EQUIPMENT.
PART I. LOCOMOTIVES.
Introduction 302
Birth and growth of the locomotive 302
The English locomotive of 1850 304
The American locomotive of 1855 305
General description 306
Mechanical and physical principles 312
Resistance to the motion of trains 312
Traction and adhesion 316
Fuel 317
Generation of steam 330
Application of steam 336
Boiler proportions and dimensions 340
Rules and tables for practice 354
Adaptation of locomotives to the movement of trains 360
Classification of engines 371
PART SECOND.
CARS.
Wheels and axles 396
Classification of cars 400
Retarding of trains 401
CHAPTER XV.
STATIONS.
Classification of buildings 403
Location of buildings 403
Terminal passenger house 403
Terminal freight house 405
Engine house and appurtenances 405
Way passenger and freight house 407
Wood shed and tank 407
CHAPTER XVI.
MANAGEMENT.
Organization of employees 413
Duties of employees 415
Number of trains to be used 418
Amount of service of engines 418
Expenses, receipts, profits 420
Express trains 428
Comparative cost of working heavy and light trains 434
Branch roads 436
Reproduction of road and of stock 437
Working railroads by contract 439
Classification of freight 439
Time tables 443
Locomotive registers 444
Electric telegraph 454
New York and Erie Railroad 456
APPENDIX.
A.—Decimal Arithmetic 459
B.—Algebraic formulæ 461
C.—Weights and measures 464
D.—Value of the Birmingham gauges 465
E.—Locomotive boilers 466
F.—Effect of grades on the cost of working 468
G.—Form for a locomotive specification 471
H.—Relative cost of transport by railroad and by stage 476
I.—Form for experimental trips with locomotives 478
K.—Proper weight for locomotives 479
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 “_WL^2_ = 4_Sbd^2_,” read “_WL_ = 4_Sbd^2_.”
— 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:—
Span 30 feet, Whence—
Length 34 feet, Length 34 feet,
Load 10 tons at centre. Span 30 feet,
Depth 25½ inches,
Lower flange 32.58 square inches,
Upper flange 5.34 square inches,
_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′_ = (π_F_)/(4_ph_),” put “_D_ = √(¾[_V^2_ –
_d^2_]) – √(¾[_l^2_ – _d^2_]).
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_)/(2_R′_ × _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 “_R^2_ – (_R_ – 8)^2,” read “_R^2_ – (_R_ –
_g_)^2.”
— 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,
Sides, twice length, etc., read “Sides, twice length by height, etc.,
Back, twice height, etc., Back, height by width, etc.,
Front, twice height, etc., Front, height by width, etc.,
Top, twice length, etc.,” Top, length by width, etc.”
— 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:—
In 1828, there were 3 miles.
In 1830, 41 miles.
In 1840, 2,167 miles.
In 1850, 7,355 miles.
In 1856, 23,242 miles.
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:—
│ WHEAT. │ CORN.
│By R. R. By Wagon.│By R. R. By Wagon.
At market,│ $49.50 $49.50│ $25.60 $25.60
10 miles,│ 49.25 48.00│ 24.25 23.26
50 miles,│ 48.75 42.00│ 24.00 17.25
100 miles,│ 48.00 34.50│ 23.25 9.75
150 miles,│ 47.25 27.00│ 22.50 2.25
200 miles,│ 46.50 19.50│ 21.75 0.00
250 miles,│ 45.75 12.00│ 21.00 0.00
300 miles,│ 45.00 4.50│ 20.25 0.00
330 miles,│ 44.55 0.00│ 19.80 0.00
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.
Footnote 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]
Footnote 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]
Footnote 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.
[Illustration: 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_.
[Illustration: 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.
[Illustration: 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.
[Illustration: Fig. 4.]
[Illustration: 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.
[Illustration: 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_.
[Illustration: Fig. 7.]
[Illustration: Fig. 8.]
[Illustration: 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.
[Illustration: 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.
[Illustration: Fig. 11.]
[Illustration: Fig. 12.]
[Illustration: 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.
Barom. Attached Therm. Detached Therm.
Upper Station, 29.75 28.5 27.9
Lower Station, 26.80 36.8 36.3
Latitude 46° N.
We have by table A, against the bar. point, 29.75, 6108.6
also by table A, against the bar. point, 26.80, 5276.6
——————
The difference 832.0
Diff. of attached therm. 36.8°- 28.5° = 8.3° (table B) -12.2
——————
819.8
Double the sum of detached thermometers multiplied by 1/1000 of
819.8 is
2(27.9 + 36.3) × .8198 = + 105.3
——————
925.1
Correction (see table C) for lat. 46° N. and approximate height
925.1 + 3.1
——————
928.2
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.
TABLE A.
┌───────────────┬───────────────┐
│English Inches.│ Metres. │
├───────────────┼───────────────┤
│ 14.56│ 418.5│
│ 14.61│ 440.0│
│ 14.65│ 461.5│
│ 14.68│ 482.9│
│ 14.72│ 504.2│
│ 14.76│ 525.4│
│ 14.80│ 546.6│
│ 14.84│ 567.8│
│ 14.88│ 588.9│
│ 14.92│ 609.9│
│ 14.96│ 630.9│
│ 15.00│ 651.8│
│ 15.04│ 672.7│
│ 15.08│ 693.5│
│ 15.12│ 714.3│
│ 15.16│ 735.0│
│ 15.20│ 755.6│
│ 15.24│ 776.2│
│ 15.28│ 796.8│
│ 15.31│ 817.3│
│ 15.35│ 837.8│
│ 15.39│ 858.2│
│ 15.43│ 878.5│
│ 15.47│ 898.8│
│ 15.51│ 919.0│
│ 15.55│ 939.2│
│ 15.59│ 959.3│
│ 15.63│ 979.4│
│ 15.67│ 999.5│
│ 15.71│ 1019.5│
│ 15.75│ 1039.4│
│ 15.79│ 1059.3│
│ 15.83│ 1079.1│
│ 15.87│ 1098.9│
│ 15.91│ 1118.6│
│ 15.95│ 1138.3│
│ 15.98│ 1157.9│
│ 16.02│ 1177.5│
│ 16.06│ 1197.1│
│ 16.10│ 1216.6│
│ 16.14│ 1236.0│
│ 16.18│ 1255.4│
│ 16.22│ 1274.8│
│ 16.26│ 1294.1│
│ 16.30│ 1313.3│
│ 16.34│ 1332.5│
│ 16.38│ 1351.7│
│ 16.42│ 1370.8│
│ 16.46│ 1389.9│
│ 16.50│ 1408.9│
│ 16.54│ 1427.9│
│ 16.57│ 1446.8│
│ 16.61│ 1465.7│
│ 16.65│ 1484.7│
│ 16.69│ 1503.4│
│ 16.73│ 1522.2│
│ 16.77│ 1540.8│
│ 16.81│ 1559.5│
│ 16.85│ 1578.2│
│ 16.89│ 1596.8│
│ 16.93│ 1615.3│
│ 16.97│ 1633.8│
│ 17.01│ 1652.2│
│ 17.05│ 1670.6│
│ 17.09│ 1689.0│
│ 17.13│ 1707.3│
│ 17.17│ 1725.6│
│ 17.20│ 1743.8│
│ 17.24│ 1762.1│
│ 17.28│ 1780.3│
│ 17.32│ 1798.4│
│ 17.36│ 1816.5│
│ 17.40│ 1834.5│
│ 17.44│ 1852.5│
│ 17.48│ 1870.4│
│ 17.52│ 1888.3│
│ 17.56│ 1906.2│
│ 17.60│ 1924.0│
│ 17.64│ 1941.8│
│ 17.68│ 1959.6│
│ 17.72│ 1977.3│
│ 17.76│ 1994.9│
│ 17.79│ 2012.6│
│ 17.83│ 2030.2│
│ 17.87│ 2047.8│
│ 17.91│ 2065.3│
│ 17.95│ 2082.8│
│ 17.99│ 2100.2│
│ 18.03│ 2117.6│
│ 18.07│ 2135.0│
│ 18.11│ 2152.3│
│ 18.15│ 2169.6│
│ 18.19│ 2186.9│
│ 18.23│ 2204.1│
│ 18.27│ 2221.3│
│ 18.31│ 2238.4│
│ 18.35│ 2255.5│
│ 18.39│ 2272.6│
│ 18.42│ 2289.6│
│ 18.46│ 2306.6│
│ 18.50│ 2323.6│
│ 18.54│ 2340.5│
│ 18.58│ 2357.4│
│ 18.62│ 2374.2│
│ 18.66│ 2391.1│
│ 18.70│ 2407.9│
│ 18.74│ 2424.6│
│ 18.78│ 2441.3│
│ 18.82│ 2458.0│
│ 18.86│ 2474.6│
│ 18.90│ 2491.3│
│ 18.94│ 2507.9│
│ 18.98│ 2524.3│
│ 19.02│ 2540.8│
│ 19.05│ 2557.3│
│ 19.09│ 2573.7│
│ 19.13│ 2590.2│
│ 19.17│ 2506.6│
│ 19.21│ 2622.9│
│ 19.25│ 2639.2│
│ 19.29│ 2655.4│
│ 19.33│ 2671.6│
│ 19.37│ 2687.9│
│ 19.41│ 2704.1│
│ 19.45│ 2720.2│
│ 19.49│ 2736.3│
│ 19.53│ 2752.3│
│ 19.57│ 2768.3│
│ 19.61│ 2784.4│
│ 19.65│ 2800.4│
│ 19.68│ 2816.3│
│ 19.72│ 2832.2│
│ 19.76│ 2848.1│
│ 19.80│ 2864.0│
│ 19.84│ 2879.8│
│ 19.88│ 2895.6│
│ 19.92│ 2911.3│
│ 19.96│ 2927.0│
│ 20.00│ 2942.7│
│ 20.04│ 2958.4│
│ 20.08│ 2974.0│
│ 20.12│ 2989.6│
│ 20.16│ 3005.2│
│ 20.20│ 3020.7│
│ 20.24│ 3036.2│
│ 20.28│ 3051.7│
│ 20.31│ 3067.2│
│ 20.35│ 3082.6│
│ 20.39│ 3097.9│
│ 20.43│ 3113.3│
│ 20.47│ 3128.6│
│ 20.51│ 3143.9│
│ 20.55│ 3159.2│
│ 20.59│ 3174.4│
│ 20.63│ 3189.7│
│ 20.67│ 3204.9│
│ 20.71│ 3220.0│
│ 20.75│ 3235.1│
│ 20.79│ 3250.2│
│ 20.83│ 3265.3│
│ 20.87│ 3280.3│
│ 20.90│ 3295.3│
│ 20.94│ 3310.3│
│ 20.98│ 3325.3│
│ 21.02│ 3340.2│
│ 21.06│ 3355.1│
│ 21.10│ 3370.0│
│ 21.14│ 3384.8│
│ 21.18│ 3399.6│
│ 21.22│ 3414.4│
│ 21.26│ 3429.2│
│ 21.30│ 3443.9│
│ 21.34│ 3458.6│
│ 21.38│ 3473.3│
│ 21.42│ 3487.9│
│ 21.46│ 3502.5│
│ 21.50│ 3517.2│
│ 21.54│ 3531.8│
│ 21.57│ 3546.3│
│ 21.61│ 3560.8│
│ 21.65│ 3575.3│
│ 21.69│ 3589.8│
│ 21.73│ 3604.2│
│ 21.77│ 3618.6│
│ 21.81│ 3633.0│
│ 21.85│ 3647.4│
│ 21.89│ 3661.7│
│ 21.93│ 3676.0│
│ 21.97│ 3690.3│
│ 22.01│ 3704.6│
│ 22.05│ 3718.8│
│ 22.09│ 3733.0│
│ 22.13│ 3747.2│
│ 22.17│ 3761.3│
│ 22.20│ 3775.4│
│ 22.24│ 3789.5│
│ 22.28│ 3803.6│
│ 22.32│ 3817.7│
│ 22.36│ 3831.7│
│ 22.40│ 3845.7│
│ 22.44│ 3859.7│
│ 22.48│ 3873.7│
│ 22.52│ 3887.6│
│ 22.56│ 3901.5│
│ 22.60│ 3915.4│
│ 22.64│ 3929.3│
│ 22.68│ 3943.1│
│ 22.72│ 3956.9│
│ 22.76│ 3970.7│
│ 22.80│ 3984.5│
│ 22.83│ 3998.2│
│ 22.87│ 4011.9│
│ 22.91│ 4025.6│
│ 22.95│ 4039.3│
│ 22.99│ 4052.9│
│ 23.03│ 4066.6│
│ 23.07│ 4080.2│
│ 23.11│ 4093.8│
│ 23.15│ 4107.3│
│ 23.19│ 4120.8│
│ 23.23│ 4134.3│
│ 23.27│ 4147.8│
│ 23.31│ 4161.3│
│ 23.35│ 4174.7│
│ 23.39│ 4188.1│
│ 23.43│ 4201.5│
│ 23.46│ 4214.9│
│ 23.50│ 4228.2│
│ 23.54│ 4241.6│
│ 23.58│ 4254.9│
│ 23.62│ 4268.2│
│ 23.66│ 4281.4│
│ 23.70│ 4294.7│
│ 23.74│ 4307.9│
│ 23.78│ 4321.1│
│ 23.82│ 4334.3│
│ 23.86│ 4347.4│
│ 23.90│ 4360.5│
│ 23.94│ 4373.7│
│ 23.98│ 4386.7│
│ 24.02│ 4399.8│
│ 24.06│ 4412.8│
│ 24.09│ 4425.9│
│ 24.13│ 4438.9│
│ 24.17│ 4451.9│
│ 24.21│ 4464.8│
│ 24.25│ 4477.7│
│ 24.29│ 4490.7│
│ 24.33│ 4503.6│
│ 24.37│ 4516.4│
│ 24.41│ 4529.3│
│ 24.45│ 4542.1│
│ 24.49│ 4554.9│
│ 24.53│ 4567.7│
│ 24.57│ 4580.5│
│ 24.61│ 4593.2│
│ 24.65│ 4606.0│
│ 24.68│ 4618.7│
│ 24.72│ 4631.4│
│ 24.76│ 4644.0│
│ 24.80│ 4656.7│
│ 24.84│ 4669.3│
│ 24.88│ 4682.0│
│ 24.92│ 4694.5│
│ 24.96│ 4707.1│
│ 25.00│ 4719.7│
│ 25.04│ 4732.2│
│ 25.08│ 4744.7│
│ 25.12│ 4757.2│
│ 25.16│ 4769.7│
│ 25.20│ 4782.1│
│ 25.24│ 4794.6│
│ 25.28│ 4807.0│
│ 25.31│ 4819.4│
│ 25.35│ 4831.7│
│ 25.39│ 4844.1│
│ 25.43│ 4856.4│
│ 25.47│ 4868.7│
│ 25.51│ 4881.0│
│ 25.55│ 4893.3│
│ 25.59│ 4905.6│
│ 25.63│ 4917.8│
│ 25.67│ 4930.0│
│ 25.71│ 4942.2│
│ 25.75│ 4954.4│
│ 25.79│ 4966.6│
│ 25.83│ 4978.7│
│ 25.87│ 4990.9│
│ 25.91│ 5003.0│
│ 25.94│ 5015.1│
│ 25.98│ 5027.2│
│ 26.02│ 5039.3│
│ 26.06│ 5051.2│
│ 26.10│ 5063.2│
│ 26.14│ 5075.3│
│ 26.18│ 5087.2│
│ 26.22│ 5099.2│
│ 26.26│ 5111.2│
│ 26.30│ 5123.1│
│ 26.34│ 5135.0│
│ 26.38│ 5146.9│
│ 26.42│ 5158.8│
│ 26.46│ 5170.6│
│ 26.50│ 5182.5│
│ 26.54│ 5194.3│
│ 26.57│ 5206.1│
│ 26.61│ 5217.9│
│ 26.65│ 5229.7│
│ 26.69│ 5241.4│
│ 26.73│ 5253.2│
│ 26.77│ 5264.9│
│ 26.81│ 5276.6│
│ 26.85│ 5288.3│
│ 26.89│ 5300.0│
│ 26.93│ 5311.6│
│ 26.97│ 5323.2│
│ 27.01│ 5334.8│
│ 27.05│ 5346.4│
│ 27.09│ 5358.0│
│ 27.13│ 5369.6│
│ 27.17│ 5381.1│
│ 27.21│ 5392.7│
│ 27.25│ 5404.2│
│ 27.28│ 5415.6│
│ 27.32│ 5427.2│
│ 27.36│ 5438.7│
│ 27.40│ 5450.1│
│ 27.44│ 5461.5│
│ 27.48│ 5472.9│
│ 27.52│ 5484.3│
│ 27.56│ 5495.7│
│ 27.60│ 5507.1│
│ 27.64│ 5518.4│
│ 27.68│ 5529.8│
│ 27.72│ 5541.1│
│ 27.76│ 5552.4│
│ 27.80│ 5563.7│
│ 27.84│ 5575.0│
│ 27.87│ 5586.2│
│ 27.91│ 5597.5│
│ 27.95│ 5608.7│
│ 27.99│ 5619.6│
│ 28.03│ 5631.1│
│ 28.07│ 5642.2│
│ 28.11│ 5653.4│
│ 28.15│ 5664.6│
│ 28.19│ 5675.7│
│ 28.23│ 5686.8│
│ 28.27│ 5697.9│
│ 28.31│ 5709.0│
│ 28.35│ 5720.1│
│ 28.39│ 5731.1│
│ 28.43│ 5742.1│
│ 28.46│ 5753.1│
│ 28.50│ 5764.2│
│ 28.54│ 5775.1│
│ 28.58│ 5786.1│
│ 28.62│ 5797.1│
│ 28.66│ 5808.0│
│ 28.70│ 5819.0│
│ 28.74│ 5829.9│
│ 28.78│ 5840.8│
│ 28.82│ 5851.7│
│ 28.86│ 5862.5│
│ 28.90│ 5873.4│
│ 28.94│ 5884.2│
│ 28.98│ 5894.9│
│ 29.02│ 5905.8│
│ 29.06│ 5916.7│
│ 29.09│ 5927.5│
│ 29.13│ 5938.2│
│ 29.17│ 5949.0│
│ 29.21│ 5959.7│
│ 29.25│ 5970.4│
│ 29.29│ 5981.2│
│ 29.33│ 5991.9│
│ 29.37│ 6002.5│
│ 29.41│ 6013.2│
│ 29.45│ 6023.8│
│ 29.49│ 6034.4│
│ 29.53│ 6045.1│
│ 29.57│ 6055.7│
│ 29.61│ 6066.3│
│ 29.65│ 6076.9│
│ 29.69│ 6087.5│
│ 29.72│ 6098.0│
│ 29.76│ 6108.6│
│ 29.80│ 6119.1│
│ 29.84│ 6129.6│
│ 29.88│ 6140.1│
│ 29.92│ 6150.6│
│ 29.96│ 6161.1│
│ 30.00│ 6171.5│
│ 30.04│ 6182.0│
│ 30.08│ 6192.4│
│ 30.12│ 6202.8│
│ 30.16│ 6213.2│
│ 30.20│ 6223.6│
│ 30.24│ 6234.0│
│ 30.28│ 6244.4│
│ 30.32│ 6254.7│
│ 30.35│ 6265.0│
│ 30.39│ 6275.4│
│ 30.43│ 6285.7│
│ 30.47│ 6296.0│
│ 30.51│ 6306.2│
│ 30.55│ 6316.5│
│ 30.59│ 6326.7│
│ 30.63│ 6337.0│
│ 30.67│ 6347.2│
│ 30.71│ 6357.4│
│ 30.75│ 6367.6│
│ 30.79│ 6377.8│
│ 30.83│ 6388.0│
│ 30.87│ 6398.2│
│ 30.91│ 6408.3│
│ 30.94│ 6418.5│
│ 30.98│ 6428.6│
│ 31.02│ 6438.7│
│ 31.06│ 6448.8│
└───────────────┴───────────────┘
TABLE B.
┌───────────────┬───────────────┐
│ Deg.[4] │ Met. │
├───────────────┼───────────────┤
│ 0.2│ 0.3│
│ 0.4│ 0.6│
│ 0.6│ 0.9│
│ 0.8│ 1.2│
│ 1.0│ 1.5│
│ 1.2│ 1.8│
│ 1.4│ 2.1│
│ 1.6│ 2.3│
│ 1.8│ 2.6│
│ 2.0│ 2.9│
│ 2.2│ 3.2│
│ 2.4│ 3.5│
│ 2.6│ 3.8│
│ 2.8│ 4.1│
│ 3.0│ 4.4│
│ 3.2│ 4.7│
│ 3.4│ 5.0│
│ 3.6│ 5.3│
│ 3.8│ 5.6│
│ 4.0│ 5.9│
│ 4.2│ 6.2│
│ 4.4│ 6.5│
│ 4.6│ 6.8│
│ 4.8│ 7.1│
│ 5.0│ 7.4│
│ 5.2│ 7.6│
│ 5.4│ 7.9│
│ 5.6│ 8.2│
│ 5.8│ 8.5│
│ 6.0│ 8.8│
│ 6.2│ 9.1│
│ 6.4│ 9.4│
│ 6.6│ 9.7│
│ 6.8│ 10.0│
│ 7.0│ 10.3│
│ 7.2│ 10.6│
│ 7.4│ 10.9│
│ 7.6│ 11.2│
│ 7.8│ 11.5│
│ 8.0│ 11.8│
│ 8.2│ 12.1│
│ 8.4│ 12.4│
│ 8.6│ 12.6│
│ 8.8│ 12.9│
│ 9.0│ 13.2│
│ 9.2│ 13.5│
│ 9.4│ 13.8│
│ 9.6│ 14.1│
│ 9.8│ 14.4│
│ 10.0│ 14.7│
│ 10.2│ 15.0│
│ 10.4│ 15.3│
│ 10.6│ 15.6│
│ 10.8│ 15.9│
│ 11.0│ 16.2│
│ 11.2│ 16.5│
│ 11.4│ 16.8│
│ 11.6│ 17.1│
│ 11.8│ 17.4│
│ 12.0│ 17.6│
│ 12.2│ 17.9│
│ 12.4│ 18.2│
│ 12.6│ 18.5│
│ 12.8│ 18.8│
│ 13.0│ 19.1│
│ 13.2│ 19.4│
│ 13.4│ 19.7│
│ 13.6│ 20.0│
│ 13.8│ 20.3│
│ 14.0│ 20.6│
│ 14.2│ 20.9│
│ 14.4│ 21.2│
│ 14.6│ 21.5│
│ 14.8│ 21.8│
│ 15.0│ 22.1│
│ 15.2│ 22.4│
│ 15.4│ 22.7│
│ 15.6│ 22.9│
│ 15.8│ 23.2│
│ 16.0│ 23.5│
│ 16.2│ 23.8│
│ 16.4│ 24.1│
│ 16.6│ 24.4│
│ 16.8│ 24.7│
│ 17.0│ 25.0│
│ 17.2│ 25.3│
│ 17.4│ 25.6│
│ 17.6│ 25.9│
│ 17.8│ 26.2│
│ 18.0│ 26.5│
│ 18.2│ 26.8│
│ 18.4│ 27.1│
│ 18.6│ 27.4│
│ 18.8│ 27.7│
│ 19.0│ 28.0│
│ 19.2│ 28.2│
│ 19.4│ 28.5│
│ 19.6│ 28.8│
│ 19.8│ 29.1│
│ 20.0│ 29.4│
└───────────────┴───────────────┘
Footnote 4:
The degrees refer to the centigrade thermometer.
TABLE C.
┌─────────────┬─────────────┬─────────────┬─────────────┬─────────────┐
│ Approximate │ 0° │ 15° │ 40° │ 55° │
│ Height. │ │ │ │ │
├─────────────┼─────────────┼─────────────┼─────────────┼─────────────┤
│ 200│ 1.2│ 1.0│ 0.6│ 0.4│
│ 400│ 2.4│ 2.2│ 1.4│ 0.8│
│ 600│ 3.4│ 3.2│ 2.0│ 1.2│
│ 800│ 4.5│ 4.3│ 2.8│ 1.7│
│ 1000│ 5.7│ 5.3│ 3.4│ 2.2│
│ 1200│ 7.0│ 6.4│ 4.2│ 2.6│
│ 1400│ 8.2│ 7.6│ 4.8│ 3.0│
│ 1600│ 9.2│ 8.8│ 5.6│ 3.4│
│ 1800│ 10.4│ 9.8│ 6.3│ 3.8│
│ 2000│ 11.6│ 11.0│ 7.0│ 4.2│
│ 2200│ 12.8│ 12.1│ 7.6│ 4.6│
│ 2400│ 14.0│ 13.3│ 8.4│ 5.1│
│ 2600│ 15.2│ 14.4│ 9.2│ 5.6│
│ 2800│ 16.5│ 15.6│ 10.0│ 6.2│
│ 3000│ 17.7│ 16.8│ 10.8│ 6.6│
│ 3200│ 10.1│ 18.0│ 11.5│ 7.0│
│ 3400│ 20.5│ 19.3│ 12.4│ 7.7│
│ 3600│ 21.8│ 20.4│ 13.4│ 8.2│
│ 3800│ 23.1│ 21.6│ 14.3│ 8.7│
│ 4000│ 24.6│ 22.9│ 15.1│ 9.4│
│ 4200│ 25.9│ 24.3│ 15.9│ 10.1│
│ 4400│ 27.5│ 25.8│ 16.9│ 10.8│
│ 4600│ 28.9│ 27.1│ 18.0│ 11.5│
│ 4800│ 30.4│ 28.4│ 19.0│ 12.1│
│ 5000│ 31.8│ 29.8│ 19.9│ 12.7│
│ 5200│ 33.0│ 31.0│ 20.8│ 13.3│
│ 5400│ 34.3│ 32.4│ 21.7│ 13.9│
│ 5600│ 35.7│ 33.7│ 22.6│ 14.5│
│ 5800│ 37.1│ 35.0│ 23.6│ 15.1│
│ 6000│ 38.5│ 36.3│ 24.6│ 15.7│
└─────────────┴─────────────┴─────────────┴─────────────┴─────────────┘
TABLE D.
┌───────────────┬───────────────┐
│ Barometrical │ Metres │
│ Height │ │
├───────────────┼───────────────┤
│ 15.75 │ 1.71 │
│ 17.72 │ 1.39 │
│ 19.68 │ 1.11 │
│ 21.65 │ 0.86 │
│ 23.62 │ 0.63 │
│ 25.59 │ 0.42 │
│ 27.56 │ 0.22 │
│ 29.53 │ 0.03 │
└───────────────┴───────────────┘
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.
[Illustration: 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.
[Illustration: 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.
[Illustration: Fig. 15.]
[Illustration: Fig. 16.]
[Illustration: Fig. 17.]
[Illustration: 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.
[Illustration: 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.
[Illustration: 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.
[Illustration: Fig. 20.]
[Illustration: Fig. 21.]
[Illustration: 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.
[Illustration: 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.
[Illustration: 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:—
Velocity, in miles, per hour. Resistance, in lbs. per ton.
10 8.6
15 9.3
20 10.3
25 11.6
30 13.3
40 17.3
50 22.6
60 27.1
100 66.5
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
Speed, in miles, per hour. Equating number.
15 22
20 24
30 32
40 41
50 53
60 67
100 155
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.
The cost of working a power represented by unity being expressed by 100;
That of working a power 2 is expressed by 125;
That of working a power 3 is expressed by 150;
That of working a power 4 is expressed by 175;
That of working a power 5 is expressed by 200.
(See Appendix F.)
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:—
Speed, in miles, per hour. Equating number.
15 88
20 96
25 110
30 128
40 164
50 212
60 268
100 620
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.
Let the length of line A be 100 miles,
Let the length of line B be 90 miles,
Whole rise on A 2000 feet,
Whole rise on B 5100 feet,
Whole fall on A 1200 feet,
Whole fall on B 4300 feet.
Assume the number by which to equate, as ninety-six, and we shall have
Line A.
Ascending, 100 + 2000/96 = 120.83
Descending, 100 + 1200/96 = 112.50
——————
Sum 233.33
Mean 116.66
Line B.
Ascending, 90 + 5100/96 = 143.13
Descending, 90 + 4300/96 = 134.80
——————
Sum 276.93
Mean 138.46
The mean equated length of A is 116.66
The measured length of A is 100.00
——————
The difference 16.66
The mean equated length of B is 138.46
The measured length of B is 90.00
——————
The difference 48.46.
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.
[Illustration: 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:—
Angle of deflection. Radius, in feet.
¼° or 15′ 22920.0
½° or 30′ 11460.0
¾° or 45′ 7640.0
1° or 60′ 5730.0
1¼° 4585.0
1½° 3820.0
1¾° 3274.0
2° 2865.0
2½° 2292.0
3° 1910.0
3½° 1637.0
4° 1433.0
4½° 1274.0
5° 1146.0
5½° 1042.0
6° 955.4
6½° 822.0
7° 819.0
7½° 764.5
8° 716.8
10° 573.7
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.
[Illustration: 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.
[Illustration: 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.
[Illustration: 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:—
Locomotives, 40 per cent.
Cars, 20 per cent.
Way and works, 15 per cent.
——
or in all, 75 per cent.
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.
Line A. Line B. Description.
100 miles, 110 miles, Actual length,
5000 feet, 3000 feet, Rise,
3500 feet, 1500 feet, Fall,
3600° 9000° Degrees of curvature.
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,
Line A ascending 100 + 52.1 + 3.16 = 155.26 │147.46
Line A descending 100 + 36.5 + 3.16 = 139.66 │
Line B ascending 110 + 31.25 + 7.89 = 149.14 │141.31,
Line B descending 110 + 15.62 + 7.89 = 133.49 │
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.
[Illustration: 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:—
A route, A B _c_. B route, A M K _c_.
Length, 39.29 43.58
Rise A to _c_, 540.00 1087.00
Rise _c_ to A, 395.00 936.00
Whole rise and fall, 935.00 2023.00
Degrees of curvature, 2371°.00 3253°.00
Estimated cost, $746,900.00 $628,600.00
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,
Route A. A to _c_. │Mean, 46.25.
39.29 + 540/96 + 2371/1140 = 39.29 + 5.63 + 2.08 = 47.00│
│
Route A. _c_ to A. │
39.29 + 395/96 + 2371/1140 = 39.29 + 4.12 + 2.08 = 45.49│
Route B. A to _c_. │Mean, 56.96.
43.58 + 1087/96 + 3253/1140 = 43.58 + 11.32 + 2.85 = 57.75│
│
Route B. _c_ to A. │
43.58 + 936/96 + 3253/1140 = 43.58 + 9.75 + 2.85 = 56.18│
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,
or as $3,083,334 to $3,797,334
—————————— ——————————
and the sum as $3,830,234 $4,425,934
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:—
I H. E F.
Measured length, 61.14 58.53
Rise D to G, 1187 454
Rise G to D, 1049 316
Degrees curve, 7609° 4588°
Estimated cost, $1,094,950 $1,496,430
The mean equated lengths are as follows:—
Line I H. D to G. │Mean, 79.46,
61.14 + 1187/96 + 7609/1140 = 61.14 + 12.36 + 6.68 = 80.18│
│
Line I H. G to D. │
61.14 + 1049/96 + 7609/1140 = 61.14 + 10.93 + 6.68 = 78.75│
Line E F. D to G. │Mean, 66.56.
58.53 + 454/96 + 4588/1140 = 58.53 + 4.73 + 4.02 = 67.28│
│
Line E F. G to D. │
58.53 + 316/96 + 4588/1140 = 58.53 + 3.29 + 4.02 = 65.84│
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
1,094,950 to 1,496,430
+ 5,297,334 + 4,437,334
—————————— ——————————
or $6,392,284 to $5,933,764
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]
Footnote 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.