T F 572 OflO ENG, V'.V Fff-LD BOOK, CD O >- / REESE LIBRARY UNIVERSITY OF CALIFORNIA. Received.. L/tfaiZ .. , r S? / Accessions No.^-S-^d ^ Shelf No. *$ To Chief Engineers of Railroads. If you want to make up a Survey Party ! If you want an Engineer on Construction ! If you want to fill a vacancy in Maintenance of Way Department ! If you want an Engineer for Special Service ! If you want a Draughtsman ! If you want a Contractor ! Advertise in the "Wants" columns of ENGI- NEERING NEWS, and save Time, Trouble and Expense. There is but one best method of doing anything, and this is the "Best Method" of accom- plishing the above. Copy for "Want" advertisements will be re- ceived as late as 10 A. M. on Friday in time for publication in current issue. TO ALL PARTIES HAVING CON- TRACTS TO LET. There is absolutely no other method known on earth so quick in action, so fruitful in results, so satisfactory to everybody in such a case, as an advertisement in ENGINEERING NEWS. This journal is read thoroughly, and carefully preserved, by every manufacturer and dealer in railroad or water-works supplies of any note in America. All the Enterprising: and Re- sponsible Contractors read it. The civil engineers cannot get along without it. The chances of any advertisement in this paper addressed to any or all of the above classes not being seen and read in every corner of the North American Continent within a few days after publication are infinitesimal. HOW IT PAYS! HUDSON, N. Y., Aug. 21, 1889. Engineering News: Enclosed find $12.60 for advertisement, as per ac- companying bill, which please receipt and return to me. I have paid not less than $100 for insertion of same notice in daily papers at different cities. Whether any one has ever read it in those papers I don't know, as no one has ever told me that he had. But I have received letters and personal calls from contractors from almost every State from Maine to Tennessee, and from Massachu- setts to Iowa, all beginning, "Having seen your advertise- ment in ENGINEERING NEWS," etc., from all of which I judge that the best and cheapest way to circulate en- gineering news is through the paper of that name. E. G. FERRISS, Chief Engineer, Kinderhook & Hudson Railway. 543 Pages; 1 00 Illustrations; 6 Folding Plates; 65 Tables; 8vo. Cloth. Price S5.00. MASONRY CONSTRUCTION, BY IRA C. BAKER, C. E. PROFESSOR OF CIVIL ENGINEERING, UNIVERSITY OF ILLINOIS. PART I. MATERIALS. Chapter I. The Natural Stone. II. Brick. III. Lime and Cement. PART II. PREPARING AND USING THE MATERIALS. Chapter IV. Mortar, Cement and Artificial Stone. V. Quarrying. VI. Stone Cutting. VII. Stone Masonry. VIII. Brick Masonry. PART III. FOUNDATIONS. Chapter IX. Introductory. X. Ordinary Foundations. XL Pile Foundations. XII. Foundations under Water. PART IV. MASONRY STRUCTURES. Chapter XIII. Masonry Dams. XIV. Retaining Walls. XV. Bridge Piers. XVI. Culverts. XVII. Masonry Arches APPENDIX. SPECIFICATIONS FOR MASONRY. General Railroad Masonry'. Masonry for Railroad Buildings. Architectural Masonry. Laying Masonry in Freezing Weather. A full Index to the above will be sent free cm application. This is the only book on the subject of Masonry Con- struction; it is very complete, very practical, and it has at once taken its place in Engineering literature as a standard work. Sent post paid on receipt of price, by the ENGINEERING NEWS PUB. CO., TRIBUNE BUILDING, NEW YORK. ENGINEER'S FIELD BOOK BY C. S. CROSS, CIVIL ENGINEER THIRD EDITION. To which is added much valuable information on Railroad Surveying and Construction, by the late Prof. Chas. A. Smith, C. E., of Washington University, St. Louis, Mo., Wm. F. Shunk, C. E. and others. COMPILED AND EDITED BY GEO. H. FROST, C. E. NEW YORK: ENGINEERING NEWS PUBLISHING CO., 1890. ^ /> 1 i Gx*"T $5-00 action | 2.00 Baker's Masonry Construction Billing's Water- Works Construction | 2.00 Bouscaren's Specifications for Iron and Steel Highway Bridges 25 Bouscaren's Specifications for Iron and Steel Railway Bridges 25 Buchanan's Tables of Squares 2.00 Cooper's Specifications ; Iron and Steel Highway Bridges 25 Cooper's Specifications ; Iron and Steel Railroad Bridges 25 Cross' Engineer's Field Book 50 DuBois' Strains in Framed Structures 10.00 Dunham's Plat and Profile Book, 20 miles 1.00 50 miles 2.00 Fanning's Water Supply Engineering 5.00 Gilmore's Limes, Hydraulic Cements and Mortar 4.00 Gould's Specifications for Dams and Reservoirs 25 Gould's Practical Hydraulic Formulae 1.00 Greene's Bridge Trusses, Graphical Method 2.50 Greene's Arches, " " 2.50 Greene's Roof Trusses, " 1.25 Haupt's Topographer 4.00 Henck's Field Book for Railroad Engineers 2.50 Bering's Bearing Piles, 2d Ed 20 Herschel and North's Road Making and Maintenance 1.50 Hudson's Tables of Excavation and Embankment 1.00 Jacob's Storage Reservoirs (new edition) '. .50 Johnson's Theory and Practice of Surveying 3.50 Manual of American Water- Works, 1889-90 3.00 Osborn's Tables of Moments of Inertia and Squares of Radii of Gyration, 2d Ed. 2.00 Parsons' Track; A Manual of Maintenance of Way 2.00 Parsons' Turnouts 1.00 Searles' Field Engineering: 3.00 Shunks' Field Engineer 2.50 'Yrautwine's Civil Engineer's Pocket Book 5.00 Wellington's Economic Theory of the Location of Railways 5.00 Wellington's Computation of Excavation and Embankment 4.00 No. 1. Katte's Specifications for Construction of Graduation and Masonry. Con- tents: Articles of Agreement, Formation, Graduation; Masonry, including Specifications for Laying Masonry in Freezing Weather; Foundations, Tim- ber, Iron- Work, General Provisions applicable to all work. Indemnity Bond, 16 pages. Price, 25 cents. No. 2. Specifications for Standard Pile and Timber Trestle Bridging. Price, 5 cents. No. 3. Specifications for Cross Ties. Price, 5 cents. No. 4. Specifications for Track Laying. Price, 10 cents. Any book in the above list will be sent post paid to any address in the United States or Canada on receipt of the price by the ENGINEERING NEWS PUBLISHING CO., TRIBUNE BUILDING, NEW YORK. CONTENTS. PAGE. Method of Staking out and Keeping Field Notes of Railroad Curves 5-16 Railroad Curve Tables, for expeditiously determining the points at which to commence the Curving 17-30 Keeping the Field Notes of a Railroad Survey from which the Center Line is Laid, with a Map 31 Excavation and Embankment; Application of the Prismoidal For- mula 32-37 Excavation and Embankment Tables 38-43 Instructions to Division and Assistant Engineers relative to Field Notes on Surveys for the South Penna. R. R. Co 44 Engineering Field Work. By the late Prof. Chas. A. Smith, of Washington University, St. Louis, Mo 45-63 Regulations for the Engineering Department During Construction, prepared for the South Penna. R. R. Co., by Wm. F. Shunk, C. E 65-84 Howe Truss Bridges (Illustrated) > 85-88 Table for Computing Right of Way Areas. Width 100 ft 89 Pile Driving Machine (Illustrated) ...... 90-93 Metric Railway Curves 94^98 THE ECONOMIC THEORY OF THE LOCATION OF RAILWAYS, By ARTHUR MELLEN WELLINGTON. Revised and Enlarged Edition, 8vo cloth, 1,000 pp., 314 Engravings, 204 Tables, $5,00. C O1VTE1VTS: CHAP. 1. The Inception of Railway Projects and Conditions governing it. 2. The Modern Railway Corporation. 3. The Nature and Causes connected with Location modifying Volume of Railway Revenue. 4. The Probable Volume of Traffic and Law of Growth therein. 5. Operating Expenses. 6. The Minor Details of Alignment. 7. Distance. 8. Curvature. 9. Rise and Fall. 10. The Relative Importance of Gradients. 11. The Locomotive Engine. 12. Rolling Stock. 13 Train Resistance. 14. The Effect of Grades on Train Load. 15. The Effect of Train Load on Operating Expenses. 16. Assistant Engines. 17. The Balance of Grades for Unequal Traffic. 18. Limiting Curvature and Compensation Therefor. 19. The Limit of Maximum Curvature. 20. The Choice of Gradients, and Devices for Reducing them. 21. Trunk Lines and Branch Lines. 22. Light Rails and Light Railways. 23. The Economy of Construction. 24. The Improvement of Old Lines. 25. Grade Crossings and Interlocking. 26. Terminals. 27. The Art of Reconnaissance. 28. Ocular Illusions. 29. When to make Surveys. 30. The Field Work of Surveys. 31. Topography ; its Uses and Abuse. 32. Mapping and Projecting Location. 33. The Estimation of Quantities. Sent post paid on receipt of price by the ENGINEEKING NEWS PUBLISHING CO., TRIBUNE BUILDING, New York. RAILROAD CURVES. The following tables show the distance from the point of inter- section of the tangent lines to the beginning of a one degree curve, the angle of deflection (=angle at centre) being known. In the columns, under the head of degrees and opposite the min- utes, are given the distances in feet from the intersection of tan- gents to the beginning of one degree curve. To ascertain the distance for any given degree of curve, divide the distance given in the tables for a One degree curve, by the degrees of the required curve, and you have the distance from the point of intersection to the beginning or end of curve. EXAMPLE: Required the distance from the point of intersection of tangents to the beginning of a Two degrees curve, the angle of deflection being 25. In the tables under 25, and opposite 0', find 1270.28 which divided by the degrees of the curve (2) give 635.14 feet, the required dis- tance. In staking the centre line for a railroad or a canal, stakes should be driven down to near the surface of the ground, at the intersec- tion of the tangents, and at the different stations ; and nails set in indicating the centre point. These stakes serve also for leveling purposes and are useful in detecting errors while the work is being relevelled and staked out, 6 EAILEOAD CURVES. The beginning and end of curves should have reference stakes set at right angle to the centre line, similarly driven and marked, and at such convenient distance from the centre as will insure them from being displaced in making excavations and embankments ; and at all the above named points another stake for numbering, &c., should be firmly driven adjacent to them. The radius of a One degree curve is 5730 feet. The circle being divided into 360 parts of one degree (equal angle of deflection) give 360 chords of one foot in length at the circumference, and also a radius of 57.3 ft. thus : 360 114.6 = = 57.3 3.1416 The chord of One foot in length for 1 degree = 57.3 ft. Kadius. 10 feet " " " = 573.0 " 100 " " " " =5730.0 " Or the radius may be calculated by natural sines, thus : sin. 1 : 100 ft. chord : : sin. 89 30' : 5730 ft. radius. To determine the degree of curvature, having the radius given, divide the radius of a One degree curve, 5730, by the radius of the given curve. EXAMPLE : Required the degree of a curve having a radius o 1000 feet : = 5.73 = 5 43' 48" To determine the length of the curve having the angle of deflec- tion given ; divide the angle of deflection (=angle at centre) by the degrees of the curve, and you have the required length of the curve. If there are degrees and minutes in the angle of deflection, the min- utes should be converted into decimals. EXAMPLE : The angle of deflection being 20 49', |J =0.816. Then 20.816 is the distance for a One degree curve ; if for a 2 degrees curve, divide this result by 2 ; for a 3 degrees curve, divide by three, and so on. The angle of deflection being given, the following results are readily determined : RAILROAD CURVES. Angle of deflection Degree of curve Deflection per 100 feet. Radius of curve Dist. from intersec. to beginning of curve. Length of curve. 20 49' 1 030' 5730. 1052.49 2081.6 20 49' 2 100' 2865. 526.24 1040.8 20 49' 3 130' 1910. 350.83 693.8 20 49' 4 2 00' 1432.5 263.12 520.4 20 49' 5 2 30' 1146. 210.50 416.3 To ascertain the radius of a curve, having the angle of deflection, and the distance from intersection to beginning of curve given. Find the distance for the angle of deflection in the tables, which divided by 5730. gives the natural tangent of half the angle. Then divide the distance from intersection to beginning of curve by the natural tangent of half the angle, and you have the radius. EXAMPLE : Required the Radius of a curve, the angle of deflection being 20, and the distance from intersection of tangents to beginning of curve 225 feet. Under 20 and opposite 0' in the tables, find 1010.37, which divided by 5730 feet gives the natural tangent 0.17633. Then 225 ft. divided by 0.17633 gives the radius 1276 feet. FIELD NOTES FOB A ONE DEGREE CURVE. Bearing of 1st tangent N. 20 W. 2d. " N. 40 W. Angle of deflection by needle ...... 20 " graduated card ... 20 The angles measured with the card are the most reliable ; but the angles by the needle although it often indicates a slight differ- 8 RAILKOAD CURVES. ence, serves as a check to greater errors which may arise in reading the degrees on the graduated limb of the instrument. * Station No. 506.2000 Intersection of tangents. 10.1037 from intersection to beginning of curve. * Station No. 496.0963 point at which curve commences. 4- 20.0000 length of curve. Station No. 516.0963 point at which curve terminates. DEFLECTION FROM TANGENTS. Stations. Length of chords in feet. Deflection from tangent. REMAKES. 496.096 1C a * Beginning of curve. . 497. 90.37 27 1 to left. (Tang, due N.) 498. 100.00 57 499. 100.00 1 27 500. 100.00 1 57 501. 100.00 2 27 502. 503. 100.00 loo.oo 2 57 3 27 * Change point. 504. 100.00 3 57 505. 100.00 4 27 506. 100.00 4 57 507. 100.00 5 27 508. 100.00 5 57 509. 510. 100.00 100.00 6 27 6 57 * Change point. 511. 100.00 7 27 512. 100.00 7 57 513. 100.00 8 27 514. 100.00 8 57 * 515. 100.00 9 27 516. 100.00 9 57 516.0963 9.63 10 00 * End of curve. (Tangent N. 20 W.) RAILROAD CURVES. FIELD NOTES FOR A TWO DEGEEES CURVE. Bearing of 1st tangent N 10 W. 2d ' N 30 W. Angle of deflection by needle 20 ' " by graduated card 20 Station 506.200 intersection of tangents. 5.052 from do. to beginning of curve. Station. . . . 501.148 point at which the curve commences, -f- 10.000 length of the curve. Station 511.148 point at which the curve terminates. DEFLECTION FROM TANGENTS. Stations. Length of chords in feet. Deflection from tangent. REMARKS. 501.148 > 00' * Beginning of curve 2 to left. 502. 85.20 51 (Tangent N 10 W.) 503. 100.00 1 51 504. 100.00 2 51 505. 100.00 3 51 506. 100.00 4 51 507. 100.00 5 51 * Change point. 508. 100.00 6 51 509. 100.00 7 51 510. 100.00 8 51 511. 100.00 9 51 511.148 14.80 10 00 * End of curve. (Tangent N 30 W.) 10 EAILEOAD CUBVES, In curves of great length, the instrument should be moved for- ward in about every five or six hundred feet to insure accuracy, and often to avoid obstruction in line. The mode of proceeding in such cases may be illustrated with the deflections of the 2 curve. The instrument in the first place is set at station 501.148 and the deflection from tangent to station 507 is 5 51'. Now change the position of the instrument to station 507, and bring the cross hairs to bear on the staff at station 501.148 ; after clamping the instru- ment turn with the vernier as a test for station 502, 051' for " 503, 151' for " 504, 251' for " 505, 351' and for the tangential station 507 ? 551' * Ch. pt. If the stakes are found to be correct, continue the setting of the remaining stakes to end of curve, and deflect the degrees from the beginning of curve given in the field notes opposite the respective stations. When an odd number of minutes are to be turned off at the commencement and for each successive station, the inconvenience may be obviated by setting the vernier the number of minutes for the required chord in an opposite direction from that in which you would turn for the stations in the curve ; or so that the instrument when set in line with the tangent and clamped, the nonius instead of reading 0, will indicate the number of degrees or minutes which would be deflected to strike in line with the first stake to be set in the curve. Then the remainder of the stations will be free from the odd minutes which would otherwise be turned off for each successive station. When the instrument is moved forward to another station, the same mode may be adopted with reference to setting the nonius preparatory to bringing the cross hairs to bear on the staff at the beginning of curve. By determining the tangents at the various points in the curve over which the instrument may be set, the staking of the curve may be prosecuted with Jess liability to error. RAILROAD CURVES. 11 At the end of curve the instrument should be set over the stake to ascertain if the tangent produced from deflection corresponds with the course and direction of the tangential line. FIELD NOTES AND METHOD OF STAKING A3 CURVE. Bearing of 1st tangent, N. 20 W. 2d N. 40 W. Angle of deflection by needle 20. " " by graduated card 20. Station . 506.180 intersection of tangents. 3.368 from do. do. to beginning of curve. k Station . . 502.812 point at which the curve commences. 4- 6.666 length of curve. * Station . . 509.478 point at which the curve terminates. The notes are put down as represented in this diagram, and numbered from right to left when curving to the left, and from left to right when curving to the right. 12 EAILBOAD CUKVES. FIELD NOTES. Length Course of Deflect'n No. of Station chords. tangents and chords. from tangent. BEMABKS. 502.812 c< N 20 W 0' * B. C. 3 to left. 503. 18.8 20 17' 017' 504. 505. 506. 507. 100 100 100 100 22.04 25. 04 28.04 31. 04 1.47 3. 17 4.47 6. 17 * Change point. 508. 100 34. 04 7 47 509. 509.478 100 47.8 37. 04 29.04 9.17 10. 00 * E. C. 510. 52.2 N 40 00 W The number at which the curve- ends should be given to the chainman before proceeding to measurement, so that the proper signal may be made by him on arriving at the station next preced- ing the termination of the curve. Then set the instrument over the point of curve at station 502.812 and deflect from the tangent line for station 503, 17' 504, 147' 505, 3 17' and so on to the end of curve as per column of deflection, unless the instrument is moved forward. If it is necessary to move the instrument, then set it over another stake in the curve, bring the cross hairs to bear on the staff at the beginning of curve and clamp the instrument ; then turn off for the tangent at the sta- tion selected, the same number of degrees originally turned from tangent at beginning of curve in setting the stake, and 1 30' addi- tional for each successive station of 100 feet as you advance ; the angles should correspond with those given in the column of deflec- tions set opposite the respective stations. ; *It frequently occurs that the instrument has to be changed to points intermediate between two stations. If in a five degrees curve, for instance, it is necessary to change the instrument from station No. 0, there being an obstruction in KAILKOAD CUEVES. 13 the line of sight between station and station No. 3. and nothing to prevent the instrument being set over a point in the curve 30 feet distant from station 2; the deflections would be made as follows : Station Deflection = 00 B. C. 5 E. 1 " 2 30. 2 " 5 00. 2.30 " 5 45. * Change point. Then move the instrument forward, and set it over station 2.30, and bring the cross hairs to bear on the staff at the beginning of the curve, station 0; then turn off 5 45' for tangent at station 2.30 and 1 45' for 70 feet the remainder of station No. 3, making in all for station No 3 deflections 7 30' 4 " 10 00' 5 " 15 00' E. C. The angles for parts of a station on curves may be readily calcu- lated and the angles turned off in such manner as will keep the stations of uniform length throughout the line. REVERSE CURVES. These may be put in according to the formation of the ground with equal radii, or not, as the case may require. In the latter case the degree of curve may be assumed and the curve continued as far as deemed necessary ; and the tangent is then produced to the intersection and measured and the angle of deflection de- termined. These give the data from which the radius and degree of curve are determined. See Pages 6 and 7. In the former case select a point in one of the tangents and turn from tangent such angle as the case may require, and measure on this line the distance between the tangents. Then set in a point one half of this distance for the point of reversion, from which both curves may be staked out. See Pages 6 and 7. If you wish to compound a curve so that the trains will pass less abruptly from tangent into and through the curve, it may be, done in the following manner ; 14 BAILKOAD CUBVES. We will assume the angle of deflection to be 40 ; in the tables under 40 and opposite 0' find 2085.55, the distance from intersec- tion of tangents to beginning of a one degree curve. If you wi h to lay out a compound equivalent to a curve of 5 for the whole angle, divide the distance found (2085.55) by 5, de- gree of the curve ; and you have the point of beginning 417 ft. from intersection of tangents. You will then decide on what length to substitute the less degree of curve. Tf a 3 curve is decided on, and the distance 200 feet at each end of the 5 curve, then deduct 3 for each station of 100 feet, making EAILEOAD CURVES, 15 12 from the total angle of deflection, (40) and you have 28 to be divided equally between the stations of the intermediate curve, or \ B = 7, the required degree of curve. FIELD NOTES. No. of Station. Course of chords. Deflection. REMARKS. No 0. 00' Beginning of curve, 1 N 1 30' W 1 30' 2 4 30 3 00 End of curve, 3, B. C. 7 3 9 30 3 30 From tangent. 4 16 30 7 00 5 28 30 10 30 6 30 30 14 00 E. C. 7, B. C. 3. 7 35 30 1 30 From tangent. 8 38 30 3 00 E. C. 3. Tangent, N 40 W. NATURAL TANGENTS. From the tables may also be determined the natural tangent for any given number of degrees and minutes from one degree to 45, by taking the distance given in the tables for twice the angle of which the tangent is sought, and dividing the same by 5730. EXAMPLES : 1st. Eequired the natural tangent of 30. Uncier 60 (twice the angle) find in the tables 3308.21 and divide the same by 5730, and you have the natural tangent for 30 = 0.57735. 2d. Eequired the natural tangent for an angle of 7 28' ; in the 16 RAILROAD CURVES. column of distances under 14 and opposite 56' (twice the angle) find 750.97, which divided by 5730 give the natural tangent for 7 28' equal to 0.13106. MEASUREMENT WITH GUNTEB'S CHAIN. When a 66 feet chain is used for the length of stations, the radius of a one degree curve. 5730 feet, may represent 57.30 chains of 66 feet, and the distances in the tables applied the same as for chains of 100 feet in length ; but the radius as well as the length of sta- tions will be proportionally less than for stations of 100 feet in length by 3 ^ part. If a 66 feet chain is used, the distance after being found in the tables, may be divided by 66, and the stations in the curve reduced to 75.76 links which are equal to 50 feet, one half the length of the stations generally adopted in staking the center line of rail- roads ; and the curve staked out accordingly, turning off one half the number of degrees required for the stations of 100 feet in length. The degree of curvature is understood to express the number of degrees per 100 feet, and hence the convenience of making the sta- tions of such length as will give a definite idea of the degree of curve and length of radius. The following abbreviations are used by some Engineers. P. C. For Point of Curve, or Beginning of Curve. P. T. " " " Tangent, or End of Curve. P. C. C. " " " Compound Curve or end of one curve and beginning of another, curving in the same direction. P. E. C. * " " Reverse Curve, or point where the direction of the curve is changed from right to left, or vice versa. P. I. " " " Intersection of Tangents. RAILROAD CURVE TABLES 18 RAILROAD CURVE TABLES. t 1 2 3 4 5 6 7 8 / 0.00 50.02 10'XOO 150.07 200.09 250.17 300.30 350.44 400.70 1 0.83 50.85 100.83 150.90 200.92 251.00 301.14 351.28 401.54 1 2 1.67 51.69 101.67 151.74 201.76 251.84 301.97 352.11 402.37 2 8 2.50 52.52 102.50 152.57 202.59 252.67 302.80 352.95 403.21 3 4 3.33 53.35 103.34 153.41 203.43 253.51 303.64 353.79 404.05 4 5 4.17 54.18 104.17 154.24 204.26 254.34 304.47 354.62 404.88 5 6 5.00 55.02 105.01 155.08 205.10 255.18 305.31 355.46 405.72 6 7 5.83 55.85 105.84 155.91 205.93 256.01 306.14 356.30 406.55 7 8 6.67 56.68 106.68 156.75 206.77 256.85 306.98 357.13 407.39 8 9 7.50 57.52 107.51 157.58 207.60 257.68 307.81 357.97 408.23 9 10 8.33 58.35 108.35 158.42 208.44 258.52 308.65 358.81 409.06 10 11 9.17 59.18 109.18 159.25 209.27 259.35 309.48 359.64 409.90 11 12 10.00 60.01 110.02 160.09 210.11 260.20 310.32 360.48 410.74 12 13 10.83 60.85 110-85 160.92 210.94 261.03 311.15 361.32 411.57 13 14 11.67 61.68 111.69 161.76 211.77 261.86 311.99 362.15 412.41 14 15 12.50 62.52 112.52 162.59 212.61 262.70 312.83 362.99 413.25 15 16 13.33 63.35 113.36 163.43 213.45 263.54 313.66 363.83 414.08 16 17 14.17 64.18 114.19 161.26 214.28 264.37 314.49 364.66 414.92 17 18 15.00 65.01 115.02 165.09 215.11 265.20 315.33 365.50 415.75 18 19 15.83 65.85 115.86 165.93 215.95 266.04 316.16 366.34 416.59 19 20 16.67 66.68 116.69 166.76 216.78 266.87 317.00 367.17 417.43 20 21 17.50 67.51 117.53 167.60 2x7.62 267.71 317.84 368.01 418.26 21 22 18.33 68.35 118.36 168.43 218.45 268.54- 318.67 368.85 419.10 22 23 19.17 69.18 119.20 169.27 219.29 269.38 319.50 369.68 419.94 23 24 20.00 70.01 120.03 170.10 220.12 270.21 320.34 370.52 420.77 24 25 20.83 70.85 120.87 170.94 22096 271.05 321.18 371.36 421.61 25 26 21.67 71.68 121.70 171.77 221 79 271.88 322,01 372.19 422.45 26 27 22.50 72,51 122.54 172.61 222.63 272.72 322.85 373.03 423.28 27 28 23.33 73.34 123.37 173.44 223.46 273.54 323.68 373.86 424.1-2 28 29 24.17 74.18 124.21 174.28 224.30 274.38 324.52 374.70 424.95 .29 30 2500 75.01 125.03 175.10 225.13 275.21 325.35 37554 425.79 30 31 25.83 75.84 125.87 175.88 225.96 276.05 326.19 376.38 426.63 31 32 26.67 76.68 126.70 176.72 226.80 276.88 327.02 377.22 427.47 32 33 27.50 77.51 127.53 177.55 227.63 277.72 327.86 378.05 428.31 33 34 28.33 *78.34 128.37 178.39 22847 278.55 328.69 378.89 429.15 34 35 29.17 79.17 129.20 179.22 229.30 279.39 329.53 379.73 429.98 35 36 30.00 80.01 130.04 180.06 230.14 280.23 330.37 380.57 430.82 36 37 30.83 80.84 130.87 180.89 230.97 281.06 331.20 381.41 431.66 37 38 31.67 81.67 131.71 181.73 231.81 281.90 332.04 382.24 432.50 38 39 32.50 82.51 132.54 182.56 232.64 282.73 332.87 383.08 433.34 39 40 33.33 83.34 133.38 183.40 233.48 283.57 333.71 383.92 434.18 40 41 34.17 84.17 134.21 184.23 234.31 284.41 334.55 384.76 435.02 41 42 35.00 85.01 135.05 185.07 235.15 285.24 335.38 385.60 435.86 42 43 35.83 85.84 135.88 185.90 235.98 286.08 336.22 386.43 436.70 43 44 36.66 86.67 136.72 186.74 236.82 286.91 337.05 387.27 437.54 44 45 37.50 87.51 137.55 187.57 237.65 287.75 337.89 388.11 438.37 45 46 38.33 88.34 138.38 188.40 238.48 288.59 338.73 388.95 439.21 46 47 39.17 89.17 139.22 189.24 239.32 289.42 339.56 389.79 440.05 47 48 40.00 90.00 140.05 190.07 240.15 290.26 340.40 390.62 440.89 48 49 40.83 90.84 140.89 190.91 240.99 291.09 341.23 391.46 441.73 49 50 41.67 91.67 14172 191.74 241.82 291.93 342.07 392.30 442.57 50 51 42.50 92.50 142.56 192.58 242,66 292.77 342.91 393.14 443.41 51 52 43.33 93.34 143.39 193.41 243.49 293.60 343.74 393.98 444.25 52 53 44.17 94-17 144.23 194.25 244.33 294.44 344.58 394.81 445.09 53 54 45.00 95.00 145.06 195.08 245.16 295.27 345.41 395.65 445.93 54 55 45.83 95-84 145.90 195,92 246.00 296.11 346.25 396.49 446.76 55 56 46.67 9ti.67 146.73 196.75 246.83 296.95 347.08 397.33 447.60 56 57 47.50 97.50 147.57 197.59 247.67 297.78 347.92 398.17 448.44 57 58 48.33 98.33 148.40 198.42 248.50 298.62 348.76 399.01 449.28 58 69 49.17 99.17 149.24 199.26 249.34 299.46 349.60 399.85 450.12 59 19 RAILROAD CURVE TABLES. ; 9 10 11 12 13 14 15 16 17 / 450-95 501.32 551.74 602.22 652.87 703.53 754.35 805.29 856.35 1 451.79 502.16 552.58 603.06 653.71 704.38 755.20 806.14 857.20 1 2 452.63 503.00 553.42 603,91 654.56 705.23 75605 806.99 858.05 2 3 453.47 503.84 554/26 604.75 655.40 706.07 756.89 807.84 858.90 3 4 454.31 504.68 555.10 605.60 656.25 706.92 757.74 808.64 859.76 4 5 455.14 505.52 555.94 606.44 657.09 707.7.7 758.59 809.54 860.61 5 6 455.98 506.36 556.78 607.28 657.93 708.62 759.44 810.39 861.46 6 7 456.82 507. '20 557.62 608.13 658.78 709.47 760.29 811.24 862.31 7 8 457.66 508.04 558.46 608.97 659.62 710.31 761.13 812.09 863.16 8 9 458.50 508.88 559.30 609.82 660.47 711.16 761.98 812.94 864.01 9 10 459.34 509.72 560.14 610,66 661.31 712.01 762.83 813.79 864.87 10 11 460.18 510 56 560.98 611.50 6(52.15 712.86 763.68 814.64 865.72 11 12 461.02 511.40 561.82 612.35 663.00 713.71 7(54.53 815.49 866.57 12 13 461.86 512.24 562.66 613.19 663.84 714.55 765.37 816.34 867.42 13 14 462.70 513.08 563.50 614.04 664.69 715.40 766.22 817.19 868.27 14 15 463.53 513.92 564.34 614.88 665.53 716.25 767.07 818.04 869.12 15 16 464.37 514.76 565.18 615.72 6(56.37 717.10 767.92 818.89 869.98 16 17 465.21 515.60 566.02 616.57 667.22 717.95 768.77 819.74 870.83 17 18 406.05 516.44 566.86 617.41 6t>8.06 718.79 769.61 82059 871.68 18 19 466.89 517.28 567.70 618.26 668.91 719,64 770.46 821.44 872.53 19 20 467.73 518.12 568.54 619.10 669.75 720.49 771.31 822 29 873.38 20 21 468.57 518.96 569.38 619.94 670.59 721.35 772.16 823.14 874.23 21 22 469.41 51980 570.22 620.79 671.44 722.20 773.01 823 99 875.09 22 23 470.25 520.64 571.06 021.63 672.28 723.04 773.85 824.84 875.94 23 24 471.08 521.48 571.90 622.48 673.13 723.89 774.70 825 69 876.79 24 25 471.92 522.32 572.74 623.32 673.97 724.74 775.55 826.54 877.64 25 26 472.76 523.16 573.58 624.16 674.81 725.59 776.40 827.39 878.49 26 27 473.60 524.01 574.42 625.01 675.66 726.44 777.35 828.24 879.34 27 28 474.43 524.85 575.27 625.85 676.51 727.28 778.09 82909 880.20 28 29 475.26 525.69 576.11 626.70 677.35 728.13 778.94 829.94 881.05 29 30 476.10 526.53 576.95 627.55 678.20 7'28.97 779.79 830.79 881.90 30 31 476.94 527.37 577.79 6'28.39 679.04 729.82 780.64 831.64 882.75 31 32 477.78 528.21 578.63 629.24 679.89 730.66 781.49 832.49 883.61 32 33 478.62 529.05 579.48 630.08 680.73 731.51 782.34 833.35 884.46 33 34 479.46 529.89 580.32 630.93 681.58 732.35 783.19 834.20 885.32 34 35 480.30 530.73 581.16 631.77 682.42 733.20 784.04 835.05 886.17 35 36 481.14 531.57 582.00 632.61 683.26 734.05 784.89 835.90 887.02 36 37 481.99 532.41 582.84 633 46 684.11 734.89 785.74 836.75 887.88 37 38 482.83 533.25 583.69 634.30 684.95 73.").74 786.59 837.61 888.73 38 39 483.67 534.09 5H4.53 635.15 685.80 736.58 787.44 838.46 889.59 39 40 484.51 534.93 585.37 635.99 686.64 737.43 788/29 839.31 890-44 40 41 485.35 535.77 586.21 636.83 687.48 738/28 789.14 840.16 891.29 41 42 486.19 536.61 587.05 637.68 688.33 739.12 789.99 841.01 89-'. 15 42 43 487.03 537.45 587.90 638.52 689.17 739.97 790.84 841.87 893.00 43 44 487.87 538.29 588.74 639.37 690.02 740.81 791.69 842.72 893.86 44 45 488.71 539.13 589.58 640.21 690.86 741.66 792.54 843.57 894.71 45 46 48956 539.97 590.42 641.05 691.70 742.51 793.39 8,14.42 89551 46 47 490.40 540.81 591.26 641.90 692.55 743.35 794.24 845.27 896.42 47 48 491.24 511.65 592.11 642.74 693.89 744.20 795.09 846.13 897.27 48 49 492.08 542.49 592.95 643.59 694.24 745.04 795.94 846.98 898.13 49 50 492.92 543.33 593.79 644.43 695.08 745.89 796.79 847.83 898.98 50 51 493.76 541.17 594.03 645.27 695.92 746.74 797.64 848. 6S 899.83 51 52 494.60 545.01 595.47 646.12 696.77 747.58 798.49 849.53 900.69 52 53 495.44 545.85 596.32 646.96 697.61 748.43 799.34 P50.39 901.54 53 54 496.28 546.69 597.16 647.81 69846 749.27 800.19 851.24 902.40 54 55 497.12 547.53 598.00 648.65 699.30 750.12 801.04 852.09 903.25 55 56 497.96 548.37 598.84 649.49 70014 750.97 801.89 852.94 904.10 56 57 498.H1 549.21 599.68 650.34 700.99 751.81 802.74 853.79 904.96 57 58 499.65 550.06 600.53 651.18 701.83 752.66 803.59 854.65 905,81 58 59 500.48 550.90 601.38 652.03 702.68 753.50 804.44 855.50 906.67 59 20 RAILROAD CURVE TABLES. r 18 19 20 | 21 | 22 1 23 | 24 25 | 26 / 907.52 958.86 ' 1010.37 : 1062.00 1113.80 1165.76 1217.96 i 1270.28 1322.88 1 908.38 959.72 1011.23 i 1062.86 1114.67 1166.63 1218.83 1271.16 1323.76 1 2 90J.23 960.57 1012.09 1063.73 1115.53 1167.50 1219.70 1272.03 1324.63 2 3 910.09 961.43 1012.95 1064.59 1116.40 1168.37 1220.57 1272.91 1325.51 3 4 910.94 962.30 1013.81 1065.45 1117.26 1169.24 1221.45 1273.79 1326.39 4 5 911.80 963.15 1014.67 1066.32 1118.13 1170.11 1222.32 1274.66 1327.27 5 6 912.65 964.00 1015.53 1067.18 1118.99 1170.98 1223.19 1275.54 1328.14 6 7 913.51 964.86 1016.39 1068.04 1119.86 1171.85 1224.06 1276.42 1329.02 7 8 914.36 965.72 1017.24 1068.91 1120.72 1172.71 1224.93 1277.29 1329.90 8 9 915.22 966.58 1018.10 1069.77 1121.59 1173.58 1225.80 1278.17 1330.78 9 10 916.07 967.43 1018.96 1070.63 1122.45 1174.45 1226.67 1279.05 1331.65 10 11 916.93 968.29 1019.82 1071.50 1123.32 1175.32 1227.54 1279.92 1332.53 11 12 917.78 969.15 1020.68 1072.36 1124.18 1176.19 1228.42 1280.80 1333.41 12 13 918.64 970.00 1021.54 1073.22 1125.05 1177.06 1229.29 1281.69 1334.28 13 14 919.49 970.86 1022.40 1074.09 1125.91 1177.93 1230.16 1282.55 1335-16 14 15 920.35 971.72 1023.26 1074.95 1126.78 1178.80 1231.03 1283.43 1336.04 15 16 921.20 972.58 1024.12 1075.81 1127.64 1179.67 1231.90 1284.31 1336.92 16 17 922.06 973.43 1024.98 1076.68 1128.50 1180.54 1232.77 1285.18 1337.79 17 18 922.91 974.29 1025.84 1077.54 1129.37 1181.41 1233.64 1286.06 1338.67 18 19 923.77 975.15 1026.70 1078.40 1130.24 1182.28 1234.51 1286.94 1339.55 19 20 924.63 976.01 1027.56 1079.27 1131.10 1183.15 1235.39 1287.81 1340.43 20 21 925.48 976.86 1028.42 1080.13 1131.97 1184.02 1236.26 1288.69 1341.30 21 22 926.34 977.72 1029.27 1080.99 1132.83 1184.88 1237.13 1289.57 1342.18 22 23 927.19 978.58 1030.13 1081.86 1133.70 1185.75 1238.00 1290.44 1343.06 23 '24 928.05 979.44 1030.99 1082.72 1134.56 1186.62 1238.87 1291.32 1343.94 24 25 928.90 980.29 1031.85 1083.58 1135.43 1187.49 1239.74 1293.20 1344.81 25 26 929.76 981.15 1032.71 1084.45 1136.29 1188.36 1240.61 1293.07 1345.69 26 27 930.61 982.01 1033.57 1085.31 1137.16 1189.23 1241.49 1293.95 1346.57 27 28 931.47 982.86 1034.43 1086.17 1138.02 1190.10 1242.36 1294.83 1347.44 28 29 932.32 983.72 1035.29 1087.04 1138.89 1190.97 1243.23 1295.70 1348.32 29 30 933.18 984.58 1036.15 1087.90 1139.75 1191.84 1244.10 1296.58 1349.20 30 31 934.04 985.44 1037.01 1088.76 1140.62 1192.71 1244.97 1297.46 1350.08 31 32 934.89 986.30 1037.87 1089.63 1141.48 1193.58 1245.85 1298.33 1350.96 32 33 935.75 987.16 1038.74 1090.49 1142.35 1194.45 1246.72 1299.21 1351.85 33 34 936.60 988.02 1039.60 1091.35 1143.22 1195.32 1247.59 1300.09 1352.73 34 35 937.46 988.88 1040.46 1092.22 1144.09 1196.19 1248.46 1300.96 1353.61 35 36 938.32 989.74 1041.32 1093.08 1144.95 1197.06 1249.34 1301.84 1354.49 36 37 939.17 990.60 1042.18 1093.94 1145.82 1197.93 1250.21 1302.72 1355.37 37 38 940.03 991.46 1043.05 1094.81 1146.69 1198.80 1251.08 1303.59 1356.25 38 39 940.88 992.32 1043.91 1095.67 1147.55 1199.68 1251.95 1304.47 1357.14 39 40 941.74 993.18 1044.77 1096.53 1148.42 1200.55 1252.83 1305.35 1358.02 40 41 942.60 994.04 1045.63 1097.40 1149.29 1201.42 1253.70 1306.22 1358.90 41 42 913.45 994.90 1046.49 1098.26 1150.15 1202.29 1254.57 1307.10 1359.78 42 43 944.31 995.76 1047.36 1099.12 1151.02 1203.16 1255.44 1307.98 1360.66 43 44 945.16 996.62 1048.22 1099.99 1151.89 1204.03 1256.32 1308.85 1361.54 44 -15 946.03 997.48 1049.03 1100.85 1152.76 1204.90 1257.19 1309.73 1362.43 45 46 946.88 998.34 1049.94 1101.71 1153.62 1205.77 1258.06 1310.61 1363.31 46 47 947.73 999.19 1050.80 1102.58 1154.49 1206.64 1258.93 1311.48 1364.19 47 48 948.59 1000.95 1051.67 1103.44 1155.36 1207.51 1259.81 131-2.36 136507 48 49 919.44 1000.91 1052.53 1104.30 1156.22 1208.38 1260.68 1313.24 1365.95 49 50 950.30 1001.77 1053.39 1105.17 1157.09 1209.25 1261.55 1314.11 1366.83 50 51 951.16 1002.63 1054.25 1106.03 1157.96 1210.12 1262.42 1314.99 1367.72 51 5-2 952.01 1003.49 1055.11 1106.89 1158.82 1210.99 1263.30 1315.87 1368.60 52 53 952.87 1004.35 1055.98 1107.76 1159.69 1211.86 1264.17 1316.74 1369.48 53 54 953.72 1005.21 1056.84 1108.62 1160.56 1212.73 1265.04 1317.62 1370.36 54 55 954.58 1006.07 1057.70 1109.48 1161.43 1213.61 1265.92 1318.50 1371.24 55 56 955.44 1006.93 1058.56 1110.35 1162.29 1214.48 1266.79 1319.37 1372.12 56 57 956.29 1007.79 1059.42 1111.21 1163.16 1215.35 1267.66 1320.25 j 1373.01 57 58 957.15 1008.65 i 1060.28 1112,07 1164.03 1216.22 1268.53 1321.13 i 1373.89 58 59 958.00 1009.51 . 1031.14 1112.94 1164.89 1217.09 1269.41 1322.00 1374.77 59 RAILROAD CURVE TABLES. i 27 28 29 30 31 32 33 34 35 e 1375.65 1428.65 1481.89 1535.30 1589.04 1643.08 1697.28 1751.S3 1806.67 1 1376.53 1429.54 1482.78 1536.20 1589.94 1643.98 1698.19 175-2.74 1807.59 i 2 1377.41 1430.42 1483.67 1537.09 1590.84 1644.88 1699.10 1753.66 1808.50 2 3 1378.30 1431.31 1484.56 1537.99 1591.74 1645.78 1700.01 1754.57 1809.42 3 4 1379.18 1432.20 1485.45 1538.88 1592.64 1646.69 1700,92 1755.48 1810.34 4 5 1380.06 1433.08 1486.34 1539.78 1593.54 1647.59 1701.83 1756.40 1811.25 5 6 1380.94 1433.97 1487.23 1540.67 1594.44 1648.49 1702.74 1757.31 1812.17 6 7 1381.82 1434.86 1488.12 1541.57 1595.34 1649.39 1703.65 1758.22 1813.09 7 8 138-2.70 1435.74 1489.01 1542.47 1596.24 1650.29 1704.55 1759.13 1814,00 8 9 1383.59 1436.63 1489.90 1543.36 1597.14 1651.19 1705.46 1760.05 1814.92 9 10 1384.47 1437.52 1490.79 1544.26 1598.04 1652.09 1706.37 1760.96 1815.84 10 11 1385.35 1438.40 1491.68 1545.15 1598.94 1652.99 1707.28 1761.87 1816.75 11 12 1386.23 1439.29 1492.57 1546.05 1599.84 1653.90 1708.19 1762.79 1817.07 12 13 1387.11 1440.18 1493.46 1546,94 1600.74 1654.80 1709.10 1763.70 1818,59 13 14 1387.99 1441.06 1494.35 1547.84 1601.64 1655.70 1710.01 1764.61 1819.50 14 15 1388.88 1441.95 1495.24 1548.74 1602.54 1656.60 1710.92 1765.53 1820.42 15 16 1389.76 1442.84 1496.13 1549.63 1603.44 1657.50 1711.83 1766.44 182134 16 17 1390.64 1443.72 1497.02 1550.53 1604.33 1658.40 1712.74 1767.35 1822.25 17 18 1391.52 1444.61 1497.91 1551.42 1605.23 1659.30 1713.65 1768.26 1823.17 18 19 1392.40 1445.50 1498.80 1552,32 1006.13 1660.20 1714.56 1769.18 1824.09 19 20 1393.28 144(5.38 1499.69 1553.21 1607.03 1661.11 1715.47 1770.09 1825.00 20 21 1394.17 1447.27 1500.58 1554.11 1607.93 1662.01 1716.38 1771.00 1825.92 21 22 1395.05 1448.16 1501.47 1555.00 1608.83 1662.91 1717.28 1771.92 1826.84 22 23 1395.93 1449.04 1502.36 1555.90 1609.73 1663.81 1718,19 1772.83 1827.75 23 24 1396.81 1449.93 1503.25 1556.80 1610.63 1664.71 1719.10 1773.74 1828.67 24 25 1397.69 1450,82 1504.U 1557.69 1611.53 1665.61 1720.01 1774.66 1829.59 25 26 1398.57 1451.70 1505,03 1558.59 1612.43 1666.51 1720.92 1775.57 1830.50 26 27 1399.46 1452.59 1505.92 1559.48 1613.33 1667.42 1721.83 1776.48 1831.42 27 28 1400.34 1453.48 1506.81 1560-38 1614.23 1668.32 1722.74 1777.39 1832.34 28 29 1401.22 1454 36 1507.70 1561.28 1615.13 1669.22 1723.65 1778.31 1833.25 29 30 1402.10 1455.25 1508.59 1562.17 1616.03 1670.12 1724.56 1779.22 1834.17 30 31 1402.99 1456.U 1509.48 1563.07 1616.93 1671.03 1725.47 1780.14 1835.09 31 32 1403.87 1457.03 1510.37 1563.96 1617.83 1671.93 1726.38 1781.05 1836.01 32 33 1404.76 1457.91 1511.26 1564.86 1618.74 1672.64 1727.29 1781.97 1836.93 33 34 1405.64 1458.80 1512.15 1565.75 1619.64 1673.74 1728.20 1782.88 1837.85 34 35 140ti.53 1459.69 1513.04 1566.65 1620.54 1674.65 1729.10 1783.80 1838.77 35 36 1407.41 1460.58 1513.93 1567.54 1621.44 1675.55 1730.01 1784.71 1839.69 36 37 1408.30 1461.47 1514.82 1568.44 1622.34 1076.46 1730.92 1785.63 1840.61 37 38 140SU8 1462.35 1515.71 1569.34 1623.24 1677,36 1731.83 1786.54 1841.54 38 39 1410.07 1463.24 1516.60 1570.23 1624.15 1678.27 1732.74 1787.46 1842.46 39 40 1410.95 1464.13 1517.49 1571.13 1625.05 1679.17 1733.65 17H8.37 1843.38 40 41 1411.84 1465,02 1518.38 1572.02 1625.95 1080.08 1734.56 1789.29 1844.30 41 42 1412.72 1465.91 1519.27 1572.92 1626.85 1680.98 1735.47 1790.20 1845.22 42 43 1413.01 1466.79 1520.16 1573.81 1627.75 1681.89 1736.38 1791.12 1846.14 43 44 1414.49 1467.68 1521.05 1574.71 1628.65 1682.79 1737.29 1792.03 1847.06 44 45 1415.38 1468.57 1521.94 1575.61 1629.56 1683.70 1738.20 1792.95 1847.98 45 46 1416.26 1469.46 J1522.83 1576.50 1630.46 1684.61 1739.10 1793.86 1848,90 46 47 1417.15 1470.35 1523.73 1577.40 1631.36 1685.51 1740.01 1794.78 1849.82 47 48 1418.03 1471.23 1524.62 1578.29 1632.26 1686.42 1740.92 1795.69 1850.74 48 49 1418.92 1472.12 1525.51 1579.19 1633.16 1687.32 1741.83 1796.61 1851.66 49 50 1419.80 1473.01 1526.40 1580.08 1634.06 1688.23 1742.74 1797.52 1852.58 50 51 1420.69 1473.90 1527.29 1580.98 1634.97 1689.13 1743.65 1798.44 1853.50 51 52 1421.57 1474.79 1528.18 1581.88 1635.87 1690.04 1744.56 1799,35 1854.43 52 53 1422.46 1475.67 1529.07 1582.77 1636,77 1690.94 1745.47 1800.27 1855.35 53 54 1423.34 1476.56 1529.96 1583.67 1637.67 1691.85 1746.38 1801.18 1856,27 54 55 1424.23 1477.45 1530.85 1584.56 1638.57 1692.75 1747,29 1802.10 1857.19 55 56 1425.11 1478.34 1531.74 1585.46 1639.47 1693.66 1748.19 1803.01 1858.11 56 57 1425.99 1479.23 1532.63 1586.35 1640.38 1694.56 1749.10 1803.93 1859.03 57 58 1426.88 1480.11 1533.52 1587.25 1641.28 1695.47 1750.01 1804.84 1859.95 58 59 1427.77 1481.00 1534.41 1588.15 1642.18 1696.37 1750.92 1805.76 1860,87 59 22 RAILROAD CURVE TABLES. / 36 37 38 39 40 41 42 43 44 r 1861.79 1917.26 1973.01 2029.11 2085.55 2142.33 2199.52 2257.10 2315.09 1 1862.71 1918.19 1973.94 2030.05 2086.50 2143.28 2200.48 2258.06 2316.06 1 2 1863.64 1919.11 1974.88 2030.99 2087.44 ; 2144.24 2201.44 1 2259.03 2317.03 2 3 1864.56 1920.04 1975.81 2031.93 ! 2088.39 ! 2145.19 2202.40 2259.99 2318.00 3 4 1865.48 1920.97 1976.75 2032.87 2089.33 2146.14 2203.35 2260.96 2318.97 4 5 1866.41 1921.89 1977.68 2033.81 2090.28 2147.10 2204.31 2261.92 2319.94 5 6 1867.33 1922.82 1978.61 2034.75 2091.22 2148.05 2205.27 2262.89 2320.91 6 7 1868.25 1923.74 1979.55 2035.69 2092.17 2149.00 2206.23 2263.85 2321.88 7 8 1869.17 1924.67 1980.48 2036.63 2093.11 2149.95 2207.19 2264.82 2322.85 8 9 1870.10 1925.60 1981.42 2037.67 2094.06 2150.91 2208.15 226578 2323.82 9 10 1871.02 1926.52 1982.35 2038.51 2095.00 | 2151.86 2209.11 2266.75 2324.79 10 11 1871.94 1927.45 1983.28 2039.45 2095.95 1 2152.81 2210.07 2267.71 2325.76 11 12 1872.86 1928.38 1984.22 2040.39 2096.89 2153.77 2211.02 2268.68 2326.73 12 13 1873.78 1929.30 1985.15 2041.33 2097.84 2154.72 2211.98 i 2263.64 2327.70 13 14 1874.71 1930.23 1986.09 2042.27 2098.78 ! 2155.67 2212.94 2270.61 3328.67 14 15 1875.63 1931.15 1987.02 2043.21 2099.73 2156.63 2213.90 2271.57 2329.64 15 16 1876.55 1932.08 1987.95 2044.15 2100.67 2157.58 2214.86 2272.54 2330.61 16 17 1877.48 1933.01 1988.89 2045.08 2101.62 2158 53 2215.82 2273.50 2331.59 17 18 1878.40 1933.93 1989.82 2046.02 2102.57 2159.48 2216.78 2274.46 2332.56 18 19 1879.32 1934.86 1990.76 2046.96 2103.51 2160.44 2217.74 2275.43 2333.52 19 20 1880.24 1935.79 1991.69 2047.90 2104.46 2161.39 2218.69 2276.39 2334.49 20 21 1881.16 1936.71 1992.62 2048.84 2105.40 2162.34 2219.65 2277.36 2335.46 21 22 1882.09 1937.64 1993.56 2049.78 2106.35 2163.30 2220.61 2278.32 2336.44 22 23 1883.01 1938.56 1994.49 2050.72 2107.29 2164.25 2221.57 2279.29 2337.41 23 24 1883.93 1939.49 1995.43 2051.66 2108.24 .2165.20 2222.53 2280.25 2338.38 24 25 1884.86 1940.42 1996.36 2052.60 2109.18 2166.16 2223.49 2281 22 2339.35 25 26 1885.78 1941.34 1997.29 2053.54 2110.13 2167.11 2224.45 2282.18 2340.32 | 26 27 1886.71 1942.27 1998.23 2054.48 2111.07 2168.06 2225.40 2283.15 2341.29 27 . 28 1887.63 1943.20 1999.16 2055.42 2112.02 2169.01 2226.36 2284.11 2342.26 28' 29 1888.55 1944.12 2000.10 2056.36 2112.96 2169.97 2227.32 2285.08 2343.23 i 29 30 1889.47 1945.05 2001.03 2057.30 2113.91 2170.92 2228.28 2286.04 2344.20" 30 31 1890.40 1945.98 2001.97 2058.24 2114.86 ; 2171.87 2229.24 2287.01 2345.17 31 32 1891.32 1946.91 2002.90 2059.18 2115.80 ; 2172.83 2230/20 2287.98 2346.15 ! 32 33 1892.25 1947.85 2003.84 2060.13 2116.75 2173.78 2231.16 2288.94 2347.12 | 33 34 1893.17 1948.78 2004.77 2061.07 2117.70 | 2174.73 2232.12 2289.91 2348.10 i 34 35 1894.10 1949.71 2005.71 2062.01 2118.65 i 2175 69 2233 08 2290.88 234907 35 36 1895.03 1950.64 2006.65 2062.95 2119.59 2176.64 2234.04 2291.85 2350.04 36 37 1895.95 1951.57 2007.58 2063.89 2120.54 i 2177.59 2235 00 2292.82 2351.02 37 38 1896.88 1952.51 2008.52 2064.83 2121.49 i 2178.55 2235.97 2293.79 2351.99 38 39 1897.81 1953.44 2009.45 2065.78 2122.44 2179.50 2236.93 2294.75 2352.97 39 40 1898.73 1954.37 2010.39 2066.72 2123.38 21*0.45 2237.89 2295.72 2353.94 40 41 1899.66 1955.30 2011.33 2067.66 2124.33 2181.41 2238.85 2296.69 2354.91 41 42 1900.59 1956.23 2012.26 2068.60 2125.28 2182.36 2239.81 2297.66 2355.89 42 43 1901.51 1957.17 2013.20 2069.54 2126.22 2183.31 2240.77 2298.63 235686 43 44 1902.44 1958.10 2014.34 2070.48 2127.17 2184.27 2241.73 2299.60 2357.84 44 45 1903.36 1959.03 2015.07 2071.43 2128.12 2185.22 2242.69 2300.56 2358.81 45 46 1904.29 1959.96 2016.01 2072.37 2129.07 2186.17 2243.65 2301.53 2359.78 46 47 1905.22 1960.89 2016.94 2073.31 2130.01 2187.13 2244.61 2302.50 236076 47 48 1906.14 1961.83 2017.88 2074.25 2130.96 2188.08 2245.57 230347 2361.73 48 |49 1907.07 1962.76 2018.81 2075.19 2131.91 2189.03 2246.53 2304.44 2362.71 49 150 1908.00 1963.69 2019.75 2076.13 2132.86 2189.99 2247.49 2305.41 2363.68 ! 50 ! 51 1908.92 1964.62 2020.69 2077.08 2133.80 2190.94 2248.45 2306.37 2364.65 51 i52 1909.85 1965.55 2021.62 2078.02 2134.75 2191.89 2249 42 2307.34 2365.63 ! 52 153 1910.77 1966.49 2022.56 2078.99 2135.70 2192.85 2250.38 2308 31 23('6.60 53 54 1911.70 1967.42 2023.49 2079.90 2136.65 2193.80 2251.34 2309.28 2367.58 54 55 1912.63 1968.35 2024.43 2080.84 2137.59 2194.75 2252.30 2310.25 2368.55 55 56 1913.55 1969.28 2025.37 2081.78 2138.54 2195.71 2253.26 2311.22 2369.52 56 57 1914.48 1970.21 2026.30 2082.73 2139.49 2196.66 2254.22 2312.18 2370.50 57 58 1915.41 1971.15 2027.24 2083.67 2140.43 2197.61 2255.18 2313.15 2371.47 58 59 1916.33 1972.08 2028.17 2084.61 2141.38 2198.57 2256.14 2314.21 2372.45 59 23 RAILROAD CURVE TABLES. / 45 46 47 48 49 | 50 51 52 | 53 t 2373.42 2432.21 2491.46 2551.11 2611.27 2671.90 2733.04 2794.69 2856.86 1 2374.40 2433.20 2492.45 2552.11 2612.28 2672.92 2734.07 2795.72 2857.90 1 U 28 i 5. 38 2434.18 2493.45 2553.11 26 1 3.29 2673.94 2735.09 2796.76 2858.95 2 3 2376.35 2435.17 2494.44 2554.11 2614.30 2674.95 1 2736.12 2797.79 2859.99 3 . 4 2377.33 2436.15 2495.43 2555.11 2615.31 2675.97 2737.14 2798.82 2861.03 4 i 5 2378.31 2437.14 249*6.43 2556.11 2616.32 2676.99 2738.17 2799.86 2862.08 5 6 2379.29 2438.12 2497.42 2557.12 2617.32 2678.01 2739.19 280J.89 2863.12 6 7 2380/27 2439.11 2498.41 2558.12 2618,33 267903 '/740.22 2801.92 2864.16 7 8 2381.24 2440.10 2469.40 2559.12 2619.34 2680.04 2741.25 2802.96 2865.20 8 9 2382.22 2441.08 2500.40 2560.12 2620.35 2681.06 2742.27 2803.99 2866.25 9 10 2383.20 2442.07 2501.39 2561.12 2621.36 2682.08 2743.30 2805.02 2867.29 10 11 2384.18 2443.05 2502.38 2562.12 2622.36 2683.10 ! 2744.32 2806.06 2868.33 11 12 2385.16 2444.04 2503.38 2563.12 2623.37 2684.12 2745.35 2807.09 2869.38 12 13 2386.13 2445.02 2504.37 2564.12 2624.3S 2685.13 2746.37 2808.12 2870.42 13 14 2387.11 2446.01 2505.36 2565.12 2625.39 2686.15 2747.40 2809.16 2871.46 14 15 2388.09 2447.00 2506.36 2566.12 2626.40 2687.17 2748.43 2810-19 2872.51 15 36 2389.07 2447.98 2507.35 2567.13 2627.41 268.19 2749.45 2811.22 2873.55 16 ! 17 2390.05 2448.97 2508.34 2568.13 2628.41 2689.21 2750.48 2812.26 2874.59 17 18 2391.02 2449.95 2509.33 2569.13 2629.42 2690.22 2751.50 2813.29 2875.63 18 19 2392.00 2450.94 2510.33 2570.13 2630.43 2691.24 2752.53 2814.32 2876.68 19 UO 2392.98 2451.92 2511.32 2571.13 2631.44 2692.26 2753.55 2815 36 2877.72 20 21 2393.96 2452.91 2512.32 2572.13 2632.45 2693.28 2754.58 2816.39 2878.76 21 22 2394.94 2453.89 2513.31 2573.13 2633.46 2694.30 2/55.61 2817.42 2879.81 22 23 2395.91 2454.88 2514.30 2574.13 2634.47 2695.31 2756.63 2818.46 2880.85 23 24 2396.89 2455.87 2515.30 2575.13 2635.48 2696.33 2757.66 2819.49 2881.89 24 25 2397.87 2456.85 2516.29 2576.13 2636. *9 2697.55 2758.68 2820.52 2882.94 25 26 2398.85 2457.84 2517.28 2577.13 2637.50 2698.37 2759.71 2821.56 2883. y 8 26 27 2399.83 2458.82 2518.27 2578.13 2638.50 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2425.34 2484.53 2544.14 2604.24 2664.81 2725.90 2787.48 2849 59 2912-23 53 54 2126.32 2485.52 2545.14 2605.24 2665.83 2726.92 2788.51 2850.63 2913.28 54 55 2427.30 2480.5! 2546.13 2606.24 2666.* 4 2727.94 2789.54 2651.67 2914.32 55 56 2428-28 2487.0 2547.13 26 17.25 2667.85 272896 2790.57 2852.70 2915.36 56 57 2429.27 2488.49 2548.12 2608.25 2668. P6 2729.98 2791.60 2853.74 2916.41 57 58 2430.25 2489.48 2549.12 2609.26 2669.87 2731.00 2792.63 2854.78 2917.46 5S 59 2431.2 J 2490.47 ; 2550.11 2610.26 2670.89 [ 2732.02 L 2793.66 i 2855.82 2918.50 59 24 RAILROAD CURVE TABLES. / 54 55 56 57 58 | 59 60 | 61 | 62 2919.55 2982.81 3046.64 3111.10 I 3176.14 3241.86 3308.21 3375.20 3442.93 1 29.:0.60 2983.87 3047.71 3112.18 3177.23 3242.96 3309.32 3376.33 3444.07 1 2 2921.65 2984.93 3048.78 3113.26 3178.32 3244.06 3310.44 3377.45 3445.20 2 3 2922.71 2986.00 3049.86 3114.34 3179.42 3245.17 3311.55 3378.58 3446.34 3 4 2923.76 2987.06 3050.93 3115.42 3180.51 3246.27 3312.67 3379.70 3447.48 4 5 2924.81 2988.12 3052.00 3116.51 3181.60 3247.37 3313.78 3380.83 3448.61 5 6 2925.86 2989.18 3053.07 3117.59 3182.69 3248.47 3314.89 3381.95 3449.75 6 7 2926.92 2990.24 3054.14 3118.67 3183.79 3249.57 3316.01 3383.08 3450.88 7 8 21)27.97 2991.31 3055. '/I 3119.75 3184.88 3250.68 3317.12 3384.20 3452.02 8 g 2929.02 2992.37 3056.-29 31-20.83 3185.97 3251.78 3318.24 3385.33 3453.16 9 10 2930.07 2993.43 3057.36 3121.91 3187.06 3252.88 3319.35 3386.45 3454.29 10 11 2931.13 2994.49 3058.43 3122.99 3188.16 3 j 53.98 3320.46 3387.58 3455.43 11 12' 2932.18 2995.55 3059.50 3124.07 3189.25 3255.08 3321.58 3388.70 3456.57 12 13 2933.23 2996.62 3060.57 31-25.15 3190.34 3256.19 3322.69 3389.83 3457.70 13 14 2934.28 2997.68 3061.64 3126.23 3191.43 3257.29 3323.80 ! 3390.95 3458.84 14 15 2935.33 2998.74 3062.72 3127.32 3192.52 3258.39 33-24.92 3392.08 3459.97 15 16 2936.39 2999.80 3063.79 3128.40 3193.62 3259.49 3326.03 3393.20 3461.11 16 17 2937.44 3000.86 3064.86 3129.48 3194.71 3260.59 3327.15 3394.33 3462.25 17 18 2938.49 3001.93 3065.93 3130.56 3195.80 3261.70 33-28.26 3395.45 3463.38 18 19 2939.54 3002.99 3067.00 3 1 31.64 3196.89 3262.80 3329.36 3396.58 3464.52 19 20 2940.60 3004.05 3068.07 3132.72 3197.99 32(13.90 3330.49 3397.70 3465.66 20 21 2941.65 3005.11 3069.15 3133.80 3199.08 3265.00 3331.60 3398.83 3466.79 21 22 2942.70 3006.17 3070.22 3134.S8 3200.17 3266.10 3332.71 3399.95 3467.93 22 23 2943.75 3007.24 3071.29 3135.96 3201.26 3267.21 3333.83 3401.08 3*69.07 23 24 2944.81 3008.30 3072.36 3137.04 3202.36 3268.31 3334.94 3402.20 3470.20 24 25 2945.86 3009.36 3073.43 3138.13 3203.45 3269.41 3336.05 3403.33 3471.34 25 26 2946.91 3010.4-2 3074.50 3139.21 3204.54 3270.51 3337.17 3404.45 3472.47 26 27 2947.96 3011.48 3075.58 3140.29 3205.63 3271.61 3338.28 3405.58 3473.61 27 28 2949.01 3012.55 3076.65 3141.37 3206.73 3272.72 3339.40 3406.70 3474.75 28 29 2950.07 3013.61 3077.72 3142.45 3207.82 3273.82 3340.51 3407.83 3475.88 29 30 2951.12 3014.67 3078.79 3143.53 3208.91 3274.92 3341.62 3408.95 3477.02 J30 31 2952.18 3015.74 3079.87 3144.62 3210.01 3276.03 3342.74 3410.08 3478.16 31 32 2953.23 3016.80 3080.94 3145.70 3211.11 3277.14 3343.86 3411.22 3479.31 32 33 2954.29 3017.87 3082.02 3146.79 3212.20 3278.25 3344.98 3412.35 3480.45 33 34 2955.35 3018.93 3083.10 3147.88 3213.30 3279.36 3346.10 3413.48 3481.60 34 35 2956.40 3020.00 3084.18 3148.97 3214.40 3280.47 3347.22 3414.61 3482.74 35 36 2957.46 3021.06 3085.25 3150.05 3215.50 3281.58 3348.34 3315.75 3483.88 36 37 2958.51 3022.13 30H6.33 3151.14 3216.60 3282.69 3349.46 3416.88 3485.03 37 38 2959.57 3023.20 3087.41 3152.23 3217.70 3283.80 3350.58 3418.01 3486.17 38 39 2960.63 3024.26 3088.48 3153.31 3218.80 3284.91 3351.69 3419.14 3487.32 39 40 2961.68 3025.33 3089.56 3154.40 3219.89 3286.02 3352.81 3420.28 3488.46 40 41 2962.74 3026.39 3090.64 3155.49 3220.99 3287.13 3353.93 3421.41 3489.60 41 42 2963.80 3027.46 3091.71 3156.57 3222.09 3288.24 3355.05 3422.54 3490.75 42 43 2964.85 3028.52 3092.79 3157.66 3223.19 3289.35 3356.17 3423.68 3491.89 43 44 2965.91 3029.59 3093.87 3158.75 3224.29 3290.46 3357.29 3424.81 3493.04 44 45 2966.96 3030.66 3094.95 3159.84 3225.38 3291.57 3358.41 3425.94 3494.18 45 46 2968.02 3031.72 3096.02 3160.92 3226.48 3292.68 3359.53 3427.07 3495.32 46 47 2969.08 3032.79 3097.10 3162.01 3227.58 3293.78 3360.65 3428.21 3496.47 47 48 2970.13 3033.85 3098.18 3163.10 3228.68 3294.89 3361.77 3429.34 3497.61 48 49 2971.19 3034.92 3099.25 3164.18 3229.78 3296.00 3362.89 3430.47 3498.77 49 50 2972.25 3035.98 3100.33 3165.27 3230.88 3297.11 3364.01 3431.60 3499.90 50 51 2973.30 3037.05 3101.41 3166.36 3231.97 3298.22 3365.13 3432.74 3501.04 51 52 2974.36 3038.11 3102.48 3167.44 3233.07 3299.33 3366.25 3433.87 3502.19 52 53 2975.41 3039.18 3103.56 3168.53 3234.17 3300.44 3367.37 3435.00 3503.33 53 54: 2976.47 3040.25 3104.64 3169.62 3235.27 3301.55 3368.48 3436.13 3504.48 54 55 2977.53 3041.31 3105.72 3170.71 3236.37 3302.66 3369.60 3437.27 3505.62 55 56 2978.58 3042.38 3106.79 3171.79 3237.47 3303.77 3370.72 3438.40 3506.76 56 57 2979.64 3043.44 3107.87 3172.88 3238.56 3304.88 3371.84 3439.53 3507.91 67 58 2980.70 3044.51 3108.95 3173.97 3239.66 3305.99 3372.96 3440.67 3509.05 58 59 I 2981.75 3045.57 3110.02 3175.05 3240.76 3307.10 3374.08 3441.80 3510.20 59 25 RAILROAD CURVE TABLES. / 63 | 64 65 66 j 67 68 69 70 71 | ' 3511.34 3580.45 3650.41 3721.06 3792.57 3864.88 3938.11 4012.15 | 4087.15 1 3512.49 3581.61 3651.59 3722.15 3793.77 3866.10 3939.34 4013.40 ! 4088.41 1 2 3513.64 3582.78 3652.76 3723.44 3794.97 3867.31 3940.57 4014.64 4089.67 2 3 3514.78 3583.94 3653,94 3724.62 3796.17 3868.5.3 3941.80 4015.89 409D.93 3 4 3515.93 3585.10 3655.11 3725.81 3797.38 3869.75 3943.03 4017 14 4092.19 4 6 3517.08 3586.27 3656.29 3727.00 3798.58 3870.97 3944.26 4018.39 4093.45 5 6 3518.23 3587.43 3657.46 3726.19 3799.78 3872.18 394549 4019.63 4094.71 6 7 3519.38 3588.59 3658.64 3729.38 3800.98 3873.40 3946.72 4020.88 4095.97 7 8 3520.52 35S9.75 3659.81 3730.56 3802.18 3874.62 3947.95 4022.13 4097.24 8 .) 3521.67 3590.92 3660.99 3731.75 3803.38 3.S75.83 3949.18 4023.37 4098.50 9 10 3522.82 3592.08 3662.16 3732.94 3804.58 3877.05 3950.41 4024.62 i 4099.76 10 11 3523.97 3593.24 3663.33 3734.13 3805.78 3878.27 3951.64 4025.87 4101.02 11 12 3525.12 3594.41 3664.51 3735.32 3806.99 3879.48 3952.87 4027.11 4102.28 12 13 3526.26 3595.57 3665 68 3736.50 3808.19 3880.70 3954.10 4028.36 4103.54 13 U 3527.41 3596.73 3666.86 3737.69 3809.39 3881.92 3955.33 4029.61 4104.80 14 15 3528.56 3597.90 3668.03 3738.88 3810.59 3883.14 3956.56 4i 30.86 4106.06 15 16 3529.71 3599.06 3669.21 3740.07 3811.79 3884.35 3957.79 4032.10 4107.32 16 17 3530.86 3600.22 3670.38 3741.26 3812.99 3885.57 3959.02 4033.35 4108.58 17 18 3532.00 3001.38 3671.56 3742.44 3814.19 3S86.79 3960.25 4031.60 4 1 09.84 18 19 3533.15 360255 3672.73 3743.63 :-*815.39 3888.00 3961.48 4035.84 4111.10 19 20 3534.30 3603.71 3673.90 3744.82 3816.60 3889.21 3962.71 4037.09 4112.36 20 21 3535.45 3604.87 3675.08 3746.01 3817.80 3890.43 3963.94 4038.34 4113.62 21 22 3536.60 3606.04 3676.25 3747.20 3819.00 3891.64 3965.17 4039.58 4114.89 22 23 3537.74 3607.20 3677.43 3748.38 3820.20 3892.86 3966.40 4040.83 4116.15 23 21 3538.89 3608.36 3678.60 3749.57 3821.40 3894.08 3967.63 4042.08 4117.41 24 25 3540.04 3609.53 3679.78 3750.76 3822.C.O 3895.29 3968.86 4043.33 4118.67 25 26 3541.19 3610.69 3680.95 3751.95 3823.80 3896.51 3970.09 4044.57 4119.93 26 27 3542.34 3611.85 3682.13 3753.14 3825.01 3897.73 3971-32 4045.82 4121.19 27 28 3543.48 3613.01 3683.30 3754.32 3826.21 3898.95 3972.55 4047.07 4122.45 28 2'.) 3544.63 3614.18 3684.48 3755.51 3827.41 3900.16 3973.78 4048.31 4123.71 29 30 3545.78 3615.34 3685.65 3756.70 3828.61 3901.38 3975.01 4049.56 4124.97 30 31 3546.94 3616.51 3686.83 3757.90 3829.82 3902.60 3976.25 4050.81 4126.24 31 32 3548.09 3617.68 3688.01 3759.09 3831.03 3903.83 3977.49 4052.07 4127.51 32 33 3549.25 3618.85 3689.19 3760.29 3832.24 3905.05 3978.72 4053.32 4128.78 33 34 3550.40 3620.02 3690.37 3761.48 3833.45 3906.28 3979.96 4054.57 4130.05 34 35 3551.56 3621.19 3691.55 3762.68 3834.66 31107.50 3981.20 4055-83 4131.32 35 36 3552.72 3622.35 3692.73 3763.87 3835.86 3908.73 3982.44 4057.08 4132.59 36 37 3553.87 3623.52 3693.91 3765.07 3837.07 3909.95 3983.68 4058.33 4133.86 37 38 3555. C 3 3624.69 3695.09 3766.27 3838.28 3911.17 3984.91 4059.58 4135.13 38 39 3556.18 3625.86 3696.27 3767.46 3839.49 3912.40 398(5.15 4060.84 4136.40 39 40 3557.34 3627.03 3697.45 3768.66 3840.70 3913.62 3987.39 4062.09 4137.67 40 41 3558.49 3628.20 3698.63 3769.85 3841.91 3914.85 3988.63 4063.34 4138.94 41 42 3559.65 3629.37 3699.81 3771.05 3843.12 3916.07 3989.87 4064.60 4140.21 42 13 3560.80 3630.54 3 00.99 3772.24 3844.33 3917.30 3991.10 4065.85 4141.48 43 44 3561.96 3631.71 3702.17 3773,44 3845.54 3918.52 3992.34 4067.10 4142.75 44 -:5 3563.12 3612.88 3703.35 3774.64 3846.75 3919.74 3993.58 4068.36 4144-02 45 46 3564.27 3634.04 3704.53 3775.83 3847.95 3920.97 3994.82 4069.61 4145.29 46 ! 47 3565.43 3635.21 3705*72 3777.03 3849.16 3922.19 3996.06 4070.86 4146.56 47 18 3566.58 3636.38 3706.90 3778.22 3850.37 3923.42 3997.29 4072.11 4147.83 48 4 it 3567.74 3637.55 3708.08 3779.42 3851.58 3924.61 3998.52 4073.37 4149 10 49 60 3568.89 3638.72 3709.26 3780.61 3852.79 3925.87 3999.77 4074.62 4150.37 50 51 3570.05 3639.89 3710.44 3781.81 3854.00 3927.09 4001.01 4075.87 4151.64 51 52 3571.21 3841.06 3711.62 3783.01 3855.21 3928.31 4002.25 4077.13 4152.91 52 i53 3572.36 3642.23 3712.80 3784.20 3856.42 3929.54 4003 48 4078.38 4154.18 53 54 3573.52 3613.40 3713.98 3785.40 3857.63 3930.76 4004.72 4079.63 4155.45 54 55 3574.67 3644.57 3715.16 3786.59 3858.84 3931.99 4005.96 4080.89 4156.72 55 56 3575.83 3(545.73 3716.34 3787.79 3860.04 3933.21 4007.20 4082.14 4157.99 56 57 3576.99 3646.90 3717.52 3788.98 3861.25 3934.44 4008.44 4083.39 41 59.26 57 58 3578.14 36S8.07 3718.70 3790.18 3862.46 3935.66 4009.67 4084.64 416053 58 59 3579.30 3649.24 3719.88 3791.38 3863.67 3936.88 4010.91 4085.90 , 4161.80 59 26 RAILROAD CURVE TABLES. ' 72 | 73 74 75 76 j 77 78 79 80 j ' 4163.07 4239.97 4317.84 4396.74 4476.73 4557.81 4640.04 4723.41 4808.04 1 4164.35 4241.26 4319.15 4398.07 4478.08 4559.18 4641.43 4724.82 4809.47 1 2 4165.63 4242.56 4320.46 4399.40 4479.42 4560.54 4642.81 4726.22 4810.89 2 3 4166.90 4243.85 4:321.77 4400.73 4480.77 4561.91 4614.20 4727.63 4812.32 3 4 4168.18 4245.14 4323.08 4402.06 4482.12 4563.27 4645.58 4729.03 4813.74 4 5 4169.46 4246.44 4324.39 4403.39 4483.46 4564.64 4646.97 4730.44 4815.17 5 6 4170.74 4247.73 4325.70 4404.71 4484.81 4566.01 4648.35 4731.85 4816.59 6 7 4172.02 4249.02 4327.01 4406.04 4486.16 4567.37 4649.74 4733.25 4818.02 7 8 4173.29 4250.31 4328.32 4407.37 4487.51 4568.74 4651.12 4734.66 4819.44 8 9 4174.57 4251.61 4329.63 4408.70 4488.85 4570.10 4652.50 4736.06 4820.87 9 10 4175.85 4252.90 4330.94 4410.03 4490.20 4571.47 4653.89 4737.47 4822.29 10 11 4177.13 4254.19 4332.25 4411.36 4491.55 4572.83 4655.27 4738.87 4823.72 11 12 4178.41 4255.49 4333.56 4412.69 4492.89 4574.20 4656.66 4740.28 4825.14 12 13 4179.68 4256.78 4334.87 4414.02 4494.24 4575.56 4658.04 4741.68 4826.57 13 14 4180.96 4258.07 4336.18 4415.35 4495.59 4576.93 4659.43 4743.09 4827.99 14 15 4182.24 4259.36 4337.49 4416.68 4496.93 4578.30 4660.81 4744.50 4829.42 15 16 4183.52 4260.66 4338.80 4418.01 4498.28 4579.66 4662.20 4745.90 4830.84 16 17 4184.80 4261.95' 4340.11 4419.34 4499.63 4581.03 4663.58 4747.31 4832.27 17 18 4186.07 4263.24 4341.42 4420.67 4500.98 4582.39 4664.97 4748.71 4833.69 18 19 4187.35 4264.54 4342.73 4422.00 4502.32 4583.76 4666.35 4750.12 4835.12 19 20 4188.63 4265.83 4344.05 4423.33 4503.67 4585.12 4667.73 4751.52 4836.54 20 'A 4189.91 4267.12 4345.36 4424.65 4505.01 4586.49 4669.12 4752.93 4837.97 21 22 4191.19 4268.42 4346.67 4425.98 4506.35 4587.86 4670.50 4754.34 4839.39 22 23 4192.46 4269.71 4347.98 4427.31 4507.70 4589.22 4671.89 4755.74 4840.82 23 '24 4193.74 4271.00 4349.29 4428.64 4509.05 4590.59 4673.27 4757.15 4842.24 24 25 4195.02 4272.29 4350.60 4429.97 4510.39 4591.95 4674.66 4758.55 4843.67 25 26 4196.30 4273.59 4351.91 4431.30 4511.74 4593.32 4676.04 4759.96 4845.09 26 '27 4197.57 4274.88 4353.22 4432.63 4513.09 4594.69 4677.43 4761.37 4846.52 27 28 4198.85 4276.17 4354.53 4433.96 4514.44 4596.05 4678.81 4762.77 4847.94 28 29 4200.13 4277.47 4355.84 4435.29 4515.78 4597.42 4680.20 4764.18 4849.37 29 30 4201.41 4278.76 4357.15 4436.62 4517.13 4598.78 4681.58 4765.58 4850.79 30 31 4202.70 4280.06 4358.47 4437.96 4518.49 4600.15 4682.97 4766.99 4852.23 31 32 4203.98 4281.36 4359.79 4439.29 4519.84 4601.53 4684.37 4768.41 4853.66 32 33 4205.27 4282.67 4361.11 4440.63 4521.20 4602.91 4685.76 4769.83 4855.10 33 34 4206.55 4283.97 4362.43 4441.97 4522.55 4604.28 4687.16 4771.24 4856.53 34 35 4207.84 4285.27 4363.75 4443.30 4523.91 4605.66 4688.55 4772.66 4857.97 35 36 4209.12 4286.58 4365.07 4444.64 4525.27 4607.03 4689.94 4774.07 4859.41 36 37 4210.41 4287.88 4366.39 4445.98 4526.62 4608.41 4691.34 4775.49 4860.84 37 38 4211.69 4289.18 4367.71 4447.32 4527.98 4609.78 4692.73 4776.90 4862.28 38 39 4212.98 4290.48 4369.03 44*8.65 4529.33 4611.16 4694.13 4778.32 4863.71 39 40 4214.26 4291.79 4370.35 4449.99 4530.69 4612.53 4695.52 4779.73 4865.15 40 41 4215.55 4293.09 4371.67 4451.33 4532.05 4613.91 4696.92 4781.15 4866.59 41 42 4216.83 4294.39 4372.99 4452.66 4533.40 4615.28 4698.31 4782.56 4868.03 42 43 4218.12 4295.69 4374.31 4454.00 4534.76 4616.66 4699.70 4783.98 4869.46 43 44 4219.40 4297.00 4375.63 4455.34 4536.11 4618.03 4701.10 4785.39 4870.90 44 45 4220.69 4298.30 4376.94 4456.67 4537.47 4619.41 4702.49 4786.81 4872.33 45 46 4221.98 4299.60 4378.26 4458.01 4538.83 4620.78 4703.89 4788.22 4873.77 46 47 4223.26 4300.91 4379.58 4459.35 4540.18 4622.16 4705.28 4789.64 4875.21 47 48 4224.55 4302.21 4380.90 4460.69 4541.54 4623.53 4706.67 4791.05 4876.61 48 49 4225.83 4303.51 4382.22 4462.02 4542.89 4624.91 4708.07 4792.47 4878.08 49 50 4227.12 4304.81 4383.54 4463.36 4544.25 4626.29 4709.47 4793.89 4879.52 50 51 4228.40 4306.12 4384.86 4464.70 4545.61 4627.66 4710 86 4795.30 4880.95 51 52 4229.69 4307.42 4386.18 4466.03 4546.96 4629.04 4712-25 47%. 72 4882.39 52 53 4230.97 4308.72 4387.50 4467.37 4548.32 4630.41 4713.G5 4798.13 4883.83 53 54 4232.26 4310.02 4388.82 4468.71 4549.67 4631.79 4715.04 4799.55 4885.26 54 55 4233.54 4311.33 4390.14 4470.04 4551.03 4633.16 4716.44 4800.96 4886.70 55 56 4234.83 4312.63 4391.46 4471.38 4552.39 4634.54 4717.83 4802.38 4888.13 56 57 4236.11 4313.93 4392.78 4472.72 4553.74 4635.91 4719.22 4803.79 4889.57 57 58 4237.40 4315.23 4394.10 4474.06 4555.10 4637.29 4720.62 4805.21 4891.00 68 59 4238.68 1 4316.54 4395.42 4475.39 4556.45 4638.66 4722.01 4806.62 4892-44 59 RAILROAD CURVE TABLES. ' ! 81 82 83 84 85 | 86 87 88 | 89 | ' 4893 88 4980.97 5069.44 5159.29 5250.57 5343.28 5437.54 5533.35 5630.81 i 4895.33 4982.44 5070.93 5160.80 5252.11 5344.84 5439.13 5534.97 5632.46 1 2 4896.77 4983 91 5072.42 5162.32 5253.65 5346.41 5440.72 5536 59 5634.10 2 3 4898.22 4985.38 5073.92 5163.83 5255.19 5347.97 5442.31 5538.20 5635.75 3 4 4899.66 4986.85 507541 5165.35 5256.73 5349.54 5443.90 5539.82 5637.39 4 5 4901.11 4988.32 5076.90 5166.86 5258.27 5351 10 5445.50 5541.44 5639.04 5 6 4902.56 4989.78 5078.39 5168.38 5259.81 5352 67 5447.09 5543.06 5640.69 6 7 4904.00 4991.25 5079.88 5169.89 5261.35 5354.23 544868 5544.68 5642.33 7 8 4905.45 4992.72 5081 38 5171.41 5262.88 5355.79 5450.27 5546 29 5643.98 8 9 4906.89 4994.19 5082.87 5172.92 5264.42 5357.36 5451.86 5547.91 564563 9 10 4908.34 4995.66 5084.36 5174.44 5265.96 5358.92 5453.45 5549.53 5647.27 10 11 4909.78 4997.13 5085.85 5175.95 5267.50 5360.49 5455.04 5551.14 5648.92 11 12 4911.23 4998.60 5087.34 5177.47 5269.04 5362 05 5456.63 5552.76 5650.57 12 13 4912.68 5000.07 5088.84 5178.98 5270.58 5363.62 5458.22 5554.38 5652.21 13 14 4914.12 5001.54 5090.33 5180.50 5272.12 5365.18 5459.81 5556.00 5653.86 14 15 4915.57 5003.01 5091.82 5182.01 5273.66 5366.74 5461.41 5557.62 5655.50 15 16 4917.01 5004.47 5093.31 5183.53 5275.20 5368.31 5463.00 5559.24 5657.15 16 17 4918.46 5005.94 5094.80 5185.04 5276.74 5369.87 5464.59 5560.85 5658.80 17 18 4919.91 5007.41 5096.30 5186.56 5278.28 5371.44 5466.18 5562 47 5660.44 18 19 4921.35 5008.88 5097.79 5188.07 5279.82 5373.00 5467.77 5564.09 5662.09 19 20 4922-79 5010.35 5099.28 5189.58 5281.36 5374.57 5469.36 5565.70 5663-74 20 21 4924.24 5011.82 5100.77 5191.10 5282.90 5376.13 5470.95 5567.32 5665.38 21 22 4925.69 5013.29 5102.26 5192.61 5284.44 5377.69 5472.54 5568.94 5667.03 22 23 4927.13 5014.76 5103.76 5194.13 5285.97 5379.26 5474.13 5570.56 5668.67 23 24 4928.58 5016.23 5105.25 5195.64 5287.51 5380.82 5475.72 5572.18 5670.32 24 25 4930.02 5017.69 5106.74 5197.16 5289.05 5382.39 5477.32 5573.79 5671.97 25 26 4931.47 5019-16 5108.23. 5198.67 5290.59 5383.95 5478.91 5575.41 5673.61 26 27 4932.92 5020.63 5109.72 5200.19 5292.13 5385.51 5480.50 5577.03 5675.26 27 28 4934.36 5022.10 5111.22 5201.70 5293.67 5387.08 5482.09 5578.65 5676.91 28 29 4935.81 5023.57 5112.71 5203.22 5295.21 5388.64 5483.68 5580.27 5678.55 29 30 4937.25 5025.04 5114.20 5204.73 5296.75 5390.21 5485.27 5581.88 5680.20 30 31 4938 71 5026 52 5115.70 5206.26 5298.30 5391.79 5486.87 5583.51 5681.86 31 32 4940.16 5028 00 5117.21 5207.79 5299.85 5393.37 5488.48 5585.14 5683.52 32 33 4941.62 5029.48 5118.71 5209.31 5301.40 5394.94 5490.08 5586.77 5685.18 33 34 4943.08 5030.96 5120.21 5210.84 5302.95 5396.52 5491 68 5588.40 5686.84 34 35 4944 54 5032 44 5121.72 5212.37 5304.51 5398.10 5493.29 5590.04 5688.50 35 36 4945.99 5033.92 5123.22 5213.90 5306.06 5399.68 5494.89 5591.67 5690.16 36 37 4947.45 5035.40 5124.72 5215.43 5307.61 5401.25 5496.49 5593.30 5691.82 37 38 4948.91 5036.88 5126.22 5216 95 5309.16 5402.83 5498.09 5594.93 5693.48 38 39 4950.36 5038 36 5127.73 5218.48 5310,71 5404.41 5499.70 5596.56 5695.14 39 40 4951.82 5039.84 5129.23 5220.01 5312.26 5405.99 5501.30 5598.19 5696.80 40 41 4953.28 5041.32 5130.73 5221.54 5313.81 5407.56 5502.90 5599.82 5698.46 41 42 4954.74 5042.80 5132.24 5223 07 5315.36 5409.14 5504.50 5601.45 5700.12 42 43 4956.19 5044.28 5133.74 5224.59 5316.91 5410.72 5506.11 5603.08 5701.78 43 44 4957.65 5045.76 5135.24 5226.12 5318.46 5412.30 5507.71 5604.71 5703.44 44 45 4959.11 5047.24 5136.75 5227.65 5320.02 5413.88 5509.31 5606.35 5705.10 45 46 4960.57 5048.72 5138.25 5229.18 5321 57 5415.45 5510.91 5607.98 5706.76 46 47 4962.02 5050 20 5139.75 5230.71 5323.12 5417.03 5512.52 5609.61 5708.42 47 48 4963.48 5051.68 5141.25 5232.23 5324.67 5418.61 5514.12 5611.24 5710.08 48 49 4964.94 5053.16 5142.76 5233.76 5326.22 5420.19 5515.72 5612.87 5711.74 49 50 4966.40 5054.64 5144 26 5235.29 5327.77 5421.76 551732 5614.50 5713.40 50 51 4967.85 5056.12 5145.76 5236.82 5329.32 5423 34 5518.93 5616.13 5715.06 51 52 4979.31 5057.60 5147.27 5238.35 5330.87 5424.92 5520.53 5617.76 5716.72 52 53 4970.77 5059.08 5148.77 5239.87 5332.42 5426.50 5522.13 5619.39 5718 38 53 54 4972.22 5060.56 5150.27 5241.40 i 5333.97 5428.07 5523.74 5621.02 5720.04 54 55 4973.68 5062.04 5151.77 5242.93 5335.53 5429.65 5525.34 5622.66 5721.70 55 56 4975.14 5063.52 5153.28 5244.46 5337.08 5431.23 5526.94 5624.29 5723.36 56 57 4976.60 5065.00 5154.78 5245.99 5338.63 5432.81 5528.54 5625.92 5725.02 57 58 4978.05 5066.48 5156.28 5247.51 5340.18 5434.39 5530.15 5627.55 5726.68 58 59 4979.51 5067-96 5157.79 5249.04 5341.73 5435.96 5531.75 5629.18 5728.34 59 28 TABLE or MINUTES WITH COK- KESPONDING DECIMALS. TABLE OF SECONDS WITH COKEES- PONDING DECIMALS. M. | D. | M. | D. S. D. | S. D. / 1 o 0.0166 i 31 o 0.5167 1 it 0.0002778 n 31 0.0086111 2 0.0333 32 0.5333 2 0.0005556 32 0.0088888 3 0.0500 33 0.5500 3 0.0008333 33 9.0091666 4 0.0667 34 0.5667 "^4 0.0011111 34 0.0094444 5 0.0833 35 0.5833 5 0.0013888 35 0.0097222 6 0.1000 36 0.6000 6 0.0016666 36 0.0100000 7 0.1167 37 0.6167 7 0.0019444 37 0.0102777 8 0.1333 38 0.6333 8 0.0022222 38 0.0105555 9 0.1500 39 0.6500 9 0.0025000 39 0.0108333 10 0.1667 40 0.6667 10 0.0027777 40 0.0111111 11 0.1833 41 0.6833 11 0.0030555 41 0.0113888 12 0.2000 42 0.7000 12 0.0033333 42 0.0116666 13 0.2167 43 0.7167* 13 0.0036111 43 0.0119444 14 0.2333 44 0.7333 14 0.0038888 44 0.0122222 15 0.2500 45 0.7500 15 0.0041666 45 0.0125000 16 0.2667 46 0.7667 16 0.0044444 46 0.0127777 17 0.2833 47 0.7833 17 0.0047722 47 0.0130555 18 0.3000 48 0.8000 18 0.0050000 48 0.0133333 19 0.3167 49 0.8167 19 0.0052777 49 0.0136111 20 0.3333 50 0.8333 ' 20 0.0055555 50 0.0138888 21 0.3500 51 0.8500 21 0.0058333 51 0.0141666 22 0.3667 52 0.8667 22 0.0061111 52 0.0144444 23 0.3833 53 0.8833 23 0.0063888 53 0.0147222 24 0.4000 54 0.9000 24 0.0066666 54 0.0150000 25 0.4167 55 0.9167 25 0.0069444 55 0.0152777 26 0.4333 56 0.9333 26 0.0072222 56 0.0155555 27 0.4500 57 0.9500 27 0.0075000 57 0.0158333 28 0.4667 58 0.9667 28 0.0077777 58 0.0161111 29 0.4833 59 0.9833 29 0.0080555 59 0.0163888 30 0.5000 60 1.0000 30 0.0083333 60 0.0166666 RAILROAD CURVE TABLE. The following Table shows the distance from the point of inter- section of the Tangent lines to the beginning of one degree curves, for each 30 feet, the angle of deflection ( = angle at centre) being known. I. = The given angle of deflection. II. = The sought for distance. III. = Difference for intermediate angles. 30 RAILROAD CURVE TABLE. I II III | I II III i ! ii III 0' 25.00 25.0 30 30' 1562.17 26.8 60 30' 3341.62 33.4 1 50.02 25.0 31 1589.04 26.9 61 3375.20 33.6 1 30 75.01 25.0 31 30 1616.03 27.0 61 30 3408.95 33.8 2 9999 25.0 32 1643.08 27.0 62 3142.93 34.0 2 30 125.03 25.0 32 30 1670.12 27.0 62 30 3477.02 34.1 3 150.07 25.0 33 1697.28 27.2 63 3511.34 343 3 30 175.05 25.0 33 30 1724.56 27.3 63 30 3545.78 34.4 4 200.09 25.0 34 1751.83 27.3 64 3580.45 3i.7 4 30 225.13 25.0 34 30 1779.22 27.4 64 30 3615.34 31.9 5 250.17 25.0 35 1808.67 27.4 65 3650.41 351 5 30 275.21 25.0 35 30 1834.17 27.5 65 30 3685 65 35.2 6 300.30 25.0 36 1861.79 27.6 66 3721.06 35.4 6 30 325.35 25.0 36 30 1889.47 27.7 66 30 3756.70 356 7 350.44 25.1 37 1917.26 27.8 67 3792.57 359' 7 30 375.54 25.1 37 30 1945.05 27.8 67 30 3828.61 36.0 8 400.70 25.1 38 1973.01 27.9 68 3864.88 36.3 8 30 425.79 25.1 38 30 2001.03 28.0 68 30 3901.38 36.5 9 450.95 25.1 39 2029.11 28.1 69 3938.11 36.7 9 30 476.10 25.1 39 30 2057.30 28.2 69 30 3975.01 36.9 10 501.32 25.2 40 2085.55 28.3 70 4012.15 37.1 10 30 526.53 25.2 40 30 2113.91 2-1.4 70 30 4019.56 37.4 11 551.74 25.2 41 2142.33 28.4 71 4087.15 37.6 11 30 576.95 25.2 41 30 2170.92 28.6 71 30 4124.97 37.8 12 602.22 25.3 42 2199.52 28.6 72 4163.07 3-1.1 12 30 627.55 25.3 42 30 2228.28 28.8 72 30 4201.41 38.3 13 652.87 25.3 43 2257.10 28.8 73 4239.97 38.6 13 30 678.20 25.3 43 30 2286.04 28.9 73 30 4278 76 38.8 14 703.53 25.3 44 2315.09 29.0 74 4317.84 38.9 It 30 728.97 25.4 44 30 2344.20 29.1 74 30 4357.15 39 3 15 754.35 25.4 45 2373.42 29.2 75 4396.74 39.6 15 30 779.79 25.4 45 30 2402.76 29.3 75 30 4436.62 * 39.9 16 805.29 25.5 46 2432.21 29.4 76 4476.73 40.1 1C 30 830.79 25.5 46 30 2161.78 29.6 76 30 4517.13 40.4 17 856.35 25.5 47 2491 46 29.7 77 4557.81 40.7 17 30 881.90 25.5 47 30 2521.26 29.8 77 30 4598.78 41,0 18 907.52 25.6 48 2551.11 29.8 78 4640.04 41.3 18 30 933.18 25.6 48 30 2581.13 30.0 78 30 4681.58 415 19 958.86 25.7 49 2611.27 30.1 79 4723.41 41.8 19 30 984.58 25.7 49 30 2641.53 30.3 79 30 4765.58 42.2 10 1010.37 25.8 50 2671.90 30.4 80 4808.04 42.5 20 30 1036.15 25.8 50 30 2702.44 30.5 80 30 4850.79 42.7 21 1062.00 25.8 51 2733.04 30.6 81 4893.88 43.1 2t 30 1089.90 25.9 51 30 2763.81 30.8 81 30 4937.25 43.3 22 1113.80 25.9 52 2791.69 30.9 82 4980.97 43.7 22 30 1139.75 25.9 52 30 2825.68 31.0 82 30 5025.04 44,1 23 1165.76 26.0 53 2856.86 31.2 83 5069.44 44.4 23 30 1191.84 26.1 53 30 2888.15 31.3 83 30 5114.20 44.8 24 1217.9f5 26.1 54 2919.55 31.4 84 5159.29 45.1 24 30 1244.10 26.1 54 30 2951.12 31.6 84 30 5204.73 45.4 25 1270.28 26.2 55 2982.81 31.7 85 5250.57 45.8 25 30 1296.58 26.3 55 30 3014.67 31.9 85 30 5296.75 46.2 26 1322.88 26.3 56 3046.64 32.0 86 5343.28 46.5 26 30 1349.24 26.4 56 30 3078.79 32.2 86 30 5390.21 46.9 27 1375.65 26.4 57 3111.10 32.3 87 5437.54 47.3 27 30 1402.10 26.4 57 30 3143.53 32.4 87 30 5485.27 47.7 28 1428.65 26.5 58 3176.14 32.6 88 5533.35 48.1 28 30 1455.25 26.6 58 30 3208.91 32.8 88 30 5581.88 48.5 29 1481.89 26.6 59 3241.86 32.9 89 5630.81 48.9 29 30 1508.59 26.7 59 30 3274.92 33.1 89 30 5680.20 49.4 30 1535.30 26.7 60 3308.21 33.3 90 5730.00 49.8 31 RAILROAD CURVES. THE FOLLOWING TABLE SHOWS THE METHOD OF KEEPINGS THE FIELD NOTES OF A SURVEY, FROM WHICH THE CENTER LINE IS LAID ON THE MAP From sta- tion. TO sta- tion. Length of tan- gents in feet. Length of curves in feet Angle at in- tersection of tangents or angle at centre. Course of tangent, and degree and direc- tion of curves. Radius of curves in feet. No. of ft. from intersec- tion of tangents tobegng. of curve. Tangent S 19 21' E 0. 2. 200. 7 24' 3 42' L 1548.65 100.14 2. 26. 2400. 24 00' 1 00' R 5730. 1217.98 26. 43.556 1755.60 Tangent S 2 45' E 43.556 61.681 1812.5 36 15' 2 00' R 2865. 937.82 61.681 93.650 3196.90 Tangent S 33 30' W 93.650 102.517 886.7 13 18' 1 30' L 3820. 445.37 102 517 143.90 4138.30 Tangent S 20 12'W 143.90 155.766 1186.66 23 44' 2 00' L 2865. 602.02 155.766 170.43 1466.40 Tangent S 3 32' E 170.43 181.296 1086.66 21 44' 2 00' 11 2865. 550.00 181.296 184.506 321.00 Tangent S 18 12' W 184.506 193.195 868.89 13 02' 1 30' R 3820. 436-37 193.195 213.064 1986.9 Tangent S 31 14' W 213.064 220.908 784.44 11 46' 1 30' L 3820. 393.61 220.908 230.546 963-8 Tangent S 19 28' \V 230.546 242.496 1195.00 23 54' 2 00' R 2865. 606.37 242.496 252.356 98600 Tangent S 43 22' W 252.356 263.756 1140.00 17 06' 1 30' L 3820. 574.30 263.756 266.02 226.40 Tangent S 26 16' W 266.02 268.02 200.00 3 1 30' L 3820. 100.05 268.02 277.21 918.89 27 34' 3 L 1910. 468.55 277.21 279.21 200.00 3 00' 1 30' L 3820. 100.05 279.21 289.011 980.1 Tangent S 7 18' E 289.011 291.011 200.00 3 00' 1 30' R 3820. 100.05 291.011 301.422 1041.10 31 14' 3 00' R 1910. 53'..88 301.422 303.00 157.80 2 22' 1 30' R 3820. 78.90 303.00 321.00 1800. Tangent S 29 18' W 321.00 334.00 1300. 26 2 L 2865. 661.44 334. 338.71 471.00 Tangent S 3 18' W 338.71 347.15 844.16 16 53' 2 00' R 2865. 425.19 347.15 364.00 1685.00 Tangent S 20 D 11' W 364. 376.633 1263.33 37 54' 3 it 1910. 655.80 376.633 389.53 389.70 Tangent S 58 3 05' W 380.53 392.38 1185. 23 42' 2 R 2865. 601.14 392.38 402-92 1054.00 Tangent S 81= 47' W 402.92 404.92 200. 3 00' 1 30' L 3820. 100.05 404.92 418.198 1327.77 39 50' 3= 00' L 1910. 632.04 418.198 420.198 200. Tangent S 38 3 57' W 420.198 441.002 2080.41 83 13' 4 L 1432. 1272.21 441.002 442.582 158. 4 00' 2 32' L 22G1.87 79.99 442.582 449. 641.8 Tangent S 48 D 16' E 22.262.90 22.637.31 32 EXCAVATION AND EMBANKMENT. APPLICATION OF THE PEISMOIDAL FOBMULA IN DETEKMINING THE QUANTITIES OF RAILKOADS AND CANAL EXCAVA- TIONS AND EMBANKMENTS. In order to obtain the mean area from transverse sections, con- struct from the average cuttings and average horizontal distances of the slopes of the end section, a middle section ; and add to four times the area of this section the area of the end sections, and take one-sixth of the product for the mean area. The following diagrams show most of the figures which occur in taking cross sections of railroads, and serve to illustrate the ap- plication of the formula. In practice, however, intermediate sec- tions would be taken between station and station 1, and at such other joints as any sudden or material change in the surface would seem to require. The cuttings- and horizontal distances from the centre to the ter- mination of the slopes, are set down in tabular form. The notes of the middle section may at convenience be interlined in the space between the notes of the end sections. From this form the factors for the areas are made without resorting to diagrams. Page 34. *It will be seen by inspecting the diagrams that the embankment between stations 3 and 4 assumes the shape of a pyramid, and hence one-third of the area of the embankment set opposite station 4, should be multiplied by the distance between stations 3 and 4 to obtain the quantity. Between stations 4 and 5 the excavation as- sumes the same form, and should also be calculated as a pyramid ; or construct the middle section as before described, and calculate the distance from the centre to the point where the surface and the grade intersect ; and make out the factors accordingly. Having obtained the mean areas, proceed as hereinafter des- cribed to ascertain the cubic yards, EXCAVATION AND EMBANKMENT. r~w jo ; jo jo ea.TB jo BOTH Tre9|\[ -rag; jo Beay -xg; o -JO+ 93TB1S J9;n9o raojj -JO+ 91SUV -JO+ J9^U90 J9^U90 raojj -JO+ 93fB}S UT S 53 10 -* OO T-H 3 S? S5 00 CO ' t>. JO CD t~ S* 8 l>- Oi !> CO * O Ut> CO (M -H O n 00 CD 10 U$ (M* O ' 00* *** O G3lGt~ THO-^QO->* -+TTTTTT 1 1 1 i 1 ft 1 (M +++++ i i i >-00'* i i T 8888888 EXCAVATION AND EMBANKMENT. 35 JMV113AJN tt.iYl.ttJN T. STATION 0. AKEAS. On n nnn STATION 4. AREAS. MIDDLE SECTION. 16. X 5. = 80. 20. X 6. =120. 25. X 8. =200. 19. X 5. = 95.^-2.= 47.5. MIDDLE SECTION. 400.-r-2.=200. STATION 1. 22. X 10. =220. 19. 15. X 5.5=104.5 X 1. = 15. 119.5-^-2.= 59.75. zU. X 15s. z4U. 40. X 16. =640. STATION 5. 1100.-h2.=550. MIDDLE SECTION. 19.75 X 8. =158. 9.50 X 20. =190. 32.50 X 12. =390. 19. 20. X 6. =114. X 2. = 40. 154. -^2.= 77. 738.-^-2.=369. STATION 2. 17.50 X 6. =105. 20. X 7. =140. 25. X 8. =200. 20.5 20. 16. MIDDLE SECTION. X 7. =143.5 X 5. =100. X 4. = 64. 445.-r-2.=222.5. MIDDLE SECTION. 13.75 X 3. = 41.25 20. X 4.5= 90. 22. X 6. =132. 22. 20 307.5-r-2.=153.75. STATION 6. X 8. =176. X 8 1fiO 263.25. ~2.=131.62. 22. X 8. =176. 20. X 2. = 40. 19. X 4. = 76. 512.-r-2.=256. 116. -=-2.= 58. MIDDLE SECTION. 12.8 X 1. = 12.80 18.25 X 3.5= 63.88 16. 20. 16. MIDDLE SECTION. X 4. = 64. X 4. = 80. X 4. = 64. 76.68. -4-2.= 38.34. STATION 4. 17.5 x 3. = 52.5 -f-2.= 26.25. STATION 5. _ n 0. 208. -f- 2=104. STATION 7. ft EXCAVATION AND EMBANKMENT. The cubic yards between station and station 1 according to the method of adding the end areas and taking one-half for the mean area = 1018.51 c. yds. { c. yds. By 2d (or Prismoidal method)= 833.33 " f 185.18 2d 1st 2d 1st 2d 1st 2d Error on 500 lineal There are other methods which approximate nearer than the averaging method. For instance, taking |iths of the difference between the end areas, (or tne difference 0X0.46) and adding it to the lesser end area for the mean. This method approximates nearer the true quantity. The prin- cipal discrepancy occurs where the embankment assumes the wedge or pryamidal form. ,atioi 1 1 and 2 = land 2 1430.55 1387.96 1 42.59 2 and 3 2 and 3 519.44 498.14 [ 21.30 3 and 4 3 and 4 156.01 146.66 ' 1 9.35 4 and 5 48.59 < ( 4 and 5 32.40 ' 1 16.19 feet of excavation - - =274.61 By 3d "2d method between station and 1 " (or Prismoidal) and 1 937.03 833.33 i cubic yards. 4- 103.70 "3d "2d " between station 1 and 2 1 and 2 1382.03 1387.96 \ 5.93 "3d "2d 2 and 3 2 and 3 495.08 498.14 \ 3.06 "3d "2d u i ' 3 and 4 3 and 4 151.31 146.66 i 4.65 "3d "2d r> ' 4 and 5 4 and 5 44.72 32.40 i f 12.32 Error on 500 lineal feet of excavation 102.38 Another method is to multiply of the distance between trans- verse sections, by the sum of the end areas, added to four times half their sum ; and dividing by 27 for the cubic yards. The results are the same as by the first method except between stations and 1. EXCAVATION AND EMBANKMENT. 3v EXPLANATION OF THE FOLLOWING TABLES. The tables are calculated for a distance of 100 feet between trans- verse sections. In the left hand column are given the areas in feet. To obtain the cubic yards for areas, without decimals, look in the second column under the head of 0, and opposite the given area, find the cubic yards. EXAMPLE. Kequired the number of cubic yards for an area of 190 feet. In the second column, under the head of 0, and opposite 190 in the first column, find 703.70 cubic yards. To obtain the cubic yards for a less distance than 100 feet, multi- ply the cubic yards found in the tables bv the given distance, and point off the fractional parts of 100 feet. If the area has decimal parts, pass the eye to the right, opposite the area of the whole number, and under the head of such decimal will be found the number of yards. EXAMPLE. Eequired the cubic yards for an area of 105.4 feet. In the sixth column, under the head of 40, and opposite 105 in the first column, are given 390.37 cubic yards. If the yards for an area greater than 354.90, and not exceeding 3549 feet, are required, the decimal point of the area given in the tables, and that of the cubic yards, being removed one figure to the right, will give the required yards. If there are decimal parts, add the cubic yards found opposite in the first column, under the head of such decimal. EXAMPLE. Eequired the cubic yards for an area of 1975 feet ; re- move the decimal point one figure to the left, and find the yards for an area of 197.5 feet = 731.48, then remove the decimal point one figure to the right and you have 7314.8 cubic yards. If there is a decimal, add the cubic yards found for such decimal. Or, to obtain the cubic yards for an area exceeding 3549 feet, take one half of the area, and seek the corresponding yards in tables and multiply the same by 2. 38 EXCAVATION AND EMBANKMENT TABLES. | 0.00 | 0.10 | 0.20 0.30 |0.40 0.50 | 0.60 0.70 0.80 |0.90 0.00 0.37 0.74 1.11 1.48 1.85 2.22 2.59 2.96 3.33 1 3.70 4.07 4.45 4.81 5.19 5.56 5.93 6.30 6.67 7.04 2 7.41 7.78 8.15 8.52 8.89 9.26 9.63 10.00 10.37 10.74 3 11.11 11.48 11-85 12.22 12.59 12.96 13.33 13.70 14.07 14.44 4 14.82 15.19 15.56 15.93 16.30 16.67 17.04 17.41 17.78 18.15 5 18.52 18.89 19.26 19.63 20.00 20.37 20.74 21.11 21.48 21.85 6 22.22 22.59 22.96 23.33 23.70 24.07 24.44 24.82 25.19 25.56 7 25.93 26.30 26.67 27.04 27.41 27.78 28.15 28.52 28.89 29.26 8 29.63 30.00 30.37 30.74 31.11 31.48 31.85 32.22 32.59 32.96 9 33.33 33.70 34.07 34.44 34.82 35.19 35.56 35.93 36.30 36.67 10 37.04 37.41 37.78 38.15 38.52 38.89 39.26 39.63 40.00 40.37 11 4074 41.11 41.48 41.85 42.22 42.59 42.96 43.33 43.70 44.07 12 44.44 44.82 45.19 45.56 45.93 46.30 46.67 47.04 47.41 47.78 13 48.15 48.52 48.89 49.26 49.63 50.00 50.37 50.74 51.11 51.48 14 51.85 52.22 52.59 52.96 5^.33 53.70 54.07 54.44 54.82 55.19 15 55.56 55.93 56.30 56.67 57.04 57.41 57.78 58.15 58.52 58.89 16 59.26 59.63 60.00 60.37 60.74 61.11 61.48 61.85 62.22 62.59 17 62.96 63.33 63.70 64.07 64.44 64.82 65.19 65.56 65.93 66.30 18 66.67 67.04 67.41 67.78 68.15 68.52 68.89 69.26 69.63 70.00 19 70.37 70.74 71.11 71.48 71.85 72.22 72.59 72.96 73.33 7370 20 74.07 74.44 74.82 75.19 75.56 75.93 76.30 76.67 77.04 77.41 21 77.78 78.15 78.52 78.89 79.26 79.63 80.00 80.37 80.74 81.11 22 81.48 81.85 82.22 82.59 82.96 83.33 83.70 84.07 84.44 84.82 23 85.19 85.56 85.93 86.30 86.67 87.04 87.41 87.78 88.15 88.52 24 88.89 89.26 8963 90.00 90.37 90.74 91.11 91.48 91.85 92.22 25 92.59 92.96 93.33 93-70 94.07 94.44 94.82 95.19 95.56 95.93 26 96.30 96.67 97.04 97-41 97.78 98.15 98.52 98.89 99.26 9963 27 100.00 100.37 100.74 101-11 101.48 101.85 102.22 102.59 102.96 103.33 28 103.70 104.07 104.44 104-82 105.19 105.56 105.93 106.30 106-67 107.04 29 107.41 107.78 108.15 108-52 108.89 109.26 109.63 110.00 110-37 110.74 30 111.11 111.48 111.85 112-22 112.59 112.96 113.33 113.70 114-07 114.44 31 114.81 115.18 11556 115-92 116.29 116.67 117.03 117.40 117.77 118.15 32 118.52 118.89 119.26 119-63 120.00 120.37 120.74 121.11 121-48 121.85 33 122.22 122.59 122.96 123-33 123.70 124.07 124.44 124.81 125.18 125.55 34 125.92 126.30 126.66 127-03 127.40 127.77 128.14 12851 128.88 129.26 35 129.63 130.00 13037 130-74 131-11 131.48 131.85 132.22 132-59 132.96 36 133.33 133.70 134.07 134-44 134.81 135.18 135.55 135.92 136-29 136.67 37 137.04 137.41 137.78 138-15 338.52 138.89 139.26 139.63 140-00 140.37 38 140.74 141.11 141.48 141-85 142.22 142.59 142.96 143.33 143-70 144.07 39 144.44 144.81 145.18 145-55 145.92 146.29 146.66 147.03 147-40 147.78 40 148.15 148.52 148.89 149-26 149.63 150.00 150.37 150.74 151.11 151.48 41 151.85 152.22 152.59 152-96 153.33 153.70 154.07 154.44 154-81 155.18 42 155.55 155.92 156.29 156-66 157.03 157.40 157.77 158.14 158-51 158.89 43 159.26 159.63 160.00 160-37 160.74 161.11 161.48 161.85 162-22 162.59 44 162.96 163.33 163.70 164-07 164.44 164.81 165.18 165.55 165-92 166.30 45 166.67 16704 167.41 167-78 168.15 168.52 168.89 169.26 169.63 170.00 46 170.37 170.74 171.11 171-48 171.85 17-2.22 172.59 172.96 173.33 173.70 47 174.07 174.44 174.81 175-18 175.55 175.92 176.29 176.66 177.03 177.41 48 177.78 178.15 178.52 178-89 179.26 179.63 180.00 180. 87 180.74 181.11 49 181.48 181.85 182.22 182-59 182.96 183.33 183.70 184.07 184.44 184.81 50 185.18 185.55 18592 186-29 186.66 187.03 187.40 187.77 188.14 188.52 51 188.89 189.26 189.63 190-00 190.37 190.74 191.11 191.48 191.85 192.22 52 192.59 192.96 193.33 193-70 194.07 194.44 194.81 195.18 195.55 195.93 53 196.30 196.67 197.04 197-41 197-78 198.15 198.52 19889 199.26 19963 54 200.00 200.37 200.74 201-11 201-48 201.85 202.22 202.59 202.96 203.33 55 203.70 204.07 204.44 204.81 205.18 205.55 205.92 206.29 206.66 207.03 56 207.41 207.78 208.15 208.52 208.89 209.26 209.63 21000 210.37 210.74 57 211.11 211.48 211.85 212.22 212.59 212.96 213.33 213.70 214.07 214.44 58 214.81 215.18 215.55 215.92 216.29 216.66 217.03 217.40 217.77 218.15 59 218.52 218.89 219.26 219.63 220-00 220.37 220.74 221.11 221.48 221.85 EXCAVATION AND EMBANKMENT TABLES. |o.oo 0.10 0.20 0.30 0.40 0.50 j 0.60 0.70 0.80 0.90 60 222.22 222.59 222.96 223.33 223.70 224.07 224.44 224.81 225.18 225.55 61 225.92 226.29 226.66 227.03 227.40 227.77 228.14 228.51 228.88 229.26 62 229.63 230.00 230.37 230.74 231.11 231.48 231.85 232.22 232.59 232.96 63 233.33 233.70 234.07 234.44 234.81 235.18 235.55 235.92 236.29 236.67 64 237.04 237.41 237.78 238.15 238.52 238.89 239.26 239.63 240.00 240.37 65 240.74 241.11 241.48 241.85 242.22 242.59 242.96 243.33 243.70 244.07 66 244.44 244.81 245.18 245.55 245.92 246.30 246.67 247.04 247.41 247.78 67 248.15 248.52 248.89 249.26 249.63 250.00 250.37 250.74 251.11 251.48 68 251.85 252.22 252.59 252.96 253.33 253.70 254.07 254.44 254.81 255.18 69 255.56 255.93 256.30 256.67 257.04 257.41 257.78 258.15 258.52 258.89 70 259.26 259.63 260.00 260.37 260.74 261.11 261.48 261.85 262.22 262.59 71 262.96 263.33 263.70 264.07 264.44 264.81 265.18 265.55 265.92 266.30 72 266.67 267.04 2<>7.41 267.78 268.15 268.52 268.89 269.26 269.63 270.00 73 270.37 270.74 271.11 271.48 271.85 272.22 272.59 272.96 273.33 273.70 74 274.07 274.44 274.81 275.18 275.55 275.92 276.29 276.66 277.04 277.41 75 277.78 278.15 278.52 278.89 279.26 279.63 280.00 280.37 280.74 281.11 76 281.48 281.85 282.22 282.59 282.96 283.33 283.70 284.07 284.44 284.81 77 285.18 285.56 285.93 286.30 286.67 287.04 287.41 287.78 288.15 288.52 78 288.89 289.26 289.63 290.00 290.37 290.74 291.11 291.48 291.85 292.22 79 292.59 292.96 293.33 293.70 294.07 294.44 294.81 295.18 295.55 295.93 80 296.30 296.67 297.04 297.41 297.78 298.15 298.52 298.89 299.26 299.63 81 300.00 300.37 300.74 301.11 301.48 301.85 302.22 302.59 302.96 303.33 82 303.70 304.07 304.44 31*4.81 305.18 305.55 305.92 306.29 306.66 307.03 83 307.41 307.78 308.15 308.52 308.89 309.26 309.63 310.00 310.37 310.74 84 311.11 311.48 311.85 312.22 312.59 312.96 313.33 313.70 314.07 314.44 85 314.81 315.19 315.56 315.93 316.30 316.67 317.04 317.41 317.78 318.15 86 318.52 318.89 319.26 319.63 320.00 320.37 320.74 321.11 321.48 321.*5 87 322.22 322.59 322.96 323.33 323.70 324.07 324.44 324.81 325.18 32555 88 325.92 326.30 326.67 327.04 327.41 327.78 328.15 328.52 328.89 329.26 89 329.63 330.00 330.37 330.74 331.11 331.48 331.85 332.22 332.59 332.96 90 333.33 333.70 334.07 334.44 334.81 335.18 335.55 335.92 336.29 336.67 91 337.04 337.41 337.78 338.15 338.52 338.89 339.25 339.62 339.99 340.37 j 92 340.74 341.11 341.48 341.85 342.22 342.59 342.96 343.33 343.70 344.07 93 344.44 344.81 345.18 345.56 345.93 346.30 346.67 347.03 347.40 347.78 94 348.15 348.52 348.89 349.26 349.63 350.00 350.37 350.74 351.11 351.48 95 351.85 352.22 352.59 352.96 353.33 353.70 354.07 354.44 354.81 355.18 96 355.55 355.93 356.30 356.67 357.04 357.41 357.78 358.15 358.52 358.89 97 359.26 359.63 360.00 360.37 360.74 361.11 361.48 361.85 362.22 362.59 98 362.96 363.33 363.70 364.07 364.44 364.81 365.18 365.55 365.93 366.30 99 366.67 367.04 367.41 367.78 368.15 368.52 368.89 369.26 369.63 370.00 100 370.37 370.74 371.11 371.48 371.85 372.22 372.59 372.96 373.33 373.70 101 374.07 374.44 374.81 375.18 375.55 375.92 376.29 376.67 377.04 377.41 102 377.78 378.15 378.52 378.89 379.26 379.63 380.00 380.37 380.74 381.11 103 381.48 381.85 382.22 382.59 382.96 383.33 383.70 384.07 384.44 38481 104 385.18 385.55 385.92 386.29 386.67 387.04 387.41 387.78 388.] 5 388.52 105 388.89 389.26 389.63 390.00 390.37 390.74 391.11 391.48 391.85 392.22 106 392.59 392.96 393.33 393.70 394.07 394.44 394.81 395.18 395.55 395.92 107 396.30 396.67 397.04 397.41 397.78 398.15 398.52 398.89 399.26 399.63 108 400.00 400.37 400.74 401.11 401.48 401.85 402.22 402.59 402.96 403.33 109 403.70 404.07 404.44 404.81 405.18 405.55 405.92 406.29 406.67 407.04 110 j 407.41 407.78 408.15 408.52 408.89 409.26 409.63 410.00 410.37 410.74 111 : 411.11 411.48 411.85 412.22 412.59 412.96 413.33 413.70 414.07 414.44 112 414.81 415.18 415.55 415.92 416.29 416.67 417.04 417.41 417.78 418.15 113 418.52 418.89 419.26 419.63 420.00 420.37 420.74 421.11 421.48 421.85 114 422.22 422.59 422.96 423.33 423.70 424.07 424.44 424.81 425.18 425.56 115 425.93 426.30 426.67 427.04 427.41 427.78 428.15 428.52 428.89 429.26 116 429.63 430.00 430.37 430.74 431.11 431.48 431.85 432.22 432.59 432.96 117 433.33 433.70 434.07 434.44 434.81 435.18 435.55 435.92 436.29 436.67 118 ! 437.04 437.41 437.78 438.15 438.52 438.89 439.26 439.63 440.00 440.37 119 440.74 441.11 441.48 441.85 442.22 442.59 442.96 443.33 443.70 444.07 EXCAVATION AND EMBANKMENT TABLES. |o.oo 0.10 0.20 0.30 0.40 0.50 0.60 |0.70 0.80 0.90 120 444.44 444.81 445.18 445.55 445.92 446.29 446.67 44704 447.41 447.78 121 448.15 448.52 448.89 449.26 449.63 450.00 450.37 450.74 451.11 451.48 122 451.85 452.22 452.59 452.96 453.33 453.70 454.07 454.44 454.81 455.18 123 455.55 455.92 456.29 456.67 457.04 457.41 457.78 458.15 458.52 458.89 124 459.26 459.63 460.00 460.37 460.74 461.11 461.48 461.85 462.22 462.59 125 462.96 463.33 463.70 464.07 464.44 464.81 465.18 465.55 465.93 46630 126 466.67 467.04 467.41 467.78 468.15 468.52 468.89 469.26 469.63 470.00 127 470.37 470.74 471.11 471.48 471.85 472.22 472.59 472.96 473.33 473.70 128 474.07 474.44 474.81 475.18 475.56 475.93 476.30 476.67 477.04 477.41 r;9 477.78 478.15 478.52 478.89 479.26 479.63 480.00 480.37 480.74 481.11 130 481.48 481.85 482.22 482.59 482.96 483.33 483.70 484.07 484.44 484.81 131 485.18 485.55 485.92 486.29 486.67 487.04 487.41 487.78 488.15 488.52 132 488.89 489.26 489.63 490.00 490.37 490.74 491.11 491.48 491.85 492.22 133 492.59 492.96 493.33 493.70 494.07 494.44 494.81 495.19 495.56 495.93 134 496.30 496.67 497.04 497.41 497.78 498.15 498.52 498.89 499.26 499.63 135 500.00 500.37 500.74 501.11 501.48 501.85 502.22 502.59 502.96 503.33 136 503.70 504.07 504.44 504.81 505.18 505.56 505.93 506.30 506.67 507.04 137 507.41 507.78 508.15 508.52 508.89 509.26 509.63 510.00 510.37 510.74 138 511.11 511.48 511.85 512.22 512.59 512.96 513.33 513.70 514.07 514.44 139 514.81 515.18 515.55 515.92 516.29 516.67 517.04 517.41 517.78 518.15 140 518.52 518.89 519.26 519.63 520.00 520.37 520.74 521.11 521.48 521.85 141 522.22 522.59 522.96 523.33 523.70 524.07 524.44 524.81 525.19 525.56 142 525.93 526.30 526.67 527.04 527.41 527.78 528.15 528.52 528.89 529.26 143 529.63 530.00 530.37 530.74 531.11 531.48 531.85 532.22 532.59 532.94 144 533.33 533.70 534.07 534.44 534.81 535.18 535.56 535.93 536-30 536.67 145 537.04 537-41 537.78 538.15 538.52 538.89 539.26 539.63 540.00 540.37 146 540.74 541.11 541.48 541.85 542.22 542.59 542.96 543.33 543.70 544.07 147 544.44 544.81 545.18 545.56 545.93 546.30 546.67 547.04 547.41 547.78 148 548.15 548.52 548.89 549.26 549.63 550.00 550.37 550.74 551.11 551.48 149 551.85 552.22 552.59 552.96 553.33 553.70 554.07 554.44 554.81 555.18 150 555.55 555.93 556.30 556.67 557.04 557.41 557.78 558.15 558.52 558.89 151 559.26 559.63 560.00 560.37 560.74 561.11 561.48 561.85 562.22 562.59 152 562.96 563.33 563.70 564.07 564.44 564.81 565.18 565.56 565.93 566.30 153 566.67 567.04 567.41 567.78 568.15 568.52 568.89 569.26 569.63 570.00 154 570.37 570.74 571.11 571.48 671.85 572.22 572.59 572-96 573.33 573.70 155 574.07 574.44 574.81 575.18 575.56 575.93 576.30 576.67 577.04 577.41 156 577.78 678.15 578.52 578.89 579.26 579.63 580.00 580.37 580.74 581.11 157 581.48 581.85 582.22 582.59 582.96 583.33 583.70 584.07 584.44 584.81 158 585.18 585.55 585.92 586.29 586.66 587.04 5x7.41 587.78 588.15 588.52 159 588.89 589.26 589.63 590.00 590.37 590.74 591.11 591.48 591.85 59222 160 592.59 592.96 593.33 593.70 594.07 594.44 594.81 595.18 595.55 595.92 161 596.29 596.67 597.04 597.41 597.78 598.15 598.52 598.89 599.26 599.63 162 600.00 600.37 600.74 601.11 601.48 601.85 602.22 602.59 602.96 603.33 163 603.70 604.07 604.44 604.81 605.18 605.55 605.92 606.30 606.67 607.04 164 607.41 607.78 608.15 608.52 608.89 609.26 609.63 610.00 610.37 610.74 165 611.11 611.48 611.85 612.22 612.59 612.96 613.33 613.70 614.07 614.44 166 614.81 615.18 615.55 615.92 616.29 616.67 617.04 617.41 617.78 618.15 167 618.52 618.89 619.26 619.63 620.00 620.37 620.74 621.11 621.48 621.85 168 622.22 622.59 622.96 623.33 623.70 624.07 624.44 624.81 625.18 625.56 169 625.93 626.30 626.67 627.04 627.41 627.78 628.15 628.52 628.89 629.26 170 629-63 630.00 630.37 630.74 631.11 631.48 631.85 63222 632.59 632.96 171 633.33 633.70 634.07 634.44 634.81 635.18 635.55 635.92 636.29 636.66 172 637.04 637.40 637.77 638-14 638.51 638.88 639.25 639.62 639.99 640.37 173 640.74 641.11 641.48 641.85 642.22 642.59 642.96 643.33 643.70 644.07 174 644.44 644.81 645.18 645.55 645.92 646.29 646.66 647.03 647.41 647.78 175 648.15 648.52 648.89 64926 649.63 650.00 650.37 650.74 651.11 651.48 176 651.85 652.22 652.59 652.9(5 653.33 653.70 654.07 654.44 654.81 655.18 177 655.56 655.93 656.30 656.67 657.04 657.41 657.78 658.15 658.52 658.89 178 659.26 659.63 660.00 660.37 660.74 661.11 661.48 661.85 662.22 662.59 179 662.96 663.33 663.70 664.07 664.44 664.81 665.18 665.55 665.92 666.29 41 EXCAVATION AND EMBANKMENT TABLES. 0.00 0.10 0.20 0.30 0.40 0.50 | 0.60 0.70 0.80 0.90 180 606.67 667.04 667.41 667.78 668.15 668.52 668.89 669.26 669.63 670.00 181 670.37 670.74 671.11 671.48 671.85 672.22 672.59 672.96 673.33 673.70 182 674.07 674.44 674.81 675.18 675.55 675.93 67630 676.67 677.04 677.41 183 677.78 678.15 678.52 678.89 (579.26 679.63 680.00 680.37 680.74 681.11 184 681.48 681.85 682.22 682.59 682.96 683.33 684.70 684.07 684.44 684.81 185 685.18 685.56 685.93 686 30 686.67 687.04 687.41 687.78 688.15 688.52 186 688.89 689.26 689.63 690.00 690.37 690.74 691.11 691.48 691.85 692.22 187 692.59 692.96 693.33 693 70 694.07 694.44 694.81 695.18 695.55 695.92 188 696.30 696.67 697.04 697.41 697.78 698.15 698.52 698.89 699.26 699.63 ' 189 700.00 700.37 700.74 701.11 701.48 701.85 702.22 702.59 702.96 703.33 190 703.70 704.07 704.44 704.81 705.18 705.55 705.92 706.29 706.6H 707.03 191 707.40 707.77 708.14 708.51 708.89 709.26 70963 710.00 710.37 710.74 192 711.11 711.48 711.85 712 22 712.59 712.96 713.33 713.70 714.07 714.44 193 714.81 715.18 715.55 715.92 716.29 716.67 717.04 717.41 717.7S 718.15 194 718.52 718.89 719.26 719.63 720.00 720.37 720.74 721.11 721.48 721.85 195 722.22 722.59 722.96 723.33 723.70 724.07 724.44 7-24.81 725.18 725.55 196 725.92 726.29 726.66 727.03 727.40 727.77 728.14 728.51 728.88 729.25 197 729.63 730.00 730.37 730.74 731.11 731.48 731.85 732.22 732.59 732.96 198 733.33 733.70 734.07 734.44 734.81 735.18 735.55 735.93 736.30 736.67 199 737.04 737.41 737.78 738.15 738.52 738.89 739/26 739.63 740.00 740.37 200 740.74 741.11 741.48 741.85 742.22 742.59 742.96 743.33 743.70 744.07 201 744.44 744.81 745.18 74555 745.93 746.30 746.67 747.04 747.41 747.78 202 748.15 748.52 748.89 749.. 6 T49.63 750.00 75037 750.74 751.11 751.48 203 751.85 752.22 752.59 752.96 753.33 753.70 754.07 754.44 754.81 755.18 204 755.55 755.93 756.30 756.67 757.04 757.41 757.78 758.15 758.52 758.89 205 759.26 759.63 760.00 760.37 760.74 761.11 761.48 761.85 762.22 762.59 206 762.96 763.: !3 763.-70 764. U7 764.44 764.81 765.18 765.55 765.93 766.30 207 766.66 767.01 767.41 767.78 768.15 768.52 76889 769.26 769.63 770.00 208 770.37 770.74 771.11 771.48 771.85 772.22 772.59 772.96 773.33 773.70 209 774.07 774.44 774.81 775.18 775.55 775.93 776.30 776. C>6 777.04 777.41 210 777.7H 778.15 778.52 778.89 779.26 779.63 780.00 780.37 780.74 781.11 211 781.48 781.85 782.22 78259 78-2.96 783.33 783.70 784.07 784.44 784.81 212 785.18 785.55 785.93 78630 786.66 787.04 787.41 787.78 788.15 788.52 213 788.89 789.26 789.63 790.00 790.:;7 790.74 79111 791.48 791.85 792.22 214 792.59 792.96 793.33 793.70 794.07 794.44 794.81 795.18 795.55 795.93 215 796.30 796.66 797.04 797.41 797.78 798.15 798.52 798.89 799.'26 799.63 216 sno.oo 800.37 800.74 801 11 801.48 801.85 80222 802.59 802.96 803.33 217 803.70 804.07 804.44 80481 805.18 805.55 805.93 806.30 806.66 807.04 218 807.41 807.78 808.15 808.52 808.89 d09.26 80963 810.00 810.37 810.74 219 811.11 811.48 811.85 812.22 812.59 812.96 813.33 813.70 814.0? 814.44 220 814.81 815.18 815.55 815.93 816.30 816.66 817.04 817.41 817.78 818.15 221 818.52 818.89 819.26 819.63 8,0.00 820.37 820.74 821.11 821.48 821.85 222 822.22 822.59 822.96 823.33 823.70 824.07 824.44 824.81 825.18 825.55 223 825.93 826.30 826.66 827.04 827.41 827.78 828.15 828.52 828.89 829.26 224 829.63 830.00 8U0.37 830.74 831.11 831.48 831.85 832.22 832.59 832.96 225 833.33 833.70 834.07 834.44 834.81 835.18 83555 835.93 836.30 836.66 226 837.04 837.41 837.78 83815 838.52 838.89 83926 839.6 J 840.00 840.37 | 227 840.74 841.11 841.48 841.85 842.22 842.59 H42.96 843.33 843.70 844.07 I 228 844.44 844.81 845.18 845.55 845.93 846.30 846 66 847.04 847.41 847.78 229 848.15 848.52 848.89 849.26 849.63 850.00 850.37 850.74 851.11 851.48 230 851.85 852.22 852.59 852 96 853.33 853.70 854.07 854.44 854.81 855.18 231 855.55 855.9} 856.S& 85666 857 04 857.41 85778 858.15 858.52 858.89 232 859.26 859.63 860.00 86037 860.74 861.11 861.48 861.85 862.22 862.59 233 862.96 863.33 863.70 864 07 864.44 864.81 865.18 8C.5.55 865.93 866.30 234 866.66 867.04 867.41 867.78 868.15 868.52 868.89 869.26 869.63 870.00 235 870.37 870.74 871.11 871.48 871.85 872.22 872.59 872.96 873.33 873.70 236 874.07 874.44 874.81 875.18 875.55 875.93 876.30 876.66 877.04 877.41 237 877.78 878.15 | 878.52 878.89 879.26 879.63 880.00 880.37 880.74 881.11 238 881.48 8sl.85 882.22 882.59 882.96 883.33 88370 884.07 884.44 884.81 239 885.18 885.55 885.93 ' 886.30 886.66 887.04 887.41 887.78 888.15 888.52 42 EXCAVATION AND EMBANKMENT TABLES. 0.00 0.10 0.20 0.30 0.40 | 0.50 0.60 0.70 | 0.80 1 0.90 240 888.88 889.26 889.63 890.00 890.37 890.74 891.11 891.48 891.85 892.22 241 892.59 892.96 893.33 893.70 894.07 894.44 894.81 8-J5.18 895.55 895.93" 242 896.30 896.66 897.04 897.41 897.78 898.15 898.52 898.88 899.26 899.63 243 900.00 900.37 900.74 901.11 901.48 901.85 902.22 902.59 902.96 903.33 244 903.70 904.07 904.44 904.81 905.18 905.55 905.93 906.30 906.66 907.04 245 907.41 907.78 908.15 908.52 908.88 909.26 909.63 910.00 910.37 910.74 246 911.11 911.48 911.85 912.22 912.59 912.96 913.33 913.70 914.07 914.44 247 914.81 915.18 915.55 915.93 J16.30 916.66 917.04 917.41 917.78 91815 248 918.52 918.88 919.26 919.63 920.00 920.37 920.74 921.11 921.48 921.85 249 922.22 922.59 922.96 923.33 923.70 924.07 924.44 924.81 925.18 925.55 250 925.92 926.30 926.66 927.04 927.41 927.78 928.15 928.52 928.88 929.26 251 929.63 930.00 930.37 930.74 931.11 931.48 931.85 932.22 932.59 932.96 252 933.33 933.70 934.07 934.44 934.81 935.18 935.55 935.92 936.30 936.66 253 937.04 937.41 937.78 938.15 938.52 938.88 939.26 939.63 940.00 940.37 254 940.74 941.11 941.48 941.85 942.22 942.59 942.96 943.33 943.70 944.07 255 944.44 944.81 945.18 945.55 945.92 946.30 946.66 947.04 947.41 947.78 256 948.15 948.52 948.88 94t).26 949.63 950.00 950.37 950.74 951.11 951.48 257 951.85 952.22 952.59 952.96 953.33 953.70 954.07 954.44 954.81 955.18 258 955.55 955.92 956.30 956.66 957.04 957.41 957.78 958.15 958.52 958.88 259 959.26 959.63 960.00 960.37 960.74 961.11 961.48 961.85 962.22 962.59 260 962.96 963.33 963.70 964.07 964.44 964.81 965.18 965.55 965.92 266.30 261 966.66 967.04 967.41 967.78 968.15 968.52 968.88 969.26 969.63 970.00 262 970.37 970.74 971.11 971.48 971.85 972.22 972.59 972.96 973.33 973.70 263 974.07 974.44 974.81 975.18 975.55 975.92 976.30 976.66 977.04 977.41 264 977.78 978.15 978.52 978.88 979.26 979.63 980.00 980.37 980.74 981.11 265 981.48 981.85 982.22 982.59 982.96 983.33 983.70 984.07 984.44 984.81 266 985.18 985.55 985.92 986.30 986.66 987.04 987.41 987.78 988.15 988.52 267 988.88 989.26 989.63 990.00 990.37 990.74 991.11 991.48 991.85 992.22 268 992.59 992.96 993.33 993.70 994.07 994.44 994.81 995.18 995.55 995.92 269 996.30 996.66 997.04 997.41 997.78 998.15 998.52 998.88 999.26 999.63 270 1000.00 1000.37 1000.74 1001.11 1001.48 1001.85 1002.22 1002.59 1002.96 1003.33 271 1003.70 1004.07 1004.44 1004.81 1005.18- 1005.55 1005.92 1006.30 1006.66 1007.04 272 1007.41 1007.78 1008.15 1008.52 1008.88 1009.26 1009.63 1010.00 1010.37 1010.74 273 1011.11 1011.48 1011.85 1012.22 1012.59 1012.96 1013.33 1013.70 1014.07 1014.44 274 1014.81 1015.18 1015.55 1015.92 1016.30 1016.66 1017.04 1017.41 1017.78 1018.15 275 1018.52 1018.88 1019.26 1019.63 1020.00 1020.37 1020.74 1021.11 1021.48 1021.85 276 1022.22 1022.59 1022.96 1023.33 1023.70 1024.07 1024.44 1024.81 1025.18 1025.55 277 1025.92 1026.30 1026.66 1027.04 1027.41 1027.78 1028.15 1028.52 1028.88 1029.26 278 1029.63 1030.00 1030.37 1030.74 1031.11 1031.48 1031.85 1032.22 1032.59 1032.96 279 1033.33 1033.70 1034.07 103i.44 1034.81 1035.18 1035.55 1035.92 1036.30 1036.66 280 1037.04 1037.41 1037.78 1038.15 1038.52 1038.88 1039.26 1039.63 1040.00 1040.37 281 1040.74 1041.11 1041.48 1041.85 1042.22 1042.59 1012.96 1043.33 1043.70 1044.07 282 1044.44 1044.81 1045.18 1045.55 1045.92 1046.30 1046.66 1047.04 1047.41 1047.78 283 1048.15 1048.52 1048.88 1049.26 1049.63 1050.00 1050.37 1050.74 1051.11 1051.48 284 1051.85 1052.22 1052.59 1052.96 1053.33 1053.70 1054.07 1054.44 1054.81 1055.18 285 1055.55 1055.92 1056.30 1056.66 1057.04 1057.41 1057.78 1058.15 1058.52 1058.88 286 1059.26 1059.63 1060.00 1060.37 1060.74 1061.11 1061.48 1061.85 1062.22 1062.59 287 1062.96 1063.33 1063.70 1064.07 1064.44 1064.81 1065.18 1065.55 1065.92 1066.30 288 1066.66 1067.04 1067.41 1067.78 1068.15 1068.52 1068.88 1069.26 1069.63 107000 289 1070.37 1070.74 1071.11 1071.48 1071.85 1072.22 1072.59 1072.96 1073.33 1073.70 290 1074.07 1074.44 1074.81 1075.18 1075.55 1075.92 1076.30 1076.66 1077.04 1077.41 291 1077.78 1078.15 1078.52 1078.88 1079.26 1079.63 1080.00 1080.37 1080.74 1081.11 292 1081.48 1081.85 1082.22 1082.59 1082.96 1083.33 1083.70 1084.07 1084.44 1084.81 293 1085.18 1085.55 1085.92 1086.30 1086.66 1087.04 1087.41 1087.78 1088.15 1088.52 294 1088.88 1089.26 1089.63 1090.00 1090.37 1090.74 1091.11 1091.48 1091.85 1092.22 295 1092.59 1092.96 1093.33 1093.70 1094.07 1094.44 1094.81 1095.18 1095.55 1095.92 296 1096.30 1096.66 1097.04 1097.41 1097.78 1098.15 1098.52 1098.88 1099.26 1099.63 297 1100.00 1100.37 1100.74 1101.11 1101.48 1101.85 1102.22 1102.59 1102.96 1103.33 298 1103.70 1104.07 1104.44 1104.81 1105.18 1105.55 1105.92 1106.30 1106.66 1107.04 299 1107.41 1107.78 1108.15 1108.52 1108.88 1109.26 1109.63 1110.00 1110.37 1110.74 43 EXCAVATION AND EMBANKMENT TABLES. 0.00 OJO | 0.20 0.30 0.40 0.50 | 0.60 0.70 0.80 0.90 300 1111.11 1111.48 1111.85 1112.22 1112.59 1112.96 1113.33 [1113.70 1114.07 1114.44 301 1111.82 1 S15.19 1115.56 1115.93 1116.30 1116.67 1117.04 1117.41 1117.78 1118.15 302 1118.52 1118.89 1119.26 1119.63 1120.00 1120.87 1120-74 1121.11 1121.48 1121.85 303 1122.22 1122.59 1122.96 1123.33 1123.70 1124.07 1124.44 1124.82 1125.19 1125.56 304 1125.93 1126.30 1126.67 1127.04 1127.41 1127.78 1128.15 1128.52 1128.89 1129.26 305 1129.63 1130.00 11150.37 1130.74 1131.11 1131.48 1131.85 1132.22 1132.59 1132.96 306 113:i.33 1133.70 1134.07 1134.44 1134.82 1135.19 1135.56 1135.93 1136 30 1137.617 307 1137.04 1137.41 1137.78 1138.15 1138.52 1138.89 1139.26 1139.63 1140.00 1140.37 308 1140.74 1141.11 1141.48 1141.85 1142.22 1142.59 1142.96 1143.33 1143.70 1144.07 309 1144.44 1144.82 1145.19 1145.56 1145.93 1146.30 1146.67 1147.04 1147.41 1147.78 310 1148.15 11-18.52 1148.89 1149.^6 1149.63 1150.00 1150.37 J1150.74 115111 1151-48 311 1151.85 1152.22 1152.59 1152.96 1153.33 1153.70 1154.07 U154.44 1154.82 1155.19 312 1155.56 1156 93 1156.30 1156.67 1157.ec.-lonff. bulkheada Details of Pile Driving Machine. PILE DRIVING MACHINE. 01 The hull is 56 ft. 6 ins. long and 23 ft. 6 ins. wide over all; each of the sides of the hull is made of four pieces of yellow pine, the two lower each 8 X 14 in., the third 7 X 14 in., the top piece 6 X 14 in., all securely tied by through bolts; the bow planking is -oak, 5 ins. thick; the bottom and end plank yellow pine, 3 ins. thick. The bow is further strengthened by a 16 X 16 in. cross timber at top, and at the stern is an 8 X 12-in. cross timber of yellow pine. Oak is used on the bow as being better adapted to stand the constant wear of the piles hauled against it, and to prevent knots or inequalities on the piles interfering with their position under the hammer; the bow planking overhangs 6 ins. in its total height. The chief end in the design of a hull for a floating pile driver is to obtain longitudinal stiffness, so that the strains between the bow and engine may be properly distributed. To this end our hull is strengthened lengthwise by four wooden bulkheads or kelsons, each 6 ins. thick (Fig. 2) and braced laterally by four sets of X braces of 6 X 6 'timber. The hull is further braced in the center by two 3 X 12 in. Y. P. braces, and tie rods or "hog chains" of iron, If ins. in diameter. Wale pieces and fender plank 3 ins. thick protect the outside of the hull against chafing; the deck has a "crown" of about 6 ins. in its total width. The hammer-guides are made of two pieces of 12x12 Y. P. 67 feet long from out to out with inside guides of 5x4 in. stuff protected by plate iron J ins. thick ; f-in. bolts with countersunk heads fasten the inner guides to the main sticks and at the same time secure the iron work to the same. The bottoms of the main guides are connected with the 12x12 bed pieces, shown in Fig. 3, by two timber knees, and are tied at top by the cap shown in Fig. 6. The dimensions and general arrangement of the back-bracing is fully shown in Figs. 1 and 3 ; the bolts used in this portion of the frame work are $ in. diameter. The side braces are round timbers 16-ins. diameter at the butt, and they are anchored to the hull by two heavy timber knees to each. The bed pieces, as shown at Fig. 3, are fastened down to the hull by four bolts each, 1 in. in diameter, the forward bolts passing through the 16xl6-in. oak piece on bow, and the after-bolts passing into a cross timber 6x 14 ins. , as shown at Fig. 4. The foot of the back- bracing is secured to the bed timbers by one 1 in. strap-bolt in each timber, the strap portion of bolt being 2Xi in. in section. A -in. through-bolt ties the three braces together. The iron stay-rods running from head of guides to after part of hull are two in number, and are each 1 in. in diameter. 56' 6- Lonff.Sec. showing internal bracmff. Pile Driving Machine. PILE DRIVING MACHINE. 93 The hoisting sheaves on top are two in number, placed side by side. They are 12 ins. in working diameter, 1 ins. from out to out, and 3 ins. wide ; and the pin passing through them is 2 ins. diameter at the sheaves, and 2 ins. diameter in the boxes. Experience teaches that these proportions are none too great to stand the severe work frequently put upon it in hoisting heavy weights and tearing out timber. The fall rope attached to the hammer is 2 ins. in diameter, and the " runner" used in hoisting up piles is If ins. diameter. The hoisting engine is a double-drummed Mundy engine of a nominal 25 horse power. Fig. 5 shows the hammer used with this machine. The drawing is sufficient to show its general design. The weight is 3,300 Ibs. Fig. 7 shows the method of attaching the two 5 X 12 in. horizontal braces to the round side braces, as further shown in Fig. 2. METRIC RAILWAY CURVES. [From Engineering News, Oct. 13, 1883.] Several inquiries have appeared from time to time in ENGINEERING NEWS for a metric table of railway curves. We to-day present one pre- pared by an engineer who, after practicing the American method of lay- ing out curves in the United States, has been for two years occupied in railroad surveying with the metric system in Mexico. The table is explained by the headings of the columns. Curves are designated (as in the first column) by the angle which, according to the American system, has to be turned off repeatedly at a point on the cir- cumference, and is subtended by successive equal chords. This angle is called by Trautwine and Shunk the " tangential " angle ; by Henck and Searles the "deflection" angle. Jn the first article of the appendix to his revised edition. Prof. Henck suggests the use of this angle for designat- ing curves run by the metric system. An obvious advantage thus gained is that the angle to be measured in staking jut a curve in a field is simply the angle named in speaking of the curve. The equal chords successively measured according to the metric system should be 20 meters in length, as was abundantly enforced by numerous writers who discussed the point in ENGINEERING NEWS a year and a half ago. As to the adaptability of that length to railroad engineering, it may be noticed that in the first er- ample of staking out a curve given in Shunk's "Field Engineer," the length of chord is taken to be 20.12 m., which he calls 66 feet. The stakes, set at successive 20-meter intervals, are to be marked with the suc- cessive even numbers, 2, 4, 6, 8, etc. , so as to constitute the dekameter the unit of stake numbering. Each stake is thus designated by its distance in dekameters from the zero point, and each kilometer stake is marked by an exact hundred. The angle by which the curve changes its direc- tion per unit of length as thus marked is, therefore, one-half of its change of direction between the extremities of the 20-meter chord; that is, it is exactly the " 20-meter chord " angle used to stake it out and. to designate it; and the total change of direction made by any length of the curve is simply the product of this angle multiplied by the Difference METRIC RAILWAY CURVES. 95 in the numbers of the stakes at its beginning and end, just as in the pres- ent practice in the United States. For convenience in staking fractional parts of the 20-meter chain, the second column of the table is given, showing the number of minutes to be turned off with the transit per meter, being simply one-twentieth of the angle in the fir>t column. Here a slight advantage over the 100-ft- chord is seen, because 60 bears a simpler relation to 20 than to 100. The column of radii presents a simplicity superior to the 100-ft. system, in that the metric radius is just 10 times the co-secant of the angle in the first column, and can therefore be taken directly from a trigonometrical table by altering the decimal point, or in the case of the logarithm, the characteristic. The computation in the present United States practice is a little more complicated. The dfference thereby produced in the figures may be seen by comparing the columns of 20-meter chord angle and radius with the columns of degree of curve and radius in the field-books commonly used in this country. The metric radii, instead of being fig- ured exactly one-tenth of the expression in feet corresponding to the same angle, have slightly larger decimals. The discrepancy is so small, however, that for the greater part of railroad work the old tables might be used with the metric system, by taking the old degrees for the 20-meter chord angles and dividing all the old radii by 10, that is, merely changing the decimal point one place. It is different with the figures for deflection distances and ordinates, which, in the metric table, are almost exactly four-tenths of what they are in the old tables for the same angle in first column. The precise length of the curve, in contradistinction to that of the chords by which it is staked out, is seldom required. The last column in the table is inserted chiefly with a view to exhibiting the percentage to be added to such a chord to get the length of arc it subtends. This percent- age is clearly seen when we move the decimal point of the last column one place to the left; and it may be made useful in connection with such tables as are given at the end of Shunk's " Field Engineer" and of the re- vised edition of Henck's " Field Book." For example, those tables give, among other very useful data, the distance from the intersection point to either extremity of a one-degree curve whose total length varies between and 90. Mr. Shunk calls this the "apex distance ; " Prof. Henck, the "tangent." For a curve 90 in length, Mr. Shunk's table gives 5730 ft. Prof. Henck's, 5729.7 ft., the same, of course, as the radius. Either of these divided by 10 can be used in practice for the metric 1 curve, whose 96 METRIC CURVE TABLE. J5 TJ rt 1 Quarter Middle.) point. M o3 ^ B DEFLECTION + "5a & *: | w ORDINATE |. S w . I ffe RADIUS a . at distance from end-chord. 2 o c | _H K'C a? Ed 3a METERS From fo^' 2 1? tan- r rom chord. Of 10 Of 5m. S gent. in* HJ O10' OJ^' 3437.75 3.5362745 .058 .116 .Olo .011 10.0000 20' 1' 1718.38 3.2352463 .116 .233 .029 .022 10.0001 30' 1145.93 3.0591581 .175 .349 .044 .033 10.0001 40' 2' 859.46 2.9342237 .233 .465 .058 .044 10.0002 50' 2Ji' 687.57 2.8373192 .291 .582 .073 .055 10.0004 1 0' 3' 572.99 2.7581447 .349 .698 .087 .065 10.0005 10' 491.14 2.6912059 .407 .814 .102 .076 10.0007 20' 4' 429.76 2.6332231 .405 .931 .116 .087 30' 41^' 382.02 2.5820810 .524 1.047 .131 .098 loioon 40' 5' 343.82 2.5363351 .582 1.163 .145 .109 10.0014 50' 312.58 2.4949553 .640 1.280 .160 .120 10.0017 2 0' 6' 286.54 2.4571808 .698 1.396 .175 .131 10.0020 10' 264.51 2.4224340 .756 1.512 .189 .142 10.0024 20' 7' 245.62 2.3902659 .814 1.629 .204 .153 10.0028 30' 7V' 229.26 2.3603204 .873 1.745 .218 .164 10.0032 40' 8' 214.94 2.3323107 .9.31 1.861 .233 .175 10.0036 50' 8fcS' 202.30 2.3060020 .989 1.977 .247 .186 10.0041 3 0' 9' 191.07 2.2811998 1.047 2.093 .262 .196 10.0046 10' 9^' 181.03 2.2577414 1.105 2.210 .276 .207 10.0051 20' 10' 171.98 2.2354889 1.163 2.326 .291 .218 10.0056 30' 163.80 2.2143247 1.222 2.442 .306 .229 10.0062 40' 11' ^ 156.37 2.1941477 1.280 2.558 .320 .240 10.0068 50' 149.58 2.1748701 1.338 2.674 .335 .251 10.0075 4 0' 12' 143.36 2.1564155 1.396 2790 .349 .262 10.0081 10' 137.63 2.1387167 1.454 2.916 .364 .273 10.0088 20' 13' 132.35 2.1217146 1.512 3.022 .378 .284 10.0095 30' L3V^' 127.45 2 1053567 1.570 3.138 .393 .295 10.0103 40' L4' 122.91 2.0895961 1.629 3.254 .407 .306 10.0111 50' 118.68 2.0743911 1.687 3.370 .422 .317 10.0119 6 0' 15' 114.74 2.0597040 1.745 3.486 .437 .328 10.0127 20' 16' 107.58 2.0317513 1.861 3.718 .466 .349 10.0145 40' 17' 101.28 2.0055032 1.977 3.950 .495 .371 10.0163 6 0' 18' 95.67 1.9807654 2.093 4.181 .524 .393 10 0183 20' 19' 90.65 1.9573751 2.210 4.413 .553 .415 10.0204 40' 20' 86.14 1.9351943 2.326 4.044 .582 .437 10.0226 7 0' z y, 82.06 1.9141055 2.442 4.875 .612 .459 10.0249 20' 78.34 1.8940076 2558 5.106 .641 .481 10.0274 40' 23' 74.96 1.8748128 2.674 5.336 .670 .503 10.0299 8 0' 24' 71.85 1.8564447 2.790 5.567 .699 .525 10.0326 20' 25' 69.00 1.8388361 2.906 5.797 .729 .547 10.0353 40' 26' 66.36 1.8219279 3.022 6.027 .758 .569 1U.0382 9 0' 27' 63.92 1.8056676 3.138 6.257 .787 .591 10 0412 20' 28' 61.66 1.7900083 3.254 6.487 .816 .613 10.0444 40' 29' 59.55 1.7749082 3.370 6.717 .846 .635 10.0476 1O 0' 30' 57.59 1.7603298 3.486 6.946 .875 .657 10.0510 METRIC RAILWAY CURVES. 97 radius is 572.99. (It would be still better in using the metric system to have a new table calculated expressly for radius 572.958.) To get with very close approximation the corresponding dimensions for any other curve we divide by the degree designating the curve. Hence, for a 90 length of a metric 10 curve we should get a tangent or apex distance of 57.30 m. In the case of so sharp a curve the question arises whether this is sufficiently accurate for our purpose, and this question is answered by reference to the last column in the 'metric table. After moving the deci- mal point as above directed, we find 1.0051 for the 10 curve, showing that our 57.30 is in error by one-half of one per cent. To get exactly the dis- tance required, multiply 5730 by 1.005, and we get 57.59, just as given in the metric table for the radius of the 10 curve. The same percentage correction is applicable to the other tabulated data as well as to the tan- gent or apex distance. In computations like that discussed in the preceding paragraph, the 20- meter chord has the advantage over that of 100 ft. that it is a shorter length, and consequently the arc it subtends in any circle differs by a smaller percentage from the chord. Hence, the tabulated data above mentioned can be applied without requiring correction to a larger range of metric curves than of the curves used in the American foot practice. For example, observe that in the curves of b6.14 and 90.65 meters radius the percentage is less than one-quarter of one per cent. Between the two lies the 20 curve, as given in the Ame rican tables, with a radius of 287.9 ft., in which the 100-ft. chord subtends an arc of 100.5 ft., showing a per- centage of one-half of one percent. Accordingly, if we start 5,730 ft., the tabulated tangent or apex distance above cited for 90 length of an American l c curve, and take one-twentieth of it for the corresponding dimension of thetcircle of 287.9 ft., radius, we have 286.5 ft., and must add 1.4 ft. to get the correct value equal to radius. On the other hand, suppose we had started with 573 meters as the tangent or apex distance in the metric 1 curve, to get the corresponding dimension of the circle of 86.14 meters radius observe that that circle is designated by the 20 m. chord angle of 6; three-twentieths of 573 m. is 85.95 m., and to get the correct value equal to radius we must add 0.19 m., which is lees than half of 1.4 ft., and less than one quarter of one per cent. Engineers accustomed to thinking of curves by their American desig- nations may find it convenient in making mental comparisons to bear in mind that if any curve has its 20-m. chord angle multiplied by 3, the pro- duct is nearly the " degree" used to designate the curve in this country; 98 METRIC RAILT UNIVERSITY OF CALIFORNIA LIBRARY for 100 ft. is very little more than 3 last spoken of, having a radius of 86 of 6 , is almost the same as the Aim number of 20 is given in the metric t laid off per meter in staking out, as radius; and all of the numbers in tl minutes, might be regarded as th< curves, in which case the correspond the true value of meters of the radii ( 30m-7,'12 10871 ENGINEERING NEWS AND AMERICAN RAILWAY r *ages 10 ^ more than ds, water- 2nce ; it is y officials r al in this o .inage dis- ind it the dvertising neers and .umns for Dntractors 'ermanent iverybody ion, plan- ient to be and the 20 CtS. y dailies, tly to the ir advan- r ADVER- when its , , . 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