Transcriber’s Note:

The cover image was created by the transcriber and is placed in the public domain.

HANDBOOK
OF
RAILROAD CONSTRUCTION;
FOR THE USE OF
AMERICAN ENGINEERS.
CONTAINING THE
NECESSARY RULES, TABLES, AND FORMULÆ
FOR THE
LOCATION, CONSTRUCTION, EQUIPMENT, AND MANAGEMENT OF RAILROADS, AS BUILT IN THE UNITED STATES.
With 158 Illustrations

BY

GEORGE L. VOSE,

CIVIL ENGINEER

“Rules themselves oblige us to reflect, that we may see whether we have not departed from them.”—Napoleon.

BOSTON AND CAMBRIDGE:

JAMES MUNROE AND COMPANY.

1857.

Entered according to Act of Congress, in the year 1857, by

JAMES MUNROE AND COMPANY,

In the Clerk’s Office of the District Court of the District of Massachusetts.

CAMBRIDGE:

ALLEN AND FARNHAM, PRINTERS.

PREFACE.

The object of this work is to give in the plainest possible manner all instructions, rules, and tables necessary for the location, construction, equipment, and management of railroads.

As a general thing, American engineers are not educated for their business; and when they do possess a knowledge of pure science, they are at a loss how to apply it.

The reader is presumed acquainted with the elements of arithmetic, geometry, algebra, and mechanics: being thus provided, he will, by a perusal of what follows, be enabled to correctly proportion bridges, of wood, stone, and iron: abutments, piers, retaining walls, superstructure, and locomotive engines; and to plan and lay out, execute, and estimate any description of work occurring upon railroads.

As the object has been more to be useful than original, the best engineering writers and experimenters have been consulted; among whom are,—Gauthey, Navier, Vieat, Tredgold, Barlow, Totten, Fairbairn, Hodgkinson, Clark, and Lardner. Also a great number of reports by American civil engineers upon railroad matters.

If assumptions take the place of demonstration, it will be on good authority. Readers will bear in mind that the work is a “handbook,” and not a “treatise.” It is intended more as an office companion than as a text-book for students. It will give in all cases the actual numerical result needed, whether it be the scantling of a bridge chord, the thickness of a wall, or the dimensions of a locomotive boiler.

In connection, it will be found convenient to use the works of Trautwine and Henck, on Field Work: of Lieutenant Smith, on Topography; Davies, on Surveying; and Gurley, on the Use of Instruments.

Any one wishing a complete treatise on the principles of bridge construction is referred to the excellent work of Hermann Haupt.

I take this opportunity of heartily thanking the engineers who in many ways have aided in making the work, as it is believed, of some worth.

G. L. V.

GENERAL TABLE OF CONTENTS.

ANALYTICAL INDEX.

ADDITIONS, ALTERATIONS, AND CORRECTIONS.

The reader is particularly requested to apply the following errata before perusing the work. They are partly mistakes in printing, and partly errors in the original MS. The only excuse the writer can offer for the number is, that, being engaged in Missouri, while his publishers were in Boston, he has been prevented from seeing a single proof-sheet in time for its correction.

Page [5], line 7, for “499.999,” read “499,999.”

— [5], l. 9, for “49.999,” read “49,999.”

— [10], l. 1, for “can be,” read “can never be.”

— [12] to [23], headings, for “reconnoitre,” read “reconnoissance.”

— [18], l. 24, for “36.9,” read “36.8.”

— [19], l. 6, for “table B,” read “table D.”

— [24], l. 1, for “any thing,” read “every thing.”

— [25], l. 17, for “horizontal line m m m,” read “line 1, 2, 3,” etc.

— [26], l. 2, for “land,” read “level.”

— [27], l. 1, for “at the place,” read “at the right place.”

— [28], l. 29, for “reconnoitre,” read “reconnoissance.”

— [30], l. 3, for “A c d B,” read “A C D B.”

— [32], l. 2, the point m in the cut, is one whole division above C; it should be only three fourths of a division.

— [38], l. 10 from bottom, for “276,” read “268.”

— [39], l. 10 from bottom, for “142.13,” read “143.13”; and last line, for “58.46,” read “48.46.”

— [40], l. 7, for “10310,667,” read “10,277,333.”

— [42], l. 9, for “Thus,” read “These.”

— [42], l. 8 from bottom, for “2°.81 or 2° 48′.6” read “2°.86 or 2°.51.6.”

— [43], l. 27, for “Hencke,” read “Henck.”

— [47], [48], [49], for “McCullum,” read “McCallum.”

— [47], l. 18, for “distance,” read “resistance.”

— [48], l. 6, for “infringing,” read “impinging”; line 9, for “slacking,” read “shackling”; l. 8 from bottom, for “increased,” read “increases.”

— [50], l. 17, for “110 + 15.60,” read “110 + 15.62.”

— [52], l. 15, for “45.59,” read “45.49”; also l. 17, for “1132,” read “11.32.”

— [58], l. 10, for “of size,” read “and size.”

— [58], l. 5 from bottom, for “one cent,” read “
100 of a cent.”

— [61], l. 3, for “are necessary,” read “are not necessary.”

— [63], l. 28, for “stretches,” read “stretchers.”

— [65], l. 15, for “spanded,” read “spandrel.”

— [71], l. 6 from bottom, for “left,” read “let.”

— [73], l. 19, for “chains,” read “chairs.”

— [74], l. 5, for “across ties,” read “on cross-ties.”

— [74], l. 12, for “28 inches,” read “27 inches.”

— [75], l. 18, for “land,” read “haul.”

— [76], l. 8, for “top,” read “bottom,” and for “charred when,” read “charred where.”

— [76], l. 11, for “twopenny,” read “tenpenny.”

— [78], l. 1 and 2, for “base,” read “basis.”

— [84], l. 13, for “as,” read “or.”

— [89], l. 6, for “Whenever,” read “Wherever”; l. 12, for “Letting,” read “Setting.”

— [90], l. 4, for “cost,” read “cut.”

— [93], l. 6, for “37 and 38,” read “36 and 37.”

— [95], l. 1, for “beach,” read “bench”; l. 3, for “to so,” read “so to”; l. 13, for “b being 10 ft. back of 2 is ... 100.00,” read “b being 10 ft. back of 2 is 0.1 ft. higher than 2, or ... 100.10.”

— [102], l. 1, head of middle col., for “Slopes 1¼,” read “Slopes 1½.”

— [103], l. 4 from bottom, for “and ten feet,” read “and one end ten feet.”

— [104], l. 9, for “any,” read “very.”

— [108], l. 9, for “Elwood,” read “Ellwood.”

— [115], l. 5, for “a loam,” read “a berm”; l. 16, for “a rent,” read “a vent.”

— [117], l. 7, for “volcanic,” read “voltaic.”

— [117], l. 9, for “Round Drum,” read “Round Down.”

— [117], l. 18, for “Col. Puseling,” read “Col. Pasley.”

— [118], l. 2, for “Maillefaut,” read “Maillefert.”

— [118], l. 16, for “insert,” read “invert.”

— [118], l. 25, for “quointed,” read “grouted.”

— [119], l. 30, for “furnished,” read “finished.”

— [120], Table, for “Nochistingo,” read “Nochistongo”; for “Supperton,” read “Sapperton”; and for “Black Rock, W. S.” read “Black Rock, U. S.”

— [121], l. 19, for “Belchingly,” read “Blechingly.”

— [125], in table at bottom, for “90
69,” read “90
66,” and for “140, 20
140, 20
160 or 0.13,” read “111, 20
111, 20
131, or 0.15.”

— [126], l. 1, for “extensive,” read “extensile.”

— [127], l. 10, for “67,200,” read “65,251.”

— [127], l. 26, for “Hodgekinson,” read “Hodgkinson.”

— [128], l. 4, for “12000,” read “11000.”

— [128], l. 15 and 22, for “Hodgekinson,” read “Hodgkinson.”

— [129], l. 5, for “12000,” read “11000.”

— [129], l. 2 from bottom, for “Sun Wood,” read “Ironwood.”

— [130], l. 7, for “WL² = 4Sbd²,” read “WL = 4Sbd².”

— [131], l. 9, for “wood 143,” read “wood 133.”

— [134], in art. 164, for “700,” read “952.”

— [136], for example there given, place the following:—

a = 6 × 10 × 12 × 30
26 × 34 × 12
16 = 32.58

and 32.58
6.1 = 5.34.

— [141], last line, Fig. 63 A was omitted; it is the same as fig. 102, page [200], inverted.

— [142], last line, for “span,” read “spans.”

— [146], head of col. 7, for “Top Washer,” read “Thickness of Washer.”

— [150], after line 9, Figs. 67 D and 67 E (page [153]) should be inserted.

— [151], l. 3, for “W = 2249,” etc., read “W = 2240,” etc.

— [151], l. 18, for “opposite to 31,416, is the diam. 1⅝,” read “opposite to 41,415, is the diam. 1⅞.”

— [151], l. 19, for “1⅝,” read “1⅞.”

— [154], last line, for “tubular,” read “tabular.”

— [156], l. 4 from bottom, for “washer band,” read “washer used.”

— [164], l. 10 to 14, inclusive. The first number of ratios should be 20 instead of 15.

— [166], l. 11, for “69 B,” read “69 A.”

— [171], head of col. 5 of table, for “Rod of Arch,” read “Rad. of Arch.”

— [173], l. 25, for “ability,” read “stability.”

— [173], l. 32, for “Whence,” read “Where.”

— [175], l. 8, for “triangular,” read “diagonal.”

— [178], l. 3, for “article,” read “outside.”

— [184], l. 4 from bottom, for “barriers,” read “voussoirs.”

— [187], fig. 96 is upside down; also, fig. 97, page [188], and fig. 98, page [189].

— [193], l. 4, col. 3 of table, for “.00000675,” read “.00000685”; also, l. 16, col. 5, for “straining,” read “shearing”; l. 7 from bottom, for “15,000,” read “18,000;” and l. 6 from bottom, for “75,000,” read “105,000.”

— [199], l. 7 from bottom, for “20,132,” read “20,312.”

— [200], l. 4, for “A C,” read “A G”; and l. 6, for “that on A R,” read “that on A K.”

— [202], l. 7, for “on page [193],” read “on page [138].”

— [204], l. 5 from bottom, for “varied line,” read “versed sine.”

— [207], l. 5 and 6, for “F G, G E, in place of E F, E C,” read “G L, G E, in place of F L, F C.”

— [210], in place of “f′ = πF
4ph,” put “D = √¾[V² – d²] – √¾[l² – d²].

where D = depression,

l = half length of curve before elongation,

V = half length of curve after elongation,

d = half distance between points of suspension.” Omit the remainder of the paragraph.

— [211], omit the 6th and 7th lines, and in place of formula there given, use that on page [210], (as corrected,) V being the length of semi-curve as elongated by heat instead of by tension; the elongations, both by heat and tension, being found by table on page [193].

— [212], l. 2, for “510.69,” read “510.80,” which result, of course, runs through the whole example.

— [213] and [214]. The remarks under “Anchoring Masonry,” are evidently wrong throughout: 1st, the whole tension should be divided by two, instead of four, as half of the whole tension acts at each point of suspension; 2d, no reduction should be made for the direction of the pulling force. One half of the tension is 3,321,250 lbs.; which is resisted by a column of masonry of 3,321,250
160 = 20,758 cubic feet, or 20 × 20 × 52 feet, or by a mass 15 × 15 × 91 feet.

— [214], l. 6, for “561,527,” read “562,542.”

— [215], l. 14 from bottom, for “STIFFENING TOWERS,” read “STIFFENING TRUSSES.”

— [225], l. 14, for “194,” read “193.”

— [226], l. 3, for “see page [128],” read “see page [193].”

— [227], l. 4, for “detensional,” read “detrusional.”

— [228], in place of equations at l. 16, put “R × a = R′ × (2 d × t)”,

whence d = R × a
2R′ × t;

where a = area of rivet,

d = distance,

t = plate thickness.

— [229], in art. 242, the strengths of “wrought iron,” have been taken for those of “boiler plate”; that is, 11,000 for 7,500, and 15,000 for 12,740, which is wrong.

— [231], l. 21, for “chopped,” read “dropped.”

— [234], l. 4, for “joint,” read “just.”

— [235], l. 14, for “0.016 feet,” read “0.047 feet.”

— [236], l. 9, for “care,” read “ease.”

— [237], l. 3 from bottom, for “representing,” read “separating.”

— [241], l. 2, for “localities,” read “locality.”

— [242], l. 7, omit “and c e, the parapets.”

— [243], l. 9, for “embankment,” read “abutment.”

— [244], l. 9, for “is thus,” read “is found thus.”

— [245], l. 17, for “latter,” read “batter.”

— [249], l. 23, for “common hydraulic,” read “common mortar, hydraulic.”

— [249], l. 27, for “argyle magnesia,” read “argil, magnesia.”

— [251], l. 16, for “7½ to 2,” read “1½ to 2.”

— [254], last l., for “corners,” read “courses.”

— [256], l. 13, for “formed,” read “found.”

— [258], art. 276, in place of “20
2 × 15 × 1 × 100 × 20
3,” put “20 × 15 × 1 × 100 × 2 × 20
3,” where 2 represents the ratio between C^a 6, and 6–2; thus, 20 × 15 × 1 × 100 × 6.6
12 × 20
3 = 111,111, for the overthrowing force in place of 100,000. The overthrowing force is thus large, because the maximum weight of earth has been assumed to press against the wall with its whole force, no allowance being made for friction. In practice, 4
10 of the height has been found amply thick for walls retaining ordinary earth.

— [262], last l. but one, for “superstratum,” read “substratum.”

— [264], in example, l. 5, for “26,667,” read “48,000.”

— [266], l. 25, for “Godwin,” read “Goodwin.”

— [266], l. 26, for “There, sands,” read “These sands.”

— [267], l. 22, for “bottom,” read “proper level.”

— [281], l. 4 from bottom, for “curve,” read “cone.”

— [282], l. 20, for “Daniel,” read “David.”

— [282], l. 4 from bottom, for “cup,” read “cap.”

— [284], l. 10, and [285], l. 8, for “compressed rails,” read “compound rails.”

— [285], l. 5, for “extension,” read “extensile.”

— [289], invert col. 1 of table, so that it shall read—

At 100° place the rails in contact.

At 90° at a distance of .00136 feet, or 0.016 inches.

At 80° at a distance of .00272 feet, or 0.032 inches Etc.

— [289], last l., for “levelled,” read “bevelled.”

— [291], last l., for “a c, 4.8,” read “a c, L 8.”

— [292], l. 9, for “e h and d k,” read “e L and d k”; same p. l. 6 from bottom, for “a, 9 is three, etc.” read “a b is three,” etc.

— [293], l. 6 and 7, for “i g, e h, b b, 8, 9, A s 79,” read “i g, e h, a c, b c.”

— [296], l. 14, for “R² – R – 8²,” read “R² – R – g².”

— [303], art. 299, for “M. Leguire,” read “M. Seguin.”

— [306], l. 2, for “R. R. & G.,” read “R. K. and G.”

— [314], l. 2, for “D. R. Clark,” read “D. K. Clark.”

— [320], l. 1, for “Railroad, three pounds (Pennsylvania),” read “Railroad (Pennsylvania), three pounds.”

— [320], l. 7, for “coal,” read “coke.”

— [331], near bottom, for “The area is, therefore,

— [334], l. 15, for “44.7 lbs.,” read “14.7 lbs.”

— [335], l. 7, for “Railway Mechanics,” read “Railway Machinery.”

— [335], l. 10, for “two velocities,” read “low velocities.”

— [336], last l., for “entering part,” read “entering port.”

— [341], l. 11, for “properties,” read “proportions.”

— [341], last l., for “Nollan,” read “Nollau.”

— [346], l. 17, for “part,” read “port,” and for “construction,” read “contraction.”

— [355], l. 7, for “6300,” read “5170”; and l. 9, for “16,905,” read “15,775.”

— [363], l. 17, for “44 × 2 = 80,” read “44 × 2 = 88.”

— [363], l. 18, for “54½ × 3 = 103½,” read “54½ × 3 = 163½.”

— [367], l. 16, for “15.0
10,” read “15.0
16,”

— [368], l. 15, for “u = 135,” read “n = 135,” etc.

— [370], l. 7, for “feet,” read “per cent.”

— [376], for “19090,” read “19050.”

— [384], in last part of example, for “5280
4½ × 3.1416 × 4 = 37300,” read “25 × 5280
4 × 3.1416 × 4 = 37348.”

— [421], bottom line, for “decision,” read “division.”

— [423] and [424], in table, for “count,” read “cost.”

— [427], l. 32, for “which,” read “we.”

— [428], l. 4, transpose “Dr. Lardner, (1850,)” to the end of line 3.

— [443], l. 28, for “valuation,” read “solution.”

— [446], l. 11, for “attained,” read “obtained.”

— [459], l. 20, for “Hectametre,” read “Hectometre.”

— [459], l. 21, for “Ridometre,” read “Kilometre.”

— [461], l. 7, for “less than a, or o,” read “less a, or 0.”

— [468], l. 30, for “fractions,” read “functions.”

— [474], l. 18, for “Balbett,” read “Babbitt.”

— [479], l. 10, for “one sixth, with much less,” read “one sixth; with sand, much less.”

HANDBOOK

OF

RAILROAD CONSTRUCTION.

INTRODUCTION.

“They build not merely roads of earth and stone, as of old, but they build iron roads: and not content with horses of flesh, they are building horses of iron, such as never faint nor lose their breath.”—Dr. Bushnell.

RISE AND PROGRESS OF RAILROADS.

1. In 1825, the Stockton and Darlington Railroad (England), was opened.

In 1827, the Quincy (of Massachusetts), and Mauch-Chunk (Pennsylvania), were completed.

In 1829, the Liverpool and Manchester road, (England), was finished.

In 1833, a road was opened from Charleston, (South Carolina), to Augusta (Georgia).

In 1840, Belgium opened 190 miles of railroad.

In 1843, the railroad from Paris to Rouen (France), was completed.

In 1844, Belgium finished her system of 347 miles.

In 1846, Russia opened a railroad from the Wolga to the Don.

In 1847, Germany had in operation 2,828 miles.

In 1852, the Moscow and St. Petersburg road was finished.

2. In 1856, the United States of America had in operation 23,000 miles, and in progress 17,000 miles; employing 6,000 locomotive engines, 10,000 passenger and 70,000 freight cars; costing in all about 750,000,000 of dollars; running annually 114,000,000 miles, and transporting 123½ millions of passengers, and 30 millions of tons of freight per annum; performing a passenger mileage of 4,750,000,000, and a freight mileage of 3,000,000,000.

3. By mileage is meant the product of miles run, by tons or by passengers carried. Thus, 500 persons carried 100 miles, and 750 persons carried 75 miles, give a passenger mileage of

500 × 100 + 750 × 75 = 106,250.

4. The rate of progress in the United States has been as follows:—

At the present time, January 1, 1857, there is probably, in round numbers, 25,000 miles of completed road, or enough to extend entirely around the world. As regards the ratio of completed road to population, and as regards the actual length of railroad in operation, the United States stand before any other country.

INFLUENCE OF RAILROADS.

5. The effect of a judicious system of railroads upon any community is to increase consumption and to stimulate the production of agricultural products; to distribute more generally the population, to cause a balance between supply and demand, and to increase both the amount and safety of travelling. It is stated that within two years after the opening of the New York and Erie Railroad, it was carrying more agricultural produce than the entire quantity which had been raised throughout the tributary country before the road was built.

6. The following table, cut from a Chicago paper, shows the effect of railroad transport upon the cost of grain in that market:—

Thus a ton of corn carried two hundred miles, costs, per wagon transport, more than it brings at market; while moved by railroad, it is worth $21.75 per ton. Also wheat will not bear wagon transport of three hundred and thirty miles; while moved that distance by railroad it is worth $44.55 per ton.

7. By railroads, large cities are supplied with fresh meats and vegetables, butter, eggs, and milk. An unhealthy increase of density of population is prevented, by enabling business men to live five, ten, or fifteen miles away from the city and yet do business therein. The amount of this diffusion is as the square of the speed of transport. If a person walks four miles per hour, and supposing one hour allowed for passing from the house to the place of business, he cannot live at a greater distance than four miles from his work. The area, therefore, which may be lived in, is the circle of which the radius is four, the diameter eight, and the area fifty and one quarter square miles. If by horse one can go eight miles per hour, the diameter becomes sixteen miles, and area two hundred and one square miles; and, if by railroad he moves thirty miles per hour, the diameter becomes sixty miles, and the area 2,827 square miles. The effect of such diffusion is plainly seen about Boston, (Massachusetts). People who in 1830 were mostly confined to the city, now live in Dorchester, Milton, Dedham, Roxbury, Brookline, Brighton, Cambridge, Charlestown, Somerville, Chelsea, Lynn, and Salem; places distant from two to thirteen miles.

8. In railroads, as in other labor saving (and labor producing) machines, the innovation has been loudly decried. But though it does render some classes of labor useless, and throw out of employment some persons, it creates new labor far more than the old, and gives much more than it takes away. Twenty years of experience shows that the diminished cost of transport by railroad invariably augments the amount of commerce transacted, and in a much larger ratio than the reduction of cost. It is estimated by Dr. Lardner, that 300,000 horses working daily in stages would be required to perform the passenger traffic alone, which took place in England during the year 1848. It is concluded, also, from reliable returns, that could the whole number of passengers carried by railroad, have been transported by stage, the excess of cost by that method above that by railroad would have been $40,000,000.

SAFETY OF RAILROAD TRAVELLING.

9. If we know that in a given time the whole distance travelled by passengers was 500,000 miles, and that in such time there occurred one fatal accident, it follows that when a person travels one mile, the chances are 499,999 against one of losing life. If he travel ten miles, the chances are 49,999 against one, or ten times as many of meeting with loss of life; and generally the chances of accident are as the distance travelled. In 1855, the whole number of miles run by passengers in the United States was, in round numbers, 4,750,000,000, while there were killed one hundred and sixteen; or one in every 41,000,000, very nearly. (The ratio in England is one in every 65,000,000.) Now if for each 400,000 miles travelled by stage passengers, (a distance equal to sixteen times round the world,) one passenger was killed, and if the whole railroad mileage could be worked by stages, there would be annually 11,875 lives lost; or one hundred times the number annually lost by railroad. Thus it would be one hundred times safer to travel by railroad than by stage. The danger of steamboat travelling is far greater than by stage.

PRELIMINARY OPERATIONS.

10. The first step to be taken in starting a railroad enterprise, is the choice of a board of directors (provisional), whose duty is to find all that can be known of the commercial, financial, and agricultural nature of the country to be traversed. To determine as near as possible its ability to build and support a road; and to obtain the necessary legislative enactments.

11. The determination of the increase of traffic which the road may be expected to excite, is a difficult matter. There can be few rules given for proceeding in such an inquiry. It seems very easy to prove by what roads have done, that any project will be profitable.

An abstract of a report lately published, tries to prove that a road will pay forty-five and one half per cent. net; the working expenses being assumed at only thirteen and one half per cent. of the gross receipts. The error here lies in assuming the working expenses too low, as few roads in the country have been worked for less than forty per cent.; a more common ratio being fifty one-hundredths of the gross receipts.

Not one half of railroads are built for the original estimate. In few cases has sufficient allowance been made for the sacrifice undergone in negotiating the companies’ securities. All general instructions that can be given relating to the determination of prospective profits, are, to keep the estimate of constructing and working expenses high, and that of the assumed traffic low; not so low, however, as to require a too lightly built road.

MECHANICAL PRINCIPLES OF LOCOMOTION.

12. The superiority which the modern railroad possesses over the common, McAdam, plank, or turnpike-road, consists, first, in the reduction of the resistance to motion, and second, in the application of the locomotive steam-engine.

13. The effect of grades of a given incline upon a railroad is relatively more than upon common roads; for as the absolute resistance on a level decreases, the relative resistance of grades augments: whence to obtain the full benefit of the system, we must reduce much more the grades and curvature upon a railroad, than on a common road. For example, if the resistance to moving one ton upon a level upon a railroad was ten pounds, and upon a common road forty pounds, where a twenty-three feet grade would be admissible upon the former, we might use an incline of ninety-three feet per mile upon the latter.

14. The resistance to the motion of railroad trains increases rapidly with the speed;[^[1]] whence the grades of a passenger road where a high average speed is used, may be steeper than those of a road doing a freight business chiefly.

[1]. See chapter XIV.

DETERMINATION OF CHARACTER OF ROAD.

15. Upon a correct idea of what the road ought to be, depends in a great degree its success. The amount of capital expended upon the reduction of the natural surface, depends upon the expected amount of traffic. The traffic remaining the same, the greater the capital expended in reducing grades and curvature, the less will be the working expense; and the less the construction capital, the greater that for maintenance. The limit of expenditure must be such as to render the sum of construction and maintaining capital a minimum.

The bad effect of grades upon the cost of maintaining and of working railroads, is not so great as many suppose. Of the whole cost of working, only about forty per cent. can be charged to locomotive power; and of this, not more than sixty-two per cent. is effected by grades.[^[2]]

[2]. See appendix F.

16. The degree of curvature to be admitted upon any road depends somewhat upon the speeds at which trains are to be run. The larger the radius of curvature, the greater may be the speed; at the same time the elevation of the exterior rail upon curves may be less, and therefore more adapted to freight trains. High rates of speed are considered upon some competing roads necessary; but are, even in such cases, necessary evils. The wear of cars and of engines, of permanent way and of bridges, increase in a rapid ratio with the velocity. The maximum speed for freight trains should never exceed fifteen miles per hour, or for passenger trains from twenty to twenty-five miles per hour.[^[3]]

[3]. See chapter XVI.

17. The agricultural nature of the country and its commercial position, will determine the nature of the traffic, whether passenger or freight, and also the amount. The amount and nature of the traffic will limit the curvature, and will partially determine the arrangement of grades.

GAUGE.

18. The question of broad and narrow gauge has led to much discussion, and both plans claim among their advocates some of the best engineers. The narrow gauge (American and English,) is four feet eight and one half inches (from inside to inside of rail). The maximum adopted, is (the Great Western of England) seven feet. The American maximum (New York and Erie, and Ohio and Mississippi) is six feet. There is also in America four feet ten inches, five feet, and five feet six inches. The advantage of the broad gauge for a road doing an extensive business, is the increased stowage room in freight cars, thus rendering admissible shorter trains; by which the locomotive power is more directly applied on curves. More comfortable passenger cars, (the same length of car of course accommodates the same number of passengers). The disadvantages of a wide gauge are, increased expense of cutting, embanking, bridging, and masonry; increased expense of engines, cars, rails, sleepers, and all machinery; more wear and tear upon curves, by reason of greater difference between the lengths of inner and outer rails, and increased atmospheric resistance to fast trains, from increased bulk.

19. The general conclusion arrived at by a commission appointed by the Great Western Railway Company, (England,) consisting of Messrs. Nicholas Wood, J. K. Brunel, and John Hawkshaw, was, that four feet, eight and one half inches was rather narrow, but still enough for a certain class of roads; that two or three inches made no material difference; that seven feet was too wide for any road; that the weight of the broad gauge engine, compared with the small increase of power, was a serious evil; that engines could be run with perfect safety upon the narrow gauge at any speed from thirty to sixty miles per hour, and that no more had been attained upon the broad; that rolling friction was less upon the broad, owing to the increased diameter of wheels, but that friction from curves and atmospheric resistance was greater.

20. D. K. Clark, in “Railway Machinery,” p. 300, 301, makes the resistance as deduced from experiments made upon both the four feet, eight and one half inches, and the seven feet gauge, considerably greater upon the former than on the latter; but as the narrow gauge trials were made upon a curved road, with rails in a bad state, in average weather, while those upon the broad were made in good weather, upon a good and straight line, he leaves the gauge question open, and uses the same formula for all widths.

21. Want of increased power, can be an apology for increased gauge, until the capacity of the narrow gauge has been filled. The strongest engines in the world are upon the four feet, eight and one half inch gauge. No engines in America surpass or compare for absolute strength, with those upon the Baltimore and Ohio Railroad. The most powerful passenger engine ever built for high speeds, is Crampton’s engine “Liverpool,” (London and North-western Railroad, England,) gauge four feet, eight and one half inches.

GENERAL ESTABLISHMENT OF ROUTE.

22. The straight and level line connecting any two points, is of course the best for the completed road; but this is seldom practicable. Way towns must be accommodated to a certain extent; but the main line should not be lengthened on that account, unless the traffic and capital furnished by such town is not only sufficient to pay for the construction and maintenance of the extra length, but also to carry the entire through traffic over such increased distance. If the town is unable to support such a burden, it may be able to build and maintain a branch.

23. Routes placed upon the immediate bank of a large stream, are generally crossed by a great number of deep gorges, which serve to drain the side lands.

24. Routes placed upon sloping land, when the axis of the road and the natural descent are at right angles to each other, are more subject to slides than when placed upon plateaus or “bottoms.”

25. Lines crossing the dividing ridges of separate waters, rise and fall a great deal; thus rendering necessary a strong motive power to work the road. Such roads are the Western of Massachusetts, passing from the valley of the Connecticut at Springfield, to the Hudson River valley at Greenbush. Also those roads crossing the Alleghanies. And such will be the Pacific road, crossing first the Rocky Mountains to the Great Basin, and second, the Sierra Nevada into the Sacramento valley.

CHAPTER I.
RECONNOISSANCE.

26. The object of the reconnoitre is to find approximately the place for the road, (i. e. within half of a mile,) to find the general form of the country, and to choose that part which with reference to the expected traffic, shall give the best gradients; to determine the elevations of summits upon competing routes; and, in fine, to prepare the way for the survey.

GENERAL TOPOGRAPHY.

27. The general topography of a country may be ascertained by reference to State maps, where such exist, and when not, by riding over the district. The direction and size of watercourses, will show at once the position of summits.

Fig. 1.

28. Water flowing as in fig. 1, indicates a fall from B to E; and also traverse slopes from a a and c c to d d.

Fig. 2.

29. Fig. 2 shows a broken ridge a a a from which the water flows in both directions; and in general, the sources of streams point towards the higher lands.

Fig. 3.

30. If it be required to join the points A and D by railroad, (fig. 3.) it may be better to pass at once from A through B and C, than to go by the streams F E, F′ E′. By the latter route the road would ascend all of the way from A to E; and descend from E′ to D. By the first if it requires steep gradients to rise from A to B, and to fall from C to D, still if the section B C is a plateau, and if the rise between A and B and A and E is the same, by grouping the grades at B and C we may so adapt the motive power, as to take the same train from A to D without breaking. The general arrangement of grades by the line A B C D is then as fig. 4; and A F E E′ F′ D, as in fig. 5. The saving in this case is by length, as the same amount of power is required to overcome a given ascent.

Fig. 4.

Fig. 5.

31. Valleys generally rise much faster near their source, than at any point lower down; also the width increases as we approach the debouch. Fig. 6 shows the cross sections of a valley from its source to the mouth.

Fig. 6.

32. In the case of parallel valleys running in the same direction, the form will be as in fig 7. Let 1 2, 1 2, etc., represent a datum level, or a horizontal plane passing through the lowest point. The line a b, shows the height of the bottom at B; c d that at D, e f that at E, and g h that at C. The broken lines i, k, l, m, n, show the general form of the land. Now by the route m m m m, from A to F, we have the profile m m m m, fig. 8, by n n n n, the profile n n n n, and by o o o, the profile o o o.

Fig. 7.

Fig. 8.

Fig. 9.

33. In the case of parallel valleys running in opposite directions, as in fig. 9, we have the form there shown; and the profiles corresponding to the several lines are shown in fig. 10. As we should always adopt the line giving the least rise and fall, other things being equal, it is plain which line on the plan we must follow.

Fig. 10.

34. In passing from A to B, figs. 11 and 12, by the several lines c, d, e, f, we have the profiles shown at c, d, e, f, from which it appears, that the nearer we cross to the heads of streams, the less is the difference of heights.

Fig. 11.

Fig. 12.

Fig. 12 (a).

35. If we wish to go from A to B, fig. 12 (a), we should of course take first the straight line; but being obliged to avoid the hill C, on arriving at d, we should not try to recover that line at e, but proceed at once to B. Also as we are obliged to pass through d, we ought to go directly to d and not by the way of c; and the same idea is repeated between A and d; the last line being A b d B. Few rules can be given in the choice of routes. Practice only will enable the engineer to find the best location for a railroad.

BAROMETRICAL LEVELLING.

36. The relative height of summits, the rate of fall of streams, and absolute elevation, within a few feet, may be easily, rapidly, and cheaply found by the barometer. This also affords an excellent check upon subsequent levelling operations. The results thus obtained depend upon the physical property, that the density of the air decreases as the square of the height.

37. The barometer is a glass tube, partly filled with mercury, having a vacuum in the upper part. By it the exact density of the air at any point is determined. Accompanying are two thermometers; one attached, showing the temperature of the barometer; the other detached, showing the atmospheric temperature.

38. Knowing now the manner of finding the density of the air at any two points, and also the relation between density and height, the operation of levelling by the barometer is very simple.

The modus operandi is as follows, (see tables A, B, C, and D):—

Let us have the notes.

Final correction by table D. The barometer at the lower station being 26.80, and the tabular number against 27.56 being 0.22, that for 26.80 will be 0.31, and we have

1000 to .31 as 928.2 to 0.287, or 0.3,

which add to 928.2 and we have as the final height

928.5 metres, or 928.5 × 3.28 = 3045.48 feet.

The tables above referred to, are those of Mr. Oltman, and are considered as the most convenient and reliable of any published.

[4]. The degrees refer to the centigrade thermometer.

CHAPTER II.
SURVEY.

TOPOGRAPHICAL SKETCHING.

39. Topographical drawing includes every thing relating to an accurate representation upon paper, of any piece of ground. The state of cultivation, roads, town, county, and state boundaries, and all else that occurs in nature. The sketching necessary in railroad surveying, however, does not embrace all of this, but only the delineation of streams and the undulations of ground within that limit which affects the road, perhaps 500 feet on each side of the line. The making of such sketches consists in tracing the irregular lines formed by the intersection of the natural surface, by a system of horizontal planes, at a vertical distance of five, ten, fifteen, or twenty feet, according to the accuracy required.

Fig. 13.

40. Suppose that we wish to represent upon a horizontal surface a right cone. The base m m, fig. 13, is shown by the circle of which the diameter is m, m. If the elevation is cut by the horizontal planes a a, b b, c c, the intersection of these planes with the conical surface is shown by the circles a, b, c, in plan. The less we make the horizontal distances, on plan, between the circles, the less also will be the vertical distance between the planes.

Wishing to find the elevation of any line which exists on plan, as 1, 2, 3, 3, 2, 1, we have only to find the intersection of the verticals drawn through the points 1, 2, 3, 3, 2, 1, and the elevation lines a a, b b, c c; this gives us the curve 4, 5, 6, 7, 6, 5, 4.

Fig. 14.

41. Again, in fig. 14, the cone is oblique, which causes the circles on plan to become eccentric and elliptic. Having given the line 1, 2, 3, as before, we find it upon the elevation in the same manner.

42. In the section of regular and full lined figures, the horizontal and vertical projections are also regular and full lined; but in a broken surface like the ground, the lines become quite irregular.

Suppose we wish to show on plan the hill of which we have the plan, fig. 15, and the sections figs. 16, 17, and 18. Let AD be the profile (made with the level) of the line AD on plan, fig. 15. B E that of B E, and C F that of CF.

Fig. 15.

Fig. 16.

Fig. 17.

Fig. 18.

To form the plan from the profiles proceed as follows:—

Intersect each of the profiles by the horizontal planes a a, b b, c c, d d, equidistant vertically. In the profile A D, fig. 18, drop a vertical on to the base line from each of the intersections a, b, c, d, d, c, b, a. Make now A 1,1 2, 2 3, 3 4, etc., on the plan equal to the same on the profile. Next draw, on the plan, the line B E, at the right place and at the proper angle with A D; and having found the distances B 1, 1 2, 2 3, etc., as before, transfer them to the line B E on plan. Proceed in the same manner with the line C F.

The points a a a, b b b, c c c, are evidently at the same height above the base upon the profiles, whence the intersections of these lines with the surface line or 1 1 1, 2 2 2, 3 3 3, etc., on the plan, are also at the same height above the base; and an irregular line traced through the points 1 1 1, or 2 2 2, will show the intersection of a horizontal plane, with the natural surface.

When as at A we observe the contour lines near to each other, we conclude that the ground is steep. And when the distances are large, as at 6, 7, 8, we know that the ground falls gently. This is plainly seen both on plan and profile.

Fig. 15.

Having now the topographical sketch, fig. 15, we may easily deduce therefrom at any point a profile. If we would have a profile of G E, on plan, upon an indefinite line G E, fig. 19, we set off G 1, 1 2, 2 3, 3 4, etc., equal to the same distances on the plan. From these points draw verticals intersecting the horizontals a a, b b, c c; and lastly, through the intersections draw the broken line (surface line or profile) a, b, c, d, d, c, b, a. Thus we see how complete a knowledge of the ground a correct topographical sketch gives.

Fig. 19.

43. Field sketches for railroad work are generally made by the eye. The field book being ruled in squares representing one hundred feet each. When we need a more accurate sketch than this method gives, we may cross section the ground either by rods or with the level.

By making a very detailed map of a survey, and filling in with sketches of this kind, the location may be made upon paper and afterwards transferred to the ground.

So far we have dealt with but one summit; but the mode of proceeding is precisely the same when applied to a group or range of hills, or indeed to any piece of ground.

44. As a general thing, the intersection of the horizontal planes with the natural surface (contour lines) are concave to the lower land in depressions, and convex to the lower land on spurs and elevations. Thus at B B B b b, fig. 20, upon the spurs, we have the lines convex to the stream; and in the hollows c c c, the lines are concave to the bottom.

45. Having by reconnoissance found approximately the place for the road, we proceed to run a trial line by compass. In doing this we choose the apparent best place, stake out the centre line, make a profile of it, and sketch in the topography right and left.

Fig. 20.

Fig. 21.

Fig. 22.

Suppose that by doing so we have obtained the plan and profile shown in figs. 21 and 22, where A a a B is the profile of A C D B, on the plan. The lowest line of the valley though quite moderately inclined at first, from A to C, rises quite fast from C to the summit; and as the inclination becomes greater, the contour lines become nearer to each other.

Now that the line may ascend uniformly from A to the summit, the horizontal distances between the contour lines must be equal; this equality is effected by causing the surveyed line to cut the contours square at 1, 2, 3, 4, and obliquely at 5, 8, 10. Thus we obtain the profile A 5 5 B.

Figs. 23 and 24.

46. Having given the plan and profile, figs. 23 and 24, where A C D B represents the bed of the stream, in profile, if it were required to put the uniformly inclined line A m m B, upon the plan, we should proceed as follows. Take the horizontal distance A m from the profile, and with A (on plan) as a centre, describe the arc 1, 3. The point m on the profile is evidently three fourths of a division above the bed of the stream. So on the plan we must trace the arc 1, 3, until we come to a, which is three fourths of b c, from b. Again, m′ is nine and one half divisions above m. From a, with a radius m n on profile, describe the arc 4, 5, 6. Now, as on the profile, in going from m to m′, we cross nine contour lines, and come upon the tenth at m′, so on the plan we must cross nine contour lines and come upon the tenth, and at the same time upon the arc 4, 5, 6.

Proceeding in this way, we find A, a, b, B, on the plan, as corresponding to A m m′ B on the profile.

To establish in this manner any particular grade, we have first to place it upon the profile, and next to transfer it to the plan.

47. It may be remembered as a general thing, that the steepest line is that which cuts the contour line at right angles; the contour line itself is level, and as we vary between these limits we vary the incline.

GENERAL ESTABLISHMENT OF GRADES.

48. Considerable has been written upon the relation which ought to exist between the maximum grade, and the direction of the traffic. Some have given formulæ for obtaining the rate and direction of inclines as depending upon the capacity of power. This seems going quite too far, as the nature of the ground and of the traffic generally fix these in advance.

49. Between two places which are at the same absolute elevation, there should be as little rise and fall as possible.

50. Between points at different elevations, we should if possible have no rise while descending, and consequently no fall while on the ascent.

51. Some engineers express themselves very much in favor of long levels and short but steep inclines. There are cases where the momentum acquired upon one grade, or upon a level, assists the train up the next incline. The distance on the rise during which momentum lasts, is not very great. A train in descending a plane does not receive a constant increase of available momentum, but arrives at a certain speed, where by increased resistance and by added effect of gravity, the motion becomes nearly regular. Up to this point the momentum acquired is useful, but not beyond.

Any road being divided into locomotive sections, the section given to any one engine should be such as to require a constant expenditure of power as nearly as possible; i. e., one section, or the run of one engine, should not embrace long levels and steep grades. If an engine can carry a load over a sixty feet grade, it will be too heavy to work the same load upon a level economically. It is best to group all of the necessarily steep grades in one place, and also the easy portions of the road; then by properly adapting the locomotives the cost of power may be reduced to a minimum.

As to long levels and short inclines the same power is required to overcome a given rise, but quite a difference may be made in the means used to surmount that ascent.

Fig. 25.

52. Suppose we have the profiles A E D and A B D, fig. 25. The resistance from A to D by the continuous twenty feet grade is the same as the whole resistance from A to B and from B to D. The reason for preferring A E D is, that an engine to take a given load from B to D would be unnecessarily heavy for the section A B; while the same power must be exerted at each point, of A E D. Also the return by A E D is made by a small and constant expenditure of power, being all of the way aided by gravity; while in descending by B, we have more aid from gravity than we require from D to B, after which we have none.

When the distances A B, B C, are sixty and twenty miles in place of six and two, we may consider the grades grouped at B D, and use a heavier engine at that point, as we should hardly find eighty miles admitting of a continuous and uniform grade.

EQUATING FOR GRADES.

53. In comparing the relative advantages of several lines having different systems of grades, it is customary to reduce them all to the level line involving an equal expenditure of power.

The question is to find the vertical rise, consuming an amount of power equal to that expended upon the horizontal unit of length. This has been estimated by engineers all the way from twenty to seventy feet. For simple comparison it does not matter much what number is used if it is the same in all cases; but to find the equivalent horizontal length to any location, regard must be had to the nature of the expected traffic.

The elements of the problem are, the length, the inclination or the total rise and fall, and the resistance to the motion of the train upon a level, which latter depends upon the speed and the state of the rails and machinery.

From chapter XIV. we have the following resistances to the motion of trains upon a level:—

The power expended upon any road is of course the product of the resistance per unit of length, by the number of units. Calling R the resistance per unit upon a level, and R′ the resistance per unit on any grade, and designating the lengths by L and L′, that there shall be in both cases an equal expenditure of power, we must have

RL = R′L′,

whence the level length must be

L = L′R′
R.

Thus assuming the resistance on a level as twenty lbs. per ton, that on a fifty feet grade is

20 + 50
5280 of 2240, or 20 + 21.2 or 41.2,

and if the length of the inclined line is ten miles, the equivalent level length is

L = 41.2 × 52800
20 = 108768 feet, or 20.6 miles.

Also 10 miles × 41.2 lbs. = 412,

and 20.6 miles × 20 lbs. = 412.

54. The above may be somewhat abridged as follows: Let R be the resistance on a level. The resistance due to any grade is expressed by

W × 1
a,

where 1
a is the fraction showing the grade, and W the weight of the load.

The vertical height in feet, to overcome which we must expend an amount of power sufficient to move the train one mile on a level, must be such that

W × 1
a = R,

or

1
a = R
W;

and to find the number by which to equate, we have only to place the values of R and W in the formula. For example, let the speed be twenty miles per hour, the corresponding resistance is 10.3 lbs. per ton. W being one ton, or 2240 lbs., we have

1
a = R
W = 10.3
2240 = 1
218 of 5280, (the number of feet in one mile,)

1
218 of 5280 = 24 feet.

In the same manner we have

Thus when we take the speed as thirty miles per hour, for each thirty-two feet rise we shall consume an amount of power sufficient to move the train one mile on a level. In descending, the grade instead of being an obstacle, becomes an aid; indeed the incline may be such as to move the trains independently of the steam power. Thus if on account of ascending grades we increase the equated length, so also in descending we must reduce the length. The amount of reduction is not, however, the reverse of the increase in ascending, as after thirty or forty feet any additional fall per mile instead of being an advantage is an evil; as too much gravity obliges us to run down grades with brakes on. Twenty-five feet per mile is sufficient to allow the train to roll down, and any more than this is of very little use. Therefore for every mile of grade descending at the rate of twenty-five feet per mile we may deduct one mile in equating, and for every mile of grade descending twelve and one half feet per mile deduct a proportional amount; but for any more fall per mile than twenty-five feet, no allowance should be made; i. e., if we descend at the rate of forty feet per mile, we may deduct one mile in equating for the twenty-five feet of fall, and throw aside the remaining fifteen feet.

55. This is a common method of equating for grades, and represents a length which is proportional to the power expended, but not proportional to the cost of working, as the ratios of power expended and cost of working under different conditions are very different, double power requiring only twenty per cent. more working capital. The above rules, therefore, require a correction.

Now the resistance on a level being at a velocity of twenty miles per hour, 10.3 lbs. per ton by the formula

1
a = R
W,

the vertical height in feet causing a double expenditure of power is twenty-four; but as above, the whole expense of a double power is increased by only twenty-five per cent.; we should not add one mile for twenty-four feet rise, but one fourth of a mile only, or one mile for each ninety-six feet; and by correcting our former table in this manner, we have the following table:—

So much for equating for the ascents. In descending, we have allowed one mile reduction for each mile of twenty-five feet of descending grade; but as in ascending we correct the first made table, so in descending we must also correct as follows. If we needed no steam power either while descending or afterwards, we should only save wood and water; as a general thing the fire must be kept up while descending, and the only gain is a small part of the expense of fuel; so small, in fine, that with the exception of roads which incline for the whole or a great part of their length, no reduction should be made.

COMPARISON OF SURVEYED LINES.

56. The requisite data for an approximate comparison of lines are, the measured length, total rise, total fall.

Assume the number by which to equate, as ninety-six, and we shall have

The cost of construction being assumed as the actual length, and that of working as the equated length, we have the final approximate comparison thus:—

Assume the construction cost as $25,000 per mile, and the cost of maintenance $4,000 per mile, and we have

The line A to the line B as

100 × 25000 + 116.66 × 4000 × 100
6 = 10,277,333, is to

90 × 25000 + 138.46 × 4000 × 100
6 = 11,480,667;

or A is to B as 10.3 to 11.5 nearly, although the line A is ten miles longer than B.

CHAPTER III.
LOCATION.

ALIGNMENT.

57. The broken line furnished by the survey is of course unfit for the centre line of a railroad. The angles require to be rounded off to render the passage from one straight portion to the other easy.

Fig. 26.

58. Let A X B, fig. 26, represent the angle formed by any two tangents which it is required to connect by a circular curve. It is plain that knowing the angle of deflection of the lines A X, B X, we obtain also the angles A C X, X C B. The manner of laying these curves upon the ground is by placing an angular instrument at any point of the curve, as at A, and laying off the partial angles E A a, E A M, E A G, etc., which combined with the corresponding distances A a, a M, M G, fix points in the curve.

These small chords are generally assumed at one hundred feet, except in curves of small radius (five hundred feet) when they are taken less.

The only calculation necessary in laying out curves, is, knowing the partial deflection to find the corresponding chord, or knowing the chord, to get the partial angle.

As the radius of that curve of which the angle of deflection is 1° is 5730 feet, the degree of curvature for any other radius is easily found. Thus the radius 2865 has a degree of curvature per one hundred feet of

5730
2865 = 2°;

again,

5730
2000 = 2°.86 or 2° 51.6.

The radius corresponding to any angle is found by reversing the operation. If the angle is 3° 30′, or 210′, we have

5730 × 60
210 = 1637 feet radius.

The following figures show the angle of deflection for chords one hundred feet long, corresponding to different radii:—

Points in any curve may also be fixed by ordinates, as a b, M D′, G F, or by E a, K M, etc.

For the details of locating, of running simple and compound curves, and of the calculations therefor, the reader is referred to the works of Trautwine, and of Henck.

Fig. 27.

59. Suppose now that we have the surveyed lines m m, and n n, fig. 27, one of which is to be finally adjusted to the ground. The shortest line is the straight one, which is generally impracticable. The most level line is the contour line, which is also impracticable. Between these two lies the right line, which is to be found by an instrumental location. The line A n n n n B, on the plan, gives the profile A n n n n B. The line A m m m m B gives the profile A m m m m B, while the finally adjusted line A 1 2 3 4 5 6 gives the profile A 1 2 3 4 5 6 B.

Fig. 28.

60. Again, in fig. 28, the straight line A n n n B gives the profile A n n n B, requiring either steep grades or a great deal of work. By fitting the line to the ground, as by the line A a b c d ... m n o B, we obtain the profile A a b c ... m n o B.

FINAL ADJUSTING OF GRADES.

Fig. 29.

61. The general arrangement of inclines must not be interfered with to save work, but a large part of the excavation and embankment may be saved by breaking up long grades so as not to affect materially the character of the road. Upon some lines the grades must necessarily undulate, as in fig. 29. The difference in the amount of work is plainly seen. The steepest grades thus applied must not be greater than the ruling grade upon the travel of one engine.

62. In long and shallow cuts and fills, the best plan is to place the grade line quite high, avoiding much cutting, and to make the embankments from side cuttings, (ditching). Banks must at least be placed two or three feet above the natural surface, first to prevent the snow from lodging too much upon the rails, second, to insure draining.

63. Snow fences are much used in the northern parts of the United States. These are high pieces of lattice-work, made roughly, but well braced; from eight to twelve feet high, and standing from sixty to one hundred feet from the road. The object of the fence is to break the current of the wind, and cause it to precipitate its snow. Close fences effect the object no better than the open ones, are more liable to blow down, and cost more.

64. In locating a road which is to have a double track eventually, regard must be paid to this fact in side-hill work. The first track should, if possible, be so placed as not to require moving when the double line is put on.

COMPARISON OF LOCATED LINES.

65. In this comparison there is an element which does not enter the approximate comparison of surveyed lines, curvature. The resistance arising from this cause has never been accurately determined. Mr. McCallum estimates the resistance at one half pound per degree of curvature per one hundred feet; i. e., the resistance due to curvature on a 4° curve, would be two lbs. per ton, (see report of September 30, 1855). Mr. Clark estimates the resistance due to curves of one mile radius and under, as 6.3 lbs. per ton, or twenty per cent. of the whole resistance. The average radius encountered, therefore, by Mr. Clark, would be, at Mr. McCallum’s estimate,

6.3
0.5 = 12° nearly, or 477.5 feet.

So small a radius is by no means allowable upon English roads; thus the estimate of Mr. Clark and of Mr. McCallum differ considerably. Experiments might easily be made with the dynamometer upon different curves, by which we might find very nearly the correct resistance caused by curves.

The curvature on any road cannot be adjusted to trains moving at different speeds.

66. The tractive power acts always tangent to the curve at the point where the engine is, and thus tends to pull the cars against the inner rail. The tangential force, generated by the motion of the cars, tends to keep the flanges of the wheels against the outer rail; and only when a just balance is made between the tractive and tangential forces, the wheel will run without impinging on either rail, (the wheel being properly coned). For these forces to balance, there must be a fixed ratio between the weight of a car and the speed, (not the weight of a train, as the shackling allows the cars to act nearly independently, some indeed rubbing hard for a moment against the rail, while the next car is working at ease). Whenever the right proportion is departed from, as it nearly always is, (and perhaps necessarily in some cases,) upon railroads, the wheels will rub against one rail or the other. Thus on any road where the speed on the same curve, or the radii of curvature under the same speed, differ, there must be loss of power, and dragging or pushing against the rails.

67. We are obliged to elevate the outer rail (see chapter XIII.), for the fastest trains, and the slower trains on such roads will therefore always drag against the inner rails. Thus in practice we generally find the inside of the outer rail most worn on passenger roads, and the inside of the inner rail upon chiefly freight roads.

68. It has been the practice of some engineers in equating for curvature, to add one fourth of a mile to the measured length for each 360° of curvature, disregarding the radius, as the length of circumference increases inversely as the degree of curvature.

69. Now in equating for grades, in doubling the power we do not double the expense of working. We however increase it more by curvature than we do by grades, because besides requiring double power, the wear and tear of cars and rails and all machinery is increased upon curves, which is not the case upon grades.

70. The analysis of expense (in Appendix F.) upon the New York system of roads, gives the following:—

Now each 360° will be equal to 75
100 of one quarter of a mile, or 75
400 of a mile; whence the number of degrees which shall cause an expense equal to one straight and level mile, will be 1920°.

71. The number of degrees by Mr. McCallum’s estimate would be thus:—

The resistance upon a level being ten lbs. per ton, and that due to curves one half pound per ton, per degree per one hundred feet; the length of a 2° curve to equal one mile will be

10 lbs.
1 lb.,

or ten miles. Also ten miles, or 530 hundred feet by 2° is 1060°.

72. Again, by Mr. Clark’s resistance of twenty per cent. of the level resistance, upon curves averaging 2°, we have as the length of 2° curve

10
2 = 5 miles,

or 265 hundred feet, which by 2° gives 530°.

73. Averaging the first and last, we have as the number of degrees which should be considered as causing an amount of expense equal to one straight and level mile, 1225°, which averaging with the estimated resistance by Mr. McCallum, gives finally 1142½° as causing an expense equal to one straight and level mile, or, in round numbers, 1140°.

74. Suppose now that we would know which of the lines below to choose.

Assuming the speed as twenty miles per hour, the number by which to equate for grades, see chapter II., is ninety-six, also the number of degrees for curvature 1140, whence,

and if the cost of construction is as the actual, and the cost of maintaining and working as the mean equated length, we have, as a final comparison,

A to B as 100 + 147.46 to 110 + 141.31,

or as

247.46 to 251.31.

Here the extra grades on the one hand nearly equal the curvature and the extra length on the other hand.

75. As a further example in the comparison of competing lines, let us take the actual case of the location of the eastern part of the New York and Erie Railroad.

It was questioned which of the two lines between Binghampton and Deposit should be adopted, and also between the mouth of Callicoon Creek and Port Jervis.

Fig. 30.

Between A and c, fig. 30, were located the lines shown in the sketch, one following the Susquehanna river from A to B, thence crossing the dividing ridge between that river and the Delaware to Deposit (c). The other passing up the Chenango river to a, thence crossing first the summit M to the Susquehanna at L, and second the summit K, to Deposit (c). The elements of the two lines are as follows:—

Assuming the number by which to equate for grades, as 96, and the equating number of degrees of curvature as 1140°; equating for grades and curvature in both directions, we have,

Assuming the cost of working and of maintaining as $4,000 per mile, we have

The cost of building A to B as $746,900 to $628,600

The cost of operating A to B as (46.25 × 4000) × 100
6 to (56.96 × 4000) × 100
6,

giving the preference of $595,700 to the route A B c, notwithstanding that the estimate thereon exceeds that on B by $118,300. The route A B c was adopted.

Again, it was doubtful whether to adopt the route E F, in going from D to G, or the line I H. The following are the elements of the two lines:—

The mean equated lengths are as follows:—

The comparison as to cost is

I H to E F as $1,094,950 to $1,496,430,

and as to working,

I H to E F as (79.46 × 4000) × 100
6 to (66.56 × 4000) × 100
6,

and the sum as

Although the cost of E F is $401,480 more than that of I H, the line E F was adopted.

CHAPTER IV.
PRELIMINARY OPERATIONS.

SPECIFICATION.

76. The object of this paper is to define exactly the terms of the contract as regards execution of work. Every thing therein should be expressed in a manner so plain as to leave no room for misunderstanding.

A AND B RAILROAD.

77. Specification for Graduation.

LINE.

The centre of the road-bed to conform correctly to the centre line of the railroad, as staked out or otherwise indicated on the ground, and to its appropriate curvatures and grades as defined and described by the engineer; and the contractor shall make such deviations from these lines or grades at any time, as the said engineer may require. The road-bed to conform to the cross section which shall be given or described, or to such other instructions as may be given as hereinafter limited; and the same of the ditches and slopes of the work, and of all operations pertinent to the satisfactory performance of the graduation or masonry on the part or parts of the line contracted for.

CLEARING.

The ground forming the base of all embankments, and five feet beyond the foot of the slopes of all embankments, to be cleared as close to the surface as practicable, of all timber, saplings, brush, logs, stumps, or other perishable material. The valuable timber to be laid aside, beyond the clearing as directed by the engineer, the rest to be burned, if this can be done safely, otherwise to be moved beyond the limits of the cleared ground. The ground for ten feet beyond the top lines of all slopes of cuttings shall be cleared in like manner, of all timber and saplings. Wherever additional ground has to be taken in widening excavations to obtain materials, or in widening embankments to dispose of surplus material, or in grading for turnouts or depot grounds, an additional amount of ground shall be cleared in like manner; and when directed by the engineer, wherever additional space is required for outside ditching, or for alterations of roads or watercourses, or otherwise.

GRUBBING.

All stumps and large roots within ten feet of the grade line shall be grubbed out to the entire width of the work, and moved at least ten feet beyond the slopes. The cost of all clearing and grubbing is included in the price for earth work, which price is also understood to include all clearing and grubbing necessary in borrowing pits, spoil banks, road crossings, alterations of roads and watercourses, the formation of ditches or otherwise. The necessary clearing and grubbing in all cases to be kept completed five hundred feet in advance of any work in progress.

MUCKING.

Wherever mud, muck, or similar soft material occurs in excavations or embankments, within two feet of subgrade, it shall be removed and replaced by compact earth or gravel.

GRADE.

The grade lines on the profiles show the true grade, and correspond with a line two inches below the bottom of the iron rail of the superstructure. What is called subgrade corresponds with a line placed eighteen inches below the grade.[^[5]]

[5]. The distance between grade and subgrade depends somewhat upon the climate, but is generally between one and two feet. See chap. XIII.

WIDTH OF ROAD, AND SLOPES.

The width of road-way, unless otherwise directed, shall be twenty-two feet wide at grade in earth excavations, and eighteen feet wide in rock excavations. Both rock and earth shall be taken out eighteen inches below grade for the entire width of road-way. The bottoming to be replaced by gravel, broken stone, or spawls, in such manner as shall be directed by the engineer, leaving the necessary ditches of the width and depth directed on either side. The contractor will not be paid for any rock excavated beyond the slope lines of one to eight from the required width, or for any earth excavated beyond slope lines of one and one half horizontal to one vertical, unless directed by the engineer to move additional rock or earth.

BLASTING.

All blasting shall be done at the risk of the first party, who shall be liable to the second parties, or to the railroad company, for any damages incurred in consequence, to dwelling-houses, individuals, or otherwise.

DITCHES.

Whenever required, ditches shall be cut along the tops of the slopes, of the form and size and in the position directed.

SURPLUS MATERIAL.

Whenever the earth or rock required for the adjoining embankments exceeds the amount in the neighboring excavations, the contractor, when required, shall increase the width of said excavations, as directed by the engineer, to a sufficient width for a double track, provided that this additional width shall not be extended so as to produce an average haul of more than eight hundred lineal feet, on said borrowed stuff. And whenever the earth or rock to be moved from any cut exceeds in amount the adjoining embankments, (unless elsewhere wanted,) it shall be applied to widening the embankment to a width for a double track, within the same limits of haul; but for a greater haul than eight hundred feet, the contractor shall be paid
100 of a cent per yard per hundred feet of excess.

BORROW PITS.

Where the excavation does not furnish sufficient material to make the adjoining embankments, borrow pits may be opened. But no earth shall be deposited in spoil banks nor borrow pits opened without the knowledge and consent of the superintending engineer, who shall take care that such operations are arranged so as not to damage the road or its slopes, nor interfere with the widening of the road-bed at a future time for additional tracks.

MATERIAL TO BE SAVED.

If materials be found in the excavations applicable to useful purposes, such as building stone, limestone, gravel, minerals, etc., they shall be laid aside in such place as the engineer may direct, for use, to be applied then or subsequently to the construction of the road under the conditions of these specifications and of the contract.

CLASSIFICATION OF MATERIALS.

Earth—every thing except solid and loose rock. Loose rock—all boulders and detached masses of rock measuring over one cubic foot in bulk and less than five cubic yards. Solid rock, includes all work in ledge, which requires drilling and splitting, and all loose rocks containing more than five cubic yards.

The prices for excavation include all earth or rock excavated in ditching, bottoming, borrowing, road crossings, alterations of road crossings and water channels, and the construction of temporary roads, provided the average distance hauled on each section, be the same as stated on the schedule here annexed; but if the actual average haul on any section is found, on completion, to have been greater or less than the distance stated, a corresponding addition or deduction shall be made, of one cent per cubic yard per hundred feet which the actual haul exceeds or falls short of that stated.

EMBANKMENTS.

The embankments to be formed fifteen feet wide on the surface, unless otherwise directed, with slopes of one and one half horizontal to one vertical. Wherever the embankment is formed from ditching on either side, such ditching, and the crest of the slopes thereof shall in no case approach within six feet, nor within double the depth of ditch, of the foot of the proper embankment slope, allowing always on one side for a double track; and no soft mud or muck shall be allowed to enter the bank. Wherever watercourses or new channels for rivers require to be formed, they shall not approach within once and one half of the depth of such stream, plus twenty-five feet. Care shall be taken in forming embankments to exclude all perishable material.

SUBSIDENCE.

To allow for the after settlement of materials on embankments, they shall, when delivered to and accepted by the second parties, be finished to the full width to the following heights above subgrades, namely: all banks below five feet in height to be finished three inches above subgrade; at ten feet in depth, five inches; at twenty feet, six inches; and twenty-eight feet, seven inches; at thirty-five feet, eight inches; and at forty feet in depth, nine inches above grade; and intermediate heights in proportion; the engineer having the power to change these proportions at his discretion.

EXTRA EXCAVATION AND EMBANKMENT.

Whenever it is considered necessary to increase the width of the road-way for turnouts, water stations, or depot grounds, whether in excavation or embankment, such work shall be done at the contract prices, as may be directed. The opening of foundation pits in simple excavation, where coffer-dams or such like expedients are not necessary, and in places where such expedients are necessary, all excavation above the water line shall also be done at such increase or decrease of the contract price as shall be deemed proper by the engineer.

EMBANKING AT BRIDGES AND CULVERTS.

The contractor for earthwork shall not carry forward in the usual way any embankments within fifty feet of any piece of masonry, finished or in progress, (counting from the bottom of the slopes,) but shall in every such case have the earth wheeled to the walls or abutments, and carefully rammed to such width and depth, and in such manner as may be directed, when the embankment may be carried on as usual. The expense attendant upon any damage or rebuilding of mason work, consequent on neglect of these directions, shall be charged to the account of the first party. In case the mason work shall not be finished when the embankment approaches it, the contractor shall erect a temporary structure to carry over the earth, and proceed with the embankment on the opposite side; and the expense of said structure shall be paid by, and charged to, the contractor for masonry, in case such contractor shall have delayed beyond the proper or required time, the construction of the mason work; but if the mason work could not have been ready in season for the bank, then shall the expense belong to the contractor for the earthwork, whose price for graduation is understood to comprehend all such contingencies. For the above work of wheeling and ramming efficiently the earth around any piece of masonry, the contractor shall be paid —— cents per cubic yard, by the engineer’s measurement.

ROADS AND WATERCOURSES.

The first party is to make good and convenient road crossings wherever directed, and shall also make such alterations of existing roads, or watercourses, or river channels, or such new pieces of these pertinent the section undertaken by him, as may be required, and shall be paid for such work, whether earth, rock, or masonry, the prices, and no more, applicable to this contract. And such road crossings or other alterations referred to, he shall make at and within such times and in such form and manner as the engineer shall direct; and whenever the operations of the first party interfere with a travelled road, public or private, either by crossing or by making required alterations on it, the first party shall so operate as to afford at all times a safe and free passage to the public travel; and the first party shall be liable for any damage to which the second parties or the railroad company may become lawfully liable by reason of his neglect to maintain a safe and properly protected passage for the current travel.

BALLASTING.

Where gravel is used for the ballasting of the road-bed, it shall be of a quality satisfactory to the engineer, and shall be spread upon the road-bed to the width and depth required. When broken stone is used, it shall be of durable quality, and shall be broken so as to pass through a ring of three inches in diameter. The quantity will be measured in the road-bed as finished, and the contractor will be required to keep the ditches trimmed and clear.

RIP-RAP, OR RUBBLE SLOPES.

The first party shall distribute rubble stone over the slopes of earth embankments, whenever required to do so, to protect said slopes from the action of water. Such stone to be arranged by competent hands, and laid to such thickness, and with stones of such size, as shall be directed. Where the contractor has rock in the neighboring cuttings which is available, it shall be reserved and applied to this purpose; and when not, good rock shall be obtained where the contractor can conveniently get it.

MEASUREMENTS.

All earth or rock necessarily moved to complete the grading of this contract according to direction, will be measured in excavation only; and if the contractor (with the consent of the engineer,) should find it convenient to waste earth from an excavation, instead of carrying it to its proper embankment, and to borrow at some nearer point earth for said embankment to replace that which was wasted, he shall be paid for the earth from the original excavation in the order of its most economical arrangement for the second parties. All earth moved from borrowing pits shall also be measured in excavation only.

78. Specification for Masonry.

FIRST CLASS MASONRY.

First class masonry will apply to bridge abutments exceeding twenty-five feet in height, to the ring stones of arches, and to the piers of bridges in running water. The stone shall be laid at the rate of one header to two stretchers, disposed so as to make efficient bond. No header to be less than forty inches long, and no stretcher to be less than eighteen inches in width. No stone less than twelve inches in thickness, no stone to have a greater height than width, all stones to be placed upon the natural bed. The masonry throughout to have hammer dressed beds and joints. Vertical joints to be continued back at least ten inches from the face of the wall. The mortar joints on the face not to exceed one fourth of an inch in thickness. The stone to be laid with regard to breaking joints in the adjoining courses. The stone must be dressed complete before laying, and not be moved after being placed in the mortar. The face will not be tooled, but only roughly hewed, except for one half inch from the beds and joints, where it will be hammered. The ring stones of arches shall have beds to conform to the radius of the arch, with the end joints vertical, and be made to set smoothly on the centering, with the beds with the proper inclination. Each stone must extend through the whole thickness of the arch, and not be less than eight inches thick on the intrados. No spawls or pinners will be admitted. The ring stone shall be dimension work, according to the plans furnished, the beds and joints being truly dressed, but the faces left rough.

All first class work shall be carefully laid in good cement mortar, (see Art. Cement). Each stone before being laid shall be carefully cleaned and moistened; and masonry built in hot weather shall be protected from the sun as fast as laid, by covering with boards. Copings shall be built of stone of equal thickness, neatly dressed and laid.

All first class masonry shall be well pointed with cement pointing.

SECOND CLASS MASONRY.

To be applied to abutments less than twenty-five feet high, ring and face walls of bridges and culverts, and to piers not in running water, shall consist of stones cut in bed and build to a uniform thickness throughout, before being laid, but not hammered; they shall be laid on a level bed, and have vertical joints continued back at right angles at least eight inches from the face of the wall. The work need not be carried up in regular courses, but shall be well bonded, having one header for every three stretchers, and not more than one third of the stones shall contain less than two cubic feet, or be less than nine inches thick; and none of that third shall contain less than one and one half cubic feet, or be less than six inches thick. No more small stones shall be used than necessary to make even beds, the whole to be laid in cement mortar and pointed.

THIRD CLASS MASONRY.

Applicable to culverts, and to the spandrel backing of arches, shall consist of strong and well built rubble masonry, laid dry for culverts, but wet for backing. The culverts to be of such form and dimensions as the engineer may direct. The foundation courses of the side walls to consist of large flat stones, from eight to ten inches in thickness, laid so as to give a solid and regular basis for the side walls. The side walls to be laid with sound stone, and of sufficient size, and with beds having a fair bearing surface and good bond. The covering stone for culverts being not less than ten inches thick for two feet culverts, twelve inches for three feet culverts, and fifteen inches for four feet culverts; to be free from flaw or defect, and to have a well bedded rest upon each side wall, of not less than twelve inches for two and three feet culverts; and not less than fifteen inches for larger ones. In case such stone cannot be obtained, a dry rubble arch may be thrown instead, well pinned and backed; but the price for the arch shall not be more than the general price for third class masonry, with an allowance for the centering.

FOURTH CLASS MASONRY.

Applicable to cattle-guards, pavement of culverts, and slope and protection walls, shall consist of stones of not less than one cubic foot in contents, so laid and bonded as to give the greatest degree of strength in preference to appearance; being laid when directed with beds perpendicular to the inclined face. Pavements under culverts shall be made by excavating one foot in depth of that part to be paved, which space shall be filled with flat stones one foot wide, set on edge, close together, and made to present an even upper face.

TIMBER AND PLANK FOUNDATIONS.

Timber and plank foundations require the beds to be perfectly well levelled, and timber of such dimensions, and so laid, as shown by the plans; to be well bedded and brought to an even and level top surface. The spaces between them to be filled and well rammed with such material as the engineer may direct. On these timbers planks shall be laid, and trenailed or spiked if required. The materials shall be of quality and shape approved by the engineer, and the price shall be in full for material and labor in laying the whole in a thorough and workmanlike manner.

PILING.

Piling may be used either as bearing piles for foundations, or for piled bridges. In the former case they will be bid for by the running foot driven, and in the latter by the stick of twenty-five feet in length. The piles in either case must be straight round timber, of a quality approved by the engineer, not less than ten inches in diameter at the small end, barked, and properly banded and pointed for driving. They shall be driven in such places, and to such depths as required, and the heads cut off square, or finished with a tenon to receive caps, as may be required. Bearing piles will be cut off so far below the lowest water that any timber foundation laid thereon shall be at all times entirely immersed.

CEMENT.

Cement when used shall be of the best quality, hydraulic, newly manufactured, well housed and packed, and so preserved until required for use. And none shall be used in the work until tested and approved by the engineer.

CEMENT MORTAR.

The proportion of sand and cement for construction shall be one of cement, to two of clean, sharp sand, unless in special cases the engineer direct otherwise, for which due allowance shall be made. It shall be used directly after mixing, and none remaining on hand over night shall be remixed.

LIME MORTAR.

Lime mortar (which in all cases shall contain cement), will consist, unless otherwise directed, of two parts of best quick lime, one of cement, and five of sand; the ordinary mortar of lime and sand being first properly made, and the cement thrown in and thoroughly mixed immediately before using.

CONCRETE.

Whenever concrete is required to be used, it shall be formed of clean broken stone, cement, and sharp, clean sand. The stone, which shall be of satisfactory quality, shall be broken so as to pass through a ring three inches in diameter. The cement and sand shall be thoroughly mixed in the proportions already described for cement mortar. Thus prepared, it shall be carefully mixed with the broken stone in the proportion of one of mortar to two or two and one half of broken stone, as the engineer upon experiment shall determine, and shall be immediately laid carefully in its place, and well rammed. The concrete shall be protected on the sides by boards, and be allowed to remain undisturbed after laying until it is properly set; and in special cases the engineer shall direct the mode of application. For the proper preparation and laying of such concrete, there shall be paid the price applicable to second class masonry. The contractor shall furnish all tools and plank necessary to the operation.

POINTING.

All masonry in cement or lime will be finished with a good pointing of cement, without extra charge.

BRICKWORK.

When bricks are required, or allowed to be used, they shall consist of sound, hard-burned brick, laid in cement, or common mortar, as directed, and no soft or salmon brick will be admitted; and none but regular bricklayers must be employed.

CENTERING AND BACKING.

The whole top of all arches, whether brick or stone, shall be finished by plastering with a good coat of cement, so as to prevent the percolation of water, and turn it away from the arch. The centering shall be such as the engineer approves of in every respect, and shall not be removed until he directs. The cost of backing to be included in the price bid. For arches of more than twenty-five feet span, compensation shall be made, at the engineer’s estimate, for the extra value and cost of the centering proper for large arches.

GENERAL PROVISION.

79. The engineer reserves the right to require the whole or any part of the above described work of masonry to be laid in cement, lime, mortar, or dry, at his discretion. First and second class masonry, and brickwork, will be bid for at prices for laying in cement, from which will be deducted fifty cents per yard if laid in lime mortar, and one dollar if laid dry. Third and fourth class masonry at prices for laying dry, to which will be added fifty cents per yard if laid in lime mortar, and one dollar if laid in cement.

SCAFFOLDING.

80. Nothing shall be allowed for workmanship or timber of any scaffolding used in the construction of timber bridges, or in carrying up abutments, piers, coffer-dams, or otherwise. Should the timber used in any coffer-dam be carried away by floods, the renewal of it shall fall upon the first party.

FOUNDATIONS.

81. The foundations for all structures shall be executed by the contractor for masonry in such manner and to such depth as to secure a safe and secure foundation, of which the engineer will judge. If a natural foundation cannot be procured at a reasonable depth, then the contractor shall prepare such artificial foundation as the engineer may direct. The stuff moved from the foundations, if of the proper quality, shall be deposited in the adjoining embankment, provided the site for said embankment has been cleared of all perishable material. So much of the stuff as shall not be fit for the embankment, and all roots, stumps, etc., shall be deposited beyond the limits of the clearing, so as not to obstruct roads, watercourses, or ditches.

For the earth moved from such foundations, and for all earth used according to direction, in the construction of coffer-dams, there shall be paid —— cents per cubic yard.

Whenever it may be necessary to pump or bale water in the foundations, the contractor shall furnish the pumps or buckets, and all scaffolding and apparatus necessary to work them. He shall be allowed the net cost of all labor employed in the operations of pumping or baling water, and shall make a monthly return to the engineer of the value of such labor, provided that these operations are conducted in an economical manner, with efficient men, pumps, and tools, under the direction and to the satisfaction of the engineer. He shall also be allowed such compensation for the use of the pumps and apparatus, and for superintendence, as the engineer shall judge to be fair and reasonable.

TRESTLE WORK.

82. Includes all wooden structures commonly used as substitutes for abutments and piers, and for farm passes, etc., etc. These shall be built according to the plans furnished, and directions given by the engineer, of sound, durable material, to be approved by him. The price bid shall be by the thousand feet board measure, and will be considered as in full for all material except iron, and for the labor of building and erecting complete. The iron used will be of the best American, and the workmanship of approved quality. The bids will be by the pound, and will cover all cost of material and the labor incident to its use. Spikes and nails when used will be furnished by the contractor at cost.

BRIDGING.

83. Contractors may submit plans for bridging in connection with, or separate from their bids; but the engineer of the company may reject such plans if he choose, and substitute others, which if the contractor decline building at the approved prices, may be let to other parties. In every case, the exact manner of building, erecting, adjusting, and finishing bridges, and the determination of the nature and amount of material, will be specified by the engineer. The price bid must be by the running foot of the whole length of bridge, as erected and finished complete.

84. Specifications for Superstructure.

SUBSILLS.

To maintain the track in good adjustment until embankments are settled, subsills will be laid on certain banks, and likewise in cuts where the imperfect nature of the bottoming may, in the opinion of the engineer, render them expedient. These subsills to be fairly bedded in the earth or ballasting, and carefully adjusted and rammed so as to correspond with the grade lines given by the engineer. An additional piece of sill, four feet long, shall be laid at each joint of the subsill, either under the sill, or alongside, as may be directed. The sills will be of 3 × 9 plank, in length of twelve, fifteen, eighteen, and twenty-one feet; of which one fourth may be below fifteen, one fourth below eighteen, and one fourth below twenty-one feet. The plank must be square at the ends, and of sound, durable material, and not have more than two inches wane on one end only. There will be about 25,000 feet, board measure, laid per mile where it may be required, and 660 joint sills, 3 × 9 inches, and four feet long. When the depth of stuff to be moved to admit the subsills exceeds six inches, an allowance shall be made for extra labor, the amount of which shall be noted by the assistants on their receiving notice of such extra labor from the contractor or his agent.

CROSS TIES.

The cross ties shall be of white, black, or yellow oak, burr oak, chestnut, red elm, black walnut, or other sound timber of suitable character in the opinion of the engineer. Eight feet long, and not more than three inches out of straight, hewn to a smooth surface on two parallel plane faces six inches apart, the faces being not less than seven inches wide for at least half of the number, and the remainder not less than six inches wide. The ties shall be carefully and solidly laid on the subsills, or ballasting, or earth previously properly prepared, so as to give the true planes required by the rails, whether on straight or curved lines. They shall be laid at the rate of eight ties to each eighteen feet rail. All imperfect ties shall be excluded by the tracklaying party. The surface of the ties to be faithfully adjusted to the grades given, and to the web of the rail; and the rail to be truly laid and firmly spiked so as to correspond neatly to the alignment of the road. There will be about 2,500 ties required per mile of road.

CHAIRS AND JOINTS.

When chairs are used, they shall be such as directed by the engineer, and furnished by the company, and shall be well and accurately placed and spiked in such manner and position as required. When chairs are used, the largest ties shall be selected for the joints. When the joint is made by fishing, there will be no tie directly under the joint.

RAILS.

The rails will weigh about sixty pounds per lineal yard. No rail shall be laid on the tangents which is in any way twisted or bent. It shall be the duty of the first party to correct and make true any crooked rails received by him, also to bend to the proper curve, and in such a manner as not to affect the strength of the bar, all rails laid in curves. Punching of rails, and cutting, will also be done by the contractor.

TRACK LAYING.

The materials composing the track will be furnished by the company, and it will be laid in the best manner according to the conditions following. The track will be laid on cross-ties, and the ties at the proper places on subsills. Where the sills are used, they will be laid with four feet blocks at the joints, and with six feet blocks at the rail joints, the whole being set to their places by stakes, and by the engineer’s directions, and mauled down to a perfect bearing, being settled at least half an inch by mauling. The cross ties will be placed uniformly distant, (twenty-eight inches from centre to centre). The iron must be so cut or selected that the joints of the parallel rails shall be within two inches of being opposite to each other; no joint tie being allowed a greater amount of askew than this, whether on tangents or curves. A slip of metal shall be inserted at the rail joints while laying, to keep the rails apart sufficiently to allow for expansion, which thickness, (depending upon the temperature,) shall be fixed by the engineer. Notches to be cut at the centre of each bar, to correspond with half a spike, to prevent longitudinal motion of the rails. Each joint chair to be fastened with four spikes. Two spikes at each end of each tie upon straight lines and upon curves of less than 1,500 feet radius at the outer end of the tie two spikes outside and one inside, and at the inner end two spikes outside and one inside of the rail. Upon curves the outer rail to be raised by such an amount, depending on the radius of curvature, as the engineer may direct.

TURNOUTS.

The contractor to put in such turnouts and sidings, with the necessary frogs and switches, as may be required; the frogs and switches to be firmly and truly placed in position so as to work easily.

FILLING AND DITCHING.

The stuff moved in bedding the sills and ties, to be placed between the latter. The ditches to be properly cleaned out after the track is laid; the filling never to rise higher than the top of the cross tie. Any surplus stuff to be moved out of the cuts, or if on embankment, to be thrown over the bank, leaving the track and road-bed in a neat and workmanlike shape.

DELIVERY OF MATERIALS.

The ties and sills to be delivered at some point on the road as near as possible to the places where they are to be used, in no case requiring more than one thousand feet of haul; to be so piled as easily to be counted and inspected. The bids for ties will be by the piece; the proposal stating the number and conditions; the sills to be bid for by the thousand, board measure. All material furnished in connection with track laying to be delivered in such manner and time as to comply in good season with the contract for laying the rails.

MEASUREMENT OF TRACK.

The measurement of track laid shall include the turnouts, measuring from heel to heel of switch. No extra allowance being made for putting in frogs or switch machinery.

85. Specification for Fencing.

Bids for fencing will be by the running foot, or mile, including both sides of the road. Where required, it will consist of posts placed eight feet apart from centre to centre, set three feet into the ground, either by digging or boring, and not by mauling. The posts shall be of oak, elm, chestnut, or other durable wood, not less than eight inches in diameter at the bottom, barked and charred where put into the ground. The boards to be 6 × 1 inches, and to square sixteen feet long, to be placed six inches apart vertically, and fastened to the posts with tenpenny nails at each bearing, and breaking joint with each other. There will be five bars in depth, the top of the uppermost being five feet from the ground. In side hill and in ground liable to slide, particular care shall be taken to place the posts firmly in the ground. At cattle guards, the fence will be turned in to the proper distance, and such arrangement made as to prevent the passage of animals.

86. General Provisions.

CLASSIFICATION.

The classification of material excavated will be referred to the engineer, in all cases where the nature of the material is questioned, and his judgment taken thereon. Also all material used in structures will be submitted to the inspection of the engineer or his assistants.

QUANTITIES AND QUALITIES APPROXIMATE.

The quantities and qualities of work presented in the schedule are merely approximate, and the information given on the maps and profiles in relation thereto is according to the best present knowledge. The company retains the right to change at any time during the progress of the work, the alignment, grades, and width of the road, or any part thereof; and also the limits of the sections, or to alter the character, vary the dimensions, or change the location of structures, or substitute one kind of work or material for another, or to omit entirely, when found necessary, or to require to be built where not now contemplated; and the contractor shall carry into effect all such alterations when required, without the contract prices being thereby affected, unless the aggregate value of all work contemplated by the contract be changed full twenty per cent., in which case a fair allowance, either for the company or the contractor, shall be made by the engineer. In case, however, the aggregate value of the work be changed by over twenty per cent. of the original amount, and the contractor be not satisfied with the altered compensation, then said contractor may throw up said contract, on condition, that within ten days after receiving notice from the engineer of such alteration, he give written notice to the engineer or the company of his desire to do so. In which case, as in other cases of throwing up the contract, he shall as soon as desired, give peaceable possession to the company or their agents; leaving also in their possession any tools or machinery upon which they have advanced any thing; and the company may then settle with the contractor on the measure of damages which either shall suffer.

BASIS FOR ESTIMATING EFFECT OF CHANGES.

The basis for estimating any changes as above mentioned is understood to be the schedule exhibited at the letting.

NO LIQUOR, AND GOOD ORDER.

The contractor shall not sell, or allow to be sold or brought within the limits of his work any spirituous liquors, and will in every way discountenance their use by persons in his employ. He will do all in his power by his own act, or by assisting the officers of the county, or of the corporation, in maintaining the laws and such regulations as conduce to good order and peaceable progress, and prevent encroachment on the rights of persons or property; and he shall discharge from his service, when required by the engineer, any disorderly, dangerous, insubordinate, or incompetent person, and refuse to receive into his employ any who may have been discharged for such cause from other parts of the work.

MONTHLY ESTIMATES.

Measurements and estimates shall be made by the engineer once in each month, by means of which may be known approximately the amount of work done, and the contractor shall be entitled to payment therefor at such rates below his contract prices as the engineer or president of the company deems expedient; it being understood that the contractor has no claim on account of any material not laid in its place in the road-way, or for labor bestowed thereon; and the quantities shall be estimated from the dimensions when so laid, though on the advice of the engineer, advances may be made on such material when delivered for use, in which case it becomes the property of the company, in the contractor’s care and keeping, and he becomes liable for its loss or injury.

EXTRA WORK.

No claim for extra work or for work not provided for in the contract shall be allowed, unless a written order to perform such work shall have been given by the engineer; or that the work be subsequently certified by him, and the certificate produced at the time of demanding the payment of the monthly estimate next after such work shall have been performed.

SUB-CONTRACTS.

The contractor will be required to perform the work himself, and no sub-contracts relieving him from the responsibility of a proper performance of his contract will be permitted, unless by the written consent of the president of the company. And no moneys shall be paid to any such sub-contractor for work or materials, without sufficient authority from the principal contractor.

WHEN WORK TO BE COMMENCED.

On the acceptance of a proposal, the chief engineer will give notice thereof to the person proposing, by letter directed to his stated address; and in twenty days from the date of such notice, provided there be no impediment on the part of the company, or in twenty days after such impediment is removed if there be, the work shall be begun with an adequate force, and from that time be prosecuted vigorously until its completion.

HOW TO PROGRESS.

It shall be understood that proper progress is not made, if the amount of work done in each month is not in due proportion to the total amount to be done up to the time fixed for completion by the contract; in which case the engineer shall call the attention of the contractor (or whoever may be in charge of the work if the contractor be absent,) to the fact, and state to him what additional exertion is necessary to be made, and what further force is required, in such reasonable time as may be prescribed.

PUTTING ON MORE FORCE.

In default of the contractor’s making such additional exertion, and supplying such force, the chief engineer, or president of the company may have such force sent to the work, and the necessary buildings may be erected to receive them at the contractor’s charge and expense, who shall receive the said force in his employ, and work it at whatever price it may have been found necessary to employ it, without diminishing the previous force of the work, and regarding always such extra force as if employed by himself.

CAUSES FOR DETENTION.

There shall be no claim for detention on account of work not being laid out, unless a written notice three days in advance, that it is required, shall have been given to the engineer; and the damage for such detention shall be estimated by the engineer. The right of way shall be furnished by the company, but if it fail to do so for any particular place, damages for detention shall not be claimed unless the contractor be detained full twenty days after he shall have given written notice to the engineer of his wish to commence work at such place. Then the engineer may either estimate to him the amount of damage which he shall take as satisfactory, or he may extend the time of the completion of such work by as many days beyond the contract time, as the contractor is detained beyond the twenty days following his notice to the engineer.

THE ENGINEER.

In all cases where the word “engineer” is used, the engineer in charge of construction is meant; but the directions of any subordinate engineer shall be obeyed when given in regard to any of the ordinary operations, or where they are evidently in accordance with the specifications, or when transmitting the orders of his superiors. In other cases they may be referred to the resident engineer, and finally to the chief engineer, he being the authorized officer, at the time acting in that capacity.

CONTRACTOR.

The word “contractor” applies to and includes all persons contracting jointly, any one of whom shall be considered the authorized agent for and in behalf of his associates, and empowered to receipt payment of moneys, receive and act upon orders.

THE CONTRACT.

87. This is the mutually binding legal article of agreement between the contractor and the company, specifying the times of completing, manner of payment, and describing the work which is to be done. Thus:—

A AND B RAILROAD COMPANY.

Contract.

Graduation on sections A C D,

Masonry on sections A C D,

Ballasting on sections A C D,

Bridging on sections A X T,

Fencing on sections O O O,

Sills and ties on sections O O O,

Track laying on sections O O O.

____________ }

____________ } Contractors.

Articles of agreement made and concluded this first day of January, A. D. 1857, between —— of the first part, and the A and B Railroad Company of the second part, being a company duly incorporated by the State of —— of the second part, whereby it is mutually agreed as follows, namely: The said party
parties of the first part hereby agree to and with the said party of the second part that he
they will perform in a substantial and workmanlike manner the following work, namely:—

[The work here described.]

The said work to be performed and completed agreeably to the directions and to the approval of the chief engineer of said company for the time being, and subject to all the general provisions of the specification attached to and forming a part of this agreement, and also subject to such of the special provisions of said specifications as are applicable to the work hereby contracted for.

And in consideration of the full and faithful performance by the said party
parties of the first part of this agreement on his
their part, the said party of the second part hereby agrees to pay for the same in the time and in the manner hereinafter mentioned, at the rates as follows, namely:—

[Here insert the items and corresponding prices.]

It is mutually agreed that this contract applies only to those items to which prices are attached, and that where it embraces both labor and materials introduced in the work, such prices are in full compensation therefor when introduced in the manner required. When it embraces materials only, such prices are in full compensation for the materials and the labor necessary to deliver the same to the company, and when it embraces labor only, such prices are in full compensation for such labor, and every incident to its complete and proper performance. In every case the estimate for ascertaining the amount of compensation shall be made by the engineer from the actual work, from the material furnished, or from that on which the labor contracted for is bestowed.

It is also agreed that partial payments shall be made from time to time during the progress of the work as follows:—

[Times and manner of payment.]

And that in thirty days after the contract is fully completed to the satisfaction of the chief engineer of the company for the time being, and the work is surrendered to and accepted by the company, a final measurement and estimate thereof shall be made under the direction of the chief engineer, and be duly certified by him, on the return of which to the president of the company the whole amount then found to be due to the said party
parties of the first part shall be paid to him
them on demand as follows:—

[Insert mode of payment.]

And it is also hereby further agreed, that bank-bills current in the State of —— shall be accepted for cash in payment for all claims under this contract.

And the said party
parties of the first part further agree
agrees that in twenty days after he
they shall be notified to do so, as provided for in said specifications, he
they will begin the work hereby contracted to be performed, with a force of all kinds sufficient for its completion in the time herein prescribed, and that he
they will finish and deliver the same to the company fully completed in all its parts as follows:—

And the said specifications hereunto annexed are hereby made a component part of this contract and (except so far as any provision therein may not be pertinent to the subject-matter of the contract or may be specially modified herein,) shall be looked to in ascertaining the meaning, extent, and purport of this agreement, and in determining the rights, powers, duties, privileges, and obligations of the contracting parties as to any particular embraced therein.

In virtue whereof the said party
parties of the first part has
have hereunto set his
their hand and seal, and the said party of the second part have caused their president to subscribe his name and affix the corporate seal of the company hereto, all done in triplicate the day and year first above written.

Contractor’s name,      [SEAL.]

President’s name,       [SEAL.]

SOLICIT FOR BIDS.

88. The approximate estimates, plans, and profiles being made, and other preliminaries settled, proposals for executing work are solicited by the public papers. Thus:—

New York, January 1, 1857.         }

Office of the A and B Railroad Company. }

Proposals for executing the graduation, bridging, masonry, and track laying, and for the supply of materials upon the A and B railroad will be received at this office until the 31st day of January, 1857.

Plans, profiles, and schedules of amounts of work may be seen, and blank bids obtained by application at this office.

All proposals must be directed to the chief engineer of the A and B Railroad Company.

No bids will be received after January 31st, at 12, M.

Per order,

C. D., Secretary A and B R. R. Co.

FORM FOR A BID.

89. That proposers may make their bids in a convenient form for comparison, a blank, somewhat like the following, is given them to fill out.

This form being filled out, evidently gives the cost of each or all of the items upon any one or all of the sections, the cost of all the items upon any one section being at the foot of that section, and the whole cost of any one item at the extreme right and on the line of that item.

On the bottom of the form is printed, “The undersigned having read the specifications, and made due examination, hereby proposes to the A and B Railroad Company, to perform the work in the above schedule, to which he
they has
have set figures, at those prices and under the conditions described, and upon acceptance of this proposal by the company, binds
bind himself
themselves to enter into a written contract to that effect, and to furnish the required security.

Name,

Address,

Name of Surety,

Address of Surety.”

COMPARISON OF BIDS.

90. The bids being received, are compared as follows:—

From which the names may be easily selected either for one or more sections, for any or all of the items, that shall give the least cost.

CHAPTER V.
LAYING OUT WORK.

91. The running of the line consists in placing a stake at every one hundred feet upon tangents, and at every fifty feet distance upon sharp curves; also a permanent post at each tangent point, and at points of compound and reversed curvature. This is the centre line, the axis of the road, and the base of all field operations. Wherever the work is going on, the centre pins should be referred to fixed points outside of the ground occupied by the road.

92. The first operation in preparing for excavation is to place side stakes at one half the width of road-bed plus the ditch, on each side of the centre line.

SLOPES.

93. Setting out slopes is a term applied to laying off upon the ground, on each side of the centre, the distance to which the slope, commencing at the outer edge of the ditch, will extend, depending upon the angle of slope, width of road-bed and ditch, and depth of cutting. There are here five distinct cases which may occur:—

In embankment when the natural surface is horizontal. In embankment when the natural surface is inclined. In excavation when the natural surface is horizontal. In excavation when the natural surface is inclined.

In mixed work (side hill,) when the road-bed is partly in cut and partly in fill. In both excavation and embankment, when the natural surface is horizontal, we have only to add the cut, in feet and decimals, multiplied by the slope, to one half the width of road-bed plus ditch.

and we have

(20.55 × 1½) + 10.25 + 3.0 = 44.075 feet.

When the ground is inclined transversely to the axis of the road, first assume a point upon the ground, (apparently right) find its height above grade with the level, multiply this by the slope and add one half the distance between the outer edge of ditches, and see how near it comes to the measured distance from the centre to the assumed point; if within a foot, it will answer; if not, a second trial will fix the place.

CULVERTS.

94. The length of any structure passing under a railroad embankment is L – 2Rh, where L is the distance between slope stakes, R inclination of slopes, h the height of structure from the natural surface. Thus, suppose the distance between slope stakes to be 100 feet, slope 1½ to 1, and h 10 feet, we have

L = 100 – (10 × 1½ × 2) = 100 – 30 = 70 feet.

The length of an oblique structure will of course be greater than that of one at right angles to the road; the length depending upon the obliquity.

MASONRY.

95. There are eight general cases which may occur in laying out such structures as bridge abutments with wings.

1. A right bridge on a level tangent.

2. A right bridge on a level curve.

3. A skew bridge on a level tangent.

4. A skew bridge on a level curve.

5. A right bridge on an inclined tangent.

6. A right bridge on an inclined curve.

7. A skew bridge on an inclined tangent.

8. A skew bridge on an inclined curve.

And these eight cases will vary again according to the natural surface of the ground, whether horizontal, or inclined transversely.

96. The general position of wing walls and general form of the line inclosing the base of the bridge, is shown from fig. 31 to fig. 38. Fig. 31 represents case one. The points A, B, C, D, are fixed by squares from the centre line at E F, G H.

Fig. 31.

Fig. 32 represents case two. The wings 3c, 4d, must evidently have a different inclination from A1, B2. The points A, B, c, d, 1, 2, 3, 4, as before, are laid off by squares from a tangent to the curve.

Fig. 32.

Fig. 33 explains itself.

Fig. 33.

Fig. 34.

Fig. 34, case five. Here the wings A1, C4, are the same, as also B2, D3, the former being longer, on account of the greater depth of the fill.

Fig. 35.

Fig. 35, case seven. Here each wing is peculiar; the figure being a compound of figs. 33 and 34.

Figs. 36 and 37.

Figs. 36 and 37, case 8. This is the most difficult of all. No two wings have the same length or inclination on plan. The natural surface being horizontal, the line inclosing the bridge is A″ B″ C″ D″. If the natural surface descended from C″ to A, the position taken would be A, B, C, D. Fig. 37 is the elevation of the position A B C D. The several points are laid off from the line n, n.

The general manner of fixing the lines of figures 31 to 38, is to assume the angle of some one wing, as A 1, in fig. 34, to draw A C parallel to E F; and from C, the intersection of A C with the base of the embankment, C 4 gives the other wing. Local circumstances will of course often fix at once the length and angle of the wings. Upon simple curves, as in fig. 32, the lines A c and B d are made radial.

97. In curving a viaduct, the axes of the piers are made radial to the centre of the located curve, and the planes of the springing lines are made parallel to the axes of the arches. The pier thus becomes a wedge, and should be strengthened by a starling, upon the outside of the curve, to resist the resultant of the thrusts of two adjoining arches.

98. We should never try to stake out the exact horizontal projection of a complicated piece of work upon rough ground, but only the trenches, which being cut, give a horizontal surface to work upon. In placing the stakes, we must be careful to have them so far outside of the work that they will remain undisturbed while operations are going on. The pegs for cutting pits and trenches may be placed at the angles of the latter, but the working pegs must be so placed that the lines stretched from one to the other will define the masonry. All measurements made in laying out work should be made by graduated rods, and carefully checked.

99. In founding piers, and in aquatic operations generally, two stakes upon the shore, or a fixed transit, will define any line in the water. Two transits will define points.

100. A permanent bench mark should be carefully fixed at each structure, from which its levels may be obtained.

101. In adjusting oblique bridges, care must be taken so to place the bridge seats that the floor beams shall lie in a correct plane, and not be at all warped or winding.

Fig. 38.

102. As an example of laying out work with regard to heights, take the case of fig. 38. Let the grade of the centre line be one in 100, the angle of obliquity 45°, the width of bridge twenty feet, and span on the skew one hundred feet. Required the elevations of the points a, b, c, d.

TUNNELS.

103. The maintaining a correct centre line through tunnels is generally considered difficult. The fixing of the line in deep shafts requires great care, owing to the short distance between the only two fixed points, that can be transferred from the surface to the bottom of the pit. This is a matter of manual skill and of instrumental manipulation. There is no difficulty in aligning the upper ends of two plumb-lines; and the lower ones will certainly be governed by their position. The following method has been found to answer every purpose.

Let the opening of the shaft be ten feet in diameter. Place two horizontal bars at right angles to the road across the opening, upon which slide blocks holding the upper end of the plumb-lines. Adjust these lines, at the surface, with a transit; and when fixed, place iron pins at the point marked by the plumbs at the bottom of the shaft. Upon these pins fix the exact centres. For keeping the line in the shaft headings, a straight rod, with steel points at each end, should be used, which being placed upon the iron centre pins, fixes the centre line of the tunnel. When the tunnel is curved, the line should be laid off by offsets from the tangent to the curve at the shaft.

By this method points at ten feet distance may be fixed within 1
100 of an inch, a difference of which would cause an error of ⅒ of an inch per one hundred, or an inch per thousand feet.

CHAPTER VI.
EARTHWORK.

FORM OF RAILROAD SECTIONS.

104. The reader is presumed to be acquainted with the manner of finding the areas and cubes of simple geometric figures and bodies. The following fifteen figures show the forms which may be taken by the cross section of a railroad in cutting; for embankment invert the same. They are easily separable into simple figures.

Fig. 39.

Fig. 40.

Fig. 41.

Fig. 42.

Fig. 43.

Fig. 44.

Fig. 45.

Fig. 46.

Fig. 47.

Fig. 48.

Fig. 49.

Fig. 50.

Fig. 51.

Fig. 52.

Fig. 53.

Fig. 54.

105. The formation of tables for the amount of earth in level cutting is very simple. The area of the following section, where B is the base, and R the horizontal dimension of the slope, is

B + B + 2R
2 × h, or 2B + 2R
2 × h,

or finally

B + R × h,

i. e., the base of a rectangle by its height. Multiply this by 100 and divide the product by 27; or divide by 27
100, and we have the cubic amount in a prism one hundred feet long. The road-bed being nineteen feet wide, and slopes one and a half to one, the formula for the amount of a prism one hundred feet long is

(19 + 1½h)h
0.27,

and assuming the base of rock cutting as eighteen feet, and slope one quarter to one, and embankment eighteen feet at subgrade, we have, rock,

(72 + h)h
1.08,

and embankment,

(18 + 1½h)h
0.27,

the figure being inverted for embankment. For a prism of ten or of one thousand feet in length, we have only to move the decimal point. In forming a table, proceed as follows:—

Fig. 55.

It is evident from inspection of fig. 55, that c exceeds c^o by h × 2r; and that c″ exceeds c′ by h′ × 2r′; and so on as far as we go; this increase being constant, we have then to find the area of c, and for the area c + c′ double c, and add the increment; whence the rule:—

Having found the increase (which varies with the angle of the slope) for the second section, add the increase to twice the first. For the third, add twice the increase to three times the first; and for the nth, add n – 1 times the increment to n times the first area, or algebraically calling a the first area, a′ the second, a″ the third, aⁿ the nth area, and we have

We might operate at once upon the cubic contents, but for the length to which some decimals run; some indeed circulating.

106. The table thus made may be of the following form:—

i. e., cut being eight feet, each one hundred feet length gives nine hundred and nineteen cubic yards; one thousand feet, 9190 yards, and ten feet of length 91.9 cubic yards.

107. The preceding system is intended only for approximate estimates. Let one person read off the cuts or fills from the profile, a second give the corresponding number of yards by the table made as above, while a third sets the figures down; being careful to separate the cuts from the fills.

For final measurements, none but the prismoidal formula should be used; the length of the prismoids being taken at each one hundred feet, and nearer when the ground is rough.

108. As an example of the comparative amounts given by the above formula, and by the common method of averaging end areas, take the following, the slopes being 1½ to 1.

By averaging end areas we have

And by the prismoidal formula,

cubic feet in favor of the method of end areas.

109. The prismoidal formula is algebraically

a + a′ + 4a″
6L = c,

when L = length,

c = cubic contents,

a = area of one end,

a′ = area of other end,

a″ = middle area;

or, verbally, to the sum of the end areas add four times the middle area, and multiply the result by one sixth of the length; the middle area being the area made upon the mean height of the two ends. Thus if the length is one hundred feet, and one end ten feet high, the other twenty feet high, and slopes one and a half to one, the cubic amount is, (the base being twenty-two feet,)

[(22 + 22 + 30
2 × 10) + (22 + 22 + 60
2 × 20) + (22 + 22 + 45
2 × 15 × 4)] × 100./6

EXCAVATION AND EMBANKMENT.

110. Some writers have considered that the grades of a road should be so adjusted as to equalize the cutting and the filling. The total rise and fall might not be much affected by this, but the mechanical effect of grades might. A perfect balance between the cuts and fills is not to be desired. The whole cost of earthwork must be a minimum, and it is often cheaper to waste and borrow, than to make very long hauls, and to form the grade line by interchange of material on the profile only.

111. The transverse slopes depend upon the nature of the soil in which the cut is made. Gravel will stand at a slope of one and a half horizontal to one vertical, and in some cases one and a quarter, or even one to one. Clay stands nearly vertical for some time, but finally assumes a very flat slope, in some cases two, three, and even four horizontal to one vertical. In places where a stratum of clay underlies more reliable earth, to avoid a very long slope, it may be economical to support the clay by a wall, and to slope the earth only.

112. Care should be taken in every case to secure good drainage and to protect the slopes by surface drains at the top. The drains in long cuts should be slightly inclined to insure the running off of the water. A fall of ten feet per mile is enough; five will answer in many cases. On side hill cuts a surface drain along the top of the upper slope will do good service. On many high embankments, catchwater drains, commencing at the road-bed and gradually sloping to the base, will prevent, in a great degree, cutting of the bank.

113. Embankments, when made rapidly, should be finished to the full width, somewhat above true grade, to allow for the after settlement. (See specification.)

114. The following allowances have been made for the shrinkage of material in some parts of America.

The bulk of quarried rock on the contrary increases from twenty-five to fifty per cent.

115. When embankments are carried up slowly, in layers of three or four feet at a time, the after settling is very little; when carried up all at once it will be more. The full width must be kept, even above the required height. Fig. 56 shows the forms of a bank both before and after settlement.

Fig. 56.

The best method of forming a bank of bad material is to ram the layers as in fig. 57; thus the tendency is to consolidate by settling, and not to destroy the work by sliding.

Fig. 57.

TRANSPORT OF MATERIAL.

116. In the formation of embankments it is not always advisable to make the whole bank from an adjoining cut or cuts. The length of haul may be too long. In this case it is customary to waste a part of the cut and to borrow earth from some nearer point for the bank. That the transport shall be effected in the most economical manner, the product of the cube of earth, by the mean distance, (the distance between the centres of gravity, of excavation and embankment) must be a minimum. To determine the theoretical minimum expense, the problem becomes very complicated on account of the great number of variable elements entering therein; and the result obtained is applicable only to a particular case. Local circumstances more than any other thing, determine the position of a borrow pit, and the path over which the material is to be transported.

OF THE AVERAGE HAUL.

117. To find the cost of the movement of earth on any section, we must have, the total amount of earth to be moved, and the average haul; the latter being the distance through which, if the whole amount were moved, the cost would be the same as the sum of the costs of moving the partial amounts their respective distances. To find the average haul proceed as follows: First, find the distance between the centres of gravity of each mass both before and after moving, which may be done with sufficient accuracy for practice by inspection of the profile. Next,

118. Divide the sum of the products of the partial amounts by their respective hauls, by the total amount; the result is the average haul in feet. Or algebraically, representing the partial amounts by m, m′, m″, m‴, the respective hauls by d, d′, d″, d‴, the total amount by S, and the average haul by D, we have

md + m′d′ + m″d″ + m‴d‴
S = D.

Example.—Let column 1 show the partial amounts in cubic yards. Column 2 the corresponding hauls.

and 7,600,000
16,000 = 475 feet average haul.

Proof.—Assume the cost of moving 1,000 yards one foot as ten cents, the costs of the separate masses are

also the cost of moving 16,000 yards 475 feet is

16 × 475 × 10 = $760.00.

119. The movement of earth is effected by shovels, barrows, horses and carts, or by cars. In round numbers we can move earth

As the haul increases, the number of vehicles of transport remaining the same, the number of excavators must decrease. Earths easily removed do not admit of so large a haul, with a given number of excavators, as hard earths. The nature of the ground, form of carts, kind of horses, season of the year, and price of labor are some of the elements entering the problem of transport. The best illustration of the matter will be found among the very able writings of Ellwood Morris, Esq., C. E., in the Journal of the Franklin Institute. Knowing the value of wages, the nature of the earth and length of haul, it is easy to see what mode of transport must have the preference.

CONTRACTOR’S MEASUREMENTS.

120. The price of executing any piece of work is paid to the contractor at stated intervals, generally once each month. The amount of work done at these partial payments is obtained by instrumental reference to the ground. Towards the completion of operations the most correct and easiest method of finding the rate of progress is to deduct the amount already done from the total as given by primary measurement. The full price is not paid to the contractor, but a percentage is kept back, which insures a faithful performance of work. It is impossible to establish a pro rata price at first, owing to the uncertain nature of the work; what appears to be earth may be rock. By deducting a maximum price estimate for all but one of the items, an approximate pro rata value for that one may be determined. An analysis of cost will define the minimum limit for advantage to the contractor; and the pro rata value less the percentage, the maximum for the company’s benefit.

DRAINING.

121. When a level is to be drained, or the water carried off from the surface of a swamp, the first point to be ascertained is the location of the lowest outfall. The direction in which aquatic plants lie show the natural fall of the water, these always pointing down stream. When the most available outlet has been decided upon, a main drain should be set out, from which oblique branches are to be cut, pointing in the direction of the current; into these all minor cuts are to be collected so that the whole district may be equally drained. The fall should be greatest at the most remote points, decreasing as the amount of water increases. Large and deep rivers run sufficiently fast when the fall is one foot per mile. For small rivers, double that is necessary. Ditches and ordinary drains require eight feet per mile. When the water is made to pass away from the surface, it should flow very gradually, that the sides and bottom of the ditches may not be worn away by friction; it should be in constant motion that the channel may be kept clean and increase in velocity as it proceeds. When the surface is a perfect level, the drains should of course be made straight.

After the quantity of water has been determined by careful observation, the section of the main and branches must be fixed, so that regarding both their areas and velocities, the main drain will not be overcharged.

To facilitate the current, the sides should be inclined about one and a quarter to one; and the breadth of base should be two thirds of the depth of water. These results are obtained from the practice of English engineers, who have given a great deal of attention to the subject.

Drains cut through bogs, may have sides nearly, if not quite vertical, as the fibres of plants forming the soil resist the action of the water.

SUBSOIL DRAINING.

Geology has assisted this operation very materially by rendering us acquainted with the quality and nature, as well as of the succession of strata. The soils which are impervious are usually the heaviest, and the porous are those of lighter quality. Clays, when they receive water, will only part with it by evaporation, when left in a natural state; and therefore to make such a surface fit for a useful end requires considerable ingenuity, and often great expense. Such a soil is not rendered unstable by underground springs, and may be effectually drained by boring through, and letting the water off into an under stratum, when this is of a porous nature.

When land abounds with springs, or is subject to the oozing out of subterraneous water, draining is effected in a different manner. Springs have their origin in the accumulation of rain water, which falling upon the earth, after passing the porous strata, lodges upon the impervious, and glides along the sloping surface until it crops out, generally in some valley where it forms a watercourse.

Descending streams are easily taken care of by collecting them into a body before they reach the low lands.

When a morass is to be drained, the strata upon which it reposes should be examined, and if, as is often the case, a layer of clay intervenes between the substratum and the mossy covering, which holds the water, by tapping this in well chosen places, the whole will sink away.

A fine example of embankment upon a bad bottom was performed by Mr. Stephenson, on the Great Western Railroad, England, at the crossing of Chatmoss. This moss was so soft that cattle could not walk upon it, and an iron bar sank into it by its own weight. The moss was first thoroughly drained by a system of longitudinal and cross drains, and the embankment made of the lightest material possible—the dried moss itself. Without this treatment, the moss would have sank beneath the bank alone; it now supports the passage of the heaviest railroad trains.

METHOD OF CONDUCTING OPERATIONS.

122. The organization of the engineer corps upon a railroad is as follows, differing somewhat in different parts of the country.

The Chief Engineer has entire charge of all the work, of all assistants, appointing and dismissing members of the corps, designing of all structures, making of specifications, and of all mechanical operations incident to the thorough, correct, and timely construction of the road; and should be able also to specify, generally, the amount and character of the equipment needed.

The Resident Engineer has charge of the detailed construction of from twenty-five to fifty miles of road, according to the nature of the work, being responsible to the chief engineer for the proper execution of the orders from headquarters; he returns to the chief engineer a monthly account of the exact condition of his work, both as to the amount executed, and also that remaining to be done.

The assistants of the resident engineer are a leveller and transit man; to whom, under his supervision, is the duty of laying out, measuring, and estimating the work. The leveller has with him one or more rodmen. The transit man, two chainmen, and one or more axemen.

In some cases, added to the above are inspectors of masonry, bridging, and superstructure. These are necessary only when the road embraces a great number of mechanical structures; too many to leave the proper time to the resident engineer for his other duties. Once each month the exact amount of graduation, bridging, and masonry executed is obtained by the resident and his assistants. The chief engineer applies the prices to these amounts, and the percentage deduction being made, the estimate is ready for the treasurer.

123. The abstract prepared from the monthly estimate should show clearly, without unnecessary figures, the amount of work completed, and also that remaining to be done.

For convenience, the various blanks used on railroads should fold to the same form and size. The blanks are,

The Contract,

The Specification,

The Resident Engineer’s Monthly Return,

The Assistant’s Weekly and Monthly Returns,

The Force Return,

The Pay Roll,

Vouchers.

The contract and specification are given in chapter IV. The resident’s monthly return to the chief engineer is somewhat as follows:—

Monthly return of work done on the first division of the A and B Railroad, for the month ending ——, showing also the whole amount of work up to ——; also the present estimate for completion.

The resident engineer’s assistants return to him weekly a statement of the amount and value of the force employed upon the several sections, and monthly the exact amount of work done on the same, for each of which there should be a blank. The above forms may be printed and folded in 8vo., or may be the continuous headings of a large sheet.

CHAPTER VII.
ROCKWORK.

ROCK EXCAVATION.

125. The sides of rock excavation are sometimes cut to a small slope, as one fourth or one fifth horizontal to one vertical, and sometimes cut quite perpendicularly. The earth, when it occurs, which covers the rock, is first taken out at the proper slope; a berm of one or two feet being left between the foot of the earth and the crest of the rock.

126. Rock is taken out one or two feet below grade, as well as earth, to allow the introduction of the necessary ballast.

BLASTING AND QUARRYING.

127. The most common mode of removing rock is by blasting; for this holes are drilled by steel-edged jumpers, worked either by hand or by steam. The first object in cutting a passage through rock, is to open a working face, so as to get the necessary lines of least resistance, (this line is that by which the powder finds the least opposition to a vent at right angles to the length of the drill); these lines should, if possible, be at right angles to the beds of stratification; the holes should be drilled parallel to the seams of the rock, as the powder will then lift off the strata. In working a vertical face, it may be best to blast out the lower part first, and so undermine the overhanging mass.

128. The amount of powder in different charges to produce proportional results should be as the cube of the line of least resistance; for example:—

2³ is to 4 oz. as 3³ is 13½ oz.,

or

8 to 4 as 27 to 13½;

and generally,

L³ : w :: L′³ : w′;

whence

w′ = wL′³
L³.

129. The following charges corresponding to lines of least resistance are from the works of Sir John Burgoyne.

130. After the powdered stone is removed, the powder is placed in the lower part of the hole; after which a wad of turf, or some other light material, follows; next the tamping of powdered brick, dried clay, or something similar, and finally a stopper of wet clay, or some other firm substance. A hole is left through all, communicating with the powder by ramming the tamping around a wire; through this hole a fuse is inserted by which to light the charge. The most perfect tamping would offer a resistance as great as that by the natural rock. A great improvement upon the above method is the sand blast; the powder is put in, and the hole filled with loose, dry sand, simply poured in and settled by a gentle stirring, but not at all rammed; the explosion of the powder spreads the sand as a wedge, and causes the power of the blast to be exerted sideways. In some cases a small cone of wood has been placed (base down) in the hole with the sand, which aids very much in stopping the exit of the blast through the drill.

131. Of late years an admirable method of lighting large charges simultaneously has been employed, namely, voltaic electricity.

132. A gigantic example of the application of this method has been furnished by the English engineers in overthrowing a portion of Round Down Cliff, about two miles from Dover, (England). Two chambers, 13 × 5½ × 4½, and one 10 × 5½ × 4 feet were cut in the rock. Within these were placed fifty bags of powder, amounting in all to eight and one half tons. The charges were lighted by the voltaic system, by which operation a mass of rock (chalk) 380 × 360 × 80 feet, amounting to 400,000 cubic yards, was thrown into the sea, and by which there was estimated to have been saved nearly $40,000.

133. The following table from Colonel Pasley’s memoranda on mining, shows the capacity of different drills for powder, by weight, and also the depth of holes of different diameters, to contain one pound of powder.

134. Blasting under water has been practised to some extent, and with great success by Messrs. Maillefert and Raasloff, both in New York harbor and in the St. Lawrence River. The method is merely to explode bodies of powder upon the surface of the rock, the water itself being a sufficient source of reaction to the blast.

TUNNELLING.

135. Tunnels are driven through hills to avoid very deep cutting. When in rock of a solid nature, the roof supports itself; but when in earth or in loose rock, an artificial arched lining becomes necessary. Figs. 58 and 59 show sections in both rock and earth; the invert b b is placed in a bed of concrete. In excavating earth, a temporary roof is made use of while the work is in progress, which is afterwards replaced by an arch of brick or stone. The back of the arch must be closely wedged, grouted, and the earth well rammed in.

Fig. 58.

Fig. 59.

The great disadvantages attending the construction of tunnels are want of air, light, room, and drainage. To facilitate the latter requirement, a very light grade may be introduced; this may easily be done, as they generally occur on summits, or on the approach to summits; 1
1000 or five feet per mile is sufficient.

In working a tunnel which is upon a grade, one end naturally drains itself if the approach is taken out; the other drains the wrong way, to meet which obstacle we must resort to pumps which follow the work, keeping always in the lowest place, or by sinking a well at the shaft through which the water is raised to the surface.

The ventilation of tunnels is effected by drawing off the bad air when a fresh supply must enter.

136. In taking out the rock, the expense will depend much upon the nature and stratification of the rock encountered.

SHAFTS.

137. In tunnels of considerable length, a long time would be consumed in working from the ends only. In such cases it is customary to sink shafts at the most convenient places (the shallowest when at the proper distance,) and to commence at the bottom of these to work both ways. This operation involves considerable expense, as all draining, ventilating, and removal of excavated materials must be effected through the shaft.

In leaving openings for the exit of smoke and for admission of light in artificial arches, regard must be had to their position. They should be at the springing rather than at the crown of the arch, as they will thus less affect the strength of the masonry.

The approaches of tunnels in cities and in other places where appearance is of importance, are finished with face coping and wings.

138. Tunnels, when conducted in the most expeditious manner, require for their completion a long time. The following table shows the rate of progress upon some of the most important tunnels of America.

The following table also gives the time and cost of other tunnels in different parts of the world.

The cost per cubic yard for excavating tunnels in some places has been as follows:—

The Blue Ridge tunnel on the Virginia Central Railroad is 4,280 feet long, made for a single track, 21 × 15 feet. Lining about four feet thick. Excavation where lining is used is 26 × 23.

The Hoosac tunnel (Massachusetts) is proposed to be four and one half miles long, 23 × 22 feet section. To have two shafts eight hundred and fifty and seven hundred and fifty feet deep, and ten feet in diameter.

Artificial ventilation becomes necessary in headings over four hundred and fifty or five hundred feet in length.

The cost of the shafts of the Blechingly tunnel, (England,) ninety-seven feet deep, and ten and one half feet in diameter, cut through blue clay, and lined, was $68.44 per yard down.

The shafts of the Blaisy tunnel average five hundred feet deep, through clay and chalk and loose earth, (being lined,) cost $139.11 per yard down.

The shafts of the Black Rock tunnel, one hundred and thirty-nine feet deep, in hard slate, cost $18.72 per cubic yard.

CHAPTER VIII.
WOODEN BRIDGES.

139. Wooden bridging, owing to its cheapness and fitness for universal application, has been and is being adopted in all parts of the country. Almost any variety of form may be seen upon our railroads, and though less durable than stone or iron, it may with proper precaution be made to last a long time.

OF THE FORCES AT WORK IN BRIDGES.

140. There are four distinct strains to which a piece of timber or a bar of metal may be exposed, each of which tends to destroy the piece in a different manner. The amount and character of these strains, depend upon the position of the bar or beam, and upon the direction of the force.

A beam may be pulled apart by stretching,—Tension.

It may be destroyed by crushing,—Compression.

It may be broken transversely,—Cross strain.

It may be crushed across the grain,—Detrusion.

TENSION.

141. If one thousand pounds were hung from the end of a suspended timber, so that the direction of the weight coincides with the axis of the timber, then will the tension upon the beam be one thousand pounds.

If the direction of the force is vertical, and the beam is inclined, then the strain is increased by as much as the diagonal of inclination exceeds the vertical; for example, let one thousand pounds be suspended from the lower end of a beam ten feet long, inclined at an angle of 45°. The diagonal being ten, the vertical will be 7.07 feet, and the strain is increased as follows:—

7.07 to 10 as 1,000 to 1,414 lbs.

As the angle of inclination, from the horizontal, increases, the strain from a given load decreases, until the beam is vertical, when a weight acts with its least power.

COMPRESSION.

142. If a vertical post is loaded with one thousand pounds, the compressive strain upon that post will also be one thousand pounds. If a post is inclined, the amount of strain is increased, as noticed in the case of tension, and to the same amount, that is, depending upon the inclination.

A piece of wood or metal acting as a post, or pillar, must not only be able to resist crushing, but also bending or bulging laterally.

143. A cylinder of which the length is only seven or eight times the diameter, will not bulge by any force that can be applied to it longitudinally, but will split. When the length exceeds this, it will be destroyed by a similar movement to that produced by a cross strain. When the length of a cast-iron pillar is thirty diameters, the fracture is produced by bending alone; when less, partly by bending and partly by fracture. When the column is cast hollow, and enlarged towards the middle, the strength is increased in a very great ratio.

144. The formula for finding the weight which any beam acting as a post, will support before bending, is, according to Barlow, who considers the weight as varying inversely as the length, as follows:—

WL²
80E = bd³,

and the value of W is

bd³ × 80E
L²,

and the weight being given, and the sectional dimensions assumed, we have

d = ∛(WL²
80Eb),

and

b = WL²
80Ed³,

Where W represents the weight in pounds,

L represents the length in feet,

E represents a constant,

d represents the depth in inches,

b represents the breadth in inches.

CROSS STRAIN.

145. The amount of strain caused by any weight applied in a transverse direction, to a beam supported at both ends, is as the breadth, as the length inversely, and as the square of the depth. Whatever depression takes place, tends to shorten the upper, and to extend the under-side; whence the fibres of the top part suffer compression, and those of the bottom extension. The amounts of compression and extension must of course be equal, and therefore if any material resists these two strains in a different degree, the number of fibres opposing each will also be different.

The top being compressed, while the bottom is extended, of course at some point within the beam there exists a line which suffers neither compression nor extension. The position of this line (the neutral axis) depends upon the relative power of the material to oppose the strains, upon its form and upon its position. Thus if wood resists two thousand pounds per square inch of extension, and one thousand pounds of compression, the axis will be twice as far from the top as from the bottom.

In some materials the neutral axis changes its place while the bar is at work; thus wrought iron, after being a little compressed, will bear a great deal more compression than when in its original state; also the lower fibres, after being extended, will resist less than at first; the effect of which two actions is to move the neutral axis up.

146. The following table shows the relative resisting powers of wood, wrought and cast-iron; with the corresponding positions of the axis, with sufficient accuracy for practice.

Thus in beams subjected to a cross strain, as well as to a direct extensile or compressive one, the resistance is effected by the incompressibility and inextensibility of the material.

147. The formula for dimensioning any beam to support a given weight transversely is

S = 4bd²
e,

Where S represents the ultimate strength in lbs.

b represents the breadth in inches,

d represents the depth in inches,

e represents the length in inches,