BOO m UCSB tIBRARij John -W- Donofjue, THE ROPERTY OF Inhn 1A/ Rfi ! Jullil W, UUi ENGINEER'S OOK BY C. S. CROSS, CIVIL ENGINEER. COMPILED AND EDITED BY GEO, H. FROST, C. E. EDITIO1ST. NEW YORK : ENGINEERING NEWS PUBLISHING CO., 1893. COPYRIGHT, 1893, BY ENGINEERING NEWS PUBLISHING COMPANY. CONTENTS. CHAPTER I. PAGES. CROSS' ENGINEER'S FIELD BOOK 5-44 Railroad Curves, 5. Radius and Degree of Curve, 6. Examples, 7. Deflection from Tangents, 8. Field Notes for a Two-degree Curve, 9. Field Notes for a Three-degree Curve, 11. Reverse Curves, 13. Com- pound Curves, 14. Formulas, 17. Railroad Curve Tables, 18-27. Table for Converting Minutes and Seconds to Decimals of a Degree, 28. Curve Table, 29-30. Field Notes of a Survey, 31. Prismoidal Formula, 32. Field Notes for Sections, 34. Computation of Earth- work, 35. Excavation and Embankment Tables, 37-43. Charles S. Cross, 44. CHAPTER II. SMITH'S ENGINEERING FIELD WORK 45-64 Preliminary Organization of Field Party, 46. Care of Men, 47. The Transitman, 47. The Leveller, 49. The Head Chainman, 50. The Rear Chainmau, 52. Location, 53. The Topographer, 54. Keeping Transit Notes, 55. Compound Curves, 58. Land Lines, 59. Preserv- ing the Lines, 60. Centers and Grades, 61. Culverts and Masonry, 62. Earthwork Measurement, 62. Responsibility of an Engineer, 63. CHAPTER III. SKUNK'S REGULATIONS DURING CONSTRUCTION 65-85 Organization, 65. Preparatory Work, 66. Right of Way, 68. Final Preparations for Construction, 69. Structure Plans, 70. Field and Office Records, 71. Inspectors and Timekeepers, 76. Estimates, 77. Accounts, Supplies and Sundries, 78. Miscellaneous Instructions and Suggestions, 79. Barnes' Instructions relative to Field Notes, 85. CHAPTER IV. TOPOGRAPHY AND STAKING-OUT PROBLEMS 86-102 Table for Computing Right of Way Areas, 86. Topographical Field Work, 87. Method of Locating Contours, 87. Field Notes, 88. Field Plotting, 89. Locating Buildings, 89. Methods of Setting Slope Stakes, 90. I. For Level Sections, 90. II. For Irregular Sections, 90. III. With a Patent Tape, 92. IV. By Computation from Form- ulas, 93. Flattening a Curve, 94. Le Baron's Methods for Staking- out Switches, 95. Metric Railway Curves, 98. 4 CONTENTS. CHAPTER V. TRANSITION OB EASEMENT CURVES 103-117 The Tapering Curve, 103. The Railroad Spiral, 104. The Pennsylvania Method, 104. The Transition Spiral, 105. Spalding's Location of the Cubic Parabola, 106. Location by Ordinates, 107. Location by Deflec- tion Angles, 109. Special Cases, 113. Table of Ordinates for Locating the Cubic Parabola, 114. Table of Deflections for Locating the Cubic Parabola, 115. Table for Corrections, 116. Elevation of the Outer Rail, 116. CHAPTER VI. EARTHWORK AND MASONRY 118- 130 Fisher's Method of Estimating Overhaul in Earthwork, 118. 1. Compi- lation of Data, 119. 2. Plotting the Profile, 120. Taking off the Re- sults, 121. Expansion of Rock in Embankment, 122. Specht's Notes on Earthwork, 122. Wellington's Rules for Earthwork Computation, 121. Levee Construction, 125. Specifications for Masonry, 126. Brick for Buildings and for Arches, 127. Rubble, 127. Squared Stone Ma- sonry, 128. Ashlar Masonry, 129. CHAPTER VII. CULVERTS AND BRIDGES 131-145 Standard Timber Box Culverts, 131. Low's Formula and Tables for Maximum Spans of Box Culverts, 135. Specifications for Stone Box Culverts, 136. Specifications for Arch Culverts, 137. Howe Truss Bridges, 139. Cost of Labor in Framing and Erecting a Howe Truss Bridge, 143. Howe Trusses on Canadian Pacific Railway, 144. For- mulas for the Weights of Bridges, 145. CHAPTER VIII. CONSTRUCTION DETAILS 146-159 Centers for Arches, 146. Repairs to the Arch of the Musconetcong Tun- nel, 150. Standard Fences and Gates on Canadian Pacific Railway, 153. Substructure for a Water Tank, 154. A Pile Driving Machine, with two Plates, 155. Age of Railroads in Different Countries, 158. Rules for Measuring Work, 159. Directions for Making Drawings for Reproduction, 159. APPENDIX. BOOKS FOR RAILROAD ENGINEERS 160-165 Mathematics. Surveying. Drawing. Mechanics. Astronomy and Geodesy. Bridges and Roofs. Construction. Hydraulics. THE PSGPFRTY W CHAPTER I. Cross' Engineer's Field Book. 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: Eequired 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 stak* d out. 6 RAILROAD 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 3.1416 2 The chord of One foot in length for 1 degree = 57.3 ft. Radius. " 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 01 lOOO feet : 5J3U = 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', f =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 bv 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 DEGEEE CUBVE. 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 RAILROAD 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. + 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. REMARKS. 496.096 (C it * 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. 100.00 2 57 Change point. 503. 100-00 3 27 504. 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 ! T 27 512. 100.00 ! T 57 513. 100.00 8 27 514. 100.00 8 D 57 ' 515. 100.00 9 27 516. 100.00 9= 57 516.0963 9.63 10^ 00 * End of curve. (Tangent N. 20 W.) BAILED AD CUBVES. FIELD NOTES FOR A TWO DEGREES 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. + 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. 501.118 *j > 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 3 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 N30 W.) 10 BAILBOAD CURVES, 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 sett ing 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 maybe 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 less 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 CUKVE. Bearing of 1st tangent, N. 20 W. 2d N. C 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. " 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 CUEVES. FIELD NOTES. Length Course of Deflect'n No. of of tangents from REMARKS. Station I chords. and chords. tangent. 502.812 1; tt N 20 W 0' * B. C. 3 to left. 503. 18.8 20~ 17' 0" 17' 504. 100 22.04 1. 47 505. 506. 100 100 25.04 28. 04 3. 17 4. 47 * Change point. 507. 100 31. 04 6. 17 508. 100 34. 04 7. 47 509. 100 37 04 9 17 509.478 47.8 29. 04 10. 00 * E. C. 510. 52.2 N 40 5 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, 1- 47' 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 RAILROAD CURVES. 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 R. 1 " 2 30. " 2 " 5 00. 2.30 " 5 45. * Chancre 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 mav 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 stak, d 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 : BAILBOAD CURVES. 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 wish 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 RAILROAD 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 ze 7 5 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. Required the natural tangent of 30. Under 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. Required the natural tangent for an angle of 7 28'; in the 16 BAILEOAD CURYES. 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 GUNTEE'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 J 4 - 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 ore 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. R. C. " ' J 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 CURVES. 17 [Values of the radius corresponding to different degrees of curve are shown in the following table: Degree. Radius. Degree. Radius. Degree. Radius. 30' 11459.2 6 30' 881.95 13 441.68 1 5729.6 7 819.02 14 410.27 1 30 3819.8 7 30 764.49 15 383.06 2 2864.9 8 716.78 16 359.27 2 30 2292.0 8 30 674,69 17 338 ! 27 3 1910. 1 9 637 27 18 319 62 3 30 1637.3 9 30 603.81 19 302.94 4 1432.7 10 573.69 20 287.94 4 30 12/3.6 10 30 546.44 2^ 231.01 5 1146. 3 11 521.67 30 193.18 5 30 1012.1 11 30 499. 06 35 166.28 6 955.4 12 478.^4 40 146.19 Let I be the angle of inclination between the two tangents, d the de- gree of the curve, R its radius, and T the distance from P. I. to P. C. or P. T. Then the following formulas may be used to give accurate results: 50 For the radius R = sin i d For the tangent distance T = R tan | /. These formulas will often be needed in the field for curves of over 6 degrees. For instance, when I = 20 and d = 10, the rule of page 6 gives R = 573.0 feet and page 20 gives T = 101.04 feet, while the accu- rate formulas give R = 573.69 feet and T = 101.16 feet. If d is assumed and / is given, the value of T may be found, without computing the radus, from the formula d and this in general must be used in careful location, particularly when- ever d is greater than five or six degrees. THE EDITOR.] 18 RAILROAD CURVE TABLES. I 1 2 3 4 5 go | 70 8 r 0.00 50.02 101.00 150.07 200.09 250.17 300.30 350.44 400.70 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 3 2.50 52.52 102.50 152.57 202.59 252.67 302.80 352.95 40:5.21 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 57.5-2 107.51 157.58 207.60 257.68 307.81 357.97 408.23 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 16 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 2^7.62 267.71 317.84 368.01 418.26 21 22 18.33 (58.35 118.36 168.43 218.45 268.54 318.67 368.85 419.10 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 20 27 22.50 72.51 122.54 172.61 222.63 272.72 322>5 373.03 423.28 27 28 23.33 73.34 123.37 173.44 223.46 273.54 323.68 373.86 424.12 28 29 24.17 74.18 124.21 174.28 224.30 274.38 324.52 374.70 424.95 29 HO 25 00 75.01 125.03 175.10 225.13 275.21 325.35 375 54 425.79 30 31 25.83 75.84 125.87 175.88 225.96 276.05 326.19 376.38 426.63 31 32 26.67 76.68 126.70 176.72 226.80 276.88 327.0* 377.22 427.47 sa 33 27.50 77.51 127.53 177.55 227.63 277.72 327.86 378.06 428.31 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.C7 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 1 185.90 235.98 286.08 336.22 38fi.43 4:16.70 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 18s.40 238.48 288.59 338.73 3H8.95 439.21 46 47 39.17 N9.17 139.22 189.24 239.32 289.42 339.56 389.79 440.05 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 91.67 141 72 191.74 241.82 291.93 342.07 392.30 442.57 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 63 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 U5.84 145.90 195.92 246.00 296.11 346.25 396.49 446.76 55 56 46.t,7 9C,.67 146.73 196.75 246. a3 296.95 347.08 397.33 447.00 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 i 198.42 248.50 298.62 348.76 399.01 449.28 58 59 49.17 99.17 149.24 199.26 249.34 i 299.46 349.60 399.85 450.12 69 19 RAILROAD CURVE TABLES. / 9 10 11 12 13 14 15 16 17 I 450.95 501.32 551.74 602.22 652.87 703.53 754.35 805.29 866.35 1 451.79 502.16 552.58 603.06 653.71 704.38 755.20 806.14 857.20 1 2 452.63 f-03.00 55.1.42 603,91 654.56 705.23 75605 806.99 858.05 2 3 453.47 503. H4 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 5 455.14 505.52 555.94 606.44 657.09 707.77 758.59 809.54 860.61 5 6 455.98 506.36 656.78 607.28 657.93 708.62 759.44 810.39 861.46 6 7 456.82 507.10 557.62 608.13 658.78 709.47 760.29 811.24 862.31 7 8 457.6(5 508.04 538.46 608.97 659.62 710.31 761.13 812.09 863.16 8 9 458.50 508.88 559.30 609.82 660.47 711.16 761.98 812.94 864.01 9 10 4.i9.34 509.72 560.14 610,66 661.31 712.01 762.83 813.79 864.87 TO 11 460.18 510 56 560.98 611.50 66215 712.86 763.68 814.64 865.72 11 12 461.02 fill. 40 561.82 612.35 663.00 713.71 7H4.53 815.49 866.57 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 16 464.37 514.76 565.18 615.72 666.37 717.10 767.92 818.89 869.98 16 17 465.21 515.60 666.02 616.57 667.22 717.95 768.77 819.74 870.83 17 18 466.05 516.44 566.86 617.41 668.06 718.79 769.61 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 22 469.41 519 80 570.22 620.79 671.44 722.20 773.01 823 99 875.09 22 23 470.25 520.64 571.06 621.63 672.28 723.04 773.85 824.84 875.94 23 24 471.08 521.48 571.90 622.48 673.13 723.89 774.70 82569 876.79 24 26 471.92 522.32 572.74 623.32 673.97 724.74 775.55 826.54 877.64 25 26 472.76 523.16 573.58 624.16 674.81 726.59 776.40 827.39 878.49 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 30 476.10 526.53 576.95 627.55 678.20 728.97 779.79 830.79 881.90 30 31 476.94 527.37 677.79 628.39 679.04 729.82 780.64 831.64 882.75 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 34 479.46 629.89 580.32 630.93 681.58 732.35 783.19 834.20 885.32 34 35 480.30 530.73 581.16 631.77 682.42 733.20 784.04 835.05 886.17 35 3G 481.14 531.57 682.00 632.61 683.26 734.05 784.89 835.90 887.02 36 37 481.99 532.41 582.84 63346 684.11 734.89 785.74 836.75 887.88 37 38 482.83 533.25 583.69 634.30 684.95 735.74 786.59 837.61 888.73 38 39 483.67 534.09 584.53 635.15 685.80 736.58 787.44 838.46 889.59 39 40 484.51 534.93 585.37 635.99 686.64 737.43 788.29 839.31 890-44 40 41 485.35 535.77 686.21 636.83 687.48' 738.28 789.14 840.16 891.29 41 42 486.19 536.61 687.05 637.68 688.33 739.12 789.99 841.01 89-.U5 42 43 487.03 537.45 587.90 638.52 689.17 739.97 790.84 841.87 8'.)3.00 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 530.97 590.42 641.05 691.70 742.51 793.39 844.42 895.56 46 47 490.40 540.81 591.26 641.90 692.55 743.35 794.24 845.27 896.42 47 48 491.24 541.66 592.11 642.74 693.39 744.20 795.09 846.13 897.27 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 51 493.76 544.17 594.63 645.27 695.92 746.74 797.64 848.68 899.83 51 52 494. (50 545.01 695.47 646.12 696.77 747.58 798.49 849.53 900.69 52 53 495.44 545.85 596.32 646.96 697.61 748.43 799.34 850.39 901.54 53 54 496.28 546.69 597.16 647.81 698.46 749.27 800.19 851.24 902.40 54 55 497.12 547.53 698.00 648.65 699.30 750.12 801.04 852. mi 903.25 55 56 497.96 548.37 598.84 649.49 700.14 750.97 801.89 852.94 904.10 56 57 498.H1 549.21 599.68 650.3* 700.99 751.81 802.74 H53.79 ' 901.96 57 58 499.65 550.06 600.53 651.18 701.83 752.66 803.59 851.65 905.81 68 59 500.48 550.90 601.38 652.03 702.68 753.50 804.44 855.50 906.67 59 20 RAILROAD OURVE TABLES. / 18 19 20 21 22 23 24 25 | 26 | ' 907.52 958.86 1010.37 1062.00 1113.80 : 1165.76 : 1217.96 1270.28 1322.88 1 908.38 959.72 1011.23 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 13 917.78 969.15 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 I 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 9-22.06 973.43 1024.98 1076.68 1128.50 1180.54 1232.77 1285.18 1337.79 17 18 922.'J1 974.29 1025.84 1077.54 1129.37 1181.41 1233.64 1286.06 1338.67 18 19 92:i.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 1080.99 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 1292.20 1344.81 25 26 929.76 981.15 1032.71 , 1084.45 1136.29 1188.36 j 1240.61 1293.07 1345.69 26 27 930.61 982.01 1033.57 1085.31 1137.16 1189.23 1241.49 1293.95 134657 27 M 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 i 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 i 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 1 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 9U.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 45 946.02 997.48 1049.08 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 i 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 1312.36 136507 48 49 949.44 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.% 1210.12 1262.42 1314.99 1367.72 51 52 952.01 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 131H.50 1371.24 55 56 955.44 1006.93 1058.56 1110.36 1162.29 1214.48 1266.79 1319.37 1372.12 56 r>7 956.29 1007.79 1059.42 1111.21 1163.16 1215.35 1267.66 1320.25 1373.01 57 58 957.15 1008.65 1060.28 1112.07 1164.03 1216.22 1268.53 1321.13 1373.89 58 59 958.00 1009.51 1061.14 1112.94 1164.89 1217.09 1269.41 1322.00 1374.77 59 21 RAILROAD CURVE TABLES. / 27 28 29 30 31 32 33 34 35 f 1375.65 1428.65 1481.89 1535.30 1589.04 1643.08 1697.28 1751.83 1806.67 1 1370.53 1429.54 1482.78 1536.20 1589.94 1643.98 1698.19 1752.74 1807.59 1 2 1377.41 14:10.42 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 1755.18 1810.34 4 5 i:tH0.06 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 1484.86 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 1436.61 J489.90 1543.36 1597.14 1651.19 1705.46 1700.05 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 1062.99 1707.28 1761.87 1816.75 11 12 1380.23 1439.29 1492.57 1546.05 1599.84 1653.90 1708.19 1762.79 1817.67 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 154S.74 1002.54 1656.60 1710.92 1765.53 1820.42 15 16 1389.76 1412.84 1496.13 1549.03 1603.44 1657.50 1711.83 1766.44 1821 34 16 17 1390.04 1443.72 1497.02 1550.53 1604.33 1058.40 1712.74 1767.35 1822.25 17 18 1391.52 14*4.61 1497.91 1551.42 1005.23 1659.30 1713.65 1768.26 1823.17 18 19 1392.40 1445 50 1498.80 1552,32 1606.13 1660.20 1714.56 1769.18 1824.09 19 20 1393.28 144.J. 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 1007.93 1662.01 1716.38 1771.00 1825.92 21 2'2 13H5.05 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 1003.81 1718,19 1772.83 1S27.75 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 1504.14 1557.69 1611.53 1665.61 1720.01 1774.66 1829.59 25 28 1398.57 1451.70 ]505,03 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 1 507.70 1561.28 1615.13 1669.22 1723.65 1778.31 1833.^6 29 30 1402.10 1455.25 1508.59 1662.17 1616.03 1670.12 1724.56 1779.22 1834.17 30 SI 1402.99 145(5.14 1509.48 1563.07 161h.93 1671.03 1725.47 1780.14 1835.09 31 32 1403.87 1457.03 1510.37 15(53.'J6 1017.83 1671.93 1726.38 1781.05 1836.01 32 33 1404.76 1457.91 1511.26 1564.86 1618.74 1672.84 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 35 140(5.53 1459.69 1513.04 1566.65 1(520.54 1674.65 1729.10 1783.80 1838.77 35 36 1407.41 1460.58 1513.93 1507.54 1021.44 1075.55 1730.01 1784.71 1839.69 36 37 1408.30 1461.47 1514.82 1568.44 1022.34 1(576.46 1730.92 1785.63 1840.61 37 38 140X18 1462.35 1515.71 1569.34 1023.24 1677,36 1731. S3 1786.54 1841.54 38 39 1410.07 1403.24 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 1733.05 17H8.37 1843.38 40 41 1411.84 14(55.02 1518.38 1572.02 1625.95 1080.08 1734.56 1789.29 1844.30 41 4'2 1412.72 1465.91 1519. 27 1572.92 1626.85 1680.98 1735.47 1790.20 1845.22 42 43 1413.61 1466.79 1520.16 1573.81 1027.75 1681.89 1736.38 1791.12 1846.14 43 41 1414.49 14(57.08 1521.05 1 1574.71 1628.65 1682.79 1737.29 1792.03 1847.06 44 45 1415.38 1468.57 1521.94 1575.61 1029.56 1683.70 1738.20 1792.95 1847.98 45 40 1416.26 1469.46 1522.83 1576.50 1630.46 1684.61 1739.10 1793.80 1848.00 46 47 1417.15 1470.35 J1523.73 1577.40 1631.36 1685.51 1740.01 1794.78 1849.82 47 48 1418.03 1471.23 1524.6'2 1578.29 1632.26 1686.42 1740.92 1795.69 1850.74 48 49 1418.92 1472.12 1525.51 1579.19 1033.16 1687.32 1741.83 1796.61 1851.00 49 no 1419.80 1473.01 1526.40 1580.08 1634.06 1688.23 1742.74 1797.52 1852.58 50 61 1420.69 1473.90 1527.29 1580.98 1(534.97 1689.13 1743.65 1798.44 1853 50 51 5a 1421.57 1474.79 1528.18 ; 1581.88 1635.K7 1690.04 1744.56 1799.35 1854.43 52 53 1422.46 1475.67 1529.07 1582.77 1036,77 10U0.94 1745.47 1800.27 1855.35 53 54 1423.34 1476.56 1529.96 1583.67 1037.67 1091.85 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 66 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 11586.35 1640.38 1694.56 1749.10 1803.93 1859.03 57 58 142688 1480.11 1533.52 !l587.25 1641.28 1695.47 1750.01 1804.84 1859.95 58 59 1427.77 1481.00 1534.41 1588.15 164218 1696.:!7 1750.92 1805.70 ' 1800.87 59 22 RAILROAD CURVE TABLES. ' i 36 37 38- 39 | 40 | 41 42 43 | 44 i 1861.79 1917.26 1973.01 2029.11 2085.55 2142.33 i 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 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 t 2146.14 2203.35 3360.96 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 2265.78 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 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 3369.64 2327.70 13 14 1874.71 1930.23 1986.09 2042.27 2098.78 i 2155.67 2212.94 2270.61 3328.67 14 15 1875.63 1931.15 1987.02 2043.21 2099.73 i 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 -Jl 22 1882.09 1937.64 1993.56 2049.78 ; 2106.35 2163.30 2220.61 2278.32 233ti.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 1*84.86 1940.42 1996.36 2052.60 : 2109.18 ; 2166.16 2223.49 228122 2339.35 25 26 18*5.78 1941.34 1997.29 2053.54 2110.13 i 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 i 2000.10 2056.36 2112.96 2169.97 2227.32 2285.08 2343.23 29 30 1889.47 1945.05 ' 2001.03 2057.30 ' 2113.91 2170.92 2228.28 2286.04 2344.20 :m 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.S4 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 34 35 1894.10 1949.71 2005.71 2062.01 2118.65 2175 69 2233 08 2290.88 2349 07 3.1 36 1895.03 1950.64 2006.65 2062.95 2119.59 2176.64 2234.04 2291.85 2350.04 :;6 37 1895.95 1951.57 2007.58 2063.89 2120.54 2177.59 2235 00 2292.82 2351.02 37 38 1896.88 1952.51 2008.52 2064.83 2121.49 2178.55 2235.97 2293.79 2351. '.. 39 1897.81 1953.44 2009.45 2065.78 21-22.44 2179.50 2236.93 2294.75 2352.97 39 40 1S'.I8.73 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 3296.69 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 21-26.22 2183.31 224077 2298.63 2 566 86 43 44 1902.44 1958.10 2014.34 2070.48 2127.17 2184.27 2241.73 229960 2357.84 44 45 1903.36 1959.03 2015.07 2071.43 2128.12 2185.22 2242.69 230056 2358.81 45 46 1904.29 1959.% 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 2303.60 2360 76 47 48 1906.14 1961.83 2017.88 2074.25 2130.96 2188 08 2245.57 2303 47 1 2361.73 48 49 1907.07 1962.76 2018.81 2075.19 2131.91 2189.03 2246.53 2304.44 1 2362.71 49 50 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 224845 2306.37 2364.65 r,l 52 1909.85 1965.55 2021.62 2078.02 2134.75 2191.89 2249 42 2307.34 2365 f,3 52 53 1910.77 1966.49 2022.56 2078.99 2135.70 ' 2192.85 2250.38 230831 23 6 60 53 54 1911.70 1967.42 2023.49 2079.90 2136.65 2193 80 2-251.34 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 i 2197.61 2255.18 2313.15 2371.47 58 59 1910.33 1972.08 2028.17 2084.61 2141.38 i 2198.57 2256.14 2314.21 2372.45 59 23 RAILROAD CURVE TABLES. ' | 45 46 47 48 | 49 50 | 51 52 53 j ' 2373.42 2432.21 2491.46 2551.11 2611.27 2671.90 i 2733.04 2794.69 2856.86 o 1 2374.40 2433.20 2492.45 2552.11 2612.28 2672.92 2734.07 2795.72 2857.90 ; 2 '23.'5.:i8 2434.18 2493.45 2553.11 2613.29 2673.94 2735.09 2796.76 2858.95 J 3 2376.35 2435.17 2494.44 2554.11 2614.30 2674.95 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 5 2378.31 2437.14 2496.43 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 2800.89 2863.12 6 7 2380.27 243U.11 2498.41 2558.12 2618,33 2679.03 2740.22 2801.92 2864.16 \ 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 < 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 2624.38 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 16 2389.07 2447.98 2507.35 2567.13 2627.41 26M8.19 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 20 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 2755.61 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 21 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 2636.49 2697.35 2758.68 2820.52 2882.94 25 26 2398.85 2457.84 2517.28 2577.13 2637.50 2698.37 2759.71 2821.56 2883.98 26 27 2399.83 2458.82 2518.27 2578.13 2638.50 2699.39 2760.73 2822.59 2885.02 27 28 2400.80 2459..81 2519.27 2579.13 2639.51 2700.40 2761.76 2823.62 2886.06 28 29 2401.78 2460.80 2520.26 2580.13 2640.52 2701.42 2762.79 2824.66 2887.11 29 30 2402.76 2461.78 2521.25 2581.13 2641.53 2702.44 2763.81 2825.69 2888.15 30 31 2403.74 2462.77 2522.25 2582.13 2642.54 2703.46 2764.84 2826.73 2889.20 31 32 2404.72 2463.76 2523.24 2583.14 2643.55 2704.48 2765.87 2827.77 2890.24 32 33 2405.71 2464.75 2524.24 2584.14 2644.57 2705.50 2766.90 2828.81 2891.29 33 34 2406.69 2465.74 2525.23 2585.15 2645.58 2706.52 2767.93 2829.85 2892.34 34 35 2407.67 2466.73 2526.23 2586.15 2646.59 2707.54 2768.96 2830.89 2893.39 35 36 2408.65 2467.72 2527.22 2587.16 2647.60 2708.56 2769.99 2831.92 2894.43 36 37 2409.63 2468.71 2528.22 2588.16 2648.62 2709.58 2771.02 2832.96 2895.48 37 38 2410.61 2469.69 2529.21 2589.17 2649.63 2710.60 2772.04 2834.00 2896.53 38 39 2411.60 2470.68 2530-21 2590.17 2650.64 2711.62 2773.07 2835.04 2897.57 39 40 2412.58 2471.67 2531.20 2591.18 2651.65 2712.64 2774.10 2836.08 2898.62 40 41 2413.56 2472.66 2532.20 2592.18 2652.67 2713.66 2775.13 2837.12 2899.07 41 42 2414.54 2473.65 2533.19 2593.18 2653.68 2714.68 2776.16 2838.16 2900.71 42 43 2415.52 2474.64 2534.19 2594.19 2654.69 2715.70 2777.19 2839.20 2901.76 43 44 2416.50 2475.63 2535.18 2595.19 2655.70 2716.72 2778.22 2840.24 2902.81 44 45 2417.49 2476.62 2536.18 2596.20 2656.71 2717.74 2779.25 2841.28 2903.86 45 46 2418.47 2477.61 2537.17 2597.20 2657.73 2718.76 2780.28 2842.31 2904.90 46 47 2419.45 2478.60 2538.17 2598.21 2058.74 2719.78 2781.31 2843.35 2905.95 47 48 2420.43 2479.59 2539.17 2599.21 2659.75 2720.80 2782.34 2844.39 2907.00 48 49 2421.4] 2480.58 2540.16 2600.22 2660.76 2721.82 2783.37 2845.43 2908.04 49 50 2422.39 2481.57 2541.16 2601.22 2661.78 2722.84 2784.40 2846.47 2909.09 50 51 2423.38 2482.56 2542.15 2602.23 2662.79 2723.86 2785.43 2847.51 2910.14 51 52 2424.36 2483.54 2543.15 2603.23 2603.80 2724.88 2786.45 2848.55 2911.18 52 53 2425.34 2484.53 2544.14 2604.24 2664.81 2725.90 2787.48 2849.59 2912.23 53 54 2426.32 2485.52 2545.14 2605.24 2665.83 2726.92 2788.51 2850.63 2913.28 54 55 2427.30 2486.51 2546.13 2606.24 266 V 4 2727.94 2789.54 2851.67 2914.32 55 56 2428-28 2487.EO 2547.13 2607.25 2667.85 2728.95 2790.57 2852.70 2915.36 56 57 2429.27 2488.49 2548.12 2608.25 2668.86 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 58 59 2431.23 2490.47 2550.11 2610.26 j 2670.89 2732.02 2793.66 2855.82 2918.50 19 KAILROAD CURVE TABLES. / 54- 55 | 56 57 58 59 J | 60 61 1 62 1 ' 2919.55 2982.81 3046.64 3111.10 3176.14 1 3241.86 3308.21 3375.20 3442.93 j 29.U60 2983.87 3047.71 3112.18 3177.23 3242.% 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 6 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 : 8383.08 3450.88 7 8 2927.97 2991.31 3055.-J1 3119.75 3184.88 9250.68 3317.12 i 3384.20 3452.02 8 9 2929.02 2992.37 3056.29 3120.83 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 I 2931.13 2994.49 3058.43 3122.99 3188.16 3i53.98 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 29%.62 3060.57 3125.15 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 3324.92 3392.08 3459.97 15 10 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 2-J3H.49 3001.93 3065.93 3130.56 3195.80 3261.70 3328.26 3395.45 34G3.38 18 19 2939.54 3002.99 3067.00 3 1 31.64 3196.89 3262.80 3329.36 3396.58 3464.52 19 20 2940.00 3004.05 3068.07 3132.72 3197.99 3263.90 3330.49 . 3397.70 3465.66 20 21 2941.65 3005.11 3069.15 3133.80 3199.08 3265.00 3331.60 : 3398.83 r 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 3469.07 23 24 2944.81 3008.30 3072.36 3137.04 3202.30 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 3010.42 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 8077.79 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 30 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 30-13.10 3147.88 3213.30 3279.36 3346.10 3113.48 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 9066.26 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 3486.03 37 38 2'.T,'.i.57 3023.20 3087.41 3152.23 3217.70 3283.80 3350.58 :i418.01 3486.17 38 39 296U.63 3034.26 3088.48 3153.31 3218.80 3284.91 3351.69 3419.14 3487.32 39 40 2961.C8 3026.33 3089.56 3154.40 3219.89 3286.02 3352.81 : 3420.28 3488.46 40 41 i 2962.74 3026.39 3090.64 3155.49 3220.99 3287.13 3353.93 3421.41 3489.60 41 42 2%3.80 3027.46 3091.71 3156.57 3222.09 3288.24 3355.05 3422.54 i 3490.75 42 43 2964.85 3028.52 3092.79 3157.66 3223.19 3289.35 3356.17 1 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.% 3030.66 3094.95 3159.84 3225.38 3291.57 3358.41 ! 3425.94 ; 3494.18 45 46 2368.02 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 i 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 32%.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 i 3501.04 51 r.2 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 31G8.53 3234.17 3300.44 3367.37 3435.00 3503.33 53 r, t 2976.47 j 3040.25 3104.64 3169.62 3235.27 3301.55 3368.48 3436.13 3504.48 54 :,.-, 2977.53 i 3041.31 3105.72 3170.71 3236.37 3302.66 3369.60 3437.27 3505.62 55 5'i 2978.58 3042.38 3106.79 3171.79 3237.47 3303.77 ! 3370.72 3438.40 3506.76 56 57 2979.64 1 3043.44 3107.87 3172.88 3238.56 3304.88 3371.84 3439.53 3507.91 67 :,* 2980.70 3044.51 3108.95 3173.97 3239.66 3305.99 3372.96 3440.67 3509.05 58 59 2981.75 3045.57 3110.0.! :;175.05 3240.76 3307.10 3374.08 3441.80 . 3510.20 59 25 RAILROAD CURVE TABLES. ' | 63 | 64 65 66 67 68 69 70 71 | ' 3511.34 3580.45 3650.41 3721.06 3792.57 3864.88 3938.11 4012.15 4087.15 1 8512.49 3581.61 3651.59 3722.25 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 3868.53 3941.80 4015.89 4090.93 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 3728.19 3799.78 3872.18 3945.49 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 3589.75 3659.81 3730.56 3802.18 3874.62 3947.95 4022.13 4097.24 8 9 3521.67 3590.92 3660.99 3731.75 3803.38 3875.83 3949.18 4023.37 4098.50 9 3522.82 3592.08 3662.16 3732.94 3804.58 3877.05 3950.41 4024.62 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 3 3526.26 3595.57 3665.68 3736.50 3808.19 3880.70 3954.10 4028.36 4103.54 13 4 3527.41 3596.73 3666.86 3737.69 3809.39 3881.92 3955.33 4029.61 4104.80 14 5 3528.56 3597.:33.15 3602.55 3672.73 3743.63 3815.39 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 35:37.74 3607.20 3677.43 3748.38 3820.20 3892.86 3966.40 4040.83 4116.15 23 24 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 3822.60 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 35 12.: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 29 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.H5 34 35 H551.56 3621.19 3691.55 3762.68 3834.66 3907.50 3981.20 4055-83 4131.32 35 36 3552.72 3622.35 3092.73 3763.87 3835.86 3908.73 3982.44 4057.08 4132.59 36 37 3553.87 3623.62 3693.91 3765.07 3837.07 3909.95 3983.68 4058.33 4133.86 37 38 3555.C3 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 3986.15 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 8698.63 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 43 3560.80 3630.54 3700.99 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 45 3563.12 36:32.88 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 48 3566.58 3636.38 3706.90 3778.22 3850.37 3923.42 3997.29 4072.11 4147.83 48 49 3567.74 3637.55 3708.08 3779.42 3851.58 3924.64 3998.52 4073.37 4149.10 49 50 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 61 52 3571.21 3641.06 3711.62 3783.01 3855.21 3928.31 4002.25 4077.13 4152.91 52 53 3572.36 3642.23 3712.80 3784.20 3856.42 3929.54 4003 48 4078.38 4154.18 63 54 3573.52 3643.40 3713.98 3785.40 3857.63 3930.76 4004.72 4079.63 4155.45 54 56 3574.67 3644.57 3715.16 3786.59 3868.84 3931.99 4005.96 4080.89 | 4156.72 65 66 3675.83 3646.73 3716.84 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 4159.26 57 58 3578.14 3648.07 3718.70 3790.18 3862.46 3935.66 4009.67 4084 64 4160 53 58 59 3579.30 3649.24 3719.88 3791.38 3863.67 ( 3936.88 4010.91 4086.90 4161.80 69 26 RAILROAD CURVE TABLES. ' | 72 73 ! 74 75 76 I 77 78 79 80 | ' 4163.07 4239.97 4317.84 4396.74 4476.73 4557.81 4640.04 4723.41 4808.04 i 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 4321.77 4400.73 4480.77 4561.91 4644.20 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 1 4169.46 4246.44 4324.39 4403.39 4483.46 4564.64 4646.97 4730.44 4815.17 5 e 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 4668.74 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 U 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 21 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 4671.8'J 4755.74 4840.82 23 M 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 4001.53 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 4866.53 34 35 4207.84 4-285.27 4363.75 44*3.30 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 i 4291.79 4370.35 4449.99 4530.69 4612.53 4695.52 4779.73 4865.15 40 41 4215.55 4293.09 i 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 4-<69.46 43 44 4219.40 4297.00 4375.63 4455.34 4536.11 4618.03 4701.10 4785.39 4870.'.iO 44 45 4220.69 4298.30 4376.94 4456.67 4537.47 4619.41 4702.49 4786.81 4872.33 45 46 42-21.98 4299.60 ; 4378.26 4458.01 4538.83 i 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 t 4623.53 4706.67 4791.05 4876.6 1 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 5-2 4229.69 4307.42 4386.18 4466.03 4546.96 4629.01 4712.25 4796.72 4882.39 62 53 4230.97 4308.72 4387.50 4467.37 4548.32 4630.41 4713.65 4798.13 4883.83 53 54 1 4232.26 4310.02 4388.82 4468.71 i 4549.67 ' 4631.79 4715.04 4799.56 4885.26 54 65 i 4233.54 431U33 4390.14 4470.04 4551.03 4633.16 4716.44 4800.96 4886.70 56 56 4234.83 4312.63 4391.46 4471.38 4552.39 4634.54 4717.83 4802.38 4888.13 66 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 58 59 4238.68 4316.54 4395.42 4475.39 , 4556.45 4638.66 ; 4722.01 4806.62 > 4892.44 69 27 RAILROAD CURVE TABLES. , ' | 81 | 82 J j 83 | 84 85 86 j 87 88 89 4893 88 4980.97 5069.44 5159.29 5250.57 5343.28 5437.54 ! 5533.35 5630.81 1 4895.33 4982.44 5070.93 6160.80 5252.11 5344.84 5439.13 6534.97 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 6635.75 3 4 4899.66 4986.85 5075.41 6165.35 6256.73 5349.54 5443.90 5539.82 5637.39 4 5 4901.11 4988.32 5076.90 5166.86 6258.27 5351.10 6445.50 5541.44 5639.04 5 6 4902.56 4989.78 5078.39 5168.38 5259.81 5352.67 5447.09 6543.06 6640.69 6 7 4904.00 4991.25 5079.88 6169.89 5261.35 5354.23 5448.68 5544.68 6642-33 7 8 4905.45 4992.72 5081 38 5171.41 5262.88 5355.79 5450.27 5546.29 6643.98 8 9 4906.89 4994.19 5082.87 6172.92 5264.42 6357.36 5451.86 5547.91 6645.63 9 10 4908.34 4995.66 6084.36 5174.44 5265.96 6358.92 5453.45 5549.53 5647.27 10 11 4909.78 4997.13 5085.85 6175.95 6267.50 6360.49 6455.04 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 6270.58 5363.62 5458.22 5554.38 6652.21 13 14 4914.12 5001.54 5090.33 5180.50 5272.12 6365.18 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 6369.87 5464.59 5560.85 5658.80 17 18 4919.91 5007.41 5096.30 5186.56 5278.28 6371.44 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 6099.28 5189.58 6281.36 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 6377.69 5472.54 5568.94 5667.03 22 23 4927.13 6014.76 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 6671.97 25 26 4931.47 5019-16 5108.23 5198.67 5290.59 5383.95 5478.91 5575.41 5673.61 26 27 4932.92 502063 5109.72 5200.19 5292.13 5385.51 5480.50 5577.03 5675.26 27 28 4934.36 5022.10 5111.22 6201.70 5293.67 5387.08 5482.09 5578.65 6676.91 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 6390.21 548S..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 6683.52 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 5191 68 5588.40 5686.84 34 35 4944 54 503244 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 6695.14 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 6701.78 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 60 4966.40 5054.64 5144 26 5235.29 5327.77 5421.76 5517.32 5614.50 5713.40 50 51 4967.85 5056.12 5145.76 5236.82 532932 5423.34 5518.93 5616.13 5715.06 61 52 4979.31 5057.60 5147.27 5238.35 5330.87 5424.92 5520.53 6617.76 5716.72 52 53 4970.77 5059.08 5148.77 5239.87 5332.42 5426.50 5522.13 5619.39 571838 53 . 64 4972.22 5060.56 5150.27 5241.40 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 5'537.08 5431.23 5526.94 5624.29 5723.36 56 67 4976.60 6065.00 6154.78 5245.99 5338.63 5432.81 5528.54 5625.92 5725.02 57 68 4978.05 5066.48 5156.28 5247.51 5340.18 !H34 39 5530.15 5627.55 5726.68 58 69 4979.51 5067-96 5157.79 5249.04 5341.73 5135.96 5531.75 5629.18 1 5728.34 59 28 TABLE OF MINUTES WITH COB- IIESPONDING DECIMALS. TABLE OF SECONDS WITH COKKES- PONDING DECIMALS. M. | D. | M. | D. S. | D. | S. | D. i o i o '/ it o 1 0.0166 31 0.5167 1 0.0002778 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 intersection of the tangent lines to the beginning of one degree curves, for each 30 minutes, 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. [This table is an abridgement of the preceding one, and is to be used for approximate work in running trial curves. When the curve is sharper than five degrees it will be well, in order to secure good results, to com- pute T by one of the formulas given on page 17. In using both tables it should be borne in mind that the 100-foot chain can alone be used, and that the degree of curve is the angle subtended at the center by a chord 100 feet long. THE EDITOR.] 30 RAILROAD CURVE TABLE. I II | III I II | III | I | II | III 0' 25.00 25.0 30 D 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 99.99 25.0 32 1643.08 27.0 62 3442.93 34.0 2 30 125.03 25.0 32 30 1670.12 27.0 62 30 3477.02 34.1 3 150.07 23.0 33 1697.28 27.2 61 3511.34 34.3 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 34.7 4 30 225.13 25.0 34 30 1779.22 27.4 64 30 3615.34 34.9 5 250.17 25.0 35 1806.67 27.4 or. 3650.41 35.1 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 35.9 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 (V.i 3938.11 36.7 9 30 476.10 25.1 i 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 4049.56 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 38.1 1-2 30 627.55 25.3 42 30 ; 2228.28 28.8 1-2 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 14 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 16 30 830.79 25.5 46 30 2461.78 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 I 4681.58 415 19 958.86 25.7 49 2611.27 30.1 79 1 4723.41 41.8 19 30 984.58 25.7 49 30 2641.53 30.3 79 30 4765.58 42.2 20 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 HO 30 4850.79 42.7 21 1062.00 25.8 51 2733.04 30.6 81 4893.88 43.1 21 30 1089.90 25.9 51 30 2763.81 30.8 81 30 4937.25 43.3 22 1113.80 25.9 52 2794.69 30.9 82 4980.97 43.7 22 30 1139.75 25.9 52 30 2825. W 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 1217.96 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 sr, 5250.57 45.8 25 30 129658 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 5437.64 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 1431.89 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 KEEPING THE FIELD NOTES OF A SURVEY, FROM WHICH THE CENTER LINE IS LAID ON THE MAP Course of No. of Angle at in- tangent. ft. from From To Length Length of tersection and Badius intersec- sta- sta- of tan- curves in of tangents degree of tion of tion. tion. gents in feet or angle at and direc- rurves tangents feet. centre. tion of in feet. to begng. curves. of curve. Tangent S 19 21' E 0. 2. 200. 7 24' 3 42' L 1548.65 100.14 2. 26. 2400. 24 D 00' 1 00' B 5730. 1217.96 26. 43.556 1755.60 Tangent S 2 45' E 43.556 61.681 1812.5 30= 15' 2 00' E 2865. 937.82 61.681 93.650 3190 90 Tangent S 33 30' W 93.650 102.517 88G.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' B 2865. 550.00 181.296 184.506 321.00 Tnngent S 18 12' W 184.506 193.195 868.89 13 02' 1 30' B 3820. 436-37 193.195 213.064 1986.9 T.ingent S 31 14' W 213.064 220.908 78444 11 46' 1 30' L 3820. 393.61 220.908 230.546 063.8 Tangent S 19 28' \V 230.546 242.496 1195 00 23 54' 2 00' B 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 3<*20. 100.05 268.02 277.21 918.89 27 34' 3 L 1910. 468.55 277.21 279.21 20000 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' B 3820. 100.05 291.011 301.422 1041.10 31 14' 3 00' B 1910. 53 1.88 301.422 303.00 157.80 2 22' 1 30' B 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 Tnngent S 3 18' W 338.71 347.15 844.16 16 53' 2 00' B 2865. 425.19 347.15 364.00 1685.00 Tangent S 20 11' W 364. 376.633 1263.33 37 54' 3 li 1910. 655.80 376.633 389.53 389.70 Tangent S 58 05' W 380.53 392.38 1185. 23 42' 2 B 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 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 2261.87 79.99 442.582 449. 641.8 Tangent S 48 16' E 22.262.90 22.637.31 32 EXCAVATION AND EMBANKMENT. APPLICATION OF THE PKISMOIDAL FOBMULA IN DETERMINING THE QUANTITIES OF RAILROADS 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 points 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. 33 o s .TO. o' IP. 12. OJ r< o h- 1 EH a w GO W s H gs 5 EH P5 O PR CO H H O 5Z5 s s z jo JO B&J.'B UKdJ\[ -uig; jo ija -xg o -JO+93JUJ8 joinao raojj CO . OS -( SO Tj m t> oo cp e; CO OO Oi * CO 00 CO -* rH b- to w ** oi CO CO .63 81 300.00 300.37 300.74 301.11 301.48 301.85 302.22 302.59 302.96 303.33 82 303.70 304.07 304.44 304.81 305.18 305.55 305.92 306.29 306.66 307.03 83 307.41 307.78 308.15 308.. r >2 308.89 309.26 309.63 310.00 310.37 310.74 84 311.11 311.48 311.85 31-2.22 312.59 312.96 313.33 31:3.70 1314.07 314-44 85 314.81 315.19 315.56 315.93 316.30 316.67 317.04 317.41 317.78 318.15 86 318.52 318.89 319.26 319.63 320.00 320.37 320.74 321.11 321.48 321.1-5 87 322.22 322.59 322.96 323.33 32:i.70 324.07 324.44 324.81 325.18 325 55 88 325.92 326.30 326.67 327.04 327.41 327.78 328.15 328.52 328.89 S29..6 89 329.6:3 330.00 330.37 330.74 331.11 331.48 331.85 332.22 332.59 332.96 90 333.33 333.70 334.07 334.44 334.81 335.18 335.55 335.92 336.29 336.67 91 3:37.04 337.41 337.78 338.15 338.52 338.89 339.25 339.62 339.99 310.37 ; 92 340.74 341.11 341.48 341.85 342.22 342.59 342.96 343.33 343.70 344.07 93 344.44 344.81 345.18 345.56 345.93 346.30 346.67 347.03 347.40 317.78 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.SI6 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 35889 97 359.26 359.63 360.00 360.37 360.74 361.11 361.48 361.85 362.22 362.59 98 362.96 363.33 368.70 364.07 364.44 364.81 365.18 365.55 365.93 366.30 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 3713.70 101 374.07 374.44 374.81 375.1H 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 | 385.18 385.55 385.92 386.29 386.67 387.04 387.41 387.78 388.15 388.52 105 388.89 389.26 389.63 390.00 390.37 390.74 391.11 391.48 391.85 392.22 106 392.59 392.96 393.33 393.70 394.07 394.44 394.81 395.18 395.55 395.92 107 396.30 396.67 397.04 397.41 397.78 398.15 398.52 398.89 399.26 399.63 108 400.00 400.37 400.74 401.11 401.48 401.85 402.22 402.59 402.96 403.33 109 403.70 404.07 404.44 404.81 405.18 405.55 405.92 406.29 406.67 407.04 110 407.41 407.78 408.15 408.52 408.89 409.26 409.63 410.00 410.37 410.74 111 411.11 411.48 411.85 412.22 412.59 412.96 413.33 413.70 414.07 414.44 112 414.81 415.18 415.55 415.92 416.29 416.67 417.04 417.41 417.78 418.15 113 418.52 418.89 419.26 419.63 420.00 420.37 420.74 421.11 421.48 421.85 114 422.22 422.59 422.% 423.33 423.70 424.07 424.44 424.81 425.18 425.56 115 425.93 426.30 426.67 4-27.04 427.41 427.78 428.15 428.52 428.89 429.26 116 429.63 430.00 430.37 430.74 431.11 431.48 431.85 432.22 432.59 432.96 117 433.33 433.70 4:i4.07 434.44 434.81 435.18 435.55 435.92 436.29 436.67 118 437.04 437.41 437.78 438.15 438.52 438.89 439.26 439.63 440.00 440.37 119 440.74 441.11 441.48 441.85 442.22 442.59 442.96 443.33 44:3.70 444.07 40 EXCAVATION AND EMBANKMENT TABLES. 0.00 0.10 0.20 j 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 44667 447 04 447.41 447.78 121 448.15 448.52 448.89 449.26 449.63 450.00 450.37 450.74 451.11 451.48 122 451.85 452.22 452.59 452.96 453.33 453.70 454.07 454.44 454.81 455.18 123 455.55 455.92 456.29 456.67 457.04 457.41 457.78 458.15 458.52 458.89 124 459.26 459.63 460.00 460.37 460.74 461.11 461. -18 461.85 462.22 462.59 125 462.96 463.33 463.70 464.07 464.44 464.81 465.18 465.55 465.93 466.30 126 466.67 467.04 467.41 467.78 468.15 468.52 468.89 469.26 469.63 470.00 127 470.37 470.74 471.11 471.48 471.85 472.22 472.59 472.% 473.33 j 473.70 128 474.07 474.44 474.81 475.18 475.56 475.93 476.30 476.67 477.04 477.41 199 477.78 478.15 478.52 478.89 479.26 479.63 480.00 480.37 480.74 481.11 130 481.48 481.85 482.22 482.59 482.96 483.33 483.70 484.07 484.44 484.81 131 485.18 485.55 485.92 486.29 486.67 487.04 487.41 487.78 488.15 488.52 132 488.89 489.26 489.63 490.00 490.37 490.74 491.11 491.48 491.85 492.22 133 492.59 492.96 493.33 493.70 494.07 494.44 494.81 495.19 495.56 495.93 134 496.30 496.67 497.04 497.41 497.78 498.15 498.52 498.89 499.26 499.63 135 500.00 600.37 500.74 501.11 501.48 501.85 502.22 502.59 502.96 503.33 136 503.70 604.07 504.44 504.81 505.18 505.56 505.93 506.30 506.67 507.04 137 507.41 507.78 508.15 508.52 : 508.89 509.26 509.63 510.00 510.37 610.74 138 511.11 511.48 511.85 512.22 512.59 512.96 513.33 513.70 514.07 514.44 139 514.81 515.18 515.55 515.92 516.29 516.67 517.04 517.41 517.78 518.15 140 518.52 518.89 519.26 519.63 520.00 520.37 520.74 521.11 521.48 521.85 HI 522.22 522.59 522.96 523.33 523.70 524.07 524.44 524.81 525.19 525.56 142 525.93 526.30 526.67 627.04 527.41 527.78 528.15 528.52 628.89 529.26 143 529-63 630.00 530.37 530.74 631.11 531.48 531.85 | 532.22 532.59 532.94 144 533.33 533.70 534.07 534.44 534.81 535.18 535.56 ! 535.93 536-30 536.67 145 537.04 537-41 537.78 638.15 638.52 538.89 539.26 539.63 540.00 540.37 146 540.74 541.11 541.48 541.85 i 542.22 542.59 542.96 543.33 543.70 644.07 147 544.44 544.81 545.18 545.56 1 545.93 546.30 546.67 1 547.04 547.41 547.78 148 548.15 548.52 548.89 549.26 549.63 550.00 550.37 550.74 551.11 551.48 149 551.85 552.22 552.59 552.96 553.33 553.70 554.07 554.44 554.81 555.18 150 555-55 555.93 656.30 556.67 557-04 557.41 557.78 i 558.15 558.52 558.89 151 559.26 559.63 560.00 560.37 560.74 561.11 661.48 561.85 562.22 562.59 152 562.96 563.33 563.70 564.07 564.44 564.81 565.18 565.56 565.93 566.30 153 566.67 667.04 567.41 567.78 568.15 568.52 568.89 569.26 569.63 570.00 154 570.37 570.74 571.11 571.48 671.85 572.22 572.59 572-% 573.33 573.70 155 574.07 574.44 574.81 575.18 575.56 575.93 576.30 576.67 577.04 577.41 156 577.78 578.15 578.52 578.89 579.26 579.63 580.00 580.37 580.74 581.11 157 581.48 581.85 582.22 582.59 582.96 5*3.33 583.70 584.07 584.44 584.81 158 585.18 585.55 585.92 586.29 686.66 587.04 5S7.41 587.78 588.15 588.52 159 588.89 589.26 589.63 590.00 590.37 590.74 591.11 591.48 591.85 59222 160 592.59 592.96 693.33 593.70 594.07 594.44 594.81 595.18 595.55 595.92 161 596.29 596.67 597.04 597.41 597.78 598.15 B98.M 598.89 599.26 599.63 162 600.00 600.37 600.74 601.11 601.48 601.85 602.22 i 602.59 602.% 603.33 163 603.70 604.07 604.44 604.81 605.18 605.55 605.92 606.30 606.67 607.04 164 607.41 607.78 608.15 608.52 608.89 609.26 609.63 610.00 610.37 610.74 165 611.11 611.48 611.85 612.22 612.59 612.96 613.33 613.70 614.07 614.44 166 614.81 615.18 615.55 615.92 616.29 616.67 617.04 617.41 617.78 618.15 167 618.52 618.89 619.26 619.63 620.00 620.37 620.74 621.11 621.48 621.85 168 622.22 622.59 622.96 623.33 623.70 624.07 624.44 624.81 625.18 625.56 169 625.93 626.30 626.67 627.04 627.41 627.78 628.15 628.52 628.89 629.26 170 629-63 630.00 630.37 630.74 631.11 631.48 631.85 632.22 632.59 632.% 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 17.1 640.74 641.11 641.48 641.85 642.22 642.59 642.96 643.33 643.70 644.07 174 644.44 644.81 645.18 645.55 645.92 646.29 646.66 i 647.03 647.41 647.78 175 648.15 648.52 648.89 649 26 649.63 P50.00 650.37 650.74 651.11 651.48 176 651.85 652.22 652.59 652.9i", 653.:i3 653.70 654.07 654.44 654.81 655.18 177 655.56 655.93 65R.30 656.67 657.04 657.41 657.78 658.15 658.52 658.89 17H 659.26 659.63 660.00 660.37 660.74 661.11 661.48 66185 662.22 662.59 179 662.% 663.33 663.70 664.07 664.44 664.81 665.1S 665.55 665.92 666.29 41 EXCAVATION AMD EMBANKMENT TABLES. 0.00 0.10 | 0.20 | 0.30 0.40 0.50 0.60 0.70 | 0.80 0.90 180 GGG.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 C,79.26 679.63 680.00 680.37 680.74 681.11 184 681.48 681.85 682.22 682.59 682.96 683.33 684.70 684.07 684.44 684.81 185 685.18 685.56 685.93 686 30 686.67 687.0 i 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 69370 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.% 703.33 190 703.70 704.07 704.44 704.81 705.18 705.55 705.92 706.29 706.66 707.03 191 707.40 707.77 708.14 708.51 708.89 709.26 70963 710.00 710.37 710.74 192 711.11 711.48 711.85 712 22 712.59 712.96 713.33 713.70 714.07 714.44 193 714.81 715.18 715.55 715.92 716.29 716.67 717.04 717.41 717.78 718.15 194 718.52 718.89 719.26 7W.63 72000 720.37 720.74 721.11 721.48 721.85 195 722.22 722.59 722.96 723.33 723.70 724.07 724.44 724.81 725.18 725.55 196 725.92 726.29 726.66 727.03 727.40 727.77 728.14 728.51 728.88 729.25 197 729.63 730.00 730.37 730.74 731.11 731.48 731.85 732.22 732.59 732.96 198 733.33 733.70 734.07 734.44 734.81 735.18 735.55 735.93 736.30 736.67 199 737.04 737.41 737.78 738.15 738.52 738.89 739/26 739.63 740.00 740.37 200 740.74 741.11 741.48 741.85 742.22 742.59 742.96 743.33 743.70 744.07 201 744.44 744.81 745.1H 74555 745.93 746.30 746.67 747.04 747.41 747.78 202 748.15 748.52 748.89 749. 6 "49.63 750.00 75037 750.74 751.11 751.48 203 751.85 752.22 752.59 752.96 753.33 753.70 754.07 754.44 754.81 755.18 204 755.55 755.93 756.30 756.67 757.04 757.41 757.78 758.15 758.52 758.89 205 759.26 759.63 760.00 760.37 760.74 761.11 761.48 761.85 762.22 762.59 206 762.96 763.1(3 763.70 764.07 764.44 764.81 765.18 765.55 765.93 766.30 207 766.66 767.04 767.41 767.78 768.15 768.52 768 89 769.26 769.63 770.00 208 770.37 770.74 771.11 771.48 771.85 772.22 772.59 772.96 773.33 773.70 209 774.07 774.44 774.81 775.18 775.55 775.93 776.30 776.66 777.04 777.41 210 777.7S 778.15 778.52 778.89 779.26 779.63 780.00 780.37 780.74 781.11 211 781.48 781.85 782.22 782 59 782.96 783.33 783.70 784.07 784.44 784.81 212 785.18 785.55 785.93 78630 786.66 787.04 787.41 787.78 788.15 788.52 213 788.89 789/26 789.63 790.00 790.37 790.74 79111 791.48 791.H5 792.22 214 792.59 792.96 793.33 793.70 794.07 794.44 794.81 795.18 795.55 795.93 215 796.30 796.66 797.04 797.41 797.78 798.15 798.52 798.89 799/26 799.63 216 800.00 800.37 8(10.74 801 11 801.48 801.85 802 22 802.59 802.96 803.33 217 803.70 804.07 804.44 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 810.00 810.37 810.74 219 811.11 811.48 811.85 812.22 812.59 812.96 813.33 813.70 814.0T 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 8.0.00 820.37 820.74 821.11 821.48 821.85 222 822.22 822.59 822.96 823.33 823.70 824.07 824.44 824.81 825.18 825.55 223 825.93 826.30 826.66 827.04 827.41 827.78 828.15 828.52 828.89 829.26 224 829.63 830.00 830.37 830.74 831.11 831.48 831.85 832.22 832.59 832.96 225 833.33 833.70 834.07 834.44 834.81 835.18 83555 835.93 836.30 836.66 226 837.04 837.41 837.78 838 15 838.52 838.89 83926 839.63 840.00 840.37 227 840.74 841.11 841.48 841.85 842/22 842.59 842.96 843.33 843.70 844.07 228 844.44 844.81 845.18 845.55 845.9.! 846.30 84666 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 R54.07 854.44 854.81 855.18 231 855.55 855.93 856.30 856.66 857 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 07 864.44 864.81 865.18 805.55 865.93 866.30 234 866.66 867.04 867.41 867.78 868.15 868.52 868.89 869.26 869.63 870 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 8<1.85 882.22 882.59 **_> '.H ; 883.33 883 70 884.07 884.44 884.81 239 885.18 885.55 885.93 886.30 886.66 887.04 887.41 887.78 888.15 888.52 42 EXCAVATION AND EMBANKMENT TABLES. | 0.00 f 0.10 | 0.20 0.30 0.40 | 0.50 0.60 | 0.70 0.80 j 0.90 240 888.88 889.26 889.63 890.00 890.37 , 890.74 I 891.11 891.48 891.85 892.22 241 892.59 892.96 893.33 893.70 894.07 891.44 894.81 8tf5.18 895.55 895.93 242 806.90 896.66 897.04 897.41 897.78 898.15 K93.52 898.88 899.26 899.63 343 900.00 900.37 900.74 901.11 901.48 902.2-2 902.59 902.96 903.33 244 903.70 904.07 904.44 904.81 905.18 905.55 905.93 906.30 906.66 907.04 215 907.41 907.78 908.15 908.52 908.88 909.26 909.63 910.00 910.37 910.74 24(i 911.11 911.48 911.85 912.2-2 912.59 91-2.90 913.33 913.70 914.07 914.44 247 914.81 915.18 915.55 915.93 5)16.30 916.66 917.04 917.41 917.78 918 15 348 918.52 918.88 919.26 919.63 920.00 920.37 920.74 921.11 921.48 921.85 249 922.22 922.59 922.96 923.33 923.70 924.07 924.44 924.81 925.18 925.55 250 925.9-2 926.30 926.66 927.04 9^7.41 927.78 928.15 9-28.32 928.88 9.9.26 261 929.63 930.00 930.37 930.74 931.11 931.48 931.85 932.22 932.59 932 9fi 369 933.33 933.70 934.07 934.44 934.81 935.18 935.55 935.92 936.30 936.66 253 937.04 937.41 937.78 938.15 938.52 938.88 939.26 939.63 94000 940.37 254 940.74 941.11 941.48 941.85 942.22 942.59 942.96 943.33 943.70 944.07 255 944.44 944.81 945.18 945.55 945.92 946.30 946.66 947.04 947.41 947.78 360 948.15 948.52 948.88 94J.26 949.63 95H.OO 950.37 950.74 951.11 951.4S 257 951.85 962.22 952.59 952.96 953.33 953.70 954.07 954.44 1*4.81 955.18 955.55 955.92 956.30 956.66 957.04 957.41 957.7S 958.15 95*.52 958.88 959.26 959.63 960.00 960.37 960.74 961.11 961.48 961.85 962.22 962.59 360 962.96 963.33 963.70 964.07 964.44 964.81 965.18 965.55 965.92 966.30 261 966.66 967.04 967.41 967.78 968.15 968.52 968.88 969.26 969.63 970.00 263 970.37 970.74 971.11 971.48 971.85 972.22 972.59 972.96 973.33 973.70 363 974.07 974.44 974.81 975.18 975.55 975.92 976.30 976.66 977.04 977.41 364 977.78 978.15 978.52 | 978.88 979.26 979.63 980.00 980.37 980.74 981.11 205 981.48 981.85 982.22 982.59 982.96 98.J.33 983.70 9*4.07 984.44 984.81 1266 985.18 985.55 9-v<5.92 98f,.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 i 268 992.59 992.96 993.33 993.70 994.07 994.44 994.81 995.18 995.55 995.92 ' 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 -71 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 10Q&88 1009.26 1009.63 1010.00 1010.37 ! 1010.74 27:5 1011.11 1011.48 1011.85 1012.22 101'2.59 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 10-20.74 1021.11 1021.48 10-21.85 27>; 1022.22 1022.59 1022.96 1023.33 1023.70 10-24.07 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 10-29.-26 278 1029.63 1030.00 1030.37 1030.74 1031.11 1031.48 1031.85 1032.22 1032 59 1032 96 279 1038.33 1033.70 1034.07 1031.44 1034.81 10:i5.18 1035.55 10:55.92 1036 30 1036.0)6 380 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 1042.23 104-2.59 10.2.96 1013.33 1043.70 1044.07 2 -'2 1044.44 1044.81 1045.18 1045.55 1045.92 1046.30 1046.66 1047.01 1047.41 1047.78 V!3 1048.15 1048.52 1048.88 1049.-.G 1049.63 1050.00 1050.37 1050.74 1051.11 1051.48 2S4 1051.85 1052.22 1052 59 1052.96 1053.33 1053.70 1054.07 1054.44 1054.81 1055.18 2.-0 10.-55.55 1066.93 1056.30 1056.66 1057.01 1067.41 1057.78 105^.15 1058.52 1058.88 1 (159.26 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 : 064. 81 1065.18 1065.55 1065.92 1066.30 I <>66.66 1067.04 10.V7.41 1067.78 1068.16 1068.52 1068>8 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 107481 1075.18 1075 55 1075.92 1076.30 1076.66 1077.04 1077.41 291 1077.78 1078.15 1078.52 li '78.88 1079.26 1079.69 1080.00 1080.37 1080.74 1081.11 1031.48 1081.85 1082.22 1082.96 W3.33 1083.70 1084.07 1084.44 1084.81 2'.i3 10*5.18 1085.55 1085.92 1086.K6 1087.04 1087.41 1037.78 1088.15 1088.52 2:it 1088.88 1-9.2M 1089.63 1090.00 10 0.74 lo-.n.ii 1091.48 1091.85 1092.22 295 1092.59 10;I2.96 1093.33 j 1094.07 1094.44 1094.81 1095.18 109o.55 1095.92 296 1096.30 1096.66 J 097/4 ]0'.i7.41 1097.7s 1098.52 1098.88 1099 26 :i099.63 297 1100.00 1100.37 1100.74 110l.lt 1101.48 1 01.85 1102.22 110259 1102.96 1103.33 29- 1103.70 1104.' 7 1104.44 1104.81 1105.18 1105.55 11105.92 110630 110666 1107.04 -'99 1107.41 1107.78 1108.15 1108 52 1108.88 .1109.26 1109.63 1110.00 1110.37 1110.74 43 EXCAVATION AND EMBANKMEKT TABLES. 0.00 0.10 j 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 1115.19 1115.56 ! 1115.93 lll(i.30 1116.67 1117.04 1117.41 1117.78 1118.15 302 ! 1118.52 1118.89 1119.26 1119.03 11 '21 LOO 1120.37 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 1125.56 301 1125.93 1126.30 1126.67 1127.04 1127.41 i 1127.78 1128.15 1128.52 1128 89 1129.26 305 I 1129.G3 1130.00 1130.37 1130.74 1131.11 : 1131.48 1131.85 1132.22 1132.59 1132.96 306 ' 113S.33 1133.70 1134.07 1134.44 1134.82 j 1135 19 1135.56 1135.93 1136.30 1137.W 307 1137.04 1137.41 1137.78 1138.15 1138.52 1138.89 1139.26 1139.63 1140.00 1140.37 308 1110.74 1141.11 1141.48 1141.85 1142.22 1142.59 1142.96 (1143.33 1143.70 1144.07 ;joy 1144.44 1144.82 U45.19 1145.56 1145.93 1146 30 1146.67 1147.04 1147.41 1147.78 310 1148.15 1148.52 1148.89 1119.. 6 1149.63 115000 1150.37 1150.74 1151.11 1151-48 311 1151.85 115-2.22 1152.5!) 1152.96 1153.33 1153.70 1154.07 1154.44 1154.82 1155.19 312 1155.56 1135 93 1156.30 1156.67 1157.1 4 i 1157.41 1157.78 1158.15 1158 52 1158.89 313 1159.26 1159.63 j 1160.HO 1160.37 1160 74 1161.11 1161.48 1161.85 1162.22 1162.59 314 1162.9(i 1163.33 1163.70 1164.07 1164.44 1164.82 1165.19 1165.56 1165.93 1166.30 315 1166.67 1167.04 1167.41 1167.78 1108.15 1168.52 1168.89 1169.26 1169.63 1170.00 316 1170. ,7 1170.74 1171.11 1171.48 1171.85 1172.22 1172.59 1172.96 1173.33 1173 70 :i!7 1174.07 1174.44 1174.82 1175.19 1175.56 1175.9J 1176. 1176.67 1177.04 1177.41 318 1177.78 1178.15 1178.52 1178.89 1179.26 1 1179.63 1180.00 1180.37 1180.74 1181 11 31!) 1181.48 1181.85 1182.22 1182.59 1182.96 1183.33 1183.70 1184.07 1184.44 1184.82 3-20 1185.19 1185.56 1185.93 1186.30 1186.67 1187.04 1187.41 1187.78 1188.15 1188.52 321 1188.89 1189.26 1189.63 1190.00 1190.37 1190.74 1191.11 1191.48 1191 85 1192.22 322 1192.59 1192.96 1193.33 1193.70 1194.07 1194.44 1194-82 1195.19 1195.56 1195.93 323 1196.30 1196.67 1197.04 1197.41 1197.78 1198.15 1198.52 1198. 89 1199.26 1199.63 324 1200.00 1200.37 1200.74 1201.11 1201.48 1201.85 1202.22 1202.59 1202.96 1203.33 325 1203.70 1-204.07 1204.44 1-204.82 1205.19 1205.56 1205.93 1206.30 1206.67 1207.04 326 1207.41 1207.78 ' 1208.15 1208.52 1208.89 1209.26 1209.63 1210.00 1210.37 1210.74 327 1211.11 1211.48 1211.85 121-2.22 1212.59 1212.96 1213.33 1213.70 1214.07 1214.44 3-28 1214.82 1215.19 | 1215.56 ! 1215.93 1216.30 1216 67 1217.04 1217.41 1217.78 1218.15 829 1218.52 1218.89 I 1219.26 1219.63 1220.00 1220.37 1220.74 1221.11 1221.48 1221.86 330 1222.22 1222.59 1222.96 1223.33 1223.70 1224.07 1224.44 1224.81 1225.18 1225.55 331 1225.93 1226.30 1226.67 1-27.04 1227.41 1227.78 122815 1228.52 1228.*9 1229.26 332 1229.63 1230.00 ! 1230.37 1230.74 1231.11 1231-48 1231.85 123222 1232.59 1232.96 333 1233.33 1233.70 1234.07 1234.44 1234.82 1235.19 1235.56 1235.93 1236.30 1236.67 334 1237.04 1237.41 1237.78 I 1238.15 1238.52 12 !8.89 1239.26 1239.6! 1240.00 1240.37 335 1240.74 1241.11 1241.48 1241.85 1242.22 124259 1242.96 1243 33 1243.70 1244.07 836 1244.44 1244.82 1245.19 1245.56 1245.93 1246.30 1246.67 1247.04 1247.41 1247.78 337 1248.15 1248.52 1248.89 1249.26 1249.63 1250.00 1250.37 1250.74 1251.11 1251.48 338 1251.85 12.V2.22 1252.59 1252.96 125333 1253.7D 1-254.07 1254.44 1254.82 1255.19 3:59 1255.56 1255.93 1256.30 1256.67 1257.04 1257.41 1-257.73 1258.15 1258.52 1258.89 340 1-59.26 1259.63 1260.00 1260.37 1260.74 1261.11 1261 48 1261.85 1262 22 126259 341 1262.96 1263.33 1263.70 1264.07 1264.44 1264.82 1265.19 j 1265.56 1365.93 1266.30 312 1266.67 1267.04 1-267.41 1367.78 1268.15 126s. 52 1268.89 1269.26 1269.63 1270.00 34 f 1270.37 1270.74 1271.11 1271.48 1271.85 1-27-2. -2-2 1272.59 1272. Wi 1273.33 1273.70 ,'H4 1274.07 1274.44 1274.82 1275.19 1275.56 1275.93 1276.30 1276.67 1277.04 1277.41 315 1277.78 1278.15 1278.52 1278.89 1279.26 1279.6 ! 1280.nO 1280.37 1280.74 1281.11 316 1281.4S 1281.85 1282.22 1282.59 1282 96 1283.33 1281.70 1284.07 1284.44 128482 347 1-285.19 1285.56 l28:i.93 1-20.;0 1286.67 1287.04 1287.41 1287.78 1288.15 1288.52 348 1288.89 1289.26 1280.0 ! 1290.' I2!i0.:i7 1-290.71 1291.11 11291.48 1291.85 1292.22 349 1292.59 1292.96 1293.33 1293.70 j 1294.07 1294 44 1294.82 1295.19 1295.56 1295.93 350 1296.30 1296.67 1297.04 1297.41 1297.78 1298.15 1298.52 1298 89 1299.26 1299 63 351 1300.00 1300.37 1300.74 1301.11 1301.48 1301.85 1302.22 1302.59 1302 96 1303 33 352 1303.70 1304.07 1304.44 1301.^2 1 1305.19 1305.56 1305.93 1306.30 1306 67 1307.04 353 1307.41 1307.78 1308.15 i 1308.52 1308.89 1309.26 1309.63 1310.00 131037 1310.74 35 t 1311.11 1311.48 1311.85 1312.22 ; 1312.59 1312.96 1313.33 1313.70 131407 131444 355 1314.82 1315.19 1315.56 j 1315-93 1316.30 1316.67 1317.04 1317.41 1317.78 1318.15 356 1318.52 1318.89 1319.26 1319.63 jl '20.00 1320.: 7 1320.74 1321.11 1321.48 1321.86 357 132J.22 1322.59 1322.96 1323.33 1323.70 1324.07 1324.44 1324.81 1325.18 1325.55 358 1325.9:! 1326.30 H26.67 1327.04 1:127.41 1H27.78 1328.15 1328.63 1328.89 132926 359 1323.63 1330.00 I 1U30.:J7 13^0-74 1331.11 1331.48 1331 85 1332.22 1332.59 1332.96 44 ENGINEER'S FIELD BOOK. CHARLES S. CROSS, the author of the preceding pages, was graduated from the Rensselaer Polytechnic Institute in 1838. He was engaged on railroad location and construction in New York until 1852, when he went to Panama to report on the railway then there building. Returning in the same year, he was mostly employed on surveys for the location of lighthouses until 1857, when he went to Minnesota on railroad work. It was at this period that he made the computations for the tables of his pocketbook. Later he had an extensive practice in engineering field work in New York and New England, and filled many responsible posi- tions. He was a man of great integrity of character, beloved by all who knew him. He died in Brooklyn in 1680 or 1881. Abstract from memoir of his life in Engineering News, May 8, 1886. A good engineer must be of inflexible integrity, sober, truthful, accu rate, resolute, discreet, of cool and sound judgment, must have command of his temper, must have courage to resist and repel attempts at intimi- dation, a firmness that is proof against solicitation, flattery or improper bias of any kind, must take an interest in his work, must be energetic, quick to decide, prompt to act, must be as fair and impartial as a judge on the bench, must have experience in his work and in dealing with men, which implies some maturity of years, must have business habits and knowledge of accounts. Men who combine these qualities are not to be picked up every day. Still they can be found. But they are greatly in demand, and when found, they are worth their price ; rather, they are beyond price, and their value cannot be estimated by dollars. Chief En- gineer Starling's Report to the Miss. Levee Commissioners. CHAPTER II. Engineering Field Work.* THE SURVEYS. The three classes of surveys, viz : Preliminary, Location, and Construction, form as good divisions as can be suggested for this subject, and we will consider them in order. PRELIMINARY. The object of a Preliminary survey is to ascertain whether'it be feasible to build a line of railway between two points upon the sur- face of the earth, and this information is obtained for certain parties \nho wish to make money in some way or other by con- structing or having such line of railroad constructed. For this purpose the parties employ a more or less competent engineer to make these surveys, giving him authority to employ one or more field parties according to the magnitude of the work, and the money they may think they can spend upon it. If only one party is employed it is sometimes under the direction of the chief en- gineer himself, but more commonly under an assistant employed by him. ORGANIZATION OF FIELD PARTY. The organization of this field party is usually, as follows : 1. The Assistant in charge of the party. 2. The Transitman, whose work is running the line and keeping all notes thereof. 3. The Leveler, whose work is taking levels, drawing the profiles and making the estimates therefrom. 4. The Level rodman, assistant to the Leveler. 5. The head chainman, who should also carry the transit rod and get therewith the lines given by the transitman. 6. The hind chainman, who should also number the stakes and keep a record of all distances measured. 7. From one to five axemen according to the amount of chop- ping required by the work. * Written by the late CHA.S. A. SMITH, C. E.. Professor of Civil and Mechanical Engineering at Washington University, 8t. Louis, and published in ENGINEEB- INO NEWS, Vol. III. 1876. 46 ENGINEERING FIELD WOKK. These may be considered about all the men needed for the professional part of the work, and if the country is inhabited will be all that will be employed ; if there are only a few inhabitants a team and driver may be advantageous, but if uninhabited and it becomes necessary to take a camp outfit, at least two more men are indispensable a teamster and a cook, the latter being a very im- portant member of the party. THE ENGIKEEB-IN-CHARQE. The duties of the engineer-in-charge of the party are too many for enumeration here, but he has to see that the greatest amount of work possible is done for the money expended ; his business is to get information for the chief engineer and to keep his party running without delay. A word of brotherly advice to him may not come amiss and is meant kindly if it is not necessary. CAEE OF MEN. In selecting your party for a start use judgement and your know- ledge of human nature; don't get two men who have a feud with each other in the same party if it can be helped. Stu;ly your men all the time and be frank and free with them ; do not talk much with them in working hours, but watch all hands very closely, for the first few days especially. Remember that your men are men, and treat them well: show them that you know how the work should be done, but don't "nag" them all the time ; if you have A horse, don't keep them at work till dark and then ride off and leave them to walk three or four miles to supper, but either quit work in decent season or lend your horse to some fellow who is fagged, and walk in with your men ; don't hang round in the morn- ing and let your men wait for you, but pick up an axe or rod and start first for the work ; get into good training for walking, and if you start for supper last passall the men on the road ; don't shirk work yourself, and don't let any body else shirk ; never ask a man to do any work you would not be willicg to do yourself, we remem- ber " stripping to the buff " and wading a stream four feet deep when the cakes of ice were coming down, because we thought the men hung back and did not want to go into the water ; don't worrv the transitman's wits out of his head by asking him questions ; find out what he is doing and recording, but don't crowd him too hard or bluster about him ; don't swear habitually before the men if you THE COOK ON THE LINE THE TRANSITMAN. 47 can help it ; you may want to swear at them some times, and if not used to it they will be more apt to obey ; don't scold a man when you are angry yourself, if you can help it, but wait and talk to him after supper, when you have cooled down. THE COOK. In selecting a camp outfit be especially careful to get a good cook, and we advise a good cooking stove of cast iron with enough pipe to draw well, we remember a sheet iron stove which had to be taken down every morning and the soot kicked out of it before a fire could be made to "draw," and we also remember the satis- faction with which the boys kicked the miserable thing to pieces after it had been "returned" at headquarters. We are more particular in this matter, not only because we like to be well fed, but because men must be well fed in order to work well and you must remember that poor food will make bad temper and bad work, and that the interests of your employers demand that you keep your men contented with their job. So much for the care of the men. ON THE LINE. Don't let your leveler get too far behind the transit work, and see that he checks his levels and establishes benches at proper intervals. After the work is well started you will be obliged to go ahead and make yourself familiar with the features of the country and select the points where your line must be run. A preliminary line is usually run without curves, and the work of the transitman is much easier than in location surveys, and the line work is much more easily carried on than when locating ; and this brings us to the work of the transitman. But before leaving this part of the subject let me remind you, that as your work progresses, you will have to come in contact with the property holders and residents of the country, and you should always bear in mind that you repre- sent large interests and can give them by your manner a favorUble or unfavorable impression as you choose. THE TRANSITMAN. The transitman has the hardest work of the party to perform ; he has to stand with one eye at his instrument as long as the men can set stakes, and then when he is called up, the whole chain and axe force have to be idle till he arrives at the place where they are 48 ENGINEERING FIELD WORK. and has set up and lined his instrument; he is supposed to direct the work in the absence of his superiors, to know the topography of the country ahead and run his line to suit the ground to keep all the men at work and not let them loaf around to keep all notes, and if possible sketch all the topography; to act as chie assistant in every way, to be book-keeper and cashier of the party ; if in camp, to purchase supplies and see that things go right gen- erally. The skill of the transitman in the field consists in his realization of the peculiar features of the ground and his judgment in running to them, and to his being able to work under mental pressure. The mere instrumental work in a preliminary survey is easy to do, as it consists only in running bearings, noting angles and giving the line to the men at the chain. A few words to the transitman: Carry your instrument yourself ; don't let any of the men take it at night unless you are just ready to drop with fatigue. Your men may very probably offer to carry your instrument, as a common courtesy, or even to make friends with you, but don't accept such favors ; among working men, from which class your chain men and axemen will most probably come, there is but one standard of comparison, and that is strength, and although one of them may be perfectly willing to shoulder your fifteen pound transit for three or four miles, you will not gain his respect by letting him do it for you. If you have not strength, make up for it in endurance and quiet pluck, and if you want to grumble, don't do it before the men. You and the engineer-in-charge must be in perfect accord, at least in appearance, if you want to further the interests of your employers and your own also. In setting up a transit on sideling ground it is generally better to put one leg of the tripod up hill and two down, but you must exercise a little common sense in the matter; try to keep the lower "parallel plate " as level as possible, as by so doing time in " leveling up " will be saved ; try to make yourself master of your instrument as there is a great range in the value of transitmen, and try to "set up" each time a little quicker than before, and also a little better. The acme of setting a transit may be considered reached when one shove on each leg of the tripod brings the "plumb-bob" exactly over the point in the stake, while the instrument is found level "both ways.". Try and see how many times you can do this every day, but don't waste tin>e studying how to do it at each " set." It is rather better to keep the plates clamped together at zero, and do all lining of the instrument with the lower clamp and tangent; THE LEVELER LEVELING. 49 take bearings on both fore and back sights as you may detect errors in reading angles by so doing, and be careful to record which way angles are turned. It is most convenient to run your transit ahead always and read the same end of the needle if the instrument is in as good adjustment as it should be. The stability of the adjustment differs very widely in different instruments. We have worked with an instrument for three months which never had to be touched, and also with another from the same maker which would not reverse truly for the day, although adjusted every morning ; it becomes necessary, therefore, to learn the peculiarities of your instrument, and know, not guess at, its condition at all times. The reversal should be tested each morning before going to work until you are sure of the instrument. Learn which way to get the slack of the tangent screws, and to do good work with a poor transit. THE LEVELEK. The leveler on a preliminary survey may have to work at his best to keep up with the transit party, and as the leveler and rodman have to work completely in unison, w.e will give them our advice together after their field work. Of course, in the office, or in camp they are two very different people, the leveler being one of the commissioned officers of the party, if we may use a military term, while the rodman is about the grade of a sergeant only. Still there should be very little difference of feeling between them. The leveler keeps all field notes and the rodman should also carry a book and keep the turning point sights and work out all heights of the instrument and elevations of turning points and benches in t e field. Readings for turning points and benches may be ta ken to the thousandths, but for station heights the nearest tenth only should be read. LEVELING. Make all t!ie vertical height you can in going up or down hill as you may save a setting thereby. Study the ground as to what is coming ahead and never select turning points or set up the instru- ment without having fully considered what is to be done next. Be sure of the adjustments of the instrument and that the rod is held "plumb " (if the cross hairs are right, the man at the instru- 50 ENGINEERING FIELD WORK. ment can see by the vertical hair if the rod is "plumb " one way, and by gently swinging the cod in the plane of the instrument after setting the target if the target rises above the hair, the rod was not held "plumb;" if the target on swinging the rod, falls below and just comes up to the hair, the rod has been held vertically). Make your signals with some system, and move the rod according to the signal in amount of motion as well as direction, speak your numbers distinctly and don't mistake the word seven for eleven, or the reverse. Leveling can be hurried in open country by employing two rod- men and rods, and running them alternately, the employment of a fourth man to keep notes in such case being a great help, although such great haste is not often required or desirable. Put in benches at least once in 1,500 feet in open country, and every 1,000 feet in rough country, as it may save you a good deal of work; select good points for benches and turning points, and always be sure that the instrument may be moved before you move it,"and that you can find at least half of the turning points in the day's work. In running " check levels " check up the benches every mile, and if the agreement is within one-tenth, call bench right and go on. Try to keep the check levels within two miles of each other, as it may save a good deal of annoyance. The work of the rest of the party is much the same for location and preliminary surveys, and will be described further on. The engineer in charge of the party and the transitman are the ones whose work is increased the most, and their duties will be described again for location survey. THE HEAD CHAINMAN. The head chainman holds an important position and must be a man with sound judgment, and must understand his work. He should hold the transit rod with one hand, and the chain with the other, showing discretion as to holding the chain level and taking short lengths on hilly ground ; he should understand the signals of the transitman and obey them intelligently; should have a good eye for line and use it every time he holds his rod up, so as to be as nearly right as may be before the transitman begins to signal to him ; and he should always look at the transitman when lining, instead of gazing around at other things. His work is perhaps best conducted in the following order When the chain is pulled out HEAD CHAINMAN TRANSIT POINTS. 51 he turns around, and holding the rod with one hand, tries to place it as nearly correct as he can by lining over the last stake to the instrument, while with the other hand he is trying to " straighten out the chain ;" he then moves the rod in obedience to the motions of the man at the instrument, and after getting the line, holds the chain up to the rod with both hands and gets the distance ; then dropping the chain he stands up straight, plumbs the rod carefully and receives the line again ; then pressing the rod into the ground he makes the hole with the point, and takes it off the ground : a stake is then driven and the measurement should be repeated to see if the distance is correct, after which the rod is held on the stake " for line," the chain is then dragged on and the operation repeated. Time may be lost by neglecting the order of operations given above, or by not looking to see where the line is, and leaving all the move- ments to be signalled from the instrument, or by jerking the chain while trying to straighten it, or by not watching the transitman closely, and thus missing his signals. If you are so far away that the motion cannot be seen, take your handkerchief or hat and make a signal (imitating the lining signals) and the transitman will understand that you wish him to take his handkerchief, (when snow is on the ground, his hat) to increase the visibility of his sig- nal. Kemember that the transitman can see you plainly, and can guess what you may wish him to do. When you wish him to line you hold up your rod and wave it to catch his eye, and when you are sure that the line can go no further without a change in the position of the instrument, you must call his attention by holding your rod in both hands horizontally above your head ; then after carefully lining and centering, you can call him up by beckoning with both hands, holding the rod above your head or by any other previously arranged signal. SELECTION OF TRANSIT POINTS. By far the most important duty in point of difficulty, is the selec- tion of the transit points, which muet be so chosen that the greatest distance ahead may be seen from them ; in general they should be on the upper edges of hills, where a view of the valley on both slopes can be obtained, and if possible, where a full view of the tran- sit rod can be had, as it is only allowable in case of necessity to sight at but a small part of the rod, and therefore great care must be taken to hold "plumb" at all times, as you do not know just how much of the rod may be observed. You must exercise consid- 52 ENGINEEBING FIELD WOEK. erable judgment in the matter^ and never be astonished if your views and the transitman's differ on this point. And here let us say a word to all the men ; remember that the transitman has to work all the time, and that he has to take all the blame from the engineer-in-charge for all mistakes, and that' if he does scold you for things that are not your fault, just wait till the matter devel- opes, but do not try to argue during working hours about the work ; if you have been to blame, you deserve "jawing," and if you have not, it will not hurt you a bic in the eyes of anybody whose opinion is worth having. The same remarks will apply to the transitmen and levelers in their relations to their superior ; let them remember that the engineer-in-charge has more things to think about in a day than they have in a week, and if they don't believe it, wait until they have the same position and can see for themselves. THE BEAK CHAINMAN. The work of the rear chainman is to hold the chain while it is being pulled along ; we say hold it, for if you let the end go you may have to call the front chainman back for 10 or 20 feet after he has passed his proper distance, and he won't like that. Don't hang on the chain and be dragged by it, but be ready to give it a shake and clear it if it catches on brush or rocks. The rear chainman is responsible for the numbering oi.' the stakes, and for all distances with "plus " numbers; he must be careful to assist in straighten- ing the chain, to be on hand promptly in measuring, and not get in the line nor walk on the line, and not to jerk the front chainman's arms off by suddenly stopping. The keeping of the numbers right is a more difficult task than it seems to be, and requires a good memory; in all cases of doubt, go back and find out at the last stake what is right and don't guess at it. Be careful that the chain is in good order that the links are straight and that the rings are not pulled open. Do it up from the handle and keep the strap around it ; learn to throw a chain over a stream ; one end of an ordinary heavy chain can be thrown over a 50 feet stream. And by making two bundles with say 15 feet between them, and using two men to throw, one after the other (at say half a second interval), we have thrown the end of a heavy chain 75 feet. Be careful that the chain is not dragged against the transit legs, and do not hit them while trying to stand the straightening as inflicted by the head chainman; be prompt to assist in making short chains on hilly ground, and on curves, if there are any, and wfll k the outer side AXEMEN LOCATION CARELESSNESS, ETC. 53 of the line lest you get in the " line " of the instrument without knowing it. THE AXEMEN. The axemen are under the general direction of the head chain- man who gives the line for cutting brush and timber with his rod. One axeman must be in charge of the stakes and must never let the chain work wait for him a second, but must keep up at all risk, t Sometimes a large basket is useful in carrying stakes. The stakes should be numbered by the chainman, and if he marks a number of them in the basket, care must be taken to see that in "plus " stations the numbered stakes are not used, or the numbers may get " mixed." LOCATION. In location surveys the only difference in the work of the men is in the curve work, where the head chainman has to offset from the line of the last stake to find the transit "line " by an amount known as the chord "deflection," for which see "Henck's Field Bock." We always gave the chainraan a list of " chord deflections " for the even degrees, and let him guess at the amount of the ground, and found that it saved time. The centering of the stakes should be attended to a little more carefully than on preliminary work, and the measurements made with more care. A back rodman will be necessary, and we can only caution him to stand up, with his rod in position all the time, or if near enough to see, whenever the transitman turns over his telescope, he must be on hand. Although the job is not very interesting it is impor- tant. We used to let the back rodman carry the coats, and if we took our dinner along, a basket with the "grub." Each man in the party must be held strictly responsible for what tools or instruments are put into his hands, and a careful property account must be kept and reported from time to time. WASTEFULNESS OF CARELESS LOCATION. Location surveys differ from preliminary surveys in being more carefully carried out, as to the exact position of the line, and in the curve running, which is usually omitted on the preliminary work. The exact position of the line is a matter of great importance, for many dollars are thrown away by careless locations and in many cases the theory of wilful ignorance is the only excuse that can be 54 ENGINEEKING FIELD WORK. made for them. There are needed careful judgment, long experi- ence, and a groat deal of real hard work on the part of the engineer in charge of the locating party, to make successful locations. THE TOPOGEAPHEE. The party is usually organized with the same force as in the pre- liminary survey, viz: An engineer-in-charge, transitman, leveler, level rodman, two chainmen and from one to five axemen. To these are often added a topographer, and sometimes a cross-section leveler and helper or rodman. The topographer takes sketch-notes of the contours and surrounding country, roads, buildings etc., which have to be shown in the plans, and if he carries a pocket " azimuth compass," or a pocket sextant, he will find it a great help to him, but for his work we especially recommend a small plane table, 18 inches square, with the paper on it in " block " fashion, the board fitted with a shoulder strap, and Jacob staff mountings, and a folding "alidade " or ruler, with sights. With this outfit a topo- grapher can produce a line map which will make his chief engineer's heart glad, and which will go a long way towards con- vincing the directors that the party have done a lot of work. Tht use of the plane table for this purpose is not common, but such ar arrangement costs very little, and nothing else will show as much of the country in a very short time. The field use of the instrument is very simple ; the line already run being platted before taking the field, the " orientation " can be performed from stakes and it can be used anywhere. The cross-section leveling is only performed in very rough coun- try ; a 10-foot pole with a short spirit level placed on it, and then held witli one end on the ground and the other against a graduated rod on which the rise or fall in 10 feet is noted, is used; the infor- mation obtained in this way is very considerable ; there is a good deal of work to get it but the men are not required to have a very high grade of mental organization and do not draw a very high pay. ENGINEER IX CHARGE. All of the increased care and skill required and already men- tioned has to come from two men the engineer-in-charge and the transitman the former has all the responsibility of the added im- portance of the survey, and the constant study of the ever changing ground, and the greater or less difficulty of the work itself: ENGINEER IN CHAKGE-TRANSIT NOTES. 55 the latter has all the curve work, with increased watchfulness aud greater accuracy, to attend to ; those two men have their work nearly doubled, while the work of the rest of the party is only in- creased by the additional care and attention which has to be enforced on all the party. To the engineer-in-charge we shall say very little, and to a man in that position little can be said if he does not know his business he certainly ought not to be in the place, and if he does know it, our advice is unnecessary, yet if he does not think it beneath him to read what we have to say to transitmen, he may here and there find a hint to help him in watching the work of that indispensable assistant. And here let us say that no money is ever sa ed by making the engineer-in-charge of the location run either transit or level, as he needs all of his faculties to be at all times shar- pened to their utmost degree to attend to his own duties, and if the tedious instrumental work is put upon him he cannot keep every- thing going at once properly. And let us say also, that if the engineer-in-charge wishes to make every man do his very utmost, that he had better take the head of the chain himself when he can spare tne time, especially on long tangents, which he has already determined. By so doing he will be near all the men of the transit party, and they will work when they are right under the eye of the " boss," and he will be sure that no time will be lost in picking out the transit stations, and that the stakes are kept well up; the transitman will always hurry up to him, and if he cannot keep them all " on the jump," he is not fit for his place. Of course, he has frequently to go ahead and pick out the ground, and go back to see how the profile will plat, and tell the transitman what must be done in his absence, and in this he must be his own judge of his time and of its disposition, but still, when he wishes to drive matters, he can do so best from the head of the chain, in the meantime letting the head chainman take the transit rod and keep up the centers ; the mental work which he has to perform all the time will not suffer from the mere manual labor of being head chainman. KEEPING TRANSIT NOTES. The transitman has after all a hard place to fill, for there is no variety in his mental work ; he has to keep a sharp watch on the men when his superior is absent, and has the constant computa- tion of deflection angles to attend to on curves, at the same time 56 ENGINEERING FIELD WORK. using all possible diligence as to figures. And here a hint as to the easiest way of keeping the curve notes and doing the transit work. The method originated we know not how, and may have have been used by large numbers of transitmen, although we have never happened to meet them. The basis of all circular curve work with the transit is the well known theroem : the angle between a tangent chord, or between any two chords which meet at a point on the curve, is measured by half the intercepted arc. And as the point where the chords meet on the curve may be anywhere on that curve, it follows that the sum of any consecutive angles or series of angles is the same no matter where the instrument be placed on the curve for given arcs, and that if the deflection angles be all computed from the B. C., as far as may be desired, at any station on the curve the number can be used, as the differences will be the same for the same stations. To illustrate this, we must assume an example. Let it be required to run a five degree curve from sta. 131 + 40, and let us first look at a page in a field book : STATIONS. DEFLEC- TIONS. CURVE. TRUE COURSE. NEEDLE COURSE. 1'29 X 161 W N 16 W 130 B. C. +40 .1 ()' 5R. N 16-15' W 2 1 30' 3 4 ()' 4 6 30' 5 9-0' i +50 10 15' 6 11 30' 7 14=0' 8 16 : 30' E. C. +25 177?, 34 C 15' N 18- 0' E N 17f E We see the book is ruled with five columns and usually on the left hand page, the right hand page being reserved for " remarks." The column for Stations explains itself, the signs ' plus " being used, decimal points for a hundred foot unit, and the ordinary "decimal" being reserved for feet and fractions of feet. The letters B. C. and E. C. are used for beginning and end of the curve, instead of the P. C. and P. T. used often for " point of curve " and "point of tangent," being more in accordance with the usage of ordinary geometry and has been our custom for several years. KEEPING TRANSIT NOTES. 57 The column of deflections contains the deflection angles com- puted from B. C. as far as convenient, say to station 135, ana the stakes set and centered, for same reason 135 + 50 becomes necessary ' and has to be put in ; then the transit is turned back to and turned over on the back sight to be sure that nothing has slipped and carried up to 135-1-50, and set up. The instrument is then set a* and sighted at B. C. and then if turned to 10 C 15' it would be on the tangent at 135+50, and if turned to 11 30', it will be on the chord from 135 + 50 to 136, and by adding these 2 30' for each hun- dred feet the curve is run to 138 and the transit is moved to that place after taking a back sight as before, with the plates at 0. After setting up at 138 if we could see B. C. we should set at again, and turning to 16 30' we would be on the tangent ; but B. C. is supposed invisible, and we shall therefore set the instrument at 10 15' and sight it back at 135 + 50 and the result is that the lower plate is in the same position as if B. C. had been visible, and we had as above suggested set and sighted thereat; by turning to 16 30' we shall be on the tangent at 130 and if we find that 1 20' more will be needed to strike the desired direction from there, we will put 1 15' more in the curve or 37' deflection which corresponds to 25 feet ; we run out the 25 feet and turn tolO|' and sight the stake in, and then turning to 1015', we turn over to the back sight ; af- ter satisfying ourselves that it is all right, we go to 138 + 25 and being sure the instrument reads 1015, we sight again at 135 + 50 and turn to \T1\' and are at the tangent. By taking the differences and comparing distances it will easily be seen that the angles are all right. Now in what does this method consist that is better than the practice of counting stations and multiplying by the deflection angle ? Only this, that the counting and multiplication are both performed already. Each station is attached to the angle opposite to it in the note book, and once there it is good for all the work that you can do with it. The mental labor thus saved is a great help. It was once our fortune to have to "break in" two " green " transitmen in five weeks, and in all that time we com- puted every angle that was used at the instrument, mentally, and kept at the head of the chain most of the time ; by asking the man at the instrument what reading he had and what station he was at and what his back rodman was at, we never let a mistake pass our notice. (Note. We are not anxious to repeat this experi- ence of our transit running from the head of the chain.) 58 ENGINEERING FIELD WORK. For the transitman himself this system of notes is a great relief as he is free from the constantly recurring question "what is your next deflection?" with its importunate worrying when he has just setup on an odd "plus" and knows that his back rod- man is also on an odd "plus," he simply asks himself, what are the readings for these two stations knowing that the difference between them has been computed carefully once as they come along, and it will be all right now. COMPOUND CURVES. On compound curves the same method can be followed all around, but the back rodman and the instrument must be on the same branch ( the P. C. 0., point of compounding of curve, is of course on both branches). The next column of the note book is headed " curves " and in it are recorded the degree and direction of the curves and the central angle, or angle of intersection ; it is twice the last deflection angle always. In the next column is put up the com- puted courses from the first one, and the next one contains the needle readings; the use of these is a check to the transitnian/s work and sudden variations are not common. If " local attraction " exist, it can be found by reading the compciss at each end of the tangent. We remember a local attraction which bothered us all one morning and which never seemed to be the same for two min- utes running, and which quite frightened our " boss " but as ve were within fifty feet of a north and south track, we talked "earth currents " at him (they were east and west ) and as we were sure of our work we let it go unexplained ; in the afternoon we discovered .the innocent cause to be a small " Smith & Wesson " in our over- coat breast pocket, and we have never seen any such local attrac- tion since. LONG TANGENTS. Long straight lines require a good deal of care, and the instru- ment should be reversed " both ways " on them, and if a long sight can be obtained backward so as to overlook two o - three transit points, they should be tested by the direct instrument. If great care is needed, the instrument should be used "both ways " without reversing, and the slack of the clamp screws watched. Tangent screws are now so generally made double that the play of the motion screws can be prevented from interfering with the ac- COMPOUND CUBVES LONG TANGENTS. 59 curacy of the work, but the clamps will wear loose a little and must be watched. LAND LINES. In Railway field work, after the location survey, follows legi- timately the land surveyor "land lines" as they are called in the east, and although most of this work is included in com- mon surveying, yet there are some points of difference which it will be well to touch upon. In cities and towns where land is valuable, it is of course quite important to have the work done accurately ; and although in the western country, where the land is very com- monly given to the railroad company it is not so essential, still it is always desirable to know how to do good work, and a few words as to general surveying will scarcely be out of place. In the first place be sure that your work is definitely connected with points which can be found again, and that the connection with the main line is right, and that it is simple ; any complex mea- surement is to be avoided. In the next place, measure every dis- tance pertinent to the work which can be directly measured. Cal- culate as little as possible. If the land to be taken is very irregular in form, a " traverse " is the best method of attack if all the sides can be measured; don't have any " omissions " to supply if you can help it; be careful to take all offsets at right angles ; take the angles with a transit if one can be had, and do not use ths com- pass in any way but as a check on the transit; for sighting right angles quickly, some of the forms of the " optical square " may be found very convenient; for ordinary work in cities most of the measurements for land will be at right angles or nearly so, and the work can be laid out on four lines forming a trapezium ; do not- trust to any building for a right angle or to any two walls of the same building to have parallel faces ; brick laying is not by any means the most exact of trades, and although for a map the errors will not show, yet for other work to be connected to that in progress, it may lead to serious errors. For railroad purposes the land is usually found in long narrow strips of varying width ; and it is sufficient to find the length* on the centre line, and directions of bounding lines which cross ; it is however, desirable to have all "land lines" within four or five hundred feet of the track, and this requires measurements on the crossing lines. In getting the direction of a fence, when the instru- 60 ENGINEERING FIELD WORK. ment is placed at one side, measure the distance from the instru- ment to the fence at right angles to it and have a similar " offset" made as far as possible from the instrument ; of course the main iine should have been run and the transit placed in the line before the direction can be obtained. For street surveying the best method is that of a line in the mid- dle, with offsets and measurements connecting, the offsets at the end as well as the line run. In very crowded streets we have some- times run a line down each footwalk, connected them carefully at- their ends, and then proceeded as described for a single line. CAREFUL NOTES In all work of this kind the most important thing is to take good notes ; always put these down as if you expected to die before morning, and wanted to leave them in such good condition that in ten years time a stranger with no previous acquaintance, and with no one of the old party to help him, could take your book and proceed on the job without delay ; if this can be done, your notes must be about right, but you never will have them too complete. We have never used any but the "sketch system " for taking notes, and we always made them in the field, and copied them over on the next page in ink, thus keeping the rough set with the original figures, and the finished set to explain them; the original figures have more weight as evidence, but the explanation given by a neat ink copy is a very great help in interpreting them. For city work take all angles with the transit more than once, that is to say, "repeat them," three or four times which is enough ; the object of the " re- peating " being to check the angle and not to subdivide the vernier reading. PRESERVING THE LINES After the completion of the land survey comes the actual field work preparatory to the construction, and here it is customary to reduce the number of men in the party and to begin to " cut down expenses " in the engineering department. The first thing to be done is to " preserve " the line, that is, to con- nect all tangent points with stakes that are away from the line and far enough from it not to be disturbed by the operations of grading" and earthwork ; at the same time the slope stakes should be set and marked with the cut and fill also the cut or fill should be marked on the centre stakes this work can all be done on the same job, and. CENTEES AND GRADES-QUALIFICATION. ETC. 61 thus the contractors can make a start at once if they so wish ; of course a record of all Held work is required, and the results should all be put in the grade book. For setting slope stakes the only sat- isfactory method is with the Leveling instrument, though for com- paratively smooth ground and light work, there are various devices for setting slopes which involve much less work, and are sufficiently accurate for use. CENTRES AND GRADES. Most of the work for railroads in construction consists in setting " centres " and " grades ;" for the former, in nine cases out of ten, the line can be run in without an instrument, if the known points are convenient ; the Tangent Deflections are useful for running curves with only the chain and rods for lining ; for approximation there is a very convenient method of computing angles and distances (measured as arcs) which it is well to be familiar with in the absence of all "pocket-books." At one hundred feet distance three-hun- dredths of one foot subtends one minute of arc. Strictly speaking it is twenty-nine one thousandths instead of three one hundredths. At the same distance one foot and three-quarters subtends one degree of arc, but one and eight-tenths can generally be used. With this once fixed firmly in the mind, mental computations can be made with the greatest ease. As an example of this let it be required to find Tangent and Chord Deflection for 100 feet chord, and for 60 feet chord, and ordinate at centre of 100 feet chord for a 5 curve : 5X1.8 =9.00 for the Chord Deflection, and 45' for the Tangent Deflection 100 feet chord: 4.5X0.6=2.7' 2.7X0.6.=1.62 Tangent Deflection for the 60 feet chord, and ^ of the Tangent Deflection for 100 feet chord =!' for the middle ordinate. These values are all in excess, and if the deflections are to be used for running the curve more than one station, the value lf'X5=8f should be used, and this is in error only about f of an inch. A great many other computations may be thus performed mentally, and the work already done checked by these approximations, and the real blunders found. QUALIFICATIONS FOR LEADER. There are many ways of doing most kinds of field work, and many methods are described in the books under various heads but a good knowledge of geometry and trigonometry, and possibly a little familiarity with analytic geometry, combined with a cool head, and an appreciation of the external circumstances, will en- 62 ENGINEEKING FIELD WOKK. able a man, after a limited experience, to become competent to take charge of a party in the field, as far as the mere theory of the operations is concerned but a knowledge of human nature and sound judgment are required to give satisfactory results. CULVERTS AND MASONRY. We would say a word about the staking out of culverts and masonry, and will begin with a hint about box culverts. On ma- sonry of this class it is well to put in four stakes on the lines of the face of each wall, one at each end of each line, and two stakes, one on each end of a line terminating the culvert at the proper distance out, found as in slope stakes. These stakes must all be placed outside of the trenches, and should be at such a distance from the work that they will be safe during the construc- tion. BRIDGE ABUTMENTS. Bridge abutments on shore can be given in the same way, and if in the water by parallel lines, or sighting frames made out of strips of wood. Piers can be located by sights on shore, or as they are commonly termed "ranges." EARTHWORK MEASUREMENT. If earthwork is to be measured in a "borrow pit," the best way is to run out two sets of lines at right angles over the ground, denoting distances in one direction by letters, and in the other direction by numbers, and taking the levels all over the ground denoting the stake by both letter and number, and then every month as the work is done, these stakes can be replaced and the levels taken again. The bounding lines of this system should be carefully put in, and the stakes may have permanent " sights " put up over them ; in this case the stakes of the system can be replaced without a transit. Of course the bounding lines should be wholly outside the work and there can be little trouble in taking care of the work in this way. RETAINING WALLS. Retaining walls are very usually set out by stakes, but "sighting frames " outside the wall and in line with it are to be prepared, if the height is not too great. TUNNELS RESPONSIBILITY OF AN ENGINEER. 63 TUNNELS. Underground work in tunnels is usually kept in line and grade by points on the roof ; their stability and permanence are much greater than if given on the bottom of the tunnel. In rock work where stakes can not be used, chisel marks are made to serve as points. Such work requires less frequent attention, but is more important. RESPONSIBILITY OF ENGINEER. And now in closing, let us add a word as to the responsibility resting upon the engineer when setting out work. Few beginners appreciate the necessity for correct work, and do not realize that a blunder undetected may cause a loss to the con- tractor of a great deal of money, and that if he, as the company's authorized agent, makes a mistake in his work, the company may become liable for many times his salary, and that his discharge is a very small amelioration of matters which he has mixed. Pecuni- ary responsibility must be fully appreciated in order to have accurate work done. Mistakes in wor,k are not only discreditable but they are dishon- orable, and to the feelings of the suffering party they seem crimi- nal. Now as man is liable to error, work must always be in some way checked, and a mistake which is discovered by the maker in- time to be rectified by him before any damage is done is in no way discreditable, provided however that it does not happen too often, and that the same class of mistake is not made the second time. Nothing gives a contractor less respect for the engineer than finding his mistakes, even if they have caused no damage, ENGINEERING FIELD WORK. STAKING OUT. "What is that, mother?" 'The Rodman, my child. His footsteps are weary, his accents are wild; His hair, how disordered! his eyeballs, how blear! And see where his necktie hangs under his ear." "Rod up there! Hold her steady! ! Go on down the hill ! ! ! 7.8. Cut 2.2 No, begosh it's a fill, Half the roadbed; 13 + the slope 1.1; No, it's 1| though, as sure as a gun. Well, that makes let's see O! stick her in there. It'll do. Perhaps the contractor will swear. But no difference: We're the big dog in this fight. No matter what's wrong, just swear it's all right. A contractor don't know a beefsteak from a bone. Now pick up your tools, and let's pull out for home." J. H. K. B., Laurel Hill Swamp Angel. From the S. P. R. R. Transit, CHAPTER III. REGULATIONS FOR THE ENGINEERING DEPARTMENT DURING CONSTRUCTION.* BY WM. F. SHUNK, C. E. I. ORGANIZATION. 1. The chief engineer will have exclusive control of this department. 2. He may be aided by a consulting engineer, without executive pow- ers, and an associate engineer, acting under his immediate direction, to whom all official communications from subordinates should be addressed, and whose orders concerning the work, or matters thereto appertaining, shall be received as authoritative. 3. The associate engineer shall be aided by such a staff of division en- gineers, principal assistant engineers, draughtsmen, clerks, and other helpers as shall be approved by the chief engineer. 4. Each division engineer shall have charge of the construction of about thirty miles of road, in sections approximating one mile long and subdi- visions composed of from six to ten sections. 5. Principal assistant engineers may be appointed to special charges, such as important structures, the compilation of records, the preparation of plans and the like. Where such charges fall within the territorial limits of a division engineer, strict definition of responsibility will be made and hearty co-operation expected. * South Pennsylvafiia R.R. 66 ORGANIZATION-PREPARATORY WORK. 6. Division engineers shall have power to employ one draughtsman for the division headquarters office, and such resident engineer, inspectors, time keepers, and other helpers on the line of road as may be necessary for the proper conduct of the work for which they are immediately re- sponsible, subject beforehand to the approval of the associate engineer ; and to suspend or discharge such employes for sufficipnt causa The power of removal should be exercised discreetly, and seldom without reference to the associate engineer. 7. Each resident engineer shall be aided by one rodman, competent to use transit and level, two tapernen, and one axeman, until the line is cross sectioned. Thereafter one tapeman may be dispensed with. Special as- signments of force will be made, when necessary, to divisions which in- clude large tunnels. Each resident engineer shall have power to appoint, suspend or remove his own subordinates, subject to the approval of the division engineer. 8. Good discipline and orderly management require that all official communications, verbal or written, shall pass from the superior to his im- mediate subordinate, or from the subordinate to his immediate superior. Should any emergency necessitate a deviation from this rule, the party intermediately concerned should be informed of it. II. PREPARATORY WORK. 1. First of all, division engineers shall cause the centre line of location on their respective divisions to be accurately retraced, established and test leveled. 2. This done, they shall furnish promptly to the associate engineer a map in duplicate of their respective divisions, scale four hundred feet to an inch, one copy to be on mounted drawing paper, the other on tracing linen, showing the centre line and proposed right-of-way boundaries in red; intersected and adjacent property lines with names of owners, political boundaries, contours, streams, roads, woodland, buildings, and other ob- jects proper to a working map, in black; also a profile, similarly duplica- ted, to "Plate A" scale, upon which shall be marked the estimated quan- tities in each cut and fill, the character of the material, the alignment corresponding to map, and the proposed grade line, the latter to be pen- ciled on the paper duplicate and drawn very finely on the tracing in red, with its rates per centum and elevations of change points clearly figured. 3. The paper copy of each of said duplicates will be returned, with PREPARATORY WORK. 67 such alterations as the chief engineer may think proper to make or approve, and endorsed with his approval, or that of his associate, to the division engineer, who shall place them on file in his office. 4. Thereafter no change of line or grade will be permitted, excepting upon compliance with the like form of procedure, namely: The submis- sion of duplicate drawings of the change proposed, and the return of copies approved by the chief engineer or his associate. 5. Division engineers shall cause to be prepared for each of their Residents copies, from the foregoing approved map and profile, of the respective subdivisions, and also a pencil record of location, in the fol- lowing form, to be called the "Location Record, Div. No. . , Subdiv.' No. Sta. Deflec. Align- ment. Mag. Course. Gradient. ELEVATION. Cross Sections. Remarks. Ground. Grade. 6. In the station column, transit points should be marked with a circle, as usual, and turning points inclosed with a triangle in addition to the circle. Directly below every turning point record the note should be made, "B. S. to . . . ." indicating the backsight point; and in the deflection column should be recorded the total deflection, at each turning point, from the range of backsight to that of foresight. By means of such a record the line can in future be retraced, not only over the same points, but, failing one or more of them, with the same angles used on the establishment of location. 7. The alignment column must show the calculated course and the length of each tangent, thus; N. 64 35'. W. 3,972 feet; and the degree, length, angle, and apex distance of each curve, thus: 5 C. R. (or L.) 650 ft.; angle, 32 30'; A. D. 334 feet. 8. The column of remarks should contain notes of benches, land, stream, timber, and road lines, and other matters of interest relating to the line or the work to be constructed. The cross-section columns should be reserved. Stations should be entered on every third line of the book only, thereby recording about eight hundred feet per page, to pro- vide for subsequent additions. 9. The original book from which the copies are made, should be re- tained by the division engineer. 68 RIGHT OF WAY. HI. RIGHT OF WAY. 1. Division engineers shall next cause the necessary surveys for right-of-way to be made, and maps thereof to be prepared on "Topo- graphy" paper, scale two hundred feet to an inch, slewing the plan of land to be taken, the contents of severalties in acres and hundredth^, the Township, County and State wherein situated, owners' names, road crossings, streams, buildings, woodland, meridian line, and other objects needful or useful in such an exhibit. 2. These maps shall be consecutively numbered, and shall have a blank margin two inches wide on the left edge, that they may be bound in volumes for the Company's archives. When more than one property is represented on a sheet, the severalties shall be designated by the sheet number and an annex letter, "a," "6," etc. 3. Division engineers shall furnish to the land agent appointed by the Company, when requested by him, a tracing from these maps num- bered and sub-lettered to correspond with the original, together with a description of each property, for incorporation with the deeds. 4. Currently with the purchase of right-of-way, or as soon thereafter as more important service shall permit, division en- gineers shall cause the boundaries of the Company's property to be marked by corner and line stones, or other endurable monuments. This should be done before ground is broken, if possible, and said monu- ments should be carefully maintained during the progress of construction. 5. Division engineers, in laying out proposed land purchases on the maps, prescribed in (TI.,2,) should provide amply for station grounds extra tracks, borrow pits, and spoil banks, and call attention thereto by explanatory notes on said maps. 6. The lay-out shall be for a double-track railroad, tracks thirteen feet between centres. Sixty feet shall be the minimum width taken in any case, without the express approval of the chief engineer or his associate ; and as a general rule, a berm twelve feet wide on each side of the road formation shall be included in the Company's right- of-way. 7. The Company's boundary line shall generally be parallel to the centre line of the railroad, and right-of-way widths shall change by jogs square to said centre line, excepting at the bounds of severalties, where changes of width should be located, whenever convenient, and conform- ably to existing land lines. FINAL PREPARATIONS FOR CONSTRUCTION. 69 IV. FINAL PREPARATIONS FOR CONSTRUCTION. 1. The centre line having been established and test-leveled, agreeably to (II., l,)it should now be gone over with the level very carefully, setting stakes at "grade" points and at changes of surface necessitating additional cross-sections, marking the variations on the backs of centre stakes, noting the elevations of roads, stream beds and high water lines, and making new bench marks at intervals of about one thousand feet, preferably near the sites of structures and heavy cuts, where most needed, and out of the way of probable disturbance. 2. Then traverse the line again with the transit, over the old points and with the same deflections recorded on the establishment of the loca- tion if found correct, trueing the interpolated stakes last set by level, and placing and referencing centre plugs at "grade" points, grade summits, and wherever else they are likely to be convenient during construction. 3. Any discrepancies in line or level with former work, discovered during these operations, should be reported immediately to the division engineer. 4. Slope staking follows next in order. Division engineers shall personally ascertain the probable character of the material in excavations, boring or sinking test pits when, in their judgment, the importance of such knowledge warrants it ; and they will instruct their subordinates as to the formation slopes to be adopted in every questionable case. 5. In addition to setting the usual grade and slope stakes, the ground should be cross-sectioned a sufficient width to provide for possible slips, 1'urther changes of slope, or a four-track road. Stakes or plugs should be firmly driven at these limit points of observation, whether the work be in cut or fill, in range crosswise with the centre and slope stakes, which should always be placed at right angles to the road axis, their distance from centre line and elevations as to grade being noted for record, and for use if needed subsequently. They may prove to be very convenient, during construction at cuts through uncertain material, and when measuring for estimates. 6. On hillsides where the road bed is partly in excavation and partly in embankment, its dimensions shall be compounded of those given in the standard drawings for excavation and embank- ment, 7. Borrow pits, grading at stations, ditches, and all other incidental 70 STRUCTURE PLANS. excavations, should be staked and recorded with the same exactness as the road formation. They should be worked in a regular manner, so as to be readily measured, and present a shapely appearance after com- pletion. 8. Masses of rock found in cuts and isolated from the slopes should be measured and recorded in the proper books and shown in the cross-section drawings. 9. The accurate establishment and subsequent protection of tunnel lines should claim the early personal attention of division engineers. They will be duly authorized by the chief engineer to acquire the temporary use of ground for observatories and guide lines outside the Company's right-of-way, when expedient to do so. 10. The alignment and levels at tunnel sites should be retraced and re- peated until the possibility of error is reduced to an unimportant mini- mum. Such work is best done early in the day, while the air is equable ani free from refractory currents. 11. Resident engineers shall personally attend to the staking of all found- ation pits. Before masonry is started, the division engineer should inspect such pits, and assure himself by sounding or otherwise, that they are of sufficient depth and firmness. When judged prudent, the bottom earth should be compacted with rammers. 12. Currently with the foregoing operations, the location record, pre- scribed in (II., 5,) should be perfected by the addition of the cross-section notes, and the latter line and level notes, and all permanently entered in ink. 13. Division engineers should traverse their charges weekly. Resident engineers should be constantly on the line by day, excepting when foul weather or important office work prevents. They should give grade and line weekly, and whenever asked by contractors. They are thus in the way of correcting errors at the outset, of instructing foremen seasonably to prevent errors, and of ascertaining the various character of material for estimates, to the furtherance of the work and the due service of the contractors, who should not have reasonable ground for dissatisfaction with this department. V. STRUCTURE PLANS. i. The chief engineer will cause standard drawings o f the road forma- tion and ordinary structures to be furnished to each division office. Di- FIELD AND OFFICE RECORDS. 71 vision engineers shall supply duplicates of these drawings to their resident engineers, as needed. 2. Division engineers shall cause necessary modi Ications to be made in masonry plans to adapt them to various localities, altering the flare or length of wing wall, for example, to fit irregular ground, skewing for oblique channels or roads, sizing for heights intermediate to those pro- vided for in the standards, and the like ; but the elevations and square widths of bridge seats shall not be altered except by warrant from the chief engineer or his associate. 3. Special instructions will be given as to structures on steep in- clines and skew openings sharper than forty-five degrees from the centre line. 4. Plans modified by division engineers, and also the standard struc- tures which they propose as being anywhere suitable, shall have the approval of the chief engineer or his associate before the work is laid out. 5. Where special structures are required, such as viaducts, large bridges, or other exceptional work, not provided for in the standard plans, the division engineer shall cause the ground to be surveyed and mapped to five feet contours ; scale, ten feet to an inch, with correspond- ing profile, and submit the same, accompanied by illustrative notes and such suggestions as he may think proper to add, to the associate engineer, who will, thereupon, cause a plan to be made, or give orders for its making to the division engineer. Exhibits of this kind should include high and low water marks, character of bottom or sub-soil, and, in the cases of road-crossings, a profile of the same for five hundred feet each way. 6. All plans of railroad buildings shall originate at the central office, and copies thereof will be furnished by the chief engineer or his associate, with suitable instructions, to the division or principal assistant engineer charged with their erection. 7. Copies of all plans prepared by division engineers for their residents shall be preserved in the division office. VI. FIELD AND OFFICE RECORDS. 1. Resident engineers fchall prepare a series of cross-section drawings, including the tunnels, of their respective subdivisions, in bound books of uniform size furnished for that purpose, showing the original surface of 72 FIELD AND OFFICE RECORDS. the ground as widely as observations extend, the slope staking for road formation, the staking for incidental excavations, the proposed formation lines, and the computed quantities before grading, in India ink; copies, or written abstracts, of which cross-sections they shall transmit to the divis- ion engineer from time to time as they are made, marked with the name of the division and other distinguishing particulars. 2. On completion of each road-section the resident engineer shall amend and perfect his original cross-section book by drawing thereon, in permanent red, the actual formation as completed, showing the parting lines between various classes of material, and the actual quantities of said various classes as contained in the final estimate of the graduation of said road-section; together with a statement of the cost of said graduation to the contractors and the Company, which amendments the division engi- neer shall thereupon cause to be incorporated in his own copies of the cross-sections, after revision by him, and shall, when requested, or on the completion of the work, transmit the originals to the associate engineer, endorsed with his approval. 3. The statement of cost to the contractor should comprise, as nearly as can be ascertained, the value per item, and the amount of labor, material, use of tools and machinery, superintendence and sundries, distributed and assigned in such detail as information on hand shall war- rant. The statement of cost to the Company should be a summary of the final estimate. 4. The cross-section books will be paged with consecutive numbers; no erasures shall be made in them, nor shall any leaf be removed therefrom for any cause whatsoever. If errors occur cancel the page in such manner as not to obscure the errors, and use the next page. 5. Resident engineers shall also prepare a series of masonry drawings, on white paper sheets of uniform size furnished for the purpose, in which all such structures, including drain pipes, shall be represented on a scale of four feet to the inch, or eight feet to the inch, as the division engineer may prescribe for structures of various magnitude. Such drawings shall show the said structures in plan, elevation, and section as actually built, inclusive of foundations, foundation pits, substructure if any, grade line, and elevations of leading details. There shall be also a legend on the drawings of each separate structure, stating clearly the actual quantities of the various classes of work included in the final estimate, and a sum- mary, such as is prescribed for graduation, of the actual cost to the con- tractors and to the Company. FIELD AND OFFICE RECORDS. 73 6. On the completion of each subdivision said cross-section, tunnel and masonry drawings shall be transmitted to the division engineer, and by him, when so requested, after correction therefrom of the copies on his files, transmitted, with his approval affixed, to the associate engineer. 7. Each drawing of the two sets described above shall be exactly local- ized, in its title, with the name of the division, subdivison, section, sta- tion and plus. 8. Each division engineer, at or before the time of transmitting his first monthly estimate, shall send to the associate engineer a complete profile, on mounted "Plate A," paper, of his division, showing align- ments, gradients, and other full details as finally established for construc- tion. 9. Then, and thereafter with each monthly estimate, he shall forward to the associate engineer tracing exhibits, or written memoranda, indi- cating the condition of the work at the date of said estimate, from his progress profile, in order that the progress profile in the central office may be supplemented to match. 10. All progress profiles shall represent the work done during each month in transparent washes of color, as follows: January .......... Carmine. July, ............ Scarlet. February ......... Green. August .......... Dark Green. March ............ Yellow. September ....... Orange. April ............. Cobali Blue. October .......... Purple. May, .............. Burnt Sienna. November ...... Burnt Umber. June ....... ...... Black. December. 11. Division engineer shall cause to be prepared, on mounted white roll paper, a complete map and profile of his division, horizontal scale four hundred feet, vertical scale forty feet to an inch, both on the same sheet, showing the centre line, grade line, and land lines. of the road in red, streams in blue, brick and frame buildings in carmine and burnt sienna respectively, faintly colored; all other details in India ink, with ten feet contours finely drawn, each even hundred slightly heavied, and the outer limits of road formation that is to say, the crests of cuts and the toes of fills indicated in plan by dotted lines. This document to lie on the stocks in the division office, gradually perfecting, and finally in- cluding all the company's lands and buildings, together with such sup- plemental plans, to larger scales, as the chief engineer shall order, of town properties or particular reaches of the road, whereupon it shall be filed FIELD AND OFFICE RECORDS. in the central office as a permanent record. The above map should em- brace, if possible, all the topography obtained during the surveys within one mile on each side of the located line, and should be neatly and accurately executed. 12. Each division engineer, contemporaneously with the foregoing map and profile, shall cause to be prepared a complete record and description, by sections, of the finished roadway on his division, after the following general form, to be furnished from the central office : Div. No , Sec. No RT. OB ELEVT. S CROSS GRADUATION C. Y. WAY. ^ . SECTIONS. 4J "a -d a a .2 l X A n . d a 4 00 .2 Q Q 5 g L. R. 2 o g o 1 CJ S L. C. R. ) We are now ready to stake out the switch or turnout. Two cases may occur : 1st. The location of the switch throw may be fixed. 2d. The location of the frog in the track may be fixed. In the first case the position of the switch throw being fixed, we will drive a hub with nail in the center (v) of the proposed turnout opposite the switch throw, determining its position by measuring from the rail one- half the gauge of the track plus the throw of the switch, which last we will consider to be 5 ins Tneoretically, this should be measured at right angles to the position of the switch rail in the j, _ turnout ; but, practically, it can be measured JP^>^ c M ain T rac i, at right angles to the rails of the main track. Mark a point (D) on the inside of the rail of the main track opposite this for t'le end of the switch rail, and measure back on the iron the length chosen for the switch rail, and mark a point (A) on the inside of the rail for the heel of the switch rail. The length of the switch rail is generally 20 or 22 ft., but this may be varied to 96 TOPOGRAPHY AND STAKING-OUT PROBLEMS. save cutting the iron. Short switch rails are more easily worked and are safer, but less than 18 ft. is objectionable, as not apt to make a smooth running curve and liable to jar the train. We now measure off the chord (BF), which we have previously found by computation from the throat of the switch, and .42 of afoot from the inside of the rail of the main track, swinging: in the dist. (BF) to such a point (F) as it will touch the inside edge of the rail of the main track. This gives the position of the point of the frog in the track, which we mark on the rail. The section master will set the frog in the track at this point without further marking. We now set up the transit on the hub at x and lay off the curve of the turnout the radius of which we have already computed by setting stakes in the center line every 12 ft., using a parallel to the switch rail in its position in the turnout, for tangent and deflecting as usual. We know the radius of the turnout, and we can consequently compute the ordinate for bending the rails by the formula on page 14 of Henck, Jf m = , in which m equals the ordinate required in decimals of a foot, 2R and I equals the length of the rail used. It can also be taken from Table I. (ibid). The angle S which the switch rail makes with main track is easily computed, as we know or assume the length of the switch rail and the d throw of the same, and therefore sin. S = . I The frog angle F is known or easily found by measuring the frog, and computing, or by taking a paper pattern of the point angle and applying a protractor. In the second case, where the point of the frog is fixed in the main track, we have to locate the switch throw from this point by measuring back the chord BFto a point B, 0.42 ft. from the main track rail. In the case of a switch with a double throw, where two turnouts leave the main track from the same point, it is well to paint the stakes of each turnout a different color, to avoid confusing the trackmen. We have supposed the main track to be on a straight line. If the turn- out is from a curve the problem is more complicated, but it can easily be solved by prob. 57, page 38, Henck. As a check upon the somewhat long computation required when the turnout is from the inside of a curve I have sometimes adopted the fol- STAKING OUT SWITCHES. 97 lowing mechanical method of obtaining the position of the point of the frog and the frog angle : I set up the transit on the switch throw at B and lay out the outer rail of the turnout by deflection angles to any assumed radius, finding the point of the frog by repeated trials of deflection, and then measuring the frog angle by means of a light board with a nail driven through it at the point of the frog. This nail in the board is set over the point of the frog when found, and a pattern of the frog angle made on it by means of de- flections with the transit, to establish the curve on the board. From this curve the tangent T at F is laid off and the frog angles measured with a protractor, or otherwise. This method uses the rad. for the outer rail only, and saves computa- tion for the frog angle and position. The method I have described makes the turnout curves tangent to the switch rail, and consequently compounds the curve from B to A. This is no practical detriment, for generally the difference in radius is very slight, between the radius of the switch rail and the rest of the turnout, which is more than overcome by the manipulations of the trackmen. S">me engineers, however, prefer to make the curve tangent at the heel of the switch rail A. In that case the throw of the switch rail must sometimes be slightly changed (only a slight change is admissible with ordinary iron) or the length of the switch rail must be changed. But for safety in traffic the length of the switch rail should not be much in- creased, and if diminished nothing is gained. Engineering News, Sept. 9, 1892. 93 TOPOGRAPHY, AND STAKING-OUT PROBLEMS. METRIC RAILWAY CURVES. [Fom 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 Trautvvine and Shunk the " tangential " angle ; by Henck and Searles the "deflection" angle. In 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 ex- 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 an le 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. 99 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 100 TOPOGRAPHY, AND STAKING-OUT PROBLEMS. Quarter S. t, IB ** 2 Middle. point. ttS 2 '33-3 & g ORDINATE f 3 g RADIUS a at distance g j) IN a trom end-cnord. "" K-B M S a S METKRS '- tit From tan- From chord. Of 10 Of 5m. fcfl o i 3 gent. m. s 010' OJ' 3437.75 3.5362745 .058 .116 .Olo .011 10.0000 20' i' 1718.38 3.235246:5 .116 .233 .029 .022 10.0001 30' i^j' 1145.93,3.0591581 .175 .349 .044 .033 10.0004 40' 2' 859.462.9342237 .233 .465 .058 .044 10.0002 50' 2*' 687.57 2.8373192 .291 .582 .073 .055 10.0004 ! 0' 3' 572.99 2.7581447 .349 .698 .087 .065 10.0005 10' 3^' 491.14 2.6912059 .407 .814 .102 .076 10.0007 20' 4' 429.762.6332231 .405 .931 .116 .087 10.0.00 30' 4Jr' 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' lOVij' 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 54' 118.68 2.0743911 1.687 3.370 .422 .317 10.0119 5 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 100183 20' 19' 90.65 1.9573751 2.210 4.413 .553 .415 10.0204 40' 20' 86.14 1.9351943 2.326 4.644 .582 .437 10.0226 7 0' 21' 82.06 1.9141055 2.442 4.875 .612 .459 10.0249 20' 22' 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 1.85644i7 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 10.0382 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 6.7l7 .846 .635 10.0476 10 0' 30' 57.59 1.7603298 3.486 6.946 .875 .657 10.0510 METRIC RAILWAY CURVES. 101 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, showingthat 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 86.14 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 1" 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 mefc.-s 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; 102 TOPOGRAPHY, AND STAKING-OUT PROBLEMS. for 100 ft. is very little more than 3 dekameters. For instance, the curve last spoken of , having a radius of 80.14 m. and designated by the angle of 6f , is almost the same as the American curve of 20 , or 3 X 6f. The number of 20 is given in the metric table in the column of minutes to be laid off per meter in staking out, as belonging to the curve of 86.14m. radius; and all of the numbers in that column, instead of being read as minutes, might be regarded as the "degrees" designating American curves, in which case the corresponding figures of radii would be nearly the true value of meters of the radii of those American curves. CHAPTER V. Transition or Easement Curves. Professor Arthur N. Talbot, of the University of Illinois, Champaign, 111., has published a valuable paper on easement curves in The Technograph, 1890-91, from which we quote as follows : THE TAPERING CURVE. The Tapering Curve is a compound curve consisting of a series of cir- cular curves of the same length, whose degree-of-curve increases by some constant difference up to the degree of the main curve. Thus, if the taper is 1 for each 30 feet, the approach from a tangent to a 6 curve will be made by 30 feet of 1 curve, 30 feet of 2 curve, 30 feet of 3 curve, 30 feet of 4 curve, and 30 feet of 5" curve, after which the 6 curve is run in. If the degree of the main curve is not a multiple of the common dif- ference of the tapers, at the end of the last full chord a fractional chord is used, proportional to the difference of the degree of the main curve and last taper. Thus, for a taper of 2 30' per 30 feet, an 8 curve would be reached by 30 feet of 2 30' and 30 feet of 5 curve, ending with 6 feet of 7 30' curve; since 8 is in excess of 7 30' by one-fifth of the change 2-30', one-fifth of a full chord is used. In order to run the curve with the transit at the beginning of the taper- ing curve or at some corresponding point thus saving settling at each P. C. C. a table giving deflection angles to the different P. C. C.'s is used. The tapering curve was introduced by Mr. William Hood, Chief En- gineer of the Southern Pacific Railway, and has been extensively used on the Southern Pacific, Northern Pacific, Missouri Pacific, and other western roads. It makes a good transition curve, and does not vary much from the transition spiral. However, it lacks flexibility, this property being secured only by a wide range of tapers, necessitating many tables. 104 TRANSITION OR EASEMENT CURVES, THE RAILROAD SPIRAL. The Railroad Spiral, as developed by Win. H. Searles, C. 13., is a multi- form compound curve, differing from the tapering curve by using the central angles of the successive arcs as constant quantities, and varying the length of arc or chord to secure different spirals. The first arc has 10' central angle, the second 20', the third 30', and so on to the end of the transition curve. Mr. Searles has published a little hand-book of tables and explanations for this curve. Tables of deflection angles with the transit at any chord point are given. These deflections are constant what- ever the chord length. Thus, the deflection to the end of the 8th chord is 2 07', whether the length of curve be 8 X 10 feet or 8 X 21 feet, and the central angle subtended will also be the same. However, the degree-of- curve of the arcs will vary with a change in length of chord. This ne- cessitates a set of tables giving the degree-of -curve for the last chord in the curve. As this is not an integral number, the one nearest the degree of the main curve is chosen. This is allowable, since it consists in com- pounding the last arc with the main curve. As several chord lengths with the corresponding number of chords will give about the same degree-of- curve, a variety of spirals for any main curve is secured. About sixty tables are given in Searles' " The Railroad Spiral," to which the student is referred for further information. The " railroad spiral " approaches very near the true transition spiral. With the tables given, the calculations and field work are simple and rapid. Deflections for points between the chord points are found by in- terpolating hi the tables, but only chord points may be used as transit- points. An objection has been made that the degree-of -curve for any chord is not an integral multiple of the number of the chord. This, how- ever, is not of great importance. THE PENNSYLVANIA METHOD. The Pennsylvania Railroad uses 200 ft. of 30 curve at the ends of a simple curve. For sharp curves 100 ft. of 1^ curve is put in at either end. The super-elevation begins with zero at the P. C., and increases uniformly to the full amount at the beginning of the main curve. The claim is made that in this manner the complete super-elevation is attained while the car is on a light curve where the wheels keep to the outer rail, and that the shock incident to gaining the super-elevation while on the tangent is avoided. Of course the field work is simple. It is claimed that this method is very efficient, but it is open to criticism. THE TRANSITION SPIRAL. 105 THE TRANSITION SPIRAL. The Transition Spiral is a curve whose degree-of-curve increases directly as the distance along the curve from the point of curvature. Thus, if the spiral is to change at the rate of 10 per 100 feet, at 10 feet from the beginning of the spiral the curvature will be the same as that of a 1 curve; at 25 feet, as of a 2 30' curve; at 60 feet, as of a 6 curve. Like- wise, at 60 feet, the spiral may be compounded with a 6 curve; at 80 feet, with an 8 curve, etc. This curve fulfills the requirements for a transition curve. Its curva- ture increases at the distance measured around the curve. The formulas for its use are comparatively simple and easy. The field work and the computations necessary in laying it out and connecting it with circular curves are neither long nor complicated, and are similar to those for sim- ple circular curves. The curve is extremely flexible, and may easily be adapted to the requirements of varied problems. The rate of change of degree-of-curve may be made any desirable amount according to the max- imum curve used, or according to the requirements of the ground. [For the formulas and tables deduced by Professor Talbot for the transi- tion spiral we refer to the Tei-hnograph, 1890-91.] When simple curves are left without transition curves, many track-men 'ease "the curve by throwing the P. C. inward a short distance and gradually approaching the tangent a few rail-lengths away, while the main curve is reached finally by sharpening the curve for a short dis- tance. Even this is better than no easement -curve. The objection is sometimes raised that even if track is laid out with a carefully fitted spiral there would be no possibility of keeping it in place by the methods of the ordinary track-man. This identical objection could be made with the same force against carefully laid out circular curves, yet no engineer would recommend abolishing that practice. Even if, in re-lining, the transition curve is considerably distorted, it remains an easement, and will be in far better riding condition than a distorted circular curve. By marking the P. S. and the P. C. C. with a stake or post, with possibly on long spirals an intermediate point, the track-man will be able to keep the spiral in as good condition as though ic were of uniform curvature. Properly constructed spirals would frequently allow the use of sharper curvature since the riding quality of curves may be the governing con- sideration in the selection of a maximum and thus make a savins- 'n construction. By fitting curves with proper transition spirals, roads 106 TRANSITION OR EASEMENT CURVES. using sharp curves may partially relieve the objection of the public to traveling by their routes. The transition curve has, then, a financial value largely overbalancing its cost. The adoption of such curves by many of our principal railways proves their efficiency, and the future will see a much more general adoption. LOCATION OF THE CUBIC PARABOLA. By Professor Fred P. S aiding, Cornell University. The necessity for using some form of easement curve, to connect the circular arcs upon railroad lines with the tangents, is now very generally recognized. Their adoption, however, has been greatly retarded by the difficulty met in attempting to reduce a satisfactory curve to a convenient form for ready use in the field. Two methods of location are at present in use ; first, by Froude's for- mulas for the cubic parabola as given by Rankine, the determination of the ordinates for setting out being m vde for each curve directly from the formulas ; and second, the method of the railroad spiral as given by Searles and others, in which practically the sime curve is located by means of deflection angles corresponding to various fixed chord lengths, the curve being varied by changing the chord length. The object of this paper is to show how by a simple tabulation an ap proximation to the cubic parabola may be readily located in practice, either by ordinates or deflection angles, without the necessity of makinjr calculations from formulas for each case, but at the same time allowing the use of chords of any lengths and the placing of stations wherever desired. The formulas for this curve as given by Rankine are V = (1) and s = (2) in which s is the shift or offset B C (Fig. 1) of the circular arc from the tangent, I is the length AD (Fig. 1) of the easement curve, R is the radius of the circular arc, and y is the perpendicu- lar offset from the tangent or from the circular arc to the easement curve, at any point distant x from the junction of the easement curve with the tangent or circular arc. fy. I. LOCATION BY ORDINATES. 107 If it be desired to connect two curves of different degrees, the same form of easement curve may be employed, using only the portion of it which lies between the points where its radius of curvature equals the radii of the arcs to be connected. For this case, equation (1) applies directly, while for the value of the shift (2) becomes _ l (R, - R s ) io which .R t and R a are the radii of the circular curves. LOCATION BY ORDINATES. tn order to locate an easement curve by this method, it is necessary to assume the value of either the length or the shift and calculate the other from formula (3) or (3). The shift may be fixed by topographical con- siderations, or the length may be determined by fixing the value for the ratio of the change in rail elevation to the length, authorities differing as to the best value to use for this ratio, but probably any value above the 1 m 300 recommended by Froude will give goo I results. Having thus found the value for the shift, it is to be laid off from the tangent toward the center of the proposed curve, and the circular arc run in from a parallel tangent at that distance from the main one. In other words, in locating a line upon which easement curves are to be used, the circular curves, instead of being placed in the usual manner tangent to the straight portions of the track, should be made tangent to parallel lines at a distance s from the main tangents, and in the same way the arcs of a compound curve should not be tangent to each other at the P. C. C., but the arc of smaller radius should begin at a point on the common radial line distant s inward from the end of the larger arc. The half-length of the easement curve is then laid off from the P. C. on the circular arc, and the point D (Fig. 1) so found will be the junction of the two curves ; the half-length is also laid off on the main tangent from a point opposite the P. C. (B, Fig. 1) to find the point of tangency A (Fig. ] ) of thp easement curve. Having determined these points, different values of a? less than - sub- a stituted in formula (1) will give values of y to be laid off from points dis tant x from D on the circle, and from A on the tangent, to determine points on the easement curve. Tables may now be constructed on these formulas which will give di- rectly the value of the ordinates to be used in placing the curve on the ground, and as experience has shown that comparatively few variations 108 TRANSITION OR EASEMENT CURVES. will be necessary to meet all cases in practice, such tables need not be very extended to answer all requirements. In order to construct such a table, suppose that the curvature is to in- crease 1 for every 50 ft. of distance, then for a 10 curve, I 500 ft. and I s s .rj-5 = 18.16 ft.; substituting these values in (1), if x 10 ft., y = a'*. R . 000581 ft. To find other values of y corresponding to different values of x, we notice that y varies as the cube of x, and thus construct the last column of Table 1. In order to extend the table to other curves in which the curvature varies differently, we notice that, combining formulas (1) and (2), y varies R as -j for x constant, or, approximately, inversely as the ratio between v length and curvature. In the table, the offset is given for every 10ft. of length. Intermediate values may be found by interpolation, without sensible error. To illustrate the use of the table in locating a curve, suppose that two tangents are to be connected by a compound curve composed of an arc of 5 and one of 8 curvature, and that the changes of radius are to be eased by curves, in which the curvature increases 1 for every 40 ft. of distance from the tangent. First the circular curves must be located as shown by the full lines (Fig. 1) with the proper shift from the tangents and from each other. For an increase of curvature of 1 in 40 ft., the length of easement curve for an 8 will be 320 ft. 1 s When x = (formula 1), y , and going into the table with x 2 2 1 s = = 160, we find y = 2.97 = , hence B C = s = 5.94 ft. In the 2 2 same way ML s = 1.46 ft. may be found for the 5. For the connec- tion between the two circular arcs, Z = the difference of lengths of the curves required to connect the two arcs with tangent = 320 200 120 s ft. and as before = .15 ft. may be taken from the table. 2 Now to locate the curve AD, suppose that the P. C. of the circular arc comes at sta. 10 + 65 and that it is desired to mark 50 ft. stations on the easement curve, these stations having first been located on the tangent AB and the arc CD. As the half-length of the easement curve is 160 ft. LOCATION BY DEFLECTION ANGLES. 109 the P.E.C., or point where the eauement curve leaves the tangent will be at sta. 9 + 05. The quantities necessary to lay out the easement curve may then be tabulated as follows, taking values of y to nearest tenth foot. Sta. 9 + 05 P. B.C. x = 0, y = 0.0, Measured from tangent. 9 + 50 a;= 45, y = 0.1, " 10 x= 95, y = 0.6, " " " 10 + 50 a; =145, y = 2.2, " 10 + 65P.<7. # = 160, = 3.0, " " 11 x = 125, y = 2.4, ' " " Curve CD. 11 + 50 x= 75, 2/ = 0.3, " " 12 x= 25, y = 0.0, " " " 12 + 25 P.O. x= 0, y = 0.0, " " " The location of this curve is thus seen to be a very simple matter ; cal- culations for the circular arcs may be made in the usual manner, and the use of the easement curve introduces no new element into their location, save the necessity of laying them tangent to lines parallel to the main tangents. The tangent distance on main tangent to P. E.G. may be found from. the formula T K = T + + t , in which T is the tangent distance for the a curve as ordinarily run, -j= the half-le h of the easement curve, and t a a correction due to shifting the point of intersection (see Fig. I). For a simple curve with the same shift at both ends t = s tan \ A- For a simple O curve with different values of s at the two ends, ,- = . 8 A s, cot A sin A and t 2 = . 1 A s 2 c t A For a compound curve, if s 3 be shift between S'tTt /\^ circular arcs, s a that of the curve of larger, and s t of the curve of smaller O I o /*/) 682.6 ft. or the rate of curvature of the new ex. sec % A .13257 arc is 8 24'. The length of easement curve to vary 1 in 30 ft. is then 252 ft., the half-length 126/tf., and (from the table) the half-shift is 1.95 or s = 3.9J which shows that our assumption of 4.0 ft. for the shift is sufficiently accurate ; in case it were not, it would be necessary to try a new one. Now from B, the 8 24' curve may be located ending at .Fand G, or the tangent distance may be computed from the formula, and the P.E.C. located after which the curve may be placed by the use of the tables as in the former cases. If it be desired to shift the vertex of the new curve any distance either outward or inward from the original curve, it will simply be necessary to subtract such distance from or add it to the external distance in finding the radius of the new curve. TABLE I. ORDINATES FOR LOCATING THE CUBIC PARABOLA. Curvature changes 1 for every Values otx. 20 feet. 25 feet. 30 feet. 35 feet. 40 feet. 45 feet. 50 feet. 10 feet. 0.00 feet. 0.00 feet. 0.00 feet. 0.00 feet. 0.00 feet. 0.00 feet. 0.00 feet. 20 0.01 0.01 0.01 0.01 " 0.01 0.00 " 0.00 " 30 0.04 0.03 0.03 0.02 " 0.02 0.02 " 0.02 " 40 0.09 0.07 0.06 0.05 " 0.05 0.04 " 0.01 " 50 0.18 0.14 0.12 0.10 . " 0.09 0.08 " 0.07 " 60 0.31 0.25 0.21 0.18 " 15 0.14 " 0.13 " 70 0.50 0.40 0.32 0.28 " 0.25 0.22 *' 0.20 " 80 0.74 0.60 0.49 0.42 ' 0.37 0.33 " 0.30 '' 90 1.06 0.85 C.70 0.60 ' 0.53 0.47 " 0.42 " 100 1.45 1.16 0.97 0.83 ' 0.73 0.65 " 0.58 " 110 1.93 1.55 1.29 1.10 ' 0.96 0.86 " 0.77 " 120 2.51 2.00 1.67 1.43 ' 1.25 1.12 " 1.00 " 130 3.19 2.50 2.13 1.83 " 1.60 1.42 " 1.28 " 140 3.98 3.20 2.66 2.29 " 2.00 1.77 " 1.60 " 150 4.90 3.92 3.27 2.80 " 2.45 2.18 " 1.96 " 160 3.39 " 2.97 2.64 " 2.38 " 170 4.08 " 3.57 3.17 " 2.85 " 180 4.81 " 4.24 3.76 " 3.38 " 190 5.69 " 4.98 " 4.43 " 3.98 " 200 6.64 " 5.81 " 5.16 " 4.64 " 210 5.98 " 5.38 " 220 6.87 " 6.19 " 230 7.85 " 7.07 " 240 8.92 " 8.03 " 250 10.09 " 9.08 " SPECIAL CASES. TABLE II. DEFLECTION FOR LOCATING THE CUBIC PARABOLA. 115 Values Curvature changes 1" for each of*. 20 feet. 25 feet. 30 feet. 35 feet. 40 feet. 45 feet 50 feet. 10 feet 00' 00' on' 00' 00' 0" 00 00' 20 " 02 02 01 01 01 01 01 30 " 05 Oi 03 03 02 02 02 40 " 08 00 05 04 04 03 03 50 " 13 10 03 07 06 06 05 60 " 18 15 12 10 09 08 07 70 " 25 20 16 14 12 11 10 80 " 32 26 21 19 16 14 13 90 " 40 32 27 23 20 18 16 100 " 50 40 33 29 25 22 20 110 " 1 48 40 34 30 27 24 120 " 00 58 48 41 36 32 29 130 " 12 1 08 56 49 42 38 34 140 " 25 18 1 05 56 49 43 39 150 " 38 30 15 1 04 56 50 J5 160 " 52 2 08 42 25 13 1 04 57 51 170 " 25 56 36 23 12 1 04 58 180 " 42 2 10 48 33 21 12 1 05 190 " 3 00 24 2 OC 43 30 20 12 200 " 5(0 40 13 54 40 29 20 210 " 40 56 27 2 06 50 38 28 220 " 4 02 3 11 41 17 2 01 47 37 230 " 25 32 56 31 12 58 46 240 " 48 50 3 12 45 24 2 08 55 250 " 5 12 4 10 28 59 36 19 2 05 30 260 " 38 52 45 3 13 49 30 15 270 " 6 05 4 03 29 3 02 42 28 280 " 32 5 14 21 44 16 54 37 290 " 7 00 36 40 4 00 30 3 07 48 300 " 7 30 6 00 5 00 17 45 20 3 00 310 " 4 34 4 00 3 33 3 12 321 " 43 16 48 25 330 " 5 11 32 4 02 38 340 " 30 49 17 51 350 " 50 5 06 32 4 05 ,360 " 24 48 19 370 " 42 5 04 34 380 " 6 01 21 49 390 " 20 38 5 04 400 " 40 55 20 410 " 6 la 0^ 420 " 32 53 430 " 41 6 10 440 " 7 10 27 450 " 30 45 460 " 7 03 470 " 22 480 " 40 490 " 8 00 600 " 20 116 TRANSITION OR EASEMENT CURVES. TABLE III. VALUES OF . Minus Correction for Tangent L istance of Easement Curve Located by Deflection Angles Degree Curvature changes 1 for each of Curve. 20 feet. 25 feet. 30 feet- 35 feet. 40 feet. 45 feet. 50 feet. 6deg. 0.1 feet. O.I feet. 01 feet. 7 0.1 feet. 0.1 feet. 0.2 " 0.2 " 03" 8 0.1 feat. 0.2 " 0.3 " 0.4 " 0.5 " 0.6 " 9 0.1 feet. 0.2 " 0.4 " 0.5 " 0.7 " 0.8 " 1.1 " 10 0.2 0.3 " 0.6 0.8 " 1.0 " 1.3 " 1.7 " 11 0.3 0.5 " 12 0.4 0.7 " 13 0.6 14 0.8 15 1.1 ELEVATION OF OUTER RAIL ON CURVES. The elevation of the outer rail is constant throughout the curve. Its theoretical amount (see ' Henck's Pocket Book ") is t -, in which g is the gauge, v is the velocity of the train, and R is the radius of the curve. poo rj If g is 4.7 and v is 40.44 or 27.57 miles per hour, this reduces to , or, if the elevation is in inches and the radius in feet, to . But this R numerator is the radius of a two-degree curve, from which the rule is deduced which is adopted on many railroads: " Elevate the outer rail one-half an inch for each degree of curve." Thus, for a two-degree curve elevate one inch, and for a six-degree curve, elevate three inches. If a circular curve starts directly from a tangent, theory requires an abrupt elevation at the point of curvature. As this, however, is impracti- cable, the elevation is usually run out on the first rail (or the first two) from the point of curvature, the rail being at the height of the elevated rail at one end, and at the height of the opposite rail at the other end. To avoid the theoretical difficulty of the sudden elevation of the outer rail, parabolic curves have been proposed, the radius of curvature at the be- ginning of the curve being so long as to be practically infinite, which would require no elevation; and as the radius became gradually shorter to the middle of the curve, the outer rail could be proportionately elevated. The additional labor involved in laying out the curves, and giving this ELEVATION OF OUTER RAIL ON CURVES. 117 variable elevation, has prevented the general introduction of parabolic curves in this country. However, the end of making the elevation pro- portional to the curvature gradually is accomplished by putting in, at each end of the curve, what is called a " curve of adjustment" when the rails are being laid, which is an " elastic curve," and is laid out by offsets from the centre-line stakes, the latter being set on tangents and circular curves. The method of laying out the elastic curve is given in the pre- ceding pages. It seems to be the English practice to obtain the proper elevation of the outer rail by raising the outer rail one-half of the proper amount and depressing the inner rail by the same amount. In the United States, however, it is generally all put in the outer rail, the inner rail carrying the grade of the road. CHAPTER VI. Earthwork and Masonry. ESTIMATING OVERHAUL IN EARTHWORK BY MEANS OF THE PROFILE OF QUANTITIES. BY S. B. FISHER, CHIEF ENGINEER OF THE MINNEAPOLIS, ST. PAUL & SATJLT STE. MARIE RY., MINN. No facile, practical and accurate method of calculating the overhaul of earthwork is as yet in common use. The problem itself, consisting of finding the relations between the centers of gravity of known volumes in known positions may be, from the mathematician's point of view, a com- paratively simple one; but such a lack of readiness to solve it has the engineer shown that many a contract has been executed with the privi- lege of wasting and borrowing at the end of the haul. This practice results at times in waste of energy by the contractor, and still oftener in the waste of money to the other party to the contract. By the system of wasting and borrowing, material is paid for at the full price of excavation beyond the haul, but, with the judicious use of overhaul, in many cases the material may be hauled half a mile before its price is doubled. When, from the increase of the traffic of a railroad, for example, it be- comes necessary to grade for a second track, and in so doing to remove material wasted on the margin of a cut into an adjoining borrow pit along the neighboring fill, where it ought to have been deposited in the first place, it neither increases the respect of the later engineers for their pre- decessors, nor is it a credit to the profession. Overhaul as commonly worked out is done in an approximate manner with the ordinary profile and the volumes in excavation and embank- ment. It takes longer to work it out with the " Profile of Quantities," of COMPILATION OF THE DATA. 119 which a short example is engraved, but it is done completely and accu- rately. The method of the profile of quantities was originated by Bruckner, a Bavarian engineer. It was presented by Cuhlman in bis " Graphical Stat- ics " in 1868, and translated from that by F. Reineker, then (1871-3) Principal Assistant Engineer of the Pennsylvania Co , at Pittsburg, Pa , for the use of his department. This translation was procured there by the writer, and the method adapted to American practice in a great variety of railway work, and is here given with an example of work as actually executed. The subject is presented, for convenience and clearness, in three steps 1st. The Compilation of the. Data. 2d. The Plotting of the Profile. 3d. The Taking Off of the Results. I. COMPILATION OF THE DATA. The paper containing the data is ruled in five vertical columns, as in the following sample table : SAMPLE TABLE OF COMPUTATIONS FOR CONSTRUCTING " PROFILE OF QUANTITIES " O. & S. W. R. R. data for Profile of Quantities, Section 5, Oct. 1, 1889. Sta. Incre- ments. Ordinates. Sta. Incre- ments Ordinates. Sta. Incre- ments. Ordinates . + - + - 1 2 3 4 5 6 7 8 9 240 1 2 3 4 5 6 7 8 + - + - 9 250 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 + - + - 213+34 214 5 6 7 8 9 220 1 2 3 4 5 6 7 8 9 230 'iei 328 464 493 411 367 284 221 200 180 185 156 102 59 317 83 .... 8,804 8,887 8,726 8,398 7,934 7,441 7,030 6,663 6.379 6,155 5.955 5,770 5,585 5,429 5,327 5,258 5,272 5,342 "55 156 102 146 206 237 250 274 47 83 78 65 70 124 181 189 fc5 5,425 5,503 5,568 5,638 5,762 5,943 6,132 6,217 6,052 5896 5,794 5,658 5,452 5,215 4,965 4,691 4,611 4,650 370 843 779 724 902 570 391 457 535 678 723 344 193 156 244 221 356 ' 370 1,213 1,991 2,715 3,617 4.187 4,578 5.035 5.570 6,248 6,973 7,317 7,510 7,666 7.910 s.m 8,487 .... 14 70 6 .... The first column contains the station numbers. In practice the ele- mental volume is the total excavation or embankment in a full station, whether the station distance is 100ft., 66ft., or a number of metres. 120 EARTH WORK AND MASONRY. ft E: .y^ o , the end of Teapot Kofeeson's job; E, at station 210, the dividing point between backward and forward hauls in the cut; F, station 252+30; J, junction point of forward and backward hauls in the fill; G, the point where waste commences in the second cut, and H. the end of the section. III. THE TAKING OFF TUB RESULTS. From Ato D there is no over haul, but the nature of the material and any other items can be conveniently recorded there. The fill between D and K is made from the cut between K and E. We first fix the position of the limit of haul, which here comes between stations 226 and 236, and then draw the intervening lines of over haul to each point of flexure of blue and red lines. We now read the elements of the cut between these lines of haul, from the profile m, or if we desire great accuracy, from the data prepared for plotting the profile n, and tabulate them. Each of these elements multiplied by its respective distance overhauled will give equiva- lent quantities overhauled to one station; as for example, 1,680 + 1,570 224 cy X - 1,000 = 224 X 6.25 = 1,390. The sum of these 2 partial products will give the total overhaul for the cut. The tabulation 122 EARTH WORK AND MASONRY. should always be verified, by seeing that the sum of the elements of the blue or red curve, as the case is, is equal to the difference between the ex- treme ordinates. If E K is rock or D K is a sink hole, the line E D will be inclined, and should be prolonged to an intersection with the horizontal through K. This intersection then becomes a pole, through which the lines of haul are drawn. The method is so flexible it can be applied to anything which can be executed in earthwork, and in addition gives a record of what has been done. It is also used to make the preliminary distribution of material before the woik is begun. NOTE. For the further discussion of this subject see Engineering News of April 4, 1883, and March 14, 1891. EXPANSION OF ROCK IN EMBANKMENT. The following are data of an accurate test made at Boulder, Colo., in 1882 on expansion of solid rock from cut to embankment. The point chosen offered these advantages : material all solid rock, free from an overlying earth ; surface uniform, admitting of accurate measurement ; no possible settling of the embankment, as it was directly on granite cow- pastures ; volume of the work 9,000 cubic yards in 400 ft. lengths, re- ducing wastage from blasts to a minimum, and lastly, its location being such that it was seen several times every day. Results as follows : Rock in excavation and borrow pit measured in place 3.596 yds.; the same ma- terial, measured in embankment, yielded 5,387 yds., or an expansion ratio of 1 : 1.512. NOTES ON EARTHWORK.* In making the final estimates of the St. Gothard Railroad, the quanti- ties in cut were increased by 3 in earth and 8# in rock, to equalize the amounts needed for embankments. In the levee work, under the direction of the writer, the following pro- portions were observed : 9,398 cubic yards in cut gave 9,470 in fill (ground : heavy adobe, meas- ured three weeks after finished). 10,000 cubic yards in cut gave 10,290 in fill (ground : adobe in sandy loam) 29,000 cubic yards in cut gave 30,330 in fill (ground : the same as last). 53,350 cubic yards in cut gave 58,350 in fill (ground : sandy loam with small amounts of adobe and hard pan; this is the largest increase found). * Read by the late Geo. J. Specht before the Technical Society of the Pacific Coast, May 1, 1885. NOTES ON EARTHWORK. 123 202,634 cubic yards in cut gave 208,915 in fill (this represents the work of three months). The conclusion is, that no general coefficient can be established to ex- press the proportion of earth or rock in place to earth or rock in fill. It is different with different kinds of material and with the different meth- ods of building the embankments. A. Von Kaven, President of the Royal Polytechnic Institute in Aix-la- Chapelle, says in his book on " road building" : " The volume of an embankment and its height are different at differ- ent times. 'European experience is road building is that, after the fill is finished, the earth used therein occupies a larger space than in the ground : In clay and loam 1-48 more. In soft sandstone 1-32 " In hard clay 1-20 " In rock 1-13 to 1-10 " " During the construction of the Rhine-Nahe Railroad it was observed that the increase in bulk from cut to fill was in the beginning 25 per cent, in rock, but when from one-quarter to one-third of the total bulk of the embankment was built of clay; put in simultaneously with the rock, the final increase in embankment, after the same was finished, was only 9 per cent. There are certain kinds of earth and certain conditions during the time of building, when the embankment, occupies less space than the earth measured in place. For instance, if the earth is wet, or if it is tamped, etc. The French engineer, Graeff , says that 1 cubic metre of rock measured 1.5 to 1.6 whenever in fill, but as considerable earth was used with it to fill the intermediate spaces, 1 cubic metre cut made 1 cubic metre fill in a general average. " In building the Marne-Rhine canal the loose earth was carefully tamped and 1 cubic metre embankment required 1.10 to 1.25 cubic metre in cut. He advises, therefore, not to count on any difference, but to ac- cept cut and fill alike, and allow only in very Light sand a decrease of one- tenth in fill. 'According to a series of observations " 100 cubic feet of loose sand make 115-120 cubic feet in fill. " 100 cubic feet of clay and coarse sand make 122 cubic feet in fill. " 100 cubic feet of hard clay, lias, make 124 cubic feet in fill. " 100 cubic feet of clay mixed with cobble-stones make 126 cubic feet in fill. 124 EARTHWORK AND MASONRY. " 100 cubic feet of decomposed rock, solid gravel banks, make 128 cubic feet in fill. " 100 cubic feet of rock (can be picked) make 130 cubic feet in fill. " 100 cubic feet of rock, requiring blasting, make 134-150 cubic feet in fill." Henz, the author of a Manual on Earthwork, states as the result of a large number of observations of actual work, that the permanent increase in volume from cut to fill is /.n sandy soil 1-1.5 per cent. In clay and light soil 3 " In marl 4-5 " In hard clay 6-7 In rocK 8-12 " J. C. Trautwine, in his " Pocket-Book," says: "Although earth when first dug and loosely thrown out, swells about part, so that a cubic yard in place averages about 1 or 1.2 cubic yards when dug ; or 1 cubic yard when dug is equal to f or 0.8333 of a cubic yard in place ; yet when made into embankment it gradually subsides, settles or shrinks into a less bulk than it occupied before being dug." EARTHWORK COMPUTATION. A. M. WELLINGTON. 1. Compute solidities by averaging end areas and use the results for all prpliminary purposes, monthly estimates, etc. 2. At any time before the final estimate, substract the center heights only from each other of those solids only which differ three feet or more in center height. 3. Determine a correction to be applied to each of such solids from a tabulation of the following formula : (c c')-r I Correction in cu. yds. = g - X gy in which c and c c' = center heights, r = ratio of slope and I = length of solid = 100 feet for purposes of the table. (Such a table can be made in a few minutes, as it is required only from 3 to 10 or 12 feet ranging by tenths.) 4. Determine the sum of these corrections for any given section and deduct them in gross from the end area solidity, for final estimate pur- poses. LEVEE CONSTRUCTION. 125 LEVEE CONSTRUCTION. The following methods of construction are those adopted by the Board of Mississippi Levee Commissioners and their Chief Engineer: The ground to be occupied by the levee must first be cleared of trees, stumps, logs, trash, weeds and all perishable matter ; the trees and stumps being cut level with the surface of the ground. The entire sur- face must then be thoroughly broken with a spade or plow, in order to form a bond with the earth deposited. Then a muck ditch must be cut on the river side of the center line : all stumps and roots crossing it being carefully taken out and removed beyond the base of the levee. As each section of a mile in length of the entire levee is thus cleared, broken, and ditch cut, the engineer sets the side stakes of the base of the levee ; the muck ditch is then filled in with buckshot earth or clay obtained from without the base of the levee, and the earth tamped in by horses or mules, ridden rapidly back and forward constantly while the earth is being put in, or by tamping mauls, at least one horse to every ten wheelbarrows, or one tamping maul to six wheelbarrows. This filling and tamping is kept one-quarter mile in advance of the embankment. In case of repair of old levees, all stumps, logs and trees, where they are known to exist, must be dug out and the muck ditch cut near the outside base of the old levee, if considered necessary by the engineer. The surface of all old levees must be well broken. Where the chief constituent of the levee is sand, or other other porous material, the engineer may require a wall of buckshot or clay, 5 ft. thick, to be continued up from the muck ditch to the top of the levee, the earth being tamped in by horses in the same manner as the muck ditch, as the levee is built up on each side of it, the object being to obtain a stratum through the levee, impervious to " sipe water." If the chief constituent of the levee is stiff buckshot or clay, the engineer may require a wall of sand 8 ft. thick, to be continued up from the surface of the muck-ditch to high water mark, as the levee is built up on each side of it, the object in this case being to obtain a perpendicular stratum through the levee impervious to crawfish. When the ground is prepared, the embankment will be commenced, the slopes being commenced full out to the side stakes and carried regu- larly up. The embankment must be built one- fifth higher than the grade height marked on the stakes, to allow for shrinkage or settling. Material is to be obtained from places designated by the engineer, and is not to be taken on the inside of the levee except upon the engineer's orders. At intervals of 100 ft. bermes must be left across the borrow pits 126 EARTHWORK AND MASONRY, to prevent the flow of a current along the levee. All earth for embank- ment must be entirely divested of roots, trash and other perishable mat- ter before being put in place. Where considered necessary the engineer may require a double course of sheet piling, breaking joints to be driven at the center or either side of the levee 5 ft. below the surface of the ground, and extending up to within 6 ins. of grade. The plant to be of heart red gum, white oak or cy- press, and of specified dimensions. All piling is driven in advance of the levee, and the embankment constructed on both sides of the piling simul- taneously. A breakwater may be constructed where necessary on the river slope of the levee, of post and plank wall, properly braced and filled in behind with earth. In anticipation of destructive floods during the progress of the work, a protection of timber work may be constructed around the ends of the levee, and a temporary protection levee in front of the work. SPECIFICATIONS FOR MASONRY. BRICK FOR BUILDINGS. There is not even a remote approach to uniformity in the specifications for the brick work of buildings. Ordinarily the specifications for the brick masonry are very brief and incomplete. The following conform closely to ordinary construction. Of course, a higher grade of workman- ship can be obtained by more stringent specifications. The brick in the exterior walls must be of good quality, hard burned ; fine, compact and uniform in texture ; regular in shape and uniform in size. One fourth of the brick in the interior walls may be what is known as soft or salmon brick. The brick must be thoroughly wet be- fore being laid. The joints of the exterior walls shall be from i to $ inch thick. The joints of interior division walls may be from f to * inch thick. The mortar shall be composed of 1 part of fresh, well-slaked lime and 2^ to 3 parts of clean, sharp sand. The lime paste and the sand shall be thoroughly mixed before being used. The joints shall be well filled with the above mortar ; no grout shall be used in the work. The bond must consist of five courses of stretchers to one of headers, and shall be so arranged as to thoroughly bind the exterior and interior portions of the wall to each other. The contractor mnst furnish, set up and take away his own scaffold- ing ; he must build in such strips, plugs, blocks, scantling, etc., as are required for securing the wood work ; and must also assist in placing all BRICK FOR ARCHES. 127 iron work, as beams, stairways, anchors, bed plates, etc., connected with the brick work. BEICK FOR AKCHES. The specifications for the brick arch masonry on the Atchison, Topeka and Santa Fe Railroad are as follows: " The bricks must be of the best quality of smooth, hard burnt, paving bricks, well tempered and molded, of the usual size, compact, well shaped, free from lime, cracks and other imperfections, and must stand a pressure of 4,000 pounds per square inch without crushing. No bats will be allowed in the work except for making necessary closures. All bricks will be culled on the ground after delivery, and selected in strick accord- ance with these specifications. " The mortar must be made of 1 measure of good hydraulic [Rosendalej cement and 2 measure of clean, sharp sand or such other proportion as way be prescribed by the engineer well mixed together with clean mater, in clean motar-beds constructed of boards, and must be used im- mediately after being mixed. " The brick must be laid flush in cement mortar, and mu^t be thoroughly wet when laid. All joints and beds must be thoroughly filled with mortar so as to leave no empty spaces whatever in the masonry of the walls and arches, which must be solid throughout. The thickness of mortar-joints must be as follows: In the walls and in the arch between bricks of the same ring, not less than three-eighths of an inch (f ") nor more than one- half inch Ci"). In the arch between rings, not less than one-half inch (|") nor more than five-eighths of an inch (f "). Each brick is to be driven into place by blows of a mallet. The bricks must be laid in the walls with .the ordinary English bond, fivestretcher courses to one header course. They must be laid in the arch in concentric rings, each longitudinal line of bricks breaking joints with the adjoining lines in the same ring and in the ring under it. No headers to be used in the arch." RUBBLE MASONRY. The following requirements, if properly complied with, will secure what is generally known among railroad engineers as superior rubble: Rubble masonry shall consist of coursed rubble of good quality laid in cement mortar. No stone shall be less than six inches (6") in thickness, unless otherwise directed by the engineer. No stone shall measure less than twelve inches (12") in its least horizontal dimension, or less than its thickness. At least one-fourth of the stone in the face shall be headers, evenly distributed throughout the wall. The stones shall be roughly 128 EARTHWORK AND MASONRY. squared on joints, beds and faces, laid so as to break joints and in full mortar beds. All vertical spaces shall be flushed with good cement mor- tar and then be packed full with spalls. No spalls will be allowed in the beds. Selected stones shall be used at all angles, and shall be neatly pitched to true lines and laid on hammer-dressed beds; draft lines may be required at the more prominent angles. The top of parapet walls, piers and abutments shall be capped with stones extending entirely across the wall, and having a front and end pro- jection of not less than four inches (4"). Coping stones shall be neatly squared, and laid with joints of less than one-half inch ("). The steps of wing-walls shall be capped with stone covering the entire step, and ex- tending at least six inches (6") into the wall. Coping and step stones shall be roughly hammer-dressed on top, their outer faces pitched to true lines, and be of such thickness (not less than six inches) and have such projec- tions as the engineer may direct. " The specifications for rubble masonry will apply to rubble masonry laid dry, except as to the use of the mortar.'' SQUARED-STONE MASONRY. Squared-stone masonry is employed for the piers and abutments of the Lighter bridges, for arches of 10-foot span and under, for box-culverts, for basement walls, etc. The specifications are usually about as follows: The face stones shall have quarry faces with edges pitched to a straight line. Each stone shall be dressed to a uniform thickness, with beds throughout. No stone shall be less than eight inches (8 ) thick, nor measure in its smallest horizontal dimension less than 12 inches (12"), nor less than its thickness. Joints on the face shall be broken at least eight inches (8"). The bed- joints and also the vertical joints for eight inches (8") back from the face shall be dressed to one inch d"). The masonry need not be laid up in regular courses, but shall be well bonded, having at least one header, three feet (3 ') long, to every three stretchers. The stone shall be laid in full cement mortar beds, and the joints shall be packed full. The backing shall consist of stone not less than six inches (6 ") thick. At least one-half of the stones in the backing shall measure two (2) cubic feet. The backing shall be laid in full mortar beds, and the vertical joints shall also be filled with mortar. The spaces between the large stones shall be filled with spalls set in mortar. The coping shall be formed of large flat stones of such thickness as the engineer may direct, but in no case to be less than eight inches (8"). The ASHLAR MASONRY. igg upper surface of the coping shall be bush-hammered, and the joints and beds shall be dressed to one half an inch (") throughout. Each stone must extend entirely across the wall when the wall is not more that four feet 4 ) thick. ASHLAR MASONRY. The specifications for ashlar, or " first-class masonry," as employed on railroads, are about as follows : First-class masonry shall consist of quarry-faced ashlar, laid in regular horizontal courses, having parallel beds and vertical joints of not less than ten inches (10") and not more than 30 inches (30") in tbickness, decreasing in thickness regularly from the bottom to the top of the wall. Stretchers shall not be less than two and one-half feet (2') nor more than six feet (6 ) in length; and not less than one and one-half feet (!') in width, nor less in width than one and one-fourth (J^) times their depth. Headers must not be less than three and one-half feet (3J') in length unless the thinness of the wall necessitates it, nor more than four and one-half feet (4^'); and not less than one and one-half feet (!') in width, nor less in width than they are in depth of course. The beds and sides of the stone shall be cut before being placed on the work, so as to form joints not less than one-quarter inch (") and not exceeding five- eighths of an inch (f ") in width. Every stone must be laid on its natural bed, and all stones must have their beds well dressed, parallel, and true to the proper line, and made always as large as the stone will admit. The vertical joints of the face must not be less than eight inches (8") in from the face, and as much more as the stone will admit. All corners and batter lines must be built with a neat chisel-draft one and one-half inches (1|") on each corner. The projections of the rock-face must not exceed four inches (4") beyond the draft-lines of the masonry ; in tunnel side walls this projection must not exceed two inches (2"). The masonry shall consist of headers and stretchers alternating; at least one fourth of the wall shall consist of headers extending entirely through the wall. Every header shall be immediately over a stretcher of the underlying course. The stones of each course shall be so arranged as to form a proper bond with the stones of the underlying course. A bond of less than one foot (!') will in no case be allowed. The masonry shall be laid with cement mortar consisting of 1 volume of cement of the Rosendale type and 2 volumes of sand. Each stone shall be cleaned and dampened before being set. No hammering on the wall will 130 EARTHWORK AND MASONRY. be allowed after the course is set ; but if any inequalities occur, they must be carefully pointed off. The backing shall be of good-sized, well-shaped stones, laid so as to break joints and thoroughly bond the work in all directions and leave no spaces between them over six inches (ft 1 ) wide, which spaces shall be filled with small stones and spalls set in cement mortar. All foundation courses must be laid with selected, large, flat stones not less than twelve inches (12") in thickness, nor of less superficial surface than fifteen (15; square feet. The coping shall be formed of large flat stones, which shall extend en- tirely across the wall when the same is not more than six feet (6') wide. The steps of wing walls shall be capped with stone covering the entire step and extending under the step next above at least twelve inches (12"). Coping and step stones shall be at lease twelve inches (12") thick, ano have such projections as the engineer may direct (usually 3 to 6 inches). The tops and faces of copings ard step stones shall be bush-hammered and their joints and beds cut to one quarter inch (i") throughout. CHAPTEK VII. Culverts and Bridges. STANDARD TIMBER BOX CULVERTS. Reprinted from the Railroad Gazette. There is a strong feeling among engineers, which finds expression in the construction of nearly all lines on which timber is used at all, that the use of timber box culverts is bad practice ; that where the fill is not over 6 or 8 feet high or sometimes even 10 feet high open timber culverts should be used instead, and where the fill is too great for such open cul- verts, pile or timber trestles should be used, or else masonry. The prac- tice of the Chicago, Milwaukee & St. Paul is different from this, on all the thousands of miles which it has built or is building, where stone can- not be obtained at all, or only with much difficulty and cost. In such cases, the rule on that line, even in timber work, is never to use an open culvert when timber can be used instead. In this it is not alone, but we believe it is fairly entitled to the credit of having set the fashion, which is not yet a very general fashion. It is defended by the following argument: That though it is true that the wood decays, and though it is true that there is somewhat less cer- tainty of knowing of dangerous decay in advance, yet it is not true that decay is more rapid than with open structures, nor that they are as likely to give way when they are decayed, nor that the consequences are likely to be so serious if they do give way. In the meantime the average con- dition of a poorly ballasted or wholly unballasted track is very much better than with open structures. Therefore, the practice on that line is to use timber box culverts wherever possible, to have them inspected periodically and carefully, and whenever their condition demands it and convenience serves, to renew them, not with stone but, as a rule, with iron pipes. It is not found in practice, however, that even a considerable amount of decay endangers caving in of the bank greatly, especially when the bank is of some con- siderable height. After the bank has once become solid, on the contrary, which of course is long before the timber begins to decay seriously, it is 132 CULVERTS AND BRIDGES. Sid v ide Tinttiers to te "Drift BolteS together every'6 ft. P/^ withX'x20"Drifts . 1 ' 6'Covering _8_Coverrag_ S X 12Slil3.uot more thn^SS 8 : 'ft Centre to C 3 NUTK The two Timber Culvert* wfffi opening of 3'4"and 4'8'are to be used only when Baulc w too low to admit of the Square Form, with, not lew than ft Inches of earth on top of Covering. TWO-TIMBER CULVEKTS. N Side Timberffto'be' Drift Bolted together every 6 ft. &S with %'x 20'Drifts ^Covering - Covering _ ^lOCovenng LONGITUDINAL SKTION THREE-TIMBER CULVERTS. ^ide Tlhibers-to Ibe Mfi : Bolted together every 6 ft. fteS -^ <^ T^ETCTJ Sin : mmotched-2 : th Slid 8'Thick ? ^ Everr SUtb Sticlt Notched 2" \ ^vtrr Sixth Stick Notcliei S J Notched-2^ -4 t * ( } ' ^ y> ^ SideTimbera, / <{ , ^ < 1Z '*' I J_ i .xUSlUfnotn>ontLmii K&y * ft. Centre to Centre ESS E^ LONGITUDINAL SECTION FOUR-TIMBER CULVERTS. \ Side Timbers to be Drift Bolted together every 6 A Cu^YloVfirinir (TCoverincf 10 CoVonng 0"i la'dlllf sat mon thu^T 8 ft. Centre C LONGITUDINAL SECTION FOUR TIMBER DOUBLE CULVERTS. Standard Timber Box Culverts. Chicago, Milwaukee & St. Paul By. STANDARD TIMBER BOX CULVERTS. Covering ' Thick, for all Heights of BanTis < 4'-(^ , u's^iiSW] 1 12ia , 4 j.. <8*-'i8St- Covering 6*TKlck, for U of Banks ffic S'l* ^SJj- ... Orar ft. 6 laohu Tblrtmnof Beightof TblckneMof Covering. Bank, ' Coirriaj. Indira Up to 26 ft. 6 InobM 9 Plank i . Bill i Ifgg'B' I . Wf 6^*- 1[t> 3V H'lii J'Plink 12* 4 V ' 12* TllcVntUot Bank. Corerinf, tp to 15 ft. InctM 16ft.to26ft. ginchei ~ J( lOincln* J L 9*Plank . 25) 5-'8 Standard Timber Box Culverts. Chicago, Milwaukee & St, Paul Ry. 134 CULVERTS AND BRIDGES. found that they very seldom cave in, and that in putting in the iron pipe the timber may be almost completely cut away at top, bottom and sides for the insertion of circular pipes without danger; a safe indication for the workmen being that wherever the timber is punky and rotten there can be no immediate danger in removing it altogether, and after the expiration of very much less than 15 to 20 years, which is no unusual time for these culverts to remain in service, all the interior of the wood at lease where it is exposed to the air, is pretty sure to be punky and rotten, its chief and all-sufficient function seeming to be to sustain the pressure of earth during the process of solidification only, and thereafter chiefly to protect the interior surface of the earth fill from the influence of the atmosphere, which alone suffices to restrain all considerable ten- dency to cave. It follows that the size of the iron pipes which are ordinarily used for renewal, when it is not clearly safe to use a smaller pipe, will be given by determining with a pair of dividers the largest circle which can be drawn within the exterior limits of the culvert walls without cutting away more than half or two-thirds of the thickness of the wood at top or sides at any point, the greatest liberties being taken of course with bot- tom timbers. In doing this, the first section of the pipes is entered at one end and drawn clear through to the other end by appropriate tackle, the workmen clearing away in advance of it. After the first pipe has been drawn through and placed in position, the following pipes are drawn up to it in succession, one after another, very speedily, and the whole work is complete. A masonry end may or may not be added. The pipes used range from 24 to 60 in. in diameter, and are cas-t at the com- pany's foundry of any scrap which comes convenient. They are provided with a simple bell mouth large enough merely to hold the pipes in line with each other without any attempt at calking. The sizes of pipe used, of course, depend largely on what has proved to be the requirements of the water way. When the culvert has been in \ise some years the presumption is fair that no larger water way than be- fore is necessary, and this, or even more, is readily obtained by pipes in the manner described. Whether or not this manner of using and renewing wood is good and safe practice is simply a matter of experience. Experience in almost all kinds of soil appears to indicate that it is, a notable advantage being that in the rare cases where culverts cave in they do not, as a rule, produce a dangerous disturbance of the surface, whereas if an open culvert or tres- MAX IMUM SPANS OF STONE BOX CULVERTS. 135 tie has been carelessly allowed to become too weak, an accident is almost certain, while it is almost impossible to make a new track with many open structures in it ride even fairly well. There is perhaps no detail of American practice in which foreign critics, accustomed to new lines made thoroughly solid and complete before they are allowed to be opened, are more apt to comment unfavorably than on the practice of opening first with temporary works, and completing with permanent works afterwards, which may be called the standard Ameri- can practice. Yet there is much to be said for it. There are three other considerations of great weight: Firkt. The exact requirements of the locality become better known, and costly and dangerous mistakes may be more fully avoided. Second. The work can be prosecuted in a more leisurely manner and at more appropriate seasons, and thus greater durability insured. Third. The work can be prosecuted more cheaply, there being the advantage of locomotive power for delivering stone, cement and iron work and for making fills by trains ; often at but a fraction of the cost of executing the permanent work in advance of these facilities. As for safety, there is no question but that wooden structures, properly designed and properly watched and renewed, are entirely safe, and the thing to be protested against, therefore, is lack of care and skill in using them and not the things themselves. The difference in the cost of a good and of a bad wooden structure is not so good that there is ever any excuse for the latter, though it must be admitted that they are far from un- known. For these reasons there is no apology demanded for the reasonable and cautious use of the practice of " opening roads first and building them afterwards," as it has been called, even when, as on the Chicago, Milwau- kee & St. Paul and thousands of miles of other road in the West, the use of stone structures for opening the road is wholly out of the question. MAXIMUM SPANS OF STONE BOX CULVERTS. BY EMILE LOW, C. E. The table given below shows the maximum span or horizontal inside opening of box culverts, having covering stones of good sandstone, vary- ing in thickness from six (8) to eighteen (18) inches, and being under em- bankments of from four (4) to one hundred (100) feet in height. The table has been calculated for an earth embankment, the weight of a cubic foot of earth having been taken at eighty (80) pounds. 136 CULVERTS AND BRIDGES. Should the embankment be made of heavier material, such as rock, a reduction of the span must then be made. The ultimate tensile strength of the stone has been taken at eight hun- dred and sixty four (864) pounds per square inch, but one-tenth of that, or eighty-six and four-tenths (86 4-10) pounds per square inch, has been used in the calculation of the tables. The formula used is as follows: I _ 12 y c in which 1 = clear span in feet. c = depth of covering stone in inches. H = height of earth embankment over covering stone in feet. Height of embankment. 4 9 16 25 36 49 64 81 luO Span of Box Culverts with covering stone, ihe following depth in inches. 6" 3.60 2.40 1.80 1.44 9" 5.40 3.60 2.70 2.16 1.80 12" 7.20 4.80 3.60 2.88 2.40 2.06 1.80 15" 9.00 6 00 4.50 3.60 3.00 2.57 2.25 2.00 18" 10.80 7.20 5.40 4.32 3.60 3.09 2.70 2.40 2.16 I also append a table showing the weight of the superincumbent em- bankment (taken at 80 pounds per cubic foot), for the length of one (1) foot of the same in the direction of the axis of the culvert and in width equal to the spans as given above for the different heights of embankments. Height of embankment. 4 9 16 25 M 49 64 81 100 Weight of Embankment in pounds per lineal foot of Culvert and for widths as per table above. 1152 1728 23(14 2880 1728 2592 3456 4320 2304 3456 4608 5760 2880 4320 5760 7200 5184 6912 8640 8064 10080 9216 11520 12960 3456 5184 6912 8640 10368 12096 13324 15552 17280 SPECIFICATIONS FOR STONE BOX CULVERTS.* All stone box culverts shall have a water way at least 2i X 3 feet. The side walls shall not be less than two feet (2 r ) thick, and shall be built of *Pennsylvania Railroad. SPECIFICATIONS FOR STONE ARCH CULVERTS. 137 sound, durable stones not less than six inches (6") thick, laid in cement mortar [usually 1 part Rosendale cement to 2 parts sand]. The walls must be laid in true horizontal courses, but in case the thickness of the course is greater than 12 inches (12"), occasionally two stones may be used to make up the thickness. The walls must be laid so as to be thoroughly bonded, and at least one fourth of the area of each course must be headers going entirely through the wall. The top course must have one-half its area of through stones, and the remainder of this course must consist of stone going at least one-half of the way across the wall from the inside face. The face stone of each course must be dressed to a straight edge, and pitched off to a true line. All of the coping stones of head walls must be throughs, and must have the upper surface hammer-dressed to a straight edge, and the face pitched off to a line with margin draft. Cover stones shall have a thickness of at least twelve inches (12") for opening of three feet (3'), and at least 14 inches (14") for opening of four feet (4'); and must be carefully selected, and must be of such length as to have a bearing of at least one foot(l') on either wall. The beds and vertical joints of the face stones for a distance of six inches (6") from the face of the wall shall be so dressed as to require a mortar joint not thicker than three fourths of an inch (f "). Joints be- tween the covering stones must be not wider than three-fourths of an inch (f"), and the bearing surface of cover stones upon side walls must be so dressed as to require not more than a one-inch (1") mortar joint. The paving shall consist of flat stones, set on edge, at right angles with the line of the culvert, not less than twelve inches (12") deep, and shall be laid in cement mortar and grouted. SPECIFICATIONS FOR STONE ARCH CULVERTS.* Foundations. " When the bottom of the pit is common earth, gravel, etc., the foundations of arch culverts will generally consist of a pavement formed of stone, not less than twelve inches (12") in depth, set edgewise, and secured at the ends by deep curbstones which must be protected from undermining by broken stone placed in such quantity and position as the engineer may direct. When the bottom upon which a culvert is to be built is soft and compressible, and where it will at all times be covered with water, timber well hewn, and from eight (8") to twelve inches (12") in thickness, according to the span of the culvert, shall be laid side by side * Pennsylvania Railroad. 138 CULVERTS AND BRIDGES. crosswise upon longitudinal sills; and when the position of the culvert is such that a strong current will be forced through during Hoods, three courses of sheet piling shall be placed across the foundation, one course at each end, and one in the middle, which shall be sunk from three (3') to six (6') below the top of the timber, according as the earth is more or less compact." First-Class Arch Masonry. "First-class arch masonry shall be built in accordance with the specifications for first-class masonry *[8'325], with the exception of the arch sheeting and the ring stones. The ring stones shall be dressed to such shape as the engineer shall direct. The ring stones and the arch sheeting shall be of stone not less than 10 inches (10") thick *on the intrados, shall be dressed with three-eighths of an inch (f ") joints, and shall be of the full depth specified for the thickness of the arch; and the joints shall be at right angles to the surface of the intrados. The face of sheeting stones shall be dressed to make a close centering joint. The ring stones and the sheeting shall break joints not less than one foot (!'). "The wings shall be neatly stepped with selected stones of the full width of the wing and of not less than ten inches (10") in thickness, which shall overlap by not less than eighteen inches (18 ), or shall be finished with a neatly capped newel at the free end, and a coping course on the wing. The parapets shall be finished with a coping course not less than ten inches (10") thick and of the full width of the parapet, which shall project six inches (6")." Second-Class Arch Masonry. "Second-class arch masonry is the same as second-class masonry, with the exception of the arch sheeting. The stones of the arch sheeting shall have a good bearing throughout, and shall be well bonded and of the full depth of the thickness of the arch. No stone shall less than four inches (4") in thickness on the intrados. Ring stones of all arches over eight feet (8 ) span shall be dressed accord- ing to specifications for first-class arch masonry." Baker's Masonry Construction. HOWE TRUSS BRIDGES. 139 HOWE TRUSS BRIDGES. In ENGINEERING NEWS of April 26, 1890, a double page lithographed inset was published, showing 27 strain sheets and sizes of members for Howe truss bridges from 30 feet to 150 feet span, sent by Chief Engineer A. A. Schenck, of the Oregon Pacific Railway Co., and which we believe to be safe and careful designs, in accordance with the latest and best practice in wooden bridge construction, which for a long time to come will be an important department of American engineering work, although one of continually decreasing relative importance. One fact we should especially call attention to, that these bridges are designed for a region where very long timber is readily obtained, and is no more expensive than short timbers, so that the sections given for lower chord would be much weaker in proportion to regions where equally long timber was not available. The great difference in the amount of iron required when the rods are upset or not upset, is curiously shown in the table of data herewith reprinted-. TABLE OF DATA. W. Iron. Ibs. Rods upset. No. of Span. Assumed loading per foot. Total load per foot. Ibs. Estimate of Quantities. Trusses Ibs. &* E - a , # % 1; EH Ij . *~ h u 1 360 360 400 400 450 450 540 540 600 600 620 620 720 720 720 800 800 880 880 940 940 1,000 1.000 1,050 1,050 1,100 1.100 500 5,060 5.060 4.600 4,600 4,200 4,200 3,860 3,860 3,6*0 3,640 3,600 3,600 3,560 3,560 3,560 3.500 3,500 3.400 3,400 3,300 3,300 3,200 3,200 3,150 3.150 3,100 3.100 5.620 5,920 5.500 5,500 5,150 5,150 4,900 4,900 4,740 4.740 4,720 4,720 4.780 4,780 4,780 4,800 4,800 4,780 4,780 4,740 4,740 4,70.) 4,700 4,700 4,700 4,700 4.700 10,165 6,750 13,358 9,362 19.025 12,861 22,785 20.702 29,931 27,617 35,388 32,764 42,709 41,883 40,690 48,892 46,454 54,767 50,295 62,038 59,254 70,128 66,779 78,156 76,323 86.632 88.053 2,170 1,930 2.960 3,280 5,610 4,710 6,790 5,900 9,260 8,420 11660 10,190 15,170 17,880 13,220 22.530 18.040 25,820 19,400 30.890 23,080 37,050 27,930 40.820 32,640 48,090 39.630 ,970 1,210 1,070 1,550 2.880 2,830 3,660 3,830 8.260 7,980 9,790 9,730 12,530 12,260 12.710 14,290 13,990 15,930 14,050 18.290 16,520 20,830 20,460 23,210 23,260 27,060 27.140 8,210 7,610 10,260 9,120 13,440 15,150 11,820 18,950 16,040 22,290 16,320 26.010 19,580 30,180 23,560 33,020 27,360 39,140 33.390 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25.. 26 27... 140 CULVERTS AND BRIDGES. Strains given are for one truss, and in 1,000 pounds. Sections given are for one truss (rods assumed not upset). Loads in above table are for two trusses. Strains are those due to dead load + maximum from moving load. Assumed live loads are intended to fully equal (in strains produced) those given in diagram below. Load on a floor beam, 14,000 pounds, on a panel length of chord as a beam; 36,COO pounds on an axle. Wrought iron in tension, 10,060 pounds (net section at root of thread) per square inch. Wood (in compression only) 1-6 to 1-8 of breaking load by Smith's formula. Wood (in tension only) usually 800 pounds to U 03 pounds, (500 pounds to 800 pounds in shortest span), per square inch; and as packed beam maximum section (net sec- tion) 800 tc 1,000 pounds, LATERAL SYSTEMS. DE:'K SPANS A uniform load of 150 pounds per foot (each system), ^ of it at feet of rods. A movii,g load of 150 pounds per foot leach system), all of it at feet of rods. Sway braces at each panel assumed to equalize the strains so that each system is the same (except end rods). THROUGH SPANS A uniform load of 150 pounds to 200 pounds per foot (each sys- tem). A moving load of 300 pounds per toot (lower system). Iron 13,000 to 15,000 pounds per square inch net. Timber 1-4 to 1-5 breaking load. The spans included in the diagrams are : 100 ft. through, and deck. 110 120 13G 140 150 30 ft. half -through and deck. 40 " " 50 " 60 " 70 " 80 " 90 " through, half-through and deck. This includes in all 27 different trusses, covering the entire range usually required for wooden trusses, spans exceeding 150 feet being rare- ly built of wood. In a letter transmitting these strain sheets, Mr. W. A. DOANE, M. Am. Soc. C. E., gives the following further details: Fig. 1. Top Chord End Joints for Howe Truss Spans up to 90 ft. HOWE TRUSS BRIDGES. 141 " Howe truss bridges, not yet having had their day at least in the South and West I send you a set of strain sheets from 30 feet to 150 feet spans, designed for heavy traffic. They require little explanation be- yond that given by tke attached notes and table of data. It is intended to use upset rods for all spans above 60 or 70 feet, although diameters given are those required to give the necessary area at root of thread. The table of data gives approximate weights in each case. As will be seen, from 1,000 to 9,000 pounds of iron per span are saved by up- setting the ends of rods. It is believed that some details of construction have been improved in these designs. " Fig. 1 (enlarged scale) shows the general style of joints at junction of top chord with end mains for all through spans up to 90 feet. Fig. 3. Portal Bracing for Howe Truss Through, Spans of 90 ft. and over. 142 CULVERTS AND BRIDGES. " Fig. 3 shows general style of portal bracing, etc., for through spans over 90 feet, these having a system of top lateral bracing. In no case are vertical end posts used to meet a useless prolongation of top chord in through spans. " For spans of 100 feet and over, the usual style of cast brace blocks is followed, having tubes slightly let in to chord timbers and loiig enough to reach the opposite face of chord and receive the strain transmitted from the rods through the plates. These latter are in all cases made un- usually wide, however. " In spans less than 100 feet the tubes are dispensed with, and a block of the style shown in Fig. 2 is used, having a full bearing on the chord as well as for the braces, while the radial longitudinal ribs greatly in- crease the strength. The open ends are not objectionable." Fig. 2. Cast Brace-Block for Howe Truss Spans under 100 ft. It was not practicable to reproduce the sheet of diagrams for this book. The reader who wishes to post himself on the best practice in Howe truss construction can consult the number of the journal in which the diagrams are published. COST OF ERECTING A WOODEN HOWE TRUSS BRIDGE. 143 COST OF LABOR IN FRAMING AND ERECTING A WOODEN HOWE TRUSS BRIDGE. We have had sent to us a very full and careful set of notes, detailing the actual cost for labor of framing and erecting five 'spans of 150 ft. each, of a wooden arched Howe truss bridge, built by one of the best known firms in the country. We give an abstract of these for the benefit of any whom it may concern. The general dimensions of the bridge were as follows : Number of spans 5 Numberof trusses to each span 2 Number of arches 10 each truss 2 Length of truss, c to c., of end angle-blocks 149ft. 4 in. Length of panel over pier 2ft.8in. Number of panels in each truss 14 Length of each panel lOft.Sin. Projection of chords beyond centre of end angle-block 2 ft. Height of truss between chords 20 ft. Depth of lower chord 14 in. Depth of upper chord 12 in. Widthof chord 2ft.3in. Depth of arches (3 pieces, 8 in. X 9 in ., 1 in. spaces) . 2 ft. 5 in . Width of arches . gin. Width of bridge in clear between trusses 19ft. 4 in. Width of bridge in clear between arches 18 ft. Radius of upper line of arch 108 ft. 4 in. Length of bridge centres of end angle-blocks 757ft.4in. The wages paid were as follows: Foreman, $3.60 per day; carpenters, $2.75; helpers, $2.25, and laborers, $1.85. Work was commenced in Octo- ber, 1873, and continued without interruption thereafter until July, 1874. when the bridge was completed. The cost of the work may be itemized as follows : Framing arches, cost $495.31 Painting arches, " 29.70 Total $525.01 or 660. per lin. ft. bridge. Framing trusses, cost $2.002.62 or $2.64 " Painting daps, etc., cost 105.70orl4c. ' Framing thefalse works, making " balance beams " for raising, making a flat and preparing generally for the erection of bridges cost as follows : Framing false works $57.96 Preparing for raising 173.98 Painting iron 42.75 Total $274.69 Time consumed in framing false works, 3J days' work of 7 men. The cost of raising for one foreman and 19 men, working 79 days, in- 144 CULVERTS AND BRI DG ES. eluding a bill of $220.61 for watchman, horse, blacksmithing and expen- ses was $2,989.45; reduced to cost per lin. ft. of bridge this amounted to: Falseworks $57 96 or $0.08 per lin. ft. bridge. Painting iron 103.65 or 0.14 Raising bridge 2,989.15 or 3.94 " " Or to summarize under the following general heads, the Framing coat $2,603.63 or $3.44 per lin. ft. of bridge. Raisingcost 3,151.06or 4.16 Totalcost $5,754.69 " $7.60 The cost of lumber and iron is, of course, not included in the above ac- count, which simply covers the labor. Engineering News, March 24, 1883. HOWE TRUSSES ON THE CANADIAN PACIFIC RAILWAY. The Howe trusses nearly all have the following floor : Guard rails, 8 in. X 8 in., sized to 6| in. at ties, placed 10 ft. 6 in. apart in the clear, bolted through the tie and outside stringer by f-iu. bolts (f in. X 3| in. cast washers) ; ties 8 in. X 8 in., 12 ft. long, spaced 16 in. centres ; every 5 ft. 4 in., or every fourth tie guard rail, tie and stringer bolted. The ties are sized to 7 in. at the stringers on some bridges. Six lines of stringers, all 8 in. X 10 in., two under eachrail, breaking joints and packed 3 in. apart. Packing bolts f in. (about 5 ft. apart). The other four stringers are under the guard rails. In each panel there are four f-in. bolts through one of the stringers and floor beam. The floor beams vary from 6 in. X 15 in. to 9 in. X 15 in. ; 4 to 5 per panel, bolted through the chord by f-in. bolts. All through bridges are 15 ft. wide in clear, and, where the top lateral bracing is used, are about 21 ft. from top of rail to bottom of braces. The dead load is generally 10$ greater than given by TRAUTWINE for the trusses, and 400 to 650 Ibs. per ft. for the floor. lion in tension is strained not to exceed 10,000 Ibs. per sq. in. of net section; wood in tension, 800 to 900 Ibs. Wood in compression, to i breaking load, by S. C. Smith's formula. Wood as a beam, etc., 800 to 900 Ibs. per sq. in. on extreme fibres ; keys, post blocks, packing, clamps, brace-blocks, are all of white oak. The 147-ft. spans have iron clamps and lower chord post blocks. All spans of 50 ft. and over have iron brace and lateral blocks, except the 50- ft. through span. There is the same number of panels of lateral bracing as of vertical in all trusses. Much of the counter bracing is in excess. In the skeleton diagrams the height is centre to centre of chords, and the HOWE TRUSSES ON THE CANADIAN PACIFIC RAILWAY. 145 length, from face to face of end post. All main rods have upset ends. Hexagonal nuts are used, with 8 to 10 ins. of thread at each end. With plates no washers are used. The lateral rods have square nuts 5 ins. of threads, all upset. FORMULAS FOR WEIGHTS OF BRIDGES. The following formulas for computing the approximate weights of bridges are taken from Merriman's Text Book on Roofs and Bridges : For a highway bridge let Z be the span in feet, 6 the width in feet (in- cluding sidewalks, if any) and w the weight in pounds per linear foot, then, w = 140 + Ifc 6 -f- 0.2 b I 0.4 I. For a rajjroad bridge the weight per linear foot can be roughly found from the following formulas for spans less than 300 feet in length : For single track w = 560 -f- 5.6 I. For double track w = 1,070 -f 10.7 I. Wooden bridges weigh about the same as iron of equal strength. CHAPTER Till. Construction Details. CENTRES FOR ARCHES. There is nothing connected with the construction of stone or brick arches which requires more careful attention on-the part of the builders than the centres it matters not what the shape or span, or for what par- ticular purpose the arch be intended. Aside from the choice of material and the care with which other parts of the construction are performed, the settlement and ultimate stability of the arch decidedly depends on the framing, setting and striking of the centres. The yielding of a brace of improper dimensions, or a slight change in the shape of the frame caused by an ill-seasoned timber, may result in so changing the shape of the intrados as to endanger the safety of the arch. It must be the object of the engineer, in all large-spanned arches, to determine by what combina- tion of beams and by what system of bracing the greatest strength and stiffness may be secured, combined with lightness and economy of materials. When in position the centres are placed about 5 to 7 feet centre to cen- tre and are known as ribs. Pieces of board or plank, called laggins, are placed horizontally upon them, on which rest the voussoirs until the key- stone is inserted, when the arch becomes self-supporting. The frame- work of the centre consists of short beams which are cut on the outer edge to form parts of a curve, and when put in place they unite to form the same curve as the intrados of the arch. These are held in place by horizontal tie-beams, struts, ties and braces, the arrangement, number and dimensions of which will depend upon the shape and span of the arch as well as number and position of the points of support. Experience shows that whatever be the shape or span, the arrange- ment of the ribs in the form of a polygon is the best in every case. This shape is acquired by the arrangement of the short beams or back-pieces, which usually consist of two or more pieces of plank firmly nailed to- gether and abutting end to end, forming a joint in the direction of the radius of curvature of the arch. It is obvious that the strains to which CENTRES FOR ARCHES. 147 the centres are subjected arise slowly from the pressure upon the back- pieces and laggins. Therefore the strains depend upon the span and curve of the arch and the thickness and weight of the voussoirs which rest upon the centring. All the voussoirs from one springing line to the other do not. however, press upon the frames. This depends very greatly upon the degree of curvature of the arch. In a full-centred arch the voussoirs exert no pressure upon the frames for a considerable distance above each springing line, but when the point is reached where the stones begin to exert a pressure upon the frames, such pressure increases very rapidly as we approach the crown and reaches its maximum intensity just before the key -stone course is driven into place. These voussoirs which lie near the springing-plane and exert no pressure upon the lag- gins and hack-pieces are all situated within the angle of repose in other words, the voussoirs do not begin to press upon the centring until we meet one whose lower joint makes so great an angle with the horizontal as to cause it to slide under the force of gravity. For ordinary cut stone, the argle of repose of a full-centred arch has been found by experiment to be about 30; but if the stone be laid in full mortar it will be very nearly 45. The number of stones, then, that will load the centre-frame, taking the angle of repose at 80, will depend en- tirely upon the form of the curve given to the intrados. For example, in a full centre, an oval and a flat segmental arch, having the same number of Voussoirs, it is plain that the number of stones? which do not press upon the laggins will be greatest in the first-mentioned arch, less in the second and still less in the third. Those stones which do press upon the laggins do not do so with their entire weight, owing to the friction of the sur- faces of contact which the weight of the stone is compelled to overcome. According to Rankine the total weight of each stone which presses upon the laggins is to the weight with which they actually load the frame as an arc of 60 is to twice its sine lass the same angle, or the relation may be thus expressed : Let W = total weight of voussoirs which rest on centring and iv = weight with which they load centring. Then we have W : w : : arc 60 : 2 sin 60 arc 60, W (2 sin 60 arc 60). orw = aoB ' arc 66 Now let the radius be divided into any number of equal parts, say r = 15000. The circumference will then contain 94248 and the arc of 60 15708. The sine of the arc of 60 will be r X i V~g = r X .8660 = 12990. 148 CONSTRUCTION DETAILS. Substituting these values in the above equation we have W :w :: 15708 : 2 X 12990 15708, which gives a ratio of 3 to 2, nearly. We therefore conclude that about | of the weight of those stones which lie without the angle of repose actually press upon the laggins ; and tak- ing into account the 60 contained in the angles of repose on both sides, we find that about f X f = 5 of the gross weight of the arch expresses the load of the centres. The case is entirely similar with arches which are not full centred. In order, then, to determine the gross weight of that portion of the arch which presses on the back pieces and laggins and causes stresses in the framework of the centres, it is only necessary to know the number of voussoirs, their volume and weight per cubic foot. If the centres are subject to other stresses besides those caused by the voussoirs, as is sometimes the case in tunneling where the timbering is removed before the keystone course is driven, such additional stresses must be provided for. The direction and intensity of strains caused by the voussoirs may easily be found by resorting to parallelogram of forces. For example, the weight of any arch stone or any number of arch stones, which acts vertically downward through its centre of gravity, may be resolved into two components, one of which will be normal to the lower radial joint of the arch and will represent in magnitude and direction the weight which is not supported by the rib, but which is resisted by the lower part of the arch and finally by the abutment, and the other in the direction of tne radius of curvature of the intrados representing in mag- nitude and direction the weight which must be resisted by the centring. The strains then take the direction of the radius of curvature of the in- trados. Now, to find the position of the beams which are to withstand these strains, also their number and dimensions, is next required. It is evident that a horizontal beam loaded at its middle will offer its least re- sistance to the load. If , now, one end of the beam be raised so that the direction of strain is oblique to the fibers of the beam, the resistance in the latter case will be to that in the former as the cosine of the angle made by the direction of the strain and the fibres of wood is to sine 90 D or 1. It should follow that when the angle between the beam and strain is zero the resistance becomes infinite, and if it were not for the compressibility and certain other physical causes such would be the case. However this may be, the beam is certain to be strongest in the direction of its fibres, hence the greatest stiffness and strength will be gained when the principal CENTRES FO- ARCHES. 149 pieces are placed in the direction of the strains; that is, in the direction of the radius of curvature of the arch. The practical application of this arrangement of beams is, however, restricted t > small arches, because when timbers are 30 or 40 feet long it fails utterly. For while a beam of 10 feet long will offer great resistance to compression in the direction of its fibers, a beam 40 feet long would be sure to bend and require bracing. In order, therefore, to arrive at an arrangement which will adapt itself to large arches, if we resolve the radial stresses of two symmetrical portions of the arch, with respect to a vertical plane through the center of the arch and in the direction of its length, into horizontal and vertical com- ponents, these components will represent the direction of three beams, one horizontal spanning the arch and supported at each end by a vertical beam. According to Drinker on Tunneling, this horizontal beam is placed about 45 up the arch, in practice. The voussoirs above this tie beam are then supported by another horizontal tie beam upheld by small vertical beams abutting on the lower tie. Now, then, knowing the pressure exerted on the centre, and being able to calculate the pressure upon any segment thereof ; also, having decided upon the number and arrangement of members, the strains may be found either analytically or by the graphical method. After determining the stresses the members may be proportioned with Gordon's formula, using a factor of safety of 4 to 6. The centring should be slightly higher in the middle than the intended height of the finished arch, in order to allow for deflection. By experi- ence the amount of deflection is found to be T ^ of the radius of curvature. The centring must, therefore, be made ^ ff of r higher at the crown than the finished arch is intended. When the keystone course has been driven the striking of the centres must be deferred for some days, or even weeks, in order to give the cement time to settle properly. It has been found by experience, however, that it is well to very slightly withdraw the cen- tring soon after the arch is finished, in order to allow for the deflection bp- fore the cement is perfectly settled. A very satisfactory method, with this object in view, is to have the centring supported by means of hol- low cylindrical columns filled with sand. The weight rests on the sand by means of pistons, which project into the top of the column, while the pillars rest on solid foundations. There is a small opening near the bottom of each pillar, and when the arch is ready to be decentred a small por- tion of the sand is let out, thus allowing the arch to deflect very gradu- ally. N. J. WITMEE. 150 CONSTRUCTION DETAILS. REPAIRS TO THE ARCH OF THE MUSCONETCONG TUNNEL. [Published by pernr&sion of the Lehigh Valley Railroad Co.] The Musconetcong Tunnel is situated in New Jersey, on the line of the Lehigh Valley Railroad, about twelve miles from Easton. lu the autumn of 1871 and the winter of 1872 the location was decided upon. The road was at that time divided into four divisions, Mr. Robert H. Sayre, Chief Engineer of the Lehigh Valley Rail- road, being also Chief Engineer of the Easton & Amboy Division, in which the tunnel is located. Mr. Cal- vin E. Brodhead was Principal Assist- ant : Mr. John L. Wilson, Division Engineer ; Mr. Henry S. Drinker, Resident Engineer, and Mr. Charles McFadden, of Philadelphia, Con- tractor. The tunnel is through a spur of the Musconetcong Mountains (that range which extends over Northern New Jersey and into Southern New York), and is 5,136 feet long. At the west end it passes through 770 feet of soft ground, 702 feet of which is arched, the remainder being taken out in open cut, 450 feet of lime- stone, 263 feet of loose rock and 3,731 feet of syenite, declared by competent judges to be harder and tougher than any rock encountered along the line of the Hoosac Tunnel. In April. 1872, ground was broken on the west cut, work starting soon after on the east end, and in December, 1874, the headings met. It was decided to commence by a slope down to the level of the proposed head- ings, which were then to be run in both directions. This was on the west end in the earthy portion of the tunnel, the east end being run full size. The slope having been dug, work was commenced on the headings, but the ground was very heavy, requiring careful timbering. Springs of REPAIRS TO ARCH OF MUSCONETCONG TUNNEL. 151 water were constantly encountered, and finally one spring struck with which two large pumps were unable to cope ; the water gained rapidly, the timbering was undermined and the en tire work ruined. After this the slope was abandoned ; a shaft was sunk to the west and headings run each way until the water was struck, when it was carried out through the west heading. This portion of the tunnel was the most troublesome, and has kept up its reputation in this respect ever since. That portion of the tunnel through the earth, and also where th*> loose rock was encountered at the junction of the limestone and the syenite, was arched, there being 50 feet of stone arching at the west end, the re- mainder of brick. The backing was dry rubble. For a number of years the brick arch gave good satisfaction, but finally it began to fail. Longitudinal cracks were opened, and at last it grew so bad that the bricks would fall out under the jarring of the passing trains. The cause of this failure is not known, the mortar used not having been injured by the water, as afterwards proved. It is probable that the rubble backing was not packed tight enough, thus allowing a pressure from above to be transmitted directly to that portion of the arch below, instead of being distributed uniformly over the entire arch. Several remedies were suggested and plans made, but first it became necessary to timber the failing part, or there was danger of the entire arch collapsing. The great problem was to put in solid timbering and still not interfere with the trains. The double track was changed to a single one raised on sills and timbering put in as shown in Figs. 1 and 2. The first kind (Fig. 1) was used for 255 feet at the west end, 215 feet of this having knees, and 410 feet of the second kind (Fig. 2). The tunnel starts at station 676+65, and at station 678+20 double timbering was used on account of the character of the arch at that point. The bents are five feet apart, centre to centre, of pine and hemlock, the sills are 8" X 12", the posts 12" x 12", and the corbels 12" X 12". To withstand any lateral pressure the bents are connected by short struts, 12" X 12" hemlock. It will be seen by an inspection of the figures that this timbering is put up in the most substantial manner. The second kind is considered the best, as in it no distortion can take place unless the bents break. This work was commenced in April, 1888. As for repairing the arch, many plans were suggested. One was to take out the old arch in sections and replace it by a stone arch ; another, to take out the old arch as above, replacing it by a concrete one resting upon the old side walls. Neither of these was adopted, but after much delibera- 152 CONSTRUCTION DETAILS. tion it was decided to excavate above the old arch and back of the old walls and fill in with concrete, removing the old arch after the concrete had set. In June, 1888, the old shaft was opened, and a heading run both ways along the crown of the arch. This heading was 6 feet by 6 feet, through very heavy earth and heavy timbering : bull pine in pieces of from 10 to 12 inches diameter was used and proved very satisfactory; it was much more economical than hemlock, costing less than one third as much per running foot. The bents were put 3 feet apart, centre to centre, allowing a clear space of 5 feet by 5 feet. Above Fig. 2 is shown the method of timbering these headings. After being run for about fifty feet the head- ing was then extended down along the line of the arch to a firm founda- tion back of the side walls, every other bent being knocked out for this purpose and replaced by timbering as shown in Fig. 1. Along the crown of the arch 6-inch scantling were laid on which the sills, 6 inches by 12 inches rested to support the stubs. Concrete was then put into a thick- ness of from 4 to 4| feet on the walls and haunches to 3 feet 6 inches on the crown, thoroughly tamped, and the space above, about 3 feet, tightly packed with dry rubble, the stories being about 1 feet each way. The concrete was mixed in the following proportions, by bulk : Alsen's German Portland cement 1 Clean sand 254 Stone 6k The sand was from Perth Amboy and of a high order, consisting al- most entirely of quartz with little or no loam ; the stone was* that taken from the old tunnel, syenitic gneiss and limestone. The concrete set thoroughly in four hours. It was found expedient after the work had progressed to open a new shaft. The old one was 140 feet deep, and 330 feet west, or 150 ft. from the end, of the tunnel was sunk the new one. From this shaft the headings were run to the ring stones of the tunnel facing. The old shaft was filled with 5 feet of concrete, 14 feet of puddled clay, and the remainder with the material from the tunnel. A Copeland & Bacon (N. Y.) hoisting drum was used. The concrete invert was put in in 30-f t. sections on Sundays. The wedges above the corbels being driven out, the bents were jacked up and after- wards put down on 6" X 12" blocks. The invert was laid to the arc of a circle of 44 feet radius, 21 inches thick at the extremities, 15 inches at the STANDARD FENCES AND GATES. 153 middle, laid to a form. It was kept clear of water while this work was going on by a Worthington (N. Y. and London) pump ; at the same time by levers this water could be thrown up the hill through a 1| inch pipe to be used in mixing the concrete. This mixing was all done near the shafts, the concrete being taken down for use in the invert on an inclined railway, a car descending pulled up an empty one. For pumping the water from the backing a Blake (N. Y. and Boston) pump was used. Fig. 3 shows the lines of the concrete arch. While removing the arch, the back of the masonry was so foul that an air drum had to be put in. This was a Sturtevant (Boston) drum which is guaranteed to deliver 10,000 cubic feet of air per minute, running 600 revolutions. The air was carried along by a wooden box 11 by 36 inches interior dimensions through the tunnel, and back of the masonry by branch boxes 10 inches by 12 inches interior. With a pressure of 85 pounds in the boiler this drum made 560 revolutions. Before it was put in, a number of men had been prostrated while working behind the arch. After the concrete had been in thirty days, the brick arch and sidewalls were taken, out; the 50 feet of stone arching being in excellent condition was not touched. The result is a tunnel with many unique features, and engineers may well be impatient to learn how the concrete arch will hold. Thanks are due to the officers of the Lehigh Valley Railroad for their courtesy to the writer in giving him free access to the tunnel and to the plans. THOS. C. J. BAILY, JR. STANDARD FENCES AND GATES. On so long a line as the Canadian Pacific Railway there are all kinds of fences, according to local conditions, and on a very large part of the way no fence at all; but the standard fence and' gate, which has been more used than any other, is that of a four-wire fence with a board cap and top board. The two alternate constructions for rock has been quite frequently necessary, there being considerable distances where fence is required, but where there is not soil enough to make it convenient to sink fence posts. The gate is a solid and good one, and proves quite satisfac- tory when properly put up. All depends, <3f course on having the posts well set in the ground. 154 CONSTRUCTION DETAILS. UNDERSTRUCTURE FOR A 40,000-GALLON TANK, CANADIAN PACIFIC RAILWAY. In the tank the elevation of bottom of sills is 2 ins. above base of rail. The air chamber joists are 4x8 ins., the upper and floor joists 3 X 12 ins. ; the sheeting and girting; 2x4 ins. , the braces and the struts 4x6 ins. , and the diagonal sills 4 X 12 ins. All the rest of the timber except the 9 X 9 in. diagonal cap is 12 X 12 ins. The sheeting, inside and out- side, is 1 in., dressed, seasoned and tongued and grooved. The tie rods are 1 in., with nuts at each end, and 1 in. square drift bolts, 24 ins. long, are used for connections. P. C. Girouard, in Engineering Neivs. PILE DRIVING MACHINE. 155 PILE DRIVING MACHINE. The machine illustrated is one of the very latest in model, and the heaviest in New York harbor. Plan of Guides jjf .Becl-Triecee Details of Pile Driving Machine. 156 CONSTRUCTION DETAILS. 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 y.ellow 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 6x14 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. PILE DRIVING MACHINE. - Long.Sec. showing internal bracing- 158 CONSTRUCTION DETAILS. The hoisting sheaves on top are two in number, placed side by side. They are 12 ins. in working diameter, 1-J- 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 3,800 ]bs. 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. THE AGE OF RAILROADS IN DIFFERENT COUNTRIES. England September 27, 1825 Austria September 30, 18^8 France October 1, 1828 The United States December 28, 1829 Belgium Slay 3, 1835 Germany December 7, 1885 Island of Cuba In the year 1837 Russia April 4, 1838 Italy September, 1839 Switzerland July 15, 1844 Jamaica November 21, 1845 Spain October 2i, 1848 Canada May, 1850 Mexico In the year 1850 Sweden and Peru In the year 1851 Chili January, 1852 East Indies .. April 1, 1853 Norway July, Ib53 Portugal In the year 1854 Brazil April 30, 1854 Victoria September 14, 1854 Colombia . January 28, 1855 New South Wales September 25, 1855 Egypt Januarv, 1856 Middle Australia April21,1856 Natal June 26, 1860 Turkey October 4, i860 RULES FOR MEASURING WORK-MAKING} DRAWINGS. 159 RULES FOR MEASURING WORK. Measure stone work by the cubic foot, plastering by the square yard, brick work by the cubic foot (20 brick to the cubic foot) ; roofing:, of slate, tin, gravel or shingles, by the square of 100 feet thus, 10 X 10 = 1 00 square feet ; flooring the same ; roof -painting by the square, same as flooring ; for house painting there is no rule. These are the rules gener- ally followed in New York, and their universal ue would be advantage- ous. DIRECTIONS FOR MAKING DRAWINGS FOR REPRODUCTION. 1. Use a paper with a smooth surface rather than a Whatman or other, paper with a rough surface. What is called " ledger" paper, smooth, heavy and white, is well adapted to this purpose. 2. Use very black India ink ; the prepared liquid India ink is very good and is always ready. 3. Have your drawing-pen in good condition, so that the lines are sharp and well defined. 4. Use as few shade lines as possible; or if used let them be sharp and well defined, not too close together, and in cylindrical work decreasing in thickness of line as the light is approached. 5. Make the original drawing at least four times the size of the electro- plate wanted. The work is much improved in appearance by being thus reduced, as the lines are finer, and slight errors in drawing are, to a cer- tain extent, decreased in importance. 6. In this reduction remember that all lettering and figures will be re- duced in proportion. Consequently in the drawing this lettering and figure work should be, say, twice as high as thpy are intended to appear on the finished plate, in a drawing to be reduced to one-fourth. 7. Draw the scale on the original so that it may be reduced with it. Unless the reproduced plate is to be of exactly the same size, the mere mention of the scale has no value. 8. 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The first and paramount thing is to print a steadily progressive ani reliable journal of such merit that, being once seen and read, it will create a demand for the next number." The past volumes of ENGINEERING NEWS constitute an encyclopedia of Amer- ican public works' construction that has no rival. It has the advantage over the ordinary ponderous reference book which is issued by some publisher once in a decade or two, in that it is always fresh and up to date, and if errors anpear, toey are promptly criticised and corrected. There is no engineer so thoroughly equipped intellectually and nracti^ally tha"; he cannot at times add to his knowledge fro 1 " the pages of ENGINEERING NEWS; to the young engineer just struggling "for place" in hia profession, there can be no agency more helpful than the weekly installment of this journal. The 19th year and 29th volume of ENGINEERING NEWS will commence on Jan. 5, 1893. Subscriptions, payable in advance, to United States, Canada and Mexico are: One year, $5.00; six months, $2.50; four months, $2.00. Single copies, 15 cents. To all Foreign Countries in the Postal Union add 4 cents per copy to above prices for postage. No club rates. No commission to agents. Sound volumes: Six months, $4.00; twelve months, $6.75. ENGINEERING NEWS is the best medium for advertisers who ivish to reach the engineering profession, in all its branches, civil and military; contractors for public works; and railroad officials interested in the construction and maintenance of track. These are its special departments, in which it has no superior in America. Address all correspondence to ENGINEERING NEWS PUBLISHING CO., TRIBUNE BUILDING, NEW YORK CITY. APPENDIX. BOOKS FOR RAILROAD ENGINEERS. The studies of a young railroad engineer, who has not had the advantages of a technical education, naturally lie in the same direc- tion as those pursued by students in engineering schools. In general, it may be said that a list of books used in such schools would be an ad- vantageous one for the young railroad engineer to follow, but such lists can be obtained by applying for catalogues of the institutions themselves. We will not, therefore, hen attempt to give an outline of such formal courses of study, although some of the books will be mentioned under the separate headings below. MATHEMATICS. There are so many excellent series of mathematical text-books, that a selection of any single one would be a difficult matter, and might almost seem invidious. The works of Simon Newcomb, professor in the United States Naval Observatory and in Johns Hopkins Uni- versity, are extensively used in the technical schools, and take a deservedly high rank. Among others may be mentioned tne books of Professor Bowser, of Rutgers College, and those of the late Professor Olney, of the University of Michigan. It should be said that in these and many other series there are elementary, collegiate and also ad- vanced works. It would probably be best for the railroad engineer to purchase an advanced algebra or calculus, rather than an elementary or an intermediate one; for the first certainly contains all that the others do, and besides has the advantage of covering the ground in a manner more complete, so that it may serve fpr a reference book. In higher mathematics, the field engineer will rarely have the time or opportunity to read many works, but Muir's Determinants, Hardy's Quaternions and Baker's Elliptic Functions may be noted as books introducing to the higher analysis. Ball's Short Account of the His- tory of Mathematics (12nio, 464 pages), is an interesting work for all with mathematical tendencies. The thorough treatise of Carll on Cal- (161) 162 APPENDIX. culus of Variations (8vo, $5), has special interest from the fact thai its author is blind. Thu best mathematical cyclopedia is Carr's Synopsis of Results in Pure Mathematics (London, 1880', large 8vo, U35 pages, $13.50). SURVEYING. The standard works on railroad surveying are generaly known to the young railroad engineer. Among these Searles' Field Engineering (fifteenth edition, pocket form, $3), is usually considered to be one of the best, both -in theoretical and practical lilies, and its tables are certainly most excellent for ready use in the field. The field book of Shunk, and that of Henck, have also been extensively used, and Searles has a separate small work on The Railroad Spiral. In the survey of public lands, the best work is the Manual of Surveying, by F. Hodgman (fifth edition, with tables, $2.50). As a general work, however, Johnson's Theory and Practice of Surveying (ninth edition, 754 pages, 150 cuts, with folding maps and tables, $4) may be said to cover in an excellent manner the subjects of land, city, topographic and geodetic surveying. Special books on the last mentioned branch will be noted below under Astronomy. TABLES. The best six-place logarithmic tables with which we are acquainted are those in Searles' Field Engineering, mentioned above. It is, how- ever, a matter of regret that five-place tables have not been given in field books, since they are far more convenient and are sufficiently accurate for problems in railroad surveying. Ludlow's Tables (8vo, $2). is an excellent set of five-place logarithms for office use. which compare favorably with the German ones of Gauss and Schoen. Among seven-place tables those of Vega and Schroen are counted among the best, the former having old style type and the latter modem type. In geodetic work eight-place logarithms are sometimes needed, and for this purpose Vega's Thesaurus Lognrithmorum. giving ten-place tables should be used; a photolithographic reproduction of this, with all errors corrected, has lately been published at a low price. MECHANICS. The subject of mechanics includes the fundamental principles which underlie all field construction, and particularly the design of arches, bridges, trestles and machinery. It is properly regarded as one of the most important studies in engineering schools. Wood's Principles of APPENDIX. 163 Elementary Mechanics (now in its ninth edition, 12mo, $1.25) is a standard book, which sets forth the fundamental principles in a clear and simple manner. An advanced work by the same author is the Elements of Analytical Mechanics (seventh edition, about 500 pages, octavo, $3), and there are also many excellent books by other American authors. Merriman's Mechanics of Materials (fourth edition, octavo, interleaved, $3.50) treats of the strength of materials and the theory of beams, columns and shafts. Among other works Lanza's Applied Mechanics (fifth edition, 929 pages, $7.50) and Church's Me- chanics of Engineering (834 pages, octavo, $6), may be noted as well known, both hi technical schools and as books of reference by en- gineers. The special practical applications of mechanics are found in books noted below under the headings of Roofs and Bridges, Con- struction and Hydraulics. ARCHITECTURE. Kidder's Architects' and Builders' Pocket-Book (tenth edition, 883 pages, with over 400 illustrations) is a standard work in the archi- tectural profession, occupying indeed the same place that Trautwine's does to the Civil Engineer. Birkmire's Architectural Iron "and Steel (second edition, 201 pages, $3.50), gives the most recent details con- cerning the use of iron and steel in architectural engineering. Mer- rill's Stones for Building and Decoration (a recent work, octavo, 453 pages, $5) gives an excellent general outline of the physical and chemical properties of building stones, together with a description of quarry methods, stone working machines and the weathering and preservation of building stones. Berg's Buildings and Structures for American Railroads (quarto, 500 pages, G91 figures. $7.50) is an exhaus- tive practical work which every division or resident engineer should have on his desk. ASTRONOMY AND GEODESY. Few astronomical problems are required in the practice of a rail- road engineer. The introduction of electric railways, however, which are often to be built in straight lines between distant points, requires the determination of azimuth. The elementary methods for this purpose are given in books of surveying, but when distance be- tween points becomes considerable, as. for example, in the electric line between Chicago and St. Louis, extended computations are required which involve the methods of geodesy. Johnson's Surveying gives full details regarding these problems, and a more special book for the 164 APPEl^DIX. observer is Doolittle's Treatise on Practical Astronomy (third edition, 042 pages, $4), which is well known as a standard among geodesists. The computation of geodetic latitudes and longitudes will often be found necessaiy hi this connection. These are set forth hi fullest detail hi the papers of the United States Coast and Geodetic Survey, but they may also be seen in Merrhnan's Geodetic Surveying (1892, octavo, 170 pages, $2). For the adjustment of precise observations Merrhuan's Method of Least Squares (sixth edition, 198 pages, octavo, $2) may be quoted as a well known standard text-book. Wright's Adjustment of Observations (octavo, 437 pages, $4) is a thorough work for special geodetic triangulations. BRIDGES AND ROOFS. The computation of stresses is, of course, the first part hi the in- vestigation or design of a bridge or roof truss. The first treatment of this subject was given hi 1847 by Squire Whipple, and, twenty-five years ago, his book and one by Herman Haupt (revised edition. 1871; 208 pages, with 16 plates, $3.50) were the only ones by American authors. To-day, however, there are a large number from which a choice can be made. Du Bois' Strains hi Framed Structures (eighth edition, over 500 pages, quarto, $10) is one of the most comprehen- sive, including not only computation of stresses, but the discussion and designing of details, and the preparation of working drawings. Greene's Roof Trusses and Merriman & Jacoby's Graphic Statics, give methods of determining stresses on the drawing board which will be found especially advantageous for roofs. Burr's Stresses in Bridge and Roof Trusses (475 pages, octavo, with 13 plates, $3.50) is a valuable contribution to the subject, and the seventh edition contains an appendix on cantilevers. Foster's Wooden Trestle Bridges (quarto, 150 pages, 38 plates, 150 cuts, $5) is a practical book, showing trestles of aE kinds, which also treats of methods of erection, protection against accidents, and gives numerous standard specifications. We find announced as in preparation a work on Framed Structures by Johnson, Bryan & Turneaure. and also a volume on Bridge Design by Professor Merriman, which will form Part ITT. of his Text-Book on Roofs and Bridges (Part I., Stresses, $2.50; Part II., Graphic Statics, $2.50). CONSTRUCTION AND OPERATION. Bilker's Masonry Construction (sixth edition. 550 pages, octavo. $5) takes high rank as a valuable theoretical and practical book, treating APPENDIX. 165 not only of stone work, but also of the important subject of founda- tions. Berg's Buildings and Structures for American Railroads (500 pages, 091 cuts, quarto, $7.50) is a work just published, which must necessarily be in the library of every railroad designing engineer, in- cluding as it does the details of the construction of buildings of all kinds from watchmen's shanties to large terminal passenger stations. Byrne's Highway Construction (080 pages, octavo, $5), Meyer's Modern "Locomotive Construction (1558 pages, 1,030 outs, $10), Thurstou's Materials of Construction (705 pages, octavo, 177 cuts, $5), Heriug's Recent Progress in Electric Hallways (12mo, 389 pages, 104 cuts), Mar- tin & Wetzler's Electric Motor and Its Application (quarto, 315 pages, 353 cuts), and American Practice in Block Signaling (72 pages, small quarto, $2), may be mentioned as recent authoritative books in the several departments of which they treat. Wellington's Economic Theory of the Location of Railways (fifth edition, 980 pages, 313 cuts, octavo, $5) brings together a great mass of matter relating to construc- tion and operation of railroads, as well as to location, the whole discussion being with reference to the most judicious expenditure of capital. Drinker's Tunneling, Explosive Compounds and Rock Drills (third edition, 1,143 pages, 19 plates, quarto, $25) is a most valuable historical and descriptive practical bcok. Wegmann's Masomy Dams, Merriman's Retaining Walls, Carpenter's Manual of Experi- mental Engineering, Thurston's Manual of the Steam Engine, Pea- body's Thermodynamics, Wilson's Steam Boilers, Wood's Compound Locomotives, Forney's Catechism of the Locomotive, Parson's Track. Clark's Building Superintendence, and Ihlseng's Manual of Mining an- other books which may be considered as safe, reliable and standard in their special field. Of course, the Pocket-Book of Trautwine is well known as the basis of every library, and the one book which a rail- road engineer must have; now in its forty-first thousand, it stands as a monument of patient industry on the part of its authors. HYDRAULICS. A general acquaintance with the principles of hydraulics is ab- solutely essential for the successful design of culverts, piers and other structures in water. Fundamental principles are given in Merriman's Treatise on Hydraulics (fourth edition, octavo, 384 pages, 109 cuts, many tables, $3.50), which is designed as a text-book for technical schools, and also for use of engineers. Smith's Hydraulics (quarto, 362 pages, 1C plates, $8) is an elaborate work, giving discussions of the 166 APPENDIX. coefficients derived from many experiments. Nichols' Water Supply (8vo, 232 pages, 54 cuts, 2.50) contains accounts of the methods 01 ascertaining and securing the purity of water, which is a very im- portant matter in planning water supplies for stations and other railroad buildings. Farming's Water Supply Engineering, Staley & llerson's Separate System of Sewerage, and Baumeister's Cleaning and Sewerage of Cities may be noted as standard works, covering a wide field in the important subjects of public water supply and sanita- tion. The Manual of American Water Works, published by En- gineering News Publishing Company. New York, is a comprehensive cyclopedia of statistics and historical information concerning public water supplies. 167 WORKS OK Professor Mansfield fflerriman, A TEEATISE ON HYDRAULICS, Fourth edition, revised, 8vo, cloth $3-5 A TEXT-BOOK ON THE METHOD OF LEAST SQUARES, Sixth revised edition, 8vo, cloth $2.00 THE MECHANICS OF MATERIALS, AND OF BEAMS, COLUMNS AND SHAFTS, Fourth edition, 8vo, cloth $3-5 A TEXT-BOOK ON ROOFS AND BRIDGES, PART I. STRESSES IN SIMPLE TRUSSES. Third edition, 8vo, cloth , $2.50 PART II. GRAPHIC STATICS. Third edition, 8vo, cloth $2.50 PART III. BRIDGE DESIGN. (In preparation). RETAINING WALLS AND MASONRY DAMS, 1892, 8vo, cloth $2.00 INTRODUCTION TO GEODETIC SURVEYING, Including Figure of the Earth, Method of Least Squares and Field Work of Triangulation. 8vo, cloth $2.00 -FOK, SA.IL.IE 1?Y ENGINEERING NEWS PUBLISHING Co., TRIBUNE BTJILD ISTGS-, NEW YORK. UCSB LIBRARY X - y . UC SOUTHERN REGIONAL LIBRARY FACILITY ENGINEERING NEWS AND AMERICAN RAILWAY JOURNAL. ENGINEERING NEWS PUBLISHING Co. TRIBUNE BUILDING, NEW YORK. SIXTV PAGES. 8U ..CR,PT,ONPR,C E :^|:*-- ON 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 ! Tf 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. Wednesday in time for publication in current issue.