Report on Rail-roads and Locomotive Engines, Addressed to the Chairman of the Committee of the ...

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ARTES SCIENTIA VliRirAS

I

REPORT

{

RAIL ROADS

LOCOMOTIVE ENGINES, (^^jit

ADDRESSED T'O

THE CHAIRMAN OF THE COMMITTEE OF THE LIVERPOOL
AND MANCHESTER PROJECTED RAIL-ROAD.

By CHARLES gyLVESTER,

CIVIL ENGINEER.

SECOND EDITION.

LIVERPOOL:
PRINTED BY THOS. KAYE,
45, castle-street;
amd sold by baldwin, cradock, and joy, and taylor
akd bebsey, london.

^1825.

TF
144

Liverpool, December 15, 1824.

Sir,

HA VING been requested by a friend, a

Member of your Committee, to inspect the Locomotive En-
gines and the Rail-roads near Newcastle and Sunderland,
I have prepared the following Report, which he has desired
me to publish and address to you. With my best wishes for
the success of your most important and valuable under-
tahing,

I have the honour to be,

Sir,

Your most obedient Servant,

CHARLES SYLVESTER.

To Charles Lawrence, Esq.,

Chairman of the Liverpool and Manchester
Rail-road Committee,

-a.

? REPORT ON RAIL- WAYS.

K

2>

Liverpool, "SOth November, 1824.

In every mechanical operation, whatever may be its
natare, a certain eflfect or work has to be performed
by some effort, called force or power, which is
intended to overcome other forces, or resistances,
opp6sed to the existing causes. If the whole of
these caases are properly estimated before they are
put ii^o operation, the result will be exactly fore-
seen ; if, on the contrary, any of these causes, whe*
ther impelling or resisting, have not been properly
estimated, the result will be different from that which
has been foretold. This previous estimation of effects
has been vaguely called theory, and there is a gene-
rally prevailing opinion, that theory and practice are
oftentimes at variance; for we frequently hear such
language as, things being good in theory and bad
in practice." Nothing can be more absurd. Every
thing attempted to be practised has been the result
of preconceived notions of the causes which would

c

interfere in favour of or against the result; but if
the result be not what was expected, some of the
causes have been wrongly estimated, or, perhaps,
omitted altogether. Whichever of these may have
been the case, we cannot call such a thing correct
in theory, nor can any thing be correct in theory
which does not hold«good in practice.

Although, in this investigation, I have taken great
pains to introduce all the circumstances for and
against the accomplishment of rail-ways, I am well
aware, that many have yet to be considered which
must remain to be developed by experience.

We have long been acquainted with the effects and
advantages of rail-ways in lessening the friction and
the consequent saving of horse power. These have
undergone various improvements in their means of
lessening the friction. My object, in this report, is
to explain the principles of moving wheel carriages
along rail- ways, whatever may be the power employed;
The force applied I consider as a certain pressure,
which I call the moving force, and which I shall, in
my calculations, express in pounds : the weight to
be moved along tiie plane I shall also express in
pounds.

With a view to make these principles better un-
derstood, I will propose an hypothetical plane, or
rail-way, destitute of friction, to go quite round the
earth, keeping every portion of the surface of the
rail the same distance from its centre. These
would be the precise data to constitute a level
plane. It will be clear to all who .are acquainted
with central motion, that, if a carriage or other body
be put in motion upon this hypothetical plane with

7

any given velocity, it will continue to revolve round
the earth with the same velocity, supposing it to have
no friction, nor to be otherwise resisted.

This hypothesis being admitted, I will now sup-
pose, what we shall all readily allow, that this plane
has a certain, but uniform, friction throughout, and
that, in order to overcome this friction, we will sup-
pose, it to have some power travelling with it for that
purpose. This being effected, it will, I think, be
granted, that, whatever force we add to that which
overcomes the friction, the carriage will be put in
motion, and its velocity will increase, equally in
equal times, as long as this extra force is continued.
If, at any period of its motion, this extra force be
withdrawn, leaving that still in action which balances
the friction, the body will go on with the velocity it
had acquired, and, if the path reached round the
earth, it would continue to revolve for ever.

In order to apply ^this principle to practice, I have
been anxious to get all the information I could on
the subject of friction. For these valuable facts, I
have been under much obligation to Mr. Stephenson,
your engineer, and his friend, Mr. Wood, of the
Killingworth Colliery.

They have ascertained, by experiment, that an
empty coal waggon, which weighs 23.25 cwt., requires
a force equal to about 141bs. to keep it in motion,
and they did not find, on varying the velocity,
that this force was altered. When the waggons are
loaded, the weight becomes 76.25 cwt., or 8,5401bs.
If the axletrees of the waggon had been changed,
according to the weight upon them, we should, doubt-
less, find that the friction would increase as the

8

weight ; but in this case it is not so, and the friction
of the loaded carriage, instead of being SSlbs., as the
weight would give, is only 49Ibs. In order to be
rather over than under the truth, I have called itdOlbs.
The engine is about eight tons, or 17,9201bs. I
have stated the friction at about lOOlbs.

In my examination of the locomotive engines at
the Killingworth and Hetton Collieries, I have ascer-
tained, that they are, in their present state, a great
saving, compared with the employment of horse
power ; and that they are capable of so much im-
provement, as to put the matter beyond all doubt.
My principal facts are taken from the Hetton Col-
liery. The engines and waggons, which I saw, tra-
versed a plane, very little inclined, in the direction of
the load: its length was 2,541 yards, or nearly
miles : the rise in this length about 22.75 feet

I made two journeys with the engine, which drew
16 waggons. In the first journey, we stopped for a
short time on the way, but I found the average num-
ber of strokes per minute of the engine to be 45,
which, multiplied by the circumference of the wheel,
9 feet, gives 405 feet per minute, or a little more than
4J miles per hour. The second journey was per-
formed in 15 minutes, which was at the rate of 52
miles per hour. The pressure of the steam in the
boiler was said to be 501bs. on an inch, and that
upon the working piston 301bs. ; but, as there were
no means of ascertaining this accurately, it must
have been conjecture, particularly when the engine
was going, for the safety-valve was then regulated by
a spring, the force of which was very uncertain.

In order to put the principles, which I conceive to

9

belong to rail- ways, to the test, I have applied them
to the facts which I obtained from this experiment^
making the known data the means of finding what I
did not get from observation, and comparing my re-^
suits with the facts given by the estimation of the
superintendent of the works. I have, therefore, taken
one common speed for the engine, viz. 45 strokes per
minute, which also limits the velocity to 5 miles an
hour, or 7J feet per second*

Agreeably to the principles laid down in the com-
mencement, when a force is applied equal to the fric-
tion, the smallest force above that would, if continued,
generate any required velocity. But it will be desir-
able to have such a force at command as will gene-
rate the necessary velocity in a short time, and, when
that has been accomplished, to reduce this force, but
still to leave it fully equal to the friction. If any part
of the route has an inclination, there ought to be an
extra force at command, above what would be re-
quired for a dead level. The plane, on which this
experiment was made, inclined, in the direction of
the load, about i of an inch to a yard. This is as
great, and perhaps a greater, inclination than any
rail-road ought to have, where loaded carriages go
up and down. The moving force ought, therefore, to
be always greater than the friction added to the force
which is required to overcome the inclination of the
plane. The latter force assists the body to go down,
and equally resists it in moving upwards.
. On this account I have used, or supposed, a moving
force, which will give the velocity of 5 miles an hour,
or 7J feet per second, in the space of one minute.

10

This will be performed down the above plane by the
engine making 45 strokes per minute, with a pressure
of 9.71bs. upon an inch, of each of the two cylinders,
the area of each being 63.6 square inches. The weight
of the engine and 16 waggons is equal to 154,5601b8.,
or nearly 70 tons. This velocity of 5 miles an hour
being acquired at the end of one minute, the only
force to keep the whole in motion, at the same rate,
will be the difference between the gravity of the
weight down the plane and the friction. The friction
is 9001bs. ; the gravitating force of the weight down
the plane 5401bs.; therefore 900— 540=3601bs.

If the same weight, at that speed, had to move on
a dead level, and acquired the same velocity in one
minute as before, the moving force would require to
be l,7811bs., which would require a pressure of 13.71bs.
upon 1 inch. But, after the speed is obtained, it will
require only Tibs, to keep it moving at the same rate.
If the same load were required to move up the plane,
it would require a moving force of 2,3281bs., or a
pressure upon every square inch of 18.31bs. And
this velocity would be kept up by a constant pres-
sure of l,4471bs., which will be 11.31bs. upon every
inch of the piston.

In starting the engine, in the first instance, and
giving the required velocity, it is probable the effects
will agree very nearly with these calculations;
namely, 154,S6(Hbs., moved at the rate of five miles
an hour with a pressure of 9.71bs. upon every inch
of the piston. Whether the pressure was reduced
to the difference between the friction and the force
upon the plane, which is calculated at 2.81b., it is

11

difficult to say, as there was no steam-gaage to indi-
cate the pressure when the engine was going.

In observing the working of the engine, I should
think the number of strokes should not be more than
45 or 50 in a minute. This limits the speed of these
engines not to exceed five miles an hour, for the cir-
cumference of the wheels upon the rail being about
nine feet, 45 x 9=405 feet per minute, or a little more
than 41 miles an hour. Now, it would not be advis-
able to increase the number of strokes much beyond
this rate, say 50. If, with this, it were required to go
nine miles an hour, or 792 feet per minute, then
=15.8 feet for the circumference of the engine
wheel, which will be about 5 feet in diameter.

The weight I propose to be conveyed, by one
engine, will be 88 tons, or 85,1201bs.; the friction of
tbis, on a level plane, will be 494Ibs. Hien, the
moving force to give liiis weight a velocity of nine
miles an hour, in one minute will be l,5981bs. ; and,
if we agree to have the same area, namely, 63.6, for
each cylinder, the pressure upon an inch will be
i^=I2.51bs.

127'8

In order, however, to give some idea of the power
required for different loads, I have given a table, in
which the engine is constructed about the size proper
for conveying the above weight at the rate of nine
miles an hour. I do not think it would be econo-
mical to make any engine much smaller than those
used near Newcastle. The cylinders are nine inches
in diameter, and the length of the stroke two feet.
The boiler I would make about the same diameter,
namely, four feet. I would make the' fire-grate and

12

chimney of much greater area, and the wheels, instead
of three feet, I would increase to five feet diameter.

In the principle laid down, the friction is supposed
to be the same with any velocity which will be
required. The resistance of the air, in the velocity
of nine miles an hour, would be a little more than
six ounces upon every square foot of surface ex-
posed directly to the front of the moving body.
This eflFect would vary with the direction and power
of the wind ; it will, however, be so little, that it may
be safely neglected in this calculation.

Although the experiments made by Professor
Vince, and by the French philosopher Coulomb, are
sufficient to establish the law relative to the friction of
bodies moving on planes, and that they also agree
with the experiments by Messrs. Stephenson and
Wood, at the Killingworth Colliery, it would, I
think, still be desirable to repeat these experiments
with greater velocities than have hitherto been tried.
For this purpose, I would recommend a course of
experiments upon a small scale, which would be of
great value, and would save much expense in the
construction of the real working machines. The
scale on which I would make this experiment would
be similar to that on which Mr. Smeaton made his
experiments on water-wheels and wind-mills. This
would consist of an upright revolving shaft, with an
arm or moveable radius similar to that of a horse
mill. The length of this I would make about 15 feet;
the end of it would, therefore, move in a circle of 30
feet in diameter. At the extremity of this circle
I would make a rail-way quite round the circle.

13

constructed in every respect in proportion to the pre-
sent iron rail-ways, on the most modem plan. I would
also have a carriage, or rather a series of carriages,
having wheels suitable to the rails, and loaded in the
same proportion. Round the upright central shaft I
would coil a rope, which should go over a pulley,
and have a weight to act at the end of the rope. This
weight, by its gravity, would give motion to the re-
volving arm, which would be connected with the car-
riages to be drawn along the plane or circular rail-
road. In forming the connexion between the arm
and the carriages, I should place in the connecting
chain or rope a spiral spring, similar to a spring
steelyard. The carriages bein^ loaded, and the mov-
ing force applied, it would in the first instance acce-
lerate, as was stated in the beginning, the velocity,
increasing with the time. I should have first observed,
that a force or weight should have been first applied,
which would just overcome the friction of the shaft
and pulley, aad then a weight added to give the car-
riages a certain velocity in a given time. When the
body has acquired what may be deemed a sufficient
velocity, the moving force may be diminished till the
motion becomes uniform, which may be easily ascer- *
tained by a stop watch. During the time the velocity
is increasing, the spiral spring must be carefully
observed. Previous to making the experiment, this
spiral instrument, which we may term a dynamometer,
should be graduated into pounds and parts similar to
a steelyard, by which means it will be known what
force the friction is equal to in pounds, and whether,
and how much, it increases whilst the velocity is in*
creasing,
c

14

The weight used as a moving force in this appa-
ratus, will have the same effect with the force of the
steam on the piston of the engine, and may in every
respect be compared with it, after making proper
allowance for its own friction and the rigidity of the
rope.

If these experiments should confirm this law rela-
tive to rail-ways, and even common roads, it may be
turned to greater practical advantage than has as yet
entered into the views of the present proprietors of
rail-ways. We have hitherto only seen the force of
animals applied to carriages, and the great weight
conveyed by coaches in proportion to their speed
has frequently been observed with surprise; this,
however, would create much more wonder, if a force
equal to the first power of the horse could be kept up
for a length of time. This will be best explained by
a statement of the decrease of a horse's power as the
speed increases. If a horse, standing still, can by
his strength keep a weight of 1691bs. from falling,
when suspended over a pulley, he will exert 1211bs.
when he goes 2 miles an hour, lOOlbs. when he goes
3 miles an hour, 811bs. with 4 miles an hour, 641bs.
with 5 miles, 491bs. with 6 miles, 361bs. with 7 miles,
251bs. with 8 miles, 161bs. with 9 miles, 91bs. with 10
miles, 41bs. with 11 miles, lib. with 12 miles, and at
the speed of 13 miles he is not able to exert any power.

It will be evident, that if any power be applied, of
the same energy as that of the horse in the first in-
stance, and is not diminished by the increase of
speed, the result will be very striking when com-
pared with the effects of horses. . The force of the
engine is applied to the wheels to give them, a rolling

15

motion, and on that motion depends the progressive
speed, this power not being diminished by the speed,
as is the case with the horse.

Having shown the advantages which may be de*^
rived from the application of moving force on rail-
ways, I shall give a comparative view of these with
canals.

The common roads differ from rail-ways only in
their quantity of friction being about 1& times greater
than the. best rail-ways. When this friction is over-
come by any power, supposing the road uniform, any
additional force applied will uniformly increase the
velocity of the carriage to any extent. The great
irregularity of all common roads will not allow this
fact to be verified, and we can only expect this law
to be realized in rail-ways. With respect to canals,
they are governed by a very different law from that of
rail-ways. The resistance, instead of being constant,
as in common roads or rail-ways, increases, at least,
as the square of the velocity. Whatever power is re-
quired to move a floating body with any given velocity,
it will require four times that power to give it twice
that velocity, and nine times the same to give a treble
velocity. , ■

In order to give a more precise view of the relative
advantages of rail-ways, common roads, and canals,
I have arranged them in Table II. It appears from
this table, that, at the rate of two miles an hour, the
same moving force being applied to a canal and a
rail- way, the canal has the advantage, as two to one,
but, at the rate of three miles an hour, the rail-
way has the advantage over the canal as 22,400 to
19,911, and at the rate of 2.82 miles they are equal.

16

At the rate of nine miles an hour, for which the
first table is constructed, the canal would only take a
weight of 2,2121bs., which is less than v^th of the
weight conveyed on a rail-way, with the same power.

When a powerful horse commences his draught
from a state of rest, he begins with exerting a force
equal to I74]bs. ; but his power to draw decreases
with the speed, and, as the table shows, he exerts a
power of 1251bs., at two miles an hour, by which he
conveys 20 tons, including the vessel.

It will be evident, that the speed by means of
horses, whatever may be the number, can never ex-
ceed 12 or 13 miles an hour, for at this speed they
can exert no power. It vnll, therefore, be necessary,
in order to travel at the rate of 9 to 10 miles an hour,
to empldy the power of steam, and this will be best
performed by the locomotive engine. Althoagh it
would be practicable to go at any speed, limited
by the means of creating steam, the size of the
wheels and number of strokes in the engine, it
would not be safe to go at a greater rate than 9
or 10 miles an hour. If the number of double
strokes of the engine could be as great as 60 per
minute, and the wheels on which it moved were the
enormous size of 6 feet diameter, the speed would
not be quite 13 miles an hour. If, by any chance,
the wheels of the engine should get off the rails,
which is sometimes the case^ a greater speed than
that above recommended would be attended with
proportionate danger. It will appear, from the prin-
ciples laid down, that any power greater than the
friction being applied will cause the vehicle to gain
equal velocities in equal times, as long as that excess

17

of power is continued. This may be shown from
the theorems that are given at the conclusion. With
a view to render the subject suflSciently intelligible
to those who do not read algebraic formulae, I shall
give a short analysis of the principle in common
numbers, which, for the sake of greater clearness, I
will make even numbers. Suppose 40 ,tons have to
be moved by an engine weighing 8 tons, which will
leave 32 tons for loaded carriages. The friction of
this weight will be about SOOlbs. If a moving force
equal to this be added, the body will be in a state to
move with any additional force with the same effect
as if it had no friction. Let this additional force be
SOOlbs. The whole weight being 40 tons, or 89,6001bs.,
the accelerating force will be to that of the force of
gravity as 500 to 89,600, or ^^=about -j^ijth that of
gravity. Now by gravity a heavy body falls through
a space ofl6rz feet in a second, and at the end of
tiiat time it will have attained a velocity equal to
double that space, or 32 feet per second. It is shown
by writers on mechanics, that the velocity is doubled
in 2 seconds, and trebled in 3, so that the velocity of
a falling body may always be known bj multiplying
32 by the time of its fall. But the force here stated
is only T+gth that of gravity: hence, if the velocity of
gravity be multiplied by tW» or divided by 179, the
quotient will be the velocity which the moving weight
vnll have acquired in the same time. Suppose we
wish the weight to acquire the velocity of 9 miles an
hour, or 13.2 feet per second, and it is required to
find ih6 time in which the weight with the nett force
of SOOlbs. will arrive at the above velocity. This will
be obtained by multiplying 179 by 13.2^ and dividing

18

179 X X3 2

the product by 32. Thus, ^ — =74 seconds, tfie

time required. To give this in words, as a general
proposition, multiply the whole weight to be moved
by the required velocity in feet, and divide the pro-
duct by 32 multiplied into the difference between the
friction and the moving force. This will give the
time required to gain the given velocity.

This rule applies only to a level plane. The force
which an inclined plane gives to a weight will be ob-
tained by multiplying the weight by the height of the
plane, and dividing the product by the length. This
force requires to be subtracted from the moving force
like the friction, when the weight ascends, and added
to it, when the weight descends.

Although a locomotive engine will move up a plane
a little more than Jth of an inch'*^ to a yard, it will be
found, in practice, very desirable to have the line
divided into dead levels and very short inclined planes,
if there is any difference of level between the two
places. The length of an inclined plane ought never
to be such as will prevent a person from seeing the
whole course of it from the top or bottom. As these
planes would require to have fixed engines on their
summits, it would be desirable to have as few as
possible. An apparatus may be connected with these
fixed engines, which will confine their office to the
difference of weight between the goods going different
ways. It will be evident, that the carriages going up
these planes will require to be drawn by a rope or

* When the weight upon an inclined plane becomes greater than the
friction, the wheels will turn, but no progress will be made. Agreeably
to the data given for friction, the inclination at which this will take
place is one-fifth of an inch to a yard.

19

chain,, and it would be found, as is at present the
case, that sometimes this rope breaks, and the car-
riages are precipitated and totally destroyed. Now
such an accident as this with passengers would be
fatal to the whole scheme.

Having given this subject some consideration, I
shall propose a means which perfectly obviates this
evil, and, what will still more recommend it, it will
be seep by every person that there is no danger.

The carriages and the engine, by this plan, vsrill
require to be propelled up or let down the plane,
the rope that comes from the fixed engine being at
the bottom of the plane. The hook being in the rear
of the whole and the rope under the carriages, I
would now fix this hook to a separate carriage, which
would be merely to propel them upwards. Between
every pair of bearers of the rail, which are about a
yard in length from each other, I would have pieces
of cast iron quite across the road, of sufficient strength
to resist the weight of all the carriages in the case of
the rope breaking. The hook at the end of the rope
should be fastened to one end of a bended lever
of the propelling carriage. When the whole is in
motion, the force of draught will act upon the bended
lever, and raise another part of the same above the
cross pieces of cast iron, and this will be kept in that
position by the tension of the rope. If now the rope
were to break, the end of the lever, which had been
kept up, will fall, and instantly butt against the cast
iron bar it last passed. Supposing the rope to break
immediately before it passes a bar, the weight can
never accelerate more than a yard, which would not
give a considerable shock ; at any rate, no danger
could be experienced, nor would any thing but the
rope be injured.

20

The propelling carriage here alladed to will have
to go in the rear of the carriages op the plane, and
in the front when they descend.

The fixed engines should be placed nnd^ the
road, as much short of the commencement of the
descent as will be equal to the space occupied by
the line of all the carriages.

When the locomotiTe engine, about to descend,
arrives at this station, the propelling carriage will,
have the hook of the fixed engine attached to it, and
by its 0¥m power go on with the rope and propelling
carriage. The. locomotive engine will continue to
work, till as many carriages are upon the inclined
plane as will drag the rest forward. At this period
the descending load will begin to n|ise a weight con-
nected with the other end of the rope, which will jnst
allow the weight on the plane to descend with a <
proper and uniform velocity. If the locomotive
engine works all the time, a greater weight will be
raised.

When the motion is the contrary way, and an
engine with its load comes to the foot of the plane»
the engine, in this direction, is supposed to propel
its load, and the propelling carriage is now brought
behind it The hook of the rope from the fixed
engine being attached, the whole goes up the plane,
and the weight, which was raised by the descending
load, now assists, or may be equal, to draw this load
up the plane. The locomotive engine may keep
working, if required.

The weights to be employed in raising the load,
or being raised themselves by the descending load,
may be so contrived as to admit of an exact adjust-
ment to suit the different loads, whether asc^iding or
descending.

21

By this means it will be clear, that the power
required by the fixed engines will be the excess
which the ascending load has above the descending,
and this can in general be known, very nearly, before
a rail-way is begun ; so that the power of the fixed
engine may be known beforehand. In a future work
on this subject, I shall give a more detailed descrip-
tion of the reciprocating plan, with proper drawings
for executing the work.

I hope by means of the tables, and the best descrip-
tion I have been able to give in this report, I have
rendered the principles of rail-ways as clear, as our
present experience will admit. I have avoided as
much as possible every thing technical, and have not
as yet used any jalgebraic formulae. As, however, the
theory of this important subject cannot be completely
demonstrated and made general without these for-
mulae, for the sake of those skilled in the application
of algebra to mechanics I shall subjoin the algebraic
investigations, which have led to the deductions given
in the former part of this report.

Each of the quantities, which will enter into this
investigation, will be represented by appropriate let-
ters. Let

IF:zThe whole weight in pounds to be moved, including the
carriages.

Ill := The force, also in pounds, applied to noiove the weight
vzzThe velocity in feet per second with which IF is to be

moved when at its full speed.
t^The time required for the weight W to get the velocity v.
aizThe area of the steam cylinders.
/=The length of the stroke.
N^fhe number of strokes per minute.

22

l^The diameler of the wheels of the engine which roll upon
the rails.

J'^The amount of friction of IT in pounds, which is equal to
the force that will keep it in motion with the velocity «.

JSr=:The height of the plane, which, for the sake of simplicity,
we will call i.

Xi=:The length of the plane, which, in all rail-ways, should
never be less than 360 times the height,

puzThe pressure upon a square inch of the piston, and
ap=the whole pressure on both pistons.

/*= 3.1416, the circumference of a circle, the diameter of
which is 1.

gz^lS^ feet, being the space a heavy body falls through by
gravity, in one second.
Hence

l>/=bThe circumference of the wheel.
DJk^^The number of feet per minute, and

60

Since the engine makes a doable stroke for one
revolution of the wheel, the speed of the piston to
that of the carriage will be as 2 / to Df; hence, the
moving force will require to be greater in liie ratio of

If the crank of the engine turned the wheel

upon a fixed centre, the inean effect of the same, as

a lever, would be about , .6 being the mean of

all the sines in the quadrant. Since, however, the
centre is moveable, and the fulcrum of the lever at the
ground, it becomes similar to a pulley, in which the
weight is to the power as 2 to 1. The power of this

lever will, therefore, be doubled, and -^-must be

23

added to,^ ; hence we have ^ .6 =(D + I) '3.

21

This, compounded with the. quantity gives

' ^JDf ^ ^ multiplier of the- moving force

to give the' velocity ; but this has also to be multiplied

by the velocity which gravity would give, in order to get

the velocity of the moving weight For the sake of

getting the time in which this velocity is acquired;'we

will express the velocity which gravity would* give in

the time by 2 gt Hence we have for the multiplier of

. + .6 X 2 gtl (1> .2grt

the moving f6rce — ^ sr— — ^ — ^—

Now m is stated to be the moving force to give the
velocity v in the time ^ if the body had no friction, and
supposing it to move on a level plane, such as the
hypothetical plane we imagined to go round the
world. But I have also given a quantity for that,
and must prbVide an additionid moving' fbrce just
equal to it. For the sake of simplicity, JP may be
used for that force. The true^ moving force, on a
level plane, will be m — JF, and the accelerating force

"j^ Now, 2 gt is the velocity which gravity

would give to a heavy body in the time t; hence v =
^^^2 gt. In the application of steam power the

true value of v will be

1st, v-y ^ ^

w— g _ v D f „ W vDf

W - (D + 01 .3 gtl "^-^ -(!>• + 01 .2 gtl.

24

WvDf

2d, m=. 4- F

1 .2 (1> + /) Sf«
OH ^i7-_ a -2 (D 4- /) g^O JF )

In order to make these theorems universal, when
the plane is, or is not level, vre must use the quantity

-J-- with a plus or minus sign as the load ascends or

descends. The theorem will then stand thus :

6th, m— F

vDf

iD+l)l'2gtl - L
Id order to find t, from theorem 4th, we have

1-2 gtl) ^^_q:___J= vLf

W^L W
7th. «^

— T I

|(2>+/)l-2 g/

If the plane be level, then H=o^ and in this case
^ vanishes.

In beginning to calculate the size of the engine to
convey a given weight TT on a rail-way, the rate, or

25

speed, is the first thing to be fixed, which is t;. Then
the number of strokes per minute, or n, which should
not exceed dO« Then find the diameter of the wheels,
which will be got by the following reasoning: Since
Df is equal to the circumference, nDf vfill be the
space the engine passes over in 1 minute, therefore

^^v, and consequently D =^^- Th© length of

the stroke should not exceed 2 feet. Since then n
and / are constant, the only way in which diffierent
effiects can be produced is in the alteration of a
and p, and as it will never be advisable to let p
much exceed 151bs., this will also be limited, and a
must be so taken as to accord with the above limita-
tions. It will also be advisable not to allow D to be
more than 5' or 6 feet.

In order to find the area of the cylinders, it will be
remembered, that nt, being the nett moving force
under the piston, will be equal to the area into the
pressure upon an inch, or op. If this be substituted
for m theorem 5th, we get

^ \{P+l) l-2gtt) - L f"^^'

when w=o, pa^F±i

Li

and p=-

* If p be in ponndi on an inch, a will be in inches, and for two
cylinders must be taken as eqoal to double the area of one piston.

26

When B=o, p=— and if a force equal to F±—-=r-

were to be in equilibrio with p, and act at the
paiiph^y of the wheel, when v=o,

P==*(f± a{^^lj ^^^^ *® engine moves

F±HW

uniformly with p= — the same as if at rest,

a

and in equilibrio with Ihe resisting forces, supposing
the friction not to increase with, the velocity^

Upon the whole, the advantages of a rail-road^ on
wJUcIl the locomotive power is used, are so striking
that it is matter of surprise this mode of conveyance
has not been resorted to earlier. Its adoption, how-
ever, is now inevitable; and, when applied in proper
places, and under judicious management, cannot Ml
of becoming highly beneficial, to the propiictots and'
to. the. public. But noticing can be mora^ delusive
than to suppose, that because rail-roads: are in prin^
ciple better than canals, or high jroads, they ,^ill an-
swer everywhere ; and yet the: e^dting rage for them
would seem to justify such an opinion. The preten-
sions held put by some of the projectors in various
places, do appear to me unwarranted, either by facts
or theory ; and I have no doubt, but that when the
public mind becomes more sober on the subject, the
real importance of the rail-road system, great as it
undoubtedly is, will be more correctly estimated.

* If the fall effect of these levers were to be in operation at the
same time, this denominator would be "^itLbut since the cranks are
at right angles to each other, the latter will require to be multiplied
by . 6, wfaichiwillifive .S(I>xO.

27

This new application of locomotive power is of in-
finite importance to the country, and I should regret
to see it abused.

P.S. Since commencing this report, these principles
have been given in the newspaper called the Scotsman.
The author speaks of it as a new idea, at least as it
applies to rail-ways, although it is founded upon the
facts given very long ago by Coulomb and Vince.

Whatever may be the claim to originality in this
application, I have at least an equal claim with this
author, as my introduction, which developes these
principles, was read by several of my friends here,
before the above articles were niade public.

TABLE I.

1

tiitjn

luMmittiHl,

i'

iai]iti>uv ^ r.kLe
or aloe miitM

JlipMUbdll.

LlicUBCd ptUHB
of t^lfllbafm

Unflne force
b> ptMfidt.

f-

Harltif fbrce '
Aawn the

8

MavtnffJtoreti
In pfflBfld^

Engirtfi . .
Waggon < .

17,020

230.81
110

50
S3J

100

130,81
100

380.Bt
130»1

380.81
1S0.T ■

Togethfir i.

HOJl

19U

499,31

417JI

iG4tll

With 2 ^aggDOE

35(000

440^1

07*4

200

030,81

553,41

T4SJQL

s •««•

181.1

2iS0

j 8tO401

<WpT1.

SlliJl

4 ■ f

59,080

070.81

144.8

300

070-81

S20.0i

11 15 OL

5 - « ■ >

7S0.BI

ICS, 5

1 130.81

t^02 3 1

- wm*

G{>,lGi>

890 51

102^^

1 *Hin k. 1

1 Aim at

UQft At

T « • * *

T7,T0a

1000 Jl

» ^10,9

1 J£.ilV HI

Iwliilf 1

Ilk* J at

80310

iii0Ji

209^0

0041

1171.01

i8M4l

9 * • * *

£)1,780

loi^ao

1220 81

263.3

ITTU.Dl

2034.11

10

1010^1

000

1Q0O«91

1643.81

WfM

11

lll^BfiO

1440 81

310.T

050

yoyo. 81

1780.11

2401 .51

12 . . . <

120,4UO

1550 81

334,4

700

2250,81

1016.41

2585.21

128,0 JO

1560.81

3SS.1

750

iG410.81

2052 .7 1

2708.91

137|460

1770.81

SB LB

809

8070.81

S189.01

0900.01

iQ « • « ■

)4d|010

l^BOuOl

40fi J

6fi0

2730.81

232&.31

1110*11

10 ■

164,580

1090.61

499.8

909

9890.81

»61.61

0190.01

It . p » ^

1 60,104^

2100,81

433.9

950

1930.81

959r.91

1300.71

IB i i . *

171,f>i0

2210, Bl

4Te.6

1000

331081

2734,21

308T.41

19 ....

2320.81

500.:}

1050

S37Q81 1 2870.51

387 L 11

'W^ k * • .

lg8,7»0

i 24S0.BI

6t4

noo

mo^i

3000^81

405481

it p..k

4imJl

22

-71.4

1200

3B50.B1

3270.41

4422.91

'IK ««<i*

1000

40I0;0I

0410^1

4090#t

•

1100

4lf0JI

0i«Mi

B

DESCRIPTION OF TABLE I.

Coluim

1 oontains the engine and number of carriages.

2, the weights to be moved at die rate of 9 miles an how.

3, the moving force to be applied, capable of giving that

velocity, in addition to that force which just over-
comes the friction. This is expressed by vDfW
^ , (D+l)1.2gtl.

4, the force which the weight W would exert down a plane,

the length of which, X, is equal to 360, when the
height IT is equal to 1 or ^^th of an inch to a yard-
SW

It is expressed by — J- . This force would, of coarse,
be nothing on a level plane.

5, Hie moving force in pounds equal to the friction, repre-

sented by F.

6, the moving force including that to overcome the friction,

being the sum of column 3 and 5, or the force required
on a level plane to generate a velocity of 9 miles an
hour, by keepingthe force in action one mmute. When
this velocity is attained, all the force in the 3d column
4nay be withdrawn, leaving that in the 5th column
which will be sufficient to keep up the velocity required*

7, the moving force required, when the weight goes down

the plane, to give the required velocity in one minute.
This will be found equal to the difference between
columns 4 and 5 added to column 3. After this
velocity is acquired, the last force may be withdrawn,
leaving the difference between columns 4 and 5. to
maintain the velocity required.
-6, the force required to generate the above velocity in one
minute, up the plane, being the sum of columns 3, 4,
and 5* When the rate of 9 miles an hour is acquired,
the force of column 3 is withdrawn, leaving the other
two forces to keep up t|ie speed.

VALUE OF THE LETTERS IN THE TABLE.

ITaB Weight of the engineer 17»020lb.y also of the carriages,
each»i8540lb«

J'sFiictioii of the enginet^lOOlb., also of the carriages, each
±s50lb.

vssVelooity at the rate of 9 miles per hour, or 13'2 feet per
second.

Dss Diameter of the engine wheel asd'OS feet.
/=Length of the stroke=2 feet.
#±=Time, or 00 seconds.

/xsCircamference of a circle whose diameter is 1=8*1416;

therefore 2>f, the circumference of the engine wheel =s

15*8 feet.
J9r= Height of the plane=l to
X=Ito length 360«

^ssSpace which a body falls through in a seconds Id^ feet.

TABLE IL

Moving ForoeF to

)veroooM

Friction

In Pounds.

In No. of Horses.

1

2

3

4

6

6

7

8

9

10

In
Mitet

In
Feet
per

On
a

com moo

ROMl.

lb.

On

Rail,
way.

lb.

On
CanaL

lb.

On a

oonunoo
Road
and
Railway
for thar
weights.

Off a
Canal
for its
weight.

For a
common

Road
or
Railway

For
Canal.

Moving force
to produce the

Velocity
in one minute

on the
Common road
and Railway,
in Pounds.

9

8.93

3024

22400

44800

125

126

1

1

1 CO

t

4.i

19911

281.25

1.2

2.7

221

4

6.86

11200

500

' 1.48

6

253

6

7.33

• •

7168

781.25

1.87

11.7

285

6

8.8

4978

1125

.2.42

21.8

317

7

10.26

• •

3657

1531.25

3.27

40.1

349 ^

8

11.73

2800

2000

4.66

74.6

381

9

13.2

2212

2531.26

7.21

144.9

413

10

14.66

1792

3125

12.36

309.1

445

EXPLANATION OF TABLE IL

Column.

1 18 the velocity in miles per hour with which the load is
to moTe.

2, the same in feet per second.

3, the weight to be moved on a common road supposed

to be level.

4, the same on a level rail-way.

5, the weight which can be moved on a canal.

6, the moving force to move the respective weights on the

common road and rail-way.

'7, the moving force required to take its weight on a canal.

8y the same expressed in number of horses on a common
road and rail-way.

9y the same for the canal.
10, the moving force required to give the velocity on the
common road and rail-way in one minute. The same
may be expressed in pounds upon an inch^ by dividing
these numbers by the area of the steam cylinder.

•

APPENDIX.

As I have in this report recommended the locomotive steam-
^bgine^ as the most economical power, for every part of a
rail-way in which the rise is not more than 7^ inch to a yard*,
and since this engine must be so far of the high pressure kind,
as it is destitute of the means of condensing the steam by the
air pump and cold water in a condenser^ I have deemed it
useful to give a comparative statement of the merits and de-
merits of the high and low pressure engines. This will not
be with any idea of the latter ever being used on rail-ways,
but to show how far the high pressure engine is dangerous,
under what circumstances it has been so, and in what degree
it differs from the low pressure engine in point of economy.

The low pressure engine works with steam of a pressure
equal to 34 inches of mercury, or 17lbs. upon the inch, the
effective power being 20 inches of mercury, or lOlbs. upon
an inch of the piston. Of this 7lbs., about one is caused by
the imperfection, of the vacuum, which is generally 2 inches

* On examination of the plan and section of the intended rail-road
between Liverpool and Manchester, I find the greatest rise, and that in
only one instance, is not more than ^ part of an inch ; therefore, it i»
the most favourable which could well be constructed.

34

of mercury. The other six have to be divided between the
fiiction of the steam piston and that of the air pump. ~ The
area of the latter to that of the former is about 6 to 1, and
their diameters will be as 2*45 to 1, which is the ratio of their
friction. Hence, if the 6lbs. has to be divided between the
two, we get l*74lbs. upon an inch for the frictiofi of the ahr
pump and 4*26 for the steam piston. . Thus we allow for the
low pressure engine 7lbs. to an inch for the loss of power and
4*26lbs. for the high pressure. •

In the low pressure engine, we have, dierefore, steam of
17lbs. acting against a pressure of 1, which is the value of the
vacuum, and against 6lbs., the friction of the piston. In the
high pressure engine, we have to act against 15lbs., the pres-
sure of the atmosphere, and 4^26, the friction of the piston.
Hence, in order to have a nett pressure of lOlbs. upon an inch,
as in ihe low pressure engine, we shall require steam of ti
pressure equal to 15+4*26+10=:29'26; and if the steam, in
both cases, is lost, iheir relative economy, in the consumption
pf fuel, will be in the ratio of their quantities of steam, or as
17 to 29-2d, or 1 to 1-72,

As there will be a difference of about 20"* of temperature,
there will be a somewhat greater loss of heat radiation ia
the high pressure engine. This, it must be observed, is the
greatest difference, in point of economy, that can exist
between a high and low pressure engine, since they are sup-
posed of equal size and work with the same power.

If we weie now to double the power of these engines, by
doubling the area of the cyhnder of the low pressure engine,
and doubling the working pressure of die high pressure, the
first will now be 2(1+10)+6X ^/2z=30*46, and the second
will be 20+14+4*26=38'26. The ratio is now as 1 to 1*26.

If the area of the low pressure were trebled, then the num-
ber for this ratio would be 3X(l+10)+6x >/3=43-4, that
for the hi^ pressure 3X104-14+4*26.=i 48*26. Hence the

35

iratib in which the pressure of the st^km upon ike high
engme is 4B*24» and on tSie inch will be 4^ to 4&'1i6, or as
1 to I'll. The economy til the high pressure will still ap-
proach nearer to that of the low pressure by making the Area
of Hie latter 4 times, stHl keeping the pressure on an inch
the same, and increasing the high pressure in the same propor-
tion by increasing the pressure only, the cylinder and length
jbf stroke remaining the same. In this case, the number will
be for the low pressure 4(1 +10) +6 x >/4=66, and for life
high pressure 4x10 +15+4^26= 59*28, or as 1 to 1S[)58
nearly. In all these cases the temperature of the steam cyBn-
der win be the same in the loW pres^re elighie, not much
exceeding 212'', the temperature of ordinary steam; that of
the high pressure engine increasing with the pressure. In
the first case, they are as 217^ to 248". In the second, the
temperature of the high pressure cylinder will be 264% that
of low pressure remaining the same. In the third case, the
temperature will be 280^, and in the fourth it will be a few
degrees higher. This will cause an increased waste by ra-
diation, but if the boiler and cylinder be cased, this loss may,
hi a great measure, be prevented ; and in the last case, the
high pressure engine comes very near the low pressure in
point of economy*

In this comparison of the high pressure engine with the low
Pressure, we have seen, that the economy increases with the
pressure of the latter; but it must also be remembered, that
the whole of the steam is consumed. This must necessarily
be the case in the mode of condensing the steam in low pres-
sure, but it need not be the case in . that of the high pressure
engine. Instead of discharging the steam into the open air,
as is the common practice, it may be discharged into a large
Tetsei, placed in the front of the enghe, with a view to give it
^e best chance of being cooled by the surrounding air. This
I should make of plate-^iron, about 4lb8. to the square fbot.

36

Its diameter might be three feet^ and its height a litde less
than the smoke chimney, which would be about 15 or 16 feet.
The capacity of this vessel would, therefore, be about .112
cubic feet, and its surface 144 feet. If, in throwing all the
steam into this cavity, its temperature should be kept up to
ISO**, which, I think, would be the maximum in the warmest
weather, the pressure in the interior would be equal to TJlbs.
upon an inch, supposing the vessel to be made perfectly air-
tight, and provided at the top with a valve opening outwards,
which would let steam or air out when the pressure was out*
ward, and preserve the rarification, when *the pressure was
inward. This vessel would have to be made with great care,
to be sufficiently air-tight. In the examples given, the high
pressure steam has 15lbs. upon an inch of reaction. In the
use of the condenser, in its perfect state, all the water would
be 'returned to the boiler, with the exception of what escaped
by accidental imperfection in the apparatus, and the strength
of the steam employed would be reduced T^lbs. upon an
inch.

The comparison of the high pressure engine, under tiiis im-
provement, with the low pressure, would be as follows : In
the first case, when the engines are of the same size, we have,
as before, for the low pressure 10+1+6=17, and for ibe
high pressure 10+7'6+4*26=21*76. If, as before, we
double the area of the low pressure and the pressure of the
other, we get 2(10+i)+6 x >/2=3b.^ for the low, and
2+10+7-6+4-26=31.76. We here see that with this addi-
tional vessel, when the pressure of the high pressure boiler is
not more than 31*76lbs. upon the inch, the economy of the
two is nearly equal, and very nearly all the water will be
saved. To provide, however, for the littie that may be lost,
there may be that quantity put into the vessel when starting,
and die bottom of this large vessel being connected with the
small pump for supplying the boiler, the same will be mixed