Library of
Emory University
8962?
J UN 3 1936'
SYLLABUS
OF
ICwtittM m Citiil €tigiiwri%
IN THE!
UNIYERSIlfj^ GEORGIA.
BY CHARLES P. McOAY,
Pxot of Mathematics ait ^ Civil Engineering.
SUljttts, <S"X.
CHRISTY & KELSEA.
18^3.
ERRATA.
Page 4, line 34, for England had 10000, read England had 30000,
11,
29, " less,
" loss.
14,
9, « 4 to 3,
" 3 to 4.
17,
89, « (H: S-f)
" (H-fS-/).
29,
3d, "21s,
" 2£2.
29,
SB, "
a i
7 3 0*
36,
14, after per ton,
add per hundred miles.
37,
3, " 50cts,
" per ton.
41,
1, for feet,
read inches.
44,
37, «iaoo7,
" 13006.
45,
1, " 8118,
« 9118.
54,
8, " any,
" an.
60,
36, after friction,
add for.
61,
4, " tolls,
" estimating the cost of
a horse at 50cts per day.
61,
10, " profitable, *
u in the South.
68,
5, " Oglethorpe,
" Columbus.
73,
16, " track,
" of the curves.
80,
14, for only double,
read equal to.
80,
25, " dense,
" close.
104,
33, after parallel,
add and equal.
108,
24, for line,
read sine.
109,
15, " ,3
3
1 0'
109,
16, " 916.5,
" 916.6.
HI,
19, " 16 DB,
" 16/BD.
111,
28, " treverse,
" reverse.
112,
7, « led,
" led2.
112,
29, " 43',
« 45'.
112,
32, " 200£,
" 202%,
112,
37, " xj-q,
•s x-\-a.
113,
8, " ln2c,
" lx "c.
118,
< 26, « 30
" 30o
LECTURE I
INTRODUCTION.
1. The duties of the Civil Engineer are numerous and
important.
Along the sea, he builds sea-walls to protect the shore
from being worn away by the waves: dry docks and float¬
ing docks, to receive ships for examination and repairs;
light-houses, where they are exposed to the violence of the
ocean; and break-waters, to form an artificial harbor in
which ships may ride in safety, when a storm is raging
without.
Along rivers, he constructs bridges of wood, stone or irony
when the stream is wide and. the piers exposed to uncom¬
mon injuries ; aqueducts, where a large channel of water is
to be conducted over a valley or a river ; locks, or chambers
into which loaded boats are to be floated and raised or low¬
ered from one level to another ; and dams, where the stream
is wide, or deep, or rapid, or the structure exposed to damage
from violent floods, or large masses of floating ice.
On land, he digs tunnels through hills or mountains, he
sinks Artesian wells one or two thousand feet deep, and
builds those massive machines or structures which require
great strength and superior mechanical skill in their con¬
struction.
He lays out common roads, turn-pikes, plank-roads, and
railways, and prepares them for the transportation of mer¬
chandise ; removes the obstructions from rivers, deepens
their channels, and makes them navigable in one or both
directions; and digs canals or artificial channels in which
boats or ships may be transported from one place to another.
In all these works, he selects the materials, as to their kind,
quality, cost, and amount; measures the earth-work, timber,
masonry, and carpentry; decides when all is done in a work>"
I
%
manlike maimer ; and superintends every operation, from the
first breaking of the ground to the final completion of the
work, so as to be respons:bie for the manner in which the
whole is executed.
2. To perform these duties properly requires a thorough
knowledge oj science.
To lay out his roads and canals, he must be acquainted
with Geometry, Surveying, and Levelling; to measure his
materials and work, he must understand Mensuration; and
in finding the solidity and areas of irregular figures, in dis¬
cussing the chain-curve for suspension bridges, in determin¬
ing the forms of arches, the principles of Algebra and the
Calculus will be necessary.
To lay out his railways and canals with proper skill, he
must be familiar with the laws of the inclined plane and of
water, of inertia gravity and friction, and of momentum
velocity and force. In all his structures he must under¬
stand the composition and resolution of forces, and the in¬
fluence of form, length, depth and breadth on the strength
of materials. The principles of the mechanical powers,
and in fact, every department of mechanics and hydrostat¬
ics will be of advantage to him.
In his tunnels and excavations, a knowledge of Geology
will be useful; in his selection of materials, Mineralogy,
Chemistry an Botany will be of service ; and in determin¬
ing the style and character of his work and in arranging
the tariff of tolls, the principles of Political Economy will
furnish assistance.
3. In all these sciences his knowledge must not only be
theoretical but practical.
In his mathematical calculations, he will often use ap¬
proximate methods instead of the more laborious but exact
rules of the science. He must make the usual deductions
and allowances, which can only be learned from the local
or general custom s of the trades. In natural philosophy the
laws of the lever and inclined plane, are commonly studied
without reference to friction and other resistances; but in
practice these things must be considered, as they seriously
"3
affect the results. The strength and elasticity of materials,
$heir cost and durability, their suitableness for a particular
work, the injuries to which they are exposed from violent
blows, from continued wear and tear, from the action of air,
rain, resistance, heat, frost, earth and water, can only be
learned in the school of experience.
4. Of these duties, the subject of Roads and Canals
<ind the improvement of rivers are selected for our study.
Because all would occupy more time than we can spare,
because thes<> subjects are more likely to be useful to all of
us, are closely connected with our College studies, and can
be pursued without models and without an ocular inspec¬
tion of the works that have been constructed.
5. This subject claims your interest and attention, be¬
cause of the utility of good roads.
Good roads are useful, because the diversity of soil and
climate in different parts of the world enable the agricultu¬
rist to produce an article at much less cost snd labor at one
place than another, and good roads enable the consumer to
obtain this product at a slight addition to the cost of pro¬
duction at the cheapest place.
Again, mines of coal, iron, lead, copper, salt, and other
articles are found only in particular places, and the price to
the consumer being dependent on the cost of mining and
of transportation, good roads, by lessening this last element
of cost reduce the charge to the consumer.
This same advantage is felt, when extensive water power
or cheap fuel at one place enables a manufacturer to produce
an article at a low cost ; or when all the elements necessary
to a particular production are found in juxtaposition ; as
when the iron ore, the limestone, the fuel and the water
power, needed in the manufacture of iron, are all found in
close proximity.
Besides, good roads are necessary to a proprer division of
labor. This division cheapens very much the cost of arti¬
cles, but in order to effect it, an extensive production is ne¬
cessary. As these numerous products cannot be consumed
in the immediate vicinity, they must be transported to a dis-
4
•iance, and without good roads to lessen the cost of carnage.;,
the advantages of the division of labor would be lost.
Good roads increase very much the value of land, by
bringing, as it were, the most distant places near to market.
A valley of the richest land two or three hundred miles
from a market is almost worthless without good roads, but
the opening of a railway might make this land worth
twenty or thirty, or perhaps fifty dollars per acre. This is
especially true when the product is heavy in proportion to
its value, as corn or oats, or even wheat.
The benefits of good roads are felt, both by the producer
and the consumer, by the farmer and the resident of the
city. The former buys his salt, iron, coffee and sugar
cheaper than before, and sells his cotton, tobacco, corn and
wheat for a higher price. The latter enlarges his commer¬
cial transactions oil account of the increased demand at
lower prices, and supplies his table with the products of the
country at cheaper rates. The saving in transportation is
thus divided by both parties.
Improved roads not only cheapen products, but save the
time of the man of business ; increase the safety and comfort
of travellers, and enlarge their number; and by facilitating
commerce and social intercourse, add to the civilization
refinement and happiness of society.
6. This subject farther claims attention, because of the
magnitude and importance of these Internal Improvements
in our own and other countries.
In the United States, besides the sums expended on com¬
mon roads, not less than eight hundred millions of dollars
have been expended on our canals and slack-water naviga-
, tion, turnpikes, and railroads. At the beginning of 1853,
we had 4000 miles of canals, 1000 miles of slack-water
navigation, 10000 miles of turnpike roads, and 13000
miles of railways. England had ^0000 miles of turnpikes,
3000 of canals, and 7000 of railways. These have cost her
eighteen hundred millions of dollars. On the continent of
Europe, there are 9000 miles of railways, which have cost
seven hundred millions. Nearly all these railroads have
'♦been built since 1830, and the progress, which they are
^everywhere making, warrants lis in expecting that in less
than ten years the number of miles will be doubled. An
interest so immense, controlled and managed by science,
is worthy of our attention and study.
7. This subject farther claims attention, because most
of our State Governments are interested in these Improve¬
ments.
Many political questions necessarily arise on account of
this interest. The propriety of beginning new works, of
disposing of those already built, of aiding and encouraging
others by subscriptions to the stock, or endorsements of the
bonds, by loans, gifts, charters, privileges, freedom from
taxation, must often be discussed ; and in our republican
country all of us may be called on to give our vote in the
decision of these questions.
8. This subject is well suited for college study, since it
smites mental improvement with practical utility.
The main object of education is, indeed, to develope ii}
full and perfect proportion, all the powers of the mind ; to
improve the memory; to cultivate the imagination; to
strengthen the reasoniug powers ; to accustom the intellect
to all kinds of exercise, both in the regions of probable and
demonstrative evidence ; to form habits of attention, dis¬
crimination, acuteness and accuracy ; to awaken the love of^
truth, of science and of nature ; and to make us acquainted
with the profound wisdom every where displayed in the
Avorks of creation, But, if while cultivating the mental
faculties, the useful and practical can also be pursued, they
should not be neglected. The study of Civil Engineering
combines both these objects. While we shall at all times
attend to the proof of the propositions advanced, we shall
be learning truths that will be of use to us in after life ; so
•that while the intellect is exercised, the mind will be stored
with useful knowledge.
6
L E C T IT R E II.
GRAYITY.
9. The object of the Engineer, in constructing his roads
and canals, is to reduce the resistances in Transportation, to
accommodate these to the powers at his command. and to
effect these objects in as cheap and durable a manner as
possible. %
Some of these resistances can be lessened, as friction,
obstacles, air, and water; some cannot, as gravity and iner¬
tia, Some can be reduced considerably at a slight expense.
Some almost annihilated, but at a great sacrifice of time and
money. Some can be so divided and distributed that only
a small portion is to be overcome at each instant. And the
object of the Engineer is to reduce and adjust the magni¬
tude of each resistance, that at every instant it may be
so suited to the power he is using, that the whole resistance
may be overcome, to the greatest advantage and at the small¬
est expense.
10. The powers of the Engineer are steam, the force of
animals, gravity and water-power. The resistances are
gravity, friction, obstacles, inertia, air and water.
Some of these are included under both beads; as gravity
on a descending river or on an inclined plane is at one time a
power and at another a resistance. Water-power derives its
energy from gravity, but jft'srilf be best to treat it separately.
11. These powers and%Resistances are all measured by
a common standard, and this is the momentum of a given
weight raised vertically with a given velocity.
Unless all are measured by a common standard, it is im¬
possible to compare them one^vith another, to estimate their
joint effect when acting together or opposing each other,
and. to adapt the resistance to the powers employed in over¬
coming them.
*,
7
There are two measures of force, one the distance it moves
a body in the unit of time, and the other the momentum it
gives. When the earth draws the moon a certain distance
towards it, sometimes the space is regarded as the measure
of the earth's influence, and sometimes the product, of the
space into the mass of the moon. The former is sometimes
called acting force, the latter moving force. It is this last
that we shall reckon as power or as force in Engineering.
Oar force is a momentum, a product arising from multiply¬
ing a weight into its velocity.
A road or canal is made for transportation ; a weight is
to be moved from one place to another; and the resistance
to be considered, and the force to overcome that resistance
is always a momentum. When a wagon is drawn by a
horse on a level or on an inclined plane, we may imagine
the wagon to be removed, and a rope attached to the horse
and extended horizontally over a pulley, and a v f ight of
such a size fastened to the rope, that the horse must exert
the same force to raise the weight as he did to pull the
wagon. Then not the weight, but the momentum of the
weight will measure the resistance caused by the wagon,
and also the force exerted by the horse. If a load of 1000
lbs. is moved at three miles per hour, and the effort of the
horse at A (fig. 1) is the same as if he were raising a weight
of 60 lbs. at C, attached to the rope ABO passing hori¬
zontally over a pulley at B, then the force, of the horse or
the resistance of the load is measured by 3 X 60 lbs. So
with the power of steam. The piston, moving under a
pressure on each inch of its surface, may be regarded as a
weight moving with a certain velocity, and its momentum,
is the measure of its power.,. So ".are all powers and all re-,
sistances regarded as equal .to the momentum of a weight,
moving vertically with some particular velocity.
By force then we understand moving force, or the pro¬
duct oltained by multiplying a weight into its velocity ;
,and we measure all powers and all resistances by this
standard. '
12. When a. leaded can is on an inclined plane, the ten-
3
dencij to descend, on account of gravity, is measured, by'
multiplying the weight into the height of the plane and
dividing by the length.
This may be proved by the resolution of forces. Thus,
if weight on the inclined plane AC, (fig. 2) be repre¬
sented by DE, and DE be resolved into the two weights,
DF and DG, one along AC and the other perpendicular
to AC, DF measures the whole tendency to descend. And
by similar triangles ABC and DEF
AC:CB::DE:DF. or,
DF^whole weight DE X height CB and divided by length
AC or=WH4-L,4 if W H and L represent the weight and
the height and the length of the plane.
Again, this may be proved by experiment; if a set of
wheels weighing W rest on AC, and be sustained by a
weight P suspended from a string passing over a pulley at
C and fastened to the wheels, it is found by experiment that-
P-WH+L,
13. The moving force required to drav) a body on an
inclined plane is the product of WH^r L into V, if V re¬
present the velocity at which the body is moved.
For in the experiment just referred to, P will not only
balance WH-* L at rest, but will keep it moving uniformly if
in motion. Now the momentum of P is PV, which is equal
to WHV4- L. The momentum of P is its power or moving
force. Therefore, the moving force required to draw W on
the inclined plane with a velocity of V is WHYt L.
14. The force required to move a load on an inclined
plane varies as the load, and as the velocity, and as the
height of the plane divided by the length.
This follows from the formula F=WHVt L. Withr
twice the load; or twice the velocity, or twice the rise in a
mile, the force required is doubled.
15. The whole work done hi any time is measured by'
the product of the moving force and the time during which
the force is exerted; that is, if T represent the time, the
work done is WVT.
Thus the work done by a horse drawing a weight out of
V)
a well by a rope attached, is the weight X its velocity X
the time the horse is at work. If the weight is 100 lbs.
and the velocity 3 feet per second, and the hq|se work 8
hours, the work done is 100X3X8X60X 60, or lOftlbs. raised
86400 feet. If 1200 lbs. is drawn up a hill rising one foot
in height to ten in length, with a velocity of two miles per
hour, and the horse works 7 hours, the work done is 1200
X/0X2X7 or 120 lbs. raised vertically 14 miles; because
the moving force is WHV r L or 12OOXi0X2, and the time
is 7 hours.
16. The work done in. drawing a body up the whole
length of an inclined plane is independent of the velocity.
If the velocity of the moving body is doubled, the mov¬
ing force must be doubled. But the time during which
that increased force must be exerted to carry the body to
the top of the plane must be halved, so that the product of
the moving force into the time is unchanged.
17. The work done in drawing a body up an inclined
plane is the same as in lifting it vertically through the
height of the 'plane.
Because the moving force required on the plane is
WHV 4- L and the whole work of drawing it up is
WHVT4-L, if T is the time. But VT—iL; therefore, by
substitution, the whole whole work is WHL^- L or WH.
Again, the moving force required to lift W vertically is
WV. The work done is WVT, if T is the time of lifting
it. But now VT=H ; hence, by substitution the work
done is WH, which is the same as on the inclined plane.
18. The moving force required to move a body over a
leBm.jplane. is nothing.
Bruise, the power is represented by WHY-f- L, and if
H is this product becomes zero.
19. "The moving force expended in transporting a body
between two points that are on the same level is zero, what¬
ever be the route between the points.
For if the route descends first and then rises afterwards,
as in (fig. 3,) the momentum generated in falling through AB
will carry the body up to C, if A ahd C are on the same level.
2
10
If the route rises first and then descends as 111 ADC, some
force must be exerted to raise the body up to D ; but in
descendiuggyihrough DC the final momentum acquired will
be sufficifsljifj, to raise the body as high as D ; so that the
force i*eta||fe|jkat C equals the force expended on AD, and
none is thjfprfore lost. In a similar manner this could be
proved, if The plane were undulating, rising and falling sev¬
eral times, as in AEFGC.
20. The whole work done in transporting a body, from
one point to another, whatever be the route, is the same as
if the body is lijted vertically through a space equal to'the
height of the second point above the first.
"For the whole work done in drawing a body up one
plane is (by 17) the samp as in lifting the body through its
height; and this is true for any number of planes. If some
of the planes descend, ^the momentnm gained in falling
down these will carry the body up the same height on the
next ascending plane, so that the excess'of the height of
the second plane above the first is all that is to be overcome.
21. The whole resistance offered by gravity between two
given points can in no way b& reduced or annihilated.
Whether the roufe be a regular ascent, long or short, un¬
dulating with slight ascents pr descents, rising or falling
suddenly and steeply, the resistance-is the same. No effort
of the Engineer can lessen or alter the whole force that
must be expended to transport a body between the two
points. But still, " ^
22. A good road'must avoid all steep ascents, so that the
motive power may produce the greatest useful effect.
For if the horse were loMed to his full average power on
the level, he would be either unable to draw his load up
the steep ascents, or he would be strained or injured by the
effort. If his load were limited to what he can draw on
the ascents, he is underworked on the level part of the^road,
and the time of the horse ;#nd of the attendants, $nd the
wear and tear of- the wagon and harness will be exp^gdsed
tobut little purposie. . l. .
. By making theorise at eacji moment small, and-, thus dis-?/
II
tributmg the whole force of gravity over a long space, the
total resistance to be overcome is not lessened•, but the
amount for each instant adds but a trifle to tMjfoction, so
that the joint effect of the two resistances :^^H| all the
while nearly the same, and the horse can dia|^^BIarly his
full load on the level.
So with the locomotive. Its efficiency wxQPe greater,
on a road with gentle ascents, than when the grade is steep
for a short distance and then level or undulating for the
greater portion of the way.
23. Steep ascents must be avoided for another reason.
The loss in ascending them cannot be balanced by the gain
in descending.
For if gravity be permitted to act on the descents with
its full force, the vehicle would move down with a danger¬
ous rapidity. As the brake must be applied on the railway,
and the horse compelled to hold back on the common road,
there is an expenditure of force, both in ascending and in
descending, making thus a double loss instead of a compen¬
sation for the first.
24. Undulating roads, where the ascents and descents
are not so great that the wagon or car would run down by
gravity alone, are nearly as good as level roads.
For none of the objections to steep ascents*apply to these
roads. A horse or a locomotive can do, without injury, a
little more work at one time than another; and they can do
this all day, about to the same advantage as if required to
exert a moderate uniform force for the whole time ; there
is no less of momentum 011 the descents; and the load can
be nearly as large as if the road were level.
25. A level road, whether for a horse or a locomotive, is
the best of all, and among undulating roads, the nearer
to being level the better.
The load may be greater on a level road than on any
other, and every increase in the ascent diminishes the
amount of the load.
When horses are used, their efficiency on undulating roads
is less than on a level, on account of the force required to
12
raise the horse's body up the ascents. It is easier for a
horse or a man to go down a slight declivity than to move
on a perfe||Mevel, but it is not much easier. Whereas to
ascend a^Hpivity is much more difficult than to go on a
level. in ascending is thus not made up by the
gain in .jj^^Hping. The two are balanced in a rolling
body, asfMMgon, but not with a walking one, as a man or
a horse.
It is sometimes said that a horse uses different muscles in
going up and going down hills, and thus the change is a
kind of rest to him. This can hardly apply when the road
merely undulates, so that he has to pull all the while. The
only change he then has, is between pulling much and
little. The same muscles are employed, the strain on them
being the only thing variable. And this gives no preference
to undulating roads over level ones.
LECTURE III.
FRICTION
26. The friction at the circumference of the wheel is va¬
riable and uncertain.
It is very large on soft muddy roadsfr especially when the
soil is stiff or tough. If the way. is dry and hard, this fric¬
tion is very slight. On good railways it is almost nothing.
Sometimes the rubbing of the flanges or guides on the
wheels, against the rails, may produce a large resistance on
railroads, especially on curves; but this is prevented or les¬
sened by giving a conical shape, to the wheels, the larger
diameter being on the inside next to the flange, so as td'turn
the train away from that side where the wheels are rubbing
cr about to rub against the rails.
\ 'A
This friction at the rim cannot well be reduced to any
laws worthy of our attention. ^Not so w^h frjfcion at the
axle. This resistance is important evervwhagj^Bkrl its laws
are well understood.
27. The friction at the axle increases
If a block be drawn on. a smooth'.level^^^^Bthe force
required to move this uniformly is found b^HRriment to
be doubled for double weights, and so on, increasing as the
weight. The friction, therefore, caused by the pressure of
the load on the axle increases as its weight.
Numerous experiments matfe by Viijce and Morin have
fully established this and the following law.
28. Friction is independent of the surface in contact.
If the same block is drawn on different faces, varying
very much in size, the resistance is found by experiment to
be the same. It follows from this, that the friction of a
ear is not affected by the number of the wheels. With
two, four, or eight, the rubbing surface at the axle varies,
but not the resistance. I>Nor is the friction dependent on
the length or breadth of the surface of contact between
the axle and the boxes the wheels.
29. The force required to overcome friction increases as
the radius of the axle and decreases as the radius of the
wheel. *
For the power to turn the wheel around may be regarded
as applied at the grotund .as at B (fig. 4) and pulling back¬
wards from B to A, ahd'the resistance as applid at C the cir-
A *
cumference of the axle. The arm or lever on which the
power acts is, theref^ft, BD,^while the arm on which the
resistance acts is CP. Now, according to the principles of
the lever, the long#f DC is, the greater is the efficiency of
the friction, that is «t'iie greater will be the difficulty of over¬
coming it; and the longer BD is, the easier will this resis¬
tance be overcome Hence the resistance, compared with a
fixed power applffed avaries as DC directly and BD in¬
versely, or as r4- R, if r and R represent the radii of the
axle and of the wheel.
This has also been proved by experiments made by
14
Tredgold. A siftall jvagop.. with two sets of wheels was
drawn fin Kilariisiat the same velocity, by weights attached
to a strijj^^KsifUg Ajet a pulley, and the weights were
found tq^^^^Rwself as tj^e radii of the wheels. In like
manner ^^^^^raperifftetft fried for different axles.
Again,^^Hwfents^mide by*Wood showed that with
the sameT^Jpmd loa$ thet distance gone over by a loco¬
motive first with 3 feet wheels aild then with 4 feet wheels
varied as 4 to 3. , /
♦
This result might have been-expected, for the rubbing
surface at the #xle£being supposed to be dragged through
the same space by the same expenditure of force, the dis¬
tance traversed by the rim of thie wheel would increase as
the size of the wheel. That is,'the effect increases as the
radius of the wheel. The s^me reasoning applied to the
axle would show that the effect isrinversely as its radius.
Hence the effect varies.as But the resistance is inverse¬
ly as the effect, hence the resistance varies as r-r R.
30. Although the u; he els shoitlWbe as large and the axles
as sm,all as possible, thefr §ize must be suited to the pur¬
poses for which they are used. • f
On a common road larger wheels are objectionable on ac¬
count of the difficulty of loading'%n^ of turning ; and be¬
cause of their increased weight and" cost; and on railroads,
because of the elevation of the centre of gravity. This
gives a lateral motion to the train,•arf&j^auses the flanges at
the rim of the wheels k't*f rub ^ainsftthe sides of the rails.
This friction is very large, because it acts so far from the
centre of motion, and because^ ij cam^l be lessened by the
use of oil or tallow. There is a limit also to the smallness
of the axles, as they must be large effcugh to sustain the
load. Iron is thus prefera^e to wooj£ for axles, because
they can then be made smaller. " ^ y
31. The resistance from. Jrictim, a/jj& the moving force
necessary to overcome it, increases^at each instant, with the
velocity.
The weight that draws a block forward on a plane with a
small velocity, is found by experiment to be able to keep it
r.->
in motion uniformly at nil velocities. iSow. the momen¬
tum or moving force of tiiis weight increases with the
velocity. Therefore, friction increases with tlm.-velocity.
The experiments made by Morin, to test ftps law, were
varied from the slowest perceptible motiorjjto to ten feet
per second. Jk.
32. The whole work done in a given diag^nce in over¬
coming friction is independent of the velocity.
For although the moving force to be exerted at each
instant increases with the velocity, yet the time during
which this force has to be exerted decreases in the same
ratio. So that the whole force expended in transporting a
body over, given space is the same whatever be the velocity.
33. The resistance offered by gravity and friction are in
many respects similar.
Both increase with the velocity at each instant of time,
both are independent of velocity for a given distance, both
increase with the weight of the load to be moved, both are
measured by a weight suspended by a string passing over a
pulley, and both are constant forces.
34. The amount of friction on common hard roads with
the usual wheels and unguents is about one twentieth of the
load, and on railroads about one two hundred and fortieth
of the load.
That is, on a common road, one pound hung by a rope
behind the vehicle, passing over a pulley, exerts the same
resistance as 20 placed on the wheels ; on a railroad the one
pound is equivalent to 240 on the wheels.
These numbers are not exact, but average amounts. On
a common road, friction may be as small as ^-0 sometimes.
On a railroad it ranges from 7 lbs. to 11 lbs per ton, that is
from 320 to 2J4 $ but it is usually about 2\0.
The reasons of this great difference are the smaller diame¬
ters of the axle of the car compared with the load, it being
of iron; the superior unguents used on railroads; the regu¬
larity with which these are supplied ; and the greater smooth¬
ness and hardness of the railway.
'i b
35. The simplest mode of determining the amount oj
friction is by a spring balance.
If a loade^ wagon or car is drawn forward by the inter¬
vention of a spring balance between the power and the
load, the pounds indicated by the balance become a measure
of the frictSlp, if the road is level. Thus, if the load
weighed 100* lbs. and the balance was drawn out 50 lbs.,
it is evident that if the load were removed and a weight of
50 lbs. attached to a string passing over a pulley and then
fastened to the balance by which the horse was pulling, the
weight would draw out the balance 50 lbs. So that the
weight 50 lbs. produces the same effect as the load, and
therefore, measures the friction of the 1000 lbs. In like
manner, if the cars on a level railroad were attached to the
locomotive by the intervention of a balance, the pounds
indicated by the balance would be the friction of the load.
Thus, if the load were 15 tons of 2000 lbs. each, and the
pounds shown by the balance 100, the friction would be 3J0
of the load.
If the load were drawn up an inclined plane, the pounds
shown by the balance would measure gravity plus friction,
and since gravity can be calclated by the formula the
remainder, which is the friction, will be known. Thus, if
a car weighs 20 tons of 2000 lbs., and the balance shows
450 lbs., when the plane rises 33 feet in a mile ; we must
subtract from the whole resistance which is 450 lbs., the
gravity which i£ 20x2000x33-f-5280 or 250 lbs., and the
remainder 200 lbs. is the friction. The fraction which this
is of the whole load is 2J0.
To get the momentum of this weight, which is the mov¬
ing force required to overcome friction, we must multiply
these pounds by the velocity of the load.
This method of obtaining the friction, though simple, is
not very exact, because the vehicle moves forward by irreg¬
ular jerks, the resistance being variable even on the smooth¬
est roads; and consequently the balance oscillates more or less.
The average will be nearly the true resistance but not exact'
ly. On a canal the results are more regular and reliable.
i <
36. A second method of obtaining the amount of fric¬
tion is by means of a plane so inclined that a body will re¬
main at rest or descend uniformly.
On such a plane the gravity is exactly balanced by the
friction, and since the former is known the latter is also.
Thus, on a common road, if a plane falls about one foot in
twenty of its length, it is found by experience, that a wagon
will descend without any exertion from the horse either to
hold back or pull forward. Hence friction is ^ of the load.
On a railway this plane is found to fall about 22 feet in a
mile. Friction is then wLd or 22 W~r 5280 or l-r-240th of
the load on a railroad. This method is not exact in prac-
ticej because it is difficult to determine when the body
moves uniformly.
37. A third method of obtaining the amount of friction
is by noting the space described in a given time by a car
descending an inclined plane from a state of rest.
By the laws of bodies moving under the influence of a
constant force, S=wFT2
where S is the space, m 16/2 feet, F the force and
T the time. Now, on a descending plane, the force is
gravity less friction; or if f be the friction, F=H-r-L-;/"
hence S=m (H~ h-f) T2 or S-r mT2=HJr L-f or f—
H -fL-S-r mT2.
As an example by this formula; in an experiment made
by Wood, the inclination of the plane was 1 yard in 104,
and the car descended 939 feet in 108 seconds; then f=io4-
939-r 16^X11664^,5^=^.
This method, though more exact than either of the two
preceding, is imperfect, from the difficulty of noting the
exact time of starting and stopping; and a slight error in
this becomes important, since T is squared.
38. A fourth method of obtaining the amount of jrictiont
is by having two planes meeting each other, one descending
and the other ascending, and noting how jar a body will rise
on the second after running down the first.
In this case, the square of the velocity at the bottom of
the first=4mFS=4m (H : S-f) 8=Am (H-jflS), if m, F, S,
3
is
/ and H represent 16,1, feetr the force, the space fallen
through, the friction, and the height, of the plane.
On a second plane, if we represent similar quantities by
the same letters accented, the square of the velocity with
which the body must be started at the bottom of the plane
is 4mF/S/ or 4m (H'-r-S'+/) S' or 4m (H'+S'/), the fric¬
tion / being the same as before, and now aiding gravity in¬
stead of retarding it, as it did in the descent. But these
two velocities are the same; therefore, 4m(H-/S)=
4m (HU-/S') or H~yB=H'+/S' or /=(H-H')-^(S + S').
This foraiula is very simple, easily employed, and gives
very exact results.
As an example, from Wood's experiments, a carriage
having run down a plane 1467 feet long, ascended an¬
other 1166 feet long, and the difference in the level of the two
points was 11.61 feet. Therefore /= 11.61-4- 2633=2|7.
A great number of experiments have been made in this
way, and the resul t of all is that friction oil a railway ranges,
as was said before, from 7 to 11 lbs. per ton, or on an aver-'
age it is about 2|0 of the weight or load.
39. The force necessary to overcome gravity and friction,
which are the principal resistances on railways and common
roads is (H^r L-\-f)WV.
Gravity is on both WVH 4-L and friction f on one is 2V
WV< ■ and on the other 2\0 WY. Example : On a common
ro&d, rising one foot in 12, the friction to be overcome with
a load .of <1200 lbs. is 60V. Gravity is HWY4 L or
1200V or 100V, and both==160V. That is, the resistance
is the same as if 160 lbs. were suspended by a string and
raised vertically with a velocity equal to V.
On a railroad rising 11 feet in a mile with a load of 120
tons of 2000 lbs. each, gravity is 120X2000XllV-r- 5280
or 500 V; friction is 120X2000V-f 240 or 1000V and both
=1500Y; that is, the resistance is the same as if 15001bs^
were raised vertically with a velocity—V.
19
LECTURE IV.
INERTIA, OBSTACLES AND THE RESIS¬
TANCE OF THE AIR.
40. Besides gravity and friction, there are three other re¬
sistances to be overcome both on a common road and on a
railway; these are inertia, obstacles and the resistance of
the air.
These five constitute the whole resistance to be overcome
when a body is moved from one place to another.
41. Inertia is only jelt as a resistance when the velocity
with which a body moves is changed.
If the body is at rest, inertia must be overcome to set it
in motion; if it is in motion, inertia must be overcome to
give it a higher or a lower velocity or to stop it entirely.
42. Inertia causes no loss of power when the vehicle is
stopped without the application of the brake or the holding
back of the horse.
The horse and the steam expended some of their force
in starting the body, and in giving it more and more veloci¬
ty ; but the momentum the body thus acquires will carry
it forward after the horse or steam has ceased to exert any
20
force, precisely as far as the power which gave the momen¬
tum would have done. Thus the power is only loaned,
not expended.
Whenever the horse holds back or the brake is applied to
the r,ti\ tr:en the inertia is taken away and lost. The loss
is iwo-fold, since force is exerted both to give and take
away momentum.
43. On a common road, the force required to overcome
inertia is small, and the force lost still less.
It is small because the load and the velocity are both
small. Thus, if a vehicle is to move at the rate of five
miles per hour, the inertia might be overcome by making it
fall down an inclined plane at starting. Now, on inclined
planes, V2==4mFS=4wiHS4-L==4wH, if L be taken equal
to S. But if V is 5 miles per hour or 5x52804-3600 or 7J
feet per second, H is (7|)2—4X 16/2 or .83 of a foot. That
is, the descent down an inclined plane whose height is.83
of a foot would overcome entirely the inertia of the body.
The horse must then expend the same force as would raise
the body through this height. Now, to raise a body a foot,
is the same as to draw it 20 feet forwards on a common
level road, overcoming friction only, since friction is ^W.
Therefore, the same force must be expended to give a
body a velocity of five miles an hour as to carry it on a
level through the space of 20X .83 or 16.6 feet.
When a vehicle is stopped it is always done gradually.
The friction, therefore, takes away a larger or smaller por¬
tion of the inertia. The part taken away by the horse,
which is all that is lost, is but a part of the whole. That
is, the force lost is but a part of the force required to draw
the body on a level through the distance of 16.6 feet.
44. On a railroad, the force and time required to over¬
come inertia are considerable, but the force lost is a small
fart of the whole amount expended, except for trains of high
velocities.
The load and velocity both being large, the inertia is
large. If the velocity were 10 miles an hour, the height H
through which the body must fall to acquire this velocity
21
is as before =V2-/-47W. But V is now 14| feet per second ;
therefore, H =3.33. Therefore, the force required to over¬
come inertia, is in this case, the same as is required to raise
the body through the height of 3i feet, or to move it on
a level the distance of 800 feet. Now, if one-half of this be
supposed to be lost by using the brake, and the train stop
every five miles, this loss requires that the force expended
should be sufficient to move the body 5 miles +400 feet,
instead of 5 miles; that is, the whole force required is in-,
creased the 66th part, the road being level.
But if the velocity is 30 miles and the stoppages occur
every 5 miles, either to get wood or water, or to take in or
put off passengers, or for other causes, then the H calculated
as before is a trifle more than 30 feet. And the distance,
which is equivalent to this • height is, if the road be level,
240x30 or 7200 feet, or more than a mile and a third. And
if one-half of the inertia is destroyed by the brake, the force
to be exerted will be the force necessary to carry the body 5
miles +3600 feet, instead of 5 miles ; that is, it is increased
about one-seventh.
45. The resistance from obstacles differs from both friction
and gravity.
It may arise, on a common road, from stones or other ob¬
structions ; and on a railway, from the unevenness of the
joints of the rails, or from the surface being covered with
sand, ashes, or dust of any kind.
46. If the obstacle yields, or is crushed, as the wheel rises
over it, the loss may be considerable.
On common roads, the sandy road is known to cause a
large resistance, although the sand yields before the wheel.
And, on railroads, it was found in an experiment of Tred-
gold, that the force required to draw a car was increased 19
per cent, when the rails were slightly covered with dust.
47. If the vehicle passes over the obstacle without a shock,
the resistance is insensible.
The body, in this case, may be regarded as moving on a
curve, in which it is known there is no loss of velocity from
the change of direction.
22
48. When the obstacle gives a shock to the vehicle, the injury
done is of various kinds.
It demands force to raise the body over the obstruction,
increases the friction, lessens the velocity, injures the
cars and locomotive, and gives a jolt to the train, which
is unpleasant to the passengers, and often injurious to the
freight.
49. There is no loss of power in lifting the vehicle over the
obstacle.
Force is required to raise the body, but it is fully returned
in the descent on the other side of the obstruction. The
power is therefore not expended or lost.
50. The force required to overcome the axle friction is increased in
the ratio of R-h to R.
The absolute resistance produced by the rubbing at the
axle is not increased, but the leverage by which it is over¬
come is lessened, so that greater force must be applied.
Thus (fig. 5). the axle friction is at A, and the radius of the
wheel CB is ordinarily the lever arm by which the friction
is overcome. But when the obstacle EF meets the wheel,
the lever arm is CD; the power required must therefore
increase, in the ratio of CD to CB, or as R-A to R, if R
represent the radius of the wheel and h the height of the
obstacle EF.
51. If the obstacle be large, the increase of force required is
considerable ; but usually it is slight and unimportant.
If h—R the Vehicle would be stopped entirely. If h=z
f R, the force would be increased four fold. But on a rail¬
way or a good common road, the obstacles being small
compared with the radius, and only increasing the friction
for an instant, the additional power demanded by the friction
is quite small.
52. The principal resistance from obstacles arises from the sud¬
den change of direction in the moving bodyy by which a part of
its velocity is lost.
If a body is moving forward in the line CG, and at C
is forced to move in the line CH, the velocity in the new
direction is less than before. If CG represent the former
Velocity and GH be drawn perpendicular to Ctl, the new
velocity will be CH. The former velocity is to the new as
radius to the cosine of the angle between the two direc¬
tions.
This loss of velocity occurs at every sudden change of
direction. A single obstacle may give many shocks and
therefore cause several successive losses. Almost always
there are two shocks, one at striking the obstacle and the
other at leaving it. If the motion between these is curvili¬
near, never changing its direction suddenly, these two are
the only losses.
52. The loss of velocity when a vehicle strikes an obstacle is
Vh^r-R.
The car or wagon is here supposed to have two wheels
and both to strike the obstacle. The centres of the wheels,
as at C (fig. 5) cease to move in the line CG, and begin to
move in CH, which is perpendicular to CE, since for a mo¬
ment E is the centre of motion about which C revolves.
The centre of gravity is all the while directly above the line
joining the centres of two wheels, and therefore changes its
direction exactly as the centres of the wheels change theirs.
Now the former velocity is to the new velocity as CG:CH
or as CE:CD or as CB:CD. Hence the former velocity is
to the loss of velocity as CB:CB-CD or as CB:BD, or
V: loss of velocity:or loss of velocity is=V^-i-R.
54. The loss of velocity increases as the velocity of the vehicle
ctnd the height of the obstacle directly, and as the radius of the
wheel inversely.
This follows from the formula, the loss equals V/i-r-R.
It is greater as the car moves more rapidly, or as it meets a
higher obstacle, or as the radius of the wheel is decreased.
55. If only one wheel strike the obstacle, the loss is only
IVh'r-K
For the centre of gravity is between the two wheels, and
is now only raised half as much as when both strike. The
change of direction, and therefore the loss is also halved.
56. If the vehicle have Jour wheels and only one strike the ob¬
stacle, the loss is only ^ Vh~\-R.
24
For the centre of gravity is halfway between the two
axles, and is raised only half as much as the middle of the
axle, that is half as much as in the preceding article.
57. When the wheels pass over the obstacle and strike the ground
again, the loss is usually the same as at meeting the obstacle.
For the shock and change of direction are usually the
same in both cases. On a railway, the loss at the joints of
the rails is not doubled, there being but one shock ; but it
is doubled when a pebble or other obstruction is on the rails,
58. The force lost is found by multiplying the load into the loss
of velocity.
Because force, being a momentum, is the product of a
weight into velocity.
59. On a railway, as the weight and velocity are large and the
joints of the rails numerous, their evenness is of great importance.
When the iron is first laid down5 the two contiguous rails
are easily placed in one plane ; but from the unequal settling
of the sills, and the lateral pressure of the flanges on the
wheels, the end of one rail is raised above the other, or
moved outward beyond it. The road then becomes rough
and uneven, and the loss from obstacles is large.
60. The use of good springs is of great importance in lessening
this resistance.
When the car or wagon meets an obstacle^ the loss is not
from lifting the load over the obstacle. It is from the shock,
or from the sudden change of direction. When springs are
used the wheels still receive the shockj but the load is raised
gradually and the loss is much lessened.
61. Besides the loss of power $ the jars and jolts do harm to the
cars and the locomotive, damage the freight, and came discomfort
to the passengers.
The wear and tear of locomotives is a larger item of ex¬
pense than the cost of fuel, and the jars at the joints are
the cause of a great part of this outlay. The difference in
comfort between a smooth and well-laid road and one with
the rails displaced is immense, but cannot be expressed by
numbers.
25
62. The resistance of the air on common roads is insen¬
sible.
This is true because of the low velocity and the small front
surface presented by a common vehicle.
63. On a railway theflange friction Gaused by a high side
wind is considerable.
The flange being so far from the centre of motion, and
being rough and unoiled, presents a large resistance when it
rubs against the rail.
64. The head resistance caused by the striking of a train
against the air increases as the surface and as the square of
the velocity.
This is shown in Nat. Philosophy to- be true of all bodies
moving through fluids of any kind.
65. When the train is moving twenty miles an hour, the
head resistance is equal to one pound on each foot of the front
surface.
Instead of regarding the cars as striking the air, we may
suppose them at rest, and the air rushing against them with
the velocity of the train. To estimate this elfect, suppose the
air to be contained in a tall close vessel, having an opening
of one foot square towards the car, and rushing out of this
opening against the car on account of the downward pres¬
sure of the air in the close vessel. The velocity with which
it will issue, will depend upon the height of the column of
air pressing downwards in the tube. And by the laws of
spouting fluids, the velocity would be the same as a heavy
body would acquire in falling through the height of the
vessel. And thus knowing the height of the vessel we
learn the velocity of the air; and conversely, if we know
the velocity, we learn the height of the column. Thus,
suppose the velocity to be 20 miles per hour, or 28-§ feet
per second, the space through which a body must fall to ac¬
quire this velocity, is 12.8 feet per second, since S=4^.
Hence a column of air 12.8 high may be regarded as press¬
ing against the car at a velocity of 28-f feet per second,
or 30 miles per hour. The weight of this is nearly one
3 .
26
pound, since at 60 degrees air is 815 times lighter than wa¬
ter, and 12.8 feet of water weigh 800 pounds.
A similar result may be obtained from Hutton's experi¬
ments on cannon balls. At a velocity of 900 feet per se¬
cond, the resistance of the air on a ball 2.78 inches in diam¬
eter was found to be 35.4 pounds. Now the front is 2.782 X
.7854 or 6 inches. Hence the resistance for a square foot is
24 x35.4 lbs.=849.6 lbs. For a velocity of 28-f feet
per second, the resistance is 849.6 X28§2-*-9002 or .931bs.
This result is a little less than the former, because the
rounded form of the ball somewhat lessens the resistance.
In both cases however, the result is very near one pound.
66. The head resistance of a railway train is sensible at
common velocities, and very great at high velocities.
A car has seldom less than 60 feet front surface, the re¬
sistance then at 20 miles per hour is 60 lbs. or the same as
if a weight of 60 lbs. was suspended by a rope passing over
a pulley, and fastened behind the car. This 60 lbs. would
be equivalent to 60 lbs. X 240=14400 lbs. placed upon the
wheels, since one pound hung behind the car is equal to 240
on the wheels on a level way. At 10 miles per hour this
additional load is 3600 lbs. At 100 miles it is 360000 lbs. or
180 tons. At this high velocity no common locomotive
could overcome the resistance of the air.
LECTURE V.
RESISTANCE OF WATER.
67. In water, as in air, the resistance is very nearly as
the surface, and as the square of the velocity.
This is true of all fluids, but in the case of water it has
been established by many experiments. The most satisfac-
27
tory of these were made by Col. Beaufoy of England, and
conducted as follows: A rope was attached to a body in
water, and passed horizontally under a pulley, and then ver¬
tically over a very high one, and then attached to a weight.
As this weight descended, it first moved the body in the
water slowly, and then more rapidly, until the increased re¬
sistance of the water balanced the moving force of the
weight and the motion became uniform. When this was
attained, the weight measured the resistance of the water at
the uniform velocity.
Thus to select two of his experiments, a weight of 12
lbs. and then of 48, was attached to the rope and gave the
following velocities to a boat in each successive second:
3.64 4.94 6.68 7.20 7.24 7.36 7.31 7.33
and 5.71 8.78 12.32 13.59 14.02 14.25 14.24 14.31.
The last three, when the motion was nearly uniform, show
that a quadruple weight was necessary to give double the
velocity, or that the weight increased as the square of the
velocity. And in like manner it was shown that this in¬
creased as the surface.
68. The force necessary to overcome the resistance, is as
the cube of the velocity.
For to give double the velocity, the momentum of the
moving weight was increased eight times, viz : 12 lbs. with
a veloqity of 7 feet in the first case, was increased to 48 lbs.
with a velocity of 14 feet per second. That is, it is in¬
creased as the cube of the velocity. And so for the other
velocities.
69. The work done in transporting a body a given dis¬
tance, increases as the square of the velocity„
For the force at each instant increases as the cube of the
velocity, and the time during which that force is exerted de¬
creases as the velocity; therefore the work done or FT
varies as V3-*-Y or as V2.
With double the velocity the quadruple weight went
twice as fast, but it moved only for half the time to trans¬
port the body a given distance. In the first experiment the
12 lbs. moving 21 feet in three seconds transported the body
28
21 feet. In the second, 48 lbs. moving 42 feet in three se¬
conds transported the body 42 feet. Thus eight times the
force doubled the work done, or four times the force did the
same work, when the velocity was doubled.
70 The resistance of a body moving through the water is
three-fold, the head resistance, the plus and minus pressure,
and the jriction of the whole surface.
The first is caused by striking against the particles of wa¬
ter ; the second by a greater pressure from the water in front
than at the stern, when the boat is in motion ; and the third
by the adhesion of the water to the body.
71. When the relocity is one mile per hour, the head resis
tance is about 2^ lbs. Jor each square foot, if the bow is a
plane perpendicular to the keel.
To determine this resistance, suppose the boat at rest and
the water moving against it. The water may be supposed
to be confined in a tall close vessel, having an opening to¬
wards the boat and rushing against it on account of the
downward pressure of the water in the close vessel. The
height of this water is found by means of the formula S=J„.
For one mile per hour, or 1 ^ feet per second, S=310 of a
foot, and ^-0 of a foot of water weighs 2l2 lbs. or nearly 2J.
For a velocity of two miles, this would give 81 lbs; for three
miles it would be 19^ lbs; for four miles it would be 341bs.
Beaufoy's experiments gave for these four velocities 2.19,
8.6, 19.2, and 34 lbs.
72. IJ the bow be sharpened, the head resistance decreases
nearly as the sine of the angle which the side of the vessel
makes with the keel of the boat.
This follows from the decomposition of forces. With a
bow of 15° and a velocity of five miles an hour, this would
give 53 J x sin. 15° or 13.74 lbs. For a bow of 10° it gives
9.20 lbs.
Beaufoy's experiments gave for these angles at this veloci¬
ty 13.26, and 9.21 lbs.
73. For sharp well shaped boats the head resistance is
about \ of a lb \ for blunt boats, it is about \ of a lb ; when
the velocity is one mile per hour.
29
The first corresponds to a sharpness of 9 or 10°, the second
to 14 or 15°. The first is the shape of ships and steam¬
boats, the second of canal boats.
74. The plus and minus pressure oj boats is about \ oj
the head resistance.
This is caused by the piling up of the water in front, and
the vacuum formed behind the boat.
In narrow canals this resistance is still greater, because
the water in front cannot readily get round the sides of the
boat.
75. The friction is about 1 lb. for every 150 feet of sur¬
face in contact with the water, when the velocity is one mile
per hour.
This is about the result of Beanfoy's experiments.
76. The resistance on a common canal boat at 2 J
miles per hour, is about 7|0 of the load.
In an experiment of Mr. Bevan on the Grand Junction
Canal, a weight of 77 lbs. produced a velocity of 21 miles per
hour, when the load was 21 tons, and the weight of the boat
9 tons. Here the resistance was 77 30 x 2240 or 853.—
The width of the Canal where this experiment was made
was 142 feet; and in a narrow canal 40 or 50 feet wide,
according to the experiments of Stephenson, the resistance
was about \ more, which would give 7^.
If \£e suppose a boat to be 70 feet long, 12 feet wide, and
sunk 2 feet in the water by its load, the weight of the
water displaced, that is, the weight of the boat and its load
will be 70 x 12 X 2 X 62£, or 105000 lbs.
The head resistance for a velocity of 2J miles per hour
will be 12 X 2 X \ X 2§2 or 75 lbs. The plus and minus pres¬
sure will be I of 75 lbs. or 15 lbs. The friction will be 16x
70x2J2 --- 150 or 46-f lbs. Hence the total resistance is
75+15+46f, or 136f lbs. and this is the 7J9 part of 105000
lbs. the whole load; so that the total resistance is nearly
27Q of the load.
77. On a canal the locks should be long, the canal wide
and deep.
When the locks are long, the boats may be made long,
30
and thus the head resistance for the same load is lessened-
When the canal is wide, the plus and minus pressure is de¬
creased. When the canal is deep, the friction will not in¬
crease as fast as the load, since if the load is doubled and
the boat thus sunk twice as deep in the water, the surface in
contact is but little increased.
78. High velocities in water can only be obtained by a
large expenditure of force.
At 2\ miles per hour the resistance is 7l0 of the load, or
one third of the amount on a rail-road. At 5 miles per hour
it is 7|# of the load, or one third more than it is on the rail¬
road. At 10 miles an hour it is $0 of the load, or more than
five times as much as on a rail-road. At 20 miles per hour
it is 7f20 of the load, or nearly twice as much as on a commoj^
hard road.
LECTURE VI.
POWERS.
79. The unit by which the Engineer measures his several
powers, is a horse-power, which is the momentum of 150 lbs.
raised vertically at the rate of 2 J miles per hour.
This is rather above the average power of a horse, but if
a strong horse be attached to a rope passing horizontally over
a pulley, to which 150 lbs. is suspended, as in a well, he will
be able to move at the rate of 2J miles per hour, and con¬
tinue that effort through the whole day. This horse-power
of the .Engineer is, however a fixed, invariable quantity, and
not dependant upon the power of a horse having average or
superior strength.
31
89. Other expressions for a horse-power are 375 lbs.
raised at the rate of one mile per hour, 33000 lbs. raised at
the rate of one foot per minute, and 528 ciiibc feet of water
raised one foot high per minute.
For the momentum of all of these weights is the same ;
thus 150x 2|=375 xl & 375x 5280-60=33000x 1 and
33.000-;- 62|=528.
A horse, by acting on a lever, or by a rope passing over
a wheel, can raise either of these weights 150, or 375, or
33000 lbs, but the velocity of the larger weights would be
so much diminished that their momentum would remain the
same.
81. For the horse-power required to transport a load on a
common road or a railroad, find the gravity by the formula
WHV+-L, and the friction which is equal to JVV-t-20,
or WV-i-240, and the sum of friction and gravity divided
by 375 will give the number of horse-power.
Example. If a load of 6000 lbs. be moved at the rate
of 2J miles per hour, on a firm hard road, rising 1 foot in
10, the horse-power required is 6; for the friction is 750 lbs.
and gravity is 1500 lbs. and their sum 2250 divided by 375
gives 6.
If the road were level, the horse-power required would
be 2.
If the road descended 1 foot in 40, the horse-power re¬
quired would be 1.
If the velocity had been 5 miles per hour in each of these
cases, the horse-power would be 12, 4, and 2.
On a railway rising 44 feet in a mile, if a gross load of 120
tons, of 2000 lbs. each, move at the rate of 10 miles per
hour, the horse-power required would be 80, for the friction
is 10000 lbs. and gravity is 20000 and their sum divided
by 375 will give 80.
If the road rise 22 feet in a mile the horse-power would
be 53i.
If the road were level the horse-power would be 26§.
82. On a canal the resistance at 2 J miles per hour is TV
■i-720 and this divided by 150 will give the horse-power.
32
If a load of 54 tons were drawn at 2|- miles per hour, the
horse-power required would be 1.
83. For the horse-power on a canal at any velocity, find
the resistance at that velocity and divide it by the horse-power
at that velocity.
Example. If a load of 36 tons be drawn at a velocity of
6 miles per hour, the horse-power required would be about
9. For the resistance at 2\ miles per hour, being W --720, it
would be, at 1 mile per hour, W-f- 720 X2J2, or W-r 4500; and
for six miles per hour it would be 36 W-^- 4500 or W-^ 125.
And a horse-power at 1 mile per hour being 375 lbs, it
would be 62 J lbs. at 6 miles per hour. Now in this example,
W being 36x 2000 lbs. the resistance, W-*125, is 576, and
576-f- 62J gives about 9.
If the velocity is 10 miles per hour the resistance would
be Wf 45, and a horse-power would be 37J, and the num¬
ber of horse-power required to move the load at this velocity
would be 42§.
The horse-power required to draw 120 tons on a level
hard common road, and on a common road rising one foot
in 20, and on a level rail-road, and on a rail-road rising 22 feet
in a mile, and on a canal, at velocities of 2J, 4, and 6 miles
per hour would be, for the first road 80,128, and 192; lor the
second, they would be 160, 256 and 384; and for the third
they would be 6|, 10|, and 16: for the fourth they would
be 13J 21 J, and 32: for the fifth they would be 22, about
9.1, and about 31.
84. For the horse-power of a steam engine, multiply to¬
gether the number of inches in the piston, the number oj
pounds pressing on each inch, and the number of jeet the
piston moves through in a minute, and divide the product
by 33000.
For the piston may be regarded as a weight equal to the
number of pounds pressing on its whole surface, and the
momentum of this weight, is the power of the engine.
If the steam be cut off before the piston makes its full
stroke, the average pressure for the whole stroke must be
taken.
33
Example. If a piston 10 inches in diameter, with a
pressure on it of 50 lbs. to the square inch, make 110 dou¬
ble strokes 2 feet long, per minute, its horse-power would
be 52.
For the area of the piston is 78 inches, the weight in mo¬
tion is 50x 78, or 3900 ; the velocity is 110X 4, or 440 feet
per minute ; the momentum is 3900X 440, and the horse¬
power is 3900 X440— 33000, or 52.
85. To find the force of a water-fall, multiply the weight of the
water passing in a minute, by the number of feet in the fall,
and divide by 33000.
Example. If a stream 20 feet wide and 1 foot deep,
should move at the rate of 3 feet per second, and have a fall
of 11 feet, it would have 75 horse-power.
For the weight of water passing over in a minute is
20>< 3>< 60x 62J, or 225000. Andthisx 11 -^33000 gives 75.
86. The velocity of the water issuing from the opening in a
flume, may be found by the formula, V2=4mS or Y=8vS.
Example. Suppose a flume to have an opening 16 feet
wide, 3 inches deep, and the middle of the opening to be 27
inches below the head of the water, and the fall to be 11
feet, the horse-power would be 60.
For S=27 inches, or 2J feet, and V—8 times the square
root of 2J, or 12 feet; the area of the opening is 16xJ or 4
feet; the quantity of water falling in a minute is 4>< 12 ><60
or 2880 feet; its weight is 2880x 62J or 180000 lbs; and
180000X 11-^-33000=60 horse-power.
The stream passing through the opening is smaller than
the opening itself, and a deduction of one-third should be
made from the amount of water delivered, for this cause.
87. The horse-power required for a saw-mill cutting
1000 feet of plank per day, is 3; for a grist mill running
one pair of stones, is 5 ; for a cotton mill, one for every
two hundred spindles, and one for every twelve looms.
These are the net amounts, after deduction is made for
the loss of power on the water wheels, and the friction of
the machinery.
4
34
LECTURE VII.
THE POWER OF THE HORSE.
88. The power of a horse of average strength, is 125 lbs.
raised vertically at the rate of 2 J miles per hour, and con¬
tinued for eight hours in the day.
Watt's estimate was 150 lbs.; Desagulier's 200 lbs.; but
these were early estimates, and have since been found too
high. A set of trials published in " Wood's Treatise on
Railroads" gives an average as low as 100 lbs. But in these
the horse drew at times from 250 to 320 lbs. and when such
excessive exertion is required, the horse cannot do as much
work as if the changes were more moderate. Smeaton's
estimate was also 100 lbs.; Tredgold and Fraley put it at
125 lbs. "•
The common gross load for a horse on a canal is 40 tons,
at 2J miles per hour, which would give 111 lbs. since resis¬
tance iS 720-
In the cities where the streets are level and paved, the
usual load of a dray horse is 3000 lbs. and this would give
150 lbs. as the vertical load, but the best horses are used for
this purpose. On good roads where the maximum rise is
limited by law to 1 in 20, the usual load is 1700 lbs. and
this would give 85 lbs. on the level, and 170 lbs. on the as¬
cents, or an average of 127\ lbs. On the mountain roads
where the greatest rise is limited by law to 1 in 12, the usual
load is 1200 lbs. and this would give 60 lbs. on the level,
and 160 on the ascents, or an average of 110 lbs. On our
hilly roads the rise is often 1 in 8 and the load 1000 lbs.;
this would give 50 lbs. on the level, and 175 on the ascents,
or an average of 112J.
In all these cases the average is a little less than 125, but
35
something must be allowed for obstacles, so that 125 lbs.
may be regarded as the power exerted by a horse of average
strength.
89. The day's work of a horse is 5000 lbs. raised verti¬
cally through one mile.
For the 125 lbs. is moved at the rate of 2J miles per hour,
and the horse continues his work 8 hours. And 125x2|X
8-5000.
90. The force required to move the horse's body, is about
125 lbs. multiplied by the velocity.
For it is found by experience that he can raise 125 lbs.
and move his body 20 miles in a day; and without any load,
that he can move his body 40 miles per day; in both cases
traveling 8 hours per day. Hence if B represent the weight
raised vertically which is equivalent to moving his body
forward, we have (125+B) 20=40B. Hence B=125 lbs.
In the first case the momentum is (125+B) 2| or 250x
2| or 625; in the second case the momentum is 5B or 125
X 5 or 625.
91. When the momentum required of the horse is less
than 625 lbs. he can work longer than eight hours, so that
his whole day's work shall equal 5000 lbs. raised I mile.
Thus if his load is only 25 lbs. raised vertically, and he
travels 4 miles per hour, the momentum exerted is (25+B) 4,
or 600 lbs.; and the hours he can work are 5000+ 600
or 8J ; and the distance he can travel is 8^X4 or 33^ miles.
This is the proper load when a horse travels with a light
buggy over a good level or undulating road, and this is the
distance he can travel with such a load day after day with¬
out resting.
92. When the momentum required of the horse exceeds
625 lbs. the work done per day is decreased in proportion to
the excess.
Thus if his load is 60 lbs. raised vertically, and he travels
5 miles per hour, the momentum is (60+125) 5 or 925 lbs.
And 925: 625::5000: 3379 which is the work he can do in a
day. This 3379 divided by 925 gives 3.6 as the number of
hours he can work in the day. And 3.6X5 or 18 miles is
36
the distance he can travel in a day. This is about the load
and velocity for stage horses on good roads; but it is com¬
mon to have a heavier load and travel 20 miles per day;
but this always results in injury to the horses.
- The greatest force a horse can exert without injury, is
about double this momentum, or 1250 lbs. Thus if, unload¬
ed he travels more than ten miles per hour, his momentum
would be above 1250 lbs.; or if with a load equal to 90 lbs.
raised vertically he travel 6 miles per hour; or if with a
load equal to 300 lbs. raised vertically he travel 3 miles per
hour; in all these cases his exertion will be excessive and
injurious.
93. The cost of transportation on common roads, when
horses are advantageously employed, is $12 per ton.
Thus if five horses should carry a net load of 4000 lbs.
100 miles, and have the same back load, the time consumed;
would be ten days in traveling, and two in loading and un¬
loading, and this load at $12 per ton, would pay $4.00 per
day for the team.
94. If only two horses are used, or if there be no back
load, the cost of transportation is about $20 per ton, for 100
miles, or one cent for 100 IbsTper mile.
Thus if five horses should carry a net load of 4000 lbs.
60 miles, and return unloaded, the time employed would be
3 days going, two returning, and one loading, or 6 days in
all ; and the load at 60 cts. .per hundred, would amount to
$24; which would give $4 per day.,
95. On a rail-road'where the maximum rise is 36 feet
per mile, the cost of transportation by horses would be
about $1.75 per ton, per 100 miles.
For a gross load of 16 tons would give for friction 16 X
•2000-^-240 or 13-3 lbs. and for gravity on the ascents 32000
X36-J-5280 or 218 lbs.; so'Shat the load on the level is 133
lbs. and on the ascents 133TH-218 or 351 lbs. and the average
is 242, which would be about the load for two horses. Of
these 16 tons, the net load would be about 10 tons. To
carry this load 10® miles would require 5 days for travel¬
ing, and 2 for ldading and unloading. And tons at
37
$1.75 for 7 days would give $2.50 per day, which would
be a fair compensation.
96. On a canal the cost of transportation is about 50 cis.
per 100 miles, if a load can be had in both directions.
The common net load for two horses on a canal is about
80 tons of 2000 lbs. each. The boat will increase this
load to 90 tons, or 180000 lbs. The resistance to this load
at 2J miles per hour, 180000^- 720, or 250 lbs. which is the
power of two horses. Now $5 per day would be about the
proper pay for two horses, for two men and a boy, and for
the wear and tear of the boat. This for 7 days employed
in the trip would make $35; and $5 for extra labor of
loading and unloading would make $40 ; and $40-1- 80
would be 50 cts. per ton.
LECTURE VIII.
THE STREAM ENGINE.
97. The first application of steam to useful purposes was
by Savery, in the year 1700.
Before the Christian era Hero proposed the use of steam
to produce motion.. In the 17th century several inventors
explained how steam might be employed for this effect.
But Savery in England, first constructed an engine in which
steam was actually applied to useful purposes. In this the
steam was used to raise water from the mines. As it acted
immediately on the water and required boilers of great
strength, it was of but slight utility.
98. A piston, was first used by Newcomen and Savery,
in 1712.
This saved the immense loss of steam which was occa¬
sioned by its coming in contact with the water, and enabled
38
the inventors, by having the steam-piston large and the
pump-piston small, to raise water to any height, with steam
of moderate strength. Their engine was called the Atmos¬
pheric engine, because the motive power was the Atmos¬
phere, steam being used only to produce a vacuum. This
was extensively used in the English mines to raise water,
and where fuel was cheap, it was of great advantage.
99. The real inventor of the Steam Engine was James
Watt.
By driving the piston by the steam itself, by encasing the
cylinder so as to keep it all the while hot, by cutting off the
steam before it had driven the piston its full stroke, and by
various minor improvements he saved five-sixths of the
steam used in Newcomen's engines, and made his engine
applicable to other purposes besides the raising of water.
Watt's first engine was constructed in 1776.
100. The steamboat was first successfully introduced by
Fulton, on the Hudson river, in 1807.
Before this time boats had been driven by steam at four
or five miles per hour, both on the Delaware, and on the Clyde;
but at this velocity a steamboat could not be worked profit¬
ably. Fulton obtained a velocity of seven miles per hour,
and from that time to this they have never ceased to run on
the Hudson. Not until 1812 were they introduced into
Great Britian; and not into France, until 1816.
101. The first locomotive was constructed by Trevithick
and Vivian, in 1804.
The principle of this engine was correct, but it was not
successfully introduced until 1830. In that year the Liver¬
pool and Manchester railroad was completed, and an engine
was tried at the opening of the road, which carried three
times its weight, and moved at the rate of fifteen miles per
hour. The improvements since this time have been very
great, so that it can now draw 20, and even 30 times its
own weight, and move with a velocity of 40 or 50 miles per
hour; and for express trains 70 or 80 have been attained.
102. A locomotive is a steam engine with two cylinders
39
whose pistons act upon the radii of the driving wheels, or on '
a crank which is apart of the axle of these wheels.
If the driving wheels rested on a perfectly smooth surface,
the turning of these wheels would not move the locomotive
forward. If it rested on such a surface as ice, it would
also revolve without moving forward, if the resistance at the
rim were less than the other resistance that must be over¬
come when the train moves forward. And universally, the
adhesion at the circumference must exceed the friction at
the axles, the gravity of the train, the resistance of the air,
and all other forces which oppose the motion of the cars, or
else the train will remain stationary.
103. The greatest load a locomotive can draw, on a level
rail-road, is about 40 times the weight resting on the driving
wheels.
If a locomotive had its wheels wedged to the axle so that
they could not revolve, it could be dragged forward by a
weight attached to a rope passing over a pulley, if the weight
was J of the weight of the locomotive. This has been
proved by the experiments of Tredgold, and corresponds
with the amount of friction of iron rubbing on iron. Hence
if the train stand still, the adhesion at the rim of the driving
wheels is J of the weight resting on them. If the train move
forward the axle friction is 240 of the weight of the train.
Whichever of these two is the least will be overcome. Let D
be the weight resting on the driving wheels, and W the
weight of the train; then if is greater than the train will
move; that is, W must be less than 40 D. This weight of
the train includes thQ weight of the engine, and is the gross
load moved forwards.
104. The maximum net load on a level, is usually about
14 times the weight of the locomotive.
The driving wheels may be made to support of the
weight of the locomotive. The adhesion is therefore J X f E,
if E represent the weight of the locomotive. The load
in the cars usually about equals the weight of the cars
themselves. Then if N is the net load, 24o-,(2N-fE) is the
friction. And if the adhesion and friction are the same, we
40
have JXf E=2U2N+E) or 30E-2N+E, or N=14iE. From
this must be deducted the weight of the tender, which will
bring down the net load nearly to 14E.
105. The maximum load is still less on an inclined plane
and at high velocities, on account of the resistance of grav¬
ity and the air.
If these several resistances be calculated and compared
with the adhesion, we may determine which is the great¬
est, and therefore whether the train will move forward, or
the driving wheels revolve.
Example. Can a gross load of 120 tons, be drawn up an
inclined plane rising 36 feet in a mile at a velocity of 10 miles
per hour, by a locomotive of 12 tons and front surface 60 feet,
the tender weighing 6 tons. Here friction is ^ or 1150 lbs.;
gravity is 36W4- 5280, or 1881 lbs.; resistance of the
air is 60X 102-f 202, or 15 lbs.; total resistance 3046 lbs. The
adhesion is ^.f. 12.2000, or 3000 lbs. so that the load would
not advance, since the adhesion is less than the other resis¬
tance.
106. The adhesion may be increased by gearing several
wheels together, or by making the locomotive heavier.
The gearing of the wheels together is rendered difficult
on account of the train moving in a curve, where the dis¬
tance between the wheels is less on the inside and greater
on the outside than it is when on the straight part of the
road. This causes a slipping of the wheels which occasions
much resistance. When however the locomotive is heavier
than 14 or 15 tons, it is common to gear together two driv¬
ing wheels on each side very near each other. As they
are very near, the distance between the centres of the two
wheels is but slightly changed, and the slipping is there¬
fore small. The advantage of distributing the heavy weight
resting on the driving wheels, among four instead of two
wheels, is very considerable ; since the injury to the road¬
bed by these heavily loaded wheels moving at high veloci¬
ties is very great.
107. Two cylinders are used, to give greater unijormity
to the motion of the train.
41
The two cranks on the axle being placed at right angles
to each other, when the piston-rod of one cylinder is acting
at right angles to its crank, and producing its greatest effect,
the other piston-rod is in a line with its crank and producing
no effect at all. For other positions of the crank, the two
rods produce effects less than their maximum, so that the
sum of both is nearly constant.
108. The high-pressure Engine is always used for the
Locomotive.
Because the cold water necessary for condensing the steam
in the low-pressure engine could not be supplied or carried
conveniently.
109. The draft is obtained by the escape of the waste
steam into the chimney.
This draft is very important, and the usual mode of ob¬
taining it, in other steam engines by a high chimney, is not
convenient on a locomotive. The waste steam escaping
with great rapidity up the chimney carries with it the air
around it, and produces a vacuum which can only be filled
by air passing through the fire. The draught is thus greater
as the jets of steam become more frequent, that is as the
locomotive moves more rapidly. Thus the greater the
velocity of the engine, the greater will be the draft, the more
briskly will the fire burn, and the more rapidly will the
steam be generated.
110. The tubular boiler is the only one suited jor the lo¬
comotive.
As the weight of the locomotive is part of the load that
must be carried forward, it is desirable to have it light and
compact, so that the net load may be as great as possible.—
The fire-box is therefore surrounded on all sides with water,
and the flame and hot air and smoke are carried horizontal¬
ly through a large number of small copper tubes about two
inches in diameter, so as to present a large heating surface to
the water, and thus generate the steam rapidly.
111. The best kind of fuel is rich pine, or any wood
that will produce much flame.
The fire-box being not larger than four feet in every di-
5
42
rection, its sides and top will contain 64 square feet. The
copper tubes in the boiler being about 8 feet long, and two
inches in diameter, 100 of them will have 400 square feet of
surface. Thus the surface on which the flame acts is six
times larger than that on which the fire acts ; and it is there¬
fore important that the fuel should produce much flame.
Coal is used where wood is costly, but the bituminous suits
better than the anthracite.
LECTURE IX.
THE STEAM ENGINE CONTINUED.
112. The velocity of the locomotive depends on the evapo¬
rating power of the engine.
When the locomotive is first started, if the effective pres¬
sure on the piston is 60 lbs. per inch, and is sufficient to make
the locomotive move faster and faster, its velocity would be
increased indefinitely, if the pressure remained the same.—
For the motive power is the number of pounds pressing on
the piston multiplied by "ts velocity, and the resistance of the
train depends on its weight multiplied by its velocity ; and
as the two velocities both increase at the same rate, if the
first product is greater at first, it will continue greater al ways,
and thus increase without limit the velocity of the train.
But as the train moves faster more cylinders full of steam
are wanted ; and after a short time more steam is consumed
than the boiler can generate at this great strength. The
pressure then upon the piston becomes less until the motive
power just equals the resistance, and the train moves uni¬
formly.
Thus suppose the piston to have a stroke of 2 feet, and
the driving wheels a diameter of feet, the velocity of
43
the train will then be 4^ times the velocity of the piston. If
the diameter of the piston be 12 inches its area will be about
113 inches, and the whole pressure on it about 60X 113. If
the weight of the train be 120 tons and the road level, the
resistance will be 120x2000-^240 or 1000 lbs. And the mov¬
ing force which is 60X 113X 1 is greater than the resistance,
which is 1000X4J. Hence, if the road continued level, and
the resistance of the air be not considered, the velocity
would increase until the pressure on the piston would be re¬
duced to 40 lbs ; for then the motive force 40X 113 would
about equal 1000x4|. The train would now move uniform¬
ly, the boiler being just able to produce as much steam as is
wanted at a pressure of 40 lbs.
113. The volume of steam a boiler can produce depends
on the strength of steam that is required.
If a boiler can evaporate one cubic foot of water at the
temperature of 212° at which its pressure is about 15 lbs.,
the same amount of water can be evaporated by the same
fire at a'pressure of 30 lbs.; but the bulk of the steam will
only be half as large as before. So for other pressures, the
volume is, very nearly, inversely as the pressure.
114. The amount of st< am generated in a good locomotive
when the fire is burning briskly is about 500 cubic feet per
hour at a pressure oj 15 lbs. for every square foot in the
tubes of the boiler, and three times as much for every square
joot in the fire-box.
This is the result of experiments made by Pambour on
the Liverpool & Manchester Road.
For the engine mentioned above in article 111, where the
fire-box contained 64 feet, and the tubes 400 feet, the steam
generated in an hour at a pressure of 15 lbs., would be
400x500+ 500x64x3 or 296000 feet.
115. The velocity at which a given load can be drawn by
a given engine will be obtained, by finding the pressure that
must be exerted on the piston to move the given load, and
then finding how many cylinders full oj steam the boiler
can generate at that pressure.
Example. Suppose a locomotive - of 12 tons, generate
44
steam as in the last article (114), and has cylinders 12 feet in
diameter with 2 feet stroke, and driving wheels 5|- feet in di¬
ameter, what velocity can it attain, on a railroad rising 36
feet in a mile, with a gross load of 120 tons, and a tender of
6 tons.
Here the mass moved is 138X2000 or 276000 lbs. ; the
fjiction is 2760 0 -f240 or 1150 lbs. ; the gravity is 276000X
36 -r 5280 or 1881 lbs. The sum of these two resistances is
3031. For every double stroke of the piston the driving
wheels make one revolution : that is, while the piston moves 4
feet, the train moves 16J. Hence, the pressure on the piston
must exceed the resistance in the ratio of 16J to 4, so that
the moving force should balance the resistance. Hence, the
pressure on the pistons is 3031X 16}~ 4 or 12503 lbs. But the
two pistons have an area of 122 X .7854x2 or 226 inches.
Hence, the effective pressure of the steam on each square inch
must be 12503 226 or 55 lbs. The real pressure must be 15
lbs. more than this, because of the resistance of the atmosphere
on the other side of the piston ; and 4 or 5 more, because
of the backward pressure of the escape steam. The total
pressure of the steam must be therefore 55-|-15+5 or 75 lbs.
Now as the boiler can generate in an hour 296000 feet of
steam at 15 lbs. pressure, the amount at 75 lbs. pressure will
be 296000 -v- 5 or 59200 feet. The two cylinders contain
2x2xl2X-7854 or 3.14 solid feet. Hence,59200-^-3.l4 or
18840 will express the number of times both cylinders will
be filled in an hour. The double strokes will be 18840 -r 2
or 9420. And finally the velocity of the train will be
9420x16J -;-5280 or 29J miles per hour.
In this calculation no allowance is made for the resistance
of the air, so that the real velocity will be less than 29J miles.
If it be taken at 28|, the resistance on 60 square feet front
will be 60x28J2 ^202 or 122 lbs. If this be added to the
resistance of friction and gravity, and the calculation repeat¬
ed, the real velocity will be more accurately obtained. The
resistance of the train will be 3153 lbs. The pressure on
the piston, 13007 lbs. The effective pressure per inch, 57^
lbs. The steam generated at the required pressure in one hour,
45
57290 feet. The number of double strokes 8118. And
the velocity 281 miles per hour.
116. It is best to use steam of strong pressure, that is of
four or five atmospheres.
For although it takes twice as much fuel to generate the
same volume of steam at 80 lbs. pressure as at 40, yet since
the steam is thrown away still retaining a force of 19 or 20
lbs. the effective pressure of the first is 8(f—20 or 60 lbs.
and of the second 40—20 or 20 lbs.; that is, in this case the
effect is trebled while the fuel is only doubled.
117. The greatest useful effect is produced at low veloci¬
ties.
This is true for two reasons; because at low velocities
the fire is able to generate steam of strong pressure, and
therefore according to the last article to produce the greatest
effect. And again, because although, with half the veloci¬
ty and double the effective pressure, the gross work done
would remain the same, yet the net load, after the tender
and engine are deducted, would decrease faster than the
velocity would increase; and thus the work done would
diminish. Thus, if a given evaporating power would
move a gross load of 60 tons at 20 miles per hour, and the
same amount of steam would move 120 tons at 10 miles
per hour, the net load in the two cases would be 42 and
102 tons, if the engine and tender together weighed 18
tons. But 102 tons at 10 miles per hour is a greater useful
effect than 42 tons at 20 miles per hour.
118. When a Railroad has a single ascent of 80 or 90
feet in a mile, the usual maximum grades on the road being
40 or 50 feet, an additional TSocomotive is sometimes used
to draw the train up this ascent, but more commonly a sta¬
tionary steam engine is employed.
On a level the greatest load a locomotive can draw is 40
times the weight resting on the driving wheels; the adhe¬
sion being ^ of this weight, and the resistance of the train
being ^ of the load. On an inclined plane rising 22 feet
in a mile, gravity is 224- 5280 or 2J0. So that the whole re¬
sistance is now doubled, and the maximum load is only 20
46
times the weight resting on the driving wheels. If the plane
rises 44 feet in a mile, gravity is twice as much as the
friction, and both are £0; so that the load is 13£ times the
weight on the driving wheels. If the plane rises 88 feet in
a mile, gravity is 4 times the friction, and the total resistance
is 2®0; and the maximum load is only 8 times the weight
resting on the driving wheels.
Now it is better economy to accommodate the load to
what can be drawn on the common ascents, and to keep an
additional torce at the single steep plane, rather than to re¬
duce the load to its amount for the steep plane, and to have
only half or quarter of the load suited for the engine oil the
other | arts of the road.
119. When Jail work can be found for the steam engine,
it is always cheaper than animal power.
This is true whether the engine is of 5 horse-power, of 20,
or 100 • whether employeu on a saw-mill, a grist mill, or a
factory of any kind. But on a rail-road a locomotive is not
much cheaper than horses. On the Georgia rail-road the
cost of carrying 1 ton 100 miles is about $1.35, and this is
cheaper than it is on most other roads. The cost of Jiorses
for the same work would be $1.75, so that the difference in
expense is small.
120. The greatest advantage of a locomotive is the rapid¬
ity and regularity with which it moves, and the large amount
of work it can perform on a single road.
The saving of time is important not only to the passen¬
gers, but to the owners of freight. This is especially true
when the freight is of a costly kind, such as dry goods, drugs
or jewelry. On these, the interest on the money invest¬
ed in them for the time saved by the locomotive would often
pay the whole cost of transportation.
On the Reading rail-road they transport from the mines
about 6000 tons of coal per day. Every hour 500 tons
must be started from the terminus, and if we allow 10 tons
for a load for two horses, it would be necessary to start 50
teams in an hour. As these would be so numerous, and so
near each other, an accident to one would delay many others.
47
The breaking of a trace, or an injury to a horse or to a car,
would render it impossible to perform the work; fcr there
would be no time to repair the injury bef ire other teams
would overtake them.
Thus the locomotive excels animal power, nut so much in
its cheapness, as in the amount of its work and the rapidity
with which it is done.
LECTURE X.
GRAYITY AND WATER POWER.
121. Gravity can seldom be used advantageously as a
motive power.
If the merchandise to be transported is equal in both di¬
rections, the loss and gain from gravity would balance each
other. Thus on a rail-road continually descending, the
freight might be carried without steam or animal power in
one direction, but the increased force necessary to return
would equal the gain in going down. So on a river ; the
boat descends of itself, but the extra force required to ascend
the stream prevents us from gaining any advantage by the
descending current.
Even if the freight is all in the downward direction, gravi¬
ty is but of little benefit. On rivers, if the descent is slight,
the boat will move slowly, and the cost of attendance for a
given distance will be large. If the current is more rapid,
the expense of returning the empty boat, or of building a
new one for a second trip will be considerable; and in both
these cases it is usually found best to use the steamboat
instead of the flat boat or floating box or ark. If the
stream is very rapid, the expense of returning the boats and
48
the liability to injuries from the bending of the stream, and
from rapids, snags and other obstructions will be very con¬
siderable. On long rail-roads, since the descent must be
over 22 feet per mile to move the cars by gravity, this mo¬
tive power can seldom be used. On short roads, if the
freight is all in one direction, as from a coal mine to a
navigable river, gravity may be used to some advantage.
If the road is very short and the descent large, the loaded
cars may be used to draw up the empty ones, and then grav¬
ity is of decided advantage. It thus appears that this force
although furnished by nature without any expense, can al¬
most never be used advantageously as a prime mover.
122. A water fall is a force furnished by nature, and is the
cheapestpbwer that can be employed.
This is only true where the water is abundant, constant,
convenient to the work to be performed, and obtained by a
dam of moderate expense. For if the water fail to perform
the work, or is dependent upon the seasons, or is out of the
way so that the work has to be carried to it, or requires a
large outlay for the building of a dam and keeping it in re¬
pairs, steam may be cheaper than water power.
123. The several wheels employed in using water, are the
Overshot, the Breast, the Undershot, the Flutter, and the
Re-action wheels.
The first four are vertical wheels, and the last hori¬
zontal. In the overshot, the water acts by its weight; in
the flutter and undershot, by its impulse ; in the reaction, by
its pressure; but in all, the full effect of the water depends
on its amount, and the height of the fall. A larger or a
smaller portion of this power is, however, always lost.
124. In using the overshot wheels the loss varies from
one-fifth to one-third, of the full effect of the water.
This is occasioned in part by spilling the water out of the
buckets, but mainly because the water, when it leaves the
wheel, must have at least the velocity of the wheel, and
therefore cannot transfer to it its whole momentum.
The spilling of the water should be prevented by an arc
or apron fitting close to the rim of the wheel. The mo-
49
mentum retained by the moving water will be lessened by
making the wheel revolve very slowly. But this slowness
has a limit in practice, since the water must, move with suffi¬
cient velocity to keep clear of the wheel. According to
Smeaton's experiments, in which the fullest confidence is
placed, the velocity of the rim should be 3 feet per second.
125. The water should have a slight head, so as to strike
the wheel with at least the velocity of the wheel.
If it should fall with less velocity, it would at first be a
retarding rather than a moving force. If it should fall
with a greater velocity, some of the water would rebound
and then drive off particles from striking the wheel.
The head need not be more than .a foot, for this fall
would give a velocity of 8 feet per second, by the formula
Y=8vS,no allowance being made for retardation by friction.
126. The water should be so directed as to strike the
wheel at right angles with the radii.
Otherwise, some of its momentum would be lost by not
being in tjie direction of the moving body. This should
be particularly attended to when the water is made to fall on
the wheel on the upper side. For then, unless the water is
guided, the direction would not be at all right.
127. It is best to apply the water on the upper side and
below the top of the wheel.
For if on the upper side, the back water at the bottom
will not be so likely to retard the wheel; and by striking
below the top, the water is more easily guided in the proper
direction.
128. The buckets should be formed of two parts, one in
the direction oj the radii and the other at an angle of 120°
with the first. Fig. 15.
If the side of the bucket were at right angles with the
bottom, all the water could not escape till the bucket reach¬
ed the lowest part of the wheel. As its escape would re¬
quire a little time, some would be carried past the lowest
point, and then by acting backwards retard the wheel.
With the proper shape, the water would all escape from
6
50
the buckets, when the wheel was at rest, 30° above the low¬
est point; but when in motion, it would remain longer and
only complete its escape when it reached the lowest point
of the wheel.
129. The diameter of the wheel may exceed the fall about
one-eighth of its height.
The water must then be admitted on the upper side, as it
cannot run over the high wheel. This eighth of the fall,
added to the height of the head above the opening in the
flume, will make the water strike the wheel 35 or 40° from
the top, where it may be easily put on the wheel in the pro¬
per direction.
130. In an undershot wheel, the loss of power is about
two-thirds of the full effect of the water.
In this case the water acts by its impulse and not by its
weight. It does not fall into buckets, but strikes against
floats which are at right angles to the rim of the wheel.
For these reasons the water and the wheel must both move
with considerable velocity. And hence the water leaves
the wheel without having transferred much of its momen¬
tum to the wheel. The loss is thus large. The amount of
momentum given to the wheel being the amount lost by the
water, it is evident, that when the water leaves the wheel
rapidly, and thus retains much of its momentum, but a
small amount is given to the wheel.
131. In the flutter wheel, the loss is about five-sixths of
the full effect of the water.
This wheel is used with a high head, 10, 15, or 20 feet.
The water issuing from an opening near the bottom of the
flume, strikes the floats of the flutter wheel with great ve¬
locity and makes it revolve rapidly. As the water only
transfers to the wheel a momentum, measured by the weight
of the water multiplied by the velocity it loses, the momen¬
tum given is small.
In the overshot wheel which moves slowly, the water
leaves the wheel with a small velocity, having transferred
nearly all its power to the wheel. In the undershot, which
moves more rapidly, the water leaves the wheel with more
51
velocity, and thus transfers but a small portion of its force
to the wheel. In the flutter wheel, which moves still more
rapidly, the water retains a large portion of its velocity, and
the momentum transferred is therefore very small.
In the first case the velocity of the wheel is small, but
the mass in motion is large, making the momentum large.
In the second the velocity is greater, but the mass being re¬
duced more than the velocity is increased, the momentum
is less. In the third case the velocity is large, but the mass
being very small, the momentum is small.
132. In the breast wheel, the loss of power is about one-
half the full effect of the water.
In this the water acts partly by its weight and partly by
its impulse, and the loss is therefore between that of the
overshot and undershot wheels.
133. In the reaction wheels of the best hind, the loss is
about the same as in the overshot.
In these, the water commonly passes down a vertical
column to the centre of a drum, then passes horizontally
through the radii of this drum, and then escapes through
openings on one side of these radii. The water escaping
on one side of the radii, and pressing on the other, by its
reaction forces the drum to revolve.
It is not best to have the water pass in straight lines from
the centre to the rim of the drum, but in a spiral line bend¬
ing in a direction opposite to that in which the drum revolves.
The advantage of these wheels is that they can move at
high velocities with but little loss of power, and the drum
may revolve under water with less resistance than other
wheels.
134. The expense of water power is usually much less
than that of steam or animal power.
A good dam may cost 1500 or 2000 dollars; this at a
small annual repair of one or two hundred dollars will last
ten or twelve years, even if constructed of wood. The an¬
nual cost for interest, depreciation, and repairs, will seldom
reach one dollar per day; while a power equalt^ffi^4\^fi
forty or fifty horses may be obtained from the
52
LECTURE XI.
COMMON ROADS.
135. In laying out common roads, attention must be paid
to the selection of the route, the acclivities, and the drainage.
Of these the drainage is the most important, and the se¬
lection of the route the least.
136. The first rule for the selection of the route is that it
should be as short as possible.
This lessens the cost of making the road, the quantity of
land occupied by it, and the amount of friction to be over¬
come in passing from one point to another. It is proper
however, to deviate more or less from a straight line to avoid
a hill or a marsh, or to improve the grade of the road.
137. All deviations jrom, the direct route should be at
small angles with it.
If the angle made by the road with the direct route is small,
the distance is very little increased. Thus, if the deviation
were 12n, or 1 mile in 5, the length of the road would be
increased only 2 miles in 100. In this case, if the distance
between two places be 50 miles, the greatest deviation from
the straight line would be 5 miles, but the whole length of
the route would be increased only one mile. And univer¬
sally, since the straight route is to the indirect route as the
cosine of the deviation is to radius, and the cosine for small
angles being nearly the same as radius, and for larger differ¬
ing more and more, it is evident that the loss in distance will
increase more rapidly than the angle of deviation increases.
138. The first rule in regard to acclivities is, that in coun¬
tries generally level, no rise over 1 in 20 should be allowed.
If hills steeper than this should be met, they should be
avoided, or cut down, or ascended by an indirect route, so
that the rate of ascent should not exceed more than 1 in 20.
On such a road a horse can do nearly as well as on a level.
53
Friction is not increased, since the road is lengthened but a
trifle. There is no*lossfrom gravity, because on the descend¬
ing grades the horse does not hold back, and the advantage re¬
ceived from gravity is equal to the loss on the ascending
grades. The load may be as large as on a level road, for as
the horse is rested on the descents, he can exert without fa¬
tigue an extra force on the ascents. Thfe only loss is caused
by the increase of force necessary to raise the horse's body
up the acclivities, since it is about as difficult for him to
move his body on the descending grades as it is on a level.
To express these forces in numbers, suppose a horse to
draw a load of 2000 lbs. for three miles; first on a level road;
then 011 a road ascending 1 in 20 for one mile, level for one
mile, and then descending one in twenty for one mile.
On the first, the weight to be overcome would be 100
lbs. for friction, and 125 lbs. to move forward the horse's
body, or 225 lbs. for each one of the three miles. On the
first mile of the second road the weight to be raised
would be 100 lbs. for friction, 100 for gravity, 125 to move
forward the horse's body, and I0 of the weight of the horse's
body to be lifted up the plane, which supposing him to
weigh 1000 lbs. would be 50 lbs.; making the whole weight
100+100+125+50 or 375 lbs. on the first mile. On the
second mile the weight would be 225 lbs. On the third mile,
it would be 100—100+125 or 125 lbs. Thus on the level
road the weight for the three miles would be 225X3 or 675
lbs. ; on the undulating three miles, it would be 375+225+
125 or 725 lbs. ; the difference, 50 lbs, being caused by the
necessity of lifting the horse's body up the inclined plane.
If, however, the road were steeper than 1 in 20, the loss
in ascending could not be made up in descending, for the
horse must now hold back; force must be exerted on the
descending plane to resist gravity ; the load must be dimin¬
ished below what can be drawn on a level, else the horse
would be strained and injured, or if not, still rendered unable,
by excessive fatigue, from doing a full day's work. Besides
this, it is difficult on steep ascents to keep the road-way in
order, the accumulation of water in wet weather, and its ra-
54
pid motion, washing away the soil, and making the roac
rough and uneven.
139. In hilly or mountainous countries, no rise over 1 it
12 should be allowed.
On such a road, the weight to be raised on the steepes
part would be W ^20 + W -M2+ 125-j-H -rl2, representing
the weight of the horse's body by H. If the horse be sufferec
to exert any extra force on the steepest 'parts of the road
a proper load would be 1200 lbs. But if the road is
made steeper, the exertion necessary to raise the horse's body
up the ascents, and the double loss from holding back on the
descents, reduce the load and the amount of work done
very rapidly.
140. If a sleep hill is met, it may always be ascended by
an indirect or zigzag route, so as to reduce the grade as
much as may be desired.
This will lengthen the route, increase the cost of the road,
and also the friction of the wagons; but the gain from the
increased load of the horse will more than compensate for
these losses.
The hill may also be cut down, and the approaches to it
filled up, but the cost of this is so considerable, that it can¬
not be done to any large extent for a common road.
141. The injuries done by water, consist not only in its
making the road-bed muddy, and thus increasing the resist¬
ance ; but in its washing the soil away from the stones, and
forming channels across the way, making it rough and
uneven ; and in its 'permitting the road-bed to freeze, which
keeps it a long while rough and muddy.
The losses from these sources being greater than from in¬
creasing the length of the route, or from having slight ac¬
clivities in the road, it is proper to go out of the direct route,
and even to rise considerable ascents, to secure proper drain¬
age.
142. The road should avoid marshes, ground-springs, all
wet places, the lowest parts of a valley, or of a mountain
gorge.
As it is difficult to drain suqh places as these, it is very
55
desirable to avoid them. This can always be done in a val¬
ley or a mountain gorge, but for the others it may not al¬
ways be possible. In this case, great attention must be
paid to the drainage. Ditches should be dug at the side of
the road: blind drains should be formed in the middle, filled
with large stones and covered up with soil. Covered drains
should lead from the ground-springs, and from the blind
drains in the middl® to the sides ; and outlets should be
made from the side ditches, to carry away the water at eve-
ry,practicable point. Should these methods b£ insufficient to
make the road-bed dry, it should be raised by a suitable soil,
so high as to drain itself into the side ditches. If. this will
not succeed, the wet soil should be covered with large stones
or rails, or small trees, and these completely covered to a
considerable depth by soil, so as to prevent the wood from
decaying, and to make the way smooth and even. This
covering with soil is very important; for the stones not
only obstruct the progress of the vehicle, but injure it very
much, and cause great discomfort to the travel^. The du¬
rability of the road is also very much prolonged.
143. There should be ditches on both sides of the road
usually; but when the ground falls of on one side, one is
needed only for the upper side.
If the water runs across the way, it is impoSible to have
a good road. The ditches are to prevent this and also to re¬
ceive the rain water that falls on the.road. Much of this
runs off to the side, but some of if sihks into the^oad-bed
and percolates under the ground to the side ditches.
The side ditches should be wide and deep enough to carry
off the water; should have a fall of on^ foot in a hundred
whenever practicable, so as to keep 1 themselves open; and
should be much broader at the top than at the bottom, lest
their sides should fall in and obstruct the passage of the
water. Their outlets should be numerous, especially on a
long or steep declivity, so that they will not be overflowed
during the heaviest shower. \
144. When the water must cross the read, should be
by a culvert, or under a bridge, or by a broad shallow °ur-
56
face-drain so constructed as not to become uneven by washing.
The culverts, though most expensive at first, are the best.
By giving them a slight fall, they keep open, if sufficiently
large to pass not only the water but the leaves and rubbish
washed into them. The surface-drains are often paved.—
Their inclination should be slight, not over six inches for a
road of moderate breadth. They should be frequent on hills
or long inclined planes, to assist in divefting the rain water
off the road.
145. When two inclined planes meet, ati outlet for the wa¬
ter should be carefully made.
In a se.il of pure sand, this is not important. In fact the
water is sometimes intentionally obstructed in this case, so
that the materials carried down by the water should be depo¬
sited, and fill up the depression. But if the soil is of clay,
or contains a portion of clay, an outlet must be carefully
provided, else the water is retained, and a muddy place form¬
ed in the road.
146. Tfle^cross section of the road should be elevated in
ttye middle o*or 6 inches, to a breadth of 20 feet.
This is necessary not only to carry off the rain-water, but
to give to the water that has sunk into the ground a better
chance to esrape to the side ditches.
147. It is vest to repair roads frequently, and after wet
weather. ,
By constai^attentLen. the road can be kept all the while
good ara less cost, tKgwfi* when the repairs are made only
once or twice a year. If the road-bed is moist, the soil for
repairing can be dug jap more easily, and it will sooner con¬
solidate and unite \^th the old road.
148. The best material for repairs is a mixture of clay
and sand, in which the clay predominates.
A vegetable mould is ^ery objectionable; because it is
spongy, and absorbs and renins moisture. Sand is too soft
and yielding. Clay is tougjh when wet, and does not dry
readily. Stones make tfe£ road-way too rough, unless they
are very sAall, about an "inch cube, and of uniform size.—
Rounded gravel is too yielding, both to the feet of the horses
i)(
and the wheels of the wagons. But a soil which contains
a proper proportion of sand and clay is firm and hard, throws
off the rain water well, drys rapidly, and forms a smooth and
durable road.
LECTURE XII.
COMMON ARTIFICIAL ROADS.
149. The Roman Military Ronds were the earliest of
any extent, where a. superstructure was placed on the ground
to form the road-bed.
These centered at Rome, and led thence to every part of
the Empire; their total length being more than 50,000
miles. Though made principally for the passage of sol¬
diers and pack-horses with the baggage of their armies, light
carriages for travellers were also used on them. They were
of the most substantial kind, so that not only their ruins
are yet traced in Italy, but many portions of them are still
travelled on at the present time. They were constructed
of stones, large in size and durable in material, bound to¬
gether with a mortar or cement of the best kind, two or
three feet deep, and covered with flag.stones so as to make
them smooth and pleasant.
These would be too costly for modern use; and our
heavy wagons would disarrange the pavements so as to in¬
troduce water, and its freezing would break up the road.
150. The turnpike road consists of a road-bed made of
broken stone, 10 or 15 inches deep.
Of these 30 or 40 thousand miles have been built in En¬
gland, and more than 10000 miles in the United States.
Their cost in this country has been from 5 to 10 thousand
dollars per mile, but though of great advantage to the coun¬
try through which they pass, they have seldom been pro-
7
58
fitable to the stock holders. Since the introduction of rail¬
roads, new turnpikes haye been very few.
Before laying down the broken stone, the route is more care-
f dy selected than for common roads, the acclivities lessened
by cuttings and embankments, and the road-bed thoroughly
chained. The black vegetable mould is removed from the
s ir'ace.
If the sub-soil is of fine sand, large flat stones are laid
down as a foundation to prevent the broken stone from
T/orking down into the sand and disappearing entirely. If
the base is of clay or partly of clay, these large stones should
n:t be used. If the base is marshy, flag-stones or small trees
should form the foundation for the broken stone. If a solid
r k comes to the surface, it is well to cover this with soil;
eu-e the broken stone laid ou-tbjsare easily crushed by the
wagons, and also fail to become firm and consolidated.
The stones should be of the hardest and toughest kind,
so as to be durable. They should be small enough to pass
through a ring inches in diameter in the^'r longest direc¬
tion, else they would make the way rough and become ob¬
structions to the wheels. They should not be, however,
\ c ry small, else they would not bind together. They should
be angular and not round like gravel, or they would not form
a firm hard base to support the wheel and turn off the rain¬
water that falls on the road.
Hard granite or tough limestone, basalt, trap, and a hard
clay freestone are proper kinds of rock for the broken stone.
Common granite or limestone is too soft; so are sand-stone
and slate usually; quartz and flint are too brittle.
This mass of broken stone is not covered with clay or soil;
but, after it is used a short time, forms of itself a smooth
hard dry road-bed almost impervious to water and uninjured
by frost or wet weather.
151. The Macadamised road differs from the turnpike,
mainly in the small size of the broken stone.
The Cumberland road built by the United States Govern¬
ment, and leading from the Potomac across the Ohio at Wheel¬
ing and thence westward towards St. Louis, is of this kind.
59
Many of the English roads are Macadamised ; but in the Un¬
ited States they are found only in the neighborhood of the
large cities. Their cost is from 10 to 20,000 dollars per
mile. They are an excellent and pleasant road, but their cost
forbids their general introduction.
The size of the stones is about a cubic inch ; the greatest
length in any direction being two inches, or the heaviest be¬
ing four ounces. Hard tough angular stones of this size
will after a short use form a smooth compact surface through
which water will not penetrate.
152. The plank roadis made of planks, two or three inches
thick, laid across the road, on longitudinal sleepers 10 or 12
inches wide.
These have been used in Russia for a long time ; they
were introduced into Canada in 1840 : more recently they
have been constructed very largely in New York and to some
extent in other Northern states; the amount yet built in the
South is very small.
Before laying down the sleepers, the route is marked out
with much care, and thoroughly drained. As friction even
for common waggons is reduced to one thirtieth on these
roads, 1 in 30 is the maximum grade that should be allowed,
so that the horse may be able, without straining, to take, on
the acclivities, his full load on a level.
The sleepers should be full 12 inches wide so as to have a
broad bearing surface on the ground. Two are enough, if
the road is a single track ; for which eight feet is the proper
width. The two sleepers should be one foot from the end
of the planks, so that the distance between them would be
four feet. One should be about an inch higher than the
other, so as to give the planks a cross slope to carry off the
rain water. For a double track four sleepers are necessary,
and plank sixteen feet long. The sleepers must be buriec in
the ground, so that the plank ^ shall be supported their whole
length by the earth ; and this must be carefully rammed un¬
der them, to secure a continuous bearing, or else the plank
will decay very rapidly.
60
153. The cost of plank roads is very small] between one
and two thousand dollars per mile.
The two rows of sleepers 12 inches by 4, a mile long, will
contain 2X 4X5280 or 42000 feet. The plank, if two inches
thick, will contain 8X2X52S0 or 84000 feet. And both at
$8 per thousand will cost $1008. For the grading and pre¬
paration of the road-bed, from 300 to 800 dollars will be requir¬
ed. For putting down the superstructure $200 would be
sufficient. So that the whole cost would not exceed 1500
to 2000 dollars per mile. When lumber is cheap and the
route favorable, so as to require but little grading, the cost is
still less.
154. The durability of plank roads depends on the cli¬
mate,, and the amount and character of the freight on them.
In cold countries, as in Russia or Canada, they would last
ten years before rotting; in New York 7or 8 years; in the
South not more than 4 or 5.
Sometimes the amount of travel and of freight is so large,
that the planks are worn out before they rot; but that is al¬
ways a favorable circumstance, since the tolls will then al¬
ways pay handsome dividends to the stockholders.
155. Plank roads are suited for those localities where a
good natural road cannot be obtained.
In sandy or marshy districts the saving is very great, not on¬
ly in the increased load of the horse, but in the rapid passage
of carriages. So in prairie lands, where the deep tough
mud makes the roads almost impassable in winter. So also,
in Northern countries, where the ground becomes frozen
for two or three feet below the surface, and remains for a
long while in the spring thawing and freezing, making the
road rough and muddy to a great depth.
156. The load of a horse on an ordinary plank road is
not less than 2000 lbs.
If the grades were very good, rising one in 30 or one in
40, the load would be still larger. But where the grade is
one in 20, the friction 2000 lbs. is only 66 and gravity 100
lbs. So that the average weight to be raised on the level
and the steepest grade is only 116 lbs. which is less than
61
the power of an ordinary horse. If now the muddy or rough
common road would permit only a load of 7 or 800 lbs., the
saving would authorise the payment of 75 cents per ton per
day in the form of tolls, since two horses would do the work
of five.
The saving of time and the increase of comfort to the
traveller would be still more marked and important.
157. If a plank road should cost $1500 per mile and
last five years, 100 loaded horses should pass per day to ren¬
der it profitable.
One cent per horse per mile is as much as could be col¬
lected for toll. In muddy weather, 2 horses on the plank-
road would do the work of 5 on the common road. The
4000 lbs. would thus require three horses less. Counting
this saving at $1.50 per day, it would give 7J cents per mile
or 3f cents per horse. But when the common roads were
not much out of order, the saving would be less; and in
neither case must the whole saving be charged for toll, or no
inducement would be offered to the wagoner to use the
plank road. For passengers the toll might be 2 cents per
mile per horse, as their comfort would be much increased as
well as that of their horses. For a road 50 miles long, one
fifth of the horses being for pleasure carriages, the receipts
for 100 horses would be (80+20x2)50 or $60 per day. For
the year they would be 60x365 or $21900. Deducting
from this $900 for six toll-collectors, and $50 per mile for
repairs, the net receipts will be $18500. The cost of the
road being 50 X 1500 or $75000, the receipts would make a
dividend of 25 per cent. And this amount is needed, so as
to give the stockholders 7 per cent, and return them their
capital in five years.
158. Streets are paved with small round boulder stones
of quartz, or with blocks of granite, or with cast iron, or
with a mixture of asphaltum and chips of stone, and some¬
times with blocks of wood.
The first kind of pavement is the most common. It is
cheap, very durable, easily laid down and taken up, and
62
forms a good foot-hold for the horses. But it is rough, noisy,
and disagreeable to the passengers.
The blocks of granite have recently been introduced in
London and Paris, and to some extent in our Northern cities.
This pavement is smooth, very durable, and very pleasant.
It is expensive and often becomes so smooth that the horses
slip and fall on it. As the blocks are squared and fitted close
to each other, the rain-water cannot get under it and soften
the base, so as to make the blocks sink unequally and the
road become uneven.
Sometimes the blocks are 3 or 4 or 5 feet long and laid in
rows about 5 feet apart, so that the wheels may roll in them ;
while the space between is filled with small boulders or with
broken stone, to form a good foot-hold for the horses. Two
or three of these rows are laid, so as to accommodate the ve¬
hicles passing in both directions. This forms an admirable
road, but does not suit well for cities, where so many vehicles
are passing and meeting continually.
Plates of cast iron have been tried for pavements, but
though firm, smooth and durable, they soon become too
smooth for the horses, however rough they may be when
first laid down.
Asphaltum is a kind of mineral coal which being melted
and mixed with small chippings of hard stone, forms a cheap
cement, with which a road-bed and pavements are sometimes
made. This forms a good road, but wears unequally, and
is not very durable.
Blocks of wood cut agross the grain, and set up on the
ends, have been used for pavements. These make a very
smooth, firm and cheap road-bed lor a short time ; but how¬
ever carefully they are joined, the water will at some places
get between them and rot the wood. The decay once be¬
gun progresses rapidly by opening the seam and admitting
more and more water. If the rot could be prevented they
would form a durable road, because the wheels rub against
the ends of the grain, and therefore wear it slowly.
Sometimes a McAdamised way of broken stone is used
in cities. But this wears rapidly and becomes very dusty,
63
and carmot be taken lip readily, when it is necessary to lay
down or repair the water or gas pipes under the streets.
LECTURE XIII.
HISTORY OF RAILROADS.
159. A Rail Road is one on which the carriages roll on
a, superstructure of stone, wood, or iron.
Among the ancients the immense masses of rock used in
the public buildings were drawn from the quarries on a way
made of blocks of stone, and these may be regarded as the
first railroads ever constructed. Wooden ways were used
at Newcastle in England, early in the 17th century, for
transporting coal from the mines to the river, a mile or two
distant. These were constructed by pinning down, length¬
wise along the road, wooden sills 6 or 8 inches square, on
cross pieces of about the same size laid 2 or 3 feet apart.
By these, the load of the horse was more than doubled, be¬
ing increased from 17 to 42 cwt. As there were many
teams carrying these heavy loads, the wood wore away very
rapidly and required to be replaced in a year or two, long
before it had rotted. For convenience of replacing, a thick
plank was sometimes pinned on the sills that were laid
in the direction of the road. These planks were renewed
from time to time, while the under rails and cross-ties were
not taken up for 8 or 10 years, when from their complete de¬
cay they would no longer answer the purpose. These
wooden roads continued in use for 150 years, before iron
was substituted for the wooden rails, the first use of iron be¬
ing about the year 1767. The wooden roads were gener¬
ally used till about the year 1800, and from the cheapness
of wood in the United States they continued to be used here
64
still later. It is now found, that even for temporary purposes
the iron road is always best. If the amount of freight will
authorise the construction of a wooden track, the additional
outlay for iron will be more than compensated by the de¬
creased cost of transportation.
160. The modern railroad, for the purpose of travel and
general transportation, was not introduced until 1830.
A great number of short iron roads 2 or 3 miles long, and in
a few cases 8 or 9 miles long, were used in the coal districts
in Great Britain, at the beginning of the present century ;
and in 1800 the Surrey Railroad leading from London
southward through the county of Surrey, was chartered
for the general purposes of trade. It was 18 miles long, and
was finished in 1806. It was not successful or profita¬
ble to the stockholders. Several Railroads, 20 or 30 miles
long, were constructed between this time and 1830, with the
intention of carrying passengers and general merchandise in
part, but their main object was to transport coal and iron.—
Horses were generally employed on them, but in 1811 the
locomotive was introduced. In 1816 Stephenson improved
the locomotive of Trevithick and Yivian so that its use be¬
came'more general; but it was at low velocities ol 3 or 4
miles per hour. Not until 1830, when the Liverpool and
Manchester Railroad was opened, did the locomotive obtain
such velocity and power, that it could compete with the
stage coach for passengers and with other modes of convey¬
ance for merchandise. Before this time, no rail road was
built on the continent of Europe or America, except for short
distances, from mines or quarries, for the transportation of
coal, iron, or stone.
161. From 1830 forwards, Rail Roads have been every
where introduced with great rapidity and success.
In 1830 there were not more than 500 miles of Rail-way
in Europe and America. In 1840 there were 1000 miles in
Great Britain alone; and 7000 at the end of 1852: The
cost of these roads having been about $170000 per mile,
the amount expended on them has reached the enormous
sum of 1200 millions of dollars. So rapid an increase shows
65
that the investment must have been as profitable to the
stockholders as it was beneficial to the public.
In France, the progress has been slower and the stock less
productive. In 1830, there were no roads except in the
mineral districts. In 1840, the number of miles opened for
passengers was less than 100. At the beginning of 1853 the
amount was 2500 miles. The cost of these roads has
been about $120000 per mile, and the capital invested 300
millions of dollars.
In Belgium, there were no railways in 1830; in 1840,
there were 200 miles in operation ; and at the beginning of
1853, they reached 500 miles. Their cost has been about
$60000 per mile, and the capital invested 30 millions.—
They have been profitable and of great advantage to the
country.
In the German states, including Prussia and Austria, there
were at the beginning of 1853 about 5000 miles, construct¬
ed at a cost of $60000 per mile, involving an expenditure
of 300 millions of capital. These have been mostly built
since 1840 and have been profitable and advantageous.
In Russia, about 500 miles were finished at the beginning
of 1853, at a cost of $60000 per mile, but the lines were
principally built by the government and their receipts and
expenses have not been made known.
In Portugal, Spain, Italy, Holland, Switzerland, Turkey,
and Denmark, Rail Roads have been but little introduced;
not over 500 miles being built in all these countries.
In the United States, the first iron Rail Road was the
Q,uincy, near Boston, 3 miles long and built in 1826. The
next was the Lehigh in Pennsylvania, 9 miles long and
built in 1827. These were for transporting granite and
coal. In 1828 three long lines were commenced, for the
transportation of merchandise and travelers. Of these, the
South Carolina railroad from Charleston to Hamburg was
completed *in 1833; the Pennsylvania road from Philadel¬
phia to theJSusquehanna in 1835 ; and the Baltimore and
Ohio was not opened, the whole way through, until 1852.
The number of miles in operation on the first of January in
8
66
the years 1835 1840 1845 1850 1851 1852 1853,
was 900 2200 4500 7500 9000 11000 13500
thus doubling every five years ; and their present rate o
progress is fully as rapid as at any former period. Thei
cost has been about $30000 per mile, making the wholt
outlay 400 millions. A fe w of the lines have beenunprofit
able, but the great majority have paid handsome dividend;
on the amount invested in their construction, besides being
of immense benefit in developing the resources and in
creasing the wealth of our country.
162. The extent of Rail Roads in the United States ex¬
ceeds that of any other country, and soon it will exceed tha>
of all other countries put together.
The amount in England increased in the last five
years only 2000 miles ; in all the other countries of Europe,
the increase has been about the same amount; while in the
United States the number of miles completed has advanced
in the same time from 5700 to 13500 miles. The lines
now in progress authorise us to expect that 20000 miles will
be in operation at the beginning of 1855 ; while in no other
country excepting France is there much prospect of a rapid
increase. The present amount in Europe, which is 16000
miles, will not probably be as large as 20000 at the begin¬
ning of 1855.
163. The railroads of the United States, though far less
costly than those abroad, are but little inferior.
In England the cost of obtaining charters from Parlia¬
ment has been considerable ; the right of way and the lands
for depots have required immense sums : tunnels have been
numerous ; handsome station houses have been built, and
much money has been wasted in making the road nearly
level. Many are supplied with a double track.
In France, the Government has had much to do in con¬
structing the roads, and itsjexpenditures are always wasteful
and extravagant.
In the other countries of Europe, the cost has been but
little above ours, and that excess is principally due to the
"♦lav for land.
67
Some of our roads have been laid with light iron, some
are poorly supplied with engines and cars, with depots and
machine-shops ; hut the great majority have heavy iron, are
well equipped, and but little inferior to the European lines.
164. Among the several states of the Union, Neio York is
first in the amount of her railroads, and then follow next
in order, Ohio, Pennsylvania, Massaclmsetts, and Georgia.
The amount in N. York is 2150 miles, and the prin¬
cipal lines are from N. York to Dunkirk on Lake Erie ; and
from N. York to Buffalo through Albany. The greater
part of these roads have been very profitable.
In Ohio the amount is 1400 miles. The principal lines
are from Cincinnati to Sandusky; and from Cincinnati to
Cleaveland through Columbus. Other routes, along Lake
Erie to connect with the N. York lines \ across the middle
of the state to connect with the Pennsylvania roads ; and
along the Southern part of the State, to connect with the
Baltimore and Ohio railroad, are partly open and will soon
be completed. These have been built cheaply and have
been very profitable.
In Pennsylvania the number of miles is 1250. The prin¬
cipal lines are from Philadelphia to Ohio through Harris-
burg and Pittsburg; from Philadelphia to the coal districts
up the Schuylkill; from Philadelphia towards Baltimore,
and towards N. York. These roads have been built at great
expense and but few have made a good return for the mon¬
ey invested in them.
In Massachusetts the amount opened for travel is 1150
miles. The principal routes are from Boston, northward to¬
wards Maine ; west of north to New Hampshire ; north of
west to Vermont; westward to Albany; southwest towards
N. York; and southeast to several points on the coast.—
This State is better supplied with railroads in proportion to
its size and population than any other in the Union. They
have been built at great expense, on account of the charac¬
ter of the country; but almost all have been well managed
and profitable.
Georgia, though the ninth State in population, is the fifth
68
in the number of her railroads. The principal routes are
from Savannah northwest to Tennessee through Macon and
Atlanta; and from Augusta westward towards Alabama
through Atlanta and Lagrange. From the first, branches
lead towards Augusta, Eatonton, Oglethorpe, Rome, and
Knoxville in Tennessee; and from the second, to Warrenton
and to Athens. The length of all is over 900 miles. They
have been built very cheaply, on favorable routes, and have
all been profitable except the State Road above Atlanta.
165. After these States come next in order Indiana, Vir¬
ginia, Connecticut and South Carolina.
In Indiana the main lines are from Terre Haute, east¬
ward through Indianapolis towards Ohio ; from Madison
on the Ohio river northwest through Indianapolis towards
Chicago on lake Michigan. The number of miles now
completed is 750; but the new routes in progress are so
numerous, that she will soon rank next after Pennsylvania
in the amount of her railroads.
In Virginia the principal route is from the Potomac
through Richmond to Weldon. The whole amount in the
State is about 700 miles.
The road first built in South Carolina, was from Charles¬
ton northwest to Hamburg. From Branchville on this road
a route runs northward through Columbia towards Charlotte
in N. Carolina. From this, a line runs northeast to Camden;
and from this a line, eastward through Manchester towards
Wilmington. Another route starts from Columbia north¬
west towards Greenville. The whole amount now in op¬
eration is about 650 miles." Their cost has been higher than
in Georgia. The older roads have however been profitable:
while the rest have been too recently in operation to en¬
able us to form an opinion of them in this respect.
166. Of the other States, those east of Ohio and South
Carolina are well supplied with railroads, and most of the
rest are making rapid progress in their construction.
This progress is especially true in Alabama, Tennessee
and Illinois, though the amount now completed in these
states is small.
GO
167. The rapidity with which capital has been invested
in these enterprises is unequalled in the history of the world.
The annual gross receipts from the 2300 millions invest¬
ed in railroads in Europe and the United States, is more
than 250 millions. This exceeds the annual value of the
cotton raised throughout the whole world. It also exceeds
the whole whole of the iron produced. These two interests
have made more rapid progress than any other branch of
industry ; but their growth has been for a longer period, and
the magnitude which they have attained is less than the
Rail Road interest.
168. This rapid progress of railroads has been due main¬
ly to the invention of the Locomotive.
Without this, they must have been confinedto those min¬
eral districts where canals could not be constructed, and to
the more important routes of travel and transportation,
where large and valuable freights demanded rapid move¬
ments. Their progress commenced with the sucapss of the
Locomotive, and without it there is no doubt that but few
would have been profitable. Its rapidity arid regularity
secures to the railroad the transit of passengers and the
lighter goods, while its cheapness excludes the competition
of horse power for heavier articles. v»
LECTURE XIV.
RAIL ROADS.
169. The first iron rails used for Rail Roads were of
cast iron; but since 1830 wrought iron is exclusively em¬
ployed.
Cast iron was preferred to the wrought, because it was
cheaper, harder and not liable to rust in the open air. The
rusting, however, is slight whichever kind is used, as the
70
top surface is kept smooth and polished by constant rubbing.
The toughness of the wrought iron makes it as durable as
the cast, under the grinding action of the wheels, although
it is much softer. Since the introduction of the locomotive
with its great weight and high velocities, cast iron has been
entirely abandoned, as it is brittle under heavy blows, and a
broken rail might cause serious accidents. The wrought or
rolled rail was introduced in 1808, but since 1830 its use has
been universal.
170. The successive forms that have been used for rails,
have been the hea vy rectangular bar, the flange, the plate,
the edge, the inverted , the j^j, the inverted jj or bridge,
and the compound rail.
Thef heavy bar of cast iron was first used instead of the
wooden sleepers ; but as the metal was brittle and the loads
immense, the rails broke frequently.
To insure strength, the shape was altered, without any
change ii^tl^e amount of iron. The same material was
made de^p arM thin, since the strength increases as the square
of the demh.' Hence, the edge rail. The breadth at the
top was kapt 2 J inches, as less would cut into the wheels;
but this breadth was retained only an inch from the top,
when it was induced to one inch, and this thickness continu¬
ed for the wfiofe depth of the rail. Fig. 16.
This shape of the rail is not, however, the best for strength.
When a bar is supported at two ends, and sustains a weight
resting on the middle, the strain is mostly at the top and at
the bottom. Tne bar yields by the crushing of the atoms
at the top, or the tearing apart of those at the bottom, the
strain on the middle being very slight. Hence, more of the
metal was distributed at the bottom, and thus the and the
23 rail were introduced. Figs. 17 and 18.
The inverted (fig. 19) was introduced for the same rea¬
sons. It has a broader bearing surface on the base than the
j, rail, as the j, is broader than the H.
Of these three forms, the j,, if well shaped, is the best.
The upper broad part must be about an inch deep before it
begins to narrow, or the wheels will crush and tear off the
71
projecting part, especially on the curves, where the conical
wheels present a small bearing surface. The breadth at the
bottom not only gives strength, but prevents cutting into the
wood below. The shape is the most favorable disposition
that can be made of the material. The is not so strong
with the same amount of iron. The H has not sufficient
breadth of base, and cannot be fastened so well to the wood
and to the chairs.
To lessen the amount of iron, a plate rail resting on a
continuous bearing of wood was introduced. This being
weak, and only 2J inches wide cut into the wood, which was
of irregular hardness 011 account of knots and for other rea¬
sons, the rail became bent and loose from the wood, and
rising at the end, formed what was called snake-heads. These
were very dangerous, especially for heavy loads and high
velocities. The wood also required frequent repairs. This
rail was thus found in the end to be more expensive than
the heavy or the q, so that it is now almost every where
abandoned.
To aid in giving strength to the flat rail, a flange was add¬
ed at the side, sometimes turning upwards, and sometimes
downwards. This increased the stiffness, but was not
the best use of the material for this purpose; and both
forms of this flange rail are now no longer employed.
Whatever form of rail be adopted, the line is always weak
at the points where two rails meet. They cannot be weld¬
ed or pinned together, or firmly united to an iron base or
chair, because of the expansion and contraction of the rails
by heat and cold, as the change of temperature from zero
up to 135°, which is reached under the hot sun, will alter the
length of a 20 feet rail ^ of an inch. As they cannot be uni¬
ted firmly, it is difficult to keep the joint even, so as to pre¬
vent one rail from rising above the other or from being bent
to the right or left. This has led to the compound rail. This
has the shape of the common cut into two parts by a ver¬
tical plane running from end to end. The joint on the one
half is placed opposite the middle of the other half, so that
every where along the line the wheels are supported by half
7'i
the rail. The two halves are united together by a projection
on the side of one, fitting into a depression on the side of
the other, thus forming a single mass to support the weight.
They are farther united by pins or rivets driven through the
two halves. If there was only one pin through the middle
of each half, it would not at all prevent the expansion by
changes of temperature. If there were two or more, they
would interfere with it between the rivets, but the parts be¬
tween the rivets and the end 1 would yet be free. The ex¬
pansion between the rivets, however, being small, it has
been found, that by giving them a little play, they will not
be broken by the expansion of the bars. This compound
rail has been but recently introduced, is more expansive than
the ordinary j,, and has not yet secured general confidence;
but the trial of it both in New York and Pennsylvania has
been quite satisfactory. Should it succeed, it would increase
very much the smoothness and comfort of the road, cause a
great saving in repairs to the engines and cars and road-bed,
and remove entirely those obstructions at the joints which
no art or skill seems able to prevent with the common rail.
171. Chairs at the joints are necessary to give strength
to the line and unite the rails.
Without them the rails would cut into the wood unequally
and no longer be in the same level; the- cross-ties, having
wheels first resting on one side and then on the other, would
become tilted and thus increase the obstacle at the joints ;
nor would, the two rails remain in the same line.
They are usually of cast iron, because it is cheaper than
wrought. They are broad, so as to give a large bearing sur¬
face on the cross-ties. They have cheeks on each side to
confine the two rails in a single line. Sometimes the cheeks
are high so that two rivets are made to pass through the
cheeks and the two rails; but this plan does not allow for
expansion, even if the rivets have some play. Sometimes an
iron or a wooden wedge is driven between the high cheeks
and the hollow at the side of the rail. This fastening is
very good. If the cheeks are low, spikes are driven through
the base of the j, and the chair into the wood below. If
73
the iron ra1! has not a broad base, a chair is often put under
it at each cross-tie.
172. The rails should be 18 or 20 feet long, and weigh
50 or 60 lbs. to the yard.
The greater the length the better ; because the weakness
and obstructions at the joints are less numerous. As the up¬
per surface must be about 2| inches broad, it would require
a weight of 55 lbs. to the yard, to give a depth of 3 inches,
a breadth at the bottom of 3| inches, and a thickness in the
middle of 1 inch.
173. The raits in use range from, 45 to 75 lbs. The
guage or breadth between the inner sides of the rails is com¬
monly 4 feet Si inches. On the Southern roads it is jive
feet, and on some Jew, North and South, it is still wider.
The broad guage is a little more expensive, having more
difference between the length of the inner and outer track,
and therefore more slipping of the wheels. The axles of
the cars must be stronger and heavier, on account of their
increased length. But as the base is broader and the centre
of gavity lower for the same load, the train is more steady
and comfortable. The locomotive can be made so as to have
more power and more velocity by an increased breadth of
fire-box and flues, and therefore a greater ability to generate
steam.
Were not the narrow guage generally adopted, a width of
5J or 6 feet would no doubt be preferred. As it is, however,
often very desirable, to pass from one road to another with¬
out unloading freight or baggage, a break in the guage is
very objectionable. New .roads are therefore built of the
same width as the old ones with which they are connected.
174. The superstructure on which the rails rest should be
of wood, and not of stone.
In the earlier roads, the iron was made to rest on stone-
blocks or sills, with the design of giving greater firmness to
the track ; but as the ground, on which the blocks or sills
rested, yielded unequally, the rails soon became uneven, and
the stiff unbending masses of rock jarred and injured the
locomotive afid the cars, and caused much discomfort to thfe
9
74
passengers. These have, therefore, been entirely abandoned.
If the cross-ties are of stone, these objections are not so se¬
rious, but still they exist.
175. The best form of superstructure is a longitudinal
sill resting on cross-ties near each other.
A distance of 4 or 5 feet between the cross-ties was for¬
merly common ; but in the best recent roads, this is reduced
to 2£ or 3 from centre to centre. As this gives a greater
bearing surface, the ground is less liable to yield unequally
and make the track uneven. A string-piece of wood form¬
ing a continuous support to the rail, and resting on the cross-
ties, is better than to have the rails supported by the cross-
ties alone. As wood is very cheap in our country, the near¬
ness of the sills and the additional string-piece will add very
little to the cost of the road. To put the cross-ties 2| feet
apart instead of 4, would increase the expense in the South
only about $300 per mile, and the string-pieces would add
about $200 more; and these would be small items in the
cost of the road.
The longitudinal sill is let down into the cross-ties, and
wedged in its seat, to prevent the spreading of the track by
the action of the flanges of the wheels. The rails are con¬
fined to the string-piece by numerous spikes driven through
the base into the wood below.
Sometimes the cross-ties rest on longitudinal mud-sills to
increase the firmness and evenness of the road. In the North,
a trench is dug 2 or 3 feet deep under the cross-ties, and fill¬
ed with small broken stones. The object of this is to pre¬
vent the injury from frost. If the cross-ties rested on the
ground, the water would get under them and freeze in the
.winter, and then by expanding disarrange the whole su¬
perstructure. This is expensive but indispensable in cold
climates.
On some roads, both in England and America, a still great¬
er amount of wqod is used. A series of cross-ties is l^id
down, making an angle of about 45° with the line. Across
these are laid another set at right angles to the first, forming a
kind of lattice work. Each set is placed so near together,
that they cross each other at three places. Notches are
in both at each crossing, so that the bottom surfaces are all
in the same level. A longitudinal sill is then placed on the
top of this lattice track, to which the rail is fastened. This
plan increases the cost of the road slightly, but the saving in
the repairs of the engines and cars is considerable, on account
•of the evenness of the track; and if the business on the
road is large, this saving will soon repay the increased cost
of the superstructure.
176. The outer track on a curve should he a little higher
than the inner.
The object of this is to counteract the tendency to fly off
in a tangent to the curve. The downward sliding of the
train towards the inner rail should balance the centrifugal
•motion towards the outer rail.
The centrifugal force increases with the velocity, so that
this cannot be balanced for all velocities. It is usual to com¬
pensate for it at the higher velocities, as the resistance on the
curves is then much the greatest.
To estimate the increased height to be given to the outer
rail, consider that the centrifugal force is the versed-sine of
the arc described, and therefore equals A2 -:-2R, representing
by A and R the length of the arc and its radius. That is,
if the train have a velocity of 20 miles per hour or 28§ feet
per second, and the curve have 1000 feet radius, the centri¬
fugal force =28§2 2000 or ^ of a foot in one second. Now
we must consider what must be the inclination of the track
so that the cars would fall on it of a foot per second. The for¬
mula for this is S=mH -;-L. Here S==140 and L=5 feet for the
Georgia guage ; hence H=1 £ inches. And this is the height
of the outer rail above the inner for this radius and velocity.
177. Moderate grades are •of great importance in laying
out a route for a Railroad. i
If they are less than 22 feet in a n^^hey are but slightly
objectionable ; especially if they aij^^H^and arising suc¬
ceeds to a falling grade. The load nearly as great
as on a level, as the steam will accumu^te on the descents to
be used on the ascents.
76
If the grade is 30 feet, the disadvantage is slight; but
when it reaches 40 or 50 feet, the load is much lessened.—
At still higher grades, the efficiency of the locomotive is re¬
duced to one-fourth or one-fifth of what it can do on a level.
If the grade is generally as low as 20 or 30 feet in a mile,
the route may he much lengthened, or a heavy cutting en¬
countered, to bring a 40 or 50 feet grade down to the usual
limit. In like manner for other grades.
178. A steep grade of 100 feel or upwards was formerly
overcome by a stationary engine, but now these are always
avoided, by lengthening the road, by deep cutting, or by tun¬
nelling.
On the South Carolina road, and on the Pennsylvania road,
built many years ago, when the locomotive was quite inferi¬
or to what it now is, stationary power was used; but the
steep grades on these roads have since been avoided at great
expense by lengthening the road.
The stationary engine draws up the train by turning a large
cylinder or dram at the top of the plane, and thus winding
up a rope, attached to the cars. These ropes, whether made
of hemp or iron wire, often break and become the cause of
serious accidents. As they draw up the load slowly, and by
parts, they cause delays and loss of time. They are also very
expensive, because they carry the load but a short distance,
and act only for a short time. On account of these delays,
accidents, and expenses, it is better to lengthen the road sev¬
eral miles, and to submit to large additional outlays, rather
than have a single one of these inclined planes.
179. The cost of the Railroads in the Southern and
Northwestern States is from $10 to $20000 per mile; in the
Middle and Eastern States from $20 to $50000.
From the Carolinas to the Mississippi, and from the Ohio to
the Lakes, the country is so nearly level that the grading of a
road has seldom jgMttfed $5000 per mile. The superstruc¬
ture, including t^^Hnig it down, is hmited at $2000 per
mile. The heav^BPfincluding the chairs and spikes, count¬
ing the price at $50l|)er ton, would require $6000. The
right of way, depots, water-stations, workshops, engines, Cats,
77
&c., may be put at $5000 more. Thus the whole
cost of a good road, well equipped, would amount to $18000
per mile. In the mountainous regions of the Southern, Mid¬
dle and Eastern States, the cost of excavation and embank¬
ment, of cutting in rock, of tunnelling and bridging, has in¬
creased the expense of construction to 30, 40 and even
$50000 per mile. In some places the right of way, a
double track, an unfavorable route, and the effort to make the
track very nearly level, have raised the cost to over $50000;
and on one road, viz : the Reading, to $160000 per mile.
LECTURE XV.
IMPROVEMENT OF RIVERS.
180. Ij the navigation of rivers is interrupted by sand¬
bars, their removal is attended with great difficulty and ex¬
pense.
When the effort is made to remove them by dredging, that
is by attaching a plough or a scraper to a boat which is driv¬
en by the current or by a steam engine, the bar may be tem¬
porarily removed, but the channel is soon re-filled by the
sand brought down by the current.
If wing-dams are built out from the shore to throw the
current to the other side, so that the large volume of water
passing rapidly may make and keep open a channel, the ef¬
fect extends but a small distance down the stream. If oth¬
er wing^dams are built to continue this channel, the expense
becomes very great. Or if a wall is built up and down the
stream from the end of the first wing-dam to confine the cur¬
rent for a longer distance, the floods and drift*wood of the
next winter may break away the dam of wall, and form the
main channel at a new place, and thus render the former out¬
lays entirely useless.
78
Whatever plan be adopted, great expense is always involv¬
ed, while the advantage received is always small.
181. When the channel of a river is interrupted by rocks,
it may be ope7ied by blasting the rocks and then removing
them.
If the rocks are loose and exposed because the water has
washed away the soil around them, their removal is easy and
usually of great advantage.
If a narrow ledge runs across the stream, forming a ripple
or a fall, its removal by blasting is attended with greater ex¬
pense, especially as the channel will olten have to be opened
for a considerable distance.
But if the ripple or fall extends down the stream even for
a short distance, the cost of removal will be very great. The
expense of blasting, the high wages of hands working in
the water, and the length of the channel that has to be open¬
ed involves so large an outlay that it is seldom repaid by the
advantage that is gained.
182. When the navigation of a river is interrupted by
snags, saioyerS) water-logged timber, rafts, or other obstruc¬
tions of wood, they can generally be removed to advantage.
These are dragged out of their place by the force of steam,
or of a descending boat, then sawed into pieces, and removed.
Sometimes, they become partly covered with sand, and the
force and labor required to displace them is increased. But
in all cases they are foreign obstructions, interfering very
much with the navigation, and usually removed at a moder¬
ate expense ; so that the advantage gained more than balan¬
ces the outlay incurred.
183. When the fall is considerable or extends for a long
distance, the stream is made navigable by dams or locks.
The dam is placed at the bottom of the falls, and blacks
the water so as to deepen the channel above. If it is desired
to pass the boats only in one direction, a narrow opening is
left in the dam through which the boat may pass. Some¬
times the openings in the dam are supplied with gates to retain
the water better. Sometimes they are supplied with locks.
184. A lock is a chamber, large enough to contain the lar-
79
gest boats on the river, connecting with an upper and lower
level of water by gates, and used to raise and lower boats
from one level to another,
It may be placed in the dam itself near the shore, or in the
bank at the side. The gates are double, turn on vertical hin¬
ges, meet at an obtuse angle, and open up the stream, so that
they are kept closely shut by the pressure of the water.—
Near the bottom of each of the four gates are valves about a
foot square. The upper beam of the gates projects beyond
the hinges, and is made very heavy, so as to balance the
weight of the gate, and form a lever by which they may be
easily opened.
If a boat is to be passed upwards, the valves in the lower
gates are opened, and the water runs out of the chamber,
until it is on the same level as the water below. The low¬
er gates are then opened, the boat floated into the lock, and
the lower gates and valves closed. When the boat is thus
confined in the lock, the valves in the upper gates are open¬
ed, the water enters and gradually raises the boat until it is
as high as the water above, when the upper gates are open¬
ed and the boat floated out oil the upper level. In like man¬
ner, the boat may be transferred from the upper to the lower
level.
185. Locks are usually made of cut stone, but sometime*
of wood or of brick.
They are built very substantially, on account of the great
pressure of the water. Their depth is seldom over 12 feet,
usually 8 or 10. If a greater fall than 12 feet is to be over¬
come, two or more locks are commonly made. The largest
will pass a boat through in 8 or 10 minutes, so that very lit¬
tle time is lost. If used to pass boats drawn by two horses,
they are commonly 100 feet long and 12 feet wide. For
larger boats, or for steamboats, their size is increased.
186. The dams, whether built oj wood or stone, should
have a base three or four times greater than their height.
In building a dam of wood, it is usual to lay across the
stream two rows of sills, with a distance between them three
or four times the height of the dam. Upright posts arc then
so
raised on the lower sills. The sills and posts are all now
united firmly together, forming a triangle. On the upper face
of this, dry pine planks two inches thick are laid ; and above
the upper row of sills a piling of plank is driven into the
soil for a great depth, or until it meets the rock below. If
it reaches the rock, it must be made to fit it well by cutting
the end to the piling to a proper shape.
The strength of this form of dam is very considerable. —
The downward pressure of the water resting on the dam
helps to hold it in its place ; while the bracing of the sills
and the facing plank bind it together, and prevents it moving
downward with the current.
If the inclined plane had a base only double its length,
the vertical pressure of the incumbent water on the triangu¬
lar face of the dam, would be just equal to the lateral pres¬
sure in the direction of the stream. But as the base
is mpre than twice the length, the vertical pressure exceeds
the lateral; that is, the weight of the water helps to retain
the dam in its place.
The excess of vertical pressure, and the bracing of the
timbers supply a force to resist the momentum of the water
in time of floods, and the blows of drift-wood, ice, and oth¬
er floating bodies that may strike against the dam.
Tightness is secured by the piling and the facing plank.
These swell and form a very compact and dense surface.—
Sometimes the inclined plane is covered with soil to increase
the ability of the dam to retain the water.
These wooden dams often last 10 or 12 years, as the tim¬
bers do not rot readily when under water.
When the stream is subject to high floods and to violent
blows from drift-wood or ice, a stone dam is constructed.—
This is built essentially on the same plan as the wooden
ones ; the triangular space below the facing being filled with
stone, to give increased stability to the structure. The size
and shape, the piling and facing remain the same. Some¬
times the rocks are nqt put in every part of the dans, but in
large pens at intervals across the stream. In all cases, but
little dependence is to be placed on the bracing of the tim-
81
bers or the workmanlike masonry of the wall, since the
weight of the rock and the downward pressure of the wa¬
ter must give firmness to the mass, while the wooden facing
and piling, with dirt resting on them, must retain the water.
If the bottom of the stream is of such material that it may
be washed away by the water running over the dam, the
lower side is inclined more or less, to break the force of the
falling water and prevent its undermining the lower sills or
walls.
187. When the stream is wide, or the fall very rapid, it
is better to make a canal at the side, than to build a dam
across the stream.
On the Ohio, around the falls at Louisville, a canal is used
instead of dams. On the Schuylkill, sometimes one and
sometimes the other plan is adopted.
188. This improvement of rivers by slack-water naviga¬
tion is expensive, and very seldom pays interest on the out¬
lay.
Over 1000 miles have been improved in this way in the
United States; but several of these have been abandoned;
the greater part have returned but small dividends to their
stockholders, while a very few have been profitable.
The first cost for locks and dams is large ; the ordinary
repairs demand considerable money ; while the extraordina¬
ry damages by floods and ice, are often so great as to require
an expenditure but little less than the original outlay. In 10 or
12 years the wood work is entirely decayed, and must be re¬
placed by new materials. Thus it happens that the demand
for repairs and depreciation leaves little or perhaps nothing
for dividends to the stockholders.
10
LECTURE X V/
CANALS.
189. Canals were used for commercial purposes by the
ancients in Egypt, Persia, Italy, and China; and in the
middle ages more or less by every country in Europe.
In the earliest ages of the world canals were made, as they
now are in many countries, to aid agriculture by supplying
the fields with water ; but even before the period of authen¬
tic history, the Isthmus of Suez was crossed by a canal so as.
to unite the Mediterranean and the Red Sea. Alexander
opened canals in Persia, that had been dug before his inva¬
sion. The Romans constructed many in Italy, especially
along the Po ; and before the Christian era, the Chinese had
connected Pekin, with the provinces of the empire, so as to
transport by water a supply of rice and other grain for the
large population of their capital.
In Italy, France, Holland and Germany, a large extent of
artificial water navigation was opened before the eighteeuth
century.
190. From 1750 to 1850, the progress of canals has been
rapid; though recently, since the introduction of Railroadsr
it has been everywhere very much checked.
From 1755, when the Bridge water canal was begun in
England by Telford, to 1830 when railroads were success¬
fully introduced, more than 3000 miles were constructed in
Great Britain.
The immense transportation of coal, iron, and manufac¬
tured goods, has made these canals, for the most part, very
profitable. Some have paid 100 per cent, per annum on their
cost, and their stock has been 800 per cent above par.
In the United States, they were introduced before the Re¬
volution, but the first work of importance was the Erie canal.
Vv>
in New York, from Albany to Euilnlo, begun in 18IT, and
•completed in 1825. This was 362 miles long, and co^t about
seven millions of dollars. This main line was connected
with Lake Ontario and Champlain, and some other small
lakes, by branches which cost about seven millions more.
Large amounts have been expended recently in widening and
■deepening the Erie canal, and in enlarging its locks,
until the whole outlay has now exceeded thirty millions,
while the enlargement is not yet completed. The annual
net income on all these works has been larger than the in¬
terest on their cost; so that, although the branches have been
unprofitable, the State has gained by the expenditure, regard¬
ing her merely as a stockholder. The other advantages to
the State and the city of New York have been immense.
The whole amount of canals constructed in New York has
'been about 800 miles.
Canals have been built in Pennsylvania, along nearly all of
her rivers, so that the whole amount in operation is about
1000 miles. Most of these were built between 1830 and
1840. Their cost has been about 30 millions, and but few
of them have been profitable.
In Ohio there are 800 miles which have cost about 18
millions. They were begun in 1825 ; but most of them
were completed between 1830 and 1840, The principal
routes have been from Cincinnati to the Maumee river, and
from Portsmouth on the Ohio to Cleveland on Lake Erie,
These have not paid full interest on their cost,but have been
very beneficial to the people of the State.
The Wabash Canal* in Indiana connecting Lake Erie and
the Ohio river, by the vallies of the Maumee and Wabash
rivers, is a large and important work not yet completed ; but it
will soon be opened the whole way through.
The number of miles in all the States is over 4000, at a
cost of 120 millions. A few of these have been abandoned ;
one-third of all have paid good dividends; the rest, though
making but small returns on the capital invested in them,
have conferred great advantages on the country.
rPheir recent progress has been very slow, as they cannot
84
compete with Railroads for passengers and light freightand
the principal routes, where a large amount of heavy freight
is offered for transportation, are already occupied by canals.
191. A canal is an artificial channel oj water, from 30 to
50 feet wide, 4 or 5 feet deep, and so nearly level that the
water has but a very slight movement.
When the canal is narrow and shallow, and the locks small,
the largest boats can be drawn by a single horse. For two-
horse boats, a depth of 4 feet, and a width of 40 at the top,
and locks 90 feet long, are sufficient; since on these, boats
12 feet wide and 90 feet long may be used. The cross sec¬
tion of the water displaced by these ]>oats might have an
area of about 36 feet, and this multiplied by 80, the average
length, would give 2880 solid feet as the amount of tfater
displaced. The weight of the boat is therefore 2880X 62J
or 180000 lbs. The resistance on this ip 1^0000-^-7520 or
250 lbs., the proper load for two horses.
By making the canal wider and deeper, and thet. locks lar¬
ger, the resistance is lessened, larger boats can be used, and
the cost of attendance per ton is decreased, and the transpor¬
tation can be effected with greater economy. On the Schuyl¬
kill. the Delaware and Hudson, and the Erie, large sums
have been expended to advantage in enlarging these canals.
If water could be introduced between each set of locks,
to supply the waste from evaporation and leakage, and the
demand for the locks, there need be no current in the canal,
and each basin would be perfectly level. Buhgpt is difficult
to get such a supply of water withoJ failure, and also with¬
out injury. It is usual therefore, to introduce the water at
distances of 15 or 20 miles. Sometimes these intervals are
as long as 40 or 50 miles, but this requires too much of a
current.
A fall of 2 or 3 inches per mile is enough f0r the short in¬
tervals, and 5 or 6 inches for the longer.
192. When water is very scarce, the boats are sometimes
ransferred from one level to the other by an inclined plane.
In China, locks are not used, and the boats are dragged up
an inclined plane by the strength of men. But an overshot
85
water-wheel is sometimes employed in Europe and in Ame¬
rica for this purpose. To raise a boat of 100 tons by a lock
of 8 feet lift, requires 90X 12X8X62|-f- 2000 or 270 tons of
water. To raise the same boat by an ovreshot wheel would
require only 150 tons, one-third of the full efficiency of the
water being lost by this kind of wheel. The saving of wa¬
ter is therefore considerable.
The boats are raised by floating them on a car with wheels,
and the car is drawn up on the inclined plane by a rope which
is wound around a drum turned by the water wheel.
This method is not so simple as when locks are used; it is
more costly at first, requires more for repairs, causes delays
and accidents, and is therefore never used except when the
scarcity of water renders it indispensable.
193, The canal is usually made tight enough by the na¬
tural soil; but sometimes the bottom and sides are planked, or
covered with hydraulic cement.
If the soil is of clay, the bottom and sides of the canal are
well rammed before introducing the water. If of sand, they
are covered with a layer of clay. This does not make the
surface water-tight, but the percolation is small and decreases
after the first year, by the ordinary deposit from the water.
If the base is rocky, and the planes of stratification come to
the surface, it will be necessary to use plank or water cement
to close these openings; and if cement is used, this must be
itself covered two or three feet deep with earth to prevent
injury from the shocks and the rubbing of the boats.
When there is an embankment, the walls are made very
thick to lessen the waste of water. Not less than 8 feet at
the water surface, when the soil is very compact; and usu¬
ally 10 or 12. This wall is still thicker at the bottom, as
the slope on either side is not less than If base to 1 in per¬
pendicular height.
194. The tow-path jor the horses should be 10 or 12 feet
wide, about 2 feet above the water surface, very nearly level,
but inclining slightly outward.
This width is necessary to permit the horses to pass easily;
the height, to keep the path above the wave caused by the
so
boat; the level grade, to save the horse the labor of lifting
his body up hill; and the inclination, to give the horse a good
foothold, and to prevent the rain-water from running into the
canal.
175. The rope by which the horse draws the boat is fas~
tened to the middle of the boat and is not less than 150 feet
long.
If the rope is shorter than this, more of the horse's force
is wasted in drawing the boat towards the bank. If the rope
is 150 feet long, and the boat 15 feet from the path on which
the horse walks, the force of the horse resolved in the di¬
rection in which the boat is moving is diminished only 2J0 of
his full effect.
176. A supply of water is obtained from creeks along the
route, from feeders, or reservoirs.
When the canal crosses a stream which can be introduced
into the canal, only a limited amount of water is admitted,
for the whole might form too much of a current in the ca¬
nal. In whatever way this limiting is effected, an excess
will at times be introduced; and this must be permitted to
run off by a waste-way at the side of the canal, made of
rock, so as not to be washed away by the water escaping
from the canal.
But few of the streams that are crossed are introduced into
the canal, as it is difficult to prevent them from injuring it
in times of freshets: most of them are passed either by
a culvert when they are small, or by an aqueduct when
large.
When the route does not meet a stream high enough to be
introduced into the canal, a supply is sometimes obtained
from distant streams by what is called a feeder. These are
sometimes 10 or 15 miles long, and involve great expense.
When a sufficient supply of water cannot be obtained from
streams or feeders, large reservoirs are sometimes constructed
to collect the rain-water of winter for use in the summer.—
However large these may be, they can never be depended on
themselves, but are only an aid to streams that fail in the dry
seasons of the year.
s7
When all these sources fail, a steam engine has he-en occa¬
sionally used to raise a supply of water. This has been done
on the Thames, and on the Union canal in Pennsylvania.—
But as the demand for water for evaporation, for leakage, and
for passing the boats through the locks, is large, this meth¬
od is expensive and can seldom be used advantageously.
197. The usual velocity for loaded boats is between 2 and
miles per hour ; for passengers. 3 J to 4.
The slower the velocity, the less is the resistance and the
greater the useful effect of the horse; but below 2 or 2^ miles
a horse cannot exert his force continuously. At higher ve¬
locities the resistance increases so rapidly, that even for pas¬
sengers five miles per hour would be a wasteful expenditure
of power. Besides, at this rate, the wave caused by the
boat washes the sides of the canal and injures them so much
that this velocity is absolutely prohibited.
198. Steam can seldom be used to advantage on canals—
only when they are very wide and deep.
As high velocities cause great resistance and injure the sides
of the canal, even with the submerged paddles or the screw,
the steamboat must move slowly. Then its load or the num¬
ber of boats it can draw becomes large, and the delay of pass¬
ing through the locks wastes much time and steam. Hence
the boats and canal and locks have to be very large to use
steam advantageously. On the Erie canal horses only are used.
On the broad and deep route between Philadelphia|and New
York the steam-tug is employed.
199. The cost of a cajial oj the usual size, 40 feet wide
at the bottom, 50 at the top, and 5 Jeet deep, with locks 12 feet
long and 100 feet wide, is about $20000 per mile.
This was the first cost of the New York and Ohio canals.
If the rock-cutting is large, or the aqueducts numerous, or
the walling or planking expensive; or if the canal is wider
and deeper, and the locks larger than common, the cost may
be much increased.
200. The business that may be done on a canal is much
larger than on a Railroad.
As a load of 100 tons on a canal will only occupy 100 feet.
88
and as the boats can readily pass one another, the capacity of
the canal would seem to be immense. But the delay at the
locks imposes a limit to the number of boats. Not less than
six minutes is required for filling a lock for a 100 ton
boat, or twelve minutes for filling and emptying. This
would allow five in an hour, or sixty in a day, or 6000 tons
in one direction. But while the lock is emptying for an as¬
cending boat, it may sometimes let down a descending one ; or
while filling for a descending boat, it may raise an ascending
one. Thus 8 or 10000 tons may pass in 12 hours. By using
the locks after night, still more may bypassed. This, how¬
ever, exceeds the capacity of a common railroad, even with
a double track.
201. On account of the large capacity of a canal, and the
slight resistance in water, the charges for transportation are
lower than on a railroad.
Besides the cost of the motive force, tolls have to be paid
to repair the canal and to return interest on the first cost.
As the tonuage on which these are levied is large, the amount
per ton is small. For both reasons therefore, the cost of trans¬
portation is less on canals than it is on railroads.
■u
LECTURE XVII.
comparison between roads and
canals:
f
212. When a country is new and unproductive, common
roads are the only ones that are ma^l
The amount of freight and travel being small, they will
not pay for a more expensive road. As the country becomes
more thickly settled, and its productions, whether of agricul¬
ture or manufactures, increase, importance of good roads
is felt; and if the character of the soil is such that the roads
sO
are much cut tip and injured after rains or frosts, or if they
are very sandy or marshy, a turnpike or a plank road may be
desirable. When the freight or travel becomes still larger,
railroads or canals may be constructed.
203. If 25000 tons or 50000passengers per annum pass
over a route, a railroad may be substituted for a common
road.
As the cost of carriage on the common road is from 12 to
$20 per ton per 100 miles, if the charge on the railroad is re¬
duced to half this price, common wagons will be driven
from the route, and freight and travel will be attracted for
some distance off the line. If the charge averages $8 per
ton, the receipts will reach $200000 for 100 miles. The ex¬
penses are, for transportation 25000 X $1.35, or $33750; for
repairs of the track $500 per mile, or $50000. The net re¬
ceipts will therefore be $116250, or about 6J per cent, on a
cost of $1,800000.
The receipts for 50000 passengers, at 4 cents per mile,
would amount also to $200000. The expenses would be
about the same as for the 25000 tons, counting the cost for
two passengers and their baggage the same as a ton, because of
the high velocity, the small net load, and the expensive cars.
204. A Railroad may be built in the South to more ad¬
vantage than any other artificial road.
With turnpikes no comparison need be made ; but with
plank roads, this proposition is not so evident.
If the country is level and sandy, a plank road may be
built cheaply and to great advantage to the horses and the
travellers. Suppose the country so thickly settled that ten
passengers on an average pass in both directions every day
in the year, either in buggies or stages or carriages, and 60
loaded horses with freight.
When a plank road is built, suppose the passengers to
double and the freight to double. The passengers will then
number 20 per day, with about 10 horses ; and the freight
will not require more than 80 horses, because the efficiency
of the horse is also doubled. The toll per day would
then be, at two cents per mile for the first horses and one
11
ill)
cent for the others, for a distance of 20 miles, 4+16 or $20.
For 313 days this would give $6260. From this deduct
$450 for three toll collectors, and $1000 for annual repairs of
the road ; and the net receipts will be $4810. If the planks
be only 2 inches thick and the two sills 4 by 12, the cost of
the planks at $7 per thousand will be for the 20 miles 20X7
(8X2+4x2)5280 ^-1000 or $17741. For grading, ditching,
and bridging, $200 per mile ; for laying down the plank,
and for toll houses $200 more ; making for the 20 miles
$8000 more, or $25741. Hence, if the road should last on¬
ly five years, which is a fair limit for our warm climate, the
annual receipts ($4810) will not even return the capital
($25741) to the stockholders, much less pay them a dividend.
In this estimate, the amount of planks, and the cost of
grading are put down very low : and the tolls are as high as
could be demanded. If they were raised to lg or 2 cents
per mile per horse, the receipts would not probably be in¬
creased at all, since at this rate many of the wagons would
prefer the common road.
If a railroad were built between the same points, the pas¬
sengers will be increased to thirty or more per day. The
freight will also be increased largely, but we will put it at
what would be drawn by the 80 horses on the plank road, or
60 tons. The receipts from the passengers at 5 cents per
mile, and for the freight at $1.60 per ton will be 30+96 or
$126 per day. For the year this will give $126x313 or
$40698. The cost of transportation will be (15+60)X 313
X$1.35+ 5 or $633S. The repairs at $500 per mile would
be $10000; leaving net receipts $24360. The cost of the
road over this favorable route may be put. at $16000 per mile,
or $320000 ; so that a dividend of nearly eight per cent,
could be paid to the stockholders.
In this estimate nothing is allowed for depreciation, because
$1.35, the cost of transportation per ton for a hundred miles,
includes the repairs and depreciat'on of the cars and locomo¬
tives; and the $500 per mile for repairs will keep the super¬
structure and the iron in as good condition as when first
laid down. The shortness of the line and the small amount of
91
freight will not prevent the cheap working of the road, be¬
cause a single locomotive can make two double trips or 80
miles per day, carrying both passengers and freight.
Thus it appears that while no dividend is received by the
stockholders 011 the plank road, a railroad between the same
points will give a handsome return.
205. If the navigation of a river is interrupted much of
the year, a railroad may be built advantageously along its
banks ; but not otherwise.
The Central Railroad has entirely driven the steamboats
olf the Oakmulgee. The South Carolina Railroad car¬
ries a large portion of the cotton from Augusta ; and another
railroad is building along the Savannah to compete with its
boats. Along the Delaware and Hudson, where ice inter¬
rupts the navigation much of the year, railroads have been
built which are used advantageously in the winter. But
neither on these rivers, nor on the Ohio or Mississippi, can
railroads compete successfully with steamboats for travel or
freight, when the navigation is unobstructed. Passengers
can be carried profitably 011 a boat at less than a cent a mile,
and this amount will only pay the expenses on a railroad,
especially at high velocities, and leave nothing for dividends
to the stockholders. The whole cost of transporting pas¬
sengers on the Georgia Railroad is about $1.35 for 100 miles,
and this is as low as the average of other roads. On the Hud¬
son river road, the level grades and the well built track tend to
lessen the expense, but the large amount needed for repairs of
cars and maintainance of way, at their high velocities, bal¬
ance this in part; and there is reason to believe that the ac¬
tual cost can not be reduced as low as on the river. The
stock would thus be valueless, were it not that local freight,
the mail, and the winter travel afford them some profitable
business.
206. For light freight and travel, railroads are prefera¬
ble to canals. For heavy freight the canal is best.
For ordinary travelers whose time is valuable, the railroad is
best, on account of the rapidity of locomotion. But when time
is not important, canals are best, because they are cheapest.
'.1-1
Formerly the Eric canal earned a large number of travel¬
ers ; but since a railroad has been built along the same route,
the canal is almost deserted. Even the emigrant passengers,
who wish to travel very cheaply, for the most part prefer the
railroad. But between Liverpool and Manchester far more
pass by water than by railroad. The poor laborers, having but
little money to spare for traveling, prefer the cheapest route.
For light freight the same reasons apply. The saving of
interest with the rapid trains, and the regularity of the transit,
secure the costly freight to the railroad, although the canal
might carry it the cheapest. For coal which is worth 3 or
$4 per ton, or for iron which may be worth $50, the canal
is to be preferred.
Thus between Philadelphia and New York the freight
carried on the canal far exceeds that by the railroads ; not on¬
ly coal, but a large amount of merchandise being transport¬
ed on the canal. The whole tonnage, of all kinds, on the
Liverpool and Manchester road is about 500000 tons, while
one of the water routes between the same points has more
than twice this amount. On the New York canal the ton¬
nage exceeds two millions, although between Lake Erie and
the Hudson, two railroad routes .^ave by competition re¬
duced the charges for transportation to the lowest possible
limit.
The great Reading Railroad between Philadelphia and
Pottsville, and the Schuylkill canal on the same route, seem
at first sight to be exceptions to the general rule. Here the
freight is almost entirely coal, which is commonly worth
less than $4 per ton; yet the transportation on the railroad
has reached 1,600000 tons, while on the canal the greatest
amount has been 800000 tons.
But this road has been built with a very favorable grade
for the down freight. For the whole distance from the
mines to the Delaware, the road is either level or descending.
The load for a locomotive is therefore much larger than on
a common railroad. They work the whole year on the rail¬
road ; while the canal is interrupted 4 or 5 months by ice.
The mines are beyond the termini of both lines, andjthe
93
coal is brought by railroads to Pottsville, so that it must be
unloaded before it can be started on the canal; and this in¬
volves not only expense but a loss of coal by breakage in
the unloading. The transfer of the coal to the ships at Phila¬
delphia is less costly from the Railraod, since the terminus
is above the decks of the vessels and the load can be thrown
into the hold without any labor. The distribution of the
coal among the consumers in Philadelphia is cheaper from
the railroad, since it can be carried to the centre of the city
before it is unloaded. Yet with all these advantages, the
tonnage on the canal has been gaining on the railroad, and
will probably, before a long time, be equal to its full capacity.
The cost of transportation on a canal and a railroad was
stated before at 50 cents, and $1.35 per ton per hundred
miles; and besides this, a charge must be made for a divi¬
dend for the stockholders. But before a railroad can com¬
pete with a canal, this cost must be much reduced.
The several items that enter into this cost are for repairs
of road, for repairs of cars, for motive power, for wages of
persons employed in conducting the transportation, and for
a dividend to the stockholders on the cost of the road.
The first two of these items cannot well be diminished
on the best constructed road. If the loads are heavier and
more numerous, the iron is worn away more rapidly, the
wooden superstructure displaced, and the bridges injured.—
The cars have to be increased just as rapidly as the loads, so
that in these there can be no saving at all. Not so with
the motive power. By making the road level a locomotive
can draw a larger load without extra cost. Its wear and tear,
its fuel, its engineer and fireman remain the same. The
persons employed at the water-stations and depots are not
increased, but the break-men and conductors and laborers are
more numerous. The charge per ton for dividends to the
stockholders diminishes rapidly as the business increases.
On the Reading Railroad they have reduced the cost of
transportation from $ 1.35 to 60 cents, while 90 cents more is
sufficient for a dividend to the stockholders, so that the whole
charge is $1.50 per ton.
04
On a canal but little can be saved by increasing the busi¬
ness, or enlarging the locks and water-way. With a large
broad and deep boat, the resistance for each ton and the cost
of attendance are but slightly lessened. The return to the
stockholders for each ton decreases of course as rapidly as
the business increases. But the depreciation of the boats
and the cost of loading and unloading retnain the same. The
boats have no return load and the cost of carrying them back
is considerable, since the horses canliot move rapidly even
with an empty boat. , * ♦
On the Schuylkill canal they have not been able, for these
reasons, to reduce the cost of transportation below 50 cents
per ton, while 80 cents is necessary fojr a proper dividend to
the stockholders, so that the whole oparge is $1.30 per ton.
As the business on the canal increases, ^his may hereafter be
reduced.
y
Thus even on this superior roadf witfi all its advantages,
heavy freight cannot be transported as cheaply as on the canal.
207. Wltpn a large amount of freight is passing between
two places, a canal and railroad-should both be built.
A proper division of freight and travel is readily made by
the wants and interests of the gublic who patronise the lines ;
while competition betwe<?li the two reduces the cost and the
charges as low as possible. Thus, between the Chesapeake
and the Delaware, the Delaware ancf the Hudson, the Hud¬
son and Lake Erie, Lake Erie and the Ohio, and Lake Mich-
J
igan and the Mississippi, both raikoads and canals are built,
to the great advantage of the community,
95
LECTURE XVIII.
LEVELING.
208. In constructing a Railroad o/a Canal, great accu¬
racy is necessary in the leveling. i
The channel of a canal is so straight and regular, that a
very slight fall, only 4 or 5 inches in a mile, will give to the
water a velocity of 1 mile per hour. An error, therefore, of
a few inches might turn the wat-er back towards its source,
or give it too rapid* a motion iii'ther other direction, and thus
make a current and perhaps exhaust the supply of water.
On a railroad the same accuracy is not necessary. On neith¬
er is mathematical exac^iie&s wanted.
209. Leveling is commonly done with a Spirit Level, at¬
tached to a small Telescope, and, supported by a Tripod ; be¬
sides which, is wanted a graduated rod.
The rod being placed -successively at two stations 100 feet
apart, the telescope is directed to- it, and the height of the
line, where the horizontal wire of the telescope strikes the
rod, above the ground is observed and recorded. The height
on the first rod is called a back-height, and on the second, a
Jore-height; and the excess of the back-height over the
fore-height, gives the rise in the ground between these sta¬
tions. In like manne^ the rise of the third over the second,
and of the fourth over the third &c., are obtained. The sum
of the first two gives the height of the third above the first •
this sum added to the third rise, gives the height of the
fourth above the first. And so the height of each station
above the first is found. If the fore-height should be
more than the back-height, the difference should be regarded
as negative ; and the additions, for the elevation of each sta¬
tion above the first, performed according to the rules of
Algebra,
96
210. When the rod is more than 200 feet from the leveling
instrument, the distances of the first and last station from
the instrument should be nearly equal.
The true level being a curve, and the axis of the telescope,
or the line along which the eye looks from the instrument to
thejrod, being a tangent to this curve, the back-heights and
fore-heights will always be too large, by the space between
the tangent and the curve. This space will be equal for the
two observations, if the distances of the rod from the instru¬
ment should be the same. The errors in the back-heights
a'id fr-re-heights being equal, will disappear in the subtrac¬
tion, when the difference between them is taken to obtain the
rise.
If the distances are small, the errors though unequal, are
inappreciable. For one mile, the space between the tangent
and a curve is two-thirds of a foot, and varies as the square
of the distance. For 200 feet or of a mile, the space is
fxGe)2 or about io00 of a foot; which is the smallest amount
that can be observed on the graduated rod.
Hence, when the distances of the rod are 200 feet or less,
they need not be equal; if they are 4or 500 feet they should
be nearly equal; if they are much larger they should be made
very nearly equal.
211. Several observations are often made without moving
the instrument, and then all but the first and last are both
fore-heights and back-heights.
This is done to save time in moving and adjusting the
instrument. The second observation compared with the
first shows the rise of the second station ; and the third
compared with the second observation shows the rise of the
third station over the second ; so that the second is twice
considered; once, to be subtracted from the first, and again
to have the third subtracted from it ; and this is the same
as to regard it first as a fore-height and then as a back-height.
When several observations are thus taken at once, the dis¬
tances that should be kept equal, are the first and last; as
any errors in the intermediate heights will not affect the
last elevation.
1)7
212. Xs a check against errors in the calculations, it is
usual to find the rise of several stations by subtracting the
sum of their fore-heights from the sum of their back-heights ;
this remainder being added to the height of the first of these
stations will give the height of the last.
As this is taking the difference of the sums, and the other
method was to take the sum of the differences, the results
must be the same.
i2l3. When several observations are taken without mov¬
ing the instrument, the rise of the last of these over the first,
can be found by comparing the first and last heights; this,
added to the height of the first of these stations, will give the
height of the last
Errors of addition and subtraction being easily made, these
and other methods of checking the results are important in
practice.
214. In running a long line of levels, it is usual to take,
every mile or two, the elevation of a cut made in a tree, or of
some fixed permanent mark, to be starting points in subse¬
quent levelings. These are called bench-marks.
As the stakes driven down at each station may easily be
displaced, the necessity of this is apparent, since the line
must be often leveled before the work is completed.
215. The profile of the line may be made from the heights
oj each station above the first; the heights being exaggerat¬
ed 10 or 20 times or more, to make the rise and fall more
apparent to the eye.
If a horizontal line is drawn across the paper to represent
the level of the first station ; and by means of a scale with
divisions close to the edge, the distances between each sta¬
tion are laid down along this line ; and at each station the
scale is held perpendicular to the horizontal line by applying
its end to that line, and the heights then marked off, ex¬
aggerating each in the same ratio; a waving line drawn
through the ends of these perpendiculars will represent the
side view of the ground that has been levelled.
216. The grade line Jor a rail-road is made by drawing it
12
across the plot so that the cuttings abort- it shall be
equal to the fillings below it—both being near each other.
Th is is usually done by the eye ; but it' greater accuracy
is wanted, the cuttings and fillings may be calculated and
thus made equal. If they are within a hundred yards of
each other, they are said to be near ; but it is better to carry
the dirt, from the cuttings to a filling, 3 or 400 yards, than
to obtain it from the side of the road.
The height of the grade line at each station is obtained
by measuring it at its extreme points and noting the rise
for the whole distance, and then, by proportion, finding the
rise for each station, and then its height at each station.
217. The cutting or filling at each station will be the dif¬
ference of the heights of the ground and of the grade line.
If, for example, the ground is 113.4 feet above the base
line of the first station, and the grade 116.2 above, the
ground will be 2.8 feet below the grade, and an embank¬
ment of this amount must be made. This is marked 2.8 B.
When the ground is above the grade, the difference is mark¬
ed A. So that A and B indicate the cuttings and fillings.
The following table will illustrate the several particulars
referred to. At station 161, the back-height and fore-height
were 4.817 and 2.581. The latter being the larger, the
difference is positive and the ground rise?. The instru¬
ment is not moved until the rod is carried to station 164, so
that the fore-height of 161 is to be entered as the back-
height of 162and also of 163 and 164. The level of 160, or
its height above the first station, is 65.532and adding this
to 2.236 gives 67.768 the level of 16 L. Adding this, algebra¬
ically, to the next difference, gives the level of 162. And so
the rest are found. The level of 164 may be checked by tak¬
ing 2.438 from 4.817 and adding the difference 2.379 to the
level of 160, to get that of 164. So also 169 and 174 may
be checked. The sum of all the back heights is 89.156 and
of the fore-heights 85.647. The difference 3.509 being ad¬
ded to 65.532, gives 69.041, and is a check for 175. The
heights of the grade line at 160andat 170 being found to be
65.5 and 68.5, the difference, divided by 10. pives .3 as the
rise tor each station. This being added to 65.5, gives 65.8 as
the grade for 161. The difference between the level and
the grade of 161 or '2.0, is to be marked A, because the ground
is above the grade.
Sta¬
Dist¬
- Back-
Fore-
Differ¬
Levels
Grades
A & B
tions
ances heights
heights
ences
65.532
65.5
0.0
161
100
4.817
2.581
2.236+
67.768
65.8
2.0
A
162
4.876
2.295—
65.473
66 1
.6
B
163
6.341
1.465—
64.008
66.4
2.4
B
164
2.438
3.903+
67.911
66.7
1.2
A
165
8.343
7.813
0.530+
68.441
67.0
1.4
A
166
6.716
1.097+
69.538
67.3
2.2
A
167
5.524
1.192+
70.730
67.6
3.1
A
50
2.146
3.378+
74.108
168
5.837
3.691—
70.417
67.9
2.5
A
169
8.914
3.077—
67.340
68.2
.9
B
170
5.334
9.642
4.308-
63.032
68.5
5.5
B
171
9.818
0.176-
62.856
68.8
5.9
B
172
2.519
7.299+
70.155
69.1
1.1
A
173
"2.487
0.032+
70.187
69.4
.8
A
174
1.811
0.676+
70.863
69.7
1.2
A
175
4.362
6.184
1.822—
69.041
70.0
1.0
B
Totals
89.156
85.647
3.509+
218. The u distances out" of the side stakes from th
centre depend on the cross slope of the ground, on the slope
to be given to the sides, on the depth of the cut or the height
of the bank, and on the width of the road-way.
For a single-track rail-road, the width of an embankment
should be 16 feet, and of a cut 24 feet, to leave a space be¬
yond the track for the cars to run on, if they should get off
the track, and to lessen the chance of the rails being disturb¬
ed by a slip of the bank, and to provide for ditches on each
side at the excavations.
The depth of the cut or the height of the bank, is known
in each case, from the grade table.
The side slope that ought to be given, depends on the
100
stiffness of the soil. If a cut is made in hard clay, the base:
of the bank may be to the perpendicular height as f to 1;
if an embankment is of stiff clay, it is 1 to 1; if sand is mix¬
ed with the clay, the slope is 1J or 1J to 1; and if the soil is
of sand, the slope is 2 to 1. Thus, fig. 21, if the bank is
of sand BC : AB :: 2: 1 or is 2. The quotient of BC-f-
AB is called the slope, and always represents the base
when the perpendicular height is unity.
If the line of the ground across the road is level, the cross
slope is nothing. But this seldom happens, and the cross
slope must always be measured carefully with the levelling
instrument, else the cubic yards removed by the workmen
can not be accurately calculated.
When these four things are known, the distances out may
be easily calculated.
Thus first, fig. 21, suppose the ground HC is level; the
height of the bank LM to be d; the half breadth FL or LA
to be b; and the slope to be r; then the distance out
or MC is b+dr.
If 6 is 8 feet, d 4.8, and r 1£ to 1, the distance out, or MC,
is 15.2. MH on the other side is the same.
If the figure be supposed to be turned upside down, it will
represent a cut, instead of a bank; and the distances out can
be calculated in the same way.
When there is a cross slope, that is, when the line NR is
not level, the levelling instrument is commonly used to fix
the side stakes at N and R. On one side, when the ground
falls off, the distance out, which is now MS, being measured
horizontally, is greater by CS than the MC obtained before ;
this CS=RSxr or sr, if we call s the difference of the heights
of M and R. Hence, the practice is to observe the rod first
at M, then move it out to R, until the difference s multi¬
plied by r and then added to MC, should be equal to the mea¬
sured length of MS ; that is, 6-f tfr+sr must equal MS.
On the other side, MP the distance out to N, is less than
MH by HP, or NPxr, or sr: that is, the rod must be mov¬
ed out from M to N until b-\-dr—sr= the measured length
of MP.
101
In both cases, the distance out is b-\-dr±sr where s repre¬
sents the difference of level between the middle and the
side stakes.
219. The height of one point above another may be ob¬
tained by the theodolite, when the distance is known.
As the levelling instrument gives its results slowly, it is
sometimes desirable to obtain elevations more rapidly—even
though they only approximate to the truth. This may be
done by measuring the angle of elevation and then the true
height = the distance X tangent of the angle of elevation.
The tangent of 1° being .017455, or about If hundreths,
and the tangent of small arcs increasing nearly as the
arc itself, the elevation will = distance x degrees of ele¬
vation xlf^-100, when the arc is not over 10 or 15°.
Thus, if the angle of elevation of a point, 1200 feet dis¬
tant, was 3°25', its height would be 1200x3^xlf-f-100 cr
71.75 feet.
220. The elevation of an object may be found by direct¬
ing the telescope to it, and noticing where the line of sight
strikes two leveling rods; then leveling the telescope and
noticing where it strikes the two rods again.
The difference between the two spaces intercepted on the
two rods, between the level line and the ascending line,
will be the rise of the ascending line for the distance between
the two rods. Hence the proportion : As the distance be¬
tween the two rods, is to the rise of the ascending line, so j?
the distance of the object, to its height.
Thus, fig. 22, M being the leveling instrument, O the ob¬
ject, MN the distance, AD and EL the two rods, BF or CG
the distance between them, BO and FH the two intercepted
spaces, and GH their difference; then, CG : GH "• MN : ON.
221. If the distance is short, a level line maybe made by
the common ditchers' level.
This is a triangle, ABC, fig. 23, made by two narrow
boards AB and BC, and united by the cross bar DE, with a
plummet G, suspended by a string BFG, from B. To mark
the point F, so that the string will show when A and C are
on the same level, rest the triangle on two blocks and no o
102
where the string cuts DE: then turn it round and rest C on
As block, and A on Cs, and note again where the string cuts
DE. If the two points thus noted are the same, the blocks
are level. If not, raise or depress one, until the point mark¬
ed by the string is the same before and after the reversal.
Then mark F and the triangle is ready for use.
Other marks may be made on DE near F, indicating a rise
or fall of 1 in 100, 2 in 100, &c.
Sometimes a narrow horizontal opening or slit is cut at H,
and a larger hole atL, across which a string or wire is stretch¬
ed, and so adjusted that when A and C are level, the eye at
H, before reversal, and at L after it, may see the same distant
object M, along the line HL.
To use the instrument for ditching, cut away the ground
AC until the string BG shall indicate by the mark at F
whether the ground is level or falls at the required rate.
To use the sights H and L to mark out a level line, make
AC level, by means of the string BFG, and the eye at H
will look along the level line HLM.
To find out how much one point, as M, is higher than an¬
other, as H, raise or depress A until HLM is a straight line,
then the string BFG will indicate at F the rate at which HL
rises; and if the distance HM is known, the height of M
over H may easily be found.
LECTURE XIX.
SURVEYING.
222. The common surveyor's compass is not suited for
the operations of the Engineer, as it will not give the courses
of his lines with sufficient exactness.
The thread used for the sights is too large, the divisions on
the circle are not sufficienly minute, and the needle is broad.
103
unsteady, and subject to local attraction. To overcome the
first difficulty, a telescope with its small wires is added;
for the second, a vernier is attached, so as to read the angles
to single minutes, and sometimes to 15" ; and for the third,
the needle is dispensed with entirely, and each line is then
run by measuring the angle it makes with the preceding line.
This requires two circles in immediate contact with each
other, one fixed or movable by a screw, and the other
movable with the telescope. This is the construction of
the common Theodolite, omitting the arcs for elevations:
and this instrument is sometimes used. But as the Engin¬
eer often wishes to run straight lines, and this would require,
at every transfer of the instrument, the measuring of an arc
of 180°, this is avoided by making the telescope revolve on a
horizontal axis, and then its reversal will continue the
straight line first run. The instrument is then called a tran¬
sit, from its likeness to the Astronomical transit, which re¬
volves like this in a vertical plane.
With the transit or Theodolite, a straight line is easily
run. After beginning at the point A, as many stations are
pointed out as can be seen, and then the instrument is trans¬
ferred to the last one observed, and its centre placed carefully
over the stake, by means of a plummet. The rod is now
placed at A, and the telescope directed back towards it. If
then the telescope of the transit is made to revolve so as to
point in the opposite direction, or if the Theodolite is turned
180°, the former straight line will be continued.
223. In using the transit, the several courses are indicat¬
ed by deflections, by which is meant the angle made by a new
course with the last produced.
To change the course, for example, 3°, the operations would
be, sight back to the last position of the transit, reverse, and
deflect 3°. This is inserted on the record on the right or
left side, according as the deflection is on the right or left of
the preceding line. A compass is attached to the instru¬
ment, as a check against gross errors of observation, or of re¬
cord, or of calculation. The course of the first line being
observed by the compass, the courses of all the rest will
mi
found by applying the several deflections, and can then be
compared at any time with the needle, and gross errors de¬
tected.
224. The surveyor, besides marking out the several sta¬
tions, and recording and plotting the courses and distances,
makes a sketch of the country he passes over.
He draws a line up and down the middle of the page, and
notes on that page the fences and streams that cross his line,
and their courses and bendings, the rise and fall of the ground
on either side, the direction and extent of the ravines or ridg¬
es or irregularities, and the situation of the several objects
that are near him, such as the dwellings, the woods, and the
fields, as far as all these can be copied by a practised eye.
This sketch is transferred to his plot, which not only repre¬
sents the line surveyed, but the several objects near that
line, which it may be necessary to be acquainted with, in
the subsequent location of the route.
225. When a river, or marsh, or obstruction of any kind
interrupts the survey, the distance across may be obtained
in several ways, by the principles of Geometry and Men¬
suration.
By measuring a base line and taking the angles at each
end, the distance can easily be calculated by Trigonometry.
But the logarithmic tables not being always at hand, recourse
is often had to other methods in the field. The unknown
distance is made the side of a parallellogram or of an isosceles
triangle, and thus becomes known by its equality to other
sides. Or it may be made the side of a right-angled-triangle,
and then found by (47. 1.) Euclid. Or it may be found by
similar triangles described on the ground :
1. If MN be a marsh, the distance AD across it, may be
found by running AB any course and distance, then trans¬
ferring the instrument to D, and running DC parallel to AB.
Then, BC being measured, will be equal to AD.
2. Again. Make at A the angle DAE equal 45°; measure
AE. and make AEF equal 90°; measure EF equal to AE ;
then F will be in the line AD, and AF2= AE2+EF2.
3. Again. Make the angle DAG of any convenient size;
IQo
and GA of any length ; set tip three flags D, L, and F in
the line ; at G make the angle AGH equal half the supple¬
ment ofGAH and fix the point H in the line GH and also
in AD by means of the three L flags D, L, and P. Then
AH=AG.
These methods admit of several variations, so as to ac¬
commodate them to the different situations in which they
may be wanted. Other methods may also be adopted,
founded on similar principles.
226. If a swamp intervenes, it is sometimes desired to
return to the original line. This is done by running sever¬
al lines, as AB BC CD and DE ; then Ed dc cb and ba,
each equal to the first, and making the same angles with the
original line, but turned in the opposite direction.
It is evident that as far as AB diverts the surveyor from
the original line, just so far will ab bring him back; for
they are equal, and make equal angles with the first line.
227. The distance of any point from the line, may be
found by taking its bearing from two known points.
If these two points are in one straight line, its course be¬
ing known, the angles and one side of a triangle will be
given to find the other sides. If several courses and dis¬
tances have been run between the two points where the ob¬
servations are taken, the course and distance of the straight
line joining them may be found by taking the Algebraic sum
of all the northings and southings, and of the eastings and
westings of all the intermediate lines as the departure and
difference of latitude of the straight line between the two
points; and hence its course and distance may be found,
and then the course and distance of the given point.
13
11 M>
LECTURE XX.
LOCATION OF A RAIL ROAD.
238. The location of a road consists in laying out long
lines instead oj the short ones first surveyed, and uniting
these long lines by a circle touching both.
As the danger of running off the track is greater 011 the
curves, and as the flange friction is very large and hard to
be overcome, the curves should be few and with as large a
radius as possible. None less than a thousand feet radius
should be allowed ; and it is very desirable to keep this limit
as large as 2000 feet.
If two circles are introduced at a bend in the route, the two
must touch one another, and each touch one of the straight
lines. No sudden change of direction will thus be made in
passing from the first straight line to the first curve, or from
the first curve to the second, or from the second curve to
the straight line.
239. These circles are first marked out by running 100
feet chords ; and when the rails are laid down, by shorter
chords, as 25 feet or the length oj the rail.
It would not be possible to lay out these large circles by
revolving a long radius round a centre, since it would be
obstructed by intervening objects. The several 100 feet
chords coincide very nearly with the arc ; near enough for
the earth-work to be done along them. With the small¬
est radius (1000 feet) the distance of the middle of the chord
from the arc is only 50x50-^2000 or l£ feet. And for larger
circles the interval is still less.
When, however, the superstructure is to be laid down, the
ends of the rails are to be placed on the curve. The rail
itself is seldom bent to coincide with the curve, since even
when the radius is 1000 feet and the rail 18 feet long, the
107
deflection of the middle would only be 9x9-^ 2000, or less
than half an inch.
240. The angle at the centre of the circle subtended by a
100feet chord is called the curvature (c); the angle between
a tangent and a 100 feet chord, the tangential angle ( T);
and the exterior angle made by the two tangents to the curve,
the total deflection (2d).
Let ABD and DCE (fig. 26) be two straight lines between
which the curve B 1 2 3 4 5 C is to be located, having O its
centre, and B 1,12,23 &c.= 100 feet ; the angle BOl is the
curvature (c), DB1 is the tangential angle (T), and FDE is
the total deflection (2c?).
The following propositions concerning these angles and
this figure are easily proved :
1. The tangential angle T is equal to half the curva¬
ture c. For 1BO and T=90°, because a tangent is at right
angles to the radius; and 1BO and ic=90°, because they
are the two acute angles of the right angled triangle BOG.
Hence T~£c.
2. The angles at the circumference subtended by a 100
feet chord are equal to T ; because they are all equal to half
of c. • Thus B31=iB01=i6 = T.
3. If a long chord subtend n of the 100 feet chords, the
angle it subtends at the centre is no, and at the circumfer¬
ence nT. Thus B03=3c and B43 is 3T ; B05 is 5c and
BC5 is 5T.
4. If a long chord be produced, the exterior angle made
by it and the next 100 feet chord is (w+1) T. Thus, if
B4 be produced to L, the angle L45=(«+1)T. For (32.1.)
L45=B54+4B5=?iT + T. In like manner H12=2T.
5. The angle made by a long chord produced with a tan¬
gent is equal nT. Thus if 4M is a tangent at 4, L4M=nT ;
because L45— rcT+T and M45=T (by definition of T);
hence L4M=wT.
6. The number (n) of 100 feet chords between B and C
—2d-i-c. For FDC=BOC, since each is the supplement
of BDC; and B0C=B01 + 10 2+20 3+30 4&c.=nB01=
nc ; that is 2d—nc\ orw=2<£+e.
1US
7. The tangent BD=100</+ r, very nearly. For BD—
£(BD+DC)-=4 arc BSC nearly —£ (B1 + 12+23 + 34 + 45 +
5C)=i 100w=4(100x2</-c)=:100</+ c.
8. The tangent BD is longer than ^BSC ; so that, it is more
than 100^ + c. It is more nearly (100<Z+g?3+ 100)+ c.
9. The radius of the circle is very nearly 5730+ c. In
the triangle BOG where BG=50, if we take BOG or Jc—
301°, 1|°, and 2°, we find BO by Trigonometry to be
5729.7, 2865.0, 1910.1 and 1432.7 or very nearly 5730^. 1,
2r 3, 4 or c.
10. The deflection of the first chord B1 from BD is T ;
of the second 12 from B1 is 2T, or from BD it is 3T ; of
the third from 12 is 2T or from BD it is 5T &c., the de¬
flection of every chord from the first tangent being 2T, ex¬
cept of the first chord which is T. Hence the deflection
of the nth chord is (2n—1)T.
11. If the course of the tangent be known, the course
of the nth chord will be found by adding or subtracting
(2n—1)T to the course of the tangent.
12. The distance PI from the curve at 1 to the tangent
is J T or g c, and Varies as the square of the arc or the chord.
For it is equal to Bl sin.T. But B1 is 100, and sin". 1°=:
.01745, and sin.T=^.01745T for small arcs, and 100 sin. T
=1.745T or \ T nearly. And as it is equal to the versed line
of the arc, it varies as the square of the chord or of the arc.
241. When the ground is suitable for any curve, select
one with a very large radius, 10 or 20000 feet.
The larger the radius, the less is the flange friction and
also the danger of running off the track. To mark out the
curve on the ground, we must know from the previous survey
the total deflection or 2d. As the radius is arbitrary and
must be large, we may take c=l° or 30' or 12'; for the radius
would be in these cases 5730+ 1 or fg or ^=5730, 11460 and
28650. To find the point B where the curve begins, we
must find BD. By (7) it=100d +c or by (8) (100rf+rf3 +
100)— c. To find the number of 100 feet chords from B
to C, we have (by 6)n=2rf+ c. As T=|e, every thing is
known that is necessary to run the curve.
loo
Example. Let FDC-— 3".30 , and let the ground be level
or suitable for any curve.
Assume a curvature of IS'. That is. let 1301 — IS' and
BOG =9'. Then by Trigonometry we find BO=19098.6.
In BOD we have the angle BOD=i of 5°.30' or 2°. '15'.
Hence by Trigonometry BD=917.37. The number of 100
feet chords from B to C is H or 330— 18 or 18.33.
The tangential angle is |c or 9'. And every thing is now
known that is needed to run the curve.
This example has been solved accurately by Trigonome¬
try. It could have been done more easily by the methods
before explained. We assumed c=18'; hence T=9'; n=
2d-^r c=5°.30'-f- 18'=18.33; and BD=(by 7) 100d-:- c=
916.6 ; or more accurately (by S) (lOOd+d3-^ 100)4- c or
(275-j-20.8-f 100) ^ or 275.2084-1 or 917.36.
The 916.5 is an approximate result obtained by supposing
the tangent and the chords equal, and is sufficiently exact for
most purposes. The 917.36 obtained by the formula agrees
almost exactly with the Trigonometrical result and is as ac¬
curate as can be desired for practice.
These calculations being made, the curve may be run as
follows : Measure from the angle D backwards 917.36 feet
and B is found. Place the transit at B, sight along BD,
deflect T or 9' and the telescope points to 1; measure Bl=
100 feet and 1 is found. Deflect at B again the angle 1B2
or T or 9' and the telescope points to 2, measure 12=100
feet, and 2 is found. Deflect again 9' and measure 23=100
feet and 3 is found. And so also find 4. Suppose now
that no farther distance can be observed from B. Trans¬
fer the transit to 4 ; sight back to B; reverse it, and the
telescope points toL ; deflect L45 or (by 4) (ra+1) Tor 5T=
45', and the instrument points now to 5 ; measure 45=100
feet and 5 is obtained. Deflect at 4 the angle 546=T=9'
and measure 100 feet and 6 is found. So also mark out 7,
8, 9, 10, 11, and 12. If the ground beyond 12 can not be
seen from 4 transfer to 12; sight back to 4; reverse and
deflect (by 4) (8+1) T or 81', and the telescope now points
to 13 ; measure 100 feet and 13 is found. So also 14, 15,
1 Hi
16, 17 and IS may be found. The number ol chords to bo
run was IS 33. The fraction .33 will subtend at the in¬
strument .33T or 3;. Deflect therefore 3' and measure 33
feet, and the end of the curve C is reached. Transfer now
to C ; sight back to 12, the last position of the telescope :
reverse and deflect now (by 5) nT, u representing the num¬
ber of intervening chords; they are 6.33 ; deflect therefore
6.33T or 57' and the instrument now points along the tan¬
gent CE, and the curve is completed.
The circle has now been run with three removals of the
transit; being stationed at A, 4, 12, and C. It might have
been done by moving it at every chord ; then the deflection
every time would have been 2T or 18'. It is better and
more convenient to run several chords without removing
the transit.
If in marking out the 8th chord, it should be desired to
check its course with the compass ; suppose the course of BD
to be N 20°. 10' W and that the curve is to the east of BD.
The course of the eighth chord is now (by 10 and 11)
20°. 10'—15 T or 20°. 10'—135' or N 17°.55'W
LECTURE XXI.
LOCATION CONTINUED.
242. If the point where the curve should leave the tan¬
gent is given, find the curvature and the tangential angle ;
take for T a whole number, and find the point where this
curve will leave the tangent.
It seldom happens that the ground is suitable for any
curve. There is usually some point where it is better that
the curve should start off. so that a cutting or a filling may
be lessened or a marsh or a rock avoided, or the track in some
way improved. When that is the case, BD becomes known.
Ill
Bat (by 7) BD=100t/+ c, and hence c is found, since d is
known from the previous survey. Now T=|c; and the cur¬
vature and the tangential angle are thus determined.
As T will generally be a fraction, it would be troublesome
to read it off on the transit, and it is usual, therefore, to alter
T slightly on this account. This will change the size of the
curve and make it leave the tangent at a different point from
A. The change is, however, very slight, and the point
where the curve leaves the tangent will seldom make any
appreciable difference in the route.
Example. Let the total deflection, or 2d=6° .20' & BD
= 1200 feet.
To solve this by Trigonometry, we have in BOD the
side BD=1200 and BOD=£(6°.20'.) Hence BO=21723.
Now in BOG we have also BG=50, and hence the angle
BOG c=7'.55". If we solve it (by 7) we have 1200=
100d+ c or c=3JJ4- 12 or 190'+ 12 or 15'.50", and T=£c
or 7'.55" ; the same as before. Take now T=8', and
mark out the curve, c—2 T or 16 D B. (by 8) is (100e?-fe?3+
100)4-c or (100X3J+31.75+ 100)+ $ or (19000+19.05)+
16 or 1188.7. And 16' or 11,875. Theseele-
ments are sufficient to run the curve. Measure from D
1188.7 to B ; at B direct the telescope along BD and deflect
8' and it points to 1; measure Bl=100 feet and 1 is found.
Deflect 8' again and measure 100 feet from 1, and 2 is deter¬
mined. In like manner, fix the stakes at 3, 4, and 5. At
5 suppose it is necessary to move the transit. Transfer it
to 5, sight back to B, treverse, and deflect (by 4) (rc-|-l) T
or 6T or 48'; measure now 100 feet and 6 is found ; deflect
8 and measure another 100 feet a nd 7 is found. So mark
out 8, 9, 10 and 11. After 11, a fractional chord .875 is to
be run. Deflect .875T or 7', measure 87.5 feet and the end
of the curve or C is arrived at. Transfer now to C, sight
back to the last position of the instrument at 5, reverse, and
deflect (by 5) nT or6.875T=55' and the telescope will
then be pointed along the tangent line CE.
To find a check for the course of the 5th chord, we have
it. (by I0)=course of BDt(2/i—l)T=course of BDf72'.
112
243. To run the circle at a given distance from the angu¬
lar point where the two tangents meet, make the curvature or
c=\d2~ this distance.
For the distance from the curve to the tangent at 1 is
(by 12)=4rr or \c ; and at the distance of n chords of 100
feet, it is n2X78c. But the chords from B to S are cLl. c.
Therefore BS=*cd -l-c2 or c=-7sd2~ BS.
Example. Let FDE=15°.30' and DS=30 feet. Then
c=l(7l)2^r 30=1°.45'. T=J c or 52£'. The number
of chords to be run is 2c£-r-c or 15°.30/-4-l°.45/ or 8.857.
The distance BD=(100c?+^3^_100)^-c or 779.654-1^ or
445.5.
This solution is approximate. To make it exact, find
from the tables, the versed sine of |dand it will give DS when
the radius is unity. Divide this DS into DS as known,
and the quotient will give the radius. Then in BOG the
angle BOG or |c may be found.
Thus in the example above; versed sine of 7°45' is
.0091341, divide into 30 and we have radius 3284.8. Hence
in BOG we find BOG or Ac or T=52/.20//; nearly the same
as before.
To mark out the curve, with T=521'measure BD or
445.5 feet from D and B is found. At B deflect T and mea¬
sure 100 feet to 1. Deflect T again and the telescope points
to 2. And so 3, 4, and 5 are staked off. Move now the
instrument to 5, sight back to B, reverse, (by 7) deflect
(5—1) T or 315', and the instrument then points to 6. De¬
flect now T and 7 is found. In like manner find 8. Now
for the fractional chord, deflect .857 T or 43' and measure
85.7 feet, and we arrive at the end of the curve or C. Trans¬
fer now to C, sight back to 5, deflect (by 8) 3.857T or
200£' and the telescope is then directed along the tangent
CE.~
244. To run the curve through a given point /?, whose
distances from the tangent and the angular point RT TD,
are known. Let the number of 100 feet in BT—x and in
TD=a. Then (by 9) d^c=x~ha, and (by 12). TR
=l.v2c; and hence c may he found.
113
This when solved, gives a quadratic equation ; but it
will be best to solve it by trials, as T and c are not often
wanted exact—only to the nearest whole number.
Example. Suppose 2^=16° and DT=550 feet and
SR=2Q, it is required to run the curve through 01* very
near R.
Let c=^l° and the first equation d-rc=.r+a becomes
8—x-j-5^ or x=2^; and the second, SR=gW26- becomes 20=
gX2|2=5. This second equation not being satisfied, c is
not=l°.
Let c=45' or f of 1°; then we have x+o^=8~ £ or
57—51; and 20=1 '> s0 t^at s#econd equa¬
tion is now very nearly satisfied.
Let now c=43/; then x-h 5^=8-7- H or x=5.6fj; and 20
—3X 5 662X go=20.06; so that both equations will be almost
exactly satisfied if c=43'.
With this then run the curve. Find BD=(100c?+</3-r-
100 )-r 0=805.12x43=1123.4; and T—21J'; and n==2d4- c
or 22.325. Thus, we have the point where the curve starts,
the tangential angle, the curvature, and the number of 100
feet chords that subtend the curve between the two tan¬
gents. Which comprise every thing necessary to mark out
the curve on the ground.
245. To alter a curve already run, so that the final tan¬
gent on the new curve shall be parallel to the final tangent
on the first; find the distance between the last two tangents
measured on a line parallel to the first tangent, and start the
new curve at this distance on the first tangent Jrom the ori¬
ginal starting point.
It may happen from wrong measurements of DB, or from
other causes, that the curve BC runs too far and crosses the
line UW which it ought to touch, or fails to meet it. If the
course of UW and BD had been correctly measured, the tan¬
gent CE would be parallel to UW, but C might be inside
or outside of UW.
If now we ran CY parallel to DB and start the curve anew
at A, making BA equal to CY, it is evident that the whole
13
114
curve is removed towards A, so that it will now touch both
AD and UW.
246. To alter a part of a curve so that the final tangent
on the new part shall be parallel to the former final t>>ngent ;
return backwards n chords and run a new circle, such that
its tangential angle (T') shall be to the former tangential
angle ( T) as ]n2 T is to In2 T ± the perpendicular distance
between the two tangents.
It may happen that the first part of the carve as B123
has been already graded, or is in some way so fixed that it
is desirable to retain it, while the rest of the curve crosses
UW which *it ought to touch, the tangent CE being parallel
to UW.
It is now necessary to run a new curve 3U touching the
curve BI23 at 3 and touching also UW. Since the curves
3U and 3C have the same tangent at 3, and parallel tangents
at U and at C, they contain the same number of degrees;
hence their radii are as their versed sines. But their radii
(by 3) being=5730-f c and 5730-r c' vary inversely as c or
as T. And the versed sine of C3 or the distance of 3 from
the tangent CE is (by ll)=^2T, and the distance from the
tangent UW=4W2T-6, if we represent by b the perpendi¬
cular distance between CE and UW. Hence, T'-.T^n2
T: I n2 T—6 which is the rule given above.
If the curve 3C had fallen inside of UW the distance b
in the above proportion would have been positive instead of
negative.
As the point 3 from which the new curve starts is any point,
the new circle may be started from B and the whole curve
run anew.
Example. Suppose the curve BC to have been run with
a tangential angle (T) of 45'; that the total deflection 2d
was 16°.30'; that the curve BC extended 20 feet beyond
UW; and that the first three of the chords on BC were so
fixed that it was desirable to retain them.
Here the tangential angle T being 45', c is l£° and the
number of chords from B to c is (by 6) 16130' -f-H° or 1 I.
MS
Three of these being retained, the number from 3 to C or
n is -8. And rr T is 64xf or 48. And n2 T-b= 48-20=
28. Hence 28: 48::45': T'=77J'.
It is necessary to run the curve with this fractional angle,
if the point 3 and the tangent UW are fixed. If only 3 is fixed
and it would be allowable to change UW slightly, T might
be taken 77'..
The angle which the chord 34 on the first curve made
With BD was (by 11) (8-1) T or 7T. The angle made by
the tangent at 3 with BD was therefore 6T or 270' or 4°.30'.
Hence the angle between the tangent at 3 and CE is 16°.30;
-4°.30' or 12°. The curvature c' for the new curve is 154'7
and the number of chords or n' is 12°-r- 154' or 4.675.
To mark out the curve. Set the transit at 3, sight back
to B, reverse, deflect (by 5) 3T or 155', and the telescope
points along the tangent at 3. Deflect still farther 77', and
the telescope points to 4 on the new curve; measure 100
feet, and 4 is found. Deflect 77' and measure 100 feet and
5 is found. In like manner 6 and 7 may be staked off.
There yet remains a fractional chord of .675 to be run.
Deflect now .675 T or 52', and measure from 7 the chord
67.5 and the end of the curve or tJ is reached. Transfer
now to U, sight back to 3, deflect 4.675 T or 360' and the
telescope points along the tangent UW.
247. To mark out the arc for the rails, divide the pro-
duct of the segments of the chord by the diameter, and the
distance of the arc from the chord will be found.
This rule is nearly right (E«c. 35. 3.) for the middle of
the arc, where the perpendicular to the chord passes through
the centre; but it is also sufficiently correct for the other
points, since the perpendicular-, produced to the other side of
the circle, is very nearly equal to the diameter.
Example. Let the radius be $000 feet and the rails 18
feet. The segments of the chord'at the end of the first rail
Xvill then be 18 and 82, and the distance of the arc from the
^chord will therefore be 18X824000 or .369 of a foot.
I^or the end of the second rail, it will be 36x64-4- 4000 or
,576. For its middle, it will he 27X73-4-4000 or .493.
110
iStretch then a string from one station to another and
measure these distances from the string for the ends and
other parts of the rails.
248. To mark out the arc for the rails by the transit,
place it on the curve, direct the telescope to the end of the
chord, deflect mT-r- 100 and the telescope will be directed
to that point of the curve whose distance from the station
is m.
As the 100 feet chord subtends the angle T at the
circumference, the chord m will subtend m T-f-100.
LECTURE XXII.
MENSURATION.
249. Timber is bought by board measure, in tvhich the
unit is one foot square and *one inch thick.
If the thickness is less than an inch, it is common to count
it an inch; but if it exceeds an inch, the additional thickness
is charged for. ^
In measuring sills and sjsantling by this rule, the same
price is paid for them as'if they were sawed an inch thick.
They are therefore betteyjaid for than the inch plank.
250. Masonry is yxtfisured by the perch of 25 solid
feet; brick work by the *thousand brick, no deduction be¬
ing made for wood worked into the wall.
A linear perch or ro£U-is 16i feet; and if the wall is 1J
feet thick, the solidity will be 24f feet. The unit used by
the Engiueer is a little rriore than this, 25 and not 24f.
The number of bricks is estimated by multiplying togeth¬
er the length of all th^rows, the thickness of the wall count¬
ed in bricks, and the^iiumber in a given row, and the pro¬
duct divided by the length of that row.
1 17
251. Carpentry in measured by the hundred square feet,
no deduction being made jor doors, windows, §t.
The length and breadth being multiplied together, and
the product divided by 100 gives the number of squares;
and the trouble of adjusting the ends of the plank at any
break in the surface being considerable, the chaise includes
the cost of covering the opening.
252. Plastering and painting are usually measured by
the square yard, no deduction being made for windows, §'c.
some pieces offainting however are measured by the linear
yard or foot, and some are paid for by the piece.
Doors, windows, &c. are painted by the piece; a line of
fencing by the linear length ; the out side of a house by the
square yard, or by the 100 square feet.
253. The weight oj materials is found by multiplying
their solidity injeet by 62|, and this by the specific gravity
of the substance.
As a cubic foot of water weighs 62J lbs., and the specific
gravity shows how much heavier the material is than wa¬
ter, this product will evidently give the weight.
For rock, the specific gravity is commonly about 21;
for green timber very nearly 1; for dry pine J; for dry oak
.7; for cast iron 7.2; and for wrought iron 7.8.
Approximate rules founded on this are, that green wood
weighs about 5 lbs, per foot of board measure ; dry pine,
about 2|; and dry oak 3J. Iron about £ of a lb. per cubic
inch. About 13 feet of rock make a ton.
254. The contents of a circle are f of the square oj the
diameter ; and of a sphere, J ojthe cube of the diameter.
The true amounts are a little larger than this; but these
rules will often be near enough right.
255. To find the bushels in any space, take x80 oj the solid
feet contained in the space.
The true size of a bushel being 2^50.42, eight-tenths of
this will be 1720.336, which is nearly the same as 1728
inches or a solid foot.
256. To find the sine of a snuxll arc, take 6a0 of the num¬
ber of degrees in the arc.
1 is
As the sine of 30° is £ radius, the other small arcs as at
first approximation may be taken proportional to this. The
error in this rule will in no case exceed .05.
257. To find the sine or tangent of small arcs, take 4700 of
the degrees in the arc.
Up to 15", this will never be wrong more than .005, for1
either'sine or tangent.
2SS. To find the sine and tangent, more accurately, di-»
video. 14159 by 180 and it gives .017453 the length of one
degree of arc; subtract from this %dl~ a million, for the
sine, and add twice this jor the tangent; multiply these
results by the number of degrees in the arc.
Example. Let the arc be 8I:.30'. The length of 1° is
.017453; and ?x8P is 64; hence the sin. 8i°=(.017389)8i
©r .147807; and the fail. £ij°=(.0l7581)8|. or .149439.
The true values in the1 tabled are .147809 and .149441.
Up to 30% the results will generally be correct to four deci¬
mals.
259. To find the cosine, subtract rierstd sine from unity.
The versed sine is 3d20000. r'pftRenting the degrees by
d, or more accurately it is .i]00\523lcP-\1(.i}Q0\523\d2ft
Example. The versed sine „of 8J° is 72^x3^-20000 or
,M(i8b75- Or more accurately ; .0(>01523 tx72| is .0110044
/& j(.011O)2isj .0000202 & hence versed sineo/SJ is\0109842.
Versed sines are often wanted by the Eng Jneei?,-and this-
. mUe^-ives very accurate results up to 30.
250. Earth-work is measured by the cubic yard. If ffte
solid is,:p. ■prism, the product of the end area into the length
, will give, the stolidity.
Exa^lje. Le t a rail-road cut be 10 feet deep and 100 feet
ilong, the ^lqpe 1J:, and the breadth at the bottom 24 feet.
iHere the :half .breadth at the top is 12+10X1J or 27 feet.
And the su-ea.of th«.^ trapezoidal end is (27+12)10 or 390
.feet. And, the^solidity" in yards is 390x1004-27 or 14444.
. Algebraiqaily,; this solidity is (2b+dr)dl+-27. For the dis¬
tance out js/,6+^r. And the area of the trapezoid is (6+6+
dr)d. And( the product o.f this into the length (I) divided
tby #7.will glye.the pQli^if,y\in yards.
Ill
If the depth of the two ends is not the same, take the aver¬
age depth, and to the solidity thus found, add ^V/, repre¬
senting by x the difference oj the depths of the two ends.
If from the upper edge AB (fig. 27) of the less end, a hori¬
zontal plane ABGH be supposed to pass ; and through A and
B, two vertical planes AGL and BHM; the whole solid
ADNE will be divided into a prism ADFG, a wedge ABHL,
and two triangular pyramids AGLO and BHMN.
The solidity of the wedge, and the prism will be found
correctly by taking the average depth of the two ends as an
average prism. Not so for the pyramids.
The average gives for the two pyramids two triangular
prisms whose ends are HPR and GST, where HP is | x
and PR is \xr. Hence HPR is \x~r. And the solidity of
the two prisms is \xzrl The end area HMN of the pyramid
isJarXor. And the solidity both is ^ xarl. Hence the
difference of the true pyramids and the average prisms is
the difference of ^ and \ or ^ x~rl.
262. If there is a cross slope at one end, take the average
depth of the right and left and tniddle cuttings at each end;
and from this depth find the solidity, as if there were no cross
slope.
This rule only gives approximate results; but usually
they are sufficiently correct for practice. If great accuracy
is required, divide the figure into prisms, wedges, and pyra¬
mids, and find the contents of each by their appropriate rules.
LECTURE XXII.
MATERIALS.
263. The principal materials used by the Engineer are
stonej brick, mortar, wood and iron.
These having different qualities, as to strength, cost, and
durability will be considered separately.
rri
264. Good building stone should be large and tough, free,
and not affected by the air, by cold, or by water.
By being large and tough, their strength is increased ; by
being free, or easily broken by the hammer, the wall can be
put up rapidly and cheaply • by being unharmed by the
chemical agencies in the atmosphere, by the wearing and.
decomposing action of water, and by the freezing and ex¬
panding power of heat and cold, the structure is rendered
durable.
265. Marble, sand-stone, granite, limestone, and clay
free-stone have most of these qualities.
Marble has them all, and is besides susceptible of a fine
polish and handsome.
Some granites are too soft and friable, by an excess of
mica; in some, the mica is deficient and the rock becomes
too hard to be worked easily ; the presence of a sulphuret
of iron sometimes permits the air to decompose and crumble
it; but generally, granite makes a good building stone, es¬
pecially when hornblende is an ingredient in it.
No better test of its qualities can be had than to examine
the rocks, after they have been quarried for some years and
notice the effects produced on them by time.
Sand-stones when well cemented so as to be tough, make
an excellent building stone. Sometimes their grain is fine
and their appearance handsome.
Limestone vary much in quality. Some become harder
under the action of the weather, while others are decomposed
and destroyed. Often they are hard, durable, easily quar¬
ried, free and regular, making a good building stone.
Clay is often largly mixed with lime, as a component in
rocks, and the compound forms a good material for building.
But clay alone as in the slates, is seldom strong and durable.
266. In a wall oj stone, the layers should be horizontal
and the vertical joints should be broken.
If the ground at the foundation is not level, it should be
made so, or dug into horizontal steps. The courses of rock
should not be made level by means of mortar, or small chip-
121
pings of stone, but by having the upper and lower surfaces
of the two rocks to fit each other.
When the bed of a rock is inclined, it tends to slide, and
thus weakens the wall.
If the vertical joints are not broken by putting the middle
of a rock over the joint in the row beneath it, the wall is
rendered weak, liable to crack and yield under the weight
above it.
267. Bricks are made of a mixture of clay and sand,
and when well made are very durable.
These are used by the Engineer, when rocks are scarce,
for aqueducts, locks, tunnel-arches and culverts.
The clay and sand should be in proper proportions and
well mixed; carefully separated from the grit and small
stones ; well pressed in the mould; dried thoroughly, both
under shelter and in the open air; burned slowly at first until
the steam stops rising, and then heated just to a white heat
for about 24 hours.
268. Mortar is made with lime and sand and water, using
about 3 bushels of sand to one of lime.
The lime should be pure, with no clay in the stone from
which it is burned ; obtained from a hard carbonate, as
marble, compact limestone, shells, and not from chalk or
rotten limestone ; quick or unslacked, until it is to be used ;
and sifted, to be clear ofsilex or unburnt stone.
The sand should be not rounded or worn but rough and
sharp ; neither fine or coarse ; clean, free from clay, dirt,
and vegetable mould; and not impregnated with salt, as it is
usually when obtained on the sea-shore.
When the sand and lime have these qualities and are well
mixed together with water, they set or harden well, forming
a carbonate and silicate of lime, which becomes harder with
time and clings firmly to the stone or brick.
If the lime is good and strong, 3 bushels of sand may be
used with 1 of lime ; 4 and even 7 if well mixed, have been
tried with advantage to the strength of the mortar. With
inferior lime 1 or 1J bushels of sand are all that can be used.
The mortar should be well moistened, especially in warm
14
122
weather, so that the brick or stone shonid not absorb so
much of the water as to leave a supply insufficient for the
formation of the carbonate.
Walls should not be put up in winter, when the mortar
might freeze before setting, as such mortar would never
harden; nor should they be worked on in wet weather, as the
rain would wash the mortar from the joints and also carry
off some of the lime from the mortar.
269. When mortar, made from common lime, can be
well dried before it is exposed to water, it will suit for some
works under water, but usually hydraulic lime must be ob¬
tained.
This will harden under water in a very short time. The
limestones from which this lime is obtained are not pure, but
contain 40 or 50 per cent, of clay, sometimes clay and man¬
ganese, or clay and magnesia ; a small quantity of silex or
oxide of iron is frequently found in hydraulic limestones.
When burnt they will not slack by air or water, but have
to be pulverised by mechanical means. The best and most
convenient test of the suitableness of any rock for making
hydraulic lime, is the actual trying of the rock, and noticing
how the mortar becomes hard under water.
The hydraulic lime is mixed with sand about in the same
proportions as in common mortar. Formerly it was scarce
and costly, but it has been found in more and more lo¬
calities, uutil it is now nearly as cheap as common lime. This
mortar is called cement, but for works out of water it is not
as strong as common mortar. Thus, for a stone bridge, the
cement would be used for the piers, but not for the arches
which span the stream. Its only peculiarity is that it sets
under water.
123
LECTURE XXIV.
MATERIALS CONTINUED.
270. Wood is used for bridges, aqueducts and many other
purposes by the American Engineer, when stone or iron
would be employed in other countries.
Its abundance and cheapness permit this, although it re¬
quires to be often renewed, while the stone or iron would
last for ages. The great elasticity of wood, the ease with
which it can be worked or shaped in an]r desirable form, its
strength, toughness and lightness, make it as important to
the Engineer as any of the materials he uses.
271. Of the several kinds of wood, pine, chesnut, oak> and
cypress, are most used by the Engineer.
The abundance and cheapness of pine, its being soft and
easily cut by the plane or axe, and its high degree of
strength and durability, make it more used than all the other
kinds of wood put together. The sap wood of the trunk is
sometimes large, and this is of little value, since it decays very
rapidly. When the tree is saturated with turpentine, the
wood is almost indestructible by time, and suits admirably
for many purposes of the Engineer.
White oak and post oak are much esteemed. Both are
more durable than pine in exposed situations; both are
stronger and tougher, but they are not as easily worked nor
as cheap.
Chesnut is soft, and durable, not as strong as pine, but
as the tree soon begins to rot at the heart, it is difficult to
get large sound timbers or broad plank from it.
Gypress and cedar are mnch like chesnut, but more durable.
The common black locust is hard, strong, and very durable.
These are the most common woods, used by the Engineer,
though for particular purposes and in some localities others
are employed.
124
273. The sap remaining in the wood is the principal or
only cause of rot or decay.
Woody fibre, well seasoned, will be perserved for ages when
not exposed to moisture ; and under water, in certain conditions
it isalike durable. The sap, containing a large proportion
of albumen which is easily decomposed, begins to change
itself and then propagates its changes into the wood.
As yeast begins and extends a change in other substances,
so the sap begins the transformation of the wood.
The proof of this consists in the slow decay of some
woods in which the albumen is small, in those timbers
where the sap is nearly or entirely removed, or when it is
kept in a dry state incapable of chemical transformation, or
where it is neutralised by the introduction of foreign chem¬
ical agents.
273. The sap is farther injurious, by inviting the attacks
of insects and the growth of fungi in the wood.
It is sweet and also nourishing, while the woody fibre
will not support animal life. The albumen, beginning to
decompose, forms ammonia, and this favors the growth of a
parasitic fungus, which strikes its roots deep into the sub¬
stance of the wood and entirely destroys its texture.
274. Lumber should be cut in winter or mid-summer, and
not in spring or autumn.
In the spring the sap rises faster than the small new leaves
(can elaborate it into wood-making sap; and in the autumn
the leaves beginning to decay, are again inefficient. In
,the midsummer, the leaves transform it as fast as it rises,
and no accumulation takes place. In the winter, but little
if any rises. As the rot is caused by the sap, the winter and
midsummer, when this fluid does not abound in the tree, is
the proper time for felling.
275. The trees should be mature before felling ; 20 years
;being sufficient for chesnut, 50 for pine, and still more for
oak.
The young tree superabounds in sap-wood; and its fibres
are not so close and compact as when they are older. In
/the chesnut the time of reaching maturity is short, and the
125
heart being older than the outer layers often begins to rot
while the tree is growing with vigor.
276. To preserve timber from rotting, it should be
thoroughly seasoned, so as to remove thejsap.
This is best done by drying it in the^pen«air. For pine
a year is sufficient; for oak t^OjOr thre^tr^necessary, and
longer if the pieces are thick. ^Oak should be seasoned un¬
der cover; but pine only needs shelter* from fye sun to pre¬
vent its cracking and warping
In this operation the wood absorbs- moisture, from the
damp air, which dissolves the sap, andKlfie mixture is then
abstracted when the atmosphere becom^drier. This being
often repeated most of the sap is rembv
If the timber is steeped in water for some time, either in
the log or after being sawed, it will season afterwards very
rapidly. In this case, the sap is displa^d more or less by
the water, which water is soon removed afterwards in the dry
air, or a hot sun.
Seasoning is sometimes effected by kiln-drying. This is
a more rapid process, being completed in a week or two,
but it leaves much of the sap still in the wood in a dry state
ready to become active when an opportunity is offered for
the absorption of water. &
Steaming the timber is another method of seasoning.
This is a rapid and effective process, and if it could be done
economically it^vould generally be introdu<^d.
An expensive but effective method has been tried in Eng¬
land, in which the sap is removed by standing the timbers
in a large cast-iron cylinder, from which the air is then ex¬
hausted. This causes the internal fluids to come out rapid¬
ly and the sap is thus removed. If when thus deprived of
sap, the wood is placed in a solution of pyrolignite of iron,
this substance is absorbed, and the iron deposited permanent¬
ly in the cells, to the exclusion of moisture, so that the wood
is well preserved against rotting.
Charring is sometimes resorted to for posts, not only to
expel the sap, but to protect the surface of the part buried
126
in the ground, by a layer of charcoal which will not decay.
The advantages of this process are more or less doubtful.
280. The rotting of timber is increased by its being kept
wet and dry in succession; by the heat of warm climates/
and by emit a ckw itl^deca y h ig materials.
If all the while %Y it will, last for ages. So if kept in
water, especially^in cool climates and running streams. But
if successively wet and*diy, i£ will rot rapidly. Posts,
ground-sills, rail-road sills, deffey very rapidly for this reason.
Even for white oak or chesnut, the durability of rail-road
timbers is not ovenSfcc or eight years, and for pine not over
five or six. £
As heat favors chemJlM changes, and cold stops them en¬
tirely, timber will decay more rapidly in a southern than
in a northern climate ; while, far to the north, the winter
does no injury at af?to timber, however exposed.
If the rot begin at one part of apiece of wood, it is rapidly
propagated to the rest; so if the timber is in contact or near
other decaying pieces. So also if in pools or stagnant wa¬
ter, where vegetable matter is undergoing decomposition.
281. Besides the common rot to which timber is exposed,
it is subject to the dry rot i?i close moist places.
This begifl^on the inside while the outside appears sound
and dry. The whole mass becomes a mere powder, losing
all its strength and elasticity. This rot, once begun, spreads
with great rapidity, and is usually accompanied by a fungus
growth whose branches penetrate the whole substance of the
wood. It is likely to prevail in cellars, in the holds of ships,
in the under timbers of a house, and generally in places where
there is considerable moisture and no free circulation of
the air.
It is to be prevented by thorough seasoning of the timber,
by ventilating the confined places, and by cutting off the
rotten parts when the decay has once begun.
282. Both common and *dry rot may be prevented by im¬
pregnating the timber ivith a solution of corrosive sublimate
or of pyrolignite of iron.
As no care in seasoning will abstract all the sap, its pow-
127
er to injure is destroyed, by combining it with salts, which
form a permanent compound that can not be decomposed
by water or air at ordinary temperatures.
Corrosive sublimate, which is a bi-chloride of mercury,
will enter into a chemical union with the albumen of the sap
and form a permanent compound with it. A solution is
made containing one pound of this salt and 5, 10, or 15 gal¬
lons of water, and in this the timber is steeped 10 or 15 days.
This process was patented by Kyan in England in 1828,
and is called Kyanising. It is approved by the best chem¬
ists of the age, and has been used extensively in England,
and to some extent in this country with great success, for
preserving rail-road timbers. The wo.ptl prepared in this
way has been exposed to the severest tSsts without injury
v In 1838, upwards of 24 millions of feet l®f this Kyanised
timber was laid down on the Great Westernq;ail-ro?id in Eng¬
land, and an official report was published if?/18^14, stating
that no signs of rot had been discovered in,- §. single piece,
after an extensive examination of the track. Three rail¬
road Companies in New England have sinc^/ this time
Kyanised all their timbers, and the results have ..been satis¬
factory to the Engineers and to the Companies.
The cost of this preparation varies from 5 to 8 dfollars per
thousand feet of board measure, and may be used advantage¬
ously whenever the timber would decay in six or eight
years, and when the labor and interruption of renewing
would be considerable. -
The pyrolignite of iron is a much cheaper preparation
than corrosive sublimate. It was introduced by Boucherie
of France and is extensively used there. But the experi-"
ments with this substance have not been so long continued
and have not therefore inspired as much confidence as
with Kyanised wood.
With both, the great difficulty consists in making the solu- •
tion penetrate into all parts of the timber. To aid and ac¬
celerate this, they sometimes place the wood in a large close
iron tank over which the solution is poured and then sub¬
jected to great hydraulic pressure. If the wood is green and
128
fresh-cut, the sap vessels seem to aid the absorption, and the
pressure is not so much needed.
Boucherie tried various methods to produce the necessary
penetration. The tree yet standing was bored through,
near the bottom of the trunk, and the solution confined
around the tree by a water-tight bag. Or the trunk, soon
after being felled, was made to stand in a tank containing
the solution. A better method still was to invert the tim¬
bers so that the butt end was upwards, and confine the solu¬
tion in a bag around the upper part. All these plans, though
troublesome, were effective.
283. The crude iron as it first comes from the jurnace,
being brittle, must. be made tongh by hammering and roll-
ing, before it is suitable for rails.
These operations decarbonize the crude iron, and change
very much its mechanical properties; but as they require
fuel and Jator,.they increase its cost. This expense is, how¬
ever, indispensable, as only wrought iron can be used for
rails.
284. Charcoal iron, or anthracite, is better thatifohe coke
iron ; American is better than the English.
The fuel used in reducing the ore has a great influence
on the value of the iron. Charcoal does no injury ; but the
bituminous coal, or coke made from it, often contains sul¬
phur, and sometimes other foreign elements which depre¬
ciate the iron very much. The anthracite coal is more pure
and (Joes less harm.
In the United States, charcoal is generally used in the fur¬
nace ; sometimes anthracite ; seldom bituminous coal. In
England, most of the iron is made with coke, and is inferior
to ours.
285. Not less than five per cent, per annum should be
estimated for deprecation in the English iron rail. For the
' American, it is decidedly less.
Some rails break in the middle, and some separate into
thin layers, thus losing all their tenacity; on others the pro¬
jections at the upper part are crushed and torn off; all wear
away and rust more or less. The tonnage on different
129
roads, and the rapidity of the trains, and the weight of the
engines, and the quality of the iron, will each influence the
durability of the rail; but seldom will the average life even
of the T pattern exceed 20 years. With good American
iron their duration would be longer.
LECTURE XXV.
STATE IMPROVEMENTS.
286. The usual organization for making a rail-road or
€anal is a chartered corporation.
Individual capital being insufficient even for a short line,
the union of many into one legal body, having unity of
counsel, action, interest, and responsibility, is appropriate
and necessary.
287. %o peculiar privileges or monopolies of any kind
should be granted to these corporations, and all proper
restraints should be imposed on their powers.
They are united together for one object, the building of
a road, because individuals cannot accomplish the object;
every thing necessary for this end, and no more, should be
given them.
They should have no exclusive right to build roads, no
privilege of holding unnecessary real estate, no right to is¬
sue bank-bills, and no release from the ordinary obligations
of capital to pay taxes for the support of the State.
The privilege of taking necessary land and materials, at a
fair price, to be determined by a jury in case of disagreement
as to their value, is indispensable to the corporation, and
may be given with safety and propriety.
On the other hand, the Company should be held strictly
to account, as common carriers ; a maximum charge for
goods by weight aud by measure, and for passengers, should
tie fixed by their charter; a penalty for excessive charges
15
130
should be imposed, and a simple, easy and cheap mode of en¬
forcing this penalty should be prescribed.
Unless these and similar limitations should be provided
in the charters of Rail Road Companies, their immense
wealth, and influence enable them to impose on private in¬
dividuals and interfere with the natural course of trade and
travel,
288. Every charter asked for by individuals should be
granted, without expense or delay.
As rail-roads promote the public good and are of immense
advantage to the people, every refusal to grant a charter for a
road is an injury done to the community, and an interfer¬
ence with the rights of the people. Every attempt to de¬
press local interests for the gain of others, is an injustice
not to be permitted in a free and republican country. Free
trade and unlimifed competition is right and just in rail-roads
as in commerce. As common roads are always granted,
when the damages done to private property are fairly paid
for, so rail-roads should always be permitted, whenever capi¬
talists can be found willing to construct them. %
289. Our State Governments make many blunders in
undertaking the construction of rail-roads.
The Legislature is not a proper judge of the propriety of
building a rail-road along any particular route; they are not
enough interested in the matter to examine it carefully;
they are too much engrossed with other duties to decide on
it correctly; they are biassed by sectional or private inter¬
ests ; they are influenced by the opinions of prominent poli¬
tical favorites who may have a bias or interest of their own
in the result; and often it happens that however pure their
motives, and however anxious to decide correctly, many of
the members are unable to arrive at a proper conclu¬
sion.
When the work is once resolved on, the best line is not
selected, unprofitable branches are added and new works
projected, where none had before been thought of, in (kder to
satisfy the clamcrs of opponents or to promote sectionld or
private interests.
131
In the construction of the work, every expenditure is in¬
creased by the frauds, the incompetency, and the negligence
of the State's agents; high prices are paid to Engineers,
managers, and contractors; jobs are given to party favor¬
ites ; work is taken from the hands of contractors before it
isyfully finished; extra allowances are made for work really
included in the contracts; the most costly mode of construc¬
tion is adopted; double tracks are made, though not at all
needed ; the work is badly done, though extravagantly paid
for; and care is not taken of the finished work, so that it
soon needs repairs or renewal. 4
' The changes of parties and of the people introduce new
officers and superintendents, and these^lter without improv¬
ing the details of management, and thus increase the expen¬
diture without any corresponding benefit. It often happens
that%,a new Legislature is entirely opposed to the action of
the firs^, so that the whole work is suspended and heavy
damages paid to contractors for terminating their contracts;
the suspension is however temporary, for a change of coun¬
sellors renews the abandoned work.
After the road is finished and brought into use, the tolls
are adjusted to the clamors of the people, rather than to the
best interests of the road; the superintendent and other offi¬
cers, appointed with reference to party politics, are incompe¬
tent or inefficient; changes are continually introduced in
the management, by the ups and downs of partjes; the re¬
pairs of the track, the cars, and the engines, are pot effected
with^onomy; waste, extravagance and negligen70-accom¬
pany all the business of the road. ™ •
290. The State can neither construct or manage a rail¬
road as economically as a private company.
The first cost of the road being more than if it were built
by private capital, and the gross receipts being more largely
reduced by expensive management, the net profits are rle£-
sened by two causes, both of the utmost importance.
The State of Georgia has constructed a road, 140 miles
long, which has cost the State more than four milliansjofdol-
or if we include the interest on the outlay, about seven
, 134
fulness of private interest, and secure prudence and ecoijoix
m the management of the road, From half the stock ■
*
private hands, the State would probably receive laiger
dividends thnn from the whole of it under her own control.