331. Mr. Clark deduces as general results, from a very extensive and

carefully conducted system of experiments, the following.

That the maximum useful admission is seventy-five per cent.

The minimum useful admission is ten per cent.

The greatest possible gain by working expansively is one hundred per

cent., which is effected by an admission of ten per cent.

The best admission for engines having ports 1/14 of the area of the

piston, and blast area from 1/13 to 1/16 of piston, at high speeds (from

thirty to sixty miles per hour) and with considerable loads, is from

sixty to sixty-six per cent. With a wider port and blast area, the best

admission is seventy-five per cent.

The resistance due to the back pressure of the blast, varies as the

speed squared, and inversely as the square of the area of blast orifice.

332. From the experiments made by Daniel Gooch, with the engine “Great

Britain,” the following results appear.

The loss of fuel at seventy-five per cent. admission, the blast orifice

being from ⅒ to 1/11 of piston at sixty miles per hour, is from ⅓ to ⅒;

at thirty or forty per cent. admission, the loss is from ⅛ to 1/50; and

at thirty miles per hour, (seventy-five per cent. admission,) from 1/11

to 1/40.

The resistance from steam compressed in the cylinder, increases with the

speed, and also with the degree of expansion; it varies from eight per

cent. in full gear, (seventy-five per cent.,) to twenty-eight per cent.

at an admission of forty per cent.

At the highest velocities, the whole resistance from back pressure is

nearly the same for all expansions; for compression increases as blast

pressure decreases.

The above deductions hold good for speeds under forty miles per hour,

with steam ports at least 1/14, and blast orifice from 1/12 to 1/15 of

the piston area.

OF BOILER PROPORTIONS.

333. The dimensions of American locomotives seem to depend more upon the

shop whence they come, than upon any special duty required of them. It

is not surprising that the utmost economy is seldom attained when a

railroad president orders a lot of locomotives, from the cheapest

builder, to suit his own ideas of an engine; or when engines are ordered

by a superintendent of machinery who does not know the difference

between a sixty foot grade and a level. It is the affair of the

company’s agent and not of the machinist to know just what a railroad

needs. It is a common, and most absurd practice, for a man who is

completely ignorant of machinery to order five or ten engines, without

the least regard to the character of the road or of the traffic.

334. The particular characteristics of each class of engines is entirely

a matter of figures. There is no reason why a general table should not

be formed embracing all divisions, orders, and classes of locomotives,

in which the requirements and general dimensions corresponding thereto

should be laid down for machine shop reference. Such a table would at

once establish a mutual understanding between railroad companies and

builders. Such a general classification is shown hereafter. The

dimensions of engines are not given, as it was thought best to let each

person fill it up according to his own ideas. By so doing some valuable

general proportions may be arrived at.

335. Thus far experience has been the only guide to proportion (in

America at least). Practice, in many things, is the only correct path to

the right results, but locomotives are too expensive for philosophical

apparatus; correct experiments upon imperfect machines will lead to the

means of avoiding errors. The following is the _modus operandi_ of D. K.

Clark in his “Railway Machinery.”

A number of engines of different proportions are chosen, and

observations made upon the amounts of fuel and water consumed upon the

work done, and under what conditions. These results are so tabulated as

to show the effect in difference of construction upon the performance of

the engine, whence the proportioning of parts becomes a simple

arithmetical operation. The reduction of experiments to tables, and the

deduction from tables of formulæ, is a simple operation compared with

the skill and care required in observing the operation of a machine,

subject to so many disturbances as a locomotive engine in rapid motion.

None have had a better opportunity of observing, have conducted

experiments with more care, or have obtained results which show fewer

discrepancies than the English engineers Clark and Gooch, and the French

and German observers Le Chatlier and Nollau.

336. Three essential parts of the locomotive are the _grate area_,

_heating surface_, and _cylinders_. No two writers upon this subject

arrive at the same dimensions to perform the same work. They not only

differ, but differ widely. They cannot all be right; all but one, or all

must be wrong. American builders have fixed the dimensions of their

engines by observing the performance of constructed machines, not by

rules deduced from any systematic experiments, but upon a system of

remedying visible errors. If a chimney diameter of ten inches is found

too small and twenty too large, fifteen has been assumed as about right.

337. As an example of the difference in the results obtained by

different authors, take the following:—

An engine to do the same work must have, according to

Zerah Norris.[7] D. K. D. K.

Colburn.[6] Clark.[8] Clark.[9]

18 × 22 18 × 22 18 × 22 18 × 22 Cylinders.

5 5 5 5 Wheels.

13.00 13.86 14.00 19.60 Grate area.

1114 812 1327 1327 Heating surface.

250 324 134 134 Area of chimney.

4 23 28 28 Area of blast.

59 73 —— —— Steam room.

100 73 —— —— Water room.

Footnote 6:

Colburn on the Locomotive Engine.

Footnote 7:

Norris’s Handbook for Locomotive Engineers and Machinists.

Footnote 8:

D. K. Clark’s Railway Machinery, calculated for coke.

Footnote 9:

D. K. Clark’s Railway Machinery, calculated for wood.

From these figures, the work done being the same, Mr. Clark gives forty

per cent, more grate area than either Colburn or Norris, an easier

blast, and greater heating surface. Norris makes the steam and water

room equal, while Colburn makes the latter almost double the former. It

is to be observed that Colburn gives only rules adopted by different

builders, not vouching for their correctness, while Norris lays down his

rules as fixed and right. The engines used by the English experimenters

in their observations, vary in dimension between the following wide

limits, whence the universal application of their results.

Grate area 9 to 24 square feet.

Fire surface 50 to 100 square feet.

Tube surface 400 to 1,000 square feet.

Whole surface 450 to 1,100 square feet.

Blast orifice 10 to 20 sq. inches, area.

Speed of engine 12 to 20 miles per hour.

338. The result of some sixty experiments upon forty-five different

engines (detailed in Clark’s Railway Machinery, page 156), gives the

following formula, expressing the relations which ought to exist between

grate area, heating surface, and consumption of water; that evaporation

may be carried on in the most economical manner.

_S_ = √(_ac_) × 21.2 = surface.

Where _S_ is the heating surface in square feet.

_a_ is the grate area in square feet.

_c_ is the hourly consumption of water in cubic feet.

From which we deduce the value of _a_ or _c_ thus,

_a_ = ((_S_/21.2)^2)/_c_ = grate area;

and _c_ = ((_S_/21.2)^2)/_a_ = hourly water consumption.

The maximum evaporation which should be carried on per square foot of

grate is found, by Mr. Clark, to be sixteen cubic feet per hour. Thus,

if we wish to evaporate 160 cubic feet of water per hour, we must have a

grate area of at least 160/16 or ten square feet.

339. The above formula for the grate area gives the dimension for a

coke-burning furnace. Locomotives burning wood or coal require a

modification of the above, as follows:—

To produce a given amount of heat, a certain amount of carbon must be

burnt. As wood contains much less carbon than coke, a correspondingly

larger bulk must be burnt, and a larger grate is necessary; not,

however, larger in proportion to the larger bulk of fuel, as we may have

a deeper wood than coke fire. The relative depth of fire being as the

stowage bulk, and the actual depth of a coke fire being 1.9 feet, that

of a wood fire will be 2.5 feet.

Now let _A_ be the number of lbs. of coke per foot of water evaporated.

_B_ the number of lbs. of coal per foot of water evaporated.

_C_ the number of lbs. of wood per foot of water evaporated.

Call _d_ the depth at which if is the most economical to burn coke; _d′_

the same depth for coal, and the depth for wood _d″_. Then will the area

of a coke grate be

_A_/_d_;

Of a coal grate

_B_/_d′_;

And of a wood grate

_C_/_d″_.

To be able to fix the proper grate area for any fuel, we must know its

evaporative power, and a depth of a layer in the furnace. Knowing the

absolute value for coke, it remains only to obtain the relative value

for any other. Thus far we have disregarded the difference in _time_ of

burning wood and coke. To produce a given amount of heat, we burn a

certain chemical value of fuel; a much larger bulk of wood than of coke

is needed. If we burn wood and coke _at the same depth_ and _in the same

time_, the grate areas would be proportional to the bulks of fuel to

produce the same heat; but, _first_, we burn fuel in a depth

proportioned to the economic stowage bulk, or as 2.5 to 1.9, which

decreases the wood area; and, _second_, a layer of coke 1.9 feet deep

burns in one hour, while a layer of wood 24 feet deep burns in fifteen

minutes; whence 60 m. divided by 15 m. = 4 layers of 2½ feet deep each,

or in all ten feet, which into the bulk (equal to a mass of coke 1 foot

square × 1.9 high) or 1 foot square by 14 high, gives 14 ÷ 10 = 1.4; or,

finally, the area of the wood grate should be 1.4 times that of a grate

to burn coke.

OF THE SIZE AND USE OF THE SMOKE BOX.

340. The smoke box is the general termination of the flues, and the

place where the vacuum is produced, which causes the draft. The size of

the boiler being the same, the vacuum varies directly as the blast

pressure. The power of the blast is of course affected by the capacity

of the smoke box. Mr. Clark fixes the capacity of the exhaust chamber at

three cubic feet per square foot of grate. The vacuum in the furnace

varies from one to two thirds of that in the smoke box. The less the

resistance to the hot gases experienced in the flues, the less may be

the vacuum. Upon the vacuum depends the amount of air drawn through the

grate; upon the bulk of air drawn through the grate depends the

combustion; upon the combustion the evaporation. Whence the evaporation

_cet. par._ depends the vacuum in the smoke box.

The velocity of any fluid depends upon the power applied to it, (being

as the square root,) the pressure applied to the gases in the furnace of

a locomotive is the vacuum in the smoke box; thus the combustion or rate

of evaporation is as the square root of this vacuum. To double the

evaporation it is necessary to quadruple the vacuum.

BLAST PIPE.

341. The blast pipe conducts the waste steam from the cylinder, which

drives the air from the chimney and produces the vacuum in the smoke

box; its form should permit the freest escape of the steam from the

cylinder. The blast pipe area should nowhere be smaller than the exit

port, except at the contraction at the top. “Too much care,” says Mr.

Clark, “cannot be taken to adjust the blast pipe concentrically with the

chimney; one half inch has been known to spoil the draft of a

locomotive.” “The area of orifice is the most critical and most

important item in the composition of the locomotive.”

For the form, dimensions, and influence of this important member, the

reader is referred to Clark’s Railway Machinery.

As the grate area increases, the blast may decrease. The greater the

flue area the easier may be the blast; decrease of smoke box capacity

and of chimney diameter, both allow a milder blast.

342. The following proportions are collected from the work of Mr. Clark.

The order in which the different parts of the engine stand in importance

with relation to the blast, is shown in column 1. The figures show the

ratios (the best) which may be had under the most favorable

circumstances.

Grate area 1

Ferrule area (area of section of tubes at back flue sheet) ⅕

Tube, sectional area ¼

Capacity of smoke box, cubic feet 3

Chimney, height four diameters, area of section 1/15

Blast orifice 1/75

The vacuum in the smoke box is somewhat regulated by a damper placed in

front of the ash pan, by a valve in the chimney, or by a Venetian blind

covering the front ends of the tubes.

TUBE SECTION AND LENGTH.

343. The section of the tubes (crosswise) is the space through which the

hot gases pass off. By increasing the length or decreasing the diameter,

we of course require a stronger blast.

That the steam may escape as soon as generated, there must be a certain

clearance between the tubes, which Mr. Clark fixes as follows:—

Divide the number of tubes by thirty and the result is the clearance in

eighths of an inch; or algebraically

_C_ = ((_N_/30))/8 = clearance in inches;

Or otherwise

_C_ = _N_/240 = clearance in inches.

PROPORTIONS OF CYLINDERS AND WHEELS.

344. The above proportions depend entirely upon the nature and amount of

work to be done, and upon the character of the road. Small wheels and

long stroke are to be applied to heavy trains and steep grades. Short

stroke and large wheels to fast trains and level roads.

There are some advantages in a long cylinder, even with a constant ratio

between the stroke and wheel diameter. The steam has more time to

expand; the action of the machinery is slower, and the erratic movements

of the engine caused by the movement of the reciprocating machinery are

lessened, at the same time the centre of gravity is raised and

oscillation increased.

OF THE CARRIAGE.

345. The arrangement of the wheels, axles, springs, and draw-link, and

the distribution of the weight of the engine upon its several bearings

so as to provide the necessary adhesion, and to run steadily upon the

rails, is a matter well worthy of more attention than is commonly given

to it.

The frame is the base of the engine, to which every thing should be

attached. The cylinders and the wheel both being attached to it, it of

course becomes the counterpart to the piston and connecting rod; the

former holding the cylinder and wheel together, while the latter pushes

them apart. The frame _should_ form a rigid connection between the

piston and the wheel; and its strength must be able to resist the whole

power of the engine, applied alternately as compression and as

extension.

The wheels of a locomotive answer three several purposes, and are

classed as follows:—

Leading wheels.

Driving wheels.

Trailing wheels.

The duty of the driving wheels is to transfer the power of the engine to

the rails, by which the motion is produced. That of the leading wheels,

to guide the engine; and that of the trailing wheels, to support the

after end of the engine.

The weight upon the driving wheels must be enough for sufficient

adhesion. That upon the leading wheels, sufficient to guide the engine

upon curves, (decreasing as their distance from the centre of gravity

becomes greater, and increasing with the speed.)

The centre of gravity of an engine is generally at a distance of from

one quarter to one sixth of the length of the barrel from the furnace

horizontally and forwards, and in the lower part of the barrel,

vertically.

The weight upon any one pair of wheels is as their distance from the

centre of gravity; by changing their position we change the applied

weight.

The flange base[10] must increase as the engine becomes heavier, when

applied to fast trains, as more leverage is necessary to keep it on the

rails. Heavy freight engines with four or five pairs of wheels, and no

truck, wear the rails and strain themselves very much. We should make

the wheels of such very small and near together, in order to contract

the flange base.

Footnote 10:

_Wheel base_,—Horizontal length between centres of extreme wheels.

_Flange base_,—Horizontal length between centres of extreme fixed

flanged wheels.

DISTRIBUTION OF WEIGHT.

346. Suppose the whole load upon the wheels is 60,000 lbs. If the centre

of gravity is half-way between the wheels (there being two pairs), each

will support 30,000 lbs. If the centre of gravity is twice as near to

one axle as to the other, the furthest one will support 20,000 lbs., and

the nearest one 60,000–20,000, or 40,000 lbs.

Suppose the engine has six points of support, or three points in the

side elevation, (the ordinary four driving wheels and a truck engine).

Let the centre of gravity be one foot behind the middle axle and the

distances between the wheel centres eight feet.

The weight upon the middle axle being _H_, that upon the hind axle is

_H_/7, because that axle is seven times more distant from the centre of

gravity than the middle one, and for the same reason the weight upon the

front axle is _H_/9.

Now _H_ + _H_/7 + _H_/9 = 60,000 lbs.

Whence _H_ = 47,976 lbs.

Also, _H_/7 = 6,853 lbs.

And _H_/9 = 5,331 lbs.

And the same laws (see article Lever, in any work on Mechanics) apply to

any arrangement of wheels and to any position of centre of gravity.

Springs are employed to absorb the shocks received by the wheels from

irregularities in the surface of the rails. They must be equally stiff

on both sides of the engine, or lateral rocking will be generated.

When, as is generally the case, the springs are connected by

compensating levers, their stiffness being as the load upon them, the

arms of the connecting lever must be inversely proportional to the

applied weights. The shock received by one wheel is by the lever

communicated to the whole four, (or even more when there are such). The

truck springs of some builders are also connected by an equalizing

lever.

According to Mr. Clark, not more than twelve tons should ever be placed

upon one axle; whence engines requiring a tractive power of twelve tons

and less may be of the form shown in fig. 151. Between twelve and

twenty-four tons, of the form fig. 152; and over the forms figs. 153,

154, and 155.

[Illustration: Fig. 151.]

The weight upon the leading wheels of fast passenger engines should be

as much as one fifth of the whole weight. Upon freight engines it need

not be more than one sixth.

[Illustration: Fig. 152.]

The line of traction of a locomotive ought to be as near as possible at

the same vertical height as the driving wheel centres. If much below

this the load will tend to lift the engine off from the leading wheels,

upon the drivers as a fulcrum, thus increasing the adhesion and

lessening the leading power.

[Illustration: Fig. 153.]

If the traction bar (draw link) is above the wheel centres, it will tend

to lift the rear of the engine from the rails.

[Illustration: Fig. 154.]

The general form of engines used in America are shown in figs. 151, 152,

153, 154, and 155.

[Illustration: Fig. 155.]

Fig. 151 is the express passenger locomotive.

Fig. 152 is the ordinary passenger, mail, and mixed engine.

Fig. 153 is the heavy freight engine.

We have, also, engines with three, four, and five pairs of small wheels

without a truck, for heavy grades and large amounts of work.

OF ERRATIC MOVEMENTS.

347. The erratic movements of a locomotive in motion are due to three

separate causes.

To the motion of the machinery.

To the arrangement of the frame and wheels.

To the state of the surface of the rails.

Those caused by the motion of the machinery are as follows:

_Longitudinal fore and aft movement_, generated by the reciprocations of

the piston rod, cross head, connecting rod, and crank; and depending in

amount upon the weights of the moving parts, steam pressure, and

velocity of motion. _Pitching_ of the engine, arising from the oblique

action of the cross heads upon the guides, which tends to lift the front

end of the engine from the rails; and depends in amount upon the ratio

between the stroke and length of connecting rod. _Rocking_ laterally,

arising from the difference of time of action of the cross heads; one

acting with its greatest vertical power, when the opposite one acts with

none. _Vibration in plan_ about the centre of gravity of engine,

produced by the pressure between the piston and crank pin, and by the

momentum of the reciprocating machinery. This last, combined with

lateral rocking, produces _sinuous_ or _spiral_ motion.

The amounts of these several irregularities depend considerably upon the

arrangement of carriage; that is, upon the position of wheels; being

less as the base included by the bearing points is greater.

The influence of the state of the rails is shown by the vertical and

lateral shocks arising from the rail joints and from bad adjustment,

both horizontally and vertically.

The amounts of these irregularities increase very rapidly with the

speed. Le Chatelier’s experiments make them increase nearly as the

square of the velocity.

Longitudinal fore and aft motion is nearly balanced by applying a

counterweight to the wheel, opposite the point to which the connecting

rod is attached. The remedy for pitching consists in placing the guide

bars under the heaviest part of the engine; by which, a great weight is

opposed to the vertical action of the cross heads. Crampton’s engine is

quite free from this disturbance, as the guide bars are almost directly

under the centre of gravity.

The only counteracting effort (remedy it is not) for sinuous motion yet

applied, is extension of wheel and flange base, thus giving the guiding

wheels more control over the mass of the engine.

The remedy, however, which applies at once to all of the erratic

movements, is reduction of speed, as when we divide the velocity by two

we decrease the disturbances nearly fourfold.

REVIEW OF THE FORMULÆ AND FORMATION OF THE TABLES.

No. 1.

348. Given the weight and velocity of a train, to find the necessary

traction on a level.

_Formula._

_W_ × _R_,

_W_ being the weight of the train in tons, and _R_ the resistance in

lbs. per ton; found by the formula

(_V^2_)/171 + 8 = _R_.

By this formula is formed table 1, giving the traction required to move

trains of from fifty to one thousand tons weight, at speeds from ten to

one hundred miles per hour.

No. 2.

349. To find the traction due to a grade.

_Formula._

_W_ × _R_/_L_,

where _W_ is the weight of the train in tons, _R_ the rise, and _L_ the

length of the incline. By this rule is formed table 2, giving the

necessary traction to overcome grades from ten to one hundred feet per

mile, with loads from one to one thousand tons.

To obtain the whole traction required, add the amounts taken from tables

1 and 2; thus the traction necessary to draw five hundred tons at twenty

miles per hour over fifty feet grades is,

By table 1, 5,170 lbs.

By table 2, 10,605 lbs.

——————

In all, 15,775 lbs.

or, algebraically,

(_W_ × _R_) + (_WR_/_L_) = _T_,

the letters standing for the same quantities as above.

No. 3.

350. To find the weight to place on the driving wheels.

_Formula._

6_T_,

where _T_ is the whole tractive power. (Table 3.)

Nos. 4 and 5.

The tractive power of an engine is expressed by

_T_ = ((2_A_)_P_ × 2_S_)/_C_,

Where _T_ is the tractive power.

_P_, steam pressure in lbs. per square inch.

_S_, stroke in inches.

_C_, circumference of wheel in inches.

_A_, area of one piston in inches.

From this formula we get the values of the several factors as follows:—

The steam pressure, or _P_ = (_TC_)/((2_A_)2_S_). (A.)

The stroke, or _S_ = (_CT_)/((2_A_)(2_P_)). (B.)

The piston area, or _A_ = (_TC_)/(4_SP_). (C.)

The wheel circumference, or _C_ = (2_A_ × _P_ × 2_S_)/_T_. (D.)

And from (C) we get the diameter of piston by the following:—

_d_ = √(area/.7854).

And in like manner from (D) the diameter of wheel by

_d_ = _c_/3.1416.

(See tables 4 and 5.)

No. 7.

351. To find the capacity of cylinders of any dimension.

_Formula._

(_D^2_ × .7854 × Stroke)/1728.

This gives the capacity in cubic feet. The dimensions above (see D and

S) being in inches. (Table 7.)

No. 6.

352. To find the hourly steam consumption in terms of the capacity of

one cylinder, (that is, the number of cylinderfuls per hour).

_Formula._

_N_(5280/_c_) × 4,

where _N_ is the number of miles per hour, _c_ the wheel circumference.

(Table 6.)

No. 8.

353. Knowing the hourly consumption of steam, to reduce it to water.

_Formula._

_B_/_N_,

_B_ being the bulk of steam in cubic feet, and _N_ the relative volume

of steam and water. (The values of _N_ are given in table 8.)

No. 9.

354. Knowing the hourly water consumption, to find the grate area and

heating surface.

First, (Cubic feet of water per hour)/16 = grate area in square ft.

Second, _S_ = √(_ac_) × 21.2 = heating surface,

where _a_ is the grate area, and _c_ the hourly consumption of water in

cubic feet.

From the same formula,

Grate area, or

_a_ = ((_S_/21.2)^2)/_c_

Also water consumption, or

_c_ = ((_S_/21.2)^2)/_a_

(See table 9.)

No. 10.

355. To find the necessary number of tubes to give any amount of heating

surface.

_Formula._

_N_ = _S_/(_Ld_π),

when _N_ is the number, _S_ the required surface, _L_ the length, _d_

the diameter, both in feet, and π = 3.1416. (See Table 10.)

No. 11.

356. To find the mean cylinder pressure for any percentage of admission.

_Formula._

13.5√(_a_) – 28,

where _a_ is the percentage of admission. (See Table 11.)

As to the internal arrangement of the barrel of the boiler, we must of

course have the length of tubes the same as that of the barrel, (that

is, in the general plan of boiler, some makers have moved the back flue

plate ahead). The length of tubes will of course be the same as the

distance between the tube sheets. The number is governed by their

diameter and by the proper clearance, which is found by the formula,

(_N_/|30|)/8 in eighths of inches, or _N_/240 inches.

The upper fifteen to eighteen inches of the barrel must be left for

steam room.

OF THE DIAMETER OF BARREL.

357. To find the diameter of a barrel to contain a given number of

tubes,

Represent the inside diameter of boiler by _D_,

Diameter of one tube _d_,

Clearance between tubes _c_,

Number of tubes _n_,

Sectional area of boiler, in inches _A_,

Water section, in inches _B_,

we shall have as the area of water room per tube,

(_d_ + _c_)^2,

and the whole area of water room,

(_d_ + _c_)^2 × _n_,

the whole section of the barrel,

_A_/_B_[(_d_ + _c_)^2_n_],

and the diameter of that area,

_D_ = √(([(_d_ + _c_)^2_n_]_A_/_B_)/.7854)

which is the boiler diameter in inches, to which add _D_/16 on each

side, or in all _D_/8 as the room to be left between the sides of the

boiler and first tube.

The _diameter_ finds its maximum limit in the gauge less the two half

breadths of tire, and two or three inches allowance for attachment to

the frame and other mechanical incidentals. The _length_ must be enough

to carry the leading wheels a sufficient distance from the centre of

gravity of the engine.

ADAPTATION OF THE LOCOMOTIVE ENGINE TO THE MOVEMENT OF RAILWAY TRAINS.

358. First, as regards the nature of the traffic.

There are certain necessary causes of a bad application of power upon

railroads; for example, when the trains are very much heavier in one

direction than in the other, as we are obliged to use the same engine

both ways, because when it arrives at one end of the road it must go

back to start again. Where the traffic requires to be worked chiefly up

hill, we use an engine much heavier to _ascend with the load_ than is

necessary to _descend without a load_. Different objects of transport

require different speeds. Perishable freight, such as ice, beef, pork,

cattle, &c., requires to be moved in much less time than grain, lumber,

flour, coal, and manufactured articles. As a general thing, the

difference between the characters of freight engines, as regards the

nature of the traffic, can be adapted only with a view to amount,

disregarding the nature.

With passenger traffic, however, there is a great variety of speeds made

use of, and consequently may be a greater difference in the proportions

of engines depending entirely upon the nature of the traffic.

ADAPTATION AS REGARDS THE PHYSICAL CHARACTER OF THE ROAD.

The best adaptation of locomotive power to any system of grades, would

be that which should render the mileage a minimum; and this will be

done, as nearly as possible, by applying engines, the strength of which

shall be proportional to the resistance to be overcome. The best mode of

comparing different adaptations of power is by reducing the grades to a

level; or by equating for grades by means of the capacity of motive

power.

This is done as follows:—

The length of an incline being _L_,

The resistance on a level being _R_,

The ratio of the resistance due to the grade to the resistance on

a level by _r_,

The equivalent horizontal length by _L′_,

and we shall have,

(_R_ + _r_)_L_ = _L′_.

_Example._—Let the length of a grade be seventy-five miles; the value of

_r_ = _R_/3;

and we have

(3/3_R_+_R_/3)_L_ = ((4_R_)/3)75 = 100 miles.

Let us now compare the mileage of some of the large roads of America, as

given by a good, and also by a bad adaptation of power.

The Massachusetts Western Railroad may be divided into the four sections

below (including the Boston and Worcester road).

Length miles. Maximum grade.

Boston to Worcester, 44 30

Worcester to Springfield, 54½ 50

Springfield to Pittsfield, 52 83

Pittsfield to Albany, 49½ 45

Assume the speed of freight trains as fifteen miles per hour, the

resistance on a level will be 9.3 lbs., or for simplicity call it ten

pounds per ton.

The resistance due to a 30 feet grade is 13 lbs. per ton.

The resistance due to a 50 feet grade is 21 lbs. per ton.

The resistance due to a 83 feet grade is 35 lbs. per ton.

The resistance due to a 45 feet grade is 19 lbs. per ton.

And the value of _r_ for a 30 feet grade is 13/10 lbs. per ton.

And the value of _r_ for a 50 feet grade is 21/10 lbs. per ton.

And the value of _r_ for a 83 feet grade is 35/10 lbs. per ton.

And the value of _r_ for a 45 feet grade is 19/10 lbs. per ton.

And the relative length of the several sections will be,

Boston to Worcester, 10/10 + 13/10 = 23/10 of 44 = 101

Worcester to Springfield, 31/10 of 54½ = 169

Springfield to Pittsfield, 45/10 of 52 = 234

Pittsfield to Albany, 29/10 of 49½ = 144

——— ———

And the sums, 200 648

the equated distance being 3¼ times the actual length. This length

assumes the resistance of the several sections to be for their whole

length that given by their maximum grade. This might seem erroneous; but

its correctness will be seen when it is remembered that the greatest

load that can be taken over any section is limited by its maximum grade.

Now suppose that the engine employed is of the following dimensions (as

it is very nearly).

Cylinders 16 × 20 inches,

Wheels 54 inches.

Assume the cylinder pressure 110 lbs., and the tractive power of the

engine is 5,287 lbs.

A load of 500 tons, upon a 30 feet grade, requires a 11,500 lbs.

traction of

Upon a 50 feet grade, 15,500 lbs.

Upon an 83 feet grade, 22,500 lbs.

Upon a 45 feet grade, 14,500 lbs.

To move the above load from Boston to Worcester we should 2 engines,

require

From Worcester to Springfield, 3 engines,

From Springfield to Pittsfield, 5 engines,

From Pittsfield to Albany, 3 engines,

And the products of the number of engines by the lengths of the

corresponding divisions, are

Boston to Worcester, 44 × 2 = 88

Worcester to Springfield, 54½ × 3 = 163½

Springfield to Pittsfield, 52 × 5 = 260

Pittsfield to Albany, 49½ × 3 = 148½

————

660

Suppose that by making the engines on the several sections strong in

proportion to the resistance of those sections, one engine is capable of

taking the whole load over all of the grades. The mileage becomes as

follows:—

Boston to Worcester, 44 × 1 = 44

Worcester to Springfield, 54½ × 1 = 54½

Springfield to Pittsfield, 52 × 1 = 52

Pittsfield to Albany, 49½ × 1 = 49½

———

200 miles.

The mileage before was 660 miles,

And the saving therefore 400 miles.

or about 70 per cent. of the first mileage.

359. From a recent report of the New York and Erie Railroad it appears

that the same power will draw

28 tons on the Western division,

80 tons on the Susquehanna division,

85 tons on the Delaware division,

and 20 tons on the Eastern division,

neglecting the assistance required from Susquehanna to Deposite. In the

following table are given the actual lengths of the several divisions,

and the sum of the products of three lengths both by the relative and a

uniform resistance on each.

Miles run Miles run by

Division. Length. by an an engine Difference.

engine not adapted.

adapted.

Western, 128 128 × 3.04 128 × 1.0 261.12

Susquehanna, 139 139 × 1.06 139 × 1.0 8.35

Delaware, 104 104 × 1.00 104 × 1.0 0.00

Eastern, 88 88 × 4.25 88 × 1.0 286.00

——————

Sum of differences, 555.47 miles,

that is, the miles run by engines adapted to the work on the several

divisions will be 555.47 less than the miles run by engines not adapted.

(See Appendix F.)

PENNSYLVANIA CENTRAL RAILROAD.

360. The physical character of this road is as follows:—

Length. Max. grades.

Philadelphia to Harrisburg, 106 45

Harrisburg to Altoona, 131 21

Altoona to Johnstown, 48½ 92

Johnstown to Pittsburgh, 78½ 53

The value of _r_ will be here

45 feet grades, 19/10

21 feet grades, 9/10

92 feet grades, 39/10

53 feet grades, 25/10

Whence the equation,

106 × (10/10 + 19/10) = 307

131 × (10/10 + 9/10) = 249

42½ × (10/10 + 39/10) = 208

78½ × (10/10 + 25/10) = 275

——— ———

Sum, 358 Sum, 1039

and 1039 – 358 = 681.

361. On the Baltimore and Ohio Railroad we have,

Miles. Max. grade.

Baltimore to Harper’s Ferry, 80 82

Harper’s Ferry to Cumberland, 98 40

Cumberland to Raccoon, 88.2 116

Raccoon to 148⅔ miles, 60.5 40

148⅔ miles to Wheeling, 51.3 80

And as before,

80 × (10/10 + 35/10) = 360

98 × (10/10 + 17/10) = 265

88.2 × (10/10 + 49/10) = 520

60.5 × (10/10 + 17/10) = 163

51.3 × (10/10 + 35/10) = 231

Sum of Col. 1 = 378, Sum of Col. 3 = 1539; difference 1161.

Thus by the most correct adaptation of power, upon the above-named

railroads, the following percentages of mileage may be saved.

Massachusetts Western, 70

New York and Erie, 55½

Pennsylvania Central, 68

Baltimore and Ohio, 75

Of these roads the Baltimore and Ohio is that which has actually the

best adaptation; and the Western road of Massachusetts that which has

the worst.

362. To determine the actual dimensions of the engines which should be

used upon any road, from the tables, proceed as follows:—Let the load be

one hundred tons, the maximum grade thirty feet per mile, and speed

twenty-five miles per hour.

Referring to the tables in succession we have,

By table 1, Traction for 100 tons, on a level, at 25 miles 1,550 lbs.

per hour,

By table 2, Traction for 100 tons, on a 30 feet grade, 1,273 lbs.

—————

Whole traction required, 2,823 lbs.

By the formula, table 3, the weight upon the drivers must be

2823 × 6 = 16938 lbs., or 8 tons.

By table 4, with a wheel five feet in diameter, and a stroke of twenty

inches, we have the decimal .2122.

By table 5, the mean cylinder pressure being sixty pounds per inch, and

piston twelve inches in diameter, we have as the total pressure

On both pistons, 13,572 lbs.

And finally, 13572 × .2122 = 2,880 lbs.

The requirement being 2,823 lbs.

By table 6, we see that five feet wheels at twenty-five miles per hour,

use 33,600 cylinders of steam per hour.

By table 7, the capacity of a cylinder 12 × 20 is 1.31 cubic feet; also

33600 × 1.31 = 44016 cubic feet of steam per hour.

Assuming the mean cylinder pressure at sixty pounds, and the entering

pressure at eighty pounds, also the loss in passing from the boiler at

twenty pounds, we must generate the steam at one hundred pounds per

square inch.

By table 8, we see that when steam is produced under one hundred pounds

pressure per inch, each cubic foot of water makes 293 cubic feet of

steam; whence

44016/293 = 150,

is the number of cubic feet of water to be evaporated per hour. At

sixteen cubic feet of water per hour per square foot of grate, we thus

require

15.0/16 or 9.4 feet, nearly;

and by table 9, we find the heating surface necessary to evaporate 150

cubic feet of water per hour, with nine square feet of grate surface, to

be 779 square feet; and by the formula, with 9.4 square feet, we have,

_S_ = √(9.4 × 150) × 21.2 = 797 square feet,

the fuel being coke; for wood, multiply the grate area (as mentioned

before) by 1.4 and the grate area will be 1.4 × 9.4 = 13.16. The tube

surface of course remains the same, as, when the necessary amount of

heat is developed, the same surface only is enough to apply it to the

water.

To obtain 779 square feet of heating surface, we see, by table 10, that

it is given by

100 tubes 17 feet long and 1¾ inch diameter,

or 100 tubes 16 feet long and 1⅞ inch diameter,

or 100 tubes 15 feet long and 2 inch diameter,

or 100 tubes 14 feet long and 2⅛ inch diameter,

or 100 tubes 12½ feet long and 2⅜ inch diameter,

or 100 tubes 12 feet long and 2½ inch diameter,

or by consulting the table, and having given the number and length, the

number and diameter, or the length and diameter, we may easily find the

third factor of the surface. Thus the length being eleven feet, and

diameter two inches, 779 feet is obtained by

779/(11 × 3.1416 × 167) = 135 tubes.

To obtain the diameter of barrel to contain 135 two inch tubes, we use

the formula

D = √((_A_/_B_[_n_(_d_+_c_)^2])/(.7854)).

We have already found _d_ = 2 inches, _n_ = 135, whence _c_ will be by

formula,

_c_ = _N_/240 = 0.54,

and

_d_ + _c_ = 2.54,

also,

(_d_ + _c_)^2 = 6.45,

and

135 × 6.45 = 871+;

and allowing three fourths of the boiler cross section to be filled with

tubes, we have,

4/3 of 871 = 1161;

also,

1161/.7854 = 1478,

the square root of which is 38.5 nearly, to which add 38.5/8 or 4.8

inches, (see page 359), and we have

38.5 + 4.8 = 43.3 inches,

as the inside diameter of boiler, whence the following locomotive to

meet the requirement as stated.

Weight upon driving wheels, 16,938 lbs.,

Cylinders, 12 × 12 inches,

Wheels, 5 feet,

Tubes, 135—11 feet × 2 inches,

Grate, 13.16 square feet,

Barrel, (inside diameter,) 43.3 inches,

and under the most favorable circumstances, the chimney may be 40 inches

high, 12.7 inches in diameter; the blast orifice 5.8 inches in diameter;

and the capacity of smoke box 39½ cubic feet.

363. We may vary the tractive power of an engine by using the steam at a

greater or less degree of expansion, but the adhesion remains the same.

If an engine was built able to work a road partly level, and partly on

steep grades, varying the power simply by varying the expansion, it

would be unnecessarily heavy for the easy parts of the road. The

expansive principle may be advantageously employed in adjusting the

power to the difference of resistance on any one division of a road, and

also to the varying load which each day’s traffic will present.

Suppose we would move a load of two hundred tons over the road below;

and suppose, also, that we require the cylinder pressures set opposite

the several divisions.

10 miles, level, 60 lbs.,

10 miles, 10 feet per mile, 80 lbs.,

10 miles, 20 feet per mile, 100 lbs.,

10 miles, 30 feet per mile, 120 lbs.

The boiler pressure being 150 lbs., and the pressure at entering the

cylinder 145 lbs.,

An admission of 71 per cent. gives a mean pressure of 120 lbs.,

An admission of 55 per cent. gives a mean pressure of 100 lbs.,

An admission of 40 per cent. gives a mean pressure of 80 lbs.,

An admission of 28 per cent. gives a mean pressure of 60 lbs.,

And if the 1st notch of the sector admits, 75 per cent,

And if the 2d notch of the sector admits, 70 per cent,

And if the 3d notch of the sector admits, 65 per cent,

And if the 4th notch of the sector admits, 60 per cent,

And if the 5th notch of the sector admits, 55 per cent,

And if the 6th notch of the sector admits, 50 per cent,

And if the 7th notch of the sector admits, 45 per cent,

And if the 8th notch of the sector admits, 40 per cent,

And if the 9th notch of the sector admits, 35 per cent,

And if the 10th notch of the sector admits, 30 per cent.

We should work the engine as follows:—

From 0 to 10 miles, use the 10th notch,

From 10 to 20 miles, use the 8th notch,

From 20 to 30 miles, use the 5th notch,

From 30 to 40 miles, use the 2d notch,

APPLICATION OF LOCOMOTIVE ENGINES TO RAILROADS.

364. _Department 1. Freight._

GENERAL CLASSIFICATION.

┌─────────┬─────────┬───────────┬─────┬─────┬─────┬─────┬─────┬─────┐

│ │ │ │Order│Order│Order│Order│Order│Order│

│Number of│ Maximum │Designation│ 1 │ 2 │ 3 │ 4 │ 5 │ 6 │

│division.│ grades. │ of parts. │ 50 │ 100 │ 250 │ 500 │ 750 │1,000│

│ │ │ │tons.│tons.│tons.│tons.│tons.│tons.│

├─────────┼─────────┼───────────┼─────┼─────┼─────┼─────┼─────┼─────┤

│ │ │Grate area.│ │ │ │ │ │ │

│ │ │ Tube │ │ │ │ │ │ │

│ 1 │ Level. │ surface. │ │ │ │ │ │ │

│ │ │Cylinders. │ │ │ │ │ │ │

│ │ │ Wheels. │ │ │ │ │ │ │

│ │ │ Weight. │ │ │ │ │ │ │

├─────────┼─────────┼───────────┼─────┼─────┼─────┼─────┼─────┼─────┤

│ 2 │ 10 feet │ │ │ │ │ │ │ │

│ │per mile.│ │ │ │ │ │ │ │

├─────────┼─────────┼───────────┼─────┼─────┼─────┼─────┼─────┼─────┤

│ 3 │ 20 feet │ │ │ │ │ │ │ │

│ │per mile.│ │ │ │ │ │ │ │

├─────────┼─────────┼───────────┼─────┼─────┼─────┼─────┼─────┼─────┤

│ 4 │ 40 feet │ │ │ │ │ │ │ │

│ │per mile.│ │ │ │ │ │ │ │

├─────────┼─────────┼───────────┼─────┼─────┼─────┼─────┼─────┼─────┤

│ 5 │ 60 feet │ │ │ │ │ │ │ │

│ │per mile.│ │ │ │ │ │ │ │

├─────────┼─────────┼───────────┼─────┼─────┼─────┼─────┼─────┼─────┤

│ 6 │ 80 feet │ │ │ │ │ │ │ │

│ │per mile.│ │ │ │ │ │ │ │

├─────────┼─────────┼───────────┼─────┼─────┼─────┼─────┼─────┼─────┤

│ 7 │100 feet │ │ │ │ │ │ │ │

│ │per mile.│ │ │ │ │ │ │ │

└─────────┴─────────┴───────────┴─────┴─────┴─────┴─────┴─────┴─────┘

The speed is assumed from twelve to fifteen miles per hour. The mean

cylinder pressure is assumed at sixty lbs. per square inch; the initial

pressure at ninety pounds, and the boiler pressure at 120 lbs. per

square inch. The grate areas are designed for coke; for wood multiply

the same by 1.4.

365. _Department 2. Passenger._

┌───────────────────────┬───────┬───────┬───────┬───────┬─────────────┐

│ │Order 1│Order 2│Order 3│Order 4│ Designation │

│ Classification. │ 50 │ 100 │ 150 │ 200 │ of parts. │

│ │ tons. │ tons. │ tons. │ tons. │ │

├────────────┬──────────┼───────┼───────┼───────┼───────┼─────────────┤

│ │ │ │ │ │ │ Grate area. │

│ Division 1 │ 25 miles │ │ │ │ │Tube surface.│

│ Level. │per hour. │ │ │ │ │ Cylinders. │

│ │ │ │ │ │ │ Wheels. │

│ │ │ │ │ │ │ Weight. │

├────────────┼──────────┼───────┼───────┼───────┼───────┼─────────────┤

│ Division 2 │ 25 miles │ │ │ │ │ │

│20′ grades. │per hour. │ │ │ │ │ │

├────────────┼──────────┼───────┼───────┼───────┼───────┼─────────────┤

│ Division 3 │ 25 miles │ │ │ │ │ │

│40′ grades. │per hour. │ │ │ │ │ │

├────────────┼──────────┼───────┼───────┼───────┼───────┼─────────────┤

│ Division 4 │ 25 miles │ │ │ │ │ │

│60′ grades. │per hour. │ │ │ │ │ │

├────────────┼──────────┼───────┼───────┼───────┼───────┼─────────────┤

│ Division 5 │ 25 miles │ │ │ │ │ │

│80′ grades. │per hour. │ │ │ │ │ │

├────────────┼──────────┼───────┼───────┼───────┼───────┼─────────────┤

│ Division 6 │ 25 miles │ │ │ │ │ │

│100′ grades.│per hour. │ │ │ │ │ │

└────────────┴──────────┴───────┴───────┴───────┴───────┴─────────────┘

The engines in the Northern States require more power in winter than in

summer.

To the above classification might be added, an engine for “making up

trains,” and similar station work; such an engine should be able to

start easily the extreme weights of trains, from fifty to one thousand

tons, and should be fitted with a power of varying its adhesion.

FORMULA.

_W_ × [(_V^2_)/171 + 8] = _R_.

_Example._

The speed being thirty miles per hour, and load 250 tons.

_R_ will be [((30 × 30))/171 + 8] × 250 = 3315 lbs.

366. Table 1. Showing the required traction on a level for loads from

fifty to one thousand tons, and for velocities from ten to one hundred

miles per hour.

┌─────────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┐

│Velocity.│ 50 │ 75 │ 100 │ 250 │ 500 │ 750 │ 1000 │

│ │ Tons. │ Tons. │ Tons. │ Tons. │ Tons. │ Tons. │ Tons. │

├─────────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┤

│ 10│ 429│ 643│ 858│ 2146│ 4292│ 6435│ 8585│

│ 12│ 442│ 663│ 884│ 2210│ 4421│ 6630│ 8842│

│ 15│ 465│ 698│ 931│ 2328│ 4657│ 6982│ 9315│

│ 20│ 517│ 773│ 1034│ 2585│ 5170│ 7735│ │

│ 25│ 582│ 874│ 1165│ 2912│ 5825│ │ │

│ 30│ 663│ 994│ 1326│ 3315│ 6630│ │ │

│ 40│ 868│ 1302│ 1736│ 4340│ │ │ │

│ 50│ 1131│ 1696│ 2262│ 5655│ │ │ │

│ 60│ 1452│ 2180│ 2905│ │ │ │ │

│ 100│ 3324│ 4986│ 6648│ │ │ │ │

└─────────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┘

FORMULA.

_WR_/_L_.

_Example._

The tractive power to overcome the resistance of 750 tons upon a sixty

feet grade is

750 × 60/5280 = 19050.

367. Table 2. Showing the tractive power necessary to overcome grades

from ten to one hundred feet per mile with loads from one to one

thousand tons.

┌──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┐

│Grade.│1 Ton.│ 50 │ 75 │ 100 │ 250 │ 500 │ 750 │ 1000 │Grade.│

│ │ │Tons. │Tons. │Tons. │Tons. │Tons. │Tons. │Tons. │ │

├──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤

│ 10│ 4│ 212│ 318│ 424│ 1061│ 2121│ 3181│ 4240│ 10│

│ 20│ 8│ 424│ 636│ 848│ 2122│ 4242│ 6362│ 8480│ 20│

│ 30│ 13│ 636│ 955│ 1273│ 3170│ 6363│ 9545│ 12730│ 30│

│ 40│ 16│ 848│ 1272│ 1696│ 4244│ 8484│ 12724│ 16960│ 40│

│ 50│ 20│ 1060│ 1590│ 2120│ 5305│ 10605│ 15905│ 21200│ 50│

│ 60│ 26│ 1272│ 1910│ 2546│ 6340│ 12726│ 19050│ 25460│ 60│

│ 70│ 30│ 1500│ 2240│ 3000│ 7500│ 15000│ 22400│ 30000│ 70│

│ 80│ 33│ 1697│ 2545│ 3393│ 8489│ 16969│ 25459│ 33950│ 80│

│ 100│ 40│ 2120│ 3180│ 4240│ 10610│ 21210│ 31810│ 42400│ 100│

├──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤

│Grade.│1 Ton.│ 50 │ 75 │ 100 │ 250 │ 500 │ 750 │ 1000 │Grade.│

│ │ │Tons. │Tons. │Tons. │Tons. │Tons. │Tons. │Tons. │ │

└──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┘

FORMULA.

6_T_.

_Example._

Required traction 5,000 lbs.; upon driving axles the weight is 5000 × 6

= 30,000 lbs.

368. Table 3. Giving the weight which should be placed upon the driving

axles to secure any amount of adhesion; the latter being one sixth of

the weight.

┌─────────┬─────────┬─────────┐

│Required │Weight in│Weight in│

│traction.│ pounds. │ tons. │

├─────────┼─────────┼─────────┤

│ 500│ 3000│ 1.34│

│ 1000│ 6000│ 2.69│

│ 2000│ 12000│ 5.36│

│ 3000│ 18000│ 8.04│

│ 4000│ 24000│ 10.80│

│ 5000│ 30000│ 13.40│

│ 6000│ 36000│ 16.07│

│ 7000│ 42000│ 18.75│

│ 8000│ 48000│ 21.43│

│ 9000│ 54000│ 24.11│

│ 10000│ 60000│ 26.80│

│ 12000│ 72000│ 32.14│

│ 14000│ 84000│ 37.50│

│ 16000│ 96000│ 42.86│

│ 18000│ 108000│ 48.22│

│ 20000│ 120000│ 53.60│

└─────────┴─────────┴─────────┘

FORMULA.

(2_S_)/_c_.

Where _S_ = stroke.

_c_ = circumference of wheel, (both in inches.)

_Example._

Let stroke be twenty inches, and diameter of wheel five feet, the ratio

will be

40/188.4 = 0.2122.

369. Table of decimals, which, multiplied by the total piston pressures

(table 5) will give the traction in pounds, or ratio between double

stroke and wheel circumference. Table 4.

┌──────┬─────────────────────────────────────────────────┬──────┐

│Wheel.│ STROKE IN INCHES. │Wheel.│

├──────┼────┬────┬────┬────┬────┬────┬────┬────┬────┬────┼──────┤

│ │ 18 │ 20 │ 22 │ 24 │ 26 │ 28 │ 30 │ 32 │ 34 │ 36 │ │

├──────┼────┼────┼────┼────┼────┼────┼────┼────┼────┼────┼──────┤

│3½ │2728│3031│3334│3638│ │ │ │ │ │ │3½ │

│3¾ │2553│2837│3120│3404│3688│ │ │ │ │ │3¾ │

│4 │2386│2652│2918│3182│3444│3708│ │ │ │ │4 │

│4¼ │2250│2500│2750│3000│3250│3500│3750│ │ │ │4¼ │

│4½ │2151│2390│2593│2830│3071│3294│3529│3764│ │ │4½ │

│4¾ │2012│2235│2459│2682│2905│3129│3352│3575│3800│ │4¾ │

│5 │1910│2122│2334│2546│2766│2979│3192│3405│3617│3830│5 │

│5½ │1736│1929│2122│2315│2500│2692│2885│3077│3273│3473│5½ │

│6 │1591│1768│1945│2122│2321│2500│2678│2857│3036│3215│6 │

│6½ │1468│1632│1796│1958│2131│2295│2459│2623│2790│2951│6½ │

│7 │1364│1516│1667│1819│1970│2121│2273│2424│2576│2727│7 │

│7½ │1272│1414│1556│1691│1831│1972│2114│2254│2394│2535│7½ │

│8 │1194│1326│1417│1592│1688│1818│1948│2078│2208│2337│8 │

├──────┼────┼────┼────┼────┼────┼────┼────┼────┼────┼────┼──────┤

│Wheel.│ 18 │ 20 │ 22 │ 24 │ 26 │ 28 │ 30 │ 32 │ 34 │ 36 │Wheel.│

├──────┼────┴────┴────┴────┴────┴────┴────┴────┴────┴────┼──────┤

│ │ STROKE IN INCHES. │ │

└──────┴─────────────────────────────────────────────────┴──────┘

FORMULA.

2(_d^2_ .7854 × _p_) = _P_.

Where _d_ = diameter.

_p_ = pressure per inch.

_Example._

The whole pressure at one hundred pounds per inch on two sixteen inch

pistons will be

2[16 × 16 × 0.7854 × 100] = 40212.

370. Table 5. Total pressures upon pistons from ten to twenty-four

inches in diameter, and for steam pressures from fifty to one hundred

and fifty pounds per square inch.

┌──────┬───────┬──────────────────────────────────┬──────┐

│Diam. │Area of│ WHOLE PISTON PRESSURE ON BOTH │Diam. │

│ of │ one │PISTONS, AT A PER INCH PRESSURE OF│ of │

│cyl’r.│Piston.│ │cyl’r.│

├──────┼───────┼──────┬──────┬──────┬──────┬──────┼──────┤

│ │ │ 50 │ 60 │ 70 │ 80 │ 90 │ │

├──────┼───────┼──────┼──────┼──────┼──────┼──────┼──────┤

│ 10│ 78.5│ 7950│ 9420│ 10990│ 12560│ 14130│ 10│

│ 11│ 95.0│ 9500│ 11400│ 13300│ 15200│ 17100│ 11│

│ 12│ 113.1│ 11310│ 13572│ 15834│ 18096│ 20358│ 12│

│ 13│ 132.7│ 13270│ 15924│ 18564│ 21232│ 23906│ 13│

│ 14│ 153.9│ 15390│ 18468│ 21546│ 24624│ 27702│ 14│

│ 15│ 176.7│ 17670│ 21204│ 24738│ 28272│ 31806│ 15│

│ 16│ 201.1│ 20110│ 24132│ 28154│ 32176│ 36198│ 16│

│ 17│ 227.0│ 22700│ 27240│ 31780│ 36320│ 40860│ 17│

│ 18│ 254.5│ 25450│ 30540│ 35630│ 40720│ 45810│ 18│

│ 19│ 283.5│ 28350│ 34020│ 39690│ 45360│ 51030│ 19│

│ 20│ 314.2│ 31420│ 37704│ 43988│ 50272│ 56556│ 20│

│ 21│ 346.4│ 34640│ 41568│ 48496│ 55424│ 62352│ 21│

│ 22│ 380.1│ 38010│ 45612│ 53214│ 60816│ 68418│ 22│

│ 23│ 415.5│ 41550│ 49860│ 58170│ 66480│ 74790│ 23│

│ 24│ 452.4│ 45240│ 54288│ 63336│ 72384│ 81432│ 24│

└──────┴───────┴──────┴──────┴──────┴──────┴──────┴──────┘

┌──────┬─────────────────────────────────────────┬──────┐

│Diam. │ PISTONS, AT A PER INCH PRESSURE OF │Diam. │

│ of │ │ of │

│cyl’r.│ │cyl’r.│

├──────┼──────┬──────┬──────┬──────┬──────┬──────┼──────┤

│ │ 100 │ 110 │ 120 │ 130 │ 140 │ 150 │ │

├──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤

│ 10│ 15700│ 17270│ 18840│ 20410│ 21980│ 23550│ 10│

│ 11│ 19000│ 20900│ 22800│ 24700│ 26600│ 28500│ 11│

│ 12│ 22620│ 24882│ 27144│ 29406│ 31768│ 33930│ 12│

│ 13│ 26540│ 29194│ 31848│ 34502│ 37156│ 39810│ 13│

│ 14│ 30780│ 33858│ 36756│ 40014│ 43092│ 46170│ 14│

│ 15│ 35340│ 38874│ 42408│ 55942│ 49476│ 53010│ 15│

│ 16│ 40220│ 44242│ 48264│ 52062│ 56308│ 60330│ 16│

│ 17│ 45400│ 49940│ 54480│ 59020│ 63560│ 68100│ 17│

│ 18│ 50900│ 55990│ 61080│ 66170│ 71260│ 76350│ 18│

│ 19│ 56700│ 62370│ 68040│ 73710│ 79380│ 85050│ 19│

│ 20│ 62840│ 69124│ 75408│ 81692│ 87976│ 95260│ 20│

│ 21│ 69380│ 76208│ 83136│ 90064│ 96992│103920│ 21│

│ 22│ 77020│ 83622│ 91224│ 98826│106428│114030│ 22│

│ 23│ 83100│ 91410│ 99720│108030│116340│124650│ 23│

│ 24│ 90480│ 99528│108576│117626│126672│135720│ 24│

└──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┘

FORMULA.

_N_ = 5280/_c_ × 4.

Where _N_ = the number.

_c_ = wheel circumference.

_Example._

Speed twenty-five miles per hour, wheels four and a half feet, the

number of cylinders per hour is

25 × 5280/(4 × 3.1416) × 4 = 37348

371. Table 6. Showing the hourly consumption of steam in terms of the

capacity of one cylinder, with wheels from three and a half to eight

feet, and speeds from ten to sixty miles per hour.

┌──────┬───────┬───────────┐

│Wheel.│ Wheel │Revolutions│

│ │ in │ per mile. │

│ │inches.│ │

├──────┼───────┼───────────┤

│ │ │ │

├──────┼───────┼───────────┤

│3½ │ 42 │ 480 │

│3¾ │ 45 │ 449 │

│4 │ 48 │ 421 │

│4¼ │ 51 │ 397 │

│4½ │ 54 │ 373 │

│4¾ │ 57 │ 361 │

│5 │ 60 │ 336 │

│5½ │ 66 │ 306 │

│6 │ 72 │ 281 │

│6½ │ 78 │ 259 │

│7 │ 84 │ 240 │

│7⅛ │ 90 │ 224 │

│8 │ 96 │ 211 │

└──────┴───────┴───────────┘

┌──────┬─────────────────────────────────────────────────────┐

│Wheel.│ NUMBER OF CYLINDERS PER HOUR AT A VELOCITY OF │

│ │ │

│ │ │

├──────┼─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┤

│ │ 10 │ 12 │ 15 │ 20 │ 25 │ 30 │ 40 │ 50 │ 60 │

├──────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┤

│3½ │19200│23040│ │ │ │ │ │ │ │

│3¾ │17960│21552│26940│ │ │ │ │ │ │

│4 │16840│20208│25260│33681│ │ │ │ │ │

│4¼ │15880│19056│23820│31760│39700│ │ │ │ │

│4½ │14920│17904│22380│29840│37300│ │ │ │ │

│4¾ │14440│17328│21660│28880│36100│ │ │ │ │

│5 │ │ │20160│26880│33600│ │ │ │ │

│5½ │ │ │18360│24480│30600│36720│ │ │ │

│6 │ │ │ │22480│28100│33720│44960│ │ │

│6½ │ │ │ │20720│25900│31080│41440│51800│62160│

│7 │ │ │ │19200│24000│28800│38400│48000│57600│

│7⅛ │ │ │ │ │22400│26880│35840│44800│53760│

│8 │ │ │ │ │21109│25320│33760│42200│50640│

└──────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┘

FORMULA.

(_D^2_ × .7854 × Stroke)/1728 = _C_.

_Example._

Cubic content of a cylinder 15 × 24 is

(15 × 15 × 0.7854 × 24)/1728 = 2.44 cubic feet.

372. Table 7. Capacity of cylinders in cubic feet of from ten to

twenty-four inches in diameter, and from eighteen to thirty-six inches

stroke.

┌──────┬───────────────────────────────────────┬──────┐

│Diam. │ CAPACITY OF CYLINDERS IN CUBIC FEET, │Diam. │

│ of │ STROKE BEING │ of │

│cyl’r.│ │cyl’r.│

├──────┼───┬───┬───┬───┬───┬───┬───┬───┬───┬───┼──────┤

│ │18 │20 │22 │24 │26 │28 │30 │32 │34 │36 │ │

├──────┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼──────┤

│ 10 │082│091│100│109│118│127│136│145│ │ │ 10 │

│ 11 │093│104│115│126│137│148│159│170│181│ │ 11 │

│ 12 │118│131│144│157│170│183│196│209│222│235│ 12 │

│ 13 │133│149│165│181│197│213│229│245│261│277│ 13 │

│ 14 │160│178│196│214│232│250│268│286│304│322│ 14 │

│ 15 │184│204│224│244│264│284│304│324│344│364│ 15 │

│ 16 │208│232│255│278│301│324│347│370│393│416│ 16 │

│ 17 │235│263│289│315│341│367│393│419│445│471│ 17 │

│ 18 │263│294│323│352│381│410│439│468│497│526│ 18 │

│ 19 │ │ │361│394│427│460│493│526│559│592│ 19 │

│ 20 │ │ │400│437│474│511│548│585│622│659│ 20 │

│ 21 │ │ │ │481│521│561│601│641│681│721│ 21 │

│ 22 │ │ │ │528│572│616│660│704│748│792│ 22 │

│ 23 │ │ │ │ │625│674│723│772│821│876│ 23 │

│ 24 │ │ │ │ │681│733│785│837│889│941│ 24 │

└──────┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴──────┘

373. Table 8. Giving the volume, pressure, temperature, and density of

steam.

┌──────────┬──────────┬────────────┬──────────┬──────────┬──────────┐

│ │ Relative │ │ │ │ │

│ │volume or │ │ │Weight of │ │

│ Steam │cubic feet│Temperature.│ Total │ a cubic │ Steam │

│pressure. │of steam, │ │ heat. │ foot. │pressure. │

│ │ water │ │ │ │ │

│ │ being 1. │ │ │ │ │

├──────────┼──────────┼────────────┼──────────┼──────────┼──────────┤

│ 50 │ 552 │ 281 │ 1200 │ 1129 │ 50│

│ 60 │ 467 │ 293 │ 1203 │ 1335 │ 60│

│ 65 │ 434 │ 298 │ 1205 │ 1436 │ 65│

│ 70 │ 406 │ 303 │ 1206 │ 1535 │ 70│

│ 75 │ 381 │ 307 │ 1208 │ 1636 │ 75│

│ 80 │ 359 │ 312 │ 1209 │ 1736 │ 80│

│ 90 │ 323 │ 320 │ 1212 │ 1929 │ 90│

│ 100 │ 293 │ 328 │ 1214 │ 2127 │ 100│

│ 110 │ 269 │ 335 │ 1216 │ 2317 │ 110│

│ 120 │ 249 │ 341 │ 1218 │ 2505 │ 120│

│ 130 │ 231 │ 347 │ 1220 │ 2698 │ 130│

│ 140 │ 216 │ 353 │ 1221 │ 2885 │ 140│

│ 150 │ 203 │ 358 │ 1223 │ 3070 │ 150│

└──────────┴──────────┴────────────┴──────────┴──────────┴──────────┘

FORMULA.

_S_ =√(_ac_) × 21.2.

Where _S_ = surface.

_a_ = grate area.

_c_ = cubic feet of water per hour.

_Example._

Grate area sixteen square feet, cubic feet of water per hour two

hundred, surface is

√(16 × 200) × 21.2 = 1199.92.

374. Table 9. Showing the necessary amount of grate area and heating

surface for an hourly consumption of water.

┌──────┬─────────────────────────────────────────────────────────────┐

│Cubic │ │

│ft. of│ │

│water │ GRATE AREAS IN SQUARE FEET. │

│evap’d│ │

│ per │ │

│hour. │ │

├──────┼───┬───┬───┬────┬────┬────┬────┬────┬────┬────┬────┬────┬────┤

│ │ 7 │ 8 │ 9 │ 10 │ 11 │ 12 │ 13 │ 14 │ 15 │ 16 │ 17 │ 18 │ 19 │

├──────┼───┴───┴───┴────┴────┴────┴────┴────┴────┴────┴────┴────┴────┤

│ │ HEATING SURFACE CORRESPONDING TO ABOVE │

│ │ GRATE AREAS AND TO SIDE COLUMN. │

├──────┼───┬───┬───┬────┬────┬────┬────┬────┬────┬────┬────┬────┬────┤

│ 100│561│599│636│ 670│ 703│ 734│ 764│ 793│ 821│ 848│ 874│ 900│ 924│

│ 110│588│628│667│ 702│ 737│ 770│ 802│ 831│ 861│ 888│ 916│ 943│ 969│

│ 120│614│657│697│ 734│ 770│ 805│ 837│ 869│ 900│ 927│ 957│ 985│1013│

│ 130│639│683│725│ 764│ 801│ 837│ 871│ 904│ 936│ 965│ 996│1025│1053│

│ 140│663│709│752│ 793│ 831│ 869│ 904│ 938│ 972│1003│1034│1064│1093│

│ 150│686│734│779│ 821│ 860│ 900│ 935│ 971│1006│1038│1070│1101│1131│

│ 160│ │758│805│ 848│ 889│ 927│ 966│1004│1039│1073│1106│1138│1169│

│ 170│ │782│829│ 874│ 916│ 957│ 996│1034│1071│1106│1140│1173│1205│

│ 180│ │805│853│ 900│ 943│ 985│1025│1064│1102│1138│1173│1207│1240│

│ 190│ │ │877│ 924│ 969│1013│1053│1093│1132│1169│1205│1240│1274│

│ 200│ │ │900│ 948│ 995│1039│1081│1122│1161│1199│1236│1272│1307│

│ 210│ │ │928│ 974│1019│1064│1107│1149│1189│1229│1264│1298│1336│

│ 220│ │ │ │1000│1042│1089│1133│1176│1217│1258│1291│1324│1365│

│ 230│ │ │ │1019│1067│1114│1159│1203│1245│1286│1323│1359│1398│

│ 240│ │ │ │ │1091│1138│1184│1229│1272│1314│1354│1393│1431│

│ 250│ │ │ │ │1111│1162│1208│1254│1298│1341│1380│1422│1458│

│ 260│ │ │ │ │ │1184│1232│1278│1323│1367│1406│1450│1484│

│ 270│ │ │ │ │ │1207│1256│1303│1349│1401│1433│1478│1515│

│ 280│ │ │ │ │ │ │1279│1327│1374│1435│1460│1505│1546│

│ 290│ │ │ │ │ │ │1302│1351│1400│1452│1486│1532│1573│

│ 300│ │ │ │ │ │ │ │1374│1425│1469│1512│1558│1600│

│ 320│ │ │ │ │ │ │ │ │1469│1516│1564│1610│1654│

│ 340│ │ │ │ │ │ │ │ │ │1564│1612│1658│1704│

│ 360│ │ │ │ │ │ │ │ │ │ │1658│1706│1754│

│ 380│ │ │ │ │ │ │ │ │ │ │ │1753│1802│

│ 400│ │ │ │ │ │ │ │ │ │ │ │1800│1848│

│ 425│ │ │ │ │ │ │ │ │ │ │ │ │ │

│ 450│ │ │ │ │ │ │ │ │ │ │ │ │ │

│ 475│ │ │ │ │ │ │ │ │ │ │ │ │ │

│ 500│ │ │ │ │ │ │ │ │ │ │ │ │ │

└──────┴───┴───┴───┴────┴────┴────┴────┴────┴────┴────┴────┴────┴────┘

┌──────┬──────────────────────────────────────────────────────┐

│Cubic │ │

│ft. of│ │

│water │ GRATE AREAS IN SQUARE FEET. │

│evap’d│ │

│ per │ │

│hour. │ │

├──────┼────┬────┬────┬────┬────┬────┬────┬────┬────┬────┬────┤

│ │ 20 │ 21 │ 22 │ 23 │ 24 │ 25 │ 26 │ 27 │ 28 │ 29 │ 30 │

├──────┼────┴────┴────┴────┴────┴────┴────┴────┴────┴────┴────┤

│ │ HEATING SURFACE CORRESPONDING TO ABOVE │

│ │ GRATE AREAS AND TO SIDE COLUMN. │

├──────┼────┬────┬────┬────┬────┬────┬────┬────┬────┬────┬────┤

│ 100│ 948│ 972│ 995│1017│1039│1060│1081│1102│1122│1142│1161│

│ 110│ 994│1018│1042│1066│1089│1111│1133│1155│1176│1197│1217│

│ 120│1039│1064│1089│1114│1138│1162│1184│1207│1229│1251│1272│

│ 130│1081│1107│1133│1159│1184│1208│1232│1255│1278│1300│1323│

│ 140│1122│1150│1177│1203│1229│1254│1279│1303│1327│1351│1374│

│ 150│1161│1190│1218│1245│1272│1298│1323│1350│1373│1398│1422│

│ 160│1199│1229│1258│1286│1314│1341│1367│1393│1419│1444│1469│

│ 170│1236│1266│1296│1325│1354│1382│1409│1436│1462│1488│1514│

│ 180│1272│1303│1334│1364│1393│1422│1450│1478│1505│1532│1558│

│ 190│1307│1339│1370│1401│1431│1461│1490│1518│1546│1573│1600│

│ 200│1341│1374│1406│1437│1468│1499│1529│1558│1586│1614│1642│

│ 210│1374│1408│1441│1473│1505│1536│1566│1596│1625│1654│1683│

│ 220│1406│1441│1475│1508│1541│1572│1603│1634│1664│1693│1722│

│ 230│1437│1473│1508│1542│1575│1607│1639│1663│1701│1724│1761│

│ 240│1468│1505│1541│1575│1609│1642│1675│1692│1738│1754│1799│

│ 250│1499│1533│1572│1606│1642│1675│1709│1733│1774│1797│1836│

│ 260│1529│1560│1603│1636│1675│1708│1743│1774│1809│1840│1872│

│ 270│1557│1592│1634│1668│1692│1741│1776│1808│1843│1875│1908│

│ 280│1586│1624│1664│1700│1738│1774│1809│1842│1877│1910│1943│

│ 290│1614│1653│1693│1729│1754│1804│1841│1873│1910│1939│1977│

│ 300│1642│1682│1722│1758│1799│1834│1872│1904│1943│1968│2011│

│ 320│1696│1738│1778│1816│1859│1894│1932│1970│2008│2024│2078│

│ 340│1748│1792│1833│1872│1915│1954│1993│2032│2069│2096│2141│

│ 360│1800│1844│1886│1928│1971│2012│2050│2090│2128│2166│2204│

│ 380│1848│1894│1938│1982│2025│2066│2107│2148│2187│2226│2264│

│ 400│1900│1944│1990│2034│2077│2120│2162│2204│2244│2284│2322│

│ 425│1950│2014│2056│2077│2142│2187│2226│2268│2317│2353│2396│

│ 450│2014│2056│2120│2150│2190│2200│2300│2332│2374│2417│2459│

│ 475│ │ │2175│2210│2268│2310│2353│2416│2445│2480│2523│

│ 500│ │ │ │ │2332│2370│2412│2459│2523│2565│2608│

└──────┴────┴────┴────┴────┴────┴────┴────┴────┴────┴────┴────┘

FORMULA.

_N_ = _S_/(_Ld_π) or _S_/(_Ld_3.1416).

Where _S_ = whole surface,

Where _L_ = length,

Where _d_ = diameter, in feet,

Where π = 3.1416,

Where _N_ = the number.

_Example._

Diameter two inches, surface 1466, length fourteen feet, we have,

_N_ = 1466/(14 × 0.167 × 3.1416) = 200.

375. Table 10. Giving the number and dimensions of tubes to obtain any

given amount of surface.

┌──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┐

│L’gth.│Diam. │Diam. │Diam. │Diam. │Diam. │Diam. │Diam. │Diam. │L’gth.│

│ │ 1½ │ 1¾ │ 1⅞ │ 2 │ 2⅛ │ 2¼ │ 2⅜ │ 2½ │ │

├──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤

│ 8│ 314│ 336│ 397│ 419│ 445│ 471│ 504│ 523│ 8│

│ 8½│ 334│ 389│ 422│ 445│ 473│ 500│ 535│ 556│ 8½│

│ 9│ 352│ 411│ 447│ 471│ 507│ 530│ 566│ 588│ 9│

│ 9½│ 372│ 435│ 471│ 497│ 523│ 559│ 597│ 621│ 9½│

│ 10│ 392│ 457│ 496│ 524│ 556│ 589│ 628│ 655│ 10│

│ 10½│ 411│ 480│ 521│ 549│ 584│ 618│ 659│ 687│ 10½│

│ 11│ 431│ 503│ 545│ 576│ 612│ 647│ 690│ 720│ 11│

│ 11½│ 451│ 526│ 570│ 602│ 640│ 677│ 721│ 753│ 11½│

│ 12│ 471│ 549│ 595│ 628│ 667│ 705│ 752│ 786│ 12│

│ 12½│ 490│ 572│ 620│ 654│ 695│ 735│ 783│ 818│ 12½│

│ 13│ 510│ 595│ 645│ 681│ 723│ 764│ 814│ 851│ 13│

│ 13½│ 530│ 617│ 669│ 707│ 750│ 793│ 845│ 884│ 13½│

│ 14│ 549│ 640│ 695│ 733│ 778│ 823│ 876│ 916│ 14│

│ 14½│ 569│ 663│ 719│ 759│ 806│ 852│ 907│ 949│ 14½│

│ 15│ 589│ 686│ 744│ 785│ 834│ 882│ 938│ 982│ 15│

│ 15½│ 608│ 708│ 769│ 811│ 861│ 911│ 969│ 1015│ 15½│

│ 16│ 628│ 731│ 794│ 837│ 889│ 941│ 1000│ 1048│ 16│

│ 16½│ 648│ 754│ 819│ 863│ 917│ 971│ 1031│ 1081│ 16½│

│ 17│ 668│ 777│ 843│ 889│ 945│ 1000│ 1062│ 1114│ 17│

└──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┘

FORMULA.

13.5√(_a_) – 28,

where _a_ is the percentage of admission.

_Example._

What is the mean pressure, with an initial pressure of one hundred

pounds, and sixty per cent. admission.

13.5√(60) – 28 = (13.5 × 7.7) – 28 = 76/100 of 100, or 76 lbs.

376. Table 11. Showing the mean cylinder steam pressure for any

percentage of admission, the initial pressure being from 50 to 150 lbs.

per inch.

┌────────┬───────────────────────────────────────────────────────┐

│Initial │ │

│pressure│ MEAN CYLINDER PRESSURE, ADMISSION BEING IN HUNDREDTHS │

│ in │ OF THE STROKE. │

│pounds. │ │

├────────┼───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┤

│ │10 │15 │20 │25 │30 │35 │40 │45 │50 │55 │60 │65 │70 │75 │

├────────┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┤

│ 50│ 7│ 12│ 16│ 20│ 23│ 26│ 28│ 31│ 33│ 36│ 38│ 40│ 42│ 44│

│ 60│ 9│ 14│ 19│ 24│ 28│ 31│ 34│ 37│ 40│ 43│ 46│ 49│ 51│ 53│

│ 70│ 10│ 17│ 22│ 28│ 33│ 36│ 40│ 43│ 47│ 50│ 54│ 57│ 59│ 62│

│ 80│ 12│ 19│ 26│ 32│ 38│ 42│ 41│ 49│ 54│ 58│ 62│ 65│ 68│ 71│

│ 90│ 13│ 22│ 29│ 36│ 42│ 47│ 51│ 54│ 60│ 65│ 69│ 73│ 76│ 80│

│ 100│ 15│ 24│ 32│ 40│ 47│ 52│ 57│ 62│ 67│ 72│ 77│ 81│ 85│ 89│

│ 110│ 16│ 26│ 35│ 44│ 52│ 57│ 63│ 68│ 74│ 79│ 85│ 89│ 93│ 98│

│ 120│ 18│ 29│ 38│ 48│ 56│ 62│ 68│ 74│ 80│ 86│ 91│ 97│102│107│

│ 130│ 19│ 31│ 42│ 52│ 61│ 68│ 74│ 81│ 87│ 94│ 99│105│110│116│

│ 145│ 21│ 34│ 45│ 56│ 65│ 73│ 80│ 87│ 94│101│107│113│119│125│

│ 160│ 22│ 36│ 48│ 60│ 70│ 78│ 85│ 93│100│108│114│121│127│134│

└────────┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┘

PART II.

CARS.

WHEELS AND AXLES.

377. Of the mechanical details of car building it is not necessary here

to speak; but of those matters which fit a car for special duty, and

depend upon particular characteristics of any road, such as the gauge,

something must be said.

The trend of the wheel tire, as remarked in Chapter XIII., is not turned

cylindrical, but conical. A perfectly straight road would of course

require no cone upon the wheels; the object of the latter being to vary

the wheel diameter when upon curves. The general practice is to give a

certain standard cone to all wheels, for all gauges. This is quite

wrong, as will be seen by the following formula, which is from “Pambour

on the Locomotive Engine.”

[Illustration: Fig. 156.]

Let _m m′_, fig. 156, represent the outer rail, and _n n′_ the inner

one. The circumferences upon the same axles must evidently vary as the

length of these curves, which are included between the same radii.

Let _D_, be the diameter of the first wheel, and _d_, that of the

second; and we shall have,

(_mm′_)/(_nn′_) = (π_D_)/(π_d_),

or otherwise

_mm′_ = 3.1416 _D_,

and

_nn′_ = 3.1416 _d_.

We have also,

(_mm′_)/(_nn′_) = (_mo_)/(_no_).

Expressing the radius of curvature by _r_, and the half gauge by _e_,

the above proportion may be expressed by

(_mm′_)/(_nn′_) = (_r_ + _e_)/(_r_ – _e_),

and also

_D_/_d_ = (_r_ + _e_)/(_r_ – _e_),

and finally

_D_ – _d_ = (2_eD_)/(_r_ + _e_).

This equation shows the difference in diameters that ought to exist

between the inner and outer wheels, that the required effect, (no

dragging of the outer and no slipping of the inner wheel,) is produced.

_Example._

Let the radius of curvature be 1,000 feet.

The gauge of the road, 6 feet.

The wheel diameter, 4 feet.

And the formula becomes

(2_ed_)/(_r_ + _e_) = 24/1003 = .024 feet,

or .288 inch on both wheels, or 0.144 inch for each wheel; which for

four inches breadth, gives a curve of 1/28 of the width, or decimally,

0.144, and vulgarly, ⅐ of an inch. For a three feet wheel, the rule

gives a cone of 0.11 inch.

NOTE.—Messrs Bush and Lobdel cone their wheels 0.08 inches in a four

inch tire; or ¼ inch per foot. The formula above for a three feet

wheel, and 4′ 8½″ gauge, gives a curve of 0.09 inches.

The wheel most used upon American roads is made of cast-iron, in one

piece, and consists either of two side plates, connected by a hub and

rim, or of a central plate ribbed on the sides. Messrs Whitney and Son,

(Philadelphia,) pass all their wheels through an annealing process,

which renders them much less liable to fracture from shocks and from

cold than when the wheel is allowed to cool at once, when hot from the

foundery.

The wheels used upon English roads are made with a wrought iron rim and

spokes, with a cast hub, the tire being, put on separately. Such wheels

are less liable to fracture, but cost more than the American wheel.

378. A very frequent cause of accident upon railroads, is the breakage

of axles. Experiments made at Wolverhampton, (England,) upon differently

formed axles, show very plainly that it is quite wrong to reduce the

diameter of the axle at the middle. That if any variation exists it

should be in making the middle the largest. That the effect of a

shoulder behind the wheel was to decrease very much the strength.

Probably the strongest and most economical railroad axle, would be a

wrought iron tube. Certainly a hollow axle is much stronger in resisting

tension than a solid one containing the same amount of material.

NOTE 1.—Thomas Thorneycroft, of Wolverhampton, England, an educated

man, and a manufacturer of railway axles, observes:—That the various

forms of axles, as generally made, possess within themselves the

elements of destruction. That there are certain fixed principles to

be observed in proportioning axles, and that just as such principles

are departed from, just so much is liability to failure increased.

He says:—It is doubtful whether the wheel is the support and the

journal the loaded part, or the reverse. If the latter is the case,

then the cone of the wheels causes a lateral strain, tending to bend

the axle; and should that bending extend no further than one half of

the elastic limit, if long continued, fracture must result; and

should the elastic limit be exceeded, the plane of the wheel will be

removed from that in which it ought to revolve.

The object of the first experiment was to determine the effect of

the form of the longitudinal section of the axle upon its elastic

limit.

By reducing the diameter of the axle from 45/16 inches at centre, to

3¾ inches; the limit of elasticity was reduced from .343 to .232

inches; and the load, to produce that elasticity, from fourteen to

seven tons.

Experiment second was to ascertain the effect of a reduction of

diameter at the centre, upon the ability to resist sudden shocks.

One half of the axle was made 4½ inches in diameter from middle to

end, and the other half was reduced from 4½ to four inches at

centre. The wheel being fixed, and a ram allowed to fall upon the

journal, when the following result was obtained. Under forty-six

blows, the unreduced end was bent to an angle of eighteen degrees.

Under sixteen blows, the reduced end was bent to twenty-two degrees.

Experiment third was to ascertain the effect of a shoulder behind

the wheel, one end being turned with a shoulder of one eighth of an

inch, as a stop to the wheel, the other end turned plain. Tested by

hydraulic pressure, the shouldered end broke with sixty tons, the

plain end with eighty-four tons.

The object of the fourth experiment was to find the influence of the

position of the wheel, as regards the end of the journal. An axle

was fastened into a cast-iron frame, in a line with the neck of the

journal, when the latter was broke with seven blows of a ram falling

ten feet. The other end was keyed into the frame, with the neck of

the journal projecting 1½ inch, and broke at the twenty-fourth blow

of the same ram, falling ten feet.

The results of the trials are thus summed up by the

experimenter:—That axles should never be smaller at the centre than

at the ends, but on the contrary, that if a difference in size is

made, the centre should be the largest.

The best authorities on the strength of materials, give the hollow

tube as three times stronger in resisting twisting, than the solid

bar possessing the same weight. Thus an axle with an external

diameter of five inches, and an internal diameter of 3¾ inches, is

three times as strong as a solid axle of 3¾ inches diameter.

* * * * *

NOTE 2.—The following experiments were prepared by M. Bourville, and

executed by the Austrian government. The apparatus consisted of a

bent axle, which was firmly fixed up to the elbow in timber, and

which was subjected to torsion by means of a cog-wheel connected

with the end of the horizontal part. At each turn the angle of

torsion was twenty-four degrees. A shock was produced each time that

the bar left one tooth to be raised by the next. An index adapted to

the apparatus, indicated the number of revolutions and shocks. Seven

axles, submitted to this trial, presented the following results:—

1st. The movement lasted one hour; 10,800 revolutions and 32,400

shocks were produced. The axle, two and six tenths inches in

diameter, was taken from the machine and broken by an hydraulic

press. No change in the texture of the iron was visible.

2d. A new axle, having been tried four hours, sustained 129,000

torsions, and was afterwards broken by means of an hydraulic press.

No alteration of the iron could be discovered, by the naked eye, on

the surface of rupture; but tried with a microscope, the fibres

appeared without adhesion, like a bundle of needles.

3d. A third axle was subjected, during twelve hours, to 388,000

torsions, and broken in two. A change in its texture, and an

increased size in the grain of the iron, was observed by the naked

eye.

4th. After one hundred and twenty hours, and 3,888,000 torsions, the

axle was broken in many places; a considerable change in its texture

was apparent, which was more striking towards the centre; the size

of the grains diminished towards the extremities.

5th. An axle, submitted to 23,328,000 torsions during seven hundred

and twenty hours, was completely changed in its texture; the

fracture in the middle was crystalline, but not very scaly.

6th. After ten months, during which the axle was submitted to

78,732,000 torsions and shocks, fracture, produced by an hydraulic

press, showed clearly an absolute transformation of the structure of

the iron; the surface of rupture was scaly like pewter.

7th. Finally, as a last trial, an axle submitted to 128,304,000

torsions, presented a surface of rupture like that in the preceding

experiment. The crystals were perfectly well defined, the iron

having lost every appearance of wrought iron.

CLASSIFICATION OF CARS.

379. Railroad cars come under three general heads,

Those for passenger transport,

Those for freight traffic,

Those for repairs of the road.

380. The American passenger car consists of a body about fifty feet

long, ten feet wide, and seven feet high, containing seats for about

sixty passengers, being cushioned, warmed, lighted, and ventilated.

Except for emigrants, second and third class cars are but little used in

America.

House, box, or covered freight cars, differ from the “flat,” or platform

car, only in having a simple rectangular house, about six feet high and

nine feet wide, built upon the floor. This is used for the protection of

such freight as will not bear exposure; as furniture, books, dry goods,

hardware, and small machinery. Carriages, boxes, bales, masts, lumber,

and fuel are carried by platform cars. Bulky machinery, and first and

second class freight too large for the box cars, should be protected by

tarpaulins.

381. The general arrangement of wheels, springs, and brakes, is the same

for the several classes of cars, the chief difference being in the ease

of springs. Each car rests upon two “trucks,” consisting of four, six,

or eight wheels, so connected by levers and springs, as best to absorb

shocks, and connected with the body by a pin only, by which the passage

of curves is made quite easy.

Cars used for the movement of earth are so arranged as to allow the body

to be tipped up, that the contents may be quickly “dumped,” either at

the sides, ends, or middle, as desired.

382. Upon some roads, a continuous draw bar is passed under the whole

train, the several cars being attached to it, and to each other by

safety chains only. By adopting this, and at the same time by springing

the buffer beams tight upon each other, the whole train becomes one

piece; and the jerks at stopping and at starting are in a great measure

avoided.

As lightness combined with strength is a desideratum in all cases, it

will be found best to truss the longitudinal frame pieces of the car

with rods, rather than to use large and heavy beams, as done by many

builders.

RETARDING OF TRAINS.

383. As regards the mode of retarding trains of cars, the practice of

applying blocks to the wheels is justly considered by many as quite

wrong. The brake should be applied to the rail and not to the wheel.

Blocks drawn against the wheel are supplied with friction by means of

levers worked by a brakeman, who can at pleasure cause the wheels to

slide upon the rail. A shoe, sliding upon the rail, may be supplied with

friction from the whole weight of the car.

The retarding force should be applied at once to every car alike; if too

much in front, the rear cars are driven against those in advance; if too

much behind, the train is liable to break.

The proper place for the brakeman is upon the top of the train, where

all signals may be quickly seen.

CHAPTER XV.

STATIONS.

CLASSIFICATION OF BUILDINGS.

384. The entire establishment of buildings for operating a railroad,

consists of the

┌──────────┐

Terminal,│Passenger,│Stations.

│ Freight, │

├──────────┤

Way,│Passenger,│Stations.

│ Freight, │

└──────────┘

Engine houses.

Repair shops, (for engines).

Repair shops, (for cars).

Wood sheds.

Water tanks.

And appertaining to these, scales for the weighing of cars and freight;

turntables, transfer tables, switch and gate houses.

LOCATION OF BUILDINGS.

385. The location of the several buildings mentioned above will depend

upon the situation of the terminus, the character of the traffic, and

the number of trains arriving and departing.

TERMINAL PASSENGER HOUSE.

386. The passenger house should be at the most convenient point of

access to the persons using it. The freight buildings should be at the

most convenient point for receiving, shipping, and distributing

merchandise.

The engine and car houses, with the shops for repair, may be placed

where the land is cheap, and so distant from dwelling-houses as not to

cause inconvenience to the inmates thereof by smoke and noise. The wood

sheds, tanks, turntables, etc., etc., are generally at the engine

houses; weigh scales, etc., at the freight buildings.

387. A railroad which connects the interior with a seaport, would

probably bring two classes of freight; one for export and one for home

consumption. The first should be carried at once to the wharves and

loaded into the ships with one transshipment; while the second should be

delivered as near as possible to the centre of home trade.

The departments of arrival and departure should be kept quite distinct,

when the amount of business transacted is considerable; otherwise

operating will become complicated. The arrival part of a large passenger

house requires a great number of doors, that exit may be easy to the

large number of passengers that arrive at once. The departure rooms

require few doors, as departing passengers come singly or in small

bodies. Thus, in large cities the front of a long rectangle is given to

departure, while a long side, communicating with an outside platform,

forms the arriving room.

One thing in particular ought to be looked to by American railroad

companies,—the arrangement of public vehicles that shall secure

travellers from the impositions and extortions of hack-drivers. No

person whatever should have access to any building except passengers and

the railroad officials. The places of the several carriages, and the

rates of pay for the same, should be fixed by the company; the fare

being paid by checks bought by the traveller from a company agent at the

station.

TERMINAL FREIGHT HOUSE.

388. The terminal freight house should contain all of the apparatus

necessary for receiving and embarking freight. When the central part of

the building is occupied by tracks, and the sides by platforms, the

landing platform should incline gently from the car to the door; and

that for loading, from the door to the car. This arrangement facilitates

the handling of freight. The interior of the building may be divided

into departments, either according to the destination or the class of

the freight.

ENGINE HOUSE AND APPURTENANCES.

389. A terminal engine house, with a table in the centre, to contain

10 engines, must be 145 feet in diameter.

15 engines, must be 150 feet in diameter.

20 engines, must be 167 feet in diameter.

25 engines, must be 183 feet in diameter.

30 engines, must be 200 feet in diameter.

35 engines, must be 217 feet in diameter.

40 engines, must be 233 feet in diameter.

45 engines, must be 250 feet in diameter.

50 engines, must be 267 feet in diameter.

The diameter of the table being forty-five feet, and the engine

occupying, when off from the table, fifty feet. Again, thirty-two

engines would require a diameter of

(32 × 10)/3.1416 + (2 × 50) = 202 nearly.

The engines within the house may be supplied with water from small tanks

between each alternate pair of pits, (each tank holding five thousand

gallons,) or the entire building may be furnished from a cast-iron pipe

running around the whole, and being in connection with a large tank. In

such pipe there should be a gate over the centre of each pit, and near

its upper end. It may be convenient to connect all to a series of small

tanks, by a pipe, that the water level may be kept nearly constant.

Repair shops for engines and for cars, may be plain, rectangular

buildings, so arranged as to accommodate the necessary machinery.

Turntables consist of simply a circular framework of wood or iron,

placed at the centre upon a solid iron pintle which bears the whole

weight, and guided at the circumference by a series of fifteen,

eighteen, or twenty wheels fourteen or fifteen inches in diameter. The

wheels are placed in an independent spider frame, and run upon a curved

rail placed on the bottom masonry, and the table runs upon the top of

the wheels, so that the motion of the circumference of the table is

double that of the wheels.

The frame consists, first, of a pair of timbers ten or twelve inches

wide and fifteen or sixteen inches deep, upon which the rails are

placed, strongly trussed so as to throw the load upon the centre. At

right angles to these are placed, at a distance of eight or ten feet,

timbers 5 × 10, also trussed, which serve to connect the load more

completely with the wheels. The whole is stiffened by diagonal bracing,

and is strongly floored. The table is turned by a pinion upon itself,

working into a rack fastened to the foundation or to the side masonry.

The trusses, as also the centre bearing, should be capable of adjustment

vertically.

The cost of the table, exclusive of masonry, is from $1,200 to $1,800.

Weigh scales are made similar to, but stronger than, the ordinary

hay-scales, being rigid and strong enough to bear the weight of a

locomotive. Every car (freight) placed upon the road should have the

number and the exact weight painted upon it in some conspicuous place,

so that the contained load may, at any time, be found by placing the car

upon the scale.

WOOD SHED AND TANK.

At _way_ stations the freight and passenger houses, wood and water

station, may all be combined; the plan and size depending upon the

location and importance of the station. The relative position of the

tank, wood shed, and passenger house should be such that when the tender

is at the proper place for receiving its supplies the centre of a

passenger train of ordinary length shall be at the passenger door.

OF THE WATER SUPPLY.

390. The number of engines leaving the terminus of a road determines the

amount of water necessary at the _principal_ stations; and the character

of the road and of the traffic fixes the location and size of the _way_

water stations. The amount of traffic being pretty equally distributed

over the length of the road, the tanks should be placed at equal equated

distances; thus the engines will need to water at closer points upon

steep grades than upon level roads. Generally, however, the water is

taken where it can be got, the location of streams and springs fixing

the place. Steam, hydraulic, wind, human, or animal power may be

employed to raise the water to the tank. Oftentimes high springs will

fill the tanks without the application of artificial power. As we find

the liquid water in nature it is more or less impregnated with

vegetable, gaseous, and saline matter, which often impairs its fitness

for mechanical purposes. These admixtures are derived from the rocks and

ground over or through which the water flows. The incrustations which

form in boilers are caused by the precipitation of the impurities in

consequence of the concentration of water in the boiler. They may be

effectually removed, no matter what their nature, by boiling charcoal in

the water. If the water, previous to filtration, can be heated, to expel

all the air and carbonic acid gas, which is often the solvent of the

foreign matter, the filtering process will be accelerated, and will be

more effectual. Rain water is more pure than any other; practically,

perfectly so. River water comes next to it. Spring water is generally

adulterated with basic salts in various forms, most of which may be

precipitated by gently heating and filtering through charcoal.

391. Fig. 157 shows a convenient form for a tank house, with pump and

heater.

[Illustration: Fig. 157.]

A shows half interior section of the tank.

B, half elevation of tank.

C, pump; C′, supply pipe; _d_, suction pipe and strainer.

E, heater.

_e_, the short, and _h_, the long pipe.

H, the discharge pipe.

G, discharge valve.

I, counter weight for discharge pipe.

K, wheel for weight rope.

L, scale showing amount of water in the tank.

The heater shown in the cut is made of a coil of two inch pipe of iron.

The short pipe descends from within six inches of the bottom of the tank

to within two or three feet of the floor; then bending four or five

times around spirally, turns up through the centre of the coil, and runs

three or four feet into the tank. A small grate is placed in the lower

part of the coil, and the whole apparatus is cased in sheet iron. By

such an arrangement of pipe, circulation is obtained, and the water in

the tank is kept quite warm. The following rules and tables may be found

convenient.

392. The velocity of water in any pipe necessary to discharge a given

quantity, in a fixed time, is expressed by

(144_C_)/_a_.

Where _C_ is the number of cubic feet per hour, and _a_ the area of the

pipe.

393. The head necessary to send water through a given length of pipe, of

any diameter, is shown by the formula

_C_/(_D_ + _C′_) = _H_.

Where _C_ = a constant.

_C′_ = constant for diameter of pipe.

_D_ = diameter of pipe.

_H_ = heads required.

The experimental values of _C_ and _C′_ are as follows: Let _V_ equal

the velocity in feet per minute, and we have

V. C.

60 8.62

70 11.40

80 14.58

90 17.95

100 21.56

120 29.70

140 38.90

150 44.00

180 62.13

Also, the values of _C′_ are

Diameter of pipe. C′.

2 .000

3 .006

4 .028

5 .053

6 .078

7 .104

8 .134

EXAMPLE OF USE OF PRECEDING RULES.

Required the head of water necessary to send 1,333 cubic feet of water,

or 10,000 gallons per hour, through an eight inch pipe one thousand feet

long.

The velocity by rule _one_ will be

(1333 × 144)/(8^2 × .7854) = 3818 feet per hour, or 64 feet per minute.

By rule _two_ (the value of _C_ for 60 being 8.62, and for 70 11.40,

that for 64 is 10 nearly), we have

10/(8 + 0.134) = 1.23,

which multiplied by ten (the number of times that one hundred is

contained in one thousand feet, the distance), gives the result, twelve

inches or one foot, which is the required head; and if the entrance to

the tank is twenty feet high, we have, as the necessary head, 20 + 1 =

21 feet.

394. The formula expressing the power of an engine to raise a given

amount of water is

(_WV_)/33000.

Where _W_ is the weight of a column of water, and _V_ the velocity in

feet per minute; also 33,000 the expression of a horse-power. For

example, how many horse-power must an engine possess to raise one

thousand cubic feet of water per hour through a six inch pipe fifty feet

high?

The velocity will be

(1000 × 144)/(6^2 × 0.7854) = 5093 feet per hour,

or eighty-five feet per minute. The weight of a column of water fifty

feet high and six inches in diameter is

(6^2 × 0.7854 × 50 × 12)/1728 × 62½ = 613.6 lbs.

Also,

(612½ × 83)/33000 = 1½ horse-power nearly.

395. Among the pumps now in use for raising water at railroad stations

are Carpenter’s rotary, Worthington’s, McGowan’s, and that of Messrs.

Perkins and Bishop, either of which answers every purpose.

396. TABLE SHOWING THE WEIGHT AND COST PER FOOT OF CAST-IRON PIPE.

Diameter of Thickness of Weight of pipe Cost of pipe

bore. metal. per lineal foot. per lineal foot.

Inches. Inches. Lbs. Cents.

1 ¼ 3.06 15

1¼ ¼ 3.67 18

1½ ¼ 4.29 21

1¾ ⅜ 7.81 39

2 ⅜ 8.73 44

2¼ ⅜ 9.65 48

2½ ½ 14.70 73

2¾ ½ 15.93 80

3 ½ 17.15 86

The weight of a cubic foot of cast-iron being 450 lbs., and the price

being five cents per lb.

TABLE SHOWING THE CAPACITY OF McGOWAN’S DOUBLE ACTING PUMPS.

┌─────────────────────────────┬─────────┬─────────┬───────────────────┐

│ │ │ │ Time required to │

│ Explanation. │ No. 1. │ No. 2. │fill a 6600 gallons│

│ │ │ │ tank. │

├─────────────────────────────┼─────────┼─────────┼───────────────────┤

│Stroke in inches, │ 5│ 8½│ Hours. │

│Diameter of plunger, │ 2⅝│ 3⅛│ │

├─────────────────────────────┼─────────┼─────────┼─────────┬─────────┤

│Area of plunger, │5.278 in.│ 7.70 in.│ Small │ Large │

│Cube of half stroke in │ 0.114│ 0.283│pump, No.│pump, No.│

│ gallons, │ │ │ 1. │ 2. │

├─────────┬─────────┬─────────┼─────────┼─────────┼─────────┼─────────┤

│Discharge│ At 10 │ Full │ 136.8│ 339.6│ 49│ 19│

│ in │ At 20 │ strokes │ 273.6│ 679.2│ 24│ 10│

│ gallons │ At 30 │ per │ 410.4│ 1018.8│ 16│ 7│

│per hour.│ At 40 │ minute. │ 547.2│ 1358.4│ 12│ 5│

│ │ At 50 │ │ 684.0│ 1698.0│ 10│ 4│

│ │ At 60 │ │ 820.8│ 2037.6│ 8│ 3½│

│ │ At 70 │ │ 957.6│ 2377.2│ 7│ 3│

│ │ At 80 │ │ 1094.4│ 2716.8│ 6│ 2½│

│ │ At 90 │ │ 1231.2│ 3058.4│ 5│ 2¼│

│ │ At 100 │ │ 1368.0│ 3396.0│ 5│ 2│

└─────────┴─────────┴─────────┴─────────┴─────────┴─────────┴─────────┘

CHAPTER XVI.

MANAGEMENT.

All that is required to render the efforts of railroad companies in

every respect equal to that of individuals, is a rigid system of

personal accountability through every grade of service.—_D. C.

McCallum._

ORGANIZATION OF EMPLOYEES.

397. Railroad management may be divided into two grand departments,—

Financial management.

Operating management.

The first of these does not properly come into a work of the present

kind. It embraces the entire system of accounts. Its officers are a

president, secretary, treasurer, attorney, and directors.

398. The operating management is subdivided as follows:—

_The mercantile department._

_The mechanical department._

The first embracing every thing relating to the adjusting of tariffs,

the transport of passengers and freight, the embarking and delivering of

goods, and the weighing and measuring, ticket and receiving offices,

steamboat, stage, and railroad connections. The second, the maintaining

the road-bed, superstructure, bridging, masonry, buildings, and fixed

stock in working order; making all repairs, renewals, enlargements, and

alterations, and the purchase, inspection, maintaining, and operating of

the rolling stock. These departments are again divided and subdivided

until we come to the minutest details.

NOTE.—That part of Chapter XVI. in italics is extracted, by

permission, from the elaborate Report of D. C. McCallum to the

stockholders of the New York and Erie Railroad, (March 25, 1856).

399. The following general principles govern the formation of an

efficient system of operations.

_First. A proper division of responsibilities._

_Second. Sufficient power conferred to enable the same to be fully

carried out, that such responsibilities may be real in their character._

_Third. The means of knowing whether such responsibilities are

faithfully executed._

_Fourth. Great promptness in the report of all derelictions of duty,

that evils may at once be corrected._

_Fifth. Such information to be obtained through a system of daily

reports and checks that will not embarrass principal officers nor lessen

their influence with their subordinates._

_Sixth. The adoption of a system, as a whole, which will not only enable

the general superintendent to detect errors immediately, but will also

point out the delinquent._

400. _A system of operations to be efficient and successful should be

such as to give to the principal and responsible head of the running

department a complete daily history of details in all their minutiæ.

Without such supervision the procurement of a satisfactory annual

statement must be regarded as extremely problematical. The fact that

dividends are made without such control does not disprove the position,

as in many cases the extraordinarily remunerative nature of an

enterprise may insure satisfactory returns under the most loose and

inefficient management._

All subordinates should be accountable to, and directed by, their

_immediate superiors only_. Each officer must have authority, with the

approval of the general superintendent, to appoint all persons for whose

acts he is held responsible, and to dismiss any subordinate when in his

judgment the interests of the company demand it.

401. The following table shows the rate and direction of subordination

for a first class railroad:—

{Section men.

{Superintendent {Road-master.{Section men.

{ of Road. {Road-master.{Section men.

{ {Section men.

{

{ {Foreman Machine shop, Machinists.

{ {Foreman Blacksmith shop, Blacksmiths.

{Superintendent {Foreman Car shop, Carpenters,

{ of Machinery. {Foreman Paint shop, Painters.

{ {Engineers (not on trains), Firemen.

{ {Car-masters, Oil men and cleaners.

{

{ {Conductors {Brakemen.

{ {Mail agents. {Engineers (on trains).

{ { {Ticket collectors.

General { {

Superintendent{General passenger{Station agents.{Hackmen.

{ agent. { {Switchmen.

{ {

{ {Express agents.

{ {Police.

{

{ {Conductors. {Brakemen.

{ { {Engineers (on trains).

{General freight {Station agent.

{ agent. {Weighers.

{ {Gaugers.

{ {Yard-masters.

{

{Supply agent. {Clerks, Teamsters furnishing supplies.

{Fuel agent. {All men employed about the wood sheds.

DUTIES OF EMPLOYEES.

402. _The General Superintendent_ has entire control of all of the heads

of departments; he issues his orders to the heads only, and is the main

agent for transferring the resolves of the directors to the operating

department, and the channel through which the reports of the departments

go to the directory.

_The Superintendent of the Road_ has complete charge of the road-bed,

superstructure, bridging, masonry, and buildings; also all removals,

enlargements, and alterations. He should be a thorough civil engineer,

able in every respect to build a railroad from beginning to end.

_The Superintendent of Machinery_ has charge of the purchase,

inspection, repair, and operating of all of the rolling and fixed

machinery, of shops, engine houses, turntables, tanks, and weigh scales.

He is responsible for the good condition, proper adaptation and

efficiency of the entire equipment of engines and cars.

_The General Passenger Agent_ fixes, under the direction of the

president and general superintendent, the prices of passenger

transportation, has charge of all conductors, ticket sellers, station

police, mail and express agents, of stage, steamboat, and railroad

connections, and of all operations incident to transporting passengers.

_The General Freight Agent_ has charge of all persons occupied at all of

the stations in forwarding and receiving merchandise, in measuring and

weighing, in receiving money, and bookkeeping, station agents, and train

hands. He makes and regulates, with the approval of the president and

general superintendent, the tariff for freights; contracts with

connecting roads, and insures the benefits of such agreements, examines

all claims for damages to freight, and sees that such are properly

settled.

_The Agent for Wood_ contracts, with the approval of the general

superintendent, for the supply of the necessary amount of fuel; attends

the measurement, inspection, and delivery at the proper places;

registers each month the amount of fuel supplied and used, and the

location and amount on hand.

_The Supply Agent_ has charge of the supply of all materials in use in

all departments; iron, timber, engines, rails, bridges, and every thing

in use upon the road; charging each department with its correct quantity

and quality of material received.

_Road-masters_ will have charge, under the superintendent of the road,

of the maintenance of the road-bed and superstructure of divisions of

from twenty-five to fifty miles in length, depending upon the care that

the road-way may need. They will have charge of gravel trains, and of

wood trains, which run under the orders of the superintendent of the

road. They should pass over their divisions at least once per day. Under

them are placed section men, having care of ten miles each, being

supplied with the proper tools and signals. They must pass over their

respective sections at least once per day in a hand car. They should see

that every switch, frog, chair, and rail on their section is in proper

order, and report at once any defects, which cannot be remedied by them,

in the track, to the road-master.

_Engineers_ are subject to the superintendent of machinery when off, and

to the conductor when on, the trains. None but a man well acquainted

with the details of machinery, and who has served in a locomotive

machine shop, and is in every respect temperate and steady, should fill

this berth.

_Foremen_ of the blacksmith, machine, carpenter, and car shops, are

subject to the superintendent of machinery, and have charge of the

repairs and cleaning of the engines, cars, and other machinery.

_Car-masters_ have charge of the men employed in cleaning, oiling, and

examining the cars and their wheels. The cars should be thoroughly

examined at the end of each trip, and at each stop, by an inspector who

accompanies the train and looks to the wheels, axles, boxes, and brakes.

_Conductors._—A conductor of a train should be a machinist, a prompt,

active man, who should station himself on the top of the cars in such a

position as to see the whole train, and able at any moment to

communicate with the engineer. He should direct the running of the

train, and control the engineer and the person who takes the fares. The

latter should confine himself to the inside of the cars.

NUMBER OF TRAINS TO BE USED.

403. This is determined by the quantity and quality of the material to

be transported, and by the character of the road. The train should not

be so heavy as to be beyond the power of the engines upon the steepest

grades, nor so light as to increase unnecessarily the number. A road

doing a large passenger business must accommodate the public as far as

possible as regards the time of departure and arrival, and the

connections with other roads. A freight road must regard more the

character of the road. Some classes of freight (ice, beef, etc.) do not

admit of delay. As we increase the number of trains, the ratio of time

employed in actual work to the whole train under steam is decreased, as

there must be much time lost on sidings in waiting for trains to pass.

Liability to accidents is also incurred. Commercial circumstances, more

than any other, will determine the proper number and class of trains.

AMOUNT OF SERVICE OF ENGINES.

404. This is much less than is generally supposed. The number of engines

required to perform any amount of work is considerably greater than the

number actually in motion, because of liability to accident, time

required for cleaning and repair. The New York State Engineer’s Report

for 1854 gives, as the number of engines on 2,500 miles, 668, or one

engine per 3¾ miles. Also, 668 engines run per annum 11,393,000 miles,

or 17,055 miles per annum per engine; thus requiring .00005863 of an

engine per mile run per annum.

This is very nearly fifty-five miles per day, (313 days per annum).

Also, 968/2500 gives 27/100 of an engine per mile of road, and the same

report gives the following:—

One locomotive for 3¾ miles of road.

One passenger car for 2½ miles of road.

One freight car for 32/100 miles of road.

Or each mile needs

27/100 of a locomotive.

40/100 of a passenger car.

3 freight cars.

Or to one engine 781/100 passenger cars, and 1072/100 freight cars. From

Lardner’s Railway Economy it appears that the average daily run of an

engine is forty-two miles, or seventy-five miles per day, working four

days in the week. That the daily service is two hours working, and three

and three quarters hours standing with steam up. The maximum annual

mileage mentioned by Lardner is that upon the Belgium lines, and was

21,737. The maximum in America has been, as far as we have been able to

ascertain, 22,000, and this for eighteen years.

NOTE 1.—Two little eight ton, four wheeled, Stephenson engines,

cylinders 10 × 16, four and a half feet drivers, inside connection,

copper fire-boxes, have averaged 22,000 miles per annum, with trains

weighing forty tons exclusive of engine and tender, for eighteen

years, costing about $700 per annum each for repairs, or $3.18 cents

per mile run, upon the Bangor and Oldtown Railroad (Maine).

NOTE 2.—In the Report of the Railroad Commissioners of the State of

New York for the year ending September 30, 1855, is the following:—

One engine is required for each three and a half miles; or one

engine in constant use for five and a quarter miles. The average run

per annum by each engine in actual use is 22,823 miles; or 16,302 to

all of the engines. Also, as regards the work done by cars.

Effective in Miles per car. Distance run per

constant use. annum per car.

Passenger, 650 4 45.126

Baggage, 246 11 ——

Freight, 7500 0.35 11.970

the number of miles being 2,615.

EXPENSES, RECEIPTS, PROFITS.

EXPENSES.

405. American railroad reports as a general thing do not analyze the

cost of working. The gross expense is given, and in some cases is

primarily divided. Besides the retrospective use of a minute division of

expenses, which enables us to see what system is the most economical,

there is a prospective use, namely, the formation of estimates for

future operations and a correct base for establishing tariffs. If the

circumstances of the traffic remain the same, an estimate of what the

cost will be at any time is easy; but if they change, the data for the

estimate change also. That we may at all times possess these data, we

should know every year just the cost of working each article of traffic.

It is not enough that the gross receipt exceeds the whole expense; even

then the road may be working unprofitably. Unless each item of transport

pays for itself, we are taxing unjustly some other item, (except,

indeed, in such cases as adopting low rates in order to fill trains

running in one direction which would otherwise run empty). An analysis

of cost will also show whether or not it is best to attract an increased

amount of business by a reduction of rates.

406. The whole cost of operating and of maintaining a railroad may be

generally and specially divided as follows:—

{Cost of Road-bed.

{Cost of Superstructure.

(A) Interest on construction and equipment {Cost of Buildings.

capital. {Cost of Engines.

{Cost of Cars.

{Fixed machinery.

{Road-bed. {Material.

{ {Labor.

{

(B) Maintenance of way and works. {Buildings. {Material.

{ {Labor.

{

{Superstructure. {Material.

{ {Labor.

{ { { {Fuel, oil, and

{ { {Working. { waste.

{ {Passenger. { {Salaries.

{ { {

{ { {Maintaining. {Material.

{ { { {Labor.

{Locomotives.{

{ { { {Fuel, oil, and

{ { {Working. { waste.

{ {Freight. { {Salaries.

{ { {

{ { {Maintaining. {Material.

{ { { {Labor.

(C) Maintenance of {

the fixed and { { { {Warming,

rolling stock.{ { {Working. { lighting, and

{ { { { cleaning.

{ {Passenger. { {Oil and waste.

{ { {

{Cars. { {Maintaining. {Material and

{ { { labor.

{ {

{ { {Working. {Oil and waste.

{ {Freight. {Maintaining. {Material and

{ { { { labor.

{

{Fixed {In shops. {Machinery. {Oil and waste.

{ machinery. {On road. {Tanks and {Materials and

{ { { tables. { labor.

{ {Conductors.

{ {Ticket Sellers.

{Passenger. {Clerks.

{ {Brakemen.

(D) Salaries of hands employed in { {Porters.

and about trains. {

{ {Conductors.

{Freight. {Station agents.

{ {Brakemen.

{ {Weighers and gaugers.

{Passenger. {Warming and lighting.

{ {Police.

(E) Station expenses. {

{Freight. {Warming and lighting.

{ {Police.

{Salaries.

{Travelling expenses.

(F) General superintendence. {Office expenses.

{Stationery.

{Advertising, &c., &c.

The actual _general_ division of the operating expenses upon the New

York State system of roads was, for 1854, as follows. (See State

Engineer’s Report).

Way and works, 1,123 dollars per mile of road.

Machinery, 2,072 dollars per mile of road.

Salaries on and about trains, 640 dollars per mile of road.

Stations, 30 dollars per mile of road.

General superintendence, 333 dollars per mile of road.

—————

Total, 4,198 dollars per mile of road.

That the detailed expenses may be charged to the proper departments, and

that we may be able to take out the exact cost of working any one class

of trains, or of carrying any article of transport, the following form

should be filled.

┌──────────────────────────────────────────────────────┐

│ 407. TABLE SHOWING THE GENERAL AND DETAILED EXPENSES │

│ OF WORKING AND MAINTAINING THE RAILROADS OF NEW YORK │

│ STATE, FOR 1854, AND THE NEW YORK AND ERIE RAILROAD │

│ FOR THE YEAR ENDING SEPTEMBER 30, 1855. │

├──────────┬───────────────────────────────────────────┤

│ │ │

│ │ │

│ │ WAY AND WORKS. │

│ │ │

│ │ │

├──────────┼─────────┬───────────────┬──────────┬──────┤

│ │ │ │ │ │

│Nature of │ │ │ │ │

│ the item │ │ │ │ │

│ is shown │Road-bed.│Superstructure.│Buildings.│Total.│

│ in │ │ │ │ │

│horizontal│ │ │ │ │

│ columns. │ │ │ │ │

│ │ │ │ │ │

│ │ │ │ │ │

│ │ │ │ │ │

│ │ │ │ │ │

│ │ │ │ │ │

│ │ │ │ │ │

│ │ │ │ │ │

├──────────┤ │ │ │ │

│ Name of │ │ │ │ │

│railroad. │ │ │ │ │

│ │ │ │ │ │

├──────────┼─────────┼───────────────┼──────────┼──────┤

│Cost, in │ │ │ │ │

│dollars, │ │ │ │ │

│per mile, │ 351│ 140│ 22│F. 513│

│upon N. Y.│ │ │ │ │

│State │ │ │ │ │

│Railroads │ │ │ │ │

│ │ 453│ 88│ 27│P. 568│

├──────────┼─────────┼───────────────┼──────────┼──────┤

│Cost in │ │ │ │ │

│cents, per│ │ │ │ │

│ton, or │ │ │ │ │

│per │ │ │ │ F.│

│passenger │ .020│ .161│ .010│ .191│

│per mile │ │ │ │ │

│run, N. Y.│ │ │ │ │

│and Erie │ │ │ │ │

│Railroad. │ │ │ │ │

│ │ │ │ │ │

│ │ .035│ .207│ .011│ P.│

│ │ │ │ │ .253│

├──────────┴─────────┴───────────────┴──────────┴──────┤

│ NOTES. │

└──────────────────────────────────────────────────────┘