A.
DECIMAL ARITHMETIC.

The advantage of a Decimal system of Arithmetic and of mensuration, as applied to engineering, can hardly be overstated. Civil and mechanical engineers both use “per force” some decimal expressions, as 0.7854, 3.1416, etc., etc. Why not adopt the system entirely? All calculations are much easier made decimally, and measurements made with more exactness. The most perfect system of weights and measures is doubtless that of the French. All lengths are based upon the meter as a unit, and whether the mechanic is making a watch or a locomotive his scale is metrical. The meter is exactly 1
10000000 of the distance from the pole to the equator, and was found, by measuring a meridian line from Rhodes to Dunkirk (France), 570 miles long. The metrical scale is thus,

Millimetre	.001	or 1 1000
Centimetre	.01	or 1 100
Decimetre	.1	or ?
Metre	1.
Decametre	10.
Hectometre	100.
Kilometre	1000.
Myriametre	10000.

The metre is 3.280899 ft., or 39.370788 English inches. The English and American foot is ? of the yard; the yard is 35000
351393 of a pendulum vibrating seconds at the latitude of London, at the level of the sea, in a vacuum. The standard American scale is an eighty-two inch bar made by Troughton of London for the United States Coast Survey. In civil engineering the decimal division is almost entirely adopted; indeed, any other would lead to almost endless calculation. The chain is one hundred feet long and divided into one hundred links. The tape is graduated to feet, tenths, and hundredths. The levelling rod to feet, tenths, hundredths, and thousandths. As the English foot is so universally adopted, and as it may at any time be got from a pendulum, it might not be best to attempt to introduce the metre, but the foot should certainly be divided decimally. The division should be thus,

.001	or 1 1000
.01	or 1 100
.1	or ?
1.
10.
100.
1000.

thus preserving a constant ratio, and not changing the proportion at each increase or decrease as follows:—

As this work may come into the hands of those who are unacquainted with the solution of algebraic problems, it was thought best to give the following:—

a + a, signifies a added to a, or 2 a.

a – a, denotes a less a, or 0.

a × a, a multiplied by a, or a square, a² (see below).

a², the square of a, or a × a

a³, the third power of a, or a × a × a.

va, the square root of a, or a^½

?a, the cube or third root of a, or a^?

a + b + c
d, shows that the sum of a, b, and c, is to be divided by d.

(a + b + c) d or a + b + c × d, denotes that the sum of a, b, and c, is to be multiplied by d.

Generally in place of writing a × b to express multiplication, we put simply a b.

The above signs may be compounded in any manner; thus,

Here we have, first, the product of c by the sum of a and b; this is divided by d, and three quarters of the quotient is divided by m; and, finally, the fourth root of the last result is extracted, which is the value of the expression.

The following examples show the use of formulÆ. See Chapter VI., on Earthwork, art. Average Haul:—

Required the average haul of several masses of earth. Let m m' m mⁿ represent the several masses, and d d' d dⁿ the respective hauls; S the sum of the masses, D the average haul, and we have

If we make the values	m	=	100	also	d	=	100
	m'	=	200		d'	=	50
	m	=	300		d	=	75
	mn	=	400		dn	=	200

the sum is 1000, and we have

In Chapter VIII., Wooden Bridging, we have the expression

S becomes

In Chapter IX., Iron Bridges, we have

and making p =	4000
h =	500
f =	80

we have

In Chapter XIII., Elevation of Exterior Rail,

and when W =	50
V =	20
g =	5
R =	2000

we have

And finally, in the latter part of Chapter XIV., we have the formula

and making n =	200
d =	1
c =	1½
A =	4
B =	3

we have

Name of material.	Weight per cubic foot.
Air	0.077 lbs.
Earth	112. lbs.
Water	62.5 lbs.
Ice	58.0 lbs.
Sand	132.0 lbs.
Clay	120.0 lbs.
Chalk	155.0 lbs.
Brick	110.0 lbs.	See Chap. XI., masonry.
Brickwork	95.0 lbs.
Dry mortar	96.0 lbs.
Sandstone	140.0 lbs.
Limestone	142.0 lbs.	Average 86 to 198.
Granite	175.0 lbs.
Coal, Bituminous	60 to 80.0 lbs.
Coal, Anthracite	85 to 95.0 lbs.
Coke	50 to 65.0 lbs.
Coal, Cannel	75 to 80.0 lbs.
Wrought Iron	480.0 lbs.
Cast-Iron	450.0 lbs.
Steel	487.0 lbs.
Hard Wood.
Green	62.0 lbs.
Air dried	46.0 lbs.
Kiln dried	40.0 lbs.
Soft Wood.
Green	53.0 lbs.
Air dried	30.0 lbs.
Kiln dried	28.0 lbs.
	Weight per bushel.
Wheat	60 lbs.
Corn on the cob	70 lbs.
Corn, shelled	56 lbs.
Rye	56 lbs.
Oats	35 lbs.
Barley	47 lbs.
Potatoes, Irish	60 lbs.
Potatoes, Sweet	55 lbs.
Beans, White	60 lbs.
Beans, Castor	46 lbs.
Bran	20 lbs.
Clover Seed	60 lbs.
Timothy	45 lbs.
Hemp	44 lbs.
Flax	56 lbs.
Buckwheat	52 lbs.
Peaches, Dried	33 lbs.
Apples, Dried	24 lbs.
Onions	57 lbs.
Salt, Coarse	50 lbs.
Malt	38 lbs.
Corn Meal	48 lbs.
Salt, Fine	55 lbs.

D.
VALUE OF THE BIRMINGHAM GAUGES.

Number.	Size in inches.
0	0.340
1	.300
2	.284
3	.259
4	.238
5	.220
6	.203
7	.180
8	.105
9	.148
10	.134
11	.120
12	.100
13	.095
14	.083
15	.072
16	.065
17	.058
18	.049
19	.042
20	.035
21	.032
22	.028
23	.025
24	.022
25	.020
26	.018
27	.016
28	.014
29	.013
30	.012

E.
LOCOMOTIVE BOILERS.

If the ideas of Clark and Overman are correct, the value of vertical flues with the water inside, as compared with horizontal flues with water outside, is comparatively as follows: One half of the surface of the horizontal tube (the upper half) is available, but this half generates steam twice as fast as the same area of upright tube surface. Thus the amount of evaporation will be the same in either position, for the same absolute tube surface, not considering the increased diameter by applying the heat to the outside, or the advantage, so highly estimated by Overman, of applying the heat to the convex surface.

The following application of Montgomery’s vertical flue boiler to the locomotive engine for heat generation and application, seems to satisfy nearly all requirements. Retaining the original furnace shell, produce it forwards so that it shall just clear the driving axle, let the sides drop to within two feet of the rail, and close up the bottom. Next, inside of this place a rectangular box which shall be a continuation of the inner box, the top being about nine inches above the diametric chord of the semicircular crown, leaving a water space of three or four inches between the sides and bottom of the two boxes. Fill the inner box with vertical tubes, the top and bottom being flue plates, the tubes being screwed in at one end and fitted with a screw thimble at the other, may be removed for cleaning at any time and will effectually stay the inner box against the enormous pressure upon the top and bottom. The pressure being inside of the tubes will tend to keep the end joints tight, where, in the common boiler, the reverse is the case.

That the burning gases may retain sufficient heat to burn until they are discharged, there should be less tube surface at the back than at the front end, a requirement which is easily satisfied by decreasing the number and increasing the size of tubes from the front to the back end. In the common boiler the ferrule area being less than the flue area, a stronger blast is used than is really necessary to draw the hot gases through the tubes, while in the vertical tube boiler the gas area may be equally large at all points.

Again, any amount of oxygen may be applied to the gases at any point of their passage from the furnace to the smoke box, by the admission of fresh air to any part of the barrel. Thus the advantage of a combustion chamber (if there is any) is obtained without the sacrifice of a single inch of heating surface, as we only require to admit air between the tubes and not into them; this may be done either by hollow stay bolts or by larger openings, to be open or shut at pleasure.

If the gases in passing through the boiler are left to themselves, we get, without an effort, the effect produced by Montgomery’s third claim, namely, the application of the heat to the upper half of the tubes; and, however we wish to apply the passing heat to the flues, complete control over the motion of the gases may be had by the use of a Venetian blind damper in the smoke box, in two parts; the upper and the lower parts moving independently, allow us to throw the heat upon any part of the length of the tubes. Of course, by heating most the upper part of the flues, we stand a better chance of getting circulation.

It might be objected that so much flat boiler surface would give a form more liable to explosion than the circular barrel. Experiments lately made by William Fairbairn, (England,) induced by the bursting of a locomotive fire box, show that the flat surfaces are the strongest forms of the boiler, or, to use his own words, “are conclusive as to the superior strength of flat surfaces as compared with the top, or even the cylindrical parts of the boiler.” His experiments show that two plates one fourth and three eighths inch thick, connected by screw stay bolts four inches from centre to centre, will resist over one thousand lbs. per square inch.

By such a plan of engine we may always have any amount of heating surface with a moderate sized boiler, and a low centre of gravity.

The excess of cost of the engine, above described, over the common form would be about $500, the annual interest of which is $30, which must be saved by the new plan, (say ten cords of wood).

Any saving beyond this is pure gain.

F.
EFFECT OF GRADES ON THE COST OF WORKING RAILROADS.

The cost of working a railroad will be increased by augmenting the steepness of grades. First, because of the mechanical effect of the inclines; second, on account of decreased capacity of the road. The cost of maintaining and working a road consists of items, a few of which are functions of grades and many which are not. The chief items which are affected by grades are, fuel consumption, first cost of locomotives, and perhaps wear of rails, where grades are so steep as to require sand ascending, and application of brakes descending, the rails will be somewhat more worn. When not so steep as this the repair of superstructure will not be much increased. Steeper inclines involve the use of heavier engines, or more of them. Heavy engines generally have no more weight on one pair of wheels, and often not so much, as lighter ones; and though there is more abrasive power on increased total rolling weight, there is less deflection of rails, by means of less concentrated loads. It would seem, therefore, that the effect of grades upon the wear of superstructure was but little, if not inconsiderable. The first cost of engines may be increased from $1,000 to $2,500 to enable them to work steep grades. If the wheels are the same size in both engines, we should require greater steam pressure, consequently (see Chapter XIV.) more fuel; and if the steam power was the same, smaller wheels or larger cylinders, also requiring (Chapter XIV.) more fuel.

In doubling the work done by the engine we by no means double the amount of fuel consumed, (see Chapter XIV.,) but increase it by about ninety per cent.

The division of expenses upon five of the largest English railroads was for a certain time as follows:—

Salaries	$6.83
Way and works	15.76
Locomotives	35.15
Cars	38.14
Sundries	3.69
	$100.00
Percentage for engines	35.00

Upon the roads of Belgium,

Salaries	$5.47
Way and works	26.62
Locomotives	49.96
Cars	14.80
Sundries	3.15
	$100.00
Locomotive percentage	50.00

Upon the railroads of New York State (2,200 miles) (State Engineer’s Report, 1854),

Salaries	$10.00
Way and works	15.00
Locomotives	40.00
Cars	20.00
Sundries	15.00
	$100.00
Locomotive percentage	40.00

Average percentage of all of the above charged to locomotives 41? of the whole locomotive expense; fuel absorbs 62½ percent.; and as a double amount of work requires ninety per cent. more fuel, we have, as the cost of working a grade causing a double resistance (say twenty-five feet per mile), 90
100 of 62
100 of 42
100, or very nearly 22 per cent. of the cost of working the train; to which add ? more, interest on locomotive capital, and we have, as the bad effect of a twenty-five feet grade, when

Locomotive capital	$1,000,000
Cost of working	200,000
Annual expense of a level road (at six per cent.)		$60,000
		+ 200,000
		$260,000
And upon a road with continuous 25 feet grades		$60,000
		+ 6,000
		+ 200,000
+ 200,000 × 22 100, or		44,000
Total		$310,000

or 120 per cent. of the cost of working the level road, the increase being twenty per cent., or allowing five per cent. for other contingencies, twenty-five per cent.; also the increase due to a fifty feet grade, fifty per cent.; and so on as long as only one engine is required to draw the full train, (its power being increased by varying its dimensions). When the train has to be broken and two or more engines are needed, the percentage will of course increase. The point at which the train ought to be broken may be found easily, either as depending upon the load or the grade, by a comparison of working expenses.

G.
SPECIFICATION FOR A PASSENGER LOCOMOTIVE ENGINE FOR THE A. AND B. RAILROAD.

Requirement.

Speed 20 miles per hour, including stops; fuel, wood; weight of train 150 tons; maximum grade 60 feet per mile; sharpest curve 3° or 1,910 feet radius; rail 60 lbs. per yard on ties 2 feet from centre to centre.

General Plan and Dimensions.

Outside connections; four five feet driving wheels with best Ames’s tire, all tires being flanged; level cylinders 15 inches diameter of bore and 20 inch stroke. Centre-bearing truck, with inside and outside bearings, and Lightener boxes. Square wrought iron frame well braced, 4–30 inch Whitney and Sons’ cast-iron truck wheels, spread 60 inches centre to centre. Lifting link motion working through rockers, valves described hereafter. Truck supplied with fore and aft safety chains, and safety beams beneath axles. Weight on drivers 30,000 lbs., on truck 10,000 lbs. Tender to be mounted on two trucks, each of 4–30 inch Whitney and Sons’ wheels, spread 54 inches from centre to centre. To have square iron frames well braced with outside Lightener boxes; tank to hold 1,600 gallons.

Boiler.—Grate 38 inches wide, 54 inches long, surface 20 above rail, grate bars cast solid for 6 inches of the front end, to be 4 inches deep, and ¾ inch thick, placed ¾ inch apart in the clear; lower edges chamfered on each side by a chamfer of ½ inch deep and ¼ inch wide; centre of grate bars to be supported by a wrought iron bar 1 inch thick and 4 inches deep, attached as in drawing. Fire-box.—Outer sides of furnace shell 51 inches wide by 62 inches long; crown 8 feet above rail, to be made of ? inch iron plates with a 16 inch necking of angle iron to carry the rear dome; corners to be joined by flanges rounded to a 4 inch radius. The crown of the shell to be raised 9 inches above the barrel crown, the connection being made by a sloping offset 20 inches long on top. End plates lap jointed to sides and top; the seams joining the fire-box to the waist, to be double riveted. Furnace to be made of ½ inch copper plates, ¾ inch at tubes, lap jointed, 42¼ inches wide, and 51½ inches long inside; side water spaces to be 3 inches clear at the bottom, widening (by sloping inwards the sides of the furnace) to 4 inches at the top of inner box; front spaces 4 inches, rear spaces 4 inches at bottom and 5 inches at top. Doorway made with a wrought iron ring fastened with ? inch rivets, door of ? inch plate with ¼ inch shield. Furnace joined to shell with ? inch copper stay bolts, screwed and riveted at both ends, placed 44 inches from centre to centre. Eight roof-ribs laid widthwise of the crown of the furnace, being each 6 inches deep and ¾ inch thick, double welded at the ends and riveted at the centre, held down by T head bolts 5 inches between centres, bars to be raised above the crown sheet by ? inch thimbles. Dome opening, neckling to be made of angle iron which shall be connected with the roof-ribs by 4–1? inch stays, connected and placed as in the drawing. The back and tube sheets of the furnace are flanged over on top; the crown is flanged downwards on the sides, but not on the back and front. One dome is placed on the crown of fire-box shell 26 inches diameter and 24 inches high; opening of dome into boiler 16 inches diameter. Lower part of dome of wrought, top of cast-iron, put on with a ground joint. Furnace and shell to be connected at bottom by a wrought iron bar 3 inches wide, 2½ inches deep. The whole boiler to be thoroughly caulked inside and out. Barrel of ¼ inch best Philadelphia stamped charcoal iron, 44 inches diameter outside of main crown next the fire-box, and 43 inches next the smoke box end, 10 feet long with 3 inch angle irons at ends. Front dome of ½ inch plate worked in one piece, 23 inches diameter. End plates of boiler stayed with six 1 inch rods, cottered into blocks, riveted to plates; barrel plates riveted with ¾ inch rivets, and 1¾ inch pitch. Smoke box, 2' 4 long, same diameter as barrel, of 3
16 inch plates well riveted, bolted to the angle iron so as to be easily removed for inside repairs; front tube sheet 6
8 inch. Tubes, 140 two inch (outside) diameter No. 9 thickness at fire end, No. 14 at smoke end 10 feet long, placed ½ inch apart. The smoke box end of tubes to be closed at pleasure by a venetian blind damper. Chimney of ¼ inch iron outside, diameter 16 inches, top 6' 6 above crown of barrel, fitted with proper stack, cone, and sparker. Ash pan of ¼ inch plate made with 1½ inch angle iron, and band on upper edge, fitted with doors both before and behind, 7 inches deep and riding 6 inches clear of the rail. Steam pipes, 6 inch pipes of No. 10 copper running the whole length of the boiler, connected at the domes with 5 inch cast-iron stand pipes. Cast-iron branch pipes in smoke box leading to valve chests, 5 inches diameter. Throttle to be in a cast-iron chest in smoke box, as shown in drawing, having an area at least as large as the steam port. Changes of direction in pipes to be made by curves and not by angles. Exhaust pipe of No. 10 copper, 5 inches diameter at lower end, fitted with a variable blast orifice, ranging from eight to four square inches area, to be inclosed in a petticoat pipe.

Cylinders, 15 inches bore, and long enough for a 20 inch stroke, or 28¾ inches from outside to outside of ground faces, casting ? inch thick, covers 1? inch thick, placed level and firmly bolted to main frame and to horizontal truss brace, as shown in drawing; heads to go on with ground joint. Valve seat to have steam ports 14 × 1? inches; exhaust port 14 × 2½ inches; outside lap of valve ? inch, inside nothing; 1
16 inch lead on 4¾ inch throw of valve, gradually increasing as the throw is reduced, to scant 5
16. Steam chests bolted to a level face, ground joint with ¾ inch bolts pitched 4 inches.

Valve motion.—Shifting link with lifting shaft, sector, lever, rocker, etc., of the most approved form; four solid eccentrics of 5¼ inches throw, fastened to axle by four square ended set screws pressing hardened steel dies, cut with sharp grooves on their ends, against the axle; the friction of the dies against the axle holding the eccentric in place. Eccentric straps of cast-iron, with oil caps cast on, and grooved out inside so as to shut over the eccentric and exclude dust. Link forged solid and case hardened, 17 inches by 2¼ inches inside the slot; thickness of iron all around the slot 1½ inches, whole lateral thickness 2 inches. Eccentric rods of ? iron 3 inches deep, 5½ feet between centres, fastened to link and to eccentric, as shown in the drawing. Link curved to a radius 6 inches less than the distance between the centre of driving axle and centre of link at mid gear. The links, boxes, stack, etc., to be of wrought iron, case hardened. Pistons with one outside composition ring and two circumferential grooves filled with Babbitt metal, and one inside ring of wrought iron; outside ring cut obliquely at one place with a small wrought iron flap on each edge to prevent leakage of steam at the point of division. Glands of piston and valve rod stuff boxes of cast-iron with tight brass or composition bushings.

Frame forged from good scrap 4×2 inches, the main bar being straight from end to end with pedestals welded on; the rear end piece to be a heavy forged foot plate, the front end an oak beam 7×14 inches placed on the flat side. All the pedestals on one side having adjustable keys. Flat boiler braces averaging 4½ × ? inches with broad palms riveted to the boiler; the attachment at the furnace to be made by the Rogers expansion brace, details of the frame as in the drawing; frame to be placed true wherever needed to receive the working parts of the engine.

Wheels, axles, and springs.—Four cast-iron driving wheels tired with best flanged Ames’s tires 2 inches thick, diameter with tire five feet, tires to be turned to a true cone of .072 inches per wheel, wheels to be truly balanced. Rest scrap or bloom axles, front 7 and rear 6 inches in diameter, bearings 8 inches long, collars of cast-iron held by set screws, axles to be cylindrical and not smaller at the centre than at the end. Four springs of seventeen steel plates, each 4 × ? × 40 inches; equalizing lever between springs. Inside bearing springs of truck hung from equalizer, which latter bears upon the axle boxes.

Slides, pumps, connecting rods, etc., etc.—Slides, flat wrought iron bars 3 × 1¼ inches, case hardened. Cross head bearing of cast-iron 16 inches long and 2 inches thick. Pumps, full stroke brass pumps 5
16 inch thick with 1? inch plungers, ram of wrought iron with an eye fixed on cross head and worked by it. Waterways in body 2 inches, in valves 1¾ inches. Three ball valves with 2¼ inch hollow balls, one for suction and two for delivery; pipes ? inch thick, 2 inches diameter, suction of iron, delivery of copper, cock of brass on delivery pipe worked by rod at cab. Air chamber on forcing side of pump equal to capacity of barrel; on suction side half the same. Flat connecting rods forged from solid piles without welds. Babbett lined boxes upon all stub ends. Straps held on each by two bolts, one key to each bearing. Safety-valves, one to be 3½ inches diameter, placed on the rear dome, and one forward, 4 inches diameter, both to be well fitted and supplied with the proper beams and spring balances. Barrel to be covered with hair felting ½ inch thick, to be furnished with a Russia iron jacket. Cylinders to be protected by an ½ inch felt coat and cased in brass.

The engine to have all the usual fixtures, bell, whistle, gauges, heater, pet, blow-off, and other cocks, name plates, oil cups, sandbox, tools, oil cans, etc., etc. Pilot to be 5 feet long, of flat horizontal wooden bars 2½ × 4 inches with a heavy centre piece, the whole to be well hung and firmly braced. Cab to be neatly built, with a projecting cornice, and windows, doors, etc., to be furnished in the best manner. The whole engine to be well painted and varnished. The draw bar to be strongly attached to the frame of the engine at 30 inches above the rail, and connected by a double elliptical spring to the centre beam of the tender.

Tender.—Tank to hold 1,600 gallons, top and side plates ? inch, and bottom plate ¾ inch well riveted and caulked inside and out. Brakes to apply from a single wheel to each side of all of the wheels, that is, at sixteen points; brake blocks hung with safety chains and springs to carry them away from the wheels. One spring 26 inches long, of ten levers 3 × 5
16 inches over each wheel. Frame of seasoned oak 10 × 4 inches, centre beam 5 × 20 inches. The whole to be thoroughly painted and varnished.

General Provision.

All of the material, both of engine and tender, to be of the very best quality, and all of the construction done in the most thorough and workmanlike manner. The engine and tender being in every respect equal to the best that has heretofore been sent from the —— shops. For more detailed information, see plans accompanying.

H.
RELATIVE COST OF TRANSPORT BY RAILROAD AND BY STAGE.

Too great a reduction of the cost of travel was both expected of and given by railroad companies at the commencement of the system, as the following will show:—

Voted, “That the directors are hereby earnestly and urgently requested forthwith to increase the rates of transportation, both for passengers and freight, in all cases in which, in their opinion, they are now too low, and hereafter to decline all business that will not give to the corporation a full remuneration for expenses and a fair profit for its transportation.”

Why the railroad rates should have been placed so low, it would be hard to show.

The cost of moving eight passengers by stage one hundred miles, would be somewhat as follows. Let a common road cost one thousand dollars per mile, and suppose the stage travel to use one tenth of the capital expended; the daily interest for one trip is

(100 × 1000 × 6 100)/365 ÷ 10 or	$1.64
Ten horses and one stage,
(1500 + 500 × 6 100)/365 or	0.33
Daily salary of driver and stable hands,	5.00
Daily interest on stable cost, repairs, &c., &c.,	1.03
Whole cost of moving 8 passengers 100 miles,	$8.00
Cost of moving one passenger one mile,	.01
Again. Let a railroad cost $25,000 per mile, one hundred miles cost $2,500,000, and if we run ten trains per day the daily interest, at six per cent., for one train is
(2500000 × 6 100)/365 ÷ 10 =	$41.10
A locomotive costs $10,000,
Two cars cost 4,000,
and (14000 × 6 100)/365 is	2.30
And the daily cost of road and equipment,	$43.40
divide by 100, for the cent per mile,	0.43
The average number of passengers carried in one car, (see New York State Engineer’s Report,) is 17; two cars, 34, whence 43 34 =	1? cents
The daily cost per mile, per passenger, is then, for the use of the road and equipment,	1? cents
The cost of maintaining and working is, per passenger, per mile, (see New York State Engineer’s Report for 1854.)	1¼ cents
Whence the whole cost of carrying one passenger one mile upon a railroad will be	27 12 cents
The relative cost of transport is, then, thus,
By stage,	1 cent
By railroad,	27 12 cents
and the relative charge thus,
By stage,	5 cents
By railroad,	3 cents

And the comparative profit as 5 less 1, or 4; to 3 less 27
12, or 5
12; or as 1 to 9.6.

I.
FORM FOR RECORDING THE RESULTS OF EXPERIMENTAL TRIPS WITH LOCOMOTIVES.

In comparing the work done by different locomotives, we must know not only the relative amounts of material consumed, but also the exact nature of the work done, as depending upon speed, load, curves, and grades. The following blank, when filled, has been found to give complete information, for comparison.

Station,
Time of arriving,
Time of departing,
Time running,
Time standing,
Distance,
Rise,
Fall,
Degrees of curvature,
Equated distance,
Cars taken,
Cars left,
Load between stations,
Equated mileage of train,
Gauge pressure,
Notch of sector,
Fuel used,
Water used,
Lbs. of fuel per gallon of water,
Lbs. of fuel per equated mileage, per ton or per passenger,
Comparative effect,

K.
PROPER WEIGHT OF LOCOMOTIVES.

To move a given load the engine requires a certain amount of power; to exert such power there is needed load enough on the drivers to prevent slipping on the rail. This load varies from three times the tractive power, (in the best state of the rails,) to ten times the tractive power, and even more, (in the worst state). A fair working average (without sand), being one sixth; with sand, much less. Sand must be used upon grades and upon bad rails. To find then the proper weight, we have only to estimate the tractive power upon the hardest point of the road, and multiply it by six.

How heavy an engine is needed to draw two hundred tons (including engine and tender) at twenty miles per hour over sixty feet grades?

The resistance on a level is

200 ×(20 × 20 171 + 8) =	2,060	pounds.
The resistance due to the grade
200 × (60 5280 × 2240) =	5,200	pounds.
The resistance due to curves
200 × 5=	1,000	pounds.
And the whole resistance,	8,260	pounds.
which multiplied by 6, is	49,560	pounds.

or 22.1 tons, to which add 5 tons as the necessary load upon the truck, and the whole weight is 27.1 tons, which is the necessary weight of an engine to draw 200 tons over 60 feet grades, at 20 miles per hour.

Or, generally,

Let W	=	Weight of engine, tender, and train, in tons,
Let V	=	Speed in miles per hour,
Let a b	=	Fraction expressing the grade,
Let c	=	Resistance, in pounds per ton due to the sharpest curve, which, assume as 5 lbs., as we have no reliable data,

and we have, as the weight of the engine,

weight of engine exclusive of weight on truck.

If we assume the adhesion as one fourth of the weight on the drivers, and load 150 tons, speed twenty miles per hour, and grade forty feet per mile, the above formula becomes,

nine tons nearly.

To which add five tons, and we have as the whole weight, fourteen tons.