweight for Rectangular Plates J/4 Inch Thick and Heavier. NOTE. The weight of 1 cubic inch of rolled steel is taken at 0.2833 pounds. THICKNESS OF WIDTH OF PLATE. PLATE. Up to 75 in. 75 in. to 100 in. Over 100 in. Min.... 10 percent. 14 percent. 18 percent. 8 12 16 % 7 10 13 T 7 tf 6 8 10 5 7 9 M 4 2 6 2 8 2 Over % &A 5 6K Table of Allowances for Overweight for Rectangular Plates less than J/4 Inch in Thickness. THICKNESS OF PLATE. WIDTH OF PLATE. Up to 50 in. 50 in. and above. i^ in. up to -fa in. & f 3 * A " K " 10 per cent. 8K " 7 " 15 per cent. 12 10 Variation When Ordered to Weight (13). Plates 12^ Ibs. or heavier when ordered to weight, shall not average more variation than 2^ per cent. , either above or below the theoretical weight. Plates from 10 to 12^ Ibs., when ordered to weight, shall not average a greater variation than the following : Up to 75 inches wide, 2^ per cent., either above or below the theoretical weight. 75 inches and over, 5 per cent. , either above or below the theoretical weight. Plates under 10 Ibs. down to 5 Ibs. when ordered to weight shall not average more variation than 3 per cent, above or 5 per cent, below the theoretical weight. Plates under 5 Ibs. when ordered to weight shall not average more variation than 5 per cent, either above or below the theoretical weight. NATIONAL TUBE COMPANY. NATIONAL TUBE COMPANY. TENACITY OF METALS AT VARIOUS TEMPERATURES. Tensile Strength of Iron and Steel at High Temperatti res. James E. Howard's tests (Iron Age, April 10, 1890), shows that the tensile strength of steel diminishes as the tem- perature increases from until a minimum is reached between 200 and 300F., the total decrease being about 4,000 Ibs. per square inch in the softer steels and from 6,000. to 8,000 Ibs. in steels of over 80,000 Ibs. tensile strength. From this minimum point the strength in- creases up to a temperature of 400 to 650F. , the maxi- mum being reached earlier in the harder steels, the in- crease amounting to from 10,000 to 20,000 Ibs. per square inch above the minimum strength at from 200 to 300. From this maximum, the strength of all the steels decreases steadily at a rate approximating 10,000 Ibs. decrease per 100 increase of temperature. A strength of 20,000 Ibs. per square inch is still shown by 0.10 C. steel at about 1000 F., and by 0.60 to 1.00 C. steel at about 1600 F. The strength of wrought iron increases with tempera- ture from up to a maximum at from 400 to 600 F., the increase being from 8,000 to 10,000 Ibs. per square inch, and then decreases steadily till a strength of only 6,000 Ibs. per square inch is shown at 1,500F. Cast iron appears to maintain its strength, with a ten- dency to increase, until 900 is reached, beyond which temperature the strength gradually diminishes. Under the highest temperatures, 1,500 to 1,600 F., numerous cracks on the cylindrical surface of the specimen were developed prior to rupture. It is remarkable that cast iron, so much inferior in strength to the steels at atmos- pheric temperature, under the highest temperatures has nearly the same strength the high-temper steels then have. Strength of Iron and Steel Boiler-plate at High Tempera- tures. (Chas. Huston, Jour. K I. , 1877.) AVERAGE OF THREE TESTS OF EACH. Temperature F Charcoal iron plate, tensile strength, Ibs. . " " " contr. of area % Soft open-hearth steel, tensile strength, Ibs. " cpntr. % " Crucible steel, tensile strength, Ibs... " " " contr. % 55,366 26 54,600 47 64,000 925 65,343 21 64,350 33 21 NATIONAL TUBE COMPANY. Strength of Wrought Iron and Steel at High Temperatures. (Jour. F. /., cxii., 1881, p. 241.) Kollmann's experi- ments at Oberhausen included tests of the tensile strength of iron and steel at temperatures ranging between 70 and 2000 F. Three kinds of metal were tested, viz., fibrous iron having an ultimate tensile strength of 52,464 Ibs., an elastic strength of 38,280 Ibs., and an elongation of 17.5$; fine-grained iron having for the same elements values of 56,892 Ibs., 39,113 Ibs., and 20$; and Bessemer steel having values of 84,826 Ibs., 55,029 Ibs., and 14.5*. The mean ultimate tensile strength of each material ex- pressed in per cent, of that at ordinary atmospheric tem- perature is given in the following table, the fifth column of which exhibits, for purposes of comparison, the results of experiments carried on by a committee of the Frank- lin Institute in the years 1832-36. Temperature Degrees F. Fibrous Wrought Iron, p. c. Fine-grained Iron, per cent. Bessemer Steel, per cent. Franklin Institute, per cent. 100.0 100.0 100.0 96.0 100 100.0 100.0 100.0 102.0 200 100.0 100.0 100.0 105.0 300 97.0 100.0 100.0 106.0 400 95.5 100.0 100.0 106.0 500 92.5 98.5 98.5 104.0 600 88.5 95.5 92.0 99.5 700 81.5 90.0 68.0 92.5 800 67.5 77.5 44.0 75.5 900 44.5 51.5 36.5 53.5 1000 26.0 36.0 31.0 36.0 1100 20.0 30.5 26.5 1200 18.0 28.0 22.0 1300 16.5 23.0 18.0 1400 13.5 19.0 15.0 1500 10.0 15.5 12.0 1600 7.0 12.5 10.0 1700 5.5 10.5 8.5 1800 4.5 8.5 7.5 1900 3.5 7.0 6.5 2000 3.5 5.0 5.0 NATIONAL TUBE COMPANY. 209 MECHANICS OF MATERIALS RELATING TO TUBULAR CONSTRUCTION. STRENGTH OF MATERIALS. A tensile stress is produced in the walls of a cylindrical vessel, such as a pipe, tank, boiler, etc. when it contains a fluid such as water, steam or air, under pressure. The ultimate or breaking strength of a material is reached when the tensile stress equals its cohesive force, in which case the material is on the point of being ruptured. The working strength of a material is that fraction, or portion, of the ultimate or breaking strength that experi- ence has shown it is best to use in practice, in order to guard against failure due to unforeseen causes, such as defects and the possible action of unknown forces . The unit working strength of a material is the working strength of one square inch of cross section of that ma- terial. The factor of safety is the factor or number by which the ultimate strength is divided in order to obtain the working strength. The proper factor to use in any given case would depend upon the characteristics of the ma- terial and the nature of the forces, whether quiescent or impulsive. In tubular construction, reasonably free from vibration and shock, a factor of safety of from 5 to 6 should be ordinarily used for wrought iron and steel, and from 8 to 10 for cast iron. Where there is uncertainty as to the magnitude and nature of the forces acting, or where there is much vibration or shock, such as water hammer in steam pipes or the sudden stoppage of flow in a water pipe, these factors should be increased to from one and one-half to three or more times the values given, depend- ing upon the severity of the vibration or shock. It is best, when possible, to compute the straining ac~ tions of shocks, as for example the increase in fluid pres- sure in a long water pipe when the flow is more or less quickly checked, in which case they should be added to the normal straining action. Having provided for these abnormal forces, the ordinary factors of safety should then be used . Stress and Strain. Should the fluid pressure in a cylin- drical vessel be gradually increased from zero, it will be NATIONAL TUBE COMPANY. observed that the walls of the vessel will stretch, thus in- creasing its volume. The stretch of the material consti- tuting the walls is termed the strain due to the force tending to tear the material asunder. The molecular actions within the material which oppose the external forces, and which resist deformation, are termed stresses. An elastic material when deformed by a straining action recovers its original form when the straining action is removed; as, for example, spring steel, ivory, etc. A plastic material when deformed does not recover its original form when the straining action is removed; as, for example, lead, putty, etc. Elastic limit. Materials such as wrought iron and low carbon steel are elastic under some conditions and plastic under others. At ordinary atmospheric temperatures, these materials may be strained up to a point, termed the elastic limit, without suffering any permanent deforma- tion when the straining action is removed. Should, however, the elastic limit be exceeded, the ma- terial will but partially recover its original form when the straining action is removed, in which case it is said to have received a permanent deformation or set. Up to the elastic limit the strain is proportional to the stress, that is, strain -f- stress = a constant. Beyond the elastic limit this constant becomes ordinarily an in- creasing varible. The modulus of elasticity of a material is obtained by dividing the unit stress by the strain, for unit length. Shearing strength of a material When a cylindrical ves- sel, made up from plates, connected together in the usual manner by riveted joints, is subjected to a fluid pressure, the adjoining plates will tend to separate by sliding one upon the other, thus subjecting the material of the rivets to a shearing action. The ability of a rivet to resist this action is known as its shearing strength, and the stress created by snch action is called the shearing stress . Unit shearing strength of a material is the shearing strength of one square inch of cross -section of that ma- terial . NATIONAL TUBE COMPANY. 211 VALUES OF I (Moment of Inertia), AND S. (Section Modulus), FOR USUAL SECTIONS. SECTIONS. I S .<&-* z _bh 3 12 bh a 6 ' "*! i4P _bh 3 Min 36 24 ** Xd 4 Trd 8 =0.0491 d 4 32 =0.0982 d 3 ,-*..,, -r bh 3 b 1 li 1 3 I I 0.5h *'EBf 12 -<- 1=0.0491 (d 4 ^! 4 ) ,(<,,!.) : < b - J'"" t b^.+bn^^-b^' Min.=JL n 3 HH T bh^bjb.! 3 I 12 0.5h. x x Denotes position of neutral axis. Bending Moments and Deflections of Beams under Various 1 Systems of Loading. JF= total load. /= length of beam. 7=moment of inertia .Z?=modulus of elasticity. (1) Beam fixed at one end and loaded at the other. mp. 1- -> (2) Beam fixed at one end, and \ uniformly loaded. Maximum bending moment at point of support = Wl. Maximum shear at point of sup- Deflection =3^-7 Maximum bending moment at \ point of support^ Maximum shear at point of \ (3) Beam supported at both ends, single load in the middle '< / >' (4) Beam supported at both ends and uniformly loaded. W 1 d Maximum bending moment at middle of beam=-j- Maximum shear at points of Deflection= , ^H|f .... . j||b Maximum bending moment at middle of beam = g Maximum shear at points of (5) Beams supported at both ends, single unsymmetncal load. (6) Beam fixed at both ends and uniformly loaded. rtr I||L. ^ 1 _ a Maximum bending moment un- Maximum shear : at support Wb near a -y-; at other support _Wa Maximum deflection SSssT / ^^^ Maximum bending moment at Wl point of support= r^- Maximum shear at points of Wl* *// ; 4 NATIONAL TUBE COMPANY. 213 DEFLECTION AND STRENGTH OF PIPES TO RESIST BENDING ACTION. The bending moment of a force is obtained by multiplying the force, P, in pounds, by the lever arm, /, in inches, with which it acts. Thus in the case of a trolley pole the bending moment at the ground, G, is M=P 1, and at G l is M 1 =P1 1 . The deflection of a pipe or tube when loaded transversely, that is, so as to subject it to a bending moment, is the deformation in inches produced by the given loading, and is due, of course, to the elasticity of the materials constituting it. In case of a trolley pole the greatest deformation will be at the extreme top of the pole. For a horizontal pipe supported at equidistant points the greatest deflection will be midway between supports. The moment of inertia of a section is the sum of the products of each elementary area of the section by the square of its distance from an assumed axis of rotation. It is a necessary factor in formulae for the determination of deflection of structures considered as beams. The moment of resistance of cross-section of a beam is the moment that resists a bending action at that cross- section. The section modulus is the factor that when multiplied by the unit working strength of the material will give the moment of resistance of cross-section of a structure con- sidered as a beam. In every case when a beam, as for example a trolley pole or a horizontal pipe supported at points, is subjected to a bending action the following condition must exist at every cross-section, namely: Bending moment motnent 214 NATIONAL TUBE COMPANY. of resistance of cross-section=unit working strength of material X section modulus. Example J. A 4 inch steel pipe has one end firmly fixed in a wall so as to project horizontally a distance of 8 feet. Find the greatest safe load it will carry at the free end, also the deflection with this load. Solution : From the table of Standard Steam and Gas Pipe, we see that the outside and inside diameters are d=4.500 and d t = 4.026 inch. Assuming an ultimate strength of material = 60,000 Ibs. per sq. inch, and a factor of safety of 6, we get as a working unit strength 60,000^-6=10,000 Ibs. From the table of Section Moduli we get Section modulus =0.098 ) which multiplied by the unit working strength gives Moment of resistance^ / d i 4 \ V r> rking strengt / d i 4 e=980 I d 3 --- V d d 8 =(4.5) 3 =91.125 (see table of cubes). d x * (4.026) 4 log. =log. -- =4 log. 4.026 log. 4.5=4X0.6049 d 4.5 0.6532 = 1.7664, or = 58.4, the number whose d log. is 1.7664 Then moment of resistance =980 (91.1 58.4)=32,046 inch Ibs. NATIONAL TUBE COMPANY. 215 The bending moment at support = WL = W8X12 = 96 W inch Ibs. Since the bending moment equals the moment of resistance, then 96 W=32,046, or W=333 Ibs., the required load. For this style of loading (see table) the Wl 3 Deflection = - , In which W=333, the safe load as computed; I/ =96, the length of beam in inches; E=26,000,000. the modulus of elasticity; I = 0.049 (d 4 d t *) = 0.049 [ (4.5 4 (4.026) 4 ] = 7.21, the moment of inerta of cross-section. Substituting these values in above formula we get 333 X (96) 3 Deflection = 3 x 26>0 OQ,000 X 7.21 = 53 inch ' Example 2 A 10 inch standard lap welded steel pipe, carrying water, is suspended from the top of a tunnel, as shown in the figure, the points of support being spaced at a distance of 20 feet apart. Find the deflection, D, due to the weight of the pipe and its contained water, on the supposition that the pipe bears equally on all of its supports. Solution: From the table of Standard Steel Welded Pipe we get weight of pipe per ft. 40.06 Ibs., and weight of contained water per ft. =34. 13 Ibs., making a gross weight per foot of 74.2 Ibs., or for 20 feet a total weight of ap- proximately 1500 pounds. Since the pipe is assumed to run continuously from one support to another, the deflection will be greatest midway between supports, and will be the same as that for a beam B NATIONAL TUBE COMPANY. fixed at both ends and uniformly loaded. For this style of loading (see page 212) the Wl 3 Deflection , 384 El In which W=1500 pounds; . * 1^=20x12=240 inches; E= 26, 000,000, the modulus of elasticity; I = 0.049 (d 4 d x 4 ) = 0.049 [(10.75) 4 (10.02) 4 ] = 160, the moment of inertia of cross-section. Substituting these values in above formula we get 1500 X (240) 3 Deflection = 384 x 26,000,000 X 160 =0 ' 014 inch " In practice, where the usual rigid joints are used, it is often the case that a pipe does not bear equally upon all the hangers, and in cases of careless erecting or of shifting of hangers, the pipe may not receive any support from one or more of the hangers. Should each alternate hanger, in the above example, become inactive, owing to any cause, the maximum de- flection then would be that due to an unsupported length of 40 feet of pipe. An inspection of the formula will show that the deflection of a beam increases directly as the weight X (length)*, or, for uniformly loaded beams, since the weight increases directly as the length, as the (length)*. Since in this case the length is doubled, the deflection will be increased 16 fold (that is 2 4 ), or to an amount = 0.014X16=0.22 inch. In the same manner it can be shown that an unsup- ported portion of 60 feet in length will deflect or sag an amount = 0.014 X 3 4 = 1.13 inch. NATIONAL TUBE COMPANY. 217 Should the pipe be merely supported at the ends, and not straight and continuous from one support to another, then the conditions would be those of a simple beam uniformly loaded and supported at the ends. By comparing the deflection formulae for the case just considered and this case, it will appear tliat the deflection for this case will be- Jive times as great; or, for the three cases considered above, 0.07, 1.10 and 5.65 inches respec- tively . The maximum deflection, or sag, that should be permit- ted in practice will depend ordinarily upon the effective thickness of wall of pipe and the unit working strength of the material composing it . The effective thickness of pipe in any particular case will be the thickness remaining after deducting the depth of screw-thread (for wrought pipe with threaded ends for coupling or flange connections) plus a reasonable amount for the deterioration due to corrosion, or other causes; which amount will depend upon the nature of the service and the expected life of pipe. In every practical example the effective thickness of pipe should be used in applying all formulae relating to strength of pipe to resist either bending or bursting. STRESS DUE TO INTERNAL BURSTING PRESSURE, Owing to the difference in the nature of the stress occuring in thin and thick walls of cylinders, pipes, etc., when subjected to a fluid pressure, it will be necessary to divide them into two classes, namely, those having thin walls and those having thick walls. In the follow- ing discussion only those having thin walls will be con- sidered. NATIONAL TUBE COMPANY. Let d = internal diameter in inches ; t = thickness of cylinder wall in inches ; p = internal fluid pressure, Ibs. per sq. inch ; TT= 3.1416; f t = unit working strength in tension ; fc= " " " compression ; f s " " " " shear ; strength of joint, e = efficiency of joint, or strength of plate ' c = thickness of metal, in inches, allowed for wast- ing away due to corrosion, or other causes. STRENGTH OF THIN CYLINDERS TO RESIST BURSTING, The force tending to tear the plate along a line lying circumfer- entially around the cylinder, as, for ex- ample, along the sec- tion lying in the plane A B, will equal the fluid pressure exerted on one end of the cylinder, which equals the area of a cross-section of cylinder in square inches X in- ternal pressure per square inch, or Longitudinal bursting pressure ) *&* tending to rupture circumferentially f ^ P- This bursting pressure will be resisted by the tenacity of the metal whose cross-section lies in the plane A B, which equals the circumference, or distance around the cylinder, multiplied by the thickness of the metal. Hence Resistance to bursting pressure ) = T d t f tending to rupture circumferentially f Since the resistance to the bursting pressure must equal the pressure itself, we have Trd 2 dp 4 f 1 1 Trd t f t . = p, or t = ; p = . 4 4ft d NATIONAL TUBE COMPANY. 219 The force tending to tear the plate along a k 1-4 line extending longi- tudinally, as, for ex- ample, along the sec- tion lying in the plane C D, will equal the sum of the normal components of the fluid pressures on the inner surface of the cylinder, which it can be shown is the same as the fluid pressure on a surface equal to the length of the cylinder multiplied by its diameter, or d 1. We then have Transverse bursting pressure I = d 1 o Tending to rupture longitudinally J This bursting pressure will be resisted by the tenacity of the metal whose cross-section lies in the plane C D, which latter equals twice the length of cylinder multi- plied by the thickness of the metal. Hence Resistance to bursting pressure ) = 3 1 t f Tending to rupture longitudinally ) Since the resistance to the bursting pressure must equal the pressure itself, we have dp 2 f 1 1 2 1 1 f t = d 1 p, or t = ; p = . 2ft d From a comparison of the above formulae, it will be seen that the force due to a fluid pressure within a pipe, boiler, or other cylindrical vessel, that tends to cause rupture longitudinally is twice that which tends to cause rupture transversely, that is circumferentially or around the pipe. . From the above relations, then, it will appear that a pipe, or other cylindrical vessel having walls of uniform thickness, when subjected to a fluid pressure only, will always tend to rupture longitudinally. The strength at the joints, resisting rupture transversely, may be reduced by the cutting of threads or riveting to flanges, or other- wise, to an amount equal to one-half the strength of the NATIONAL TUBE COMPANY. metal of pipe in cross-section, without altering the ten- dency of the pipe to rupture longitudinally. Example J Find the safe working pressure and also the bursting pressure of a standard 10-inch lap-welded steel pipe, having plain ends, or welded heads. Solution: Assuming that the pipe is not subjected to shock or vibration, we will assume a unit working strength of material =10, 000 Ibs., which allows a factor of safety of 6 on the assumption that the ultimate tensile strength is 60,000 Ibs. per sq. inch. Then in the formula for the internal fluid pressure. Sfftt f t =10,000 Ibs., the unit' working strength of material; t = 0.366 inch, the thickness of wall of pipe; d =10.385, the diameter of pipe. Substituting these values we get 2 X 10.000 X 0.366 P= -- 10385 = 70o Ibs. per sq. in. The bursting pressure, on the above assumption, would be six times the working pressure, or Bursting pressure =705X6 =4, 230 Ibs. per sq. in. Example 2. Find the working ^pressure for the pipe given in example 1, when provision is made for wasting away of the metal by corrosion, or otherwise, so as to reduce the thickness of the walls by y& inch. Then t=0.366 0.125=0.241 inch, the thickness of wall after corrosion of y& inch has occurred, the other values remaining the same as before. Substituting in the form- ula for pressure we get 2 X 10,000 X 0,241 p = - = 465 Ibs. per sq. in. 10.385 In practice it is often necessary to provide, especially in steam and water pipes, for stresses due to vibration, shock, temperature changes and various other causes, in which case the factor of safety of six assumed in the above examples should be increased to from 8 to 15 for NATIONAL TUBE COMPANY. wrought pipe, depending upon the severity of these actions . Assuming a factor of safety of 12, the safe working pressure in the above examples would be for Example 1, 350 Ibs. per sq. in., and for example 2, 230 Ibs. per sq. inch. Example 3* Find the thickness of a mild steel seamless cylindrical receiver, 20 inches in diameter, to contain air at 2,000 Ibs. per sq. in. gauge pressure . Solution: Assuming a unit working strength of material of 12,000 Ibs. then in the formula for thickness, 2ft d 20, the diameter of receiver in inches; p 2,000, the internal pressure in Ibs. per sq. inch; f t 12,000, the working strength persq. in. of material; Substituting these values in the formula we get 20 X 2,000 In tubular construction, having longitudinal riveted joints intended to resist internal fluid pressure, the form- ulae for thickness of wall and for safe working pressure will become dp 2e f 1 1 t= - ; p = - ; 2e ft d In which d= diameter of vessel in inches; t= thickness of wall in inches; p=internal fluid pressure, Ibs. per sq. inch; f t =: unit working strength of material in tension; e=efficiency of riveted joint, from 0.6 to 0.8. To provide in practice for wasting away of the metal, due to corrosion, or other causes, the above formulae will become dp 2 ef t (t c) t= - -fc; p= -- . 3ef t d Or 222 NATIONAL TUBE COMPANY. Where c=reduction in the thickness, in inches, of the metal constituting the wall of the vessel, because of the wasting away of the metal in practice due to corrosion and other causes . Example 4 Find the thickness of plate for a 60-inch steam boiler, to carry 100 Ibs. gauge pressure, the longi- tudinal riveted joints having an efficiency of 0.7, the ultimate tensile strength of the material being 60,000 Ibs. per sq. inch. Solution: Assuming an actual factor of safety of five and allowing ^ inch for wasting away of plates during the life of the boiler, we have in the above formula for thickness of plate: d=60, the diameter of boiler in inches; p=100, the gauge pressure per sq. inch; f t =12,000, the unit working strength of material; e=0.7, the efficiency of longitudinal joint; c=0.125, the allowance for corrosion, etc. Substituting these values in the formula we get 60 X 100 t= SX 0.7 X 12,000 +0.185=0.48^1.. Example 5. Find the greatest steam pressure that could be carried by the boiler, in Example 4, when new, that is, before any wasting away of metal has occurred, all other conditions being the same. Solution: Making c = in the above equation, we get dp 2 e f 1 1 t = ; and p = ; 2ef t d Which are the general equations for the thickness, t, in inches and safe fluid pressure, p, in Ibs, per sq. inch, for pipes or other cylindrical vessels having longitudinal riveted joints. Substituting the values, given in Example 4, in the above formula for pressure, we get 2 X 0.7 X 12,000 X 0.48 p = = 135 Ibs. gauge. NATIONAL TUBE COMPANY. In Examples 4 and 5 an actual factor of safety at the longitudinal joints is assumed, which makes the apparent factor of safety, that is, the factor of safety on the plate itself, for the assumed conditions, =5-7-0.7=7.1. In practice an apparent factor of safety of 5 is often used, for double riveted longitudinal lap joints, resulting in an actual factor of safety of 5 X (0.68 to 0.72)= from 3.4 to 3.6. Very often no allowance is made for the wasting away of the metal, which fact in conjunction with the use of too small a factor of safety will account for a large number of the boiler explosions that have occurred in practice. STRENGTH OF CYLINDER ENDS OR HEADS. / The ends or heads of a cylindrical vessel intended to contain a fluid under pressure, should be de- signed so as to be as strong as the cylindrical part of the vessel. This can ordin- arily be best accomplished by giving the end the form of a portion of a hollow sphere, as shown in the figure, whose radius equals the diameter of the cylindrical part, in which case to be equally strong throughout the thickness should be the same as that of the cylindrical part. This is because of the fact that for a given internal fluid pressure, the stress created in the walls of a thin hollow cylinder will be the same as that created, for the same pressure, in the walls of a thin hollow sphere of double the diameter. The use of flat ends should be avoided, except for con- structions such as tube plates, where they are desirable because of constructional reasons and can be easily stayed . 224 NATIONAL TUBE COMPANY f HOLLOW, CYLINDRICAL, WROUGHT IRON PILLARS. BREAKING LOADS IN TONS. CALCULATED BY GORDON'S FORMULA (TRAUTWINE.) THICKNESS ^ INCH. OUTER DIAMETERS IN INCHES. CO OCCOJ>0T*<1000001005COI>OOOOC5 OOt~l>CO0aT*COOia<* ^THOOC^COt-OOTHCOSOO^OS^COt-^ DD1C10'*WOJTH000500J>C > 0O^CO S 00100SCOlOD0005TH^t-OiOOtOTH^}>?D ^ ^.CO COW 1 -(0050SCt'i>0?010>r5-*CO< ti (N 00 CO ^H 00 COO?Wi-HOOi0500t>DOl010^rt<^COC?0010^THCOCOCOC5C-JWrH TH ^OOS^COCOOTH1000WOOICCO^I>^05 0050000t-D10lO^^COCOWO?W^-lTH \M gSSS^SS&538gSS OOOOlxniO^^COCOWWWT-lr-li-lTHr-l ;? 8SSSS?SgSSSSSl eo^oje-^ ^eooqtsoiTH^iiHtHtH - S85Sgg5:gSS$38; 10 "* MCOOTe " H '-" H * SSSBSSSSS5iS^SSSS3 CO i>OOOSOTHCcoococ-rHC Q 1-4 T-t O O C 0002 OT-IC3 10 t NATIONAL TUBE COMPANY. 1 I 11 O OO T-H CO I T-l 1-1 W Ci o o o o o CO -i I O O5 OO SSS&cf fogs $ !S)cp . <2 CM OOlO CO CO ^t CD I>00 Oi-r-l c-co CO-^ > GOOT-(J>C O i>00 OOO NATIONAL TUBE COMPANY. c/5 S o 3| l g -- t3j Isis O O O O O OO OO 05 0-rH 03 CO "* 10 0i> D TH IO Cl CO *>TH to OS CO T*^ ^ to IC0 00 S <" S o > TH?O C?t O?t- OJt WCO COCO ^^ ^10 I II 1 -r O i> 00 J 230 NATIONAL TUBE COMPANY. WEIGHT OF RIVETS IN POUNDS PER JOO. Length from under head. One cubic ft. weighing 480 Ibs. Length M" K" H' %" y& 1" It/" iw Inches. Diam. Diam. Diam. Diam. Diam. Diam. Diam. Diam. IK 5.4 12.6 21.5 28.7 43.1 65.3 91.5 123. 1 ix 6.2 13.9 23.7 31.8 47.3 70.7 98.4 133. 1% 6.9 15.3 25.8 34.9 51.4 76.2 105. 142. 2 7.7 16.6 27.9 37.9 55.6 81.6 112. 150. 2^ 8.5 18.0 30.0 41.0 59.8 87.1 119. 159. 2V 9.2 19.4 32.2 44.1 63.0 92.5 126. 167. sg 10.0 20.7 34.3 47.1 68.1 98.0 133. 176. 3 10.8 22.1 36.4 50.2 72.3 103. 140. 184. 3K 11.5 23.5 38.6 53.3 76.5 109. 147. 193. 31^ 12.3 24.8 40.7 56.4 80.7 114. 154. 201. ^M 13.1 26.2 42.8 59.4 84.8 120. 161. 210. 4 13.8 27.5 45.0 62.5 89.0 125. 167. 218. 4K 14.6 28.9 47.1 65.6 93.2 131. 174. 227. 4/1> 15.4 30.3 49.2 68.6 97.4 136. 181. 236. ^M 16.2 31.6 51.4 71.7 102. 142. 188. 244. 5 16.9 33.0 53.5 74.8 106. 147. 195. 253. 5K 17.7 34.4 55.6 77.8 110. 153. 202. 261. 5i/ 18.4 35.7 57.7 80.9 114. 158. 209. 270. 5// 19.2 37.1 59.9 84.0 118. 163. 216. 278. 6 20.0 38.5 62.0 87.0 122. 169. 223. 287. 6 i^ 21.5 41.2 66.3 93.2 131. 180. 236. 304. 7 2 23.0 43.9 70.5 99.3 139. 191. 250. 321. 71^ 24.6 46.6 74.8 106. 147. 203. 264. 338. 8 26.1 49.4 79.0 112. 156. 213. 278. 355. gjy 27.6 52.1 83.3 118. 164. 223. 292. 372. 9 2 29.2 54.8 87.6 124. 173. 234. 306. 389. 9i/ 30.7 57.6 91.8 130. 181. 245. 319. 406. 10 32.2 60.3 96.1 136. 189. 256. 333. 423. 10^ 33.8 63.0 101. 142. 198. 267. 347. 440. 11 2 35.3 65.7 105. 148. 206. 278. 361. 457. 11/4 36.8 68.5 109. 155. 214. 289. 375. 474. 12 38.4 71.2 113. 161. 223. 300. 388. 491. Heads 1.8 5.7 10.9 13.4 22.2 38.0 57.0 82.0 ^QC^ j_^ NATIONAL TUBE COMPANY. WEIGHT IN POUNDS OF JOO BOLTS WITH SQUARE HEADS AND NUTS, One cubic foot weighing 480 Ibs. t J DIAMETER OF BOLT, INCHES. M A % A u % % 1 2 4 3 4 5* 4^ 5 h 6H 3* 9 10 11 12 13 14 15 16 17 18 19 20 4.0 4.4 4.7 5.1 5.4 5.8 6.1 6.8 7.5 8.2 8.9 9.6 10.3 11.0 11.7 12.4 13.1 6.8 7.3 7.8 8.4 8.9 9.5 10.0 11.1 12.2 13.2 14.3 15.4 16.5 17.6 18.6 19.7 20.8 10.6 11.3 12.0 12.6 13.3 14.0 14.7 16.0 17.4 18.7 20.0 21.4 22.8 24.1 25.9 27.7 29.5 33.1 36.7 40.4 44.0 15.0 16.1 17.2 18.2 19.2 20.2 21.2 23.2 25.2 27.2 29.1 31.2 33.1 35.1 37.1 39.1 41.0 45.0 49.0 53.0 57.0 23.9 25.1 26.3 27.7 29.0 30.4 31.8 34.7 37.5 40.2 43.0 45.7 48.4 51.2 54.0 56.7 59.4 64.8 70.3 75.8 81.3 86.7 92.2 97.7 103.1 108.6 114.1 119.5 125.0 40.5 42.7 44.8 47.0 49.2 51.4 53.5 57.9 62.3 66.7 71.0 75.4 79.8 84.1 88.5 92.9 97.2 106.0 114.7 123.5 132.2 140.7 149.2 157.6 166.1 174.6 183.1 191.5 200.0 70.0 73.1 76.2 79.3 82.4 85.5 88.7 95.0 101.2 107.5 113.7 120.0 126.2 132.5 138.7 145.0 151.2 163.7 176.2 188.7 201.0 213.4 225.9 238.3 250.8 263.2 275.6 288.1 300.5 m.s 124.7 128.9 137.4 145.8 159.2 167.7 176.1 184.6 193.0 201.4 209.9 218.3 240.2 257.1 273.9 290.0 307.7 324.5 341.4 358.3 375.2 392.0 408.9 425.8 iss'.o 196.0 207.0 218.0 229.0 240.0 251.0 262.0 273.0 284.0 295.0 317.0 339.0 360.0 382.0 404.0 426.0 448.0 470.0 492.0 514.0 536.0 558.0 Per in. addi- tional. 1.4 2.2 3.6 4.0 5.5 8.5 12.4 16.9 22.0 APPROXIMATE WEIGHT OF NUTS AND BOLT HEADS IN POUNDS. Diam. of Bolt in Inches X T 6 B % T 7 * -Jt % Weight of Hexagon ) Nut and Head j .017 .042 .057 .109 .128 .267 .43 Weight of Square! Nut and Head f .021 .049 .069 .120 .164 .320 .55 Diam. of Bolt in Inches % 1 1J4 1 1% 2 2^ Weight of Hexagon j Nut and Head. ...f .73 1.10 2.14 3.78 5.6 8.75 17.0 Weight of Square) Nut and Head ....f .88 1.81 2.56 4.42 7.0 10.5 21.0 } 232 NATIONAL TUBE COMPANY. Sizes and Weights of Hot Pressed Hexagon Nuts, The sizes are the usual manufacturers', not the Franklin Institute Standard. Both weights and sizes are for unfin shed Nuts. One cubic foot weighing 480 Ibs. Size of Bolt. Weight of 100 Nuts. Rough Hole. Thickness Of Nut. Short Dia- meter. Long Dia- meter. No. of Nuts in 100 Ibs. % 1.3 ft / M .58 8000. 5 2.4 ii 6 5/ .72 4170. 4.1 % M .87 2410. 6.8 It A % 1.01 1460. % 7.1 7 K % 1.01 1410. /4 9.8 TIT /4 l 1.15 1020. ft 14.0 % ft 1^ 1.30 710. 5/ / 14.7 ft % !^ 1.30 680. 5/ 19.1 TT % 1M 1.44 520. % 22.9 ft % IK 1.44 440. % 27.2 11 % 1M 1.59 370. % 39. 1? ^/ \5/ 1.73 256. % 44. 25 7/ ll/ 1.88 226. 50. ft 1 !^ 1.88 198. \ 57. % 1 !^ 2.02 176. 1 64. & ^l/ 13/ 2.02 156. 96. H 1M 2 2.31 104. i& 134. IT* 1M 2J/X 2.60 75. 1% 180. 1ft 11^ 2% 2.89 56. 1H 235. !^ 2% 3.18 42. 1 300. 370. 460. i I 1 3 3.46 3.75 4.04 33.4 26.7 21.5 2 450. 560. IS 2 33j 4.04 4.33 22.4 18.0 2>| 560. 2 2^ 4.33 17.7 2% 680. 2i/ 2M 4 4.62 14.7 810. 2}J 41^ 4.91 12.3 2?J 980. 2 T ff 2^ 4 k 5.20 10.2 3 1150. 2H 3 4% 5.48 8.7 1340. 2 1 5 3/^ 5 5.77 7.5 3/^ 1580. 3 S 3J^ 514 6.06 6.3 NATIONAL TUBE COMPANY. 233 Sizes and Weights of Hot Pressed Square Nuts. weights and sizes are for unfinished Nuts. One cubic foot weighing 480 Ibs. Size of Bolt. Weight of 100 Nuts. Rough Roll Thickness Of Nut. Side of Square Diagonal No. of Nuts in 100 Ibs 1.5 A K 1^ .71 6800. 2.9 ft /'8 .88 3480. % 4.9 H E /I 1.06 2050. Tff 7.7 H A ^ 1.24 1290. ^ 8.6 /^ K 1.24 1170. H 11.8 s s 1 1.41 850. 9 16.7 1 TV 11^ 1.59 600. % 17.7 A 5/ \y^ 1.59 570. % 22.8 1^ IK 1.77 440. 32.3 H M 1% 1.94 310. 39.8 H / 11^ 2.12 251. % 53. ft Jg 1^ 2.30 190. 7 /s 63. ^8 !M 2.47 159. 1 68. % 1 !M 2.47 146. . 1 94. -% 1 2 2.83 106. IL/ 103. 16 jr/ 2 2.83 97. 1H 137. if 1^ 2M 3.18 73. *K 145. IT* IK 2K 3.18 69. IK 186. IT* IK 2/^ 3.54 54. 1% 247. !A 1% 2M 3.89 41. IK 319. 1 6 !M 3 4.24 31.3 15 400. IA \S 3K 4.60 24.8 19^ */8 500. 620. 1 1% 1/Q sM 4.95 5.30 19.9 16.2 2 750. IT! 2 4 5.66 13.4 2/^ 780. \y^ 2/^ 4 5.66 12.8 2K 930. 2 2K 4K 6.01 10.7 2% 960. 2^ 2% 4M 6.01 10.4 1130. 2K 4^/ 6.36 8.9 2^ 1370. 2 T ff 2M 4^ 6.72 7.3 3 1610. 2 1.1 3 5 7.07 6.2 3K 2110. 2{| 3K 7.78 4.7 3>| 2750. 3i/| 3K 6 2 8.49 3.6 rr ' 234 NATIONAL TUBE COMPANY. STANDARD GAUGES. I THICKNESS IN DECIMALS OF AN INCH. rt o o ingham or Browne & United British Wash- burn & Trenton Stubs 0* Stubb's Iron Sharpe States Imperial Moen Co. Iron Co. Steel Wire * Wire ~^0 .50000 .500 6 46875 464 5 .43750 !432 .45 4 .'454 .46000 .40625 .400 .'3938 .40 3 .425 !40964 .37500 .372 .3625 .36 2 .380 .36480 .34375 .348 .3310 .33 .340 .32486 .31250 .324 .3065 .305 1 .300 .28930 .28125 .300 .2830 .285 !227 2 .284 .25763 .26562 .276 .2625 .265 .219 3 .259 .22942 .25000 .252 .2437 .245 .212 4 .238 .20431 .23437 .232 .2253 .225 .207 5 .220 .18194 .21875 .212 .2070 .205 .204 6 .203 .16202 .20312 .192 .1920 .190 .201 7 .180 .14428 .18750 .176 .1770 .175 .199 8 .165 .12849 .17187 .160 .1620 .160 .197 9 .148 .11443 .15625 .144 .1483 .145 .194 10 .134 .10189 .14062 .128 .1350 .130 .191 11 .120 .09074 .12500 .116 .1205 .1175 .188 12 .105 .08081 .10937 .104 .1055 .1050 .185 13 .095 .07196 .09375 .092 .0915 .0925 .182 14 .083 .06408 .07812 .080 .0800 .0800 .180 15 .072 .05707 .07031 .072 .0720 .0700 .178 16 .065 .05082 .06250 .064 .0625 .0610 .175 17 .058 .04526 .05625 .056 .0540 .0525 .172 18 .049 .04030 .05000 .048 .0475 .0450 .168 19 .042 .03589 .04375 .040 .0410 .0400 .164 20 .035 .03196 .03750 .036 .0348 .0350 .161 21 .032 .02846 .03437 .032 .0317 .0310 .157 22 .028 .02535 .03125 .028 .0286 .0280 .155 23 .025 .02257 .02812 .024 .0258 .0250 .153 24 .022 .02010 .02500 .022 .0230 .0225 .151 25 .020 .01790 .02187 .020 .0204 .0200 .148 26 .018 .01594 .01875 .018 .0181 .0180 .146 27 .016 .01419 .01719 .0164 .0173 .0170 .143 28 .014 .01264 .01562 .0148 .0162 .0160 .139 29 .013 .01126 .01406 .0136 .0150 .0150 .134 30 .012 .01002 .01250 .0124 .0140 .0140 .127 31 .010 .00893 .01094 .0116 .0132 .0130 .120 32 .009 .00795 .01016 .0108 .0128 .0120 .115 33 .008 .00708 .00938 .0100 .0118 .0110 .112 34 .007 .00630 .00859 .0092 .0104 .0100 .110 35 .005 00561 .00781 .0084 .0095 .0095 .108 36 .004 .00500 .00703 .0076 .0090 .0090 .106 37 .00445 .00664 .0068 .0085 .103 38 .00396 .00625 .0060 .0080 .101 39 .00353 .0075 .099 40 " .00314 .0070 .097 NATIONAL TUBE COMPANY. 235 DECIMALS OF AN INCH AND FOOT FOR EACH *V a o Decimals Decimals Decimals Decimals 5 *W r of an Inch. of a Foot. 1 aV & of an Inch. of a Foot. fa [ .015625 .0013 33 .515625 .0430 i .031250 .0026 17 .531250 .0443 , 3 .046875 .0039 35 .546875 .0456 T v .062500 .0052 T 9 * .562500 .0469 5 .078125 .0065 37 .578125 .0472 3 .093750 .0078 19 .593750 .0495 7 .109375 .0091 39 .609375 .0508 y& .125000 .0104 % .625000 .0521 3 .140625 .0117 41 .640625 .0534 5 .156250 .0130 21 .656250 .0547 1 1 .171875 .0143 43 .671875 .0560 T 3 ff .187500 .0156 H .687500 .0573 1 3 .203125 .0169 45 .703125 .0586 7 .218750 .0182 23 .718750 .0599 1 5 .234375 .0195 47 .734375 .0612 M .250000 .0208 % .750000 .0625 1 7 .265625 .0221 49 .765625 .0638 9 .281250 .0234 25 .781250 .0651 1 9 .296875 .0247 51 .796875 .0664 A .312500 .0260 ft .812500 .0677 2 1 .328125 .0273 53 .828125 .0690 11 .343750 .0286 27 .843750 .0703 2 3 .359375 .0299 55 .859375 .0716 M .375000 .0313 % .875000 .0729 2 5 .390625 .0326 57 .890625 .0742 13 .406250 .0339 29 .906250 .0755 2 7 .421875 .0352 59 .921875 .0768 .437500 .0365 if .937500 .0781 Tff 2 9 .453125 .0378 61 .953125 .0794 15 .468750 .0391 31 .968750 .0807 3 1 .484375 .0404 63 .984375 .0820 8 .500000 .0417 1 1.000000 .0833 DECIMALS OF A FOOT FOR EACH INCH. In Ft. [n. Ft. I i. Ft. n. Ft. n. Ft. In. Ft. 1 .0833 3 .2500 5 .4167 7 .5833 9 .7500 11 .9167 2 .1667 4 .3333 6 .5000 8 .6667 LO .8333 121.0000 ID , 236 NATIONAL TUBE COMPANY. WEIGHTS OF SHEETS AND PLATES OF STEEL, WROUGHT IRON, COPPER AND BRASS. BIRMINGHAM GAUGE. No. of Thickness WEIGHT PER SQUARE FOOT. Gauge. in Inches. Steel. Iron. Copper. Brass. 0000 .454 18.5232 18.16 20.5662 19.4312 000 .425 17.3400 17.00 19.2525 18.1900 00 .380 15.5040 15.20 17.2140 16.2640 .340 13.8720 13.60 15.4020 14.5520 1 .300 12.2400 12.00 13.5900 12.8400 2 .284 11.5872 11.36 12.8652 12.1552 3 .259 10.5672 10.36 11.7327 11.0852 4 .238 9.7104 9.52 10.7814 10.1864 5 .220 8.9760 8.80 9.966 9.4160 6 .203 8.2824 8.12 9.1959 8.6884 7 .180 7.3440 7.20 8.1540 7.7040 8 .165 6.7320 6.60 7.4745 7.0620 9 .148 6.0384 5.92 6.7044 6.3344 10 .134 5.4672 5.36 6.0702 5.7352 11 .120 4.8960 4.80 5.4360 5.1360 12 .109 4.4472 4.36 4.9377 4.6652 13 .095 3.8760 3.80 4.3035 4.0660 14 .083 3.3864 3.32 3.7599 3.5524 15 .072 2.9376 2.88 3.2616 3.0816 16 .065 2.6520 2.60 2.9445 2.7820 17 .058 8.3664 2.32 2.6274 2.4824 18 .049 1.9992 1.96 2.2197 2.0972 19 .042 1.7136 1.68 1.9026 1.7976 20 .035 1.4280 1.40 1.5855 1.4980 21 .032 1.3056 1.28 1.4496 1.3696 22 .028 1.1424 1.12 1.2684 1.1984 23 .025 1.0200 1.00 1.1325 1.0700 24 .022 .8976 .88 .9966 .9416 25 .020 .8160 .80 .9060 .8560 26 .018 .7344 .72 .8154 .7704 27 .016 .6528 .64 .7248 .6848 28 .014 .5712 .56 .6342 .5992 29 .013 .5304 .52 .5889 .5564 30 .012 .4896 .48 .5436 .5136 31 .010 .4080 .40 .4530 .4280 32 .009 .3672 .36 .4077 .3852 33 .008 .3264 .32 .3624 .3424 34 .007 .2856 .28 .3171 .2996 35 .005 .2040 .20 .2265 .2140 36 .004 .1632 .16 .1812 .1712 Specific Gravities Weight of a Cubic Ft. 1 In. 7.85 489.6 0.2833 7.70 480.0 0.2778 8.72 543.6 0.3146 8.24 513.6 0.2972 SL : $ gf^ ** NATIONAL TUBE COMPANY, 237 WEIGHTS OF SHEETS AND PLATES OF STEEL, WROUGHT IRON, COPPER AND BRASS. AMERICAN OR BROWNE & SHARPE GAUGE. No. of Gauge. Thickness n Inches. WEIGHT PER SQUARE FOOT. Steel. Iron. Copper. Brass. 0000 000 00 .460000 .409642 .364796 18.7680 16.7134 14.8837 18.4000 16.3857 14.5918 20.8380 18.5568 16.5253 19.6880 17.5327 15.6133 1 2 4 .324861 .289297 .257627 .229423 .204307 13.2543 11.8033 10.5112 9.3605 8.3357 12.9944 11.5719 10.3051 9.1769 8.1723 14.7162 13.1052 11.6705 10.3929 9.2551 13.9041 12.3819 11.0264 9.8193 8.7443 5 6 7 8 9 .181940 .162023 .144285 .128490 .114423 7.4232 6.6105 5.8868 5.2424 4.6685 7.2776 6.4809 5.7714 5.1396 4.5769 8.2419 7.3396 6.5361 5.8206 5.1834 7.7870 6.9346 6.1754 5.4994 4.8973 10 11 19 13 14 .101897 .090742 .080808 .071962 .064084 4.1574 3.7023 3.2970 2.9360 2.6146 4.0759 3.6297 3.2323 2.8785 2.5634 4.6159 4.1106 3.6606 3.2599 2.9030 4.3612 3.8838 3.4586 3.0800 2.7428 15 16 17 18 19 .057068 .050821 .045257 .040303 .035890 2.3284 2.0735 1.8465 1.6444 1.4643 2.2827 2.0328 1.8103 1.6121 1.4356 2.5852 2.3022 2.0501 1.8257 1.6258 2.4425 2.1751 1.9370 1.7250 1.5361 20 21 22 23 24 .031961 .028462 .025346 .022572 .020101 1.3040 1.1612 1.0341 .92094 .82012 1.2784 1.1385 1.0138 .90288 .80404 1.4478 1.2893 1.1482 1.0225 .91058 1.3679 1.2182 1.0848 .96608 .86032 25 26 27 28 29 .017900 .015941 .014195 .012641 .011257 .73032 .65039 .57916 .51575 .45929 .71600 .63764 .56780 .50564 .45028 .81087 .72213 .64303 .57264 .50994 .76612 .68227 .60755 .54103 .48180 30 31 32 33 34 .010025 .008928 .007950 .007080 .006305 .40902 .36426 .32436 .28886 .25724 .40100 .35712 .31800 .28320 .25220 .45413 .40444 .36014 .32072 .28562 .42907 .38212 .34026 .30302 .26985 35 36 .005615 .005000 .22909 .20400 .22460 .20000 .25436 .22650 .24032 .21400 238 NATIONAL TUBE COMPANY. WEIGHT OF PLATE IRON IN POUNDS PER LINEAL FOOT. (Based on 480 Ibs. per Cubic Foot. For Steel add 2 per cent.) g . THICKNESS IN INCHES. 51 T3 O M TV % ft X T 5 * X ft X 12 2.50 5.00 7.50 10.00 12.50 15.00 17.50 20.00 13 2.71 5.42 8.13 10.83 13.54 16.25 18.96 21.67 14 2.92 5.83 8.75 11.67 14.58 17.50 20.42 23.33 15 3 13 6.25 9.38 12.50 15.63 18.75 21.88 25.00 16 3.33 6.67 10.00 13.33 16.67 20.00 23.33 26.67 17 3.54 7.08 10.63 14.17 17.71 21.25 24.79 28.33 18 3.75 7.50 11.25 15.00 18.75 22.50 26.25 30.00 19 3.96 7.92 11.87 15.83 19.79 23.75 27.71 31.67 20 4.17 8.33 12.50 18.67 20.83 25.00 29.17 33.33 21 4.38 8.75 13.13 17.50 21.88 26.25 30.63 35.00 22 4.58 9.17 13.75 18.33 22.92 27.50 32.08 36.67 23 4.79 9.58 14.38 19.17 23.96 28.75 33.54 38.33 24 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 25 5.21 10.42 15. 62120.83 26.04 31.25 36.46 41.67 26 5.42 10.83 16.25 21.67 27.08 32.50 37.92 43.33 27 5.63 11.25 16.88 22.50 28.13 33.75 39.38 45.00 28 5.83 11.67 17.50 23.33 29.17 35.00 40.83 46.67 29 6.04 12.08 18.13 24.17 30.21 36.25 42.29 48.33 30 6.25 12.50 18.75 25.00 31.25 37.50 43.75 50.00 32 6.67 13.33 20.00 26.67 33.33 40.00 46.67 53.33 34 7.08 14.17 21.25 28.33 35.42 42.50 49.58 56.67 36 7.50 15.00 22.50 30.00 37.50 45.00 52.50 60.00 38 7.92 15.83 23.75 31.67 39.59 47.50 55.42 63.33 40 8.33 16.67 25.00 33.33 41.67 50.00 58.33 66.67 42 8.75 17.50 26.25 35.00 43.75 52.50 61.25 70.00 44 9.17 18.33 27.50 36.67 45.84 55.00 64.17 73.33 46 9.58 19.17 28.75 38.33 47.92 57.50 67.08 76.67 48 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 50 10.42 20.83 31.25 41.67 52.08 62.50 72.91 83.33 52 10.83 21.67 32.50 43.33 54.17 65.00 75.83 86.67 54 11.25 22.50 33.75 45.00 56.25 67.50 78.75 90.00 56 11.67 23.33 35.00 46.67 58.33 70.00 81.66 93.33 58 12.08 24.17 36.25 48.33 60.42 72.50 84.58 96.67 60 12.50 25.00 37.50 50.00 62.50 75.00 87.50 100.00 NATIONAL TUBE COMPANY. 239 WEIGHT OF PLATE IRON IN POUNDS PER LINEAL FOOT (CONTINUED.) c . ij THICKNESS IN INCHES. is r 9 * H H X H % if 1 12 22.50 25.00 27.50 30.00 32.50 35.00 37.50 40.00 13 24.38 27.08 29.79 32.50 35.21 37.92 40.63 43.33 14 26.25 29.17 32.08 35.00 37.92 40.83 43.75 46.67 15 28.13 31.25 34.38 37.50 40.63 43.75 46.88 50.00 16 30.00 33.33 36.67 40.00 43.33 46.67 50.00 53.33 17 31.88 35.42 38.96 42.50 46.05 49.59 53.13 56.67 18 33.75 37.50 41.25 45.00 48.75 52.50 56.25 60.00 19 35.67 39.58 43.54 47.50 51.45 55.41 59.37 63.33 20 37.50 41.67 45.83 50.00 54.17 58.33 62.50 66.67 21 39.38 43.75 48.13 52.50 56.88 61.25 65.63 70.00 22 41.25 45.83 50.42 55.00 59.58 64.17 68.75 73.33 23 43.13 47.92 52.71 57.50 62.30 67.09 71.88 76.67 24 45.00 50.00 55.00 60.00 65.00 70.00 75.00 80.00 ! 25 46.88 52.08 57.29 62.50 67.70 72.91 78.13 83.33 26 48.75 54.17 59.58 65.00 70.42 75.83 81.25 86.67 27 50.63 56.25 61.88 67.50 73.13 78.75 84.38 90.00 28 52.50 58.33 64.17 70.00 75.84 81.67 87.50 93.33 29 54.38 60.42 66.46 72.50 78.55 84.59 90.63 96.67 30 56.25 62.50 68.75 75.00 81.25 87.50 93.75 100.0 32 60.00 66.67 73.33 80.00 86.67 93.33 100.0 106.7 34 63.75 70.83 77.91 85.00 92.08 99.17 106.3 113.3 36 67.50 75.00 82.50 90.00 97.50 105.0 112.5 120.0 38 71.25 79.17 87.09 95.00 102.9 110.8 118.8 126.7 40 75.00 83.33 91.67 100.0 108.3 116.7 125.0 133.3 42 78.75 87.50 96.25 105.0 113.7 122.5 131.3 140.0 44 82.50 91.67 100.8 110.0 119.2 128.3 137.5 146.7 46 86.25 95.83 105.4 115.0 124.6 134.2 143.8 153.3 48 90.00 100.0 110.0 120.0 130.0 140.0 150.0 160.0 50 93.75 104.2 114.6 125.0 135.4 145.8 156.3 166.7 52 97.50 108.3 119.2 130.0 140.8 151.7 162.5 173.3 54 101.3 112.5 123.8 135.0 146.3 157.5 168.8 180.0 56 105.0 116.7 128.3 140.0 151.7 163.3 175.0 186.7 58 108.8 120.8 132.9 145.0 157.1 169.2 181.3 193.3 60 112.5 125.0 137.5 150.0 162.5 175.0 187.5 200.0 -; NATIONAL TUBE COMPANY. s ;f N - b n i ^looiNnwi^hjiiewng^oWJcioiWJB UI BIQ SUOT 'ssau'jpiqx H G < ^^!' c |! D ia^ N U^ a ff'iri'Ti"ifi r< P HEADS ,S2^x C ,^^ 5 Q Z < q Sno H n S-KW XHS.ftSS^ C/3 H Suo'q I " H D X uiBi'a H ^asBsas H ffi woqs ^ n ,a a S XSSS^SvS ;joq S saqouj |S||S||1||| ;B B9jy '?bT? c/5 Q JO B8JV < W Pf5 ffi ia JoqiptAV a o8888ooOOOO EH Q Z < PBILL Jo . t/3 H IB 'UIBIQ "- 1 O PQ qaui J9d oooo^^oooot- s P B9aqx JO "UIBIQ G ,^^ NATIONAL TUBE COMPANY. OF ST ED STATES, OR SEL UIBIQ SUO^I HH qsiuij 'ssaujpiqj, TUBIQ Suo^j bg ui pBsaqJL JO 100^ -b S ui Xpog ip JO B3J V jo JO 'UIBIQ ^H^ ^ WOOTT)-^-^TJ 3J4 3.04 7.25 21760 29000 36260 50760 72500 290000 4 ~ 3 3.50 9.62 28860 38500 48100 67350 96200 385000 NATIONAL TUBE COMPANY. When the greatest load that has to be sustained by a bolt is known, and the working strength per sq. in. of the material constituting it is determined, look in the proper column for the given load. Should the load sought be not found, then take the load next larger as found in the column, and opposite to it in the first col- umn read the required size of bolt. Effect of Initial Strain in Bolts. Suppose that bolts are used to connect two parts of a machine and that they are screwed up tightly before the effective load comes on the connected parts. Let P^ = the initial tension on a bolt due to screwing up, and P a = the load afterwards added. The greatest load may vary but little from P l or P 2 , according as the former or the latter is greater, or it may approach the value P l -f- P 2 , depending upon the rela- tive rigidity of the bolts and of the parts connected. Where rigid flanges are bolted together, metal to metal, it is probable that the extension of the bolts with any additional tension relieves the initial tension, and that the total tension is P x or P 2 , but in cases where elastic packing, as india rubber, is interposed, the extension of the bolts may very little affect the initial tension, and the total strain may be nearly P -j- P 2 - Since the latter assumption is more unfavorable to the resistance of the bolt, this contingency should usually be provided for. (See Unwin, " Elements of Machine Design" for demonstration.) WEIGHTS AND MEASURES, NATIONAL TUBE COMPANY. WEIGHTS AND MEASURES, AVOIRDUPOIS OR COMMERCIAL WEIGHT. UNITED STATES AND BRITISH. Grains. Ounces. Pounds. Hundred- weight. Gross Tons. 1. 0.002286 0.000143 0.00000128 0.000000176 437.5 1. 0.0625 0.00055804 0.00002790 7000. 16. I. 0.0089286 0.0004464 784000. 1792. 112. 1. 0.05 5680000. 35840. 2240. 20. 1. 1 pound avoirdupois = 1.215278 pounds troy. 1 net ton = 2000 pounds = 0.892857 gross tons. 1 pound troy = 0.82286 pounds avoirdupois. LINEAR MEASURE. UNITED STATES AND BRITISH. Inches. Feet. Yards. Rods. Miles. 1. 0.08333 0.02778 0.0050505 0.00001578 12. 1. 0.33333 0.0606061 0.00018939 36. 3. I. 0.1818182 0.00056818 198. 16.5 5.5 1. 0.003125 63360. 5280. 1760. 320. 1. GUNTER'S CHAIN MEASURE. USED IN SURVEYING. 1 link = 7.92 inches = 0.01 chain = 0.000125 mile. 1 chain = 100 links = 66 feet = 4 rods=0.0125 mile 1 mile = 80 chains = 8000 links. NATIONAL TUBE COMPANY. SQUARE OR SURFACE MEASURE, UNITED STATES AND BRITISH. Square Inches. Square Feet. Square Yards Square Rods. Acres. Square Miles. 006944 0007716 144 o linn 1296 g 1. 6.03306 0.0002066 39204 6272640 272.25 43560. 27878400. 30.25 4840. 3097600. 1. 160. 102400. 0.00625 1. 640. 6.00000977 0.0015625 1. 1 acre = 10 square chains. CUBIC MEASURE. 1728 cubic inches=l cubic foot, 27 cubic feet =1 cubic yard =46656 cubic inches, 1 cord wood =4 ft. X 4 ft. X 8 ft. =128 cubic feet, 1 perch of masonry=16.5 ft.Xl.5 ft.Xl ft. =24. 75 cubic feet, but is generally assumed to be 25 cubic feet. DRY MEASURE. UNITED STATES ONLY. Struck Bush. Pecks. Quarts. Pints. Gallons. Cubic Inch. 1 4 32. 64 8. 2150.4 1 8. 16 2. 537.6 1. 2 0.25 67.2 0.5 1 0.125 33.6 4. 8 1. 268.8 The United States standard unit for dry measure is the old English Winchester bushel, which contains 2,150.42 cubic inches, or 1.2445 cubic feet. The heaped bushel, the cone of which is 6 inches above the brim of the measure, contains 2,747.7 cubic inches. NATIONAL TUBE COMPANY. In New York a bushel contains 2,218. 2]cubic inches, or 1.2837 cubic feet, which is the same as the Imperial bushel of England. 33 .English or Imperial bushels are equal to 34.04 Winchester or United States bushels. LIQUID MEASURE. UNITED STATES ONLY. Cubic Inch. Pints. Quarts. Gallons. Barrels. Hogs- head. 28.875 1. 0.5 0.125 0.003968 57.75 2. 1. 0.25 0.007937 231. 8. 4. 1. 0.031746 7276.5 252. 126. 31.5 1. 0.5 14553.0 504. 252. 63. 2. 1. The British Imperial gallon = 1.20032 U. S. gallons. The United States standard unit for liquid measure is the gallon = 231 cu. in. = 8.33888 pounds, avoirdupois, of distilled water at 62 Fahr. The English standard is the Imperial gallon = 277.2738 cu. in. = 10 pounds, avoirdupois, of distilled water at 62 Fahr. NAUTICAL MEASURE. A knot or nautical mile = 1.1527 statute miles = 6086. feet = length of a minute of longitude of the earth at the equator, at the level of sea, as determined by U. S. Coast Survey. 3 knots = 1 league. SHIPPING MEASURE. 1 Register ton = 100 cubic feet. 1 U. S. Shipping ton =40 cubic feet. 1 British Shipping ton = 42 cubic feet. NATIONAL TUBE COMPANY. MEASURE OF WORK AND POWER. A unit of work = one foot pound, or a pressure of one pound exerted .through a space of one foot. A British Thermal unit = 778 foot pounds. f 33,000 foot pounds per minute, 550 foot pounds per second, 42.42 heat units per minute. A Horse Power = 4 Q ?()7 heat units per second> 746 watts, I 0.746 kilowatt. THE METRIC SYSTEM OF WEIGHTS AND MEASURES. In the Metric System, the Meter is the base of all the weights and measures which it employs. The Meter is the primary unit of length and was in- tended to be one-ten millionth part of the distance, measured on a meridian of the earth, from the equator to the pole, and equals about 39.37 inches. Upon the Meter are based the following primary units; the Square Meter the Are, the Cubic Meter or Stere the Liter, and the Gram. The Square Meter or Centare is the unit of measure for small surfaces. The Are is the unit of land measure ; this is a square whose side is ten meters in length, and which contains one hundred square meters or centares. The Cubic Meter, or Stere, is the unit of volume; this is a cube whose edge is one meter in length. The Liter is the unit of capacity ; this is the capacity of a cube whose edge is one tenth of a meter, that is, one decimeter in length. The Gram is the unit of weight ; this is the weight of distilled water at 4 centigrade, contained in a cube whose edge is the one hundredth part of a meter. From these primary units the higher and lower orders of units are derived decimally as follows : 250 NATIONAL TUBE COMPANY. Scheme of the Weights and Measures of the Metric System. Ratios Lengths Surface 5 Volumes Weights 1,000,000. Millier, or Tonneau 100 000 Quintal 10,000. 1 000. Myr'iameter Kil'ometer Myr'iagram Kil'oliter 100. 10 Hec'tometer Hect'are Hec'toliter Hec'togram I. Meter Are Ll'ter Gram 0.1 Dec'imeter Dec'iliter Dec'igram 0.01 001 Cen'timeter Mil'limeter Cen'tare Cen'tiliter Mil'liliter Cen'tigram It will be seen, from this table, that ten millimeters equal one centimeter, ten centimeters equal one deci- meter, and so on. Multiples and sub-multiples of the units, meter, liter and gram are expressed by the prefixes : Deka = 10 Deci = = 0.1 Hecto = 100 Centi = 0.01 Kilo = 1000 Milli = = 0.001 ABBREVIATIONS COMMONLY IN USE. mm, millimeter, m 8 , square meter, cm, centimeter, km 8 4 ' kilometer, dm, decimeter, mm 3 , cubic millimeter, m, meter, cm 3 ) " centimeter, km, kilc >meter. cc f mm 8 , square millimeter, dm 3 , " decimeter, cm 8 , " centimeter, m 3 , " meter, dm 8 , ' a, are ; ha, hectare ; cl, centiliter ; 1 , liter ; hi, hecto- liter ; s, stere ; mg, milligram ; eg, centigram ; g, gram; kg, kilo, or kilogram ; t, tonneau, or metric ton. NATIONAL TUBE COMPANY. METRIC AND U. S. CONVERSION TABLE. MEASURES OF LENGTH. METRIC TO U. S. 1 millimeter = 0.03937 inch. 1 centimeter = 0.3937 ." 1 meter = 39 . 37 inches. 1 " = 3.2808 feet. 1 kilometer = 0.6214 mile. U. S. TO METRIC. 1 inch =25.4 millimeters. 1 " =2.54 centimeters. 1 " = 0.254 meter. 1 foot = 0.3048 " 1 mile = 1.609 kilometers. MEASURES OF SURFACE. METRIC TO U. S. 1 sq. millimeter = 0.00155 sq. inch. 1 " centimeter == 0.155 " " 1 " meter =10.764 " feet. 1 " = 1.196 " yards. 1 hectare = 2.471 acres. 1 = 0.00386 sq. mile. 1 sq. kilometer = 0.3861 " U. S. TO METRIC. 1 sq. inch = 645.14 sq. millimeters. 1 " " = 6.452 " centimeters. 1 "foot = 0.0929" meter. 1 "yard = 0.8361 " 1 acre = 0.4047 hectares. 1 sq. mile = 259.00 " 1 ' " = 2.59 sq. kilometers. NATIONAL TUBE COMPANY. MEASURES OF VOLUME AND CAPACITY. METRIC TO U. S. 1 cu. centimeter 0.061 cu. inch. 1 " meter =35.316 " feet. 1 " = 1.308 " yards. 1 liter = 1 cu. decimeter = 61.023 cu. inch. LIQUID MEASURE. 1 liter = 1.0567 quart. 1 " = 0.2642 gallon. 1 cubic meter = 264.17 gallons. DRY MEASURE. 1 liter =0.908 quart. 1 hectoliter = 2.8375 bushels U. S. TO METRIC. 1 cu. inch = 16.39 cu. centimeters. 1 " foot = 0.0283 " meter. 1 " yard = 0.7645" 1 " foot = 28.32 liters. LIQUID MEASURE. 1 quart = 0.9463 liter. 1 gallon = 3.7854 liters. 1 " = 0.0038 cu. meter. DRY MEASURE. 1 quart = 1.1013 litres. 1 bushel = 0.3524 hectoliter. WEIGHTS. METRIC TO U. S. 1 milligram = 0.0154 grain. 1 gram = 15.432 grains. 1 kilogram = 2.2046 Ibs. (avoir.) 1 metric ton = 1.1023 net tons. 1 " " = 0.9842 gross ton. U. S. TO METRIC. 1 grain = 64.80 milligrams. 1 " = 0.0648 gram. 1 Ib. (avoir.) = 0.4536 kilogram. 1 net ton = 0.9076 metric ton. 1 gross ton = 1.0161 " tons. NATIONAL TUBE COMPANY. COMPOUND UNITS. METRIC TO UNITED STATES. 1 kilogram per meter = 0.6720 Ibs. per foot. 1 kilogram per sq. centimeter 14.223 Ibs. per sq. inch. 1 kilogram per sq. meter = 0.2048 Ibs. per sq. foot. kilogram per cubic meter = . 0624 Ibs. per cubic ft. kilogram-meter = 7.233 footpounds. chevel vapeur (metric H. P.)= 0.986 horse-power. kilo, watt =1.340 kilo, per chevel = 2.235 Ibs. per H. P. UNITED STATES TO METRIC. 1 Ib. per foot = 1.4882 kilograms per meter. 1 Ib. per sq. inch = 0.0703 kilo, per sq. centimeter. 1 Ib. per sq. foot = 4.8825 kilograms per sq. meter. 1 Ib. per cubic foot =16.0192 kilo, per cubic meter. 1 footpound = 0.1383 kilogram-meter % 1 horse-power = 1.014 che vel vapeur (metric H. P.) 1 " " =0.746 kilo watt. 1 Ib. per horse-power = 0.447 kilos per chevel. HEAT INTENSITY. Temp. Centigrade = (temp. Fahr. 32 W 9 \ Temp. Fahrenheit = (temp. C. X 5" 7+ 32. HEAT QUANTITY. A kilogram calorie =3.968 British thermal units. A pound calorie =1.8 " " A British thermal unit = 0.252 kilogram calorie A British thermal unit = 0.555 pound calorie. fir "^ 254 NATIONAL TUBE COMPANY. MECHANICAL, ELECTRICAL AND HEAT EQUIVALENTS. (H. W. LEONARD.) UNIT. EQUIVALENT VALUE IN OTHER UNITS 1,000 watt hours. 1 . 34 horse-power hours . 2,654,200 ft.-lbs. 3,600,000 joules. 3, 412 heat units. 1 K. W. 367,000 kilogram metres. Hour = 0.235 Ib. carbon oxidized with perfect efficiency. 3.53 Ibs. water evaporated from and at 212 F. 22.75 Ibs. of water raised from 62 to 212 F. 0.746 K. W. hours. 1,980,000 ft.-lbs. 2,545 heat-units. 273,740k. g. m. 1 H P 0.175 Ib. carbon oxidized with perfect Hour = efficiency. 2 . 64 Ibs. water evaporated from and at 212 F. 17.0 Ibs. water raised from 62 F. to 212 F. 1,000 watts. 1 . 34 horse-power . 2,654,200 ft.-lbs. per hour. 44,240 ft.-lbs. per minute. 1 Kilowatt 737. 3 ft.-lbs. per second. 3,412 heat-units per hour. 56.9 heat-units per minute. 0.948 heat-unit per second. 0.2275 Ib. carbon oxidized per hour. 3.53 Ibs. water evaporated per hour from and at 212 F. NATIONAL TUBE COMPANY. 255 MECHANICAL, ELECTRICAL AND HEAT EQUIVALENTS. (CONTINUED). UNIT. EQUIVALENT VALUE IN OTHER UNITS 1 H. P. = 746 watts. 0.746 K. W. 33,000 ft.-lbs. per minute. 550 ft.-lbs. per second. 2,545 heat-units per hour. 42.4 heat-units per minute. 0.707 heat units per second. 0.175 Ibs. carbon oxidized per hour. 2.64 Ibs. water evaporated per hour from and at 212 F. 1 Joule = 1 watt second . 0.000000278 K. W. hour. 0.102k. g. m. 0.0009477 heat- units. 0.7878 ft. -Ib. 1 Ft.-lb. 1.356 joules. 0.1383k. g. m. 0.000000377 K. W. hours. 0.001285 heat-units. 0. 0000005 H. P. hour. 1 Watt = 1 joule per second. 0. 00134 H. P. 3.412 heat-units per hour. 0.7373ft.-lb. per second. 0.0035 Ib. water evaporated per hour. 44.24 ft.-lbs. per minute. 1 Watt per sq. in. = 8.19 heat-units per square foot per minute. 6371 ft.-lbs. per square foot per minute. 0.193 H. P. per square foot. X ? A- 256 NATIONAL TUBE COMPANY. MECHANICAL, ELECTRICAL AND HEAT EQUIVALENTS. (CONTINUED). UNIT. EQUIVALENT VALUE IN OTHER UNITS. 1 Heat unit. 1,055 watt seconds. 778ft.-lbs. 107.6 kilogram metres. 0. 000293 K. W. hour. 0. 000393 H. P. hour. 0.0000688 Ib. carbon oxidized. 0.001036 Ib. water evaporated from and at 212 F. 1 Heat- unit, per Sq.ft. per min. = 0.122 watt per square inch. 0.0176 K. W. per square foot. 0.0236 H. P. per square foot. 1 Kilog- gram Metre = 7.888 ft.-lbs. 0. 00000365 H. P. hour. 0. 00000272 K. W. hour. 0.0093 heat-units. lib. Carbon Oxidized with perfect Efficiency 14,544 heat-units. 1.11 Ib. Anthracite coal oxidized. 2.5 Ibs. dry wood oxidized. 21 cubic feet illuminating-gas. 4.26 K. W. hours. 5.71 H. P. hours. 11,315,000 ft.-lbs. 15 Ibs. of water evaporated from and at 212 F. 1 Ib. Water Evapor- ted from and at 212 F.= 0.283 K. W. hour. 0.379H. P. hour. 965. 7 heat-units. 103,900k. g. m. 1,019,000 joules. 751,300 ft.-lbs. 0.0664 Ib. of carbon oxidized. ? MENSURATION, TRIGONOMETRY AND MATHEMATICAL TABLES. NATIONAL TUBE COMPANY. MENSURATION, TRIGONOMETRY AND MATHEMATICAL TABLES. MENSURATION. MENSURATION OF SURFACES. Area of any parallelogram = base X perpendicular height. . " " " triangle = base X K perpendicular height. " " " circle = (diameter) 2 X (0.7854, or approx. 11/14.) " " sector of circle = arc X 1/2 radius. " " segment of circle . area of sector of equal radius and arc less area of triangle. " " parabola = base X 2/3 height. " " ellipse = longest diameter X short- est diameter X 0.7854. " " cycloid = area of generating circle X3. " " any regular polygon = sum of its sides X per- pendicular from its cen- ter to one of its sides -r- 2. Surface of cylinder = area of both ends -f- (length X circumference.) " ' cone = area of base + (circum- ference of base X ^ slant height.) " " sphere = (diameter) 8 X (3. 1416, or approx. 22/7.) " " frustum = (sum of girt at both ends X K slant height) -f area of both ends. NATIONAL TUBE COMPANY. Surface of cylindrical ring = thickness of ring added to the inner diameter X by the thickness X 9. 8698. " " segment = height of segment X by whole circumference of sphere of which it is a part. AREA OF AN IRREGULAR PLANE SURFACE. Divide the surface into any number of parallel strips of equal widths, "d." Take the sum of the middle ordinates h l5 h s , etc., to h n , in- clusive ; then the sum of these middle ordinates, multi- plied by " d " will give the area required. The result, of course, is only approximate, the close- ness of the approximation depending upon the number of strips into which the surface is divided. Any degree of accuracy desired may be attained by making the number of strips sufficiently numerous. In practice it is usually best to determine the area of an irregular figure by the use of a planimeter, an instrument especially designed for measuring areas of plane figures. REGULAR POLYGONS. 1. To find the area of any regular polygon. Square one of its sides, and multiply this square by the corres- ponding number in the third column of the following table. 2. Having a side of a regular polygon, to find the radius of a circumscribing circle. Multiply the side by the corresponding number in the fourth column. 3. Having the radius of a circumscribing circle, to find the side of the inscribed regular polygon. Multiply the radius by the corresponding number in the fifth column. NATIONAL TUBE COMPANY. TABLE OF REGULAR POLYGONS. 1 Angle CO Name of Area Radius Side = contained "o Polygon. S 2 X = SX Rx between 6 two sides. 3 / Equilateral \ I triangle / .433 .5774 1.732 60 4 Square 1. .7071 1.4142 90 5 Pentagon 1.7205 .8507 1.1756 108 6 Hexagon 2.5891 1. 1. 120 7 Heptagon 3.6339 1.1524 .8678 128.57 8 Octagon 4.8284 1.3066 .7654 135 9 Nonagon 6.1818 1.4619 .684 140 10 Decagon 7.6942 1.618 .618 144 11 Undecagon 9.3656 1.7747 .5635 147.27 12 Dodecagon 11.1962 1.9319 .5176 150 In the above table S = side of polygon and R = radius of circumscribing circle. PROPERTIES OF THE CIRCLE. Diameter X 3.1416 = circumference. " X 0.8862 = side of an equivalent square. " X 0.7071 = side of an inscribed square. (Diameter) 3 X 0.7854 = area of circle. Radius X 6.2832 = circumference. Circumference -f- 3.1416 = diameter. The circle contains a greater area than any plane figure, bounded by an equal perimeter, or outline. The areas of circles are to each other as the squares of their diameter, radii or circumferences. Thus, a circle whose diameter is double that of another has four times the area of the other. NATIONAL TUBE COMPANY VOLUMES OF SOLIDS. Vol. of Cylinder = area of one end X length. " " Sphere = cube of diameter X 0.5236. " " Segment of sphere . (cube of the height -j- three times the square of radius of base X height) X 0.5236. " " Cone or pyramid. . . = area of base X % perpen- dicular height. *' " Frustum of cone. .. = (product of diameter of both ends -j- sum of their squares) X perpendicular height X 0.2618. " " Frustum of pyramid^ (sum of the areas of the two ends -J- square root of their product) X by % of the perpendicular height. ' ' " Wedge = area of base X % perpen- dicular height. " '* Frustum of wedge. . = % perpendicular height X sum of the areas of the two ends. " " Ring = (thickness -f- inner dia- meter) X square of the thickness X 2.4674. NATIONAL TUBE COMPANY. TRIGONOMETRICAL FORMULAE. EH Sine of Angle E A H = A E J} Cosine Cosecant AH A E EH AH A H EE[ E A AH E A EH TRIGONOMETRICAL EQUIVALENTS. Sin = Sin = cot Cos = V 1 sin 2 sin Cos = tan Cos = sin X cot sin Cot = Cot = Sec = Cosec = cos sin 1 tan 1 cos 1 Tan = Tan = cos 1 cot Vers =1 cos Covers = 1 sin Sin 2 + cos 2 = 1 NATIONAL TUBE COMPANY. FUNCTIONS OF SUM AND DIFFERENCE OF TWO ANGLES. Sin (x -}- y) = sin x cos y + cos x sin y Sin (x y) = sin x cos y cos x sin y Cos (x -f- y) = cos x cos y sin x sin y Cos (x y) = cos x cos y -j- s ^ n x si* 1 7 tan x -|- tan y all ( X ~T y) 1 { an x an y tan x tan y Tan (x y) = 1 + tan x tan y cot x cot y 1 cot x -|- cot y cot x cot y -f- 1 cot y cot x FUNCTIONS OF HALF AN ANGLE. Sin K z = + 4/ 1 ~ 2 COSZ Tan % z = + .i/ 1 - 0052 V 1 - SUMS AND DIFFERENCES OF FUNCTIONS. Sin (x + y) + sin (x y) = 2 sin x cos y Sin (x + y) sin (x y) = 2 cos x sin y Cos (x + y) -}- cos (x y) = 2 cos x cos y Cos (x y) cos (x -f- y) = 2 sin x sin y NATIONAL TUBE COMPANY. Then by making (x -f y) = A and (x y) = B, we have x = % (A -j- B) and y = y z (A B), whence Sin A + sin B = 2 sin % (A -f B) cos ^ (A B) Sin A sin B = 2 cos % (A -f B) sin % (A B) Cos A -f cos B = 2 cos % (A -f B) cos ^ (A B) Cos A cos B = 2 sin % (A -j- B) sin % (A B) Sin A -f sin B _ tan ^ (A + B) Sin A sin B " " Cos A + cos B _ Cos A cos B " ' tan cot (A B) (A + B) (A B) SOLUTION OF RIGHT TRIANGLE. Given A and c, to find B, a and b. B = 90 A ; A = c sin A ; b = c cos A. Given A and a, to find B, b and c. B = 90 A ; b = a cot A ; c = ^-^ . Given A and b, to find B, a and c. B = 90->_A; a = btanA;c = ^- Given c and a, to find A, B and b. Sin A = ~ ; B = 90 A ; b = a cot A. Given a and b, to find A, B and c. TanA=;-; B = 90 A ; c = a sin A' NATIONAL TUBE COMPANY. SOLUTION OF OBLIQUE TRIANGLE. LAW OF* SINES, sin A b sin B' sin B sinC' sin A sin~C LAW OF COSINES. a 3 = b 2 + c 2 2 b c cos A b 2 = a 2 -{- c 8 2 a c cos B c 2 a a 2 -|- b 2 2 a b cos C LAW OF TANGENTS. a b .__ tan % (A B) a + b a c a + c b c tan tan (A + B) (A C) (A + C) (B C) tan % (B + C) tan tan Given a, A and B, to find C, b and c. = 180 a sin B a sin C Given a, b and A, to find B, C and c. b sin A a sin C Sin B = ; C = 180 (A + B); c = NATIONAL TUBE COMPANY. Given a, b and C, to find A, B and c. b sin C a sin C * /TiTT* v r\ c = : , or = . , or =A/ a- + b 2 2 a bcosC. sin B sin A Given a, b and c, to find A, B and C . Sin K A =j/ (S ~ b) (S ~* C) ; in which S = % (a+b+c); b c Sin ab a b Tan % B = ,/(S a) (S C). V s(s-b) ' AREA OF A TRIANGLE. Area = J^ a c sin B, that is, the area of a triangle equals ^ the product of two sides multiplied by the sine of the included angle. Also area =|/S (8 a) (S b) ( S c); Where S = % (a -f- b + c). NATIONAL TUBE COMPANY. 267 ' MATHEMATICAL TABLES. 1 SINE. 89 88 87 86 85 0' 10' 20' 30' 40' 50' 60' i 2 3 4 0.00000 0.01745 0.03490 0.05234 0.06976 0.00291 0.02036 0.03781 0.05524 0.07266 0.00582 02327 0.04071 0.05814 0.07556 0.00873 0.02618 0.04362 0.06105 0.07846 0.01164 0.02908 0.04653 0.06395 0.08136 0.01454 0.03199 0.04943 0.06685 0.08426 0.01745 0.08490 0.05234 0.06976 0.08716 5 8 9 0.08716 0.10453 0.12187 0.13917 0.15643 0.09005 0.10742 0.12476 0.14205 0.15931 0.09295 0.11031 0.12764 0.14493 0.16218 0.09585 0.11320 0.13053 0.14781 0.16505 0.09874 0.11609 0.13341 0.15069 0.16792 0.10164 0.11898 0.13629 0.15356 . 17078 0.10453 0.12187 0.13917 0.15643 0.17365 84 83 82 81 80 10 11 12 13 14 0.17365 0.19081 0.20791 0.22495 0.24192 0.17651 0.19366 0.21076 0.22778 0.24474 0.17937 0.19652 0.21360 0.23062 0.24756 0.18224 0.19937 0.21644 0.23345 0.25038 0.18509 0.20222 0.21928 0.2362? 0.25320 0.18795 0.20507 0.22212 0.23910 0.25601 0.19081 0.20791 0.22495 0.24192 0.25882 79 78 77 76 75 15 16 17 18 19 0.25882 0.27564 0.29237 0.30902 0.32557 0.26163 0.27843 0.29515 0.31178 0.32832 0.26443 0.28123 0.29793 0.31454 0.33106 0.26724 0.28402 0.30071 0.31730 0.33381 0.27004 0.28680 0.30348 0.32006 0.33655 0.27284 0.28959 0.30625 0.32282 0.33929 0.27564 0.29237 0.30902 0.32557 0.34202 74 73 72 71 70 20 21 22 23 24 0.34202 0.35837 0.37461 0.39073 0.40674 0.34475 0.36108 0.37730 0.39341 0.40939 0.34748 0.36379 0.37999 0.39608 0.41204 0.35021 0.36650 0.38268 0.39875 0.41469 0.35293 0.36921 0.3853? 0.40142 0.41734 0.35565 0.37191 0.38805 0.40408 0.41998 35837 0.37461 0.39073 0.40674 0.42262 69 68 67- 66 65 25 26 27 28 29 0.42262 0.43837 0.45399 0.46947 0.48481 0.42525 0.44098 0.45658 0.47204 0.48735 0.42788 0.44359 0.45917 0.47460 0.48989 0.43051 0.44620 0.46175 0.47716 0.49242 0.43313 0.44880 0.46433 0.47971 0.49495 0.43575 0.45140 0.46690 0.48226 0.49748 0.43837 0.45399 0.46947 0.48481 0.50000 64 63 62 61 60 30 31 32 33 34 '0.50000 0.51504 0.52992 0.54464 0.55919 0.50252 0.51753 0.53238 0.54708 0.56160 0.50503 0.52002 0.53484 0.54951 0.56401 0.50754 0.52250 0.53730 0.55194 0.56641 0.51004 0.52498 0.53975 0.55436 0.56880 0.51254 0.52745 0.54220 0.55678 0.57119 0.51504 0.52992 0.54464 0.55919 0.57358 59 58 57 56 55 35 36 37 38 39 0.57358 0.58779 0.60182 0.61566 0.62932 0.57596 0.59014 0.60414 0.61795 0.63158 0.57833 0.59248 0.60645 0.62024 0.63383 0.58070 0.59482 0.60876 0.62251 0.63608 0.58307 0.59716 0.61107 0.62479 0.63832 0.58543 0.59949 0.61837 0.62706 0.64056 0.58779 0.60182 0.61566 0.62932 0.64279 54 53 52 51 50 40 41 42 43 44 0.64279 0.65606 0.66913 0.68200 0.69466 64501 0.658-25 0.67129 0.68412 0.69675 0.64723 0.66044 0.67344 0.68624 0.69883 0.64945 0.66262 0.67559 0.68835 0.70091 0.65166 0.66480 0.67773 0.69046 0.70298 0.65386 0.66697 0.67987 0.69256 0.70505 0. 65606 0.66913 0.68200 0.69466 0.70711 49 48 47 46 45 i ^ 60' 60' 40' 30' 20' 10' 0' COSINE 268 NATIONAL TUBE COMPANY. MATHEMATICAL TABLES, (CONTINUED.) 1 COSINE. Q 0' 10' 20' 30' 40' 50' 60' 1.00000 1.00000 0.9999 0.9999 0.9999C 0.9998 0.99985 89 1 0.99985 0.99979 0.9997 0.99966 0.99956 0.9994 0.99939 88 2 0.99939 0.99929 0.9991 0.99905 0.9989S 0.9987 0.99863 87 3 0.99863 0.99847 0.9983 0.99813 0.99795 0.9977 0.99756 86 4 0.99756 0.99736 0.99714 0.99692 0.9966S 0.9964 0.99619 85 5 0.99619 0.99594 0.99567 0.99540 0.99511 0.99482 0.99452 84 6 0.99452 0.99421 0.99390 0.99357 0.99324 0.99290 0.99255 83 7 0.99255 0.99219 0.99182 0.99144 0.99106 0.99067 0.99027 82 8 0.99027 0.98986 0.98944 0.98902 0.98858 0.98814 0.98769 81 9 0.98769 0.98723 0.98676 0.98629 0.98580 0.98531 0.98481 80 10 0.98481 0.98430 0.98378 0.98325 0.98272 0.98218 0.98163 79 11 0.98163 0.98107 0.98050 0.97992 0.97934 0.97875 0.97815 78 12 0.97815 0.97754 0.97692 0.97630 0.97566 0.97502 0.97437 77 13 0.97437 0.97371 0.97304 0.97237 0.97169 0.97100 0.97030 76 14 0.97030 0.96959 0.96887 0.96815 0.96742 0.96667 0.96593 75 15 0.96593 0.96517 0.96440 0.96363 0.96285 0.96206 0.96126 74 16 0.96126 0.96046 0.95964 0.95882 0.95799 0.95715 0.95630 73 17 0.95630 0.95545 0.95459 0.95372 0.95284 0.95195 0.95106 72 18 0.95106 0.95015 0.94924 0.94832 0.94740 0.94646 0.94552 71 19 0.94552 0.94457 0.94361 0.94264 0.94167 0.94068 0.93969 70 20 0.93969 0.93869 0.93769 0.93667 0.93565 0.93462 0.93358 69 21 0.93358 0.93253 0.93148 0.93042 0.92935 0.92827 0.92718 68 22 0.92718 0.92609 0.92499 0.92388 0.92276 0.92164 0.92050 67 23 0.92050 0.91936 0.91822 0.91706 0.91590 0.91472 0.91355 66 24 0.91355 0.91236 0.91116 0.90996 0.90875 0.90753 0.90631 65 25 0.90631 0.90507 0.90383 0.90259 0.90133 0.90007 0.89879 64 26 0.89879 0.89752 0.89623 0.89493 0.89363 0.89232 0.89101 63 27 0.89101 0.88968 0.88835 0.88701 0.88566 0.88431 0.88295 62 28 0.88295 0.88158 0.88020 0.87882 0.87743 0.87603 0.87462 61 29 0.87462 0.87321 0.87178 0.87036 0.86892 0.86748 0.86603 60 " 30 0.86603 0.86457 0.86310 0.86163 0.86015 0.85866 0.85717 59 31 0.85717 0.85567 0.85416 0.85264 0.85112 0.84959 0.84805 58 32 0.84805 0.84650 0.84495 0.84339 0.84182 0.84025 0.83867 57 33 0.83867 0.83708 0.83549 0.83389 0.83228 0.83066 0.82904 56 34 0.82904 0.82741 0.82577 0.82413 0.82248 0.82082 0.81915 55 35 0.81915 0.81748 0.81580 0.81412 0.81242 0.81072 0.80902 54 36 0.80902 0.80730 0.80558 0.80386 0.80212 0.80038 0.79864 53 37 0.79864 0.79688 0.79512 0.79335 0.79158 0.78980 0.78801 52 38 0.78801 0.78622 0.78442 0.78261 0.78079 0.77897 0.77715 51 39 0.77715 0.77531 0.77347 0.77162 0.76977 0.76791 0.76604 50 40 0.76604 0.76417 0.76229 0.76041 0.75851 0.75661 0.75471 49 41 0.75471 0.75280 75088 0.74896 0.74703 0.74509 0.74314 48 42 0.74314 0.74120 0.73924 0.73728 0.73531 0.73333 0.73135 47 43 0.73135 0.72937 0.72737 0.72537 0.72*37 0.72136 0.71934 46 44 0.71934 0.71732 0.71529 0.71325 0.71121 0.70916 0.70711 45 60' 50' 40' 30' 20' 10' 0' I SINE. 1 NATIONAL TUBE COMPANY. 269 MATHEMATICAL TABLES. (CONTINUED.) i TANGENT. I 0' 10' 20' 30' 40' w 60' 0.00000 0.00291 0.00582 0.00873 0.01164 0.01455 0.01746 89 1 0.01746 0.02036 0.02328 0.02619 0.02910 0.03201 0.03492 88 2 0.03492 0.03783 0.04075 0.04366 0.04658 0.04949 0.05241 87 3 0.05241 0.05533 0.05824 0.06116 0.06408 0.06700 0.06993 86 4 0.06993 0.07285 0.08578 0.07870 0.08163 0.08456 0.08749 85 5 0.08749 0.09042 0.09335 0.09629 0.09923 0.10216 0.10510 84 6 0.10510 0.10805 0.11099 0.11394 0.11688 0.11983 0.12278 83 7 0.12278 0.12574 0.12869 0.13165 0.13461 0.13758 0.14054 82 8 0.14054 0.14351 0.14648 0.14945 0.15243 0.15540 0.15838 81 9 0.15838 0.16137 0.16435 0.16734 0.17033 0.17333 0.17633 80 10 0.17633 0.17933 0.18233 0.18534 0.18835 0.19136 0.19438 79 11 0.19438 0.19740 0.20042 0.20345 0.20648 0.20952 0.21256 78 12 0.21256 0.21560 0.21864 0.22169 0.22475 0.22781 0.23087 77 13 0.23087 0.23393 0.23700 0.24008 0.24316 0.24624 0.24933 76 14 0.24933 0.25242 0.25552 0.25862 0.26172 0.26483 0. -26795 75 i 15 0.26795 0.27107 0.27419 0.27732 0.28046 0.28360 0.28675 74 16 0.28675 0.28990 0.29305 0.29621 0.29938 0.30255 0.30573 73 17 0.30573 0.30891 0.31210 0.31530 0.31850 0.32171 0.32492 72 18 0.32492 0.32814 0.33136 0.33460 0.33783 0.34108 0.34433 71 19 0.34433 0.34758 0.35085 0.35412 0.35740 0.36068 0.36397 70 20 0.36397 0.36727 0.37057 0.37388 0.37720 0.38053 0.38386 69 21 0.38386 0.38721 0.39055 0.39391 0.39727 0.40065 0.40403 68 22 0.40403 0.40741 0.41081 0.41421 0.41763 0.42105 0.42447 67 23 0.42447 0.42791 0.43136 0.43481 0.43828 0.44175 0.44523 66 24 0.44523 0.44872 0.45222 0.45573 0.45924 0.46277 0.46631 65 25 0.46631 0.46985 0.47341 0.47698 0.48055 0.48414 0.48773 64 26 0.48773 0.49134 0.49495 0.49858 0.50222 0.50587 0.50953 63 27 0.50953 0.51320 0.51688 0.52057 0.52427 0.52798 0.53171 62 0.53171 0.53545 0.53920 0.54296 0.54673 0.55051 0.55431 61 29 0.55431 0.55812 0.56194 0.56577 0.56962 0.57348 0.57735 60 30 0.57735 0.58124 0.58513 0.58905 0.59297 0.59691 0.60086 59 31 0.60086 0.60483 0.60881 0.61280 0.61681 0.62083 0.62487 58 32 0.62487 0.62892 0.63299 0.63707 0.64117 0.64528 0.64941 57 33 0.64941 0.65355 0.65771 0.66189 0.66608 0.67028 0.67451 56 34 0.67451 0.67875 0.68301 0.68728 0.69157 0.69588 0.70021 55 35 0.70021 0.70455 0.70891 0.71329 0.71769 0.72211 0.72654 54 36 0.72654 0.73100 0.73547 0.73996 0.74447 0.74900 0.75355 53 37 0.75355 0.75812 0.76272 0.76733 0.77196 0.77661 0.78129 52 38 0.78129 0.78598 0.79079 0.79544 0.80020 0.80498 0.80978 51 39 0.80978 0.81461 0.81946 0.82434 0.82923 0.83415 0.83910 50 40 0.83910 0.84407 0.84906 0.85408 0.85912 0.86419 0.86929 49 41 0.86929 0.87441 0.87955 0.88473 0.88992 0.89515 0.90040 48 42 0.90040 0.90569 0.91099 0.91633 0.92170 0.92709 0.93252 47 43 0.93252 0.93797 0.94345 0.94896 0.95451 0.96008 0.96569 46 44 0.96569 0.97133 0.97700 0.98270 0.98843 0.99420 1.00000 45 60' 50' 40 30' 20' 10' 0' Z COTANGENT. 270 NATIONAL TUBE COMPANY. MATHEMATICAL TABLES. (CONTINUED.) I COTANGENT. I 0' 10' 20' 30' 40' 50' 60' 00 343.77371 171.88540 114.58865 85.93979 68.75009 57.28996 89 1 57.28996 49.10388 42.96408 38.18846 34.36777 31.24158 28.63625 88 2 28.63625 26.43160 24.54176 22.90377 21.47040 20.20555 19.08114 87 3 19.08114 18.07498 17.16934 16.34986 15.60478 14.92442 14.30067 86 4 14.30067 13.72674 13.19688 12.70621 12.25051 11/82617 11.43005 85 5 11.43005 11.05943 10.71191 10.38540 10.07803 9.78817 9.51430 84 6 9.51436 9.25530 9.00983 8.77689 8.55555 8.34496 8.14435 83 7 8.14435 7.95302 7.77035 7.59575 7. -42871 7.26873 7.11537 82 8 7.11537 6.96823 6.82694 6.69116 6.56055 6.43484 6.31375 81 9 6.31375 6.19703 6.08444 5.97576 5.87080 5.76937 5.67128 80 10 5.67128 5.57638 5.48451 5.39552 5.30928 5.22566 5.14455 79 11 5.14455 5.06584 4.98940 4.91516 4.84300 4.77286 4.70463 78 12 4.70463 4.63825 4.57363 4.51071 4.44942 4.38969 4.33148 77 13 4.33148 4.27471 4.21933 4.16530 4.11256 4.06107 4.01078 76 14 4.01078 3.96165 3.91364 3.86671 3.82083 3.77595 3.73205 75 15 3.73205 3.68909 3.64705 3.60588 3.56557 3.52609 3.48741 74 16 3.48741 3.44951 3.41236 3.37594 3.34023 3.30521 3.27085 73 17 3.27085 3.23714 3.20406 3.17159 3.13972 3.10842 3.07768 72 18 3.07768 3.04749 3.01783 2.98869 2.96004 2.93189 2.90421 71 19 2.90421 2.87700 2.85023 2.82391 2,79802 2 . 77254 2.74748 70 20 2.74748J 2.72281 2.69853 2.67462 2.65109 2.62791 2.60509 69 21 2.605091 2.58261 2.56046 2.53865 2.51715 2.49597 2.47509 68 22 2.47509 2.45451 2.43422 2.41421 2.39449 2.37504 2.35585 67 23 2.35585 2.&S693 2.31826 2.29984 2.28167 2.26374 2.24604 66 24 2.24604 2.22857 2.21132 2.19430 2.17749 2.16090 2.14451 65 25 2.14451 2.12a32 2.11233 2.09654 2.08094 2.06553 2.05030 64 26 2.05030 2.03526 2.02039 2.00569 .99116 1.97680 1.96261 63 27 .96261 1.94858 1.93470 1.92098 .90741 1.89400 1.88073 62 28 .88073 1.86760 .85462 1.84177 .82906 1.81649 .80405 61 29 .80405 1.79174 .77955 1.76749 .75556 1.74375 .73205 60 30 .73205 1.72047 .70901 1.69766 .68643 1.67530 .66428 59 31 .66428 1.65337 .64256 1.63185 .62125 1.61074 .60033 58 32 .60033 1.59002 .57981 1.56969 .55966 1.54972 .53987 57 33 .53987 1.53010 .52043 1.51084 .50133 1.49190 .48256 56 34 .48256 1.47330 .46411 1.45501 .44598 1.43703 .42815 55 35 .42815 1.41934 .41061 1.40195 .39336 1.38484 .37638 54 36 .37638 1.36800 .35968 1.35142 .34323 1.33511 .32704 53 37 .32704 1.31904 .31110 1.30323 .29541 1.28764 .27994 52 38 .27994 1.27230 .26471 1.25717 .24969 1.24227 .23490 51 39 .23490 1.22758 .22031 1.21310 .20593 1.19882 .19175 50 40 .19175 1.18474 .17777 1.17085 .16398 1.15715 .15037 49 41 .15037 1.14363 .13694 1.13029 .12369 1.11713 .11061 48 42 .11061 1.10414 .09770 1.09131 .08496 1.07864 .07237 47 43 1.07237 1.06613 .05994 1.05378 .04766 1.04158 .03553 46 44 1.03553 1.02952 1.02355 1.01761 .01170 1.00583 .00000 45 60' 50' 40' 30' 20' 10' 0' TANGENT. NATIONAL TUBE COMPANY 271 CIRCUMFERENCES AND AREAS OF CIRCLES. Diameter from %\ to JOO, advancing chiefly by Eighths. Diam. Circum. Area. Diam. Circum. Area. Diam. Circum. Area. i .04909 .00019 2.J6 6.6759 3.5466 5. IB 17.082 23.221 i .09818 .00077 3 6.8722 3.7583 ix 17 279 23.758 3 3 5 .14726 .00173 J4 7.0686 3.9761 T 9 S 17.475 24.301 1 .19635 .00307 5 7.2649 4.2000 5X 17.671 24.850 n .29452 .00690 % 7.4613 4.4301 H 17.868 25.406 i/ .39270 .01227 7 7.6576 4.6664 M 18.064 25.967 6^ .49087 .01917 % 7.8540 4.9087 ii 18.261 26.535 & .58905 .02761 9 8.0503 5.1572 7X 18.457 27.109 A .68722 .03758 % 8.2467 5.4119 ii 18.653 27.688 11 8.4430 5.6727 M .78540 .04909 % 8.6394 5.9396 6. 18.&50 28.274 9 .88357 .06213 13 8.8357 6.2126 IX 19.242 29.465 5 .98175 .07670 % 9.0321 6.4918 i/; 19.635 30.680 n 1.0799 .09281 ii 9.2284 6.7771 % 20.028 31.919 D 1.1781 .11045 IX 20.420 33.183 13 1.2763 .12962 3. 9.4248 7.0686 % 20.813 34.472 7 1.3744 .15033 i 9.6211 7.3662 H 21.206 35.785 II 1.4726 .17257 x6 9.8175 7.6699 21.598 37.122 3 10.014 7.9798 7l3 1.5708 .19635 J4 10.210 8.2958 7. 21.991 38.485 17 1.6690 .22166 5 10.407 8.6179 IX 22.384 39.871 3 9 2 1.7671 .24850 % 10.603 8.9462 H 22.776 41.282 19 1.8653 .27688 JL 10.799 9.2806 sx 23.169 42.718 II 1.9635 .30680 Hi 10 996 9.6211 % 23.562 44.179 H 2.0617 .33824 9 11.192 9.9678 5X 23.955 45.664 H 2.1598 .37122 % 11.388 10.321 M 24.347 47.173 11 2.2580 .40574 TB 11.585 10.680 % 24.740 48.707 M 11.781 11.045 ax 2.3562 .44179 13 11.977 11.416 8. 25.133 50.265 5 2.4544 \47937 % 12.174 11.793 25.525 51.849 |g 2.5525 .51849 ii 12.370 12.177 H 25.918 53.456 2j 2.6507 .55914 sx 26.311 55.088 lyx 2.7489 .60132 4. i 12.566 12.566 /is 26.704 56.745 1 2.8471 .64504 12.763 12.962 % 27.096 58.426 16 2.9452 .69029 IX 12.959 13.364 a/ 27.489 60.132 Si 3.0434 .73708 & 13.155 13.772 % 27.882 61.862 J4 13.352 14.186 1. t 3.1416 .7854 T*8 13.548 14.607 9. 28.274 63.617 3.3379 .8866 3X 13.744 15.033 IX 28.667 65.397 |x 3.5343 .9940 T ? B 13.941 15.466 x4 29.060 67.201 A 3.7306 .1075 1^ 14.137 15.904 3X 29.452 69.029 s 3.9270 .2272 J 14.334 16.349 IX 29.845 70.882 i 4.1233 .3530 % 14.530 16.800 % 30.238 72.760 4.3197 .4849 11 14.726 17.257 7* 30.631 74.662 /e 4.5160 .6230 M 14.923 17.728 31.023 76.589 IX 4.7124 .7671 13 15.119 18.190 9 4.9087 .9175 7X 15.315 18.665 10. 31.416 78.540 % 5.1051 2.0739 if 15.512 19.147 31.809 80.516 11 5.3014 2.2365 IX 32.201 82.516 M 5.4978 2.4053 5. 15.708 19.635 /i 32.594 84.541 13 5.6941 2.5802 TB 15.904 20.129 v^ 32.987 86.590 % 5 8905 2.7612 y 16.101 20.629 % 33.379 88.664 18 6.0868 2.9483 T^ 16.297 21.135 % as. 772 90.763 I/ 16.493 21.648 % 34.165 92.886 2. 6.2832 3.1416 ^ 16.690 22.166 A 6.4795 3 3410 % 16.886 22.691 11. 34.558 95.033 flr. J 272 NATIONAL TUBE COMPANY. CIRCUMFERENCES AND AREAS OF CIRCLES. (CONTINUED.) Diam. Circum. Area. Diam. Circum. Area. Diam . Circum. Area. 11-/6 34.950 97.205 17.% 54.585 237.10 23.% 74.220 438.36 35.343 99.402 54.978 240.53 74.613 443.01 3X 35.736 101.62 % 55.371 243.98 % 75.006 447.69 x^ 36.128 103.87 M 55.763 247.45 % 36.521 106.14 % 56.156 250.95 24. 75.398 452.39 %. 36.914 108.43 75.791 457.11 % 37.306 110.75 18. 56.549 254.47 /4 76.184 461.86 J| 56.941 258.02 az 76.576 466.64 12. 37.699 113.10 57.334 261.59 /^ 76.969 471.44 38.092 115.47 3X 57.727 265.18 KX 77.362 476.26 IX 38.485 117.86 Li 58.119 268.80 3X 77.754 481.11 % 38.877 120.28 % 58.512 272.45 % 78.147 485.98 fij 39.270 122.72 a/ 58.905 276.12 % 39.663 125.19 % 59.298 279.81 25. 78.540 490.87 ax 40.055 127.68 78.933 495.79 % 40.448 130.19 19. 59.690 283.53 IX 79.325 500.74 60.083 287.27 % 79.718 505.71 13. 40.841 132.73 ix; 60.476 291.04 IX 80.111 510.71 41.233 135.30 % 60.8(58 294.83 % 80.503 515.72 IX 41.626 137.89 IX, 61.261 298.05 3X 80.89(5 520.77 % 42.019 140.50 % 61.654 302.49 % 81.289 525.84 1Z 42.412 143.14 % 62.046 306.35 KX 42.804 145.80 % 62.439 310.24 26. 81.681 530.93 % 43.197 148.49 82.074 536.05 % 43.590 151.20 20. 62.832 314.16 IX 82.467 541.19 M 63.225 318.10 % 82.860 546.35 14. 43.982 153.94 63.617 322.06 i 83.252 551.55 44.375 156.70 % 64 010 3-26.05 % 83.645 556.76 M 44.768 159.48 v& 64.403 330.06 % 84.038 562.00 32 45.160 162.30 % (54.795 334.10 % 84.430 567.27 xii 45.553 165.13 H 65.188 338.16 5/ 45.946 167.99 H 65.581 342.25 27. 84.823 572.56 i 46.338 170.87 ix 85.216 577.87 % 46.731 173.78 21. 65.973 346.36 H 85.608 583.21 /^c c,ii.:i(ii; 350.50 a2 8(5.001 588.57 15. 47.124 176.71 M 66.759 &54.66 VX, 86.394 593.96 ^ 47.517 179.67 % 67.152 358.84 % 86.786 599.37 47.909 182.65 L 67.544 363.05 3X 87.179 604.81 32 48.302 185.66 % 67.937 3(57.28 7X 87.572 610.27 /^ 48.695 188.69 M 68.330 371.54 % 49.087 191.75 % 68.722 375.83 28. 87.965 615.75 % 49.480 194.83 x4 88.357 621.26 % 49.873 197.93 22. 69.115 380.13 /x; 88.750 626 80 ix 69.508 384.46 % 89.143 632.36 16. 50.265 201.06 IX 69.900 388.82 IX 89.535 637.94 50.658 204.22 % 70.293 393.20 % H.).>28 643.55 IX 51.051 207.39 ix. 70.686 397.61 ax. 90.321 649.18 % 51.444 210.60 % 71.079 402.04 % 90.713 654.84 l 51.836 213.82 ax. 71.471 406.49 B/j 52.229 217.08 % 71.864 410.97 29. 91.106 660.52 9i 52.622 220.35 $ 91 .499 666.23 7^ 53.014 223.65 23. 72.257 415.48 91.892 671.96 $ 72.649 420.00 sz 92.284 677.71 17. 53.407 226.98 73.042 424.56 /^ 92.C.77 683.49 53.800 230.33 % 73.435 429.13 % 93.070 689.30 i M 54.192 233.71 /^ 73.827 433.74 H 93.462 695.13 NATIONAL TUBE COMPANY. 273 CIRCUMFERENCES AND AREAS OF CIRCLES. (CONTINUED.) Diam. Circum. Area. Diam. Circum. Area. Diam. Circum. Area. 29.% 93.855 700.98 36.^ 113.490 1025.0 42.% 133.125 1410.3 113.883 1032.1 133.518 1418.6 30. 94.248 706.86 a2 114.275 1039.2 & 133.910 1427.0 94.640 712.76 /^ 114.668 1046.3 M 134.303 1435.4 /4 95.033 718.69 5X 115.061 1053.5 TX 134.696 1443.8 % 95.426 724.64 M 115.454 1060.7 12 95.819 730.62 % 115.846 1068.0 43. 135.088 1452.2 % 96.211 736.62 /4 135.481 1460.7 % 96.604 742.64 37. 116.239 1075.2 /4 135.874 1469.1 % 96.997 748.69 K 116.633 1082.5 % 136.267 1477.6 117.024 1089.8 i^ 136.659 1486 2 31. 97.389 754.77 % 117.417 1097.1 R^ 137.052 1494.7 H 97.782 760.S7 /^ 117,810 1104,5 M 137.445 1503.3 98.175 766.99 % 118.202 1111.8 % 137.837 1511.9 % 98.567 773.14 a/ 118.596 1119.2 te 98.960 779.31 % 118.988 1126.7 44. 138.230 1520.5 % 99.353 785.51 ^x 138.623 1529.2 99.746 791.73 38. 119.381 1134.1 H 139.015 1537.9 % 100.138 797.98 /^c 119.773 1141.6 s2 139.408 1546.6 H 120.166 1149.1 & 139.801 1555.3 32. 100.531 804.25 a2 120.559 1156.6 i2 140.194 1564.0 If 100.924 810.54 Jij 120.951 1164.2 % 140.586 1572.8 M 101.316 816.86 % 121.344 1171.7 % 140.979 1581 6 ?B 101.709 823.21 % 121.737 1179.3 ^ 102.102 829.58 % 122.129 1186.9 45. 141.372 1590.4 % 102.494 835.97 ix 141.764 1599.3 M 102.887 842.39 39. 122.522 1194.6 H 142.157 1608.2 % 103.280 848.83 ix 122.915 1202.3 3X 142.550 1617.0 24 128.808 1210.0 ^ 142.942 1626.0 33. 103.673 855.30 sx 123.700 1217.7 % 143.335 1634.9 104.065 861.79 i^ 124.093 1225.4 M 143.728 1643.9 ^4 104.458 868.31 % 124.486 1233.2 7X 144.121 1652.9 % 104. 851 874.85 M 124.878 1241.0 J^> 105.243 881.41 7X 125.271 1248.8 46. 144.513 1661.9 % 105.1536 888.00 i^ 144.906 1670.9 M 106.029 894.62 40. 125.664 1256.6 J4 145.299 1680.0 72 106.421 901.26 126.056 1264.5 % 145.691 1689.1 H 126.449 1272.4 i^ 146.084 1398.2 34. 106.814 907.92 a? 126.842 1280.3 7& 146.477 1707.4 107.207 914.61 /^ 127.235 1288.2 M 146.869 1716.5 M 107.600 921.32 &X 127.627 1296.2 7X 147.262 1725.7 % 107.992 928.06 3 128.020 1304.2 ^ 108.385 934.82 % 128.413 1312.2 47. 147.655 1734.9 % 108.778 941.61 148.048 1744.2 9 109.170 948.42 41. 128.805 1320.3 H 148.440 1753.5 % 109.563 955.25 ix 129.198 1328.3 &z 148.833 1762.7 H 129.591 1336.4 \fa 149.226 1772.1 35. 109.956 962.11 32 129.983 1344.5 % 149.618 1781.4 H 110.348 969.00 ^ 130.376 1352.7 M 150.011 1790.8 /4 110.741 975.91 % 130.769 1360.8 % 150.404 1800.1 % 111.134 982.84 M 131.161 1369.0 % 111.527 989.80 8 131.554 1377.2 48. 150.796 1809.6 % 111.919 996.78 IX 151.189 1819.0 K 112.312 1003.8 42. 131.947 1385.4 J4 151.582 1828.5 % 112.705 1010.8 ix 182.340 1393.7 3X 151.975 1887.9 36. 113.097 1017.9 1 J4 132.732 1402.0 ^ 152.367 1847.5 874 NATIONAL TUBE COMPANY. CIRCUMFERENCES AND AREAS OF CIRCLES. (CONTINUED.) Diam. Circum. Area. Diam Circum. Area. Diam Circum. Area. 48.% 152.760 1857.0 54.% 172.395 2365.0 61. 191.637 2922.5 K 153.153 1866.5 ix 192.030 2934.5 ys 153.545 1876.1 55. 172.788 2375.8 M 192.423 2946.5 H 173.180 2386.6 RZ 192.815 2958.5 49. 153.938 1885.7 M 173.573 2397.5 ~L 193.208 2970.6 % 154.331 1895.4 % 173.966 2408.3 % 193.601 2982.7 M 154.723 1905.0 /^ 174.358 2419.2 % 193.993 2994.8 % 155.116 1914.7 % 174.751 2430.1 % 194.386 3006.9 UL 155.509 1924.4 % 175.144 2441.1 % 155.902 1934.2 % 175.536 2452.0 62. 194.779 3019.1 3X 156.294 1943.9 195.171 3031.3 % 156.687 1953.7 56. 175.929 2463.0 M 195.564 3043.5 12 176.322 2474.0 % 195.957 3055.7 50. 157.080 1963.5 M 176.715 2485.0 H 196.350 3068.0 K 157.472 1973.3 % 177.107 2496.1 % 196.742 3080.3 157.865 1983.2 LX 177.500 2507.2 ax 197.135 3092.6 H 158.258 1993.1 % 177.893 2518.3 % 197.528 3104.9 Lg 158.650 2003.0 % 178.285 2529.4 % 159.043 2012.9 ? / 8 178.678 2540.6 63. 197.920 3117.2 M 159.436 2022.8 te 198.313 3129.6 % 159.829 2032.8 57. 179.071 2551.8 198.706 3142.0 12 179.463 2563.0 s2 199.098 3154.5 51. 160.221 2042.8 IX 179.856 2574.2 j/> 199.491 3166.9 x^ 160.614 2052.8 % 180.249 2585.4 % 199.884 3179.4 /4 161.007 2062.9 L^J 180.642 2596.7 ax 200.277 3191.9 32 161.399 2073.0 SX 181.034 2608.0 % 200.669 3204.4 i 161.792 2083.1 % 181.427 2619.4 8 162.185 2093.2 % 181.820 2630.7 64. 201.062 3217.0 H 162.577 2103.3 H 201.455 3229.6 % 162.970 2113.5 58. 182.212 2642.1 IX 201.847 3242.2 K 182.605 2653.5 % 202.240 3254.8 52. 163.363 2123.7 182.998 2664.9 v& 202.633 3267.5 ^6 168.75(5 2133.9 32 183.390 2676.4 % 203.025 3280.1 H 164.148 2144.2 /^ 183.783 2687.8 ax_ 203.418 3292.8 82 164.541 2154.5 % 184.176 2699.3 % 203.811 3305.6 ^5 164.934 2164.8 % 184.569 2710.9 % 165.326 2175.1 % 184.961 2722.4 65. 204.204 3318.3 94 165.719 2185.4 H 204.596 3331.1 % 166.112 2195.8 59. 185.354 2734.0 204.989 3343.9 185.747 2745.6 a| 205.382 3356.7 53. 166.504 2206.2 /4 186.139 2757.2 LX 205.774 3369.6 M 166.897 2216.6 % 186.532 2768.8 % 206.167 3382.4 167.290 2227.0 T 186.925 2780.5 ax 206.560 3395.3 32 167.683 2237.5 % 187.317 2792.2 72 206 952 3408.2 /^ 168.075 2248.0 3X 187.710 2803.9 % 168.468 2258.5 % 188.103 2815.7 66. 207.345 3421.2 a/ 168.861 2269.1 12 207.738 3434.2 /I 169.253 2279.6 60. 188.496 2827.4 H 208.131 3447.2 M 188. S88 2839.2 32 208.523 3460.2 54. 169.646 2290.2 189.281 2851.0 12 208.916 3473.2 170.039 2300.8 2s 189.674 2862.9 % 209.309 3486.3 /4 170.431 2311.5 1^5 190.066 2874.8 ax 209.701 3499.4 a2 170.824 2322.1 7& 190.459 2886.6 % 210.094 3512.5 171 217 2332.8 % 190.852 2898.6 B 171.609 2343.5 7% 191.244 2910.5 67. 210.487 3525.7 *M 172.002 2354.3 H 210.879 3538.8 |H= ^ NATIONAL TUBE COMPANY. 275 CIRCUMFERENCES AND AREAS OF CIRCLES. (CONTINUED.) Diam. Circum. Area. Diam. Circum. Area. Diam. Circum. Area. 67. U 211.272 3552.0 73.^ 230.907 4242.9 79. g 250.542 4995.2 211.665 3565.2 231.300 4257.4 250.935 5010.9 if 212.058 3578.5 M 231.692 4271.8 % 212.450 3591.7 H 232.085 4286.3 80. 251.327 5026.5 az 212.843 3605.0 i/i 251.720 5042.3 7Z 213.236 3618.3 74. 232.478 4300.8 y. 252.113 5058.0 ^ 232.871 4315.4 % 252.506 5073.8 1 68. 213.628 3631.7 233.263 4329.9 & 252.898 5089.6 214.021 3645.0 9s 233.656 4344.5 7S 253.291 5105.4 iz 214.414 3658.4 \&> 234.049 4359.2 M 253.684 5121.2 % 214.806 3671.8 % 234.441 4373.8 % 254.076 5137.1 iz 215.199 8685.3 az 234.834 4388.5 % 215.592 3698.7 H 235.227 4403.1 81. 254.469 5153.0 a/ 215.984 3712.2 iz 254.862 5168.9 n 216.377 3725.7 75. 235.619 4417.9 H 255.254 5184.9 M 236.012 4432.6 sz 255.647 5200.8 \ 69. 216.770 3739.3 236.405 4447.4 /^ 256.040 5216.8 217.163 3752.8 8Z 236.798 4462.2 % 256.433 5232.8 H 217.555 3766.4 % 237.190 4477.0 M 256.825 5248.9 sz 217.948 3780.0 % 237.583 4491.8 % 257.218 5264.9 iz 218.341 3793.7 3Z 237.976 4506.7 % 218.733 3807.3 % 238.368 4521.5 82. 257.611 5281.0 az 219.126 3821.0 258.003 5297.1 % 219.519 3834.7 76. 238.761 4536.5 M. 258.396 5313.3 iz. 239.154 4551.4 % 258.789 5329.4 70. 219.911 3848.5 H 239.546 4566.4 L 259.181 5345.6 220.304 3862 2 az 239.939 4581.3 % 259.574 5361.8 /4 220.697 3876.0 /^ 240.332 4596.3 % 259.967 5378.1 sz 221.090 3889.8 BX 240.725 4611.4 % 260.359 5394 3 ijj 221.482 3903.6 M 241.117 4626.4 % 221.875 3917.5 % 241.510 4641.5 83. 260.752 5410.6 a 222.268 3931.4 261.145 5426.9 7Z 222.660 3945.3 77. 241.903 4656.6 M 261.538 5443.3 if? 242.295 4671.8 RZ 261.930 5459.6 71. 223.053 3959.2 H 242.688 4686.9 ty> 262.323 5476.0 ix 223.446 3973.1 3X 243.081 4702.1 KZ 262.716 5492.4 H 223.838 3987.1 \fa 243.473 4717.3 ax 263.108 5508.8 % 224.231 4001.1 % 243.866 4732.5 % 263.501 5525.3 i2 224.624 4015.2 % 244.259 4747.8 1% 225.017 4029.2 % 244.652 4763.1 84. 263.894 5541.8 H 225.409 4043.3 264.286 5558.3 % 225.802 4057.4 78. 245.044 4778.4 IX 264.679 5574.8 ^ 245.437 4793.7 9s 265.072 5591.4 72. 226.195 4071.5 245. 830 4809.0 1Z 265.465 5607.9 K 226.587 4085.7 % 246.222 4824.4 % 265.857 5624.5 J4 226.980 4099.8 ^a 246.615 4839.8 3X 266.250 5641.2 &z 227.373 4114.0 % 247.008 4855.2 7Z 266.643 5657.8 1^ 227.765 4128.2 M 247.400 4870.7 ?8 228.158 4142.5 % 247.793 4886.2 85. 267.035 5674.5 M 228.551 4156.8 267.428 5691.2 % 228.944 4171.1 79. 248.186 4901.7 \A 267.821 5707.9 ix 248.579 4917.2 az 268.213 5724.7 73. 229.336 4185.4 u 248.971 4932.7 7& 268.606 5741.5 14 229.729 4199.7 a2 249.364 4948.3 5Z 268.999 5758.3 /4 230.122 4214.1 i2 249.757 4963.9 az 269.392 5775.1 % 230.514 4228.5 % 250.149 4979.5 % 269.784 5791.9 i, JJ 276 NATIONAL TUBE COMPANY. CIRCUMFERENCES AND AREAS OF CIRCLES. (CONTINUED.) Diam. Circum. Area. Diam. Circum. Area. Diam. Circum. Area. 86. 270.177 5808.8 90.% 285.492 6486.0 95.% 300.415 7181.8 270.570 5825.7 3 300.807 7200.6 IA 270.962 5842.6 91. 285.885 6503.9 % 301.200 7219.4 % 271.355 5859.6 y& 286.278 6521.8 L 271.748 5876.5 14 286.670 6539.7 96. 301.593 7238.2 % 272.140 5893.5 s3 287.063 6557.6 i/ 301.986 7257.1 % 272.533 5910.6 Vz 287.456 6575.5 M 302.378 7276.0 72 272.926 5927.6 PB 287.848 6593.5 % 302.771 7294.9 ' M 288.241 6611.5 V% 303,164 7313.8 87. 273.319 5944.7 % 288.634 6629.6 % 303.556 7332.8 273.711 5961.8 'itA 303.949 7351.8 H 274.104 5978.9 92. 289.027 6647.6 % 304.342 7370.8 az 274.49? 5996.0 /* 289.419 6665.7 LZ 274.889 6013.2 M 283.812 6683.8 97. 304.734 7389.8 N 275.282 6030.4 % 290.205 6701.9 M 305.127 7408.9 3/: 275.675 6047.6 ^ 290.597 6720.1 305.520 7428.0 % 276.067 6064.9 % 290.990 6738.2 % 305.913 7447.1 M 291.383 6756.4 \& 306.305 7466.2 88. 276.460 6082.1 % 291.775 6774.7 7& 306.698 7485.3 276 853 6099.4 H 307.091 7504.5 ix 277.246 6116.7 93. 292.168 6792.9 % 307.483 7523.7 a2 277.638 6134.1 YB 292.561 6811.2 /^ 278.031 6151.4 292.964 6829.5 98. 307.876 7543.0 % 278.424 6168.8 % 293.346 6847.8 i/ 308.269 7562.2 a/ 278.816 6186.2 L& 293.739 6866.1 M 308.661 7581.5 7 -i 279.209 6203.7 % 291.132 6884.5 % 309.054 7600.8 ' M 294.524 6902.9 L^ 309.447 7620.1 89. 279.602 6221.1 % 294.917 6921 3 % 309.840 7639.5 279.994 6238.6 % 310.232 7658.9 24 280.387 6256.1 94. 295.310 6939.8 % 310.625 7678.3 280.780 6273.7 295.702 6958.2 2 281.173 6291.2 J4 296.095 6976.7 99. 311.018 7697.7 KX 281.565 6308.8 % 296.488 6995.3 i^ 311.410 7717.1 % 281.958 6326 4 y% 296.881 7013.8 H 311.803 7736.6 % 282.351 6344.1 % 297.273 7032.4 % 312.196 7756.1 a/ 297.666 7051.0 L/j 312.588 7775.6 90. 282.743 6361.7 % 298.059 7069.6 % 312.981 7795.2 W 283.136 6379.4 a/ 313.374 7814.8 283.529 6397.1 95. 298.451 7088.2 % 313.767 7834.4 32 283.921 6414.9 y 298.844 7106.9 IX 284.814 6432.6 299.237 7125.6 100. 314.159 7854.0 % 284.707 6450.4 a| 299.629 7144.3 H 285.100 6468.2 g 300.022 7163.0 tp -, NATIONAL TUBE COMPANY. 277 FIFTH ROOTS AND FIFTH POWERS. Power. No. or Root. Power. No. or Root. Power. No. or Root. .0000100 .1 .000796 .240 .034503 .51 .0000110 .102 .000883 .245 .038020 .52 .0000122 .104 .000977 .250 .041820 .53 .0000134 .106 .001078 .255 .045917 .54 .0000147 .108 .001188 .260 .050328 .55 .0000161 .110 .001307 .265 .055073 .56 .0000176 .112 .001435 .270 .060169 .57 .0000193 .114 .001573 .275 .065636 .58 .0000210 .116 .001721 .280 .071492 .59 0000229 .118 .001880 .285 .077760 .60 .0000249 .120 .002051 .290 .084460 .61 .0000270 .122 .002234 .295 .091613 .62 .0000293 .124 .002430 .300 .099244 .63 .0000318 .126 .002639 .305 .107374 .64 .0000344 .128 .002863 .310 .116029 .65 .0000371 .130 .003101 .315 .125233 .66 .0000401 .132 .003355 .320 .135012 .67 .0000432 .134 .003626 .325 .145393 .68 .0000465 .136 .003914 .330 .156403 .69 .0000500 .138 .004219 .335 .168070 .70 .0000538 .140 .004544 .340 .180423 .71 .0000577 .142 .004888 .345 .193492 .72 .0000619 .144 .005252 .350 .207307 .73 .0000663 .146 .005638 .355 .221901 .74 .0000710 .148 .006047 .360 .237305 .75 .0000754 .150 .006478 .365 .253553 .76 .0000895 .155 .006934 .370 .270678 .77 .000105 .160 .007416 .375 .288717 .78 .000122 .165 .007924 .380 .307706 .79 .000142 .170 .008459 .385 .327680 .80 .000164 .175 .009022 .390 .348678 .81 .000189 .180 .009616 .395 .370740 .82 .000217 .185 .010240 .400 .393904 .83 .000248 .190 .011586 .41 .418212 .84 .000282 195 .013069 .42 .443705 .85 .000320 .200 .014701 .43 .470427 .86 .000362 .205 .016492 .44 .498421 .87 .000408 .210 .018453 .45 .527732 .88 .000459 .215 .020596 .46 .558406 .89 .000515 .220 .022935 .47 .590490 .90 .000577 .225 .025480 .48 .624032 .91 .000544 .230 .028248 .49 .659082 .92 .000717 .235 .031250 .50 .695688 .93 T r 278 NATIONAL TUBE COMPANY. Fifth Roots and Fifth Powers. (CONTINUED.) Power. No. or Root. Power. No. or Root. Power. No. or Root. .733904 .94 15.9495 1.74 525.219 3.50 .773781 .95 16.8874 1.76 563.822 3.55 .815373 .96 17.8690 1.78 604.662 3.60 .858734 .97 18.8957 1.80 647.835 3.65 .903921 .98 19.9690 1.82 693.440 3.70 .950990 .99 21.0906 1.84 741.577 3.75 1. 1. 22.2620 1.86 792.352 3.80 1.10408 1.02 23.4849 1.88 845.870 3.85 1.21665 1.04 24.7610 1.90 902.242 3.90 1.33823 1.06 26.0919 1.92 961.58 3.95 1.46933 .08 27.4795 1.94 1024.00 4.00 1.61051 .10 28.9255 1.96 1089.62 4.05 1.76234 .12 30.4317 1.98 1158.56 4.10 1.92541 .14 32.0000 2.00 1230.95 4.15 2.10034 .16 36.2051 2.05 1306.91 4.20 2.28775 .18 40.8410 2.10 1386.58 4.25 2.48832 1.20 45.9401 2.15 1470.08 4.30 2.70271 1.22 51.5363 2.20 1557.57 4.35 2.93163 1.24 57.6650 2.25 1649.16 4.40 3.17580 1.26 64.3634 2.30 1745.02 4.45 3.43597 1.28 71.6703 2.35 1845.28 4.50 3.71293 1.30 79.6262 2.40 1950.10 4.55 4.00746 1.32 88.2735 2.45 2059.63 4.60 4.32040 1.34 97.6562 2.50 2174.03 4.65 4.65259 1.36 107.820 2.55 2293.45 4.70 5.00490 1.38 118.814 2.60 2418.07 4.75 5.37824 1.40 130.686 2.65 2548.04 4.80 5.77353 1.42 143.489 2.70 2683.54 4.85 6.19174 1.44 157.276 2.75 2824.75 4.90 6.63383 1.46 172.104 2.80 2971.84 4.95 7.10082 1.48 188.029 2.85 3125.00 5.00 7.59375 1.50 205.111 2.90 3450.25 5.10 8.11368 1.52 223.414 2.95 3802.04 5.20 8.66171 1.54 243.000 3.00 4181.95 5.30 9.23896 1.56 263.936 3.05 4591.65 5.40 9.84658 1.58 286.292 3.10 5032.84 5.50 10.4858 1.60 310.136 3.15 5507.32 5.60 11.1577 1.62 335.544 3.20 6016.92 5.70 11.8637 1.64 362.591 3.25 6563.57 5.80 12.6049 1.66 391.354 3.30 7149.24 5.90 13.3828 1.68 421.419 3.35 7776.00 6.00 14.1986 1.70 454.354 3.40 8445.96 6.10 15.0537 1.72 488.760 3.45 9161.33 6.20 NATIONAL TUBE COMPANY. 279 Fifth Roots and Fifth Powers. (CONTINUED.) Power. No. or Root. Power. No. or Root. Power. No. or Root. 9924.37 6.30 176234. 11.2 3043168. 19.8 10737. 6.40 192541 . 11.4 3200000. 20.0 11603. 6.50 210034. 11.6 3363232. 20.2 12523. 6.60 228776. 11.8 3533059. 20.4 13501 . 6.70 248832. 12.0 3709677. 20.6 14539. 6.80 270271 . 12.2 3893289. 20.8 15640. 6.90 293163. 12.4 4084101. 21.0 16807. 7.00 317580. 12.6 4282322. 21.2 18042. 7.10 343597. 12.8 4488166. 21.4 19349. 7.20 371293. 13.0 4701850. 21.6 20731 . 7.30 400746. 13.2 4923597. 21.8 22190. 7.40 432040. 13.4 5153632. 22.0 23730. 7.50 465259. 13.6 5392186. 22.2 25355. 7.60 500490. 13.8 5639493. 22.4 27068. 7.70 537824. 14.0 5895793. 22.6 28872. 7.80 577353. 14.2 6161327. 22.8 30771. 7.90 619174. 14 . X 4 6436343. 23.0 32768. 8.00 663383. 14.6 6721093. 23.2 34868. 8.10 710082. 14.8 7015834. 23.4 37074. 8.20 759375. 15.0 7320825. 23.6 39390. 8.30 811368. 15.2 7636332. 23.8 41821. 8.40 866171. 15.4 7962624. 24.0 44371 . 8.50 923896. 15.6 8299976. 24.2 47043. 8.60 984658. 15.8 8648666. 24.4 49842. 8.70 1048576. 16.0 9008978. 24.6 52773. 8.80 1115771. 16.2 9381200. 24.8 55841 . 8.90 1186367. 16.4 9765625. 25.0 59049. 9.00 1260493. 16.6 10162550. 25.2 62403. 9.10 1338278. 16.8 10572278. 25.4 65908. 9.20 1419857. 17.0 10995116. 25.6 69569. 9.30 1505366. 17.2 11431377. 25.8 73390. 9.40 1594947. 17.4 11881376. 26/0 77378. 9.50 1688743. 17.6 12345437. 26.2 81537. 9.60 1786899. 17.8 12823886. 26.4 85873. 9.70 1889568. 18.0 13317055. 26.6 90392. 9.80 1996903. 18.2 13825281 . 26.8 95099. 9.90 2109061. 18.4 14348907. 27.0 100000. 10.0 2226203. 18.6 14888280. 27.2 110408. 10.2 2348493. 18.8 15443752. 27.4 121665. 10.4 2476099. 19.0 16015681 . 27.6 133823. 10.6 2609193. 19.2 16604430. 27.8 146933. 10.8 2747949. 19.4 17210368. 28.0 161051. 11.0 2892547. 19.6 17833868. 28.2 280 NATIONAL TUBE COMPANY. Fifth Roots and Fifth Powers. (CONTINUED.) Power. No. or Root. Power. No. or Root. ^wer. N0 oo 0r 18475309. 19135075. 19813557. 20511149. 21228253. 21965275. 22722628. 23500728. 24300000. 26393634. 28.4 28.6 28.8 29.0 29.2 29.4 29.6 29.8 30.0 30.5 28629151. 31013642. 33554432. 36259082. 39135393. 42191410. 45435424. 48875980. 52521875. 56382167. 31.0 31.5 32.0 32.5 33.0 33.5 34.0 34.5 35.0 35.5 60466176. 36.0 64783487. 36.5 69343957. 37.0 74157715. 37.5 79235168. 38.0 84587005. 38.5 90224199. 39.0 96158012. 39.5 102400000. 40.0 _ J tf ! ^ NATIONAL TUBE COMPANY. 281 Squares, Cubes, Square Roots, Cube Roots, Logarithms, Re- ciprocals, Circumferences and Circular Areas of Nos. from \ to JOOO. (FROM CARNEGIE HAND BOOK.) No. 1 2 3 4 5 Sq. 1 4 9 16 25 Cube. Square Root. Cube Root. Log. 1000 X Recip. No. = Dia. Circ'm Area. 1 8 27 64 125 1.0000 1.4142 1.7321 2.0000 2.2361 1.0000 1.2599 1.4422 1.5874 1.7100 0.00000 0.30103 0.47712 0.60206 0.69897 1000.000 500.000 333. 333 250.000 200.000 3.142 6.283 9.425 12.566 15.708 0.7854 3.1416 7.0686 12.5664 19.6350 6 7 8 9 10 36 49 64 81 100 216 343 512 729 1000 2.4495 2.6458 2.8284 3.0000 3.1623 1.8171 1.9129 2.0000 2.0801 2.1544 0.77815 0.84510 0.90309 0.95424 1.00000 166.667 142.857 125.000 111.111 100.000 18.850 21.991 25.133 28.274 31.416 28.2743 38.4845 50.2655 63.6173 78.5398 11 12 13 14 15 121 144 169 196 225 1331 1728 2197 2744 3375 3.3166 3.4641 3.6056 3.7417 3.8730 2.2240 2.2894 2.3513 2.4101 2.4662 1.04139 1.07918 1.11394 1.14613 1.17609 90.9091 83.3333 76.9231 71.4286 66.6667 34.558 37.699 40.841 43.982 47.124 95.0332 113.097 132.732 153.938 176.715 16 17 18 19 20 256 289 324 361 400 4096 4913 5832 6859 8000 4.0000 4.1231 4.2426 4.3589 4.4721 2.5198 2.5713 2.6207 2.6684 2.7144 1.20412 1.23045 1.25527 1.27875 1.30103 62.5000 58.8235 55.5556 52.6316 50.0000 50.265 53.407 56.549 59.690 62.832 201.062 226.980 254.469 283.529 314.159 21 22 23 24 25 441 484 529 576 625 9261 10648 12167 13824 15625 4.5826 4.6904 4.7958 4.8990 5.0000 2.7589 2.8020 2.8439 2.8845 2.9240 1.32222 1.34242 1.36173 1.38021 1.39794 47.6190 45.4545 43.4783 41.6667 40.0000 65.973 69.115 72.257 75.398 78.540 346.361 380.133 415.476 452.389 490.874 26 27 28 29 30 676 729 784 841 900 17576 19083 21952 24389 27000 5.0990 5.1962 5.2915 5.3852 5.4772 2.9625 3.0000 3.0366 3.0723 3.1072 .41497 .43136 .44716 .46240 .47712 38.4615 37.0370 35.7143 34.4828 33.3333 81.681 84.823 87.965 91.106 94.248 530.929 572.555 615.752 660.520 706.858 31 32 33 34 35 961 1024 1089 1156 1225 29791 32768 35937 39304 42875 5.5678 5.6569 5.7446 5.8310 5.9161 3.1414 3.1748 3.2075 3.2396 3.2711 1.49136 1.50515 1.51851 1.53148 1.54407 32.2581 31.2500 30.3030 29.4118 28.5714 97.389 100.531 103.673 106.814 109.956 754.768 804.248 855.299 907.920 962.113 36 37 38 39 40 1296 1369 1444 1521 1600 46656 50653 54872 59319 64000 6.0000 6.0828 6.1644 6.2450 6.3246 3.3019 3.3322 3.8620 3.3912 3.4200 1.55630 1.56820 1.57978 1.59106 1.60206 27.7778 27.0270 26.3158 25.6410 25.0000 113.097 116.239 119.381 122.522 125.66 1017.88 1075.21 1134.11 1194.59 1256.64 41 42 43 44 45 1681 1704 1849 1936 2025 68921 74088 79507 85184 91125 6.4031 6.4807 6.5574 6.6332 6.7082 3.4482 3.4760 3.5034 3.5303 3.5569 1.61278 1.62325 1.63347 1.64345 1.65321 24.3902 23.8095 23.2558 22.7273 22.2222 128.81 131.95 135.09 138.23 141.37 1320.25 1385.44 1452.20 1520.53 1590.43 282 NATIONAL TUBE COMPANY. Squares, Cubes, Square Roots, Cube Roots, Logarithms, Etc. (CONTINUED.) No Sq. 2116 2209 2304 2401 Cube. Square Root. Cube Root. Log. 1000 X Recip. No = Dia. Circ'm Area. 46 47 48 49 97336 103823 110592 117649 6.7823 6.8557 6.9282 7.0000 3.5aso 3.6088 3.6342 3.6593 1.66276 1.67210 1.68124 1.69020 21.7391 21.2766 20.8333 20.4088 144.51 147.65 150.80 153.94 1661.90 1734.94 1809.56 1885.74 50 51 52 53 54 2500 2601 2704 2809 2916 125000 132651 140608 148877 157464 7.0711 7.1414 7.2111 7.2801 7.3485 3.6840 3.7084 3.7325 3.7563 3.7798 1.69897 1.70757 1.71600 1.72428 1.73239 20.0000 19.6078 19.2308 18.8679 18.5185 157.08 160.22 163.36 166.50 169.65 1963.50 2042.82 2123.72 2206.18 2290.22 55 56 57 58 59 3025 3136 3249 3364 3481 166375 175616 185193 195112 205379 7.4162 7.4833 7.5498 7.6158 7.6811 3.8030 3.8259 3.8485 3.8709 3.8930 1.74036 1.74819 1.75587 1.76343 1.77085 18.1818 17.8571 17.5439 17.2414 16.9492 172.79 175.93 179.07 182.21 185.35 2375.83 2463.01 2551.76 2642.08 2733.97 60 61 62 63 64 3600 3721 3844 3969 4096 216000 226981 238328 250047 262144 7.7460 7.8102 7.8740 7.9373 8.0000 3.9149 3.9365 3.9579 3.9791 4.0000 1.77815 1.78533 1.79239 1.79934 1.80618 16.6667 16.3934 16.1290 15.8730 15.6250 188.50 191.64 194.78 197.92 201.06 2827.43 2922.47 3019.07 3117.25 3216.99 65 66 67 68 69 4225 4356 4489 4624 4761 274625 287496 300763 314432 328509 8.0623 8.1240 8.1854 8.2462 8.3066 4.0207 4.0412 4.0615 .0817 .1016 1.81291 1.81954 1.82607 1.83251 1.83885 15.3846 15.1515 14.9254 14.7059 14.4928 204.20 207.35 210.49 213.63 216.77 3318.31 3421.19 3525.65 3631.68 3739.28 70 71 72 73 74 4900 5041 5184 5329 5476 343000 357911 373248 389017 405224 8.3666 8.4261 8.4853 8.5440 8.6023 .1213 .1408 .1602 .1793 .1983 1.84510 1.85126 1.85733 1.86332 1.86923 14.2857 14.0845 13.8889 13.6986 13.5135 219.91 223.05 226.19 229.34 232 48 3848.45 3959.19 4071.50 4185.39 4300.84 75 76 77 78 79 5625 5776 5929 6084 6241 421875 438976 456533 474552 493039 8.6603 8.7178 8.7750 8.8318 8.8882 4.2172 4.2a58 4.2543 4.2727 4.2908 1.87506 1.88081 1.88649 1.89209 1.89763 13.3333 13.1579 12.9870 12.8205 12.6582 235.62 238.76 241.90 245.04 248.19 4417.86 4536.46 4656.63 4778.36 4901.67 80 81 82 83 84 6400 6561 6724 6889 7056 512000 531441 551368 571787 592704 8.9443 9.0000 9.0554 9.1104 9.1652 4.3089 4.3267 4.3445 4.3621 4.3795 1.90309 1.90849 1.91381 1.91908 1.92428 12.5000 12.3457 12.1951 12.0482 11.9048 251.33 254.47 257.61 260.75 263.89 5026.55 5153.00 5281.02 5410.61 5541.77 85 86 87 88 89 7225 7396 7569 7744 7921 614125 636056 658503 681472 704969 9.2195 9.2736 9.3274 9.3808 9.4340 4.3968 4.4140 4.4310 4.4480 4.4647 .92942 .93450 .93952 .94448 .94939 11.7647 11.6279 11.4943 11.3636 11.2360 267.04 270.18 273.32 276.46 279.60 5674.50 5808.80 5944.68 6082.12 6221.14 NATIONAL TUBE COMPANY. 283 Squares, Cubes, Square Roots, Cube Roots, Logarithms, Etc. (CONTINUED.) No. 90 91 92 93 94 Sq. Cube. Square Root. Cube Root. Log. 1000 X Recip. No. = Dia. Circ'm Area. 8100 8281 8464 8649 8836 729000 753571 778688 804357 830584 9.4868 9.5394 9.5917 9.6437 9.6954 4.4814 4.4979 4.5144 4.5307 4.5468 1.95424 1.95904 1.96379 1.96848 1.97313 11.1111 10.9890 10.8696 10.7527 10.6383 282.74 285.88 289.03 292.17 295.31 6361.73 6503.88 6647.61 6792.91 6939.78 95 96 97 98 99 9025 9216 9409 9604 9801 857375 884736 912673 941192 970299 9.7468 9.7980 9.8489 9.8995 9.9499 4.5629 4.5789 4.5947 4.6104 4.6261 1.97772 1.98227 1 98677 1.99123 1.99564 10.5263 10.4167 10.3093 10.2041 10.1010 298.45 301.59 304.73 307.88 311.02 7088.22 7238.23 7389.81 7542.96 7697.69 100 101 102 103 104 10000 10201 10404 10609 10816 1000000 1030301 1061208 1092727 1124864 10.0000 10.0499 10.0995 10.1489 10.1980 4.6416 4.6570 4.6723 4.6875 4.7027 2.00000 2.00432 2.00860 2.01284 2.01703 10.0000 9.90099 9.80392 9.70874 9.61538 314.16 317.30 320.44 323.58 326.73 7853.98 8011.85 8171.28 8332.29 8494.87 105 106 107 108 109 11025 11236 11449 11664 11881 1157625 1191016 1225043 1259712 1295029 10.2470 10.2956 10.3441 10.8923 10.4403 4.7177 4.7326 .7475 .7622 .7769 2.02119 2.02531 2.02938 2.03342 2.03743 9.52381 9.43396 9.34579 9.25926 9.17431 329.87 333.01 336.15 339.29 342.43 8659.01 8824.73 8992.02 9160.88 9331.32 110 111 112 113 114 12100 12321 12544 12769 12996 1331000 1367631 1404928 1442897 1481544 10.4881 10.5357 10.5830 10.6301 10.6771 .7914 .8059 4.8203 4.8346 4.8488 2.04139 2.04532 2.04922 2.05308 2.05690 9.09091 9.00901 8.92857 8.84956 8.77193 345.58 348.72 351.86 355.00 358.14 9503.32 9676.89 9852.03 10028.7 10207.0 115 116 117 118 119 13225 13456 13689 13924 14161 1520875 1560896 1601613 1643032 1685159 10.7238 10.7703 10.8167 10.8628 10.9087 4.8629 4.8770 3.8910 4.9049 4.9187 2.06070 2.06446 2.06819 2.07188 2.07555 8.69565 8.62069 8.54701 8.47458 8.40336 361.28 364.42 367.57 370.71 373.85 10386.9 10568.3 10751.3 10935.9 11122.0 120 121 122 123 124 14400 14641 14884 15129 15376 1728000 1771561 1815848 1860867 1906624 10.9545 11.0000 11.0454 11.0905 11.1355 4.9324 4.9461 4.9597 4.9732 4.9866 2.07918 2.08279 2.08636 2.08991 2.09342 8.33333 8.26446 8.19672 8.13008 8.06452 376.99 380.13 383.27 386.42 389.56 11309.7 11499.0 11689.9 11882.3 12076.3 125 126 127 128 129 15625 15876 16129 16384 16641 1953125 2000376 2048383 2097152 2146689 11.1803 11.2250 11.2694 11.3137 11.3578 5.0000 5.0133 5.0265 5.0397 5.0528 2.09691 2.10037 2.10380 2.10721 2.11059 8.00000 7.93651 7.87402 7.81250 7.75194 392.70 395.84 398.98 402.12 405.27 12271.8 12469.0 12667.7 12868.0 13069.8 130 131 132 133 134 16900 17161 17424 17689 17956 2197000 2248091 2299968 235263? 2406104 11.4018 11.4455 11.4891 11.5326 11.5758 5.0658 5.0788 5.0916 5.1045 5.1172 2.11394 2.11727 2.12057 2.12385 2.12710 7.69231 7.63359 7.57576 7.51880 7.46269 408.41 411.55 414.69 417.83 420.97 13273.2 13478.2 13684.8 13892.9 14102.6 L , 284 NATIONAL TUBE COMPANY. Squares, Cubes, Square Roots, Cube Roots, Logarithms, Etc. (CONTINUED.) No Sq. Cube. Square Root. Cube Root. Log. 1000 X Recip. No. = Dia. Circ'm Area. 135 136 137 138 139 1822 1849 1876 19044 1932 246037 251545 257135 262807 268561 11.619 11.661 11.704 11.747 11.789 5.129S 5.1426 5.1551 5.1676 5.1801 2.1303 2.1335 2.1367 2.1398 2.1430 7.40741 7.35294 7.29927 7.2463S 7.19424 424.1 427.2 430.4 433.5 436.6 14313.9 14526.7 14741.1 14957.1 15174.7 140 141 142 143 144 19600 19881 20164 20449 20736 2744000 280322 2863288 2924207 2985984 11.832 11.874 11.9164 11.958 12.0000 5.1925 5.204 5.217 5.229 5.2415 2.1461 2.1492 2.1522 2.1553 2.1583 7.14286 7.0922 7.0422 6.9930 6.9444 439.8 442.9 446.1 449.2 452.3 15393.8 15614.5 15836.8 16060.6 16286.0 145 146 147 148 149 21025 21316 21609 21904 22201 3048625 3112136 3176523 3241792 3307949 12.041 12.0830 12.1244 12.1655 12.2066 5.2536 5.265b 5.2776 5.2896 5.3015 2.16137 2.16435 2.16732 2.17026 2.17319 6.89655 6.84932 6.80272 6.75676 6.71141 455.5 458.6 461.8 464.96 468.10 16513.0 16741.5 16971.7 17203.4 17436.6 150 151 152 153 154 22500 22801 23104 23409 23716 3375000 3442951 3511808 3581577 3652264 12.2474 12.2882 12.3288 12.3693 12.4097 5.3133 5.3251 5.3368 5.3485 5.3601 2.17609 2.17898 2.18184 2.18469 2.18752 6.66667 6.62252 6.57895 6.53595 6.49351 471.24 474.38 477.52 480.66 483.81 17671.5 17907.9 18145.8 18385.4 18626.5 155 156 157 158 159 24025 24336 24649 24964 25281 3723875 3796416 3869893 3944312 4019679 12.4499 12.4900 12.5300 12.5698 12.6095 5.3717 5.3832 5.3947 5.4061 5.4175 2.19033 2.19312 2.19590 2.19866 2.20140 6.45161 6.41026 6.3(5943 6.32911 6.28931 486.95 490.09 493.23 496.37 499.51 18869.2 19113.4 19359.3 19606.7 19855.7 160 161 162 163 164 25600 25921 26244 26569 26896 4096000 4173281 4251528 4330747 4410944 12.6491 12.6886 12.7279 12.7671 12.8062 5.4288 5.4401 5.4514 5.4626 5.4737 2.20412 2.20683 2.20952 2.21219 2.21484 6.25000 6.21118 6.17284 6.13497 6.09756 502.65 505.80 508.94 512.08 515.22 20106.2 20358.3 20612.0 20867.2 21124.1 165 166 167 168 169 27225 27556 27889 28224 285C1 4492125 4574296 4657463 4741632 4826809 12.8452 12.8841 12.9228 12.9615 13.0000 5.4848 5.4959 5.5069 5.5178 5.5288 2.21748 2.22011 2.22272 2.22531 2.22789 6.06061 6.02410 5.98802 5.95238 5.91716 518.36 521.50 524.65 527.79 530.93 21382.5 21642.4 21904.0 22167.1 22431.8 170 171 172 173 174 28900 29241 29584 29929 30276 4913000 5000211 5088448 5177717 5268024 13.0384 13.0767 13.1149 13.1529 13.1909 5.5397 5.5505 5.5613 5.5721 5.5828 2.23045 2.23300 2.23553 2.23805 2.24055 5.88235 5.84795 5.81395 5.78035 5.74713 534.07 537.21 540.35 543.50 546.64 22698.0 22965.8 23235.2 23506.2 23778.7 175 176 177 178 179 30625 30976 31329 31684 32041 5359375 5451776 5545233 5639752 5735339 13.2288 13.2665 13.3041 13.3417 13.3791 5.5934 5.6041 5.0147 5.6252 5.6357 2.24304 2.24551 2.24797 2.25042 2.25285 5.71429 5.68182 5.64972 5.61798 5.58659 549.78 552.92 556.06 559.20 562.35 24052.8 24328.5 24605.7 24884.6 25164.9 NATIONAL TUBE COMPANY. 285 Squares, Cubes, Square Roots, Cube Roots, Logarithms, Etc. (CONTINUED.) No. 180 181 182 183 184 Sq. Cube. Square Root. Cube Root. Log. 1000 X Recip. No. = Dia. Circ'm Area. 32400 32761 33124 33489 33856 5832000 5929741 6028568 6128487 6229504 13.4164 13.4536 13.4907 13.5277 13.5647 5.6462 5.6567 5.6671 5.6774 5.6877 2.25527 2.25768 2.26007 2.26245 2.26482 5.55556 5.52486 5.49451 5.46448 5.43478 565.49 568.63 571.77 574.91 578.05 25446.9 25730.4 26015.5 26302.2 26590.4 186 186 187 188 189 34225 34596 34969 35344 35721 6331625 6434856 6539203 6644672 6751269 13.6015 13.6382 13.6748 13.7113 13.7477 5.69PO 5 7083 5.7185 5.7287 5.7388 2.26717 2.26951 2.27184 2.27416 2.27646 5.40541 5.37634 5.34759 5.31915 5.29101 581.19 584.34 587.48 590.62 593.76 26880.3 27171.6 27464.6 27759.1 28055.2 190 191 192 193 194 36100 36481 36864 37249 37636 6859000 6967871 7077888 7189057 7301384 13.7840 13.8203 13.8564 13.8924 13.9284 5.7489 5.7590 5.7690 5.7790 5.7890 2.27875 2.28103 2.28330 2.28556 2.28780 5.26316 5.23560 5.20833 5.18135 5.15464 596.90 600.04 603.19 606.33 609.47 28352.9 28652.1 28952.9 29255.3 29559.2 195 196 197 198 199 38025 38416 38809 39204 39601 7414875 7529536 7645373 7762392 7880599 13.9642 14.0000 14.0357 14.0712 14.1067 5.7989 5.8088 5.8186 5.8285 5.8383 2.29003 2.29226 2.29447 2.29667 2.29885 5.12821 5.10204 6.07614 5.05051 5.02513 612.61 615.75 618.89 622.04 625.18 29864.8 30171.9 30480.5 30790.7 31102.6 200 201 202 203 204 40000 40401 40804 41209 41616 8000000 8120601 8242408 8365427 8489664 14.1421 14.1774 14.2127 14.2478 14.2829 5.8480 5.8578 5.8675 5.8771 5.8868 2.30103 2.30320 2.30535 2.30750 2.30963 5.00000 4.97512 4.95050 4.92611 4.90196 628.32 631.46 634.60 637.74 640.89 31415.9 31730.9 32047.4 32365.5 32685.1 205 206 207 208 209 42025 42436 42849 43264 43681 8615125 8741816 8869743 8998912 9129329 14.3178 14.3527 14.3875 14.4222 14.4568 5.8964 5.9059 5.9155 5.92(50 5.9345 2.31175 2.31387 2.31597 2.31806 2.32015 4.87805 4.85437 4.83092 4.80769 4.78469 644.03 647.17 650.31 653.45 656.59 33006.4 33329.2 33653.5 33979.5 34307.0 210 211 212 213 214 44100 44521 44944 45369 45796 9261000 9393931 95-28128 96(>3597 9800344 14.4914 14.5258 14.560-2 14.5945 14.6287 5.9439 5.9533 5.9627 5.9721 5.9814 2.32222 2.32428 2 ! 32838 2.33041 4.76190 4.73934 4.71698 4.69484 4.67290 659.73 662.88 666.02 669.16 672.30 34636.1 34966.7 35298.9 35632.7 35968.1 215 216 217 218 219 46225 46656 47089 47524 47961 9938375 10077696 10218313 10360232 10503459 14.6629 14.6969 14.7309 14.7648 14.7986 5.9907 6.0000 6.0092 6.0185 6.0277 2.33244 2.33445 2. ,33646 2.338-16 2 34044 4.65116 4.62963 4.60829 4.58716 4.56621 675.44 678.58 681.73 684.87 688.01 36305.0 36643.5 36983.6 37325.3 37668.5 220 221 222 223 224 48400 48841 49284 49729 5017( 10648000 10793861 10941048 11089567 11239424 14.8324 14.8661 14.8997 14.9332 14.9666 6.0368 6 0459 6.0550 6.0641 6.0732 2.34242 2.34439 2.34635 2.34&30 2.35025 4.54545 4.52489 4.50450 4.48431 4.46429 691.15 694.29 697.43 700.58 703.72 38013.3 38359.6 38707.6 39057.1 39408.1 t <3 286 NATIONAL TUBE COMPANY. Squares, Cubes, Square Roots, Cube Roots, Logarithms, Etc. (CONTINUED.) No. Sq. Cube. Square Root. Cube Root. Log. 1000 X Recip. No = Dia. Circ'm Area. 225 50625 11390625 15.0000 6.0822 2.35218 4.44444 706.86 39760.8 226 51076 11543176 15.0333 6.0912 2.35411 4.42478 710.00 40115.0 227 51529 11697083 15.0665 6.1002 2.35603 4.40529 713.14 40470.8 228 51984 11852352 15.0997 6.1091 2.35793 4.38596 716.28 40828.1 229 52441 12008989 15.1327 6.1180 2.35984 4.36681 719.42 41187.1 230 52900 12167000 15.1658 6.1269 2.36173 4.34783 722.57 41547.6 231 53361 12326391 15.1987 6.1358 2.36361 4.32900 725.71 41909.6 232 53824 12487168 15.2315 6.1446 2.36549 4.31034 728.85 42273.3 233 54289 12649337 15.2643 6.1534 2.36736 4.29185 731.99 42638.5 234 54756 12812904 15.2971 6.1622 2.36922 4.27350 735.13 43005.3 235 55225 12977875 15.3297 6.1710 2.37107 4.25532 738.27 43373.6 236 55696 13144256 15.3623 6.1797 2.37291 4.23729 741.42 43743.5 237 56169 13312053 15.3948 6.1885 2.37475 4.21941 744.56 44115.0 238 56644 13481272 15.4272 6.1972 2.37658 4.20168 747.70 44488.1 239 57121 13651919 15.4596 6.2058 2.37840 4.18410 750.84 44862.7 240 57600 13824000 15.4919 6.2145 2.38021 4.16667 753.98 45238.9 241 58081 13997521 15.5242 6.2231 2.38202 4.14938 757.12 45616.7 242 58564 14172488 15.5563 6.2317 2.38382 4.13223 760.27 45996.1 243 59049 14348907 15.5885 6.2403 2.38561 4.11523 763.41 46377.0 244 59536 14526784 15.6205 6.2488 2.38739 4.09836 766.55 46759.5 245 60025 14706125 15.6525 6.2573 2.38917 4.08163 769.69 47143.5 246 60516 14886936 15.6844 6.2658 2.39094 4.06504 772.83 47529.2 247 61009 15069223 15.7162 6.2743 2.39270 4.04858 775.97 47916.4 248 61504 15252992 15.7480 6.2828 2.39445 4 03226 779.12 48305.1 249 62001 15438249 15.7797 6.2912 2.39620 4.01606 782.26 48695.5 250 62500 15625000 15.8114 6.2996 2.39794 4.00000 785.40 49087.4 251 63001 15813251 15.8430 6.3080 2.39967 3.98406 788.54 49480.9 252 63504 16003008 15.8745 6.3164 2.40140 3.96825 791.68 49875.9 253 64009 16194277 15.9060 6.3247 2.40312 3.95257 794.82 50272.6 254 64516 16387064 15.9374 6.3330 2.40483 3.93701 797.96 50670.7 255 65025 16581375 15.9687 6.3413 2.40654 3.92157 801.11 51070.5 256 65536 16777216 16.0000 6.3496 2.40824 3.90625 804.25 51471.9 257 66049 16974593 16.0312 6.3579 2.40993 3.89105 807.39 51874.8 258 66564 17173512 16.0624 6.3661 2.41162 3.87597 810.53 52279.2 259 67081 17373979 16.0935 6.3743 2.41330 3.86100 813.67 52685.3 260 67600 17576000 16.1245 6.3825 2.41497 3.84615 816.81 53092.9 261 68121 17779581 16.1555 6.3907 2.41664 3.83142 819.96 53502.1 262 68644 17984728 16.1864 6.3988 2 41830 3.81679 823.10 53912.9 263 69169 18191447 16.2173 6.4070 2.41996 3.80228 826.24 54325.2 264 69696 18399744 16.2481 6.4151 2.42160 3.78788 829.38 54739.1 265 70225 18609625 16.2788 6.4232 2.42325 3.77358 832 52 55154.6 266 70756 18821096 16.8095 6.4312 2.42488 3.75940 835.66 55571.6 267 71289 19034163 16.3401 (5.4393 2.42651 3.74532 838.81 55990.3 268 71824 19248832 16.3707 6.4473 2.42813 3.73134 841.95 50410.4 269 72361 19465109 16.4012 6.4553 2.42975 3.71747 845. C9 56832.2 NATIONAL TUBE COMPANY. 287 1 Squares, Cubes, Square Roots, Cube Roots, Logarithms, Etc. (CONTINUED.) 1 No. Sq. Cube. Square Root. Cube Root. LOR. 1000 X Recip. No. = Dla. Circ'm Area. 1 270 1 271 1 272 1 273 I 274 72900 73441 73984 74529 75076 19683000 19902511 20123648 20346417 20570824 16 4317 16.4621 16.4924 16.5227 16.5529 6.4633 6.4713 6.4792 6.4872 6.4951 2.43136 2.43297 2.43457 2.43616 2.43775 3.70370 3.69004 3.67647 3.66300 3.64964 848.23 851.37 854.51 857.66 860.80 57255.5 57680.4 58106.9 58534.9 58964.6 1 275 1 276 1 277 I 278 1 279 75625 76176 76729 77284 77841 20796875 21024576 21253933 21484952 21717639 16.5831 16.6132 16.6433 16.6733 16.7033 6.5030 6.5108 6.5187 6.5265 6.5343 2.43933 2.44091 2.44248 2.44404 2.44560 3.63636 3.62319 3.61011 3.59712 3.58423 863.94 867.08 870.22 873.36 876.50 59395.7 59828.5 60262.8 60698.7 61136.2 1 280 1 281 1 282 1 283 1 234 78400 78961 79524 80089 80656 21952000 22188041 22425768 22665187 22906304 16.7332 16.7631 16.7929 16.8226 16.8523 6.5421 6.5499 6.5577 6.5654 6.5731 2.44716 2.44871 2.45025 2.45179 2.45332 3.57143 3.55872 3.54610 3.53357 3.52113 879.65 882.79 885.93 889.07 892.21 61575.2 62015.8 62458.0 62901.8 63347.1 1 285 286 287 288 289 81225 81796 82369 82944 83521 23149125 23393656 23639903 23887872 24137569 16.8819 16.9115 16.9411 16.9706 17.0000 6.5808 6.5885 6.5962 6.6039 6.6115 2.45484 2.45637 2.45788 2.45939 2.46090 3.50877 3.49650 3.48432 3.47222 3.46021 895.35 898.50 901.64 904.78 907.92 63794.0 64242.4 64692.5 65144.1 65597.2 290 291 292 293 294 84100 84681 85264 85849 86436 24389000 24642171 24897088 25153757 25412184 17.0294 17.0587 17.0880 17.1172 17.1464 6.6191 6.6267 6.6343 6.6419 6.6494 2.46240 2.46389 2.46538 2.46687 2.46835 3.44828 3.43643 3.42466 3.41297 3.40136 911.06 914.20 917.35 920.49 923.63 66052.0 66508.3 66966.2 67425.6 67886.7 295 296 297 298 299 87025 87616 88209 88804 89401 25672375 25934336 26198073 26463592 26730899 17.1756 17.204? 17.2337 17.2627 17.2916 6.6569 6.6644 6.6719 6.6794 6.6869 2.46982 2.47129 2.47276 2.47422 2.47567 3.38983 3.37838 3.36700 3.35570 3.34448 926.77 929.91 933.05 936.19 939.34 68349.3 68813.5 69279.2 69746.5 70215.4 300 301 302 303 304 90000 90601 91204 91809 92416 27000000 27270901 27543608 27818127 28094464 17.3205 17.3494 17.3781 17.4069 17.4356 6.6943 6.7018 6.7092 6.7166 6.7240 2.47712 2.47857 2.48001 2.48144 2.48287 3.33333 3.32226 3.31126 3.30033 3.28947 942.48 945.62 948.76 951.90 955.04 70685.8 71157.9 71631.5 72106.6 72583.4 305 306 307 308 309 93025 93636 94249 94864 95481 28372625 28652616 28934443 29218112 29503629 17.4642 17.4929 17.5214 17.5499 17.5784 6.7313 6.7387 6.7460 6.7533 6.7606 2.48430 2.48572 2.48714 2.48855 2.48996 3.27869 3.26797 3.25733 3.24675 3.23625 958.19 961.33 964.47 967.61 970.75 73061.7 73541.5 74023.0 74506.0 74990.6 310 311 312 313 314 96100 96721 97344 97969 98596 29791000 30080231 30371328 30664297 30959144 17.6068 17.6352 17.6635 17.6918 17.7200 6.7679 6.7752 6.7824 6.7897 6.7969 2.49136 2.49276 2.49415 2.49554 2.49693 3.22581 3.21543 3.20513 3.19489 3.18471 973.89 977.04 980.18 983.32 986.46 75476.8 75964.5 76453.8 76944.7 77437.1 n ,', 288 NATIONAL TUBE COMPANY, Squares, Cubes, Square Roots, Cube Roots, Logarithms, Etc. (CONTINUED.) No Sq. Cube. Square Root. Cube Root. Log. 1000 X Recip No = Dia. Circ'm Area. 315 99225 31255875 17.7482 6.8041 2.49831 3.17460 989.60 77931.1 316 99856 31554496 17.7764 6.8113 2.49969 3.16456 992.74 78426.7 317 100489 31855013 17.8045 6.8185 2.50106 3.15457 995.88 78923.9 318 101124 32157432 17.8326 6.8256 2.50243 3.14465 999.03 79422.6 319 101761 32461759 17.8606 6.8328 2.50379 3.13480 1002.2 79922.9 320 102400 32768000 17.8885 6.8399 2.50515 3.12500 1005.3 80424.8 321 103041 33076161 17.9165 6.8470 2.50651 3.11527 1008.5 80928.2 322 103684 33386248 17.9444 6.8541 2.50786 3.10559 1011.6 81433.2 323 104329 33698267 17.9722 6.8612 2.50920 3.0959b 1014.7 81939.8 324 104976 34012224 18.0000 6.8633 2.51055 3.08642 1017.9 82448.0 325 105625 34328125 18.0278 6.8753 2.51188 3.07692 1021.0 82957.7 326 106276 34645976 18.0555 6.8824 2.51322 3.06749 1024.2 83469.0 I 327 106929 34965783 18.0831 6.8894 2.51455 3.05810 1027.3 83981.8 1 328 107584 35287552 18.1108 6.8964 2.51587 3.04878 1030.4 84496.3 1 329 108241 35611289 18.1384 6.9034 2.51720 3.03951 1033.6 85012.3 1 330 108900 35937000 18.1659 6.9104 2.51851 3.03030 1036.7 85529.9 1 331 109501 36264691 18.1934 6.9174 2.51983 3.02115 1039.9 86049.0 1 332 110224 36594368 18.2209 6.9244 2.52114 3.01205 1043.0 86569.7 1 333 110889 36926037 18.2483 6.9313 2.52244 3.00300 1046.2 87092.0 1 334 111556 37259704 18.2757 6.9382 2.52375 2.99401 1049.3 87615.9 1 335 112225 37595375 18.3030 6.9451 2.52504 2.98507 1052.4 88141.3 1 336 112896 37933056 18.3303 6.9521 2.52634 2. 976 19 1055 6 88668.3 1 337 113569 38272753 18.3576 6.95S9 2.52763 2.96736 1058.7 89196.9 1 338 114244 38614472 1 18.3848 (>.%5S 2.52892 2.95858 1061.9 89727.0 1 339 114921 38958219 18.4120 6.9727 2.53020 2.94985 1065.0 90258.7 1 340 115600 39304000 18.4391 6.9795 2.53148 2.94118 1068.1 90792.0 1 341 116281 39651821 18.4662 6 9864 2.53275 8.98255 1071.3 91326.9 1 34* 116964 400011)88 18.4932 6.9932 2.53408 2!92308 1074.4 91863.3 1 343 117649 40453607 18.5203 7.0000 2.53529 2.91545 1077.6 92401.3 1 344 118336 40707584 18.5472 7.0068 2.53656 2.90698 1080.7 92940.9 I 345 119025 41063625 18.5742 7.0136 2.53782 2.89855 1083.8 93482.0 346 119716 41421736 18.6011 7.0203 2.53908 2.89017 1087.0 94024.7 347 120409 41781923 18.6279 7.0271 2.54033 2.88184 1090.1 94569.0 348 121104 42111192 18.6548 7.0338 2.54158 2.87356 1093.3 95114.9 349 121801 42508549 18.6815 7.0406 2.54283 2.86533 1096.4 95662.3 350 122500 42875000 18.7083 7.0473 2.54407 2.85714 1099.6 96211.3 351 123201 43243551 18.7350 7.0540 2.54531 2.84900 1102.7 96761.8 352 123904 43614208 18.7617 7.0607 2.54654 2.84091 1105.8 97314.0 353 124609 43986977 18.7883 7.0674 2.54777 2.83286 1109.0 97867.7 354 125316 44361864 18.8149 7.0740 2.54900 2.82486 1112.1 98423.0 355 126025 44738875 18.8414 7.0807 2.55023 2.81690 1115.3 98979.8 356 126736 45118016 18.8680 7.0873 2 55145 2.80899 1118.4 99538.2 357 127449 45499293 18.8944 7.0940 2.55267 2.80112 1121.5 100098 358 128164 45882712 18.9209 7.1006 2.65388 2.79330 1124.7 100660 359 128881 462(58279 18.9473 7.1072 2.55509 2.78552 1127.8 101223 , NATIONAL TUBE COMPANY. 289 Squares, Cubes, Square Roots, Cube Roots, Logarithms, Etc. (CONTINUED.) No. Sq. Cube. Square Root. Cube Root. Log. 1000 X Recip. No = Dia. Circ'm Area. 360 129600 46656000 18.9737 7.1138 2.55630 2.77778 1131.0 101788 361 130321 47045881 19.0000 7.1204 2.55751 2.77008 1134.1 102354 362 131044 47437928 19.0263 7.1269 2.55871 2.76243 1137.3 102922 . 363 131769 47832147 19.0526 7.1335 2.55991 2.75482 1140.4 103491 364 132496 48228544 19.0788 7.1400 2.56110 2.74725 1143.5 104062 365 133225 48627125 19.1050 7.1466 2.56229 2.73973 1146.7 104635 366 133956 49027896 19.1311 7.1531 2.56348 2.73224 1149.8 105209 367 134689 49430863 19.1572 7.1596 2.56467 2.72480 1153.0 105785 368 135424 49836032 19.1833 7.1661 2.56585 2.71739 1156.1 106362 369 136161 50243409 19.2094 7.1726 2.56703 2.71003 1159.2 106941 370 136900 50653000 19.2354 7.1791 2.56820 2.70270 1162.4 107521 371 137641 51064811 19.2614 7.1855 2 56937 2.69542 1165.5 108103 372 138334 51478848 19.2873 7.1920 2.57054 2.68817 1168.7 108687 373 139129 51895117 19.3132 7.1984 2.57171 2.68097 1171.8 109272 374 139876 52313624 19.3391 7.2048 2.57287 2.67380 1175.0 109858 375 140625 52734375 19.3649 7.2112 2.57403 2.66667 1178.1 110447 376 141376 53157376 19.3907 7.2177 2.57519 2.65957 1181.2 111036 377 142129 53582633 19.4165 7.2240 2.57634 2.65252 1184.4 111628 378 142884 54010152 19.4422 7.2304 2.57749 2.64550 1187.5 112221 379 143641 54439939 19.4679 7.2368 2.57864 2.63852 1190.7 112815 380 144400 54872000 19.4936 7.2432 2.57978 2.63158 1193.8 113411 381 145161 55306341 19.5192 7.2495 2.58093 2.62467 1196.9 114009 382 145924 55742968 19.5448 7.2558 2.58206 2.61780 1200.1 114608 383 146689 56181887 19.5704 7.2622 2.58320 2.61097 1203.2 115209 384 147456 56623104 19.5959 7.2685 2.58433 2.60417 1206.4 115812 385 148225 57066625 19.6214 7.2748 2.58546 2.59740 1209.5 116416 386 148996 57512456 19.6469 7.2811 2.58659 2.59067 1212.7 117021 387 149769 57960603 19.6723 7.2874 2.58771 2.58398 1215.8 117628 388 150544 58411072 19.6977 7.2936 2.58883 2.57732 1218.9 118237 389 151321 58863869 19.7231 7.2999 2.58995 2.57069 1222.1 118847 390 152100 59319000 19.7484 7.3061 2.59106 2.56410 1225.2 119459 391 152881 59776471 19.7737 7.3124 2.59218 2.55755 1228.4 120072 392 153664 60236288 19.7990 7.3186 2.59329 2.55102 1231.5 120687 393 154449 60698457 19.8242 7.3248 2.59439 2.54453 1234.6 121304 394 155236 61162984 19.8494 7.3310 2.59550 2.53807 1237.8 121922 395 156025 61629875 19.8746 7.3372 2.59660 2.53165 1240.9 122542 396 156816 62099136 19.8997 7.3434 2.59770 2.52525 1244.1 123163 397 157609 62570773 19.9249 7.3496 2.59879 2.51889 1247.2 123786 398 158404 63044792 19.9499 7.3558 2.59988 2.51256 1250.4 124410 399 159201 63521199 19.9750 7.3619 2.60097 2.50627 1253.5 125036 400 160000 64000000 20.0000 7.3681 2.60206 2.50000 1256.6 125664 401 160801 64481201 20.0250 7.3742 2.60314 2.49377 1259.8 126293 402 161604 64964808 20.0499 7.3803 2.60423 2.48756 1262.9 126923 403 162409 65450827 20.0749 7.3864 2.60531 2.48139 1266.1 127556 404 163216 65939264 20.0998 7.3925 2.60638 2.47525 1269.2 128190 290 NATIONAL TUBE COMPANY. Squares, Cubes, Square Roots, Cube Roots, Logarithms, Etc. 1 (CONTINUED.) Square Cube 1000 No. = Dia. 1 No. Sq. Cube. Root. Root. Log. X Recip. Circ'm Area. 1 405 164025 66430125 20.1246 7.3986 2.60746 2.46914 1272.3 128825 1 406 164836 66923416 20.1494 7.4047 2.60853 2.46305 1275.5 129462 1 407 165649 67419143 20.1742 7.4108 2.60959 2.45700 1-278.6 130100 1 408 166464 67917312 20.1990 7.4169 2.61066 2.45098 1281.8 130741 1 409 167281 68417929 20.2237 7.4229 2.61172 2.44499 1284 9 131382 1 410 168100 68921000 20.2485 7.4290 2.61278 2.43902 1288.1 132025 1 411 168921 69426531 20.2731 7.4350 2.61384 2.43309 1291.2 132670 1 412 169744 69934528 20.2978 7.4410 2.61490 2.42718 1294.3 133317 1 413 170569 70444997 20.3224 7.4470 2.61595 2.42131 1297.5 133965 1 414 171396 70957944 20.3470 7.4530 2.61700 2.41546 1300.6 134614 1 415 172225 71473375 20.3715 7.4590 2.61805 2.40964 1303.8 135265 1 416 173056 71991296 20.3961 7.4650 2.61909 2.40385 1306.9 135918 1 417 173889 72511713 20.4206 7.4710 2.62014 2.39808 1310.0 136572 1 418 174724 73034632 20.4450 7.4770 2.62118 2.39234 1313.2 137228 I 419 175561 73560059 20.4695 7.4829 2.62221 2.38664 1316.3 137885 1 420 176400 74088000 20.4939 7.4889 2.62325 2.38095 1319.5 138544 1 421 177241 74618461 20.5183 7.4948 2 62428 2.37530 1322.6 139205 1 422 178084 75151448 20.5426 7.5007 2.62531 2.36967 1325.8 139867 1 423 1789*9 75686967 20.5670 7.5067 2.62634 2.36407 1328.9 140531 1 424 179776 76225024 20.5913 7.5126 2.62737 2.35849 1332.0 141196 1 425 180625 76765625 20.6155 7.5185 2.62839 2.35294 1335.2 141863 1 426 181476 77308776 20.6398 7.5244 2.62941 2.34742 1338.3 142531 427 182329 77854483 20.6640 7.5302 2.63043 2.34192 1341.5 143201 1 428 183184 78402752 20.6882 7.5361 2.63144 2.33645 1344.6 143872 1 429 184041 78953589 20.7123 7.5420 2.63246 2.33100 1347.7 144545 1 430 184900 79507000 20.7364 7.5478 2.63347 2.32558 1350.9 145220 1 431 185761 80062991 20.7605 7.5537 2.63448 2.32019 1354.0 145896 1 432 186624 80621568 20.7846 7.5595 2.63548 2.31482 1357.2 146574 1 433 187489 81182737 20.8087 7.5654 2.63649 2.30947 1360.3 147254 1 434 188356 81746504 20 8327 -7.5712 2.63749 2.30415 1363.5 147934 435 189225 82312875 20.8567 7.5770 2.63849 2.29885 1366.6 148617 1 436 190096 82881856 20.8806 7.5828 2.63949 2.29358 1369.7 149301 437 190969 83453453 20.9045 7.5886 2.64048 2 28833 1372.9 149987 1 438 191844 84027672 20.9284 7.5944 2.64147 2.28311 1376.0 150674 1 439 192721 84604519 20.9523 7.6001 2.64246 2.27790 1379.2 151363 440 193600 85184000 20.9762 7.6059 2.64345 2.27273 1382.3 152053 441 194481 85766121 21.0000 7.6117 2.64444 2.26757 1385.4 152745 1 442 195364 86350888 21.0238 7.6174 2.64542 2 26244 1388.6 153439 443 196249 86938307 21.0476 7.6232 2.64640 2.25734 1391.7 154134 444 197136 87528384 21.0713 7.6289 2.64738' 2.25225 1394.9 154830 j 445 198025 88121125 21.0950 7.6346 2.64836 2.24719 1398.0 155528 446 198916 88716536 21.1187 7.6403 2.649&S 2.24215 1401.2 156228 447 199809 89314623 21.1424 7.6460 2.65031 2.23714 1404.3 156930 448 200704 89915392 21.1660 7.6517 2.65128 2.23214 1407.4 157633 449 2016011 90518849 21.1896 7.6574 2.65225 2.22717 1410.6 158337 NATIONAL TUBE COMPANY. 291 Squares, Cubes, Square Roots, Cube Roots, Logarithms, Etc. (CONTINUED.) No. 450 451 452 453 454 Sq. Cube. Square Root. Cube Root. Log. 1000 X Recip. No. = Dia. Circ'm Area. 202500 20:3401 204304 205209 206116 91125000 91733851 92345408 92959677 93576664 21.2132 21.2368 21.2603 21.2838 21.3073 7.6631 7.6688 7.6744 7.6801 7.6857 2.65321 2.65418 2.65514 2.65610 2.65706 2.22222 2.21730 2.21239 2.20751 2.20264 1413.7 1416.9 1420.0 1423.1 1426.3 159043 159751 160460 161171 161883 455 456 457 458 459 207025 207936 208849 209764 210681 94196375 94818816 95443993 96071912 96702579 21.3307 21.3542 21.3776 21 .4009 21.4243 7.6914 7.6970 7.7026 7.7082 7.7138 2.65801 2.65896 2.05992 2 66087 2.66181 2.19780 2.19298 2.18818 2.18341 2.17865 1429.4 1432.6 1435.7 1438.9 1442.0 162597 163313 164030 164748 165468 460 461 462 463 464 211600 212521 213444 214369 215296 97:536000 97972181 98611128 99252847 99897344 21.4476 21 .4709 21.4942 21.5174 21.5407 7.7194 7.7250 7.7306 7.7362 7.7418 2.66276 2.66370 2.66464 2.66558 2.66652 2.17391 2.16920 2.16450 2.15983 2.15517 1445.1 1448.3 1451.4 1454.6 1457.7 166190 166914 167639 168365 169093 465 466 467 468 469 216225 217156 218089 219024 219961 100544625 101194696 101847563 102503232 103161709 21.5639 21.5870 21.6102 21.6-333 21.6564 7.7473 7.7529 7.7584 7.7639 7.7695 2.66745 2.66839 2.66932 2.67025 2.67117 2.15054 2.14592 2.141:33 2.13675 2.13220 1460.8 1464.0 1467.1 1470.3 1473.4 169823 170554 171287 172021 172757 470 471 472 473 474 220900 221841 .'2-j;st 223729 224676 103823000 104487111 105154048 105823817 106496424 21.6795 21.7025 21.7256 21.7486 21.7715 7.7750 7.7805 7.7860 7.7915 7.7970 2.67210 2.67302 2.67394 2.67486 2.67578 2.12766 2.12314 2.11864 2.11417 2.10971 1476.5 1479.7 1482.8 1486.0 1489.1 173494 174234 174974 175716 176460 475 476 477 478 479 225625 226576 227529 228484 229441 107171875 107850176 1085313:33 109215352 109902239 21.7945 21.8174 21 .8403 21.8632 21.8861 7.8025 7.8079 7.8134 7.8188 7.8243 2.67669 2.67761 2.67852 2.67943 2.68034 2.10526 2.10084 2.09644 2.09205 2.08768 1492.3 1495.4 1498.5 1501.7 1504.8 177205 177952 178701 179451 180203 480 481 482 483 484 230400 231361 2::5:J J 233289 234256 110592000 111284641 111980168 112678587 113379904 21.9089 21.9317 21 .9545 21.9773 22.0000 7.8297 7.8352 7.8406 7.8460 7.8514 2.68124 2.68215 2.68305 2.68395 2.68485 2.08333 2.07900 2.07469 2.07039 2.06612 1508.0 1511.1 1514.3 1517.4 1520.5 180956 181711 182467 183225 183984 1485 486 487 488 489 235225 236196 237169 238144 239121 114084125 114791256 115501303 116214272 116930169 22.0227 22.0454 22.0681 22.0907 22.1133 7.8568 7.8622 7.8676 7 8730 7.8784 2.68574 2.68664 2 68753 2.68842 2.68931 2.06186 2.05761 2.05339 2.04918 2.04499 1523.7 1526.8 1530.0 isas.i 1536.2 184745 185508 186272 187038 187805 490 491 492 493 494 240100 241081 242064 243049 244036 117649000 118370771 119095488 119823157 120553784 22.U359 22.1585 22.1811 22.2036 22.2261 7.8837 7.8891 7.8944 7.8998 7.9051 2.69020 2.69108 2.69197 2.69285 2.69373 2.04082 2.03666 2.03252 2.02840 2 02429 1539.4 1542.5 1545.7 1548.8 1551.9 188574 189345 190117 190890 191665 . 292 NATIONAL TUBE COMPANY. Squares, Cubes, Square Roots, Cube Roots, Logarithms, Etc* (CONTINUED.) No. Sq. Cube. Square Root. Cube Root. Log. 1000 X Recip. No. = Dia. Circ'm Area. 495 245025 121287375 22.2486 7.9105 2.69461 2.02020 1555.1 192442 496 246016 122023936 22.2711 7.9158 2.69548 2.01613 1558.2 193221 497 247009 122763473 22.2935 7.9211 2.69636 2.01207 1561.4 194000 498 248004 123505992 22.3159 7.9264 2.69723 2.00803 1564.5 194782 499 249001 124251499 22.3383 7.9317 2.69810 2.00401 1567.7 195565 500 250000 125000000 22.3607 7.9370 2.69897 2.00000 1570.8 196350 501 251001 125751501 22.3830 7.9423 2.69984 1.99601 1573.9 197136 502 252004 126506008 22.4054 7.9476 2.70070 1.99203 1577.1 197923 503 253009 127263527 22.4277 7.9528 2.70157 1.98807 1580.2 198713 504 254016 128024064 82.4499 7.9581 2.70243 1.98413 1583.4 199504 505 255025 128787625 22.4722 7.9634 2.70329 1.98020 1586.5 200296 506 256036 129554216 22.4944 7.9686 2.70415 1.97629 1589.7 201090 507 257049 130323843 22.5167 7.9739 2.70501 1.97239 1592.8 201886 508 258064 131096512 22.5389 7.9791 2.70586 1.96850 1595.9 202683 509 259081 131872229 22.5610 7.9843 2.70672 1.96464 1599.1 203482 510 260100 132651000 22.5832 7.9896 2.70757 1.96078 1602.2 204282 511 261121 133432831 22.6053 7.9948 2.70842 1.95695 1605.4 205084 512 262144 134217728 22.6274 8.0000 2.70927 1.95312 1608.5 205887 513 263169 135005697 22.6495 8.0052 2.71012 1.94932 1611.6 206692 514 264196 135796744 22.6716 8.0104 2.71096 1.94553 1614.8 207499 515 265225 136590875 22.6936 8.0156 2.71181 1.94175 1617.9 208307 516 266256 137388096 22.7156 8.0208 2.71265 1.93798 1621.1 209117 517 267289 138188413 22.7376 8.0260 2.71349 1.93424 1624.2 209928 518 268324 138991832 22.7596 8.0311 2.71433 1.93050 1627.3 210741 519 269361 139798359 22.7816 8.0363 2.71517 1.92678 1630.5 211556 520 270400 140608000 22.8035 8.0415 2.71600 1 92308 1633.6 212372 521 271441 141420761 22.8254 8.0466 2.71684 1.91939 1636.8 213189 522 272484 142236648 22.8473 8 0517 2.71767 1 91571 1639.9 214G08 523 273529 143055667 22.8692 8.0569 2.71850 1.91205 1643.1 214829 524 274576 143877824 22.8910 8.0620 2.71933 1.90840 1646.2 215651 525 275625 144703125 22.9129 8.0671 2.72016 1.90476 1649.3 216475 526 276676 145531576 22.9347 8.0723 2.72099 1.90114 1652.5 217301 527 27773 146363183 22.9565 8.0774 2.72181 1.89753 1655.6 218128 528 278784 147197952 22.9783 8.0825 2.72263 l.S!91 1658.8 218956 529 279841 148035889 23.0000 8.0876 2.72346 1.89036 1661.9 219787 530 280900 148877000 23.0217 8.0927 2.72428 1.88679 1665.0 220618 531 281961 149721291 23.0434 8.0978 2.72509 1.88324 1668.2 221452 532 28302- 150568768 23.0651 8.1028 2.72591 1.87970 1671.3 222287 533 - 'Sins'. 151419427 23.0868 8.1079 2.72673 1.87617 1674.5 223123 534 285156 152273304 23.1084 8.1130 2.72754 1.87266 1677.6 223961 535 286225 158130875 23.1301 8.1180 2.72835 1.86916 1680.8 224801 536 28725M 153990656 23.1517 8.1231 2.7291C 1.86567 1683.9 225642 537 888861 154854153 23.1733 8.1281 2.72W; l.C)22( 1687.0 226484 538 28944 155720872 23.1948 8.1332 2.73078 1.85874 1690.2 227329 539 390521 156590819 23.2164 8.1382 2.73159 1.85529 1693.3 228175 NATIONAL TUBE COMPANY. 293 Squares, Cubes, Square Roots, Cube Roots, Logarithms, Etc. (CONTINUED.) No. 540 541 542 543 544 Sq. Cube. Square Root. Cube Root. Log. 1000 X Recip. No. = Dia. Circ'm Area. 291600 292681 293764 894849 295936 157464000 158340421 159220088 160103007 160989184 23.2379 23.2594 23.2809 23.3024 23.3238 8.1433 8.1483 8.1533 8.1583 8.1633 2 73239 2.73320 2.73400 2.73480 2.73560 1.85185 1.84843 1.84502 1.84162 1.83824 1696.5 1699.6 1702.7 1705.9 1709.0 229022 229871 230722 231574 232428 545 546 547 548 549 297025 5> ( .S11li 299209 300304 301401 161878625 162771336 1 63667323 164566592 165469149 23.3452 23.3666 23.3880 23.4094 23.4307 8.1683 8.1733 8.1783 8.1833 8.1882 2.73640 2.73719 2.73799 1-73878 2.73957 1.83486 1.83150 1.82815 1.82482 1.82149 1712.2 1715.3 1718.5 1721.6 1724.7 233283 234140 234998 235858 236720 550 551 552 553 554 302500 303601 304704 305809 306916 166375000 167284151 168196608 169112377 170031464 23.4521 23.4734 23.4947 23.5160 23.5372 8.1932 8.1982 8.2031 8.2081 8.2130 2.74036 2.74115 2.74194 2.74273 2.74351 1.81818 1.81488 1.81159 1.80832 1.80505 1727.9 1731.0 1734.2 1737.3 1740.4 237583 238448 239314 240182 241051 555 556 557 558 559 30S025 309136 310249 311364 312481 170953875 171879616 172808693 173741112 174676879 23.5584 23.5797 23.6008 23.6220 23.6432 8.2180 8.2229 8.2278 8.2327 8.2377 2.74429 2.74507 2.74586 2 74663 2.74741 1.80180 1.79856 1.79533 1.79211 1.78891 1743.6 1746.7 1749.9 1753.0 1756.2 241922 242795 243669 244545 245422 560 561 562 563 564 313600 314721 315844 316969 318096 175616000 176558481 177504328 178453547 179406144 23 6643 23.6854 23.7065 23.7276 23.7487 8.2426 8.2475 8.2524 8.2573 8.2621 2.74819 2.74896 2.74974 2.75051 2.75128 1.78571 1.78253 1.77936 1.77620 1.77305 1759.3 1762.4 1765.6 1768.7 1771.9 246301 247181 248063 248947 249832 565 566 567 568 569 319225 320356 321489 :;-J-.v,-j| 323761 180362125 181321496 182284263 183250432 184220009 23.7697 23.7908 23.8118 23.8328 23.8537 8.2670 8.2719 8.2768 8.2816 8.2865 2.75205 2.75282 2.75358 2.75435 2.75511 1.76991 1.76678 1.76367 1.76056 1.75747 1775.0 1778.1 1781.3 1784.4 1787.6 250719 251607 252497 253388 254281 570 571 572 573 574 324900 326041 327184 :;>:;.". 329476 185193000 186169411 187149248 188132517 189119224 23.8747 23.8956 23.9165 23.9374 23.9583 8.2913 8.2962 8.3010 8.3059 8.3107 2.75587 2.75664 2.75740 2.75815 2.75891 1.75439 1.75131 1.74825 1.74520 1.74216 1790.7 1793.5 1797.0 1800.1 1803.3 255176 256072 256970 257869 258770 575 576 577 578 579 330625 331776 332929 334084 335241 190109375 191102976 192100033 193100552 194104539 23.9792 24.0000 24.0208 24.0416 24.0624 8.3155 8.3203 8.3251 8.3300 8.3348 2.75967 2.76042 2.76118 2.76193 2.76268 1.73913 1.73611 1.73310 1.73010 1.72712 1806.4 1809.6 1812.7 1815.8 1819.0 259672 260576 261482 262389 263298 580 581 583 584 336400 337561 338724 339889 341056 195112000 196122941 197137368 198155287 199176704 24.0832 24.1039 24.1247 24.1454 24.1661 8.3396 8.3443 8.3491 8.3539 8.3587 2.76343 2.76418 2.76492 2.76567 2.76641 1.72414 1.72117 1.71821 1.71527 1.71233 1822.1 1825.3 1828.4 1831.6 1834.7 264208 265120 266033 266948 267865 i , 294 NATIONAL TUBE COMPANY. Squares, Cubes, Square Roots, Cube Roots, Logarithms, Etc. (CONTINUED.) No. Sq. Cube. Square Root. Cube Root. Log. 1000 X Recip. No. = Dia. Circ'm Area. 585 342225 200201625 24.1868 8.3634 2.76716 1.70940 1837.8 268783 586 848896 201230056 24.2074 8.3682 2.76790 1.70649 1841.0 269701 587 344569 21 2262003 24.2281 8.3730 2.76864 1.70358 1844.1 270624 588 345744 203297472 24.2487 8.3777 2.76938 1.70068 1847.3 271547 589 346921 204336469 24.2693 8.3825 2.77012 1.69779 1850.4 272471 590 348100 205379000 24.2899 8.3872 2.77085 1.69492 1853.5 273397 591 349281 206425071 24.3105 8.3919 2.77159 1.69205 1856.7 274325 592 3.50 J 64 207474688 24.3311 8.3967 ) 77->:!-> 1.68919 1859.8 275254 593 351649 208527857 24.3516 8.4014 2. 77305 1.68634 1863.0 276184 594 352836 209584584 24.3721 8.4061 2.77379 1.68350 1866.1 277117 595 354025 210644875 24.3926 8.4108 2.77452 1.68067 1869.3 278051 596 355216 211708736 24.4131 8.4155 2.77525 1.67785 1872.4 278986 597 356409 212776173 24.4336 8.4202 2.77597 1.67504 1875.5 279923 598 357604 213847192 24.4540 8.4249 2.77670 1.67224 1878.7 280862 599 358801 214921799 24.4745 8.4296 2.77743 1.66945 1881.8 281802 600 3600T>0 216000000 24.4949 8.4343 2.77815 1.66667 1885.0 282743 601 361201 217081801 24.5153 8.4390 2.77887 1.66389 1888.1 283687 602 362404 218167208 24.5:357 8.4437 2.77960 1.66113 1891.2 284631 603 363609 219256227 24.5561 8.4484 2.78032 1.65837 1894.4 285578 604 364816 220348864 24.5764 8.4530 2.78104 1.65563 1897.5 286526 605 366025 221445125 24.5967 8.4577 2.78176 1.65289 1900.7 287475 606 367236 222.545016 24.6171 8.4623 2.78247 1.65017 1903.8 288426 607 368449 223648543 24 6374 8.4670 2.78319 1.64745 1907.0 289379 608 369664 224755712 24.6577 8.4716 2.78390 1.64474 1910.1 290333 609 370881 225866529 24.6779 8.4763 2.78462 1.64204 1913.2 291289 610 372100 226981000 24.6982 8.4809 2.78533 1.63934 1916.4 292247 611 873881 228099131 24.7184 8.4856 2.78604 1.63666 1919.5 293206 612 374544 229220928 24.7386 8.4902 2.78675 1.63399 1922.7 294166 613 375769 230346397 24.7588 8.4948 2.78746 1.63132 295128 614 376996 231475544 24.7790 8.4994 2.78817 1.62866 I928/J 296092 615 378225 232608375 24.7992 8.5040 2.78888 1.62602 1932.1 297057 616 2:33744896 24.8193 S.50S6 2.78958 1.1W33K 298024 617 880680 234885113 24.8395 8 5132 2.79029 1.62075 193814 298992 618 381924 236029032 24.8596 8.5178 2.79099 1.61812 1941.5 299962 619 383161 237176659 24.8797 8.5224 2.79169 1.61551 1944.7 300934 620 384400 238328000 24.8998 8.5270 2.79239 1.61290 1947.8 301907 621 385641 239483061 24.9199 8.5316 2.79309 1.61031 1950.9 302882 622 386884 240641848 24.9399 8.5362 2.79379 1.60772 1954.1 303858 623 388129 241804367 24.9600 8.5408 2.79449 1.60514 1957.2 304836 624 389376 242970624 24.9800 8.5453 2.79518 1.60256 1960.4 305815 625 390625 244140625 25.0000 8.5499 2.79588 1.60000 1963.5 306796 626 391876 245314376 25.0200 8.5544 2.79657 1.59744 1966.6 307779 627 393129 246491883 25.0400 8.5590 2.79727 1.59490 1969.8 308763 628 394384 247673152 25.0599 8.5635 2.79796 1.59236 1972.9 309748 629 868641 248858189 25.0799 8.5681 2.79865 1.58983 1976.1 310736 NATIONAL TUBE COMPANY. 295 Squares, Cubes, Square Roots, Cube Roots, Logarithms, Etc. (CONTINUED.) No. Sq. Cube. Square Root. Cube Root. Log. 1000 X Recip. No. = Dia. Circ'm Area. 630 396900 250047000 25.0998 8.5726 2.79934 1.58730 1979.2 311725 631 398161 251239591 25.1197 8.5772 2.80003 1.58479 1982.4 312715 632 399424 252435968 25.1396 8.5817 2.80072 1.58228 1985.5 313707 633 400689 253636137 25.1595 8.5862 2.8ul40 1.57978 1988.6 314700 634 401956 254840104 25.1794 8.5907 2.80209 1.57729 1991.8 315696 635 4032251 256047875 25.1992 8 5952 2.80277 1.57480 1994 9 316692 636 404496 257259456 25.2190 8.5997 2.80346 1.57233 1998.1 317690 637 405769 258474853 25.2389 8.6043 2.80414 1.56986 2001.2 318690 638 407044 259694072 25.2587 8.6088 2.80482 1.56740 2004.3 319692 639 408321 260917119 25.2784 8.6132 2.80550 1.56495 2007.5 320695 640 409600 262144000 25.2982 8.6177 2.80618 1.56250 2010.6 321699 641 410881 263374721 25.3180 8.6222 2 80686 1.56006 2013.8 322705 642 412164 264609288 25.3377 8.6267 2.80754 1.55763 2016.9 323713 643 41:3449 .265847707 25.3574 8.6312 2.80821 1.55521 2020.0 324722 644 414736 267089984 25.3772 8.6357 2.80889 1.55280 2023.2 325733 645 416025 268336125 25.3969 8.6401 2.80956 1.55039 2026.3 326745 646 417316 269586136 25.4165 8.6446 2.81023 1.54799 2029.5 327759 647 418609 270840023 25.4362) 8.6490 2.81090 1.54560 2032.6 328775 648 419904 272097792 25.4558 8.6535 2.81158 1.54321 2035.8 329792 649 421201 273359449 25.4755 8.6579 2.81224 1.54083 2038.9 330810 650 422500 274625000 25.4951 8.6624 2.81291 1.53846 2042.0 a31831 651 423801 275894451 25.5147 8.6668 2.81358 1.53610 2045.2 332853 ' 652 425104 277167808 25.5343 8.6713 2.81425 1.53374 2048.3 333876 653 426409 278445077 25.5539 8.6757 2.81491 1.53139 2051.5 334901 | 654 427716 279726264 25.5734 8.6801 2.81558 1.52905 2054.6 335927 655 429025 281011375 25.5930 8.6845 2.81624 1.52672 2057.7 a36955 i 656 430336 282300416 25.6125 8.6890 2.81690 1.52439 2060 9 337985 I 757 431649 283593393 25 6320 8.6934 2.81757 1.52207 2064.0 339016 758 432964 284890312 25.6515 8.6978 2.81823 1.51976 2067.2 340049 659 434281 286191179 25.6710 8.7022 2.81889 1.51745 2070.3 341084 660 435600 287496000 25.6905 8.7066 2.81954 1.51515 2073.5 342119 661 436921 288804781 25.7099 8.7110 2.82020 1.51286 2076.6 343157 662 438244 290117528 25 7294 8.7154 2.82086 1.51057 !2079.7 344196 i 663 439569 291434247 25.7488 8.7198 2.82151 1.50830 2082.9 345237 664 440896 292754944 25.7682 8.7241 2.82217 1.50602 2086.0 346279 665 442225 294079625 25.7876 8.7285 2.82282 1.50376 2089.2 347323 666 148660 295408296 25.8070 8.7329 2.82347 1.50150 2092.3 348368 667 444889 296740963 25.8263 8.7373 2.82413 1.49925 2095.4 349415 668 446224 298077632 25.8457 8.7416 2.82478 1.49701 2098.6 350464 669 447561 299418309 25.8650 8.7460 2.82543 1.49477 2101.7 351514 670 448900 300763000 25.8844 8.7503 2.82607 1.49254 2104.9 352565 671 450241 302111711 25.9037 8.7547 2.82672 1.49031 2108.0 353618 672 451584 303464448 25.9230 8.7590 2.82737 1.48810 2111.2 354673 673 452929 304821217 25.9422 8.7634 2.82802 1.48588 2114.3 355730 674 454276 306182024 25.9615 8.7677 2.82866 1.48368 2117.4 356788 QL. ., * 296 NATIONAL TUBE COMPANY. Squares, Cubes, Square Roots, Cube Roots, Logarithms, Etc. (CONTINUED.) Square Cube 1000 No. = Dia. No. Sq. Cube. Root. Root. Log. X Recip Circ'm Area. 675 455625 307546875 25.9808 8.7721 2.82930 1.48148 2120.6 357847 676 456976 308915776 26.0000 8.77(54 2.8299: 1.47929 2123.7 358908 677 158: 129 310288733 26.0192 8.7H07 2.83055) 1.47711 2126.! 359971 678 159681 311665752 26.C384 8.7850 2.83123 1.47493 2130.0 361035 679 461041 313046839 26.0576 8.7893 2.83187 1.47275 2133.1 362101 680 462400 314432000 26.0768 8.7937 2.83251 1.47059 2136.3 363168 681 4(53761 315821241 26.09(50 8.798C 2.83315 1.46843 2139.4 364237 682 465124 317214568 26.1151 8.802: 2.83378 1.46628 2142.6 365308 683 166189 318611987 26.1343 8. SOW 2.8314;, 1.46413 2145.7 366380 684 467856 320013504 26.1534 8.8109 2.83506 1.46199 2148.9 367453 685 469225 321419125 26.1725 8.8152 2.83569 1.45985 2152.0 368528 686 170.7.16 322828856 26.15)16 8.8194 2.83632 1.45773 2155.1 369605 687 471969 324242703 26.2107 8.8237 2.8:>,09I 1.45560 2158.3 370684 688 47*144 325660672 26.2298 8.8280 2.83759 1.45349 2161.4 371764 689 474721 327082769 26.2488 8.8323 2.83822 1.45138 2164.6 372845 690 476100 328509000 26.2679 8.8366 2.83885 1.44928 2167.7 373928 691 477481 325)939371 2(5.28(59 8.8408 2.83948 1.44718 2170.8 375013 692 478864 331373888 26.3059 8.8451 2 84011 1.44509 2174.0 376099 693 480249 33281255'! 26.3249 8.8493 2.84073 1.44300 2177.1 377187 694 481636 334255384 26.3439 8.8536 2.84136 1.44092 2180.3 378276 695 483025 335702375 26.3629 8.8578 2.84198 1.43885 2183.4 379367 696 484416 337153536 26.3818 8.8621 2.84261 1.43678 2186.6 380459 697 485809 338(508873 26.4008 8.8663 2.84323 1.43472 2189.7 381554 698 487204 340068392 26.4197 8.8706 2.84386 1 . 43267 2192.8 382649 699 488601 341632099 26.4386 8.8748 2.84448 1.43062 2196.0 383746 700 490000 343000000 26.4575 8.8790 2.84510 1.42857 2199.1 385845 701 491401 344472101 26.4764 8.8833 2.84572 1.42653 2202.3 385945 702 4928041 34594840H 26.4953 8.K875 2.84634 1.42450 2205.4 387047 703 494205) 847426927 26.5141 8 8917 2.81696 1.42248 2208.5 388151 704 495616 348913664 26.5330 8.8959 2.84757 1.42046 2211.7 389256 705 497025 350402625 26.5518 8.9001 2 84819 1.41844 2214.8 390363 706 1981; ill 35185)581(5 26.5707 8.5)043 2.H4H80 1.41(543 2218.0 391471 707 499849 853893243 2(5.5895 8 9085 2.81912 1.41443 2221.1 392580 708 501264 354894912 26.6083 H.9127 2.85003 1.41243 2221.:} 35)3692 709 502681 356400829 26.6271 8.9169 2.85065 1.41044 2227.4 394805 710 504100 357911000 26 6458 8.9211 2.85126 1.40845 2230.5 395919 711 505.521 359425431 26.6616 8.925:! 2.85187 1.40647 2233.7 397035 712 506911 3(50944128 26.6888 8.9295 2.85248 1.4044!) 22-' it; 8 398153 713 506869 362467097 26.7021 8.9337 2.8530!) 1.40253 2240 !o 399272 714 509796 363994344 26.7208 8.5)378 2.85370 1.40056 2243.1 400393 715 511225 365525875 26.7395 8.9420 2.85431 1.39860 2246.2 401515 716 512656 3(570(5169(5 26.7582 8.9462 2.85491 1.. '59(565 2249.4 402639 717 514069 368601813 26.7769 8.5150:! 2.85552 1.39470 -.'252.:, 403765 718 515524 370146232 26.7955 8.9545 2.85612 1.39276 2255.7 404892 719 516961 371694959 26.8142 8.9587 2.85673 1.39082 2258.8 406020 T NATIONAL TUBE COMPANY. 297 Squares, Cubes, Square Roots, Cube Roots, Logarithms, Etc. (CONTINUED.) No. 720 721 722 723 724 Sq Cube. Square Root. Cube Root. Log. 1000 X Recip. No. = Dia. ^irc'm Area 518400 519841 521284 5241 76 :J7324NXM' 876867048 877988067 379503424 86.8888 26.8514 BftiSBSi 29.9079 BiOBTO 8.9711 B.9758 2.85733 8.85794 >.S5S51 2.S51M4 2.85974 l.:^| 1 '.38313 1.38122 2261.9 8865.1 8868.8 8871.4 2274.5 407150 408888 409416 410550 411687 725 726 727 728 729 525625 521076 531441 381078125 884940589 3s.5s-JS3.5-J 387420489 86.9958 26.9444 86.9889 86.9816 27.0000 B.9888 B.9876 8.9018 B.9969 9.0000 2.86034 j.sr.oai 2i86918 2.80273 1.37931 1.37741 1.37552 1.3:363 1.37174 2277.7 8880.8 8987!l 2290.2 419886 413965 416108 416248 417393 7:30 731 732 733 734 532900 5.",43.jl 587288 538756 389017000 89222816* 393832837 395446904 27.0185 27. 03; < > 87.0556 27.0740 27.0924 9.0041 9.0082 9! 01 64 9.0205 2.86332 J.S639-J 2.86451 J.s.151.1 liWTW 1.36612 1. 3642I 1 1.36240 2293.4 8896.6 8889.7 2302 s 2305.9 418539 419688 481986 423138 735 736 737 738 739 540225 541696 5431 im 544Vt4 546121 80M6BB7C 40081555! 401947275 403583419 27.1109 27.1293 27.1477 87.1668 27.1846 9.0246 9.0887 9.088B 9.0888 9.0410 2.8ir,25 8.8688B 8.86747 J.S'VSOO 2.86864 1.36054 1.85870 L860BE l! 35318 2309.1 2312.2 2315.4 2318.5 2321.6 424293 425448 426604 427762 428922 740 741 742 743 744 547600 549081 5.50.564 558041 553536 405224000 410172407 411830784 27.2029 27.2213 27.23517 27.2580 27.2764 9.0450 9.0491 9.0532 9.0572 9.0613 2.86923 J.S6'*-J J.S7UU) 2.S7W9 2.87157 1.35135 1.34953 1.34771 1.34590 1.34409 2324.8 J.",27. ( .t 2331.1 2334.2 2337.3 430084 431247 432412 433578 434746 745 740 747 748 749 555025 5WW16 558009 559.504 561001 413493625 415160931 H 850899! 42iiis'..74'. 27.2947 9.0654 27.3130 9.0694 27.3313' 9.0735 27.3496J 9.0775 27.3679 9.0816 J.S7J7J Z'.878M 2.87448 1.34228 1.34048 1.33865 1.33690 1.33511 2340.5 8848.6 2346.8 2349.9 2353.1 435916 437087 438259 439433 440609 750 751 752 753 754 562500 564001 565504 567009 568516 421875000 423564751 4 2.52.5'. Mjus 428661064 27.3861 9.0856 27.4044 9.0896 27.4226: 9.0937 27.4408! 9.0977 27.4591 9.1017 2.87506 8.87564 J.STti-J-J 2'.87737 1.33333 1.33156 1.32979 1.32802 1.32626 2356.2 8899.8 8868.6 8865.6 2368.8 441786 442965 444146 445328 446511 755 756 757 758 759 570025 571681 578041 574.561 576081 43a368875 432081 21 188798001 435515)512 437245479 ! 9.1057 27.4H.V, ( ..Kf.is 27.5136 9.1138 27.5318 9.1178 27.5500 9.1218 8.87796 2.S7S.5-J -J.s7.Ui nmS& 1.32450 1.32275 1.32100 1.31926 1.31752 2371.9 2375.0 8878.8 2881. J 2384.5 447697 448888 460078 451262 452453 760 761 762 763 764 577600 579121 580644 582105 5S361H 438976000 44071108 442450728 44419494" 44.5943744 27.5681 9.1258 27.5862; 9.1298 27.6043 9.1338 27.6225 H.i: :',',* 27.6405 9.1418 2.88081 J>si:is J>s-j>,-J 2.88309 1.31579 1.31406 1.31234 1.31062 1.30890 2387.6 2390 > 8898.9 8897.1 2400.2 453646 454841 456037 457234 458434 NATIONAL TUBE COMPANY. Squares, Cubes, Square Roots, Cube Roots, Logarithms, Etc* (CONTINUED.) Sq. Cube. Square Root. 451217663 452984832 27.7128 5913611 454756609 27!7308 592900 456533000 27.7489 594441 458:314011: 27.7669 595984 460099648 27.7849 597529 461889917 27.8029 599076, 463684824 27.8209 600625 465484375 602176 467288576 605284 470910952 606841, 47-2729139 608400! 474552000 609961 476379541 611524 478211768 613089 480048687 614656; 481890304 617796 485587656 619369 487443403 622521 491169069 624100 085861 074M 106617897 500566184 502459875 5048688M 506261573 508169592 510082399 640000J 512000000 513922401 519718464 28.3549 28.3725 523608616 28.3901 28.4077 27.8747 27.8927 27.9106 27.9285 27.9464 27.9643 28.0179 28,0357 28.0535 28.0713 28.1247 28.1425 28.1603 28.1780 28.1957 28.2135 Cube Root. 9.1458 9.1498 9.1537 9.1577 9.1617 9.1657 9.1696 9.1736 9.1775 9.1815 9.1855 9.1894 9.1933 9.1973 9.2012 9.2052 Log 1000 X Recip. 2.887051 2.88762; 2.88874] 2.88930; 1.30719 1.3C 1.3C 1.30208 1.3C 1.29870 1.29702 1.29534 1.29366 1.29199 . 2415.9 2419.0 2422.2 2425.8 2428.5 2431.6 9.2287 9.2326 n . 2:165 9.2404 9.2443 9.2521 9.2560 9.1688 9.2677 9.2716 9.2754 26.2480 8B.90M 28.2843 9.2832 28.3019J 9.2870 28.3196 :__; 28.3373 9.2948 9.3025 9.3063 . 9! 3140 9.3179 . 2.89042: 2.89098 2.89154; 1.29032 2434.'. 1.288661 2437.9 1.28700) 2441.0 1.28535' 2444.2 1.28370 2447.3 2.89542 2.89597 2.89653 2.89873 2.89927 2.90037 2.90091 2.90146 2 .'.it nit X) 2.90255 2.90309 2.90363 2.90417 2.90472 2.90580 2.90634 . 2.1)0711 2.9079-1 l.: 1.28041 1.27877 1.27714 1.27551 1.27389 .27226 ! 27086 .20904 .26743 .26103 .2.7.115 2450.4 2453.6 2456.' 2459.9 2463.0 2466.2 M0B.8 2472.4 2475.6 2478.7 . 2488.1 2491.3 .25786 2497.6 "* 2500." .25156: 2510.1 .25000! 2513.3 .24844! 2516.4 .24688, 2519.6 .245.33 2522.7 .24378 2525.8 .24224| 2529.0 .24069 2532.1 25:55..'} Area 459635 460837 462042 463247 464454 465663 466873 471730 472948 474168 475389 476612 477836 479062 480290 481519 482750 485216 486451 490167 491409 492652 493897 495143 496391 497641 498892 500145 501399 502655 503912 505171 50fJ4:-W 507694 508958 510223 511490 512758 514028 .' IBM * I - r. ''.I - ' H ;: ' -- j'i ;: i -' ' - ; :%.!: nMNt in : S:.: ' S:-, 300 NATIONAL TUBE COMPANY. Squares, Cubes, Square Roots, Cube Roots, Logarithms, Etc. (CONTINUED.) No. Sq. Cube. Square Root. Cube Root. Log. 1000 X Recip. No. = Dia Circ'm Area. 855~ 731025 625026375 29.2404 9.4912 2.93197 1.16959 2686.1 574146 856 732736 627222016 29.2575 9.4949 2.93247 1.16822 2689.2 575490 857 734449 629422793 29.2746 9.4986 2.93298 1.16686 2692.3 576835 858 736164 631628712 29.2916 9.5023 2.93:349 1.16550 2695.5 578182 859 737881 633839779 29.3087 9.5060 2.93399 1.16414 2698.6 579530 860 739600 636056000 29.3258 9.5097 2.93450 1.16279 2701.8 580880 861 741321 638277381 29.3428 9.5134 2.93500 1.16144 2704.9 582232 862 743044 640503928 29.3598 9.5171 2.93551 1.16009 2708.1 583585 863 744769 642735647 29.3769 9.5207 2.93601 1.15875 2711.2 584940 864 746496 644972544 29.3939 9.5244 2.93651 1.15741 2714.3 586297 865 748225 647214625 29.4109 9.5281 2.93702 1.15607 2717.5 587655 866 749956 649461896 29.4279 9.5317 2.93752 1.15473 2720.6 589014 867 751689 651714363 29.4449 9.5354 2.93802 1.15340 2723.8 590375 868 753424 653972032 29.4618 9.5391 2.93852 1.15207 2726.9 591738 869 755161 656234909 29.4788 9.5427 2.93902 1.15075 2730.0 5931C2 870 756900 658503000 29.4958 9.5464 2.93952 1 14943 2733.2 594468 871 758641 660776311 29.5127 9.5501 2.94002 1.14811 2736.3 595835 872 760384 663054848 29.5296 9.5537 2.94052 1.14679 2739.5 597204 873 762129 665338617 29.5466 9.5574 2.94101 1.14548 2742.6 598575 874 763876 667627624 29.5635 9.5610 2.94151 1.14416 2745.8 599947 875 765625 669921875 29.5804 9 5647 2.94201 1.14286 2748.9 601320 876 767376 672221376 29.5973 9.5683 2.94250 1.14155 2752.0 602696 877 769129 674526133 29.6142 9.5719 2.94300 1.14025 2755.2 604073 878 770884 676836152 29.6311 9.5756 2.94:349 1.13895 2758.3 605451 879 772641 679151439 29.6479 9.5792 2.94399 1.13766 2761.5 606831 880 774400 681472000 29.6648 9.5828 2.94448 1.13636 2764.6 608212 881 776161 683797841 29.6816 9.5865 2.94498 1.13507 2767.7 609595 882 777924 686128968 29.6985 9.5901 2.94547 1.13379 2770.9 610980 883 779689 688465387 29.7153 9.5937 2.94596 1.13250 2774.0 612366 884 781456 690807104 29.7321 9.5973 2.94645 1.13122 2777.2 613754 885 783225 693154125 29.7489 9.6010 2.94694 1.12994 2780.3 615143 886 784996 695506456 29.7658 9.0046 2.94743 1 . 12867 -.'rs.-i.r, 616534 887 786769 697864103 29.7825 9.60H2 2.94792 1.12740 2786.6 617927 888 788544 700227072 29 799: J 9.6118 2 94841 1.12613 2789.7 619321 889 790321 702595369 29.8161 9.6154 2.94890 1.12486 2792.9 620717 890 792100 704969000 29.8329 9.6190 2.94939 1.12360 2796.0 622114 891 793881 707347971 29.8496 9.6226 2.94988 1.12233 2799.2 623513 892 795664 709732288 29.8664 9 621 W 2.95036 1.12108 2802.3 624913 893 797449 712121957 29.8831 9.6298 2.95085 1.11982 2805.4 626315 894 799236 714516984 29.8998 9.6334 2.95134 1.11857 2808.6 627718 895 801025 716917375 29.9166 9.6370 2.95182 1.11732 2811.7 629124 896 802816 719323136 29.9*33 9.6406 2.95231 1.11607 2814.9 630530 897 804(10!) 721734273 29.9500 9.6442 2.95279 1.11483 2818.0 631938 898 806404 724150792 29.9666 9.6477 2.95328 1.11359 2821.2 633348 899 808201 726572699 29.9833 9.6513 2.95376 1.11235 2824.3 634760 NATIONAL TUBE COMPANY. 301 Squares, Cubes, Square Roots, Cube Roots, Logarithms, Etc. (CONTINUED.) Square Cube 1000 No. = Dia. No. Sq. Cube. Root. Root. Log. X Recip. ^irc'm Area. 900 810000 729000000 30.0000 9.6549 2.95424 1.11111 2827.4 636173 901 811801 731432701 30.0167 9.6585 2.95472 1.10988 2830.6 637587 902 813604 733870808 30.0333 9.6620 2.95521 .10865 2833.7 639003 903 815409 736314327 30.0500 9.6656 2.95569 .10742 2836.9 640421 904 817216 738763264 30.0666 9.6692 2.95617 .10619 2840.0 641840 905 819025 741217625 30.0832 9.6727 2.95665 .10497 2843.1 643261 906 820836 743677416 30.0998 9.6763 2.95713 1.10375 2846.3 644683 907 822649 746142643 30.1164 9.6799 2.95761 .10254 2849.4 646107 908 748613312 30.1330 9.6834 2.95809 .10132 2852.6 647533 909 826281 751089429 30.1496 9.6870 2.95856 .10011 2855.7 648960 910 828100 75-3571000 30.1662 9.6905 2.95904 1.09890 2858.8 650388 911 829921 756058031 30.1828 9.6941 2.95952 1.09769 2862.0 651818 912 831744 758550528 30.1993 9.6976 2.95999 1.09649 2865.1 653250 913 883566 761048497 30.2159 9.7012 2.96047 1.09529 2868.3 654684 914 835396 763551944 30.2324 9.7047 2.96095 1.09409 2871.4 656118 915 837225 766060875 30.2490 9.7082 2.96142 1.09290 2874.6 657555 916 83905(5 768575296 30.2655 9.7118 2.96190 1.09170 2877.7 658993 917 SIUSS'.I 771095213 30.2820 9.7153 2.962437 1.09051 2880.8 660433 918 842724 773620632 30.2985 9.7188 2.96284 1.08932 2884.0 661874 919 844561 776151559 30.3150 9.7224 2.96332 1.08814 2887.1 66*317 920 846400 778688000 so.asis 9.7259 2.96379 1.08696 2890.3 664761 921 848241 781229961 30.3480 9.7294 2.96426 1.08578 2893.4 666207 922 850084 783777448 30.3645 9.7329 2.96473 1.08460 2896.5 667654 923 851929 786330467 30.3809 9.7364 2.96520 1.08342 2899.7 669103 924 853776 788889024 30.3974 9.7400 2.96567 1.08225 2902.8 670554 925 855625 791453125 30.4138 9.7435 2.96614 1.08108 2906.0 672006 926 857476 794022776 30.4302 9.7470 2.96661 1.07991 2909.1 673460 927 859329 796597983 30.4467 9.7505 2.96708 1.07875 2912.3 674915 928 861184 799178752 30.4631 9.7540 2.96755 1.07759 2915.4 676372 929 863041 801765089 30.4795 9.7575 2.96802 1.07643 2918.5 677&31 930 864900 804357000 30.4959 9.7610 2.96848 1.07527 2921.7 679291 931 866761 806954491 30.5123 9.7645 2.96895 1.07411 2924.8 680752 932 868624 809557568 30.5287 9.7680 2.96942 1.07296 2928.0 682216 933 870489 812166237 30.5450 9.7715 2.96988 1.07181 2931.1 683680 934 872356 814780504 30.5614 9.7750 2.97035 1.07066 2934.2 685147 935 874225 817400375 30.5778 9.7785 2.97081 1.06952 2937.4 686615 936 876096 820025856 30.5941 9.7819 2.97128 1.06838 2940.5 688084 937 877969 822656953 30.6105 9.7854 2.97174 1.06724 2943.7 689555 938 879844 825293672 30.6268 9.7889 2 97220 1.06610 2946.8 691028 939 881721 827936019 30.6431 9.7924 2.97267 1.06496 2950.0 692502 940 883600 830584000 30.6594 9.7959 2.97313 1.06383 2953.1 693978 941 885481 833237621 30.6757 9.7993 2.97359 1.06270 2956.2 695455 942 887364 8:35896888 30.6920 9.8028 2.97405 1.06157 2959.4 696934 943 889249 &38561807 30.7083 '.(.son: 2.97451 1.06045 2962.5 698415 944 891136 841232384 30.7246 9.8097 2.97497 1.05932 2965.7 699897 302 NATIONAL TUBE COMPANY. Squares, Cubes, Square Roots, Cube Roots, Logarithms, Etc. (CONTINUED.) Square Cube 1000 No. = Dia. No Sq. Cube. Root. Root. Log. X Recip Circ'm Area. 945 893025 843908625 30.740 9.813;. 2.9754 1.0582 2968.8 701380 946 894916 84659053C 30.757 9.8167 2.9758 1.0570 2971. 702865 947 896809 84927812,' 30.7734 9.8201 2.9763 1.0559 2975. 704352 948 898704 851971392 30.7896 9.8236 2.9768 1.05485 2978.2 705840 949 900601 854670349 30.8058 9.8270 2.9772 1.05374 2981 4 707330 950 902500 857375000 30.822 9.8305 2.97772 1.0526 2984.5 708822 951 904401 860085351 30.8383 9.8339 2.97818 1.05152 2987. 710315 952 906304 862801408 30.854o 9.8374 2.97864 1.05042 2990.8 711809 953 908209 86552317" 30.870" 9.8408 2.97909 1.04932 2993.9 713306 954 910116 868250664 30.8869 9.8443 2.9795o 1.04822 2997 1 714803 955 912025 870983875 30.9031 9.8477 2.98000 1.04712 3000.2 716303 956 913936 873722816 SO. 9192 9.8511 2.98046 1.04603 3003.4 717804 957 915849 876467493 30.9354 9.8546 2.98091 1.04493 3006.5 719306 958 917764 879217912 30.9516 9.8580 2.9813" 1.04384 3009.6 720810 959 919681 881974079 30.967" 9.8614 2.98182 1.04275 3012.8 732316 960 921600 884736000 30.9839 9.8648 2.9822" 1.0416" 3015.9 723823 961 923521 887503681 31.0000 9,8683 2.98272 1.04058 3019.1 725333 962 925444 890277128 31.0161 9.8717 2.98318 1.03950 3022.2 726842 963 927369 893056347 31.0322 9.8751 2.98363 1.03842 3025.4 728354 964 929296 895841344 31.0483 9.8785 2.98408 1.03734 3028.5 729867 965 931225 898632125 31.0644 9.8819 2.98453 1.03627 3031.6 731382 966 933156 901428696 31.0805 9.8854 2.98498 1.03520 3034.8 732899 967 935089 904231063 31.0966 9.8888 2.98543 1.03413 3037.9 734417 968 937024 907039232 31.1127 9.8922 2.98588 1.03306 3041.1 735937 969 938961 909853209 31.1288 9.8956 2.98632 1.03199 3044.2 737458 970 940900 912673000 31.1448 9.8990 2.98677 1.03093 3047.3 738981 971 942841 915498611 31.1609 9.9024 2.98722 1.02987 3050.5 740506 972 944784 918330048 31.1769 9.9058 2.98767 1.02881 3053.6 742032 973 946729 921167317 31.1929 9.9092 2.98811 1.02775 3056.8 743559 974 948676 924010424 31.2090 9.9126 2.98856 1.02669 3059.9 745088 975 950625 926859375 31.2250 9.9160 2 98900 1.02564 3063.1 746619 976 952576 929714176 31.2410 9.9194 2.98945 1.02459 3066.2 748151 977 954529 9325748-33 31.2570 9.9227 2.98989 1.02354 3069.3 749685 978 956484 935441352 31.2730 9>>m 2.99034 1.02249 3072.5 751221 979 958441 938313739 31.2890 9.9295 2.99078 1.02145 3075.6 752758 980 960400 941192000 31.3050 9.9329 2.99123 1.02041 3078.8 754296 981 962361 944076141 31.3209 9.9363 2.99167 1.01937 3081.9 755837 982 964324 946966168 31.3369 9. 9: 51 1C, 2.99211 1.01833 3085.0 757378 983 966289 949862087 31.3528 9.9430 2.99255 1.01729 3088.2 758922 984 968256 952763904 31.3688 9.9464 2.99300 1.01626 3091.3 760466 985 970225 955671625 31.3847 9.9497 2.99344 1.01523 3094.5 762013 986 972196 958585256 31.4006 9.9531 2.99388 1.01420 3097.6 763561 987 974169 961504803 31.4166 9.9565 2.99432 1.01317 3100.8 765111 988 976144 964430272 31.4325 9.9598 2.99476 1.01215 3103.9 766662 989 978121 967361669 31.4484 9.9632 2.99520 1.01112 3107.0 768214 ', _ NATIONAL TUBE COMPANY. Squares, Cubes, Square Roots t Cube Roots, Logarithms, Etc. (CONTINUED.) 990 991 995 996 997 Sq. Cube. 980100 970299000 982081 973242271 984064 976191488 986049! 979146657 988036 982107784 990025 985074875 992016 988047936 994009 991026973 996004 994011992 Square Root. 31.4643 31.4802 31.4960 31.5119 31. 31.5436 31.5595 31.5753 31.5911 31.6070 Cube Root. 9.9733 9.9766 9.9866 9.9900 9.9933 9. 9967 Log 2.99564 2.99607 2.99651 2.99695 Recip. 1.01010 1.00 1.00806 1.00705 1.00604 2.99782 1.00503 .00402 2.99870 1.00301 2.99913 1.00200 2.999571 1.00100 Circ'm 3110.2 3113.3 3116.5 3119.6 3122.7 3125.9 3129.0 3132.2 3135.3 3138.5 774441 776002 INDEX. NATIONAL TUBE COMPANY. INDEX TO TABLES OF STANDARD DIMENSIONS OF TUBULAR GOODS. Axle bearings, bushing forgings for Bearings, bushing forgings for Bedstead tubing ...... Bends, offset pipe bends ..... ' ' pipe bends " stock pipe bends Black standard weight pipe . Boiler tubes, cold drawn " " special sizes .... " " standard ..... Boiler shells, seamless ..... Bowl forgings for separators .... Bushing forgings for axle bearings Caps for carbonic acid cylinders. Carbonic acid cylinders .... Casing, couplings for ..... " lap-welded Cold drawn tubes, description and uses of " ." tubing for boilers, locomotives, etc. " " tubes, tables of . Collar flanges, cast-iron ..... Converse lock joint fittings . " patent lock joint for pipe Couplings for drive pipe ..... " " line pipe .... " " regular casing .... " " steam, gas and water pipe " " tubing Cylinders, special 8" seamless standard 5" and 8" seamless " standard 5" lap- welded " 3" to 20" seamless PAGE . 91 . 91 . 14 . 44 41-44 . 43 2 . 73 . 13 10,11 . 90 . 91 . 91 . 90 83-89 . 16 6, 7 . 72 . 73 77-81 21,25 28-32 . 27 . 18 . 17 . 16 . 15 . 18 . 86 83-85 . 89 87,88 308 NATIONAL TUBE COMPANY. Deflections of National trolley poles . . 46-67 Double extra strong pipe . . . . . 4 Double riveted pipe flanges . . . . 23, 25 Drawn tubing, uses of 70-72 Drive pipe 8 " " couplings . . . . . . .18 Extra strong pipe 3 Fittings, Converse joint fittings . . . 28-32 " Matheson " " ... 33-36 Flanges, cast-iron collar 21, 25 " ' ' " double riveted ... 23, 25 " " " single " ... 22, 25 " " " lugged for special light pipe 19,25 " " " " pump column . . 20,25 " Master Steam Fitters' standard . . 26 " solid welded 24,25 " threaded, cast-iron ..... 26 Floats, seamless 90 Flush joint pipe and tubing 9 Franklin ite locomotive boiler tubes . . .12 Galvanized standard weight pipe .... 2 Gas pipe couplings . . . _. . .15 Heating surface of pipe . . . . . 5 Hot finished seamless tubes .... 74-76 Hydraulic forgings ... 90, 91 Joint, Converse lock 27 " Matheson 33 Ivap-welded casing 6 " " cylinders 89 " " pipe, special light with flanges . 19, 25 " " with collar flanges . . 21,25 " " " " double riveted flanges . 23,25 " " " " single riveted flanges 22,25 " " " " Converse lock joint . . 27 NATIONAL TUBE COMPANY. L,ap-welded pipe with Matheson joint ... 33 " " " " solid welded flanges . 24,25 " " pump columns and flanges . . 20 " " tuyere pipe . . . . . .14 Large size O. D. pipe .9 Light lap-welded pipe with cast-iron lugged flanges 19, 25 Line pipe . ....... 8 Line pipe couplings . . ' . . .17 Lock joint, Converse 27 Locomotive boiler tubes, cold drawn ... 73 " " " lap -welded, special brands 12 Lugged flanges, cast-iron for special light pipe 19, 25 " " " " pump column . . 20, 25 Master Steam Fitters' standard pipe flanges . . 26 Matheson joint fittings 34-36 " patent pipe joint ..... 33 Mechanical tubes, cold drawn . . . . .73 National trolley poles 46-67 Oil well tubing 8 Pipe bends 41-44 " couplings, see couplings " flanges, see flanges " joint, flush , . . . . . .9 Projectile forgings 91 Protecting caps for carbonic acid cylinders . . 90 Pump columns and pump column flanges . . 20 Radii for pipe bends ...... 42 Riveted pipe flanges 22, 23, 25 Salamander locomotive boiler tubes ... 12 Seamless boiler shells 90 " cold drawn boiler tubes ... 73 " tubes . . . . 77-81 cylinders 83-88 " " illustrations of . . . 83,87 310 NATIONAL TUBE COMPANY. Seamless cylinders 3" to 20" diameter . 87, 88 " drawn tubing, description and uses of 70-72 floats 90 1 ' hot finished tubes . . . 74-76 tubular goods .... 70-91 Separator bowl and tubular forgings 91 Shrapnel forgings 90 Single riveted pipe flanges .... 22, 25 Solid welded flanges 24, 25 Special 8" seamless cylinders for carbonic acid . 86 Special light lap -welded pipe with flanges . . 19, 25 ' ' sizes of boiler tubes 13 " steel lap-welded pipe with Converse joint . 27 " " " " " " Matheson joint 33 Standard boiler tubes 10, 11 " couplings for drive pipe . . . .18 " '* " line pipe .... 17 " " " regular casing . . .16 " " steam, gas and water pipe 15 " " " tubing .... 18 ' ' double extra strong pipe . . . .4 " drive pipe 8 " extra strong pipe . . . . .3 " line pipe ....... 8 " oil well tubing . . . . . .8 " seamless cylinders 5" and 8" . . 83-85 ' ' weight pipe, black and galvanized . . 2 Steam pipe couplings ...... 15 Stock pipe bends 43 Swelled tube ends 37 Threaded cast-iron pipe flanges . . . .26 Trolley pole dimensions and deflections. . 46-67 Tubes, bent 41 " seamless cold drawn .... 77-81 " " hot finished .... 74-76 ' ' special brands locomotive boiler tubes . 12 " " sizes of boiler tubes . . 13 NATIONAL TUBE COMPANY. Tubes, standard boiler tubes .... 10 with upset ends 37-40 Tubing, bedstead 14 " couplings for . . . . . .18 " oil well 8 " seamless cold drawn for boilers, etc . . 73 Tubular forgings for separators . . . .91 Tuyere pipe 14 Upset and swelled tube ends .... 37 tube ends 37-40 Valve protecting caps for carbonic acid cylinders 90 Water pipe couplings, black and galvanized . . 15 Welded flanges, pipe with .... 24-25 Working barrels 82 NATIONAL TUBE COMPANY. INDEX TO USEFUL INFORMATION. PAGE Absolute temperature ...... 164 " zero 164 Acid Bessemer process ...... 201 " open hearth process 202 Acids in feed-water 96 Adiabatic compression and expansion of air, 165, 166, 172 After-coolers for air compressors . . . 176 Air 164-192 " adiabatic compression and expansion of, 165, 166, 172 " Boyle's law for . . . . . . 164 " Charles' and Gay Lussac's law for . . 164 " composition of 164 " compression of 165-171 " compressors ...... 175-180 " " after-coolers for . . . .176 " " compound .... 175-177 " " capacity of 180 efficiency of, at different altitudes 178-179 " ' ' horse-power required for . . . 180 " " inter-coolers for . . . 175-178 " " saving due to compounding . . 177 " corrosion caused by air in water ... 96 " expansion of 165, 166 " flow of, through pipes .... 183-192 " " " " orifices 182 ' ' in feed water 96 " isothermal compression and expansion of 167, 172 " pressure curves of ..... 172 " resistance to flow by valves, etc. . . . 190 " saturated with vapor ..... 181 " specific heat of ...... 165 ' weight of 164, 181 " work of compression .... 166-170 Analysis of water ....... 98 NATIONAL TUBE COMPANY. Basic Bessemer process 201 ' ' open hearth process 202 Bearing value of rivets . . . . . 228 Bending moments of beams, etc . . . . 212,213 Bessemer process for making steel . . . 201 Boilers, acid in feed-water . . . . .96 " air in feed-water . . . . . 96 " chimneys for. .... 158-161 " commercial horse-power of . . . 152 " corrosion in ...... 96-98 " evaporation, unit of . . . . . 152 " factors of evaporation, table of . . 137 " feed- water heaters . . . . .154 " feed water, impurities in . . . 95-98 " grease and oil in . .... 96-98 " horse-power of .... 152, 153 " impurities in feed-water . . . 85-98 " incrustation 95-98 lime in feed-water .... 95.97,98 " moisture in steam .... 153 " mud in feed-water . . . . 95, 97 * " non-conducting coverings . . . 147 ' oil and grease in 96-98 " power of boilers .... 152,153 " pressure, safe working . . 157, 222 prevention of corrosion . . . 95-98 " scaling . . .95, 97, 98 salt in feed- water 96 strength of . . . . 157, 218, 222 " treatment of impure feed-water . . 95-98 " unit of evaporation .... 152 Bolts, strain in 244 ' ' strength of 243 ' ' weight of 231 Boyle's law for air and gas ..... 164 Brake horse-power 152 Brass plate, weight of . . .236, 237 British thermal unit .... . 134 NATIONAL TUBE COMPANY. Burners, services for ...... 196 Bursting pressure of pipes, etc. . . . 217-223 Capacity of air compressors 180 " " cisterns and tanks . .... 122 " " cylindrical vessels .... 119 " " pipes . . . . .118 " " rectangular tanks .... 123 Cementation process for making steel . . . 200 Charles' and Gay Lussac's law .... 164 Chimneys for boilers ..... 158, 161 Circle, properties of 260 table of, by eighths . . . .271 " " from 1 to 1000 . . . .281 Cisterns, capacity of 122 Commercial horse-power of boilers . . .152 Composition of air ...... 164 " of water . . . . . .94 Compound air compressors .... 175, 177 Compound units, Metric and U. S 253 Compressors of air 165, 171 Compressors for air ..... 175, 186* Condensation of steam in pipes .... 149 Conversion table, Metric and U. S. . . . 251 Corrosion in boilers and tubes . . . 96, 98 Cosines, table of 268 Cotangents 270 Coverings for steam pipes 147 Cubes of numbers, table of. . . . . 281 Cylinder heads, strength of 223 Decimals of an inch for each 1-64 .... 235 " "a foot for each inch .... 235 Deflection of beams 212 " pipes 212-217 Density of water 94 Depth of pump suction ...... 131 Discharge of water from orifices and nozzles . 124 NATIONAL TUBE COMPANY. 315 Discharge of water from pipes . 102, 105, 107, 108, 113 Dry steam, definition of ... . 134 Effective head for water pipes . . 112 " thickness of pipe . . 217 Efficiency of bolts . 242 " " air compressors . 178, 179 Elastic limit, definition of ... . 210 " "of materials . 206 Elastic material . 210 Elasticity, modulus of ... 206, 210 Electrical equivalents .... . 253-256 Equivalents, mechanical, electrical and heat 249, 253-256 " trigonometrical . . 262 Evaporation, unit of .... 152 Expansion of air . 165, 166 Factor of safety ..... . 209 Factors of evaporation, table of . 137 Feed-water heaters .... . 154 Feed- water, impurities in 95-98 Fifth roots and fifth powers . 277 Flow of air in pipes .... . 183-192 " " gas " " 194, 195 " " steam in pipes .... . 142-147 " " water " " . 101,105, 107, 110, 112, 113 " " air through orifices . 182 " " gas " 194, 195 " " steam " ... . 140, 141 " " water " "... . 124 Frictional heads . 110-112 Frost, trouble from, in gas pipes 194, 195 Gas . 194-198 " flow of, in pipes .... 194, 195 4 ' frost, trouble from .... . 195 ' ' holders, weight of . 197 " services for burners .... . 196 ' ' vapor contained in . 196 , NATIONAL TUBE COMPANY. Gauges, standard ...... 234 Gay lyussac's law 164 Grease in boilers 96-98 Head, definition of 101, 107 " effective ....... 112 frictional 110-112 " of water for given discharge . . . 102 table of pressures due to . . .99 Heads, strength of cylinder .... 223 Heat equivalents 249, 253-256