If we wish to alter the lead, we keep the crank in the same position, and loosening the driver which is fastened to the axle only with a screw, we turn the exccentric, unti§ the slide, which moves at the same time, opens the passage as much as is wanted. Then we replace the driver so as to fix the

Our intention being to produce that effect, by pushing the wagon aside on the road, the question is, how much the wagon must be laterally displaced.

This point depends evidently on the degree of conicalness of the wheel.

the curve, the wheel on that same side wil||
then rest on a tire of a larger diameter. Two
effects will result from this. The wagon
will no longer tend to follow a straight line.
One of its wheels growing larger than the
other, will, on the contrary, have a tendency
to turn in the direction of the curve.
Be-
At Liverpool, the wheels of the wagons
sides which, the two coupled wheels will have 3 ft. diameter at the interior part or
naturally travel different lengths of road near the flange, and 2 ft. 11 in. at the ex-
without any dragging on the rail.
terior part. The wheel is originally cylin-
This form of the wheel and its effects be-drical, but the conical form is produced by
ing very well understood, we have first to the addition of a second tire, the breadth of
determine what difference of diameter must which, not including the flange, is in. less
be created between the two wheels, in order on one side than on the other. Fig. 29,
that the wagon may turn of itself with the represents the section of that tire on a scale
curve, and how much the wagon must de- of 4. Its breadth being 34 in., we see that
viate on one side in order to produce that its conical inclination is in. on 31⁄2 in. or
differe ce of diameter. Then we shall Let us suppose in general the inclination
see how the railway must be constructed,

a (D-D');

this

displacing will produce on the thickness
of the tire, or on the radius of the wheel,
a difference of
(D-D'),
which will make on the diameter
(D—D').

in order that the centrifugal force of the of the tire expressed by. The two wheels
motion produce of itself that lateral devia-running originally upon equal tires, in order
tion. It will thus be clear, that, those dif- that the difference D-D' be produced in
ferent conditions being fulfilled, the first their diameters, by the displacing of the
species of resistance of the curve will be tire on the rail, this lateral displacing of the
destroyed by the motion itself. Coming to wheel must evidently be
the friction of the flange of the wheel against
the rail, we shall determine what degree of
couicalness the wheel must have, in order for the inclination of the tire being,
that, even in passing over the most abrupt
curve of the railway, the lateral deviation
of the wagon may never go so far as to
put the flange in contact with the side of the
rail. In this way, both by the disposition of
the rails and by the form of the wheels, the
two species of resistance will be destroyed.
Let us suppose that mm' and nn' (fig.
28) be the two lines of rails of the way. In
order that the wagon may follow without
effort the curve of the way, it is necessary
that, while the outside wheels describes the
are mm', the inside wheel describes of itself
the arc nn', which terminates at the same ra-
dius as the first. If, therefore, the length
mm' represent a circumference of the outside
wheel, nn' must also be a circumference of
the inside wheel, and the diameters of the
two wheels must be in a certain proportion
for that effect to be produced.

Let D be the diameter of the first wheel, and D' that of the second, being the ratio of the circumference to the diameter, we shall have

pro

This difference on the diameter will be
duced in plus on the outside wheel, and as
an equul difference, but in a contrary sense,
that is to say, in minus, will be produced
on the inside wheel; the result will be a
total difference of D-D' between the ac-
tual diameter of the two wheels, as we
have said.

Thus the lateral motion to be produced is

a e D

{ a ( D — D) = 2 ( r + e )

We know at present what must be the lateral displacing of the wagon, in order to destroy the first species of resistance. The question now is, to make use of the centrifugal force to produce that effect. It is its natural tendency; but it is evident mm' D, and a.. = D'. that that force must produce exactly the Now the two arcs being both terminated by necessary displacing, else the defect would the same radius, we haveby no means be corrected.

The effort of this force exerting itself in the direction of the radius, its effect will be

to push all the wagons out of the curve. If the two sides of the railway are of equal elevation, the wagons will be stopped in the lateral motion only by the friction of the flange of the wheel against the rail. But if we give to the outward rail a surplus of elevation above the inward one, it is clear that, in increasing sufficiently that elevation, we shall be able to master at last the centrifugal force, in such a manner as to permit it only to produce just the displacing we want. In fact, by raising in that manver the outward side, we change the railway in an inclined plane. The wagons placed on that plane ought, by virtue of their gravity, to slip towards the lower rail. On the other hand, the centrifugal force pushes them against the outward rail, which is the highest. We create, then, by that

ans, a counterpoise to the centrifugal

force.

Let us call y the surplus of elevation given to the outward rail (fig. 30); 2e being the breadth of the way, the inclination of the plane on which the wagons are placed, is y On this plane, the gravity If we represent by r the radius of curvation, by V the velocity of the motion, and of a body, the weight of which is P, is exby m the mass of the body moved, the cen-pressed by trifugal force produced on the curve will be, as is known, expressed by

V 2 f = m

But P being the weight of that same body, and g the accelerating force of gravitation, we have

thus

2 e D

f:

rte

P V2 g

This equation shows the difference that which is the expression of the centrifugal must exist between the diameters of the force of a body of a given weight P, movwheels, that the required effect may be ob-ing with a velocity V, on a curve the radius of curvation of which is r.

tained.

a e D

2 (r+e)

we must endeavor to find out what is the necessary inclination.

Let us then suppose the train already displaced as much as required. Let us imagine, for instance, that the train has been pushed from the position ab to the piston cd (fig. 30;) that is to say, that the point of the inside wheel that was at a be come to c, at the distance from the first point, and that at the same time, the point of the outward wheel that was at b, be come to d. In this situation, the inclination of the plane on which the train is, will

tion of
the inclination already produced by the dif-
ference of level between the rails.

which must thus be added to

Consequently the outward side of the wagon will be raised above the interior 2μ side of a quantity equal to y+ ; and as

a

y

eVi

gr

2

aD
eD
2 (r+e) rte
Knowing, then, the conical form and the
diameter of the wheels, as well as the ave-
rage velocity of the motion and the breadth
of the way, this expression will give the sur-
plus of elevation y that suits the radius of
curvation r.

Let us suppose that we have to employ
the dimensions of the railway and wagons
of Liverpool; that is to say, that we have:
V, average velocity, 20 mites an hour, or
29.3ft. per. second.

inclination of the tire of the wheel,

e, half breadth of the way, 2.35 ft.
D, diameter of the wheel at its right
place on the rail, 3 ft.

For instance, on a line, the most abrupt curve of which has 500 ft. radius, with wagons having wheels of 3 ft. diameter, and a play of 1 in. on each side of the way. the equation shows that the least inclination one ought to give to the tire of wheel is 1⁄2 ; but a more considerable inclination will answer, a fortiori.

On the Liverpool and Manchester Railway, the most abrupt curve, which is the one at the entrance of Manchester, has a radius of 858 ft. This results a conical inclination of, and this would answer in all cases; but having said that a greater inclination will fulfil the same object, we are free to adopt a greater inclination, if it suits other purposes better.

It is customary to give an inclination of

The motive for making it so considerable, is to prevent all possibility of the flange If we wish to construct on that railway a rubbing against the rail, either in case of a curve of 500 ft. radius, on which the wag strong side-wind, or in case of some fortuons may experience no additional resistitous defect in the level of the rails, by ance the equation will give

which the wagons would be thrown on the y= 0.236 ft. or in inches, y = 2.83 in. lower rail. Having seen above that, with We must, therefore, for that curve, with an inclination of, there would be no danthat wheel and that average velocity, give ager of the flange rubbing in the curves, that surplus of elevation of 2.83 in. to the out-danger will be still more impossible with an inclination of 4. ward rail.

Adopting the surplus of elevation of the rail deduced from that equation, we render it impossible, the first species of resist ance, which the passage of the curves tend to produce. However, as we only destroy that resistance by a certain lateral deviation of the wagon, it might be feared that that deviation might go so far as to make the flange of the wheel rub against the rail, in which case we would only have substituted one resistance for another. This is, therefore, the point we have still to consider.

We conclude that, with wheels having that inclination, the surplus of elevation of the rail which we have determined above, will correct the first species of resistance of the curves without creating the second, and that, consequently, the train will pass over curves without any diminution of speed.

the

From what has been said, the surplus of We have, until now, supposed the inclielevation that must be given to the outward of the tire of the wheel to be railin the curves, is determined by the follow

nation

1

a

eV 2

y

gr

given a priori. But as it is on that incli-ing formulæ : nation that depends the degree of deviation the wagon must undergo on the rails, it the base which separates the two bearing must evidently be such that, even on the points is measured by 2ep, the final re-most abrupt curve of the line, the lateral sult is that the wagon will be in the same deviation of the wagon may never be concase as if it were placed on a plane, the in-siderable enough to bring the flange of the clination of which should be wheel in contact with the rail.

If, therefore, the wagons have, for instance,
a play of 2 in. on the way altogether; that
is to say, if, in their regular position, the
flanges of the wheels keep on each side at
a distance of 1 in. from the rail, the great-
est value of the deviation p, must always be
less than 1 in. By that greatest value of μ,
we mean the deviation on the most abrupt
curve of the line. Consequently, putting
for r the radius of that curve, and for its
maximum, 1 in. or of a foot, the equation
will give the greatest value that can be given
to the quantity a, or the least value of the in-cases on railways, we make out the follow-

y, surplus of elevation to be given to the outward rail of the curve, over the inward rail, expressed in feet and decimals of feet.

Solving these formulæ in the most usual

ing table which dispenses with all calculations in that respect.

OF ELEVATION TO BE GIVEN TO THE OUT-
ORDER TO ANNUL THE RETARDING

SURPLUS

WARD RAIL IN

EFFECT OF THE CURVES, THE CURVES, IN

PRACTICAL TABLE OF THE

A

Surplus of elevation to be given to
the rail, in inches, the velocity of
the motion in miles, per

hour, being

30 miles.

€90'0

Designation of the Wagons and the Way.

Radius of the curve, in feet.

10 miles.

20 miles.

ft.

in.

in.

in.

5000

0.28

0.66

Wagon with wheel

ARTICLE II.

.

OF THE INCLINED PLANES.

§ 1. Of the Resistance of the Trains on Inclined Planes.

Inclined planes are a great obstacle to the motion on railways.

present the resistance that would be offered jare helped in passing the plane by an en-
by a load of 308 t. on a level. Conse-gine stationed at the foot of the acclivity,
quently the engine which, before, drew 100 and especially intended for that use. This
t. must now draw 408 t., or at least must engine is, consequently, constructed for a
exert the same effort as if it drew 408 t. slow motion and a considerable power.
on a level.
The cylinders have 12 or 14 in. diameter,
This is the manner in which the calcu- with the usual stroke of 16 in., and the
lation of the resistance on inclined planes wheels have only 4 ft. 6 in. Besides, in
must be established; and we have entered order to have more adhesion, the weight of
into those particulars, because it frequently he engine is 12 t. and the four wheels are
happens that, in making the calculation, coupled. These additional engines, work-
the gravity of the load is alone considered,ing less than the others, require also, in
without taking into account the gravity of general, much less repairs.

the engine, which ought also to enter for

its share.

On the Darlington Railway, the accli vities are much too numerous for an adIn speaking of the fuel, we shall sce that ditional engine to be placed at each of the inclined planes of the Liverpool Rail them. The load of the engine must thereway, which at first sight appear quite in-fore be limited so that it may ascend with significant, oblige, however, the engines to that load the most inclined of the planes. a surplus of work, which amounts to a The locomotive engines acquire, howsixth part of what they would have to do ever, a considerable augmentation of power, on a level. By this we see how important at the moment of their passage on an init is, in establishing a railway, to keep it clined plane, because their speed being on as perfect a level as possible. It fre-suddenly considerably reduced, the cylinquently happens that, by avoiding to level ders consume a smaller quantity of steam. a part of the road, that is to say, to cut The fire, strongly excited by the preceding through a hill, or to form an embankment rapidity of the engine, continuing to furthrough a valley, a great economy is ex-nish the same quantity of steam, a great pected. This is, however, a great mis- part of it must escape through the valve. ake, for, in most instances, the only eco- But the passage of the valve is too narrow nomy is that of the first outlay, whereas, to emit freely all that steam. Besides, the the annual augmentation of expense sur-spring that presses on the valve opposes passes by far the interest of the capital more and more resistance, in proportion as saved; so that, instead of an economy, we the steam tends to raise it higher, in order have in reality a greater expense. This to get a wider passage for itself. The conadditional expense may even, in some cases, go so far as to paralyze completely all the advantages of the undertaking.

In suffering inclined planes to subsist on a line of railway, it not only becomes inpossible to lower sufficiently the freight of the goods; but, what is much more important, frequent accidents occur while descending those steep acclivities, the least As soon as the trains reach these in- inconvenience of which is to destroy puclined planes, they offer a considerable sur-blic confidence in the safety of the conplus of resistance, on account of the graveyance. It is, therefore, necessary to lay vity of the total mass that must be drawn down as a principle, that the end to be up the plane.

aimed at in the construction of a railway,
is not only to make a smooth road, but
likewise a level one. It is, besides, the
only way to apply with efficacy the use of
locomotive engines.

sequence is that the steam, not being able to escape as quickly as it is generated, suffers an increase of pressure in the boiler.

This increase of pressure evidently depends on several circumstances: the size of the valve, the evaporating power of the boiler, the previous excitation of the fire, and finally the length of the lever at the extremity of which the spring-balance acts. In some engines this increase may amount to 10 lbs. per square inch, as we have remarked in speaking of the pressure.

In that case, if the usual effective pressure of the engine be 50 lbs. per square inch, it may, on ascending the inclined plane, increase to 60 lbs., that is to say, in the proportion of, which is considerable. This must, therefore, be taken into account when it is required to calculate the load the engines are able to draw on these planes. But it is necessary to observe that this is effectual only when the inclined planes are not of too considerable an extent, because, in that case, the fire ceasThe loads must either be regulated so that ing to be excited in the same proportion, they may not exceed the power of the enthe surplus of effect will be reduced. The gine in going up the plane, or it is neces- weight of the engine must, besides, always sary to give the engines the help of one or give sufficient adhesion of the wheel to the more others, according to what is required. rail, as we shall explain in the following Chapter.

Let us suppose a train of 100 t. drawn by an engine. Having seen that on a level the friction of the wagons produces a resistance of 8 lbs. per ton, the power required of the engine will be 800 lbs., when When, however, it has been impossible travelling on a level. But let us suppose to avoid the inclined planes, and when the the same train ascending an inclined plane use of stationary engines has been rejected at On that plain, besides the resis-on account of the interruption they untance owing to the friction of the wagons, avoidably cause in the service, there are a fresh resistance occurs, which is the gra-only two ways that can be resorted to. vity of the total mass in motion on the plane. That gravity is the force by virtue of which the train would roll back if it were not retained; and it is equal to the weight of the mass divided by the number that indicates the inclination of the plane. If, therefore, in this case, the load of 100 t. is drawn by an engine weighing 10 t., the total mass placed on the inclined plane will be 110 t. or 246,400 lbs. ; and thus its gravity on the inclined plane, at, will be 2,464 lbs. The surplus of traction required of the engine, on account of that circumstance, is, therefore, 2,464 lbs., and, as we have seen that on a level 1 t. load is represented by 8 lbs. trac- The trains that are too heavy for a single tion, we also see that those 2,464 lbs. re-engine, as are commonly those of wagons,

On the Liverpool Railway, the trains of coaches never being very heavy, are seldom above the power of the engines on the which the engines are obliged to exert an most inclined parts of the line, viz. in the additional effort. That is at the moment two acclivities of and In general, of starting. We have seen, in fact, that the therefore, the engines ascend these inclined power which, when the motion is once planes without help; and during the rest of created, need only to be constantly equal the trip, on the level or descending parts of to the resistance, must, on the contrary, the line, their speed is regulated by par-surpass it at the instant that it is to put tially shutting the regulator. the mass in motion. The reason is plain : in the first place, it is only necessary to maintain the speed; in the other it must be

created and maintained. It is this addi-elsewhere, or by its adhesion, as shall be
tional effort on the part of the moving mentioned in the following Chapter.
power which is improperly called vis iner-
tia because it is attributed to a particular
resistance residing in the mass.

This table, assimilating the trains drawn on inclined planes, to trains drawn on a level, gives the means to learn by the former The starting is, therefore, a difficult task tables, either the loads the engines will be for a locomotive engine heavily loaded. able to draw on given inclinations, or, vice However, at that moment the engine ac-versa, the inclined planes the engines will quires, as well as on the inclined planes, be able to ascend with given loads.

CHAPTER VIII.

OF THE ADHESION.

a considerable increase of power. Here
again the slowness of the motion produces
two effects. The pressure in the cylinder
grows equal to the pressure in the boiler,
which is itself augmented by the effect of
the spring-balance. But, notwithstanding
§ 1. Measure of that Force.
this twofold advantage, the difficulty of The series of experiments we have de-
starting still remains so great for consider-scribed above on the velocity and load of
able loads, that we should always advise the engines, solves also another question in
giving in that point a slight declivity to regard to the motion of locomotive engines
the way. By that means the trains would of which we have not yet spoken. That is
be set in motion with more ease at the the adhesion of the wheel to the rails.
departure, and it would not be necessary!
at their arrival to make use, in order to
stop them, of the powerful brakes, the
effect of which is certainly as destructive
to the wheels of the wagons as to the

rails.

§ 2. Practical Table of the Resistance of

the Trains on Inclined Planes.

In the preceding paragraph, we have seen in what manner the resistance of the trains on the inclined planes must be calculated. The following table presents the result of that calculation in the cases which occur the most frequently on the railways.

It is clear that, by the weights inscribed in the following table, it is only intended to show the resistance offered by the train, and not the weights the engines are able to draw, those weights being limited either by the power of the engine, as we have explained A PRACTICAL TABLE OF THE RESISTANCE

OF THE TRAINS ON INCLINED PLAINS.

Designation of the Engine.

Engine weighing 8 t.

Engine weighing 10 t.

helping engines, the work by the adhesion of their four wheels, as has been said elsewhere. The ATLAS is the only one of the former class that differs from the othersin that respect. This engine has six wheds, four of which are of equal size, and worled by the piston. The two others, whch are smaller, and have no flange, an be raised out of contact with the rals, by the action of the steam on a moveable piston. That ingenious arrangement, which may have more than one us:ful application, in permitting the weight of an engine to be distributed upon six whels, without making the engine more embarrissing than if it had only four, is due to Mr. J. Melling, of Liverpool, who, in this instance, made use of it in order to give the engine a much larger firebox, and corsequently the power of generating a greater quantity of steam.

We have remarked in describing the enWe have now expressed the adhesion, by gine, that the power of the steam being ap-giving the measure of its effects; but the plied to the wheel, the engine is in the same situation as a carriage which is made to advance by pushing at the spokes. Thus, as in that action, the only fulcrum of the moving power exists in the adhesion of the wheel to the rail, if that adhesion is not sufficient, the force of the steam will indeed make the wheels turn, but the wheels, but the wheels slipping on the rails instead of adhering to them, will revolve, and the engine will remain in the same place.

power itself may be expressed in a direct manner. The load of 244 t. produced a resistance, or required a traction of 1,952 lbs.; the adhesion was thus equal at least to 1,952 lbs., else the wheel would have Now the adturned without advancing. hering weight was 5.5 t. or expressed in pounds 12,320 lbs.; we see then that the force of adhesion was equal to about of the adhering weight. Considering that en-traction of a ton on a level, this expression is every 8 lbs. force corresponds with the exactly similar to the first.

The more considerable the train the gine draws, the more power it must employ, and the more resistance it must consequently find in the point on which it rests, for executing the motion. It was therefore to be feared, that with considerable trains, the engines would be unable to advance; not that the force would be wanting in the moving power itself, but in the fulcrum of the mo

tion.

The experiments related above, establish
the measure of that adhesion in the fine
season of the year. Among all these expe-

riments, not one is to be found where the
motion has been stopped or even slackened
for want of adhesion, and nevertheless we
see loads that amount to more than 200 t.
If we take, for instance, the first experi-
ment made with the FURY, on July 24;

du

ring a part of the journey, that engine drew

50
75 124 B3153191 230 307 244 t.

199 161 170 201 251 302 402
135 200 216 249 511 573 197

The engine advancing with that load, the adhesion must necessarily have been sufficient. Now the weight of the

and dirty, in consequence of damp weather, In winter when the rails are greasy the adhesion diminishes considerably.— However, except in very extraordinary cir to draw a load of 15 wagons, or 75 t., tencumstances, the engines are always able der included, that is to say, 14 times their adhering weight. In other words, the resis adhesion is always at least of the adhertance of 75 t. being 600 lbs., the force of ing weight.

Adhesion being indispensable to the creation of a progressive motion, two conditions are necessary in order that an engine may draw a given load. 1st. That the dimen sions and proportions of the engine and its boiler enable it to produce on the piston, by means of the steam, the necessary pressure, which constitutes what is properly termed the power of the engine: and, 2nd, that the

150 239251 298 371 145 592 FURY is 8.20 t,, and that weight is divided weight of the engine be such as to give a

25
50 $4 93107134162218|

45 50 5 74 91123

75 125 135 155 194 234313

100 162 178 203 254 306408
125 201 220 251 314 377 503|||it.
150 240 263 300374 14959

175 279 305 348 434 521 593
200 318 345 296 494 592 78-

sufficient adhesion to the wheel on the rail.

in such a manner, that 5.5 t. are supported These two conditions of power and weight
on the two hind wheels, which are the only must be in concordance with each other;
working wheels, the others not serving to for, if there is a great power of steam and
push the engine forward, but only to carry little adhesion, the latter will limit the
ing 244 t., or a load 444 times as conside- lost; if, on the other hand, there is too
We have thus a weight of 5.5 t. draw-effect of the engine, and there will be steam
rable as itself. The result of this is, that much weight for the steam, that weight
an engine having its four wheels coupled, will be an useless burthen, the limit of load
and which consequently adheres by its whole

own mass.
weight, is able to draw a load 44 times its being in that case marked by the steam.
§ 2. Of the Engines employed on Common
Roads.

We have said that the FURY engine ad-
On the
hered only by two of its wheels.
The considerable loads that have been
Liverpool Railway that disposition is gene-drawn by the engines in the experiments
rally adopted for all trip engines, because described above, ought to remove the fears
the adhesion of two wheels is sufficient for of such persons as suppose that the wheels
the loads they have to draw. As for the of locomotive engines on railways are con-