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[The Right of Translation is reserved.]
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Transportation
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H37
V. 2
BRICK AND STONE BRIDGES,
201
Transport.
CHAPTER IX.
PART I.
BRIDGES OF STONE AND BRICKWORK, RETAINING WALLS, MANAGE.
MENT OF MASONRY AND BRICKWORK, TECHNICAL TERMS, CEN-
TRES FOR RAILWAY ARCHES.
-
THE principal works of construction on a railway, besides tunnels,
consist of bridges and viaducts of brick, stone, wood, or iron, aqueduct
bridges, culverts, and retaining walls.
BRICK AND STONE BRIDGES.—THE ARCH.
In the following pages these will be treated of consecutively, not as
regards those gigantic works which are the wonders of the age, and the
description of one of which would alone require a large volume, but as
to the more ordinary works found on railways.
The spans of railway arches are seldom of any considerable
dimensions, and rarely exceed some 30 or 40 feet on the square. In
spanning some very wide turnpike roads, a river, or a canal, these
dimensions are occasionally exceeded, as they will be also in the arches
of lofty viaducts; but in these times the Engineer must take considerably
more pains to avoid such works than he would have to take in design-
ing or carrying them into execution.
The following table will give the depths at the crown of the arch
P
202
BRICK AND STONE BRIDGES.
for the following spans of brick arches under a railway, according to
general practice, when equally extradosed:-
Span in
Feet.
15
20
30
40
50
60
Segmental arch, of
which the rise is
not less than
1th of the span.
1' 6"
1
6
1 10/1/20
2 3
2 7/12/20
3 0
~
Elliptical arch, of
which the rise is
not less than
3rd of the span.
1′ 6″
1 6
1 10/1/10
2 7/1/2
3 0
3 4-1-20
- For bridges under
roads these dimen-
sions may be a
brick less.
1
The function of the arch at the crown is, theoretically, resistance
to crushing, and as far as this only is concerned, 13 feet in depth, for a
span of 15 feet, is too great. But we have to consider not merely a
moderate vibration, but a very sensible shaking, to resist the effects of
which, in such materials as masonry and brickwork, some mass is
required. For block in course arches we should take 2 feet instead of
1′ 10″, and 2′ 6″ instead of 2′ 3″, unless for the very best material
and workmanship.
It has been ascertained by experiment that by using a segmental
arch instead of a semicircular one we get free of two points of rupture,
and the rise in this segment is about one-third of the span (Fig. 1).
In the case of an arch with piers, we may even make the rise one-
fourth and one-fifth of the span, if we make the arch unequally extra-
dosed. This raises the height of the piers; but economy of material is
effected in these by the introduction of jack-arches.
In the case of a bridge, under a heavy embankment, we may make
use of a tunnel-shaped arch.
The theory of the arch has been treated of by one of our greatest
analysts, Professor Moseley, in a most scientific and elegant manner,
and with the greatest mathematical skill, in his Mechanical Principles
of Engineering, and in the sixth volume of the Cambridge Philosophical
Transactions. Although the calculations involved are, as the Professor
BRICK AND STONE BRIDGES.
203
observes, laborious, to these works the reader is referred for the com-
plete mathematical study of the subject. There will be merely a few
geometrical applications given in these pages, but such, as being based
on this theory, will not be without practical use.
If we imagine three stones, A, B, C, (Fig. 1) piled one upon the
other, without cement, and without any other pressure than their own
weight, and more or less overhanging each other, it will be evident that
this pressure, whatever it may be, must keep them in place, or else C
would turn over at a, and B would slide upon the bed A, and the
medium by which the pressure acts is friction.
The importance of friction in everyday occurrences is brought
forward in the following words by Professor Moseley :-" Were there
no friction, it would be impossible for a man to move from any position
in which he might be placed, without the aid of some fixed obstacle,
by means of which he might push himself forward. And were there
no horizontal power of resistance in the ground on which he treads,
to destroy the forward motion which he gives himself at every step, he
would retain that motion until some obstacle interposed to destroy it."
Equilibrium will be maintained in two bodies in contact, acted upon
by any number of forces, if the resultants of the forces be equal and in
opposite indirection, and if they pass through the area contained
within the extreme points of contact of the two bodies; further, they
must not make a greater angle with a perpendicular to the plane of
contact than the "limiting angle of resistance."
If G (Fig 3) represents the force of gravity, or weight of a stone,
H the horizontal thrust, and R the resultant of these two forces,
then, in order that this stone, lying merely in contact upon the under
one, be kept at rest, the direction of the resultant R must cut the line
of contact AB, or the upper stone would roll upon the lower; on A,
as centre, if the resultant fall inside of the arch; and on B, as a centre,
if the resultant fall outside; or, in other words, if the weight of the
stone be so great as to overcome the horizontal force H, then the stone
will roll over at A; and if H be so great as to overcome G, then the stone
will roll over at B. But, besides passing through the surface of contact
A B, the resultant must not be inclined to the perpendicular P P', at a
greater angle than the angle of friction, or limiting angle of resistance.
P 2
204
BRICK AND STONE BRIDGES.
But if we place the stones so that the lines passing through their centres.
of gravity, instead of passing also through the underlying line of
contact, should pass without it, as we do in the arch, by making the
beds radiate, or simply by making the stones overlap, or overhang each
other, we shall find that after raising up a few stones, the upper ones
will roll over, unless supported by an extraneous force. In an arch
this extraneous force is applied by the opposite segment of the arch.
An equilibrated arch, then, is a system of stones in contact, so
arranged and of such dimensions, that the resultants of all the forces
acting upon it shall fall within the curved lines bounding the arch,
and not make greater angles with the perpendiculars to the beds than
the limiting angle of resistance due to the material of which the arch
is composed.
Thus, in Fig. 4, after placing the third arch-stone, further progress
must cease, unless some opposing force be called into action. Let this
force be called P. In the case of the arch of a bridge, this force would
be offered by the opposite half segment, which would be exactly in the
same condition, and as we proceed with this subject P will designate
this opposite half segment of an arch.
In order that the fifth stone retain its place on the fourth, the
forces passing through them must have their resultants in opposite
directions, and equal and acting through the same point; this point
must be in the line of contact, and the angle made by the resultants,
with a perpendicular to IK, must not exceed the limiting angle of
resistance.
Let Pp³, the line of direction of the force P, be produced to meet
the vertical line O G³, which passes through the centre of gravity of
the arch-stone; then the direction of a force acting with P to keep the
arch-stone from falling by its weight (represented in direction and
position by the line O G³), must pass through the point O³, where
these two meet, and have the direction and amount of their resultant
by the known principles of forces in equilibrio. Let Op be this line;
produce it to cut the vertical O'G'; then, in a similar manner, O¹ p³,
which represents the third force necessary for equilibrium, must be a
line cutting the vertical in the point O', and having the direction of
the resultant of two forces, the one acting through p', and the other
BRICK AND STONE BRIDGES.
205
that of the weight acting through the vertical line O' G'. This force
must also cut the surface of contact, G H, and make an angle with
a perpendicular to the surface G H not greater than the limiting
angle of resistance. It can only be supplied by the resistance or
reaction on the surface G H.
The forces in action on these two arch-stones are, then, on L MIK,
the force P, and the weight of the stone represented by G³; on the
stone IK G H the reaction or resistance afforded by the mass below,
represented by p³, and the weight of the stone by G', and their resul-
tants, p¹ O', and p' O', which must be equal and act in opposite directions.
in order that equilibrium be maintained.
The reactionary forces, severally and respectively, balance the two
forces opposed to them; they therefore represent the stress or thrust
of the superincumbent voussoirs at the joints, the resultant or re-
action at each joint being the new force impressing the stone below it.
It is plain, then, that the last resultant, being the reaction on the
surface of the springer A B, will be compounded of the resultants and
weights of all the stones above it, together with the force P, afforded
by the reaction of the opposite half segment. This resultant, then,
will
represent the direction, and where it cuts the line, A B, the point
of application of the stress or thrust of the whole arch upon the
abutment. It must, of course, cut the surface A B within its boun-
daries, and not make a greater angle with a perpendicular to that
surface than the limiting angle of resistance, or equilibrium will not
be maintained.
-
The forces above-mentioned severally and respectively represent
the thrust of the superincumbent voussoirs at the several joints, the
resultant of the vertical and horizontal forces at each joint being the
new force impressing the stone below it. The last resultant at the
springing will be compounded of the resultants of the weights of
all the stones above it, together with the force P, by which letter
we still designate the resistance from the opposite segment of the
arch.
To make what follows more clear, it is desirable to give a demon-
stration of forces acting through a point and being in equilibrium,
which will be used in the sequel. Let the lines ab, bc, Fig. 5,
206
BRICK AND STONE BRIDGES.
represent the direction and amount of two forces acting through a
given point; then, if the points a c be joined, the line a c will be equal
to the resultant of these forces both in direction and amount.
Make A B perpendicular to a b, and BC to bc, and AC to a c.
Let these lines intersect at A, B, C; then will they be proportional to
the lines to which they have been drawn perpendicular. For in the
triangle A ca, the exterior angle, a c C, is equal to the sum of the two
interior and opposite angles ca A, c A a. And because a c C is a
right angle by construction, then A ac+CA c is equal also to a right
angle. But the angle ba A, which is made up of the two angles
bac, ca A, is also a right angle; therefore, as the angle ca A is
common to both, the angle bac is equal to the angle B A C. And the
two triangles are similar, and the lines opposite the equal angles are
proportional. Therefore, if the three lines of any triangle represent in
amount and direction three forces in equilibrio, then three lines drawn
perpendicular to these, and produced until they meet, will also
represent in amount the several forces to whose directions they are
perpendicular.
Let A DEB (Fig. 6) represent the half of a semicircular arch of
30 feet span, having a thickness of 2 feet at the crown. Let the scale
be 4 feet to 1 inch, and let the semi-arch be composed of sixteen arch-
stones, besides the half key-stone. We will proceed to consider the
backing required for such an arch, on the hypothesis that the arch-
stones are perfectly smooth, without cement and free from friction.
Let P be the horizontal thrust from the opposite half segment.
Join 1 C, 2 C, 3 C, &c.
By the scale given, the half key-stone will contain 1.75 square feet
of surface; and as the material is all the same, and the arch-stones of
equal depth, we may assume this as the measure of weight of the half
key-stone. With a scale of 10 feet to 1 inch, a horizontal line drawn
through the point K will have the portion H G, intercepted between
the two radiating lines B C, 1 C; equal to 1.75. This line, then, we
will take as a scale for the weights of the backing required. Now, in
the triangle KGC we have the line KG, being horizontal, perpen-
dicular to the direction of gravity acting upon the key-stone through
its centre of gravity, and also representing in magnitude that force, or
207
BRICK AND STONE BRIDGES.
the weight of 1.75 square feet. If we assume the line K C, which is
perpendicular to the direction of the horizontal force P, to represent it
also in magnitude, then G C must also represent the resultant of these
two forces on the half key-stone in magnitude, inasmuch as it is per-
pendicular to it in direction; for the direction of the resultant of these
two forces must be perpendicular to the face of the arch joints, and
therefore to CG, otherwise no equilibrium would exist, as by the
hypothesis there is no friction. The three lines KG, K C, and G C,
being therefore respectively perpendicular to the three forces acting on
the key-stone, and of them K G, being proportional to the force of
gravity in magnitude, the other two will to the same scale represent
the value of the horizontal force P, and the reaction (which is the
resultant of the other two-namely, gravity and the horizontal force P)
on the first joint 1 C 1'. The forces in action on the mass 1, 2, are the
reaction last formed acting in the direction Cg-the force of gravity,
or weight of the mass, acting through the centre of gravity in a vertical
direction, and the resultant of these two, or the reaction necessary to
keep the structure in equilibrio afforded by the surface of the joint 2.
This last must also by the hypothesis be perpendicular to the line 2 C;
and they must all three cut each other in the same point.
Now, in the triangle GIC, we have G C representing in magnitude
the thrust on the joint 1, and being perpendicular to it in direction; the
line I C perpendicular to the direction of the reaction on the joint 2; and
the line G I perpendicular to the direction of the force of gravity; but
in any triangle, if the sides be taken to represent the value and direc-
tion of three forces passing through the same point, these three forces
are necessarily in equilibrio; therefore the lines G I, G C, IC, represent
three forces in equilibrio. One of these lines, GC, represents the
thrusts on the joint 1, in magnitude, and is perpendicular to it in
direction; the other two lines are respectively perpendicular to the
direction of the other two forces acting on the mass, 1, 2. Conse-
quently they will respectively represent them in magnitude; also by
the proposition given above, GI, by scale, will be found to measure
6.2, which is about the weight of two arch-stones; as far as 2, there-
fore, no backing will be required. In a similar manner, in triangle
IK C, IC will represent the thrust on joint 2, acting in the direction
釘
​208
BRICK AND STONE BRIDGES.
•
g'g'; IK, the necessary weight, acting through the centre of gravity
of the mass, comprising the two arch-stones and the backing; and K C
the reaction on the joint 3. By scale, IK measures 6.7 feet; a small
portion of backing, 0.5 feet is, therefore, required to maintain equili-
brium on the conditions stated.
It will be seen that the line of thrust which before kept to the same
distance from the centre, C, throughout the first two arch-stones, where
no backing was required in this pair, approaches the extrados of the
arch. The reason of this is, that the centre of gravity of the mass,
2 2′ 3′ 7, is not the same as that of the arch-stones, which does not
sensibly differ from their centre, but has moved more towards the
abutment; the vertical line passing through this, which the directions
of the two forces g'g', 'g, must intersect in the same point, has there-
fore moved a little in the direction from C to D, and consequently the
line g'g cuts the joint 3 3", a little higher up than its centre.
It will readily appear, from a similar course of reasoning to that
given in the instances of the masses 1 2, and 2 3, that the segments of
the horizontal line, which we have taken for a scale, cut off by the
intersection of the radii produced, will represent the requisite weight,
or superficial area, and consequent amount of backing necessary to be
placed vertically over the respective portions of the arch-ring cut off
by these radii, in order that equilibrium be maintained. The portion
KL measures 8.2 feet; taking away the area of the arch-stones,
6.2 feet, there will remain 2 feet to be disposed between the vertical
lines, 7 3, m 4; 10.6 6.2 4.4 feet between the verticals, m 4, n 5;
and 16.06.2 9.8 feet between the verticals, n 5, r 6. The inter-
section of the radius, E 7, with the horizontal line is not within the
limits of the diagram; it, however, cuts off a portion measuring 30 feet,
from which 6.2 feet being subtracted, 23.8 feet remain to be disposed
of in the form of backing between the r 6, s 7. This large mass causes
the extrados to assume a most unmanageable form; and, in the case of
the lower arch-stones, the evil is immensely increased-indeed, to
produce a line of thrust at right angles to the face of the springing
stone, nothing short of backing carried up to an infinite height will
suffice.
It has, at an early part of this chapter, been observed that the
- g
=
BRICK AND STONE BRIDGES.
209
:
resultant of one set of forces must not cut the plane of contact of the
two bodies, so as to make a greater angle with a perpendicular to that
plane than the limiting angle of resistance. In the foregoing case, the
resultant has been drawn so as to coincide with the perpendicular, on
the supposition that the angle of resistance is equal to nothing, and
consequently that there is no friction, a condition which, in practice,
never exists. Numerous experiments show that it always acts in a
direction parallel to the surfaces in contact, and is for the same descrip-
tion of surface, the same fraction of the impressing force, very nearly,
whatever the amount of that force may be, and whatever the extent of
the surfaces in contact. For our purpose, we may assume this law to
hold good for every pressure, the variations being so small as to be of
no moment. This fraction has been called the co-efficient of friction.
If two stones of granite be pressed together, the co-efficient of friction
is found by experiment to be, and for sandstone. The limiting
angle of resistance has this co-efficient for its weight, and this angle we
will make use of instead of the co-efficient, as being more convenient
for drawing, and because it is the direct result of experiments. These
show that this angle varies from 25° to 40°. With fresh and finely-
ground mortar, the stones move at a less angle than when no mortar is
applied. In stone bridges it will be safest to assume the angle of 26°
for the limiting angle of resistance, although the line of pressure very
rarely makes so large an angle with the perpendicular even as this,
many causes acting to make it fall rather within than without this limit.
When the line of pressure, however, cuts the abutment, it has a
tendency, especially where the load is great, to approach this angle, and
even exceed it, unless proper means be taken to divert it downwards.
There is one condition which always controls and defines the exact
position the line of thrust will take. This is the universal prevalence
throughout Nature of the law of the economy of forces, or the principle
of least resistance, or in other words, that Nature performs her work with
the least necessary amount of labour. This principle, which is almost
self-evident, was first discovered by Moseley, and he has given the
following demonstration:-
"Let us suppose the forces of a system, which are not resistances,
to be represented by the letter A, and the resistances by B; also let
210
BRICK AND STONE BRIDGES.
any other system of forces which may be made to replace the forces B,
and sustain A, be represented by C.
"Suppose the system B to be replaced by C, then it is apparent
that each force of the system C is equal to the pressure propagated
to its point of application by the forces of the system A; or it is equal
to that pressure, together with the pressure so propagated to it by the
other forces of the system C. In the former case it is identical with
one of the resistances of the system B; in the latter case it is greater
than it.
"Hence, therefore, it appears that each force of the system B is a
minimum, subject to the conditions imposed by the equilibrium of the
whole."
Of any number of lines of resistance which may be drawn within
the boundaries of an arch-ring, this principle enables us to perceive
that one which the pressures acting upon the arch would naturally
generate.
In Fig. 7, let A, B, C, D, represent the half of a segmental arch,
of 30 feet span and 9 feet rise, the thickness of the ring being 2 feet.
Now, if this semi-arch were unsupported, it would turn on the point
C, and fall. The force by which this is prevented we have called P.
Let us suppose P to be removed, and this force replaced by a fixed
and immovable surface, A B; it is obvious that the reaction on this
plane will be the smallest possible in amount consistent with the
conditions of equilibrium; that is, the resultant of all the resistances,
which we call P, will be a minimum. There are then two forces acting
upon the mass A, B, C, D-the weight W, acting vertically in a
line through the centre of gravity, and the force P; and these two
are in equilibrium, or the moment of W round C, as a centre, is
equal to the moment of P. Now, the moment of W is made
up of the weight of the semi-arch, multiplied into the distance G, C:
both these are constant quantities, and the moment of P is made
up of the force P, multiplied into C, F, both variable within certain
limits. In order, then, that the force P be the least possible, the
distance C, F, must be the greatest possible; in other words, the
point of application of the force P must be as near as possible
to the extrados of the arch at the crown. The line of thrust
BRICK AND STONE BRIDGES.
211
must also touch the intrados of the arch at the haunches; for in this
place all arches have been observed to fail. The mode of operation of
the forces tending to cause the failure of an arch is this-first, the
edges of the arch-stones splinter off at some distance on each side of
the key-stone, the crown then sinks a little, and the haunches rise, the
lower part of the arch turns outward, and the portion above the
haunches falls inwards, dividing at the key-stone into two parts.
Before the arch completely falls, it is mostly observed that, for a short
time, the key-stone hangs by its upper corners, the joints being open
below a perceptible distance; and, at the haunches, the joints are seen
simultaneously to open above. This is precisely in accordance with the
position of the point of application of the resistance P, which we have
deduced from the principle of least resistance. The force afforded by
the resistance of the opposite semi-arch acting through the key-stone,
and pressing upon the joint 1 1' at the point c, would, as the lower
part of the arch yields, keep the upper corners of the voussoirs in con-
tact, whilst the changing form of the arch would cause the lower angles
to separate. From the principle that the force P should be the least
possible in amount, it follows that the line H, E, which is perpendicular
to it in direction, and proportional to it in magnitude, should also be
the least possible consistent with the maintenance of equilibrium; for
it must be borne in mind that, as the force P is simply a resistance, it
will vary in amount, according to the tendency of the semi-arch to fall
inwards; and it will always equal the force due to that tendency,
within the limits of the powers of resistance of the opposite semi-
arch: so that the force P varies in amount and direction with every
change in the load of the arch, inasmuch as such change of load will
always affect this tendency to fall.
Take the line H C for the scale line. To a scale of 10 feet to 1
inch, the weight of the semi key-stone will be represented by 1.5, equal
to its area, which will cut off the portion Ha.
Suppose the line a m, making with the radius 1, 1', O, an angle equal
to the limiting angle of resistance, and giving the direction of the least
possible force applied at C', at the key-stone, that would support the
semi-arch; a perpendicular to the line a m, produced, would cut the
joint 1, 1', making an angle the greatest possible, with the perpendicular
01
212
BRICK AND STONE BRIDGES.
to its surface. Hm, therefore, is the least possible under the circum-
stances. From a, on the scale line, set off equal distances, a b, bc,
cd, &c., equal to 6.2, equal to the area of a pair of arch-stones; these
divisions will represent the weight of the corresponding arch-stones,
and ag
will represent the weight of the semi-arch. Now, if lines were
drawn through these points to m, they would be inclined to the respec-
tive radii at angles too large for the limits of resistance of the surfaces
of the joints, and therefore Hm is too small for the condition of equili
brium of the whole mass.
It has before been said that the line of thrust must touch the
intrados at some point near the haunches; this is also a consequence of
the principle of least resistance; for let us suppose, as before, that the
support of the opposite semi-arch is taken away, and the arch revolves
on the point C as a centre, then it will be seen, by inspection of the
figure, that the resultant of the force P, and the weight of the semi-arch
acting vertically through its centre of gravity in the line LG, must
approach as near as possible to the point C; for, were the line LC to
cut the joint CD near to D, it would show a tendency of the arch to
revolve on D as a centre, and consequently that the horizontal force is
more than sufficient for the mere support of the arch, and therefore
larger than would be excited by the resistance of the opposite semi-
arch; but the nearer the horizontal force approaches the minimum, the
nearer the line of thrust will approach the point C. The line of thrust
will, therefore, touch the intrados of the arch at some point near the
haunches. It follows, as a consequence of this, that at the point in
question the line of thrust corresponds in direction with the circle
forming the intrados; it will, therefore, be perpendicular to the radius
at that point. This furnishes a means of ascertaining by trial the least
possible horizontal force necessary to maintain equilibrium; for, if we
draw lines severally through the points a, b, c, d, e, &c., parallel to the
respective radii 1 0, 2 0, 3 0, &c., we shall find that the line parallel
to the radius D O cuts the vertical line A O, produced at the point E,
higher up than any of the rest; that is, H E is the shortest line under
the circumstances we can get. Now the line Eg being
Now the line Eg being parallel to the
joint CD, a perpendicular to Eg will correspond in direction with that
of the circle B C at the point C-that is, it will be tangential to it. If
BRICK AND STONE BRIDGES.
213
this tangent, then, cuts the vertical through the centre of gravity of the
arch-ring L, G, in the point L, where it is cut by a line drawn perpen-
dicular to the line a E, through the point C, it will follow that this
line of thrust can be drawn without at any place cutting the boundaries
of the arch-ring, and, consequently, that the horizontal force represented
by the line H, E, is sufficient for the maintenance of equilibrium, it is
also by construction the least possible in amount.
Now, as far as this arch itself is concerned, it contains within its
boundaries the line of resistance. But, to resist the loads of passing
trains, or road traffic, such an arch without backing is insufficient.
If we increase the length of HE, the line C F will approach more
nearly to a horizontal direction, and consequently the system of lines.
will move upwards and outwards, making the intersection of the last
resultant Lg, with the joint CD, nearer to D. The horizontal force
would be increased, and it would no longer be a minimum under the
conditions imposed. Were the semi-arch continued downwards, so as
to form the half of a semicircular arch, the lower part might not
admit of the line of resistance shown to be drawn within the limits of
the arch-ring. But in every instance the line having the least hori-
zontal thrust will be found to be the one that exists. To assume a
line of resistance with greater horizontal thrust than is sufficient for
equilibrium renders necessary a larger amount of backing and greater
width of abutment.
To these subjects it will be time now to come.
We may take the weight of a locomotive engine, for goods traffic, at
25 tons, exclusive of tender; to meet emergencies, and to be on the safe
side of danger, for these calculations, take three times this weight, or 75
tons, which will, in fact, be equal to about six times the load dead weight
likely to come on one point in a railway bridge; for although, in a six-
wheeled locomotive, the driving-wheels will take more than a third of the
load; yet, even if we allowed one-half, still we should not have more than
12.5 tons at one point on each rail. This gross load of 75 tons we will
consider as over the crown of the arch at Fig. 8, where it would have
the most influence. The arch itself is drawn to a scale of 4 feet to the
inch. Whether on the longitudinal, or cross sleeper system, we shall
be secure in considering this load as distributed over 9 feet in length,
214
BRICK AND STONE BRIDGES.
which will give, say 8.5 tons per foot width of the arch. It is true the
load due to the weight of puddle, ballast, and other portions of perma-
nent way are to be considered; but we have allowed more than amply
for all this, besides which these tend to distribute and equalize the load.
In another chapter the reader will find the weights due to most
kinds of stone, and also generally their crushing weights. Take the
weight of the stone at 140 lbs. per cube foot, or 16 cube feet to the
ton; then,
8.5 × 16 136 cube feet of stone,
X
equal to the load, in terms of the material of the arch. To this amount
add that due to the key-stone, which, in this instance, taking the arch,
as before, at 1 foot in width, will be 3 cube feet;
and
136 + 3
2
of stone, applied at A, on each semi-arch.
Mark this off to any convenient scale, say 20 feet to the inch, along
the line A H, and in addition 36 feet, for the six pairs of arch-stones,
each measuring 6 feet, and we have the whole amount of vertical force
acting on the arch, on the supposition that it requires no backing.
Assume the joint of rupture at the springing CD; draw a line from
the division 36 parallel to C D, and it will cut the line AO in e; join
e with 695, which gives a line to which the direction of the line of
thrust, at its commencement, is perpendicular, on the supposition that
the rupture is at CD, and therefore that the line of thrust is there
perpendicular to CD.
The line 69.5 and e will, however, be found to make a greater
angle with the joint 1, 0, than 270, or. the limiting angle of friction,
and a perpendicular to it from C would cut the intrados almost imme-
diately. Therefore, under the load assumed, the arch cannot be
maintained in equilibrium without backing.
Through 69.5 draw a line, making exactly the limiting angle of
resistance with the joint 1, 0; let this line cut A O in E.
= 69.5= the amount of vertical force, in cubic feet
Supposing the joint of rupture still at C D, and drawing a line
parallel to this joint through e, the portion it will cut off the line
A H will represent the amount of backing and arch-ring necessary to
maintain equilibrium under the given circumstances. This amount
*
BRICK AND STONE BRIDGES.
215
= 115 feet, is much too large to be carried out in practice, and we may
conclude that the joint of rupture is much higher up than when no
load is applied. The variety of lines of thrust and dispositions of
forces, consequent upon a change in the assumed amount of horizontal
force, lead to a proper understanding of the phenomena in the subject
we are considering, and are well deserving of study.
The following extract from Professor Moseley's Mechanical Principles
of Engineering, will here much assist the reader:
..
Suppose the mass A B D C, Fig. 9, to be acted upon by any
number of pressures, among which is the pressure Q, being the
resultant of certain resistances supplied by different points in a surface
BD, common to the mass and to an immovable obstacle B E.
"Now it is clear that under these circumstances we may vary the
pressure P, both as to its amount, direction, and point of application
in A C, without disturbing the equilibrium, provided only the form and
direction of the line of resistance continue to satisfy the conditions
imposed by the equilibrium of the system; that is, that it nowhere
cut the surface of the mass except at P, and within the space BD; and
that the resultant pressure, upon no section, MN, of the mass, or the
common surface, BD, of the mass and obstacle, be inclined to the per-
pendicular to that surface at an angle greater than the limiting angle
of resistance.
"Thus varying the pressure P, we may destroy the equilibrium,
either, first, by causing the resultant pressure to take a direction
without the limits prescribed by the resistance of any section, MN,
through which it passes, that is, without the cone of resistance at the
point where it intersects that surface; or secondly, by causing the
point Q to fall without the surface BD, in which case no resistance can
be opposed to the resultant force acting in that point; or, thirdly, the
point Q lying within the surface BD, we may destroy the equilibrium
by causing the line of resistance to cut the surface of the mass some-
where between that point and P.
"Let us suppose the limits of the variation of P, within which the
first two conditions are satisfied, to be known; and varying it, within
those limits, let us consider what may be its last and greatest value, so
as to satisfy the third condition.
216
"Let P act at a given point in A C, and in a given direction. It
is evident that by diminishing it under these circumstances, the line of
resistance will be made continually to assume more nearly that direction
which it would have if P were entirely removed.
Provided then that P were thus removed, the line of resistance
would cut the surface,—that is, provided the force P be necessary to
the equilibrium,-it follows that by diminishing it, we may vary the
direction and curvature of the line of resistance, until we at length
make it touch some point or other in the surface of the mass.
"And this is the limit; for if the diminution be carried further, it
will cut the surface, and the equilibrium will be destroyed. It appears.
then, that under the circumstances supposed, when P, acting at a
given point and in a given direction, is the least possible, the line of
resistance touches the interior surface or intrados of the mass.
<<
In the same manner it may be shown that when it is the greatest
possible, the line of resistance touches the exterior surface or extrados
of the mass.
ઃઃ
BRICK AND STONE BRIDGES.
"The direction and point of application of P in A C have here been
supposed to be given; but by varying this direction and point of
application, the contact of the line of resistance with the intrados of
the arch may be made to take place in an infinite variety of different
points, and each such variation supplies a new value of P. Among
these, therefore, it remains to seek the absolute maximum and minimum
values of that pressure.
"In respect of the direction of the pressure P, or its inclination to
A C, it is at once apparent that the least value of that pressure is
obtained, whatever be its point of application, when it is horizontal.
((
There remain, then, two conditions to which P is to be subjected,
and which involve its condition of a minimum. The first is, that its
amount shall be such as will give to the line of resistance a point of contact
with the intrados; the second, that its point of application in the key-
stone A C shall be such as to give it the least value which it can
receive, subject to the first condition."
It has been observed above, in reference to Fig. 8, that the angle
of rupture, under a heavy load such as we have been dealing with,
would be much higher up, and in practice it will be found that we may
C
BRICK AND STONE BRIDGES.
217
assume that joint to be at a point where a line would form an angle of
from 34° to 40° with the vertical. The amount of backing is then not
only manageable, but also serviceable without being an overload in the
shape of an unnecessary mass on the abutment.
We shall find after going into the next, Fig. 10, that the total
weight amounts in this case to 164 cubic feet of stone, or to 1858 lbs.
per inch width of the arch; and this is distributed over the length of
the arch joint.
The line of thrust is, as already stated, the resultant of an indefinite.
number of parallel forces pressing on the face of each joint; the
pressure then communicated by one voussoir to the other is distributed
along the whole surface of the joint in such a manner that the sum of
the moments on one side of the resultant, or line of thrust, is equal to
the sum of the moments on the other, taking the point of intersection
of the line of thrust with the joint as the centre. It follows from this.
that the pressure at points on the joint remote from this intersection
is very small when the point of intersection approaches very nearly to
either the internal or external boundary of the arch-ring; inasmuch as
the greater part of the pressure is, on the shorter portion of the joint,
cut off by the line of thrust. We shall, therefore, find that the bulk
of the pressure at the joint of rupture is at the internal edge of the
voussoirs; and that in order that this be not splintered off, the position
the line of thrust will assume will not precisely coincide with that of
the tangent at this point, but be a little removed up the joint, still,
however, keeping parallel to the tangent. Assuming the ultimate
strength of the stone at 1500 lbs. per square inch, which we may do
with safety, and the value of the thrust at the joint of rupture being
found equal to 1858 lbs. along the whole joint for each inch of arch
width, we may allow something near one inch as the distance of the
line of thrust from the intrados at this joint. This is the position the
line of thrust naturally assumes, for as soon as the yielding of the
material, arising from too large a pressure at the edge, takes place, the
horizontal force slightly increases, until it throws the line of thrust
sufficiently within the arch-ring to prevent ultimate injury; indeed, it
may
be laid down as a rule, that an arch never fails at the joint of
rupture first, the line of thrust must cut the extrados somewhere below
Q
218
BRICK AND STONE BRIDGES.
this joint, or the arch will remain standing-the horizontal force
generated by the tendency to fall inwards always increasing sufficiently
to keep the line of thrust from cutting the intrados.
And now, referring again to Fig. 10, drawn to a scale of 4 feet to
1 inch, and in which the scale line A H is again drawn to 20 feet to
1 inch, we shall take the angle of rupture at 34° with the vertical,
which will be at the joint 4,4'. Any backing above the joint ab will
be worse than useless, only adding to the horizontal force.
We shall now only take the five first voussoirs, equal to 15 feet, to
be added to 69.5 feet due to the load.
Scale this off on the scale line AH, and we shall have the total
vertical pressure acting in conjunction with the horizontal force of the
opposite semi-arch upon the joint ab; the reaction on this joint must cut
the vertical line passing through the centre of gravity of the mass
1 l'ab, at the same point where it is cut by the line of thrust on the
joint 1 1'.
Draw the line 15, E, parallel to a line, making a very small angle
with the radius a O, and join the point 69.5 with E.
A perpendicular to this last line, passing through C, will cut the
vertical through the centre of gravity of the mass 1 1' a b, at a point G,
through which a line may be drawn perpendicular to the line joining
the points, 69.5 and E, which will be wholly within the arch-ring.
The oblique pressure represented by the line joining the points 15
and E, is equal to the weight of 164.5, which at 136 lbs. to the cube foot,
will be equal to a pressure of 1864 lbs. on an arch-ring of 1 inch
in thickness.
The line of thrust being found on the line a b, it will be below this
joint that we must place the backing to control it and confine it
within the arch-ring.
A small addition of the triangular piece af 4, over the voussoir
will make this latter equal to 3.6 feet; set this off on the scale line, and
join the points 3.6 and E, which gives a line to which the line of thrust
is perpendicular at its intersection with the joint 4, 4′.
Produce the line Gd to cut the vertical which passes through the
common centre of gravity of the mass a b 4' 4f, and through the
point of intersection draw a perpendicular to the line E, 36, cutting
BRICK AND STONE BRIDGES.
219
the joint 4, 4'. It will be observed that the line 36, E, makes a small
angle with the joint 4, 4', inclining from it, whilst in the angle made by
15, E, with the joint a 6, the line inclined to the joint. From this we
may infer that the line of thrust becomes tangential to the intrados
somewhere between 6 and 4', and is leaving the intrados, and taking a
direction towards the extrados, and requires backing.
If we now add 4.4 to the area 6 of the two voussoirs 4 4' 5 5', we
shall bring the line of backing to . Set off 4:46 104 upon the
scale line, and join this point with E. As before, produce the line of
thrust to cut through the line passing through the common centre
of gravity of the mass ƒ4 4′ 5′ 5 h, and through the intersection draw a
perpendicular to E, 104.
In a similar manner for the backing over the remaining two pairs of
voussoirs, we shall have to set out on the scale line 14 and 15 feet; and
then proceeding, as we have already done, with regard to the lines
passing through the two centres of gravity of the two pairs of arch-
stones and superincumbent backing, the line of thrust, and the lines.
joining 14 and 15 with E, we shall find that the line of thrust cuts the
joint CD sufficiently within the arch-ring to secure stability.
The value, in cube feet of stone, of the oblique pressures on the arch,
we can obtain by measuring with the scale the oblique lines joining E
with the figures on the scale line.
Thus, the oblique pressure on the springer will be found equal to
190 cube feet, or 2154 lbs. for every inch in width; and taking, as
already observed, 1500 lbs. pressure on the inch, nearly two inches from
the extrados at the springing must be the minimum for the extreme
limit of the line of thrust at the springing.
It will be remembered that we have taken 75 tons as the load
on the crown of the arch, a very extreme case, and one which compels
the line of thrust to assume the direction shown on the diagram, and to
come very near the extrados at the springing.
In almost all cases it will be much further inside the ring, for
it must be remembered that the only necessary points of contact,
or nearly so, are at the extrados at the crown, and at intrados at the
joint of rupture.
With regard to the thickness at the crown, let it be observed, that
Q 2
220
BRICK AND STONE BRIDGES.
at this point the line of resistance approaches very near to the extrados;
consequently the effectual pressure on the lower portion of the arch-
stones is here very inconsiderable. It is here that the arch-ring may be
diminished in depth, and proportionately increased towards the haunches
and springing, where this addition more than takes the place of so
much backing. This is now becoming a very general practice.
By altering the load on the crown, and, consequently, the load on
the scale line as well as the other dimensions, the reader will have an
opportunity of studying the lines of thrust, and, at the same time,
of obtaining the value of the oblique pressures by measuring with the
scale the oblique lines joining E to the several dimensions set off on
the scale line.
The following is given in Ware's old Treatise on Bridges as a
method of finding the extrados of an arch of equilibration, which,
however, we only introduce as regards the subject of thickness of
abutment.
(c
Having the span, intrados, and depth of arch at the crown, to find
the extrados, divide A C, Fig. 11, into any number of parts, as at 1, 2,
3, 4, 5, 6, 7, 8, &c., and through these divisions draw, O, a, O 2 b, 0
3
C, O 4 d, 0 5 e, O 6 ƒ, 0 7 g, &c. ; also through 1, 2, 3, 4, 5, 6, 7, &c.,
draw the verticals, 1 p, 2 p, 3 p, 4 p, 5 p, 6 p, &c., and make each of
these verticals equal to CD; through p, p, p, draw the horizontals p a,
p b, pc, pd, pe, pf, &c., to cut 01 a, 02b, 0 3 c, 0 4 d, &c.; and the
points of intersection a, b, c, d, e, f, &c., will be the points through which
the curve of intrados will pass; this first description refers to that side
of Fig. 11, where the extrados is dotted.
“To find the thickness of abutment-produce pa, pb, pc, pd, pu, pt,
&c., and make a y equal to p a, b x equal to p b, c w equal to p c, d v equal
top d, and e u equal top e, &c.; from t, u, v, w, x, y, let fall verticals; from
ƒ, perpendicular to 6fdraw fo; through e, perpendicular to 5 e draw
eo; through d, perpendicular to 4 d, draw do; through c, perpendicular
to 3 c, draw co; through 0, 0, 0, 0, &c., which are the points of inter-
section of the last lines drawn, and the last verticals let fall, draw
the curve 0, 0, 0, 0, &c., which will be the line of thrust; join OR, and
bisect it at G, and from G at a centre, with radius G O, describe the
curve R; join 6 R by a straight line 7 R, which will give the limits of
/
BRICK AND STONE BRIDGES.
221
abutment; this method borders remarkably near practice; if from 6 we
let fall a vertical 6 T, ST will be the thickness of abutment, and V may
be considered the point of limit for the counterfort, and the curve
0,0,0,0 V, the line to which the courses of masonry in the abutment
should be perpendicular. Fig. 12 shows an elliptic arch extradosed,
with the thickness of abutment found in the same manner.
""
The reader will not fail to see of what an excessive mass the abut-
ment and counterfort are composed; still a large number of bridges
have been, and may still be built with such proportions.
In Fig. 13 is another system, deduced from the same principles
which we have been already examining at some length, considering the
amount of space we have in these pages. The scale for the outline of
the arch is 10 feet to the inch, and for the triangle of forces 80 feet
to 1 inch.
The joint of rupture, with the arch loaded to the extent already
assumed equal to 69 6 square feet, will be at the joint 4. This quantity
is marked on the scale line. From this point to 2 O, the distance repre-
sents the amount due to 3 pairs of voussoirs, equal to 18, plus 2, due
to the small amount of backing over them. A line drawn through this
point, parallel to joint 4, cuts the vertical through H, at E, and defines
the amount of horizontal force generated by the length HE, which,
by scale, is equal to 205 square feet. The line of thrust is carried
down through the lower voussoirs by the same method we have before
pointed out. The backing is taken as high up as practicable, and
measures, together with the arch-ring, 67 feet, without the portion over
the abutment. Notwithstanding this great weight, the line of thrust,
by reason of the large proportion of horizontal thrust, forces its way
out of the boundaries of the arch-ring beyond the joint 6. The extreme
load we have assumed makes this the more forcible, and will make the
more intelligible and forcible the two following conditions :-up to this
angle build up solid, and increase the depth of the arch regularly from
the point a up to the abutment. A practical illustration is given of
this at Figs. 14 and 15, in which will also be seen the value of the
counterforts; not from their additional weight, but from their extension
of base, and increase of width gained to the abutment. Returning to
Fig. 13, the line 204 represents the oblique force on its egress from
222
BRICK AND STONE BRIDGES.
the arch-ring. Under the extreme supposed load, it will be observed
that, notwithstanding the amount of backing, as well as of the mass
CD = 60 square feet above the abutment, so great is the oblique force
generated =245 square feet, that the whole has but little influence in
controlling the direction of the line of thrust. To the level of the
springing the abutment measures 20 × 8 feet. This divided by 4 gives
40 square feet for each division in height. These quantities are marked
off on the scale line as representing their weights in feet of stone.
Observe that these masses of 40 feet have their centres of gravity in
one common line, which intersects the line of thrust at G. Draw the
lines a b, c d, ef, g h, dividing the heights of the abutment into four equal
parts perpendicular to 40′ E, 40″ E, &c., draw the lines from G; the
intersections with a b, c d, &c., will give the direction of the line of
thrust.
:
It will now easily be seen why in so many bridges the courses of
masonry are built radial to the centre from which the arch is struck.
It will also be seen in the two parallels at Figs. 14 and 15, which is
after the system long pursued in Mr. Brunel's works, that the force
opposed to the line of thrust is the power of resistance to crushing in
the materials in the small "jack-arches." It will be seen what a great
amount of saving in material is effected, notwithstanding the great
spread at the base of the abutment, which is of course one of the most
desirable objects to attain. Inasmuch, however, as many will still
adhere to the old form of abutment, another parallel is added at Fig.
16, where the mass of brickwork or masonry is reduced by jack-arches
in the face of the abutment.
We cannot keep it too strongly impressed on our minds, that one
of the greatest safeguards, equal almost to the soundness of the work
itself, consists in the plentiful earth backing and punning up in good
sound loamy stuff, or clay carried up to the full height of the abutment,
with a thickness of from 6 to 10 feet, and punned in layers of about 6
or 9 inches. This work requires careful overlooking.
The last three diagrams are drawn to a scale of 10 feet to 1 inch,
and in getting out a section for an arch and abutment, for spans from
20 to 40 feet, there is little more to do than to copy. For greater
spans, proportion will give the required dimensions.
TECHNICAL TERMS.
223
In very flat arches the backing may be carried up the level of the
soffit of the arch, particularly if the arch be under a railway; and the
arch should always be unequally extradosed, as in Figs. 15 and 16.
For arches of greater rise, say one-third of the span, it will be
sufficient if the backing be carried up to a level of within 2 or 3 feet
of the soffit, according as the arch may be under or over the rails.
On the subject of piers very few observations will be sufficient;
their thickness in practice is regulated by the span, and from one-sixth
to one-seventh of this is generally taken for the width of the pier. A
less thickness would be sufficient, but rather than diminish this width
it is better to economise material by having jack-arches in the pier, by
which a considerable saving may be effected. When piers are of a
greater height than about 20 feet, a slight batter should be given to
the face of the pier; from of an inch to 1 inch per foot, as the height
of the pier becomes very great, will be sufficient. Where this height
does not exceed some 20 or 25 feet, and the pier is brickwork, one or
two sets-off a few feet above the base will answer the purpose. The
footings should always be sufficient to give a considerably increased
width of base.
We have as yet been speaking of arches of a span equal only to
30 feet. For larger spans we should have a greater number of points
of division, but there would still be the same proportions.
Having gone through, or rather touched so far upon the subject
of the arch, abutments, piers, and counterforts, it becomes desirable to
say a few words as to the materials of which they are composed.
The word Ashlar applies to masonry of large scantling, and the
material and workmanship should be of the best; it may be 12 inches
thick, or more, 4 feet by 2 feet on the bed, or more, and laid alternately
in headers and stretchers; joints should overlap 12 or 15 inches; the
joints and beds should all be dressed fair and true, if not chiselled,
which they should be for all exterior work. The face work must be
fair tooled, or the joints may be chamfered, or a margin-draft run
round about 1 or 2 inches wide, and the interior may be left quarry-
faced. Very often Ashlar requires to be dowelled, that is, the blocks
connected by hard stone dovetailed dowels.
Whatever stone may be used, the dressing is a most important
224
TECHNICAL TERMS.
feature, and generally, the larger the blocks the greater the care
required in this particular, as to levelling the beds, or dressing them
to the proper angle, or in the squaring. If the beds are irregular, or
in winding the bearing is unequal, and the stone tends to split and
rend at bearing points, which act as fulcrums, and in fact may have
to be loaded with an enormous weight. This cannot occur if the beds.
have been well levelled, as the bearing is then equal throughout the
bed. The rent receives rain-water, and allows it to lodge, and the
structure becomes exposed, often in a dangerous manner, to the effects
of frost.
If the blocks of stone are fairly and truly dressed, the trouble of
laying them will be comparatively slight; care must be taken that, in
order to hide or disguise a thick, clumsy joint, the blocks be not
pitched forward on their edges, as they will then be sure to splinter
at the edges, from the weight bearing on the angle. To disguise the
careless dressing of blocks, and to level them when laid, workmen are
very apt to underpin large blocks of stone with wedges of wood or
splinters of stone, thereby laying the foundation of rents and fissures
when the work settles. The setting bed of each course should be
brought true and level to receive the next course, which must rest
solidly and truly upon it. The face of every stone in a wall may be
left quarry-faced, or as it comes from the quarry, but each stone should
be wrought with a setting margin.
The dressing of the beds of large blocks of stone may easily be
tested by laying the edge of a straight rod or rule (otherwise a straight
edge), along the surface of a block from angle to angle, and from side
to side, when any winding or irregularities in the setting beds will
easily be seen, by parts of the edge of the rule lying close to the
stone, whilst cavities admit the light between the bed and the rule.
In building with ashlar, or other large stone, care must be taken
that pebble and small stones be not used in the mortar, as these will
act as so many wedges on the beds; but in grouting, or filling in at
the back of masonry, there is no objection to splinters being used; and
in filling in angles and odd corners in rubble backing, they may
come in advantageously, not only to save waste of mortar, but because,
when the mortar sets, the work will be better filled; unfortunately,
TECHNICAL TERMS.
225
unless under the eye of a careful inspector, this is where masons will
often not take the trouble to use splinters of stone.
Block in course consists of masonry in which the stones are also of
a large size, but less than ashlar masonry; for instance, the blocks
may be some 7 inches thick, and 12 or 18 on the bed; or 15 by 24 on
the bed, and 9 inches thick; the beds and joints carefully hammer-
dressed, fair, true, and square; whether through stones or not, one-
fourth the length of each course should be from 2 to 3 feet long,
according to the size of the block in course, or the thickness of the
wall. These should be laid nearly equi-distant, and so as to bond into
the backing, if any.
Rubble is a coarser kind of masonry, where the stones should be
well bonded together; no stone should contain less than a cubic foot,
except for pinning, the stones should be flat-bedded, and plenty of
mortar and grouting used to make all solid. In districts where stone
is abundant, heavy walls in rubble are run up very cheap.
Another material is brickwork, of which such incredible quantities
have been consumed in railways.
Amongst the evils of omission or commission which we have to
guard against in brickwork, the following may be enumerated:-.
The beds of mortar being very unequal in thickness, and exceeding
of an inch.
The introduction of brickbats, or pieces of brick, except as closers,
whereby the perpendicular joints in two courses may lie one above the
other, which should not be.
The absence of mortar in the joints, particularly in the interior
part of the work, either on the bed, the side, or the head of a brick, and
neglecting to grout with fine mortar at least at every fourth course,
when required.
Running up side joints without any bond; bricklayers are apt to
do this where beds are horizontal by the side of battering beds.
Running up too great a height and too little width of work at a time,
thereby injuring the connexion of the courses by unequal settlement.
The neglect in dry, hot weather of wetting the bricks before they
are laid on the mortar, when, if a brick thus laid be lifted up again, it
will be found that the mortar does not in the least adhere to it.
226
TECHNICAL TERMS.
Each brick, as it is laid, should be pressed, or rather rubbed, into the
mortar.
The levelling of the courses should be carefully attended to.
In arches, where the bricks, or some of them, should be cut, this
precaution is often totally neglected. Bricklayers will sometimes in
such work, where it is concealed, make a mortar joint 1 inch thick.
All these evils bricklayers will introduce unless their work be closely
watched, and sometimes ripped up; and, although each evil by itself
may appear of trifling moment, it is only by avoiding one and all that
good brickwork, as rare in modern construction as it is sound and
deservedly admired when met with, can be built.
In the construction of brick arches, a great evil consists in the brick-
layers, when reaching the centre or keying, attempting to fill up a void
of 4 or 5 inches with one brick, and thick cement, and mortar joints, or
brickbats. Such a proceeding should be stopped, and 4 or 5 bricks
being removed at each side, their places should be filled up with the
largest-sized bricks, picked out for the purpose, so as to fill the space at
the keying in a proper manner.
In engineering work, brickwork is only employed in the construc-
tion of an arch from motives of economy, not only where stone is not
easily attainable, but also to avoid the expense of cutting the arch-
stones to their true form. In this sense, also, bricks have the advantage
of being more easily raised in moderate quantities, and, from their small
size, of being more easily handled and placed. The bond in good brick-
work gives a far better connexion than that obtained from inferior
masonry. Compared, however, with stone, brick is a frangible and porous
material; at least that description of brick too often resorted to from
motives of false economy, and rain and frost often perform quick justice
on these defects by fracturing and splintering the materials in the
intrados, which consequently drop out, thus commencing the destruc-
tion of an arch, unless careful precautions be taken to prevent the access of
surface water to the extrados, by covering the arch with an impervious
material, such as good puddle or asphalte properly prepared and laid on.
Bricks, being in rectangular forms, would necessitate guaging to
proportion their outer surface. to the outer periphery of the ring, and
this economy puts out of the question. Moreover, this precaution in
MASONS' TOols.
227
a large arch, comparatively speaking with regard to the size of bricks,
would be useless, in consequence of the small depth of a brick-ring.
The auxiliaries, therefore, to obtain the curve of the arch are a series of
wedges of mortar or cement. The latter, though more expensive, is
often used in the upper portion of an arch.
A brick arch may be considerably strengthened by the introduction
of hoop-iron between the courses, more particularly at those parts of the
intrados and extrados where there would be a disposition to open at the
joints; also by facing with stone quoins, which should be of a good
These
length and a good bond into the brickwork. See Fig. 17.
quoins should have their soffits fair tooled, and they should underlay
the bricks by a couple of inches, with their edges champered off, when
they will act as dripstones.
Much of the above observations will hold with regard to the stone
voussoirs of an arch, but in a less degree, inasmuch as the arch-stones
are cut to a radiating form, and the intervening mortar is no longer of
wedge shape. The thickness of the mortar should only be sufficient to
act as a cement, and entirely fill up vacuities between arch-stones.
The greater the span, and still more the less the rise of the
arch, the greater the necessity of strict adherence to this important
point will be.
With regard to the filling in of backing or spandrils of railway
arches, which are generally of only small or moderate span, the work
should be as sound as any other part, but appearance is not here
requisite. Rougher materials may be used, but they should be hard,
dry, and tolerably well-shaped. Sufficient mortar or cement should be
used, and in these concealed parts of a construction bricklayers and
masons will introduce as little as possible if they are not watched.
In masonry there should be sufficient binders or bond stones, and
all the work should be well and closely packed and tied together. It
must not be forgotten that, although this work is out of sight, it has
to perform the duty of resisting the thrust of the upper portion of the
arch tending to overset the lower.
MASONS' TOOLS.
These consist of a level, straight-edges, a plumb rule, a square, and
228
CENTRES FOR RAILWAY ARCHES.
a bevel; also, as cutting tools, of the point, which cuts narrow furrows
along the surface and leaves narrow edges between; the inch tool, which
cuts away the ridges; and the boaster, which leaves the surface nearly
smooth. There is also the broad tool, performing two kinds of opera-
tions. Suppose the first impression made by the whole breadth of the
tool, which may be 2 or 3 inches, be called a cavity, one operation
is to make the cavities follow one another in a straight line until the
length or breadth of the stone is gone over; then follow successive
equidistant lines of this, until the whole surface has been gone over.
This is called stroking, and gives a kind of fluted surface. In the other
operation every successive cavity is repeated in new equidistant lines.
throughout the length or breadth of the stone; a new series of this
follows, and again another, until the whole surface is brought down.
This is called tooling.
A stone is taken out of winding by the point, and then with the
inch tool.
When stones are very unshapely, a jedding axe or scabbling hammer
is used to bring it into shape. One end of the jedding axe is flat to
strike off protuberances, and the other end is pointed to bring down the
different surfaces nearly to the intended planes. The point is sometimes
called a punch, and boasting is sometimes called droving. The broad tool
is sometimes used as broaching without previous boasting, but the work
is never so regular.
Where the stone is very hard, the scabbling hammer is used for a
great deal of the work; by this tool the surface is worked until reduced
nearly to the intended plane. This manner of dressing is sometimes
called nidging. The term rubbed work is applied where the surface is
brought down by means of sand.
To describe an elliptic arch from three centres, the span and rise, or
the major and semi-minor axes being given:-In Fig. 18, let A B be
the span, and OC the rise; complete the parallelogram COBD, by
making BD parallel to OC, and CD parallel to OB; bisect BD at E,
and join EC; make O F equal to OC, and join DF, cutting CE at G ;
bisect CG at K, and draw KL perpendicular to CG, cutting Co
produced at L; from L as a centre, with radius LG, describe the curve
MGC; through MB draw M Bn; join n L, cutting A B at N, and
CENTRES FOR RAILWAY ARCHES.
229
transfer BN to AN; N, L, N', will be the three centres required
for describing the curve.
Having the span and the rise, to describe a semi-ellipsis with five
centres-In Fig. 19, let AB be the span, and OC the rise; from
centre O, with radius O A, or O B, describe the semicircle AD B, and
divide it into six equal parts at 1, 2 D, 3, 4, B, with radius OC; and
also from centre O describe the semicircle ECF, and divide this also
into six equal parts, as at a, b, C, c, dE; through 1, 2, 3, 4, draw parallels
to CO, and through a, b, c, d, draw parallels to AB; join the points of
intersection f, g, h, i, which will be points on the elliptic curve; bisect
A ƒ, fg, g C, C h, hi, i B, as at k, l, m, n, o, p; through m and n draw m G,
and n G, perpendicular to C and g C, intersecting CO produced at G,
when G will be a centre; through 7 and o draw /H, o H, perpendicular
to fg and hi, and intersecting m G and n G, at H and H'; and H and
H' will be two centres also; through k and p, perpendicular to Af and
i B, draw k K, p K', intersecting A B at K and K', which will be the
two last centres required for the curve of the arch. The greater the
number of divisions in the semicircles the more numerous the centres,
and the nearer will the curve described approach the elliptic.
TO SET OUT AN ELLIPSE.
A much better way of setting out an ellipse is in the following
manner, in which the semi-major axis and the semi-minor axis are
marked off on a slip of paper, which is so worked round that by
pricking off at the end of the semi-major axis the curve is most
correctly obtained.
Ex. Let AB, fig. 20, and CB be the semi-major and semi-minor
axis of a quarter of an ellipse, or half the headway of an arch. Take a
slip of paper and lay it along AC, the semi-major axis produced,
so that the edge of the slip coincides with this line, and prick off on the
edge the points A and C, and let C be called D.
Next lay the same edge to coincide with BC, produced, and let the
point marked A on the edge of paper coincide with B, and mark off the
point C on the same edge, and call this point C.
Now move the edge of paper round, so that the point called C
shall be on the semi-major axis, as at C, C, C, &c., and the point called
230
CENTRES FOR RAILWAY ARCHES.
1
D, on the semi-minor axis, at D, D, D, &c., until A, on the slip of paper,
is again at A on the major semi-axis, and D on C, coinciding with A C.
and
The dotted lines represent the slip of paper as it is worked round, and
by pricking off at the end A, any number of points on the curve,
marked by dots on the diagram, will be obtained. This very simple
method is well known amongst practical men generally, but there are
so many persons unacquainted with it, and so many works treating on
practical geometry in which it is omitted, that perhaps no other
apology need be offered for giving it here.
FIG. 20.

Having the rise and span of a segmental arch, to find the radius.
In the annexed figure, A B is the span, and CD is the rise. Call the
span S, and the rise V; required the radius, R.
Then,
9°
S or 900 4 V, or
D
1
I
1
1
V
R = 1/2 (1
S2
1 + 4V
Or in figures, let CD, or V, the rise be 9 feet; and let AB, or S the
span be 30 feet;
then
and
and
=
916
الا
= 4.50;
2
30² = 900;
=
B
81 × 4 = 324,
324 = 2.7777 + 1 = 3.7777;
V
or 4.50 x 3.7777 16.999651, or radius required.
2
CENTRES FOR RAILWAY ARCHES.
231
or
Or the rectangle under the segments of one chord being equal to the
rectangle under the segments of another, we may make use of the
following rule:-
or by figures
and
and
and
and
225
9
Jong
2212
2
34
2
8c - C
3
÷ V+V
2
(30)² = 225
= 25; and 25 + 9 = 34;
=
=
With regard to the width of the arch-stones at the intrados, we may
take from to of the depth at the crown, remembering that the
number of voussoirs must be an odd number, as one of them will
be the key-stone, and their number multiplied by their width should
be equal to the length of the arc, allowance being afterwards made for
mortar; the dimensions should be figured on the drawing, for the
intrados and extrados, and the Engineer should see that the arch-stones.
are worked to those dimensions, within the limits of practical means.
To rectify the arc of a circle, or to find the length of a circular line,
either of the following rules are sufficiently near for practice:-
Let C be equal to the chord of the arc, or the span, A B, 30 feet,
Fig. 21, and let c be equal to the chord of half the arc A C, 9 feet and
a the length of the curve required; then
X
R
17 = Radius.
8c-C
3
√ AD² + DC = 17.4928557;
8c 17.4928557 x 8 = 139.9428557;
=
8c C139.9428557-30 109.9428557;
=
109.9428, &c.
3
x = 36·6709 = length of arc.
= 36.6709, &c. ;
232
CENTRES FOR RAILWAY ARCHES.
Or as before, putting C for A B, span of 30 feet; and c for CD, versed
sine, or rise of 9 feet; and a for length of curve required, we have
or in figures,
and
and
and
M
16
x = C +
3
rise, or c²
c² 81 x C or 30 2430;
3 C² + 2 c² or 2700 + 162 = 2862;
194402862 = 6·7924 ;
C = 30 + 67924 = 36.7924 length of arc.
And having found this length, if we divide by about one-half the
depth of arch-stone, say 2 feet on the face, we shall obtain the number
of voussoirs or arch-stones, and also have their dimensions at the
intrados, allowance to be made afterwards for mortar; here reducing
36.79 to inches, we get 441 inches, and 441 divided by 11.31 inches
39, almost exactly, and nearer than we can
can ever obtain it in
practice; of an inch is the least quantity masons can be expected to
observe; we shall therefore have 39 voussoirs of 11.31 inches thickness
at the intrados, and if we allow inch for the mortar joint, we shall
have 10.91. For the thickness at the extrados, see page 117.
We have now the span, the rise, the radius, the depth of the arch,
the division of the arch into arch-stones, the thickness of the piers, and
the width of the abutment at the base, though circumstances will
continually modify this dimension between and of the span; under
20 feet it will be nearer .
8 c² C
C² + 2 c²
81;
= =
The practice of Engineers varies very much with regard to the
backing, or filling in of the spandrils; our railway bridges are often
equally extradosed, that is, the extrados is parallel to the intrados,
though certainly not because it is the strongest form of extrados ;
sometimes the arch-stones increase towards the springing, and the
extrados is often then a curve of contrary flexure from about an angle
of 45°; sometimes also the depth of voussoirs increases by a similar
curve to that of the intrados, becoming at the springing of twice the
CENTRES FOR RAILWAY ARCHES.
233
thickness of the crown. The spandrils may be filled by solid masonry,
surmounted by spandril arches, or by solid masonry and spandril walls,
or by solid masonry alone; the object' is to receive the thrust of the
upper portion of the arch and of the load superimposed, and to
dissipate vibration, and where spandril arches and spandril walls are
used, relieve the upper portion of the arch from vertical pressure; in
arches up to 50 feet span, the spandrils may be filled in with solid
masonry.
We may proportion the depths of the springers when used in the
following manner :-from 20 to 30 feet span, 1 foot for the depth of
springer; from 30 to 35 feet span, 1 foot 3 inches; from 35 to 40 feet,
1 foot 6 inches; 40 to 50 feet, 2 feet; 50 to 60 feet, 2 feet 6 inches
and 3 feet; less dimensions may be allowed for string courses; a good
depth of string course acts like a chain over the spandril walls; make
all mouldings plain, bold, and so weathered and throated that water
cannot lodge. Stone if at all costly may be dispensed with in most
ordinary cases.
A transverse section through an arch should show dimensions
between the faces of the arch, the thickness of spandril walls, the
dimensions of string courses, parapets and coping; and these dimen-
sions should all be figured. Where any of these parts are decorated by
mouldings, enlarged or detailed drawings should be given, showing the
centres of curves and the bevels; sections of wing walls should also
be given; and where brick is the building material, care must be taken
to count the dimensions by bricks, half, and quarter bricks, or these
dimensions have no real value beyond the drawing. The young practi-
tioner must never lose sight of one important point on the subject of
working drawings, that they are only preparatory to the construction of
a building, and that this important point, from ignorance or careless-
ness, is so often neglected, that, one or two dimensions having been
taken, the drawing becomes worthless; hence, a common observation
amongst workmen-"Who ever saw a working drawing that could be
worked from ?" An Engineer in charge of works should consider
himself responsible for the value of working drawings, making, how-
ever, some allowance for unexpected circumstances; whether the
material be stone or brick, iron or wood, a little thought, observation,
R
234
CENTRES FOR RAILWAY ARCHES.
and study of material will guide him in giving instructions for working
drawings which may be worked from; and in setting out the dimen-
sions on paper, he should consider himself as setting out the work
itself. As regards the principal lengths, widths, and heights, a cross
section to a large natural scale taken on the site determined on, will
generally save him from blundering, as regards section, elevation, and
plan; the neglect of this precaution will ensure two things, viz., a wide
difference between the work constructed and the drawing, and the
impossibility, without making a fresh drawing, of setting off the
quantities of work performed. It must not be supposed that an affecta-
tion of fastidious care is here pretended, involving useless trouble to
others and loss of time, and it must, on the contrary, be considered
that we are alluding strictly to practice generally, and that experience
alone suggests these observations.
Generally, the cases of bridge-building which we have to deal
with are bridges over a cutting, or under an embankment, or partly
of both, as where a road has to be raised; or it may be over a railway,
where the road has to be raised so as to give sufficient headway for
the locomotive. Parallels for all these will be found in Dempsey's
Brick Bridges, taken from working drawings, making allowance for
improvements. These are not recommended as copies, but to be treated
more or less according to the principles above given, in order to improve
upon former constructions.
For a double line of way, the clear width between the parapets,
piers, or abutments, may be 26 or 27 feet (Fig. 22), though often
made 28 and even 30 feet. If to this we add the thickness of the two
parapet walls, where used, we shall have the entire width of the arch.
See Fig. 22.
For roads, we must be guided by legal enactments made to
regulate the construction of railways; a short abstract of these, as
regards roads and bridges, will be given at the end of the chapter. In
crossing canals, we are generally tied down by special agreements.
We will not extend beyond a few words our remarks on the centres
of railway arches; they must be viewed as the means by which the
materials forming an arch are to be supported until the arch is keyed
in, and also as the moulds by which the intended curve is given to the
|
CENTRES FOR RAILWAY ARCHES.
235
series of stones, bricks, &c. Designs for centres are not expected from
the Engineer, it being the business of the Contractor to provide these,
but it is distinctly the business of the Engineer to see that the centres
employed be of correct form and dimensions, of sufficient strength for
their intended purpose, and so framed as to be practically unyielding
under the load they are to bear; it is, therefore, necessary that he
should take this subject into general consideration in the superin-
tendence of railway works, more particularly under certain important
points presently to be pointed out, without the slightest pretension,
however, to allude to bridges of vast span, or to those of very small
rise, where the centres become of the last importance even in minute
details of composition and construction. As soon as the voussoirs of
the arch assume an inclination to the horizon, whereby the weight of
the stone overcomes the friction between the connecting surfaces, the
arch-stones then begin to bear upon the centres, which latter must be
capable of bearing this increasing weight, and of keeping the stone
upon its inclined bed; when a soft bed of mortar is interposed between
two arch-stones, this inclination to the horizon may be considered an
angle of about 30 degrees,* after which every stone bears the more
heavily on the centre, until the power of the weight becomes sufficient
to force inwardly the sides or haunches of the centring rib, and to
force the crown upwards, unless the construction be such as to resist
this pressure; and the flatter the arch, either in a segmental or elliptical
curve, the more effective this pressure will be, and the greater, therefore;
the requirements from the centres. When a vertical drawn through
a centre of gravity falls without the lower voussoir, the whole stone
may be considered as weight on the centre; even in small spans of 30
and 40 feet this.subject requires strict attention, as there can be no
doubt that deficiency of strength in this direction, not from want of
material, but ill disposition and bad workmanship, has occasioned many
accidents to arches, as well also as the haunches of arches being loaded
prematurely. When a centre rib is thus upreared at the crown, a heavy
load must be there applied to weight it back, but it is very doubtful, in
thus weighting the centre, whether we force it back into its original
* Tredgold says 34 degrees.
R 2
236
CENTRES FOR RAILWAY ARCHES.
form; indeed this cannot be expected, and only an approximation to
the first curve can be hoped for; a very little thought will make this
apparent, and therefore, also, the necessity of attention to this subject.
The greater the number of joints in the rib, the greater the liability to
flexion, these joints being the points at which the parts of the rib
pivot, and these, therefore, require support by framing, auxiliary tim-
bers, strapping, &c. The above must be considered the first requisite
in a centre; next follow an economical erection, and an easy removal,
and economy will be best observed by employing mostly timbers of the
common scantlings, and in such manner that the timber may be employed
for general purposes afterwards. In designing or inspecting centres, it
is more particularly at the angle where the whole weight of the arch-
stones leaves, practically speaking, the lower voussoirs of the arch to
rest entirely on the centre, that we must look for resistance to this
weight, therefore, material should be disposed accordingly, and an
angle of 50 or 55 degrees may be considered to be about this point
generally, at least where the width of a voussoir is equal to about
half the depth; centre ribs may be set at from 4 to 6 feet apart, these
being extreme limits, and care must be given to secure them from any
lateral motion; on the centres come what is termed the lagging, which
are narrow planks set across from rib to rib. The supports of centres
that are raised high above the ground, as in lofty viaducts, require
particular attention, as the great length of leverage renders them
particularly liable to serious lateral motion from vibration or other-
wise; in all cases the timbers bearing the several ribs should be well
braced together in the direction of the transverse section of the arch;
it is a common custom to rest these supports on corbels projecting from
the piers; but this must be considered more economical than beneficial.
The easing and striking of centres requires care and watchfulness,
and accordingly as the setting of the centre affords the ready means of
doing this, so will be the facilities for obtaining a regular and steady
settlement of the arch; since the voussoirs rest upon the centring,
they will descend as the centring recedes from them, suddenly if the
centre is suddenly removed, unequally at each side of the arch if the
descent of the supporting centre be unequal, and this by fracture in
some of the mortar joints, if this cementing matter be dry, or by an
CAST AND WROUGHT-IRON GIRDERS.
237
unequal forcing out of the mortar, if too soft; either of these degrees
of induration being, therefore, least fit for the easing of the centres.
The means usually adopted for easing the centres of railway arches
consists of double wedges, which being driven back equally at each end
by men striking with mauls, allows the centre to descend as the wedges
retire, and the quantity of release, therefore, may be easily ascertained
as the operation proceeds; the men performing this task generally know
perfectly well what they are about, but it is as well to observe that the
great weight superimposed on these wedges during the construction of
the arch forces the fibres of the wood together, occasioning at first
great friction, which must not be overcome too suddenly and violently,
as the result would be a shock; when the settlement of the arch is
complete, the centre may be entirely removed.
PART II.
CAST AND WROUGHT-IRON GIRDERS.
As regards iron bridges, it is only proposed in these pages to go into
the subject of cast-iron girders and plate girders; by means of these we
can span a space of 150 or even 200 feet. Iron structures of a more
complicated character demand a volume to be of any service to the prac-
tical man, instead of a few pages of superficial description which can
only amuse a casual reader.
Before, however, we proceed with these subjects, it will be as well
to say a few words as to the subject of transverse strength, according to
the present received opinions.
Let A B, Fig 24, be any beam resting on two supports, A and B ;* let
the beam be loaded in the centre; then A and B each carry one-half of
the load, plus one-half the weight of the beam. Call the whole of the
weight W.
The strain on the beam is communicated by means of a
·
Mr. E. Clarke.
238
CAST AND WROUGHT-IRON GIRDERS.
bent lever, of which the longer arm is half the length between the sup-
ports, and the shorter arm is the depth of the beam.
The reaction at A or B is the half of W, therefore as C D, the depth
of the beam, is to
A B,
2
beam. From this it follows, as a consequence, that the greater the
span the greater the strain on the centre of the beam; hence the
strength is inversely as the length of the beam.
Also, every particle in the sectional area of the beam bears its pro-
portion of strain, which we will calls; hence, the strength of the beam is
directly as the sectional area multiplied by the depth-multiplied by s.
But in a beam under transverse strain, the top is under a com-
pressive force, and at the bottom this force is tensile; then the strength
at top or bottom will be directly as the sectional area multiplied by the
depth multiplied by s; the value of s depending upon the power of the
material to resist compression or tension.
Then,
d x ax s = S.
then,
or,
so is
Let / be the length of the beam, between the bearings, in inches.
d, the depth of the beam, in inches.
a, the sectional area, in inches.
W, the breaking weight, in the centre, in tons.
S, the whole strain in tons, at the centre.
s, the strain, per square inch, of sectional area, in tons.
Now is the portion, in the bent lever, of resistance to the break-
ing weight W,
And
And
W
to the pressure on the centre of the
2
d:
S;
that is, as the depth is to half the length, so is half the breaking weight
W to the whole strain S.
Put
10 = d; 100 = 7; 100 = W ;
100
2
Z
10:
10 50
:
:
::
:
-
W
2
S
CL
100
: 250;
2
50 : 250.
S
CAST AND WROUGHT-IRON GIRDERS.
239
that is, the whole strain divided by the sectional area is equal to the
strain per square inch.
S, or s, will be compressive or tensile, accordingly as they are
applied to the top or the bottom.
Thus, in the above, if there be 25 square inches in the sectional
area of the bottom flange, then
But
250
25
and if there be 5 square inches at top, then
250
5
and
then
and
And
and
""
= 10 the tensile strain per square inch;
********
=
;;
=25= the compressive strain per square inch.
#E
Sx d or s xa x d = moment of forces,
×
1
201
X
W
2
× moment of forces,
W
Q;
4 × 8 × a × d = l × W.
s x a x d
that is, that 4 times the strength per square inch multiplied by the
sectional area, multiplied by the depth, and divided by the length, is
equal to the breaking weight.
For s× 4, put C for the constant, and we get the following
formula,
4 x s x a x d
τ
axdxc
a x d x C
1
α =
W ;
W;
W × Z
X
d × a
Tons.
In calculating for the bottom flange of a plate girder, C = 75
for a straight top
59.6
<= 25'0
for the bottom flange of cast-iron girder,
رز
""
در
""
240
CAST AND WROUGHT-IRON GIRDERS.
Many of the above will be found useful in the first sketches of a
design, since the length is always given, and the weight is assumed.
The depth, if not compulsory, is some proportion of the length, and the
strain, per square inch, for compression or tension, is regulated by the
nature of the material, and the conditions of being in wrought or cast-
iron girders.
In practice we may consider that a load, uniformly distributed over
a beam, is equal to half that load applied in the centre.
In applying the formulæ in practice, reduce the feet into inches, and
take the weights as tons.
We must also remember that such an element as depth cannot be
overrated, but width must not be neglected on account of lateral strain.
Although, in all cast-iron works, a mixture of different kinds of iron
in different proportions, and the use of hot and cold-blast are of great
importance in girders, pillars, cylinders, &c., it is well known that
whatever mixtures may be ordered, we have no guarantee that instruc-
tions will be attended to. Test is therefore the only security remaining;
this should, without any exception, be freely applied under an experienced
person, but never to such an extent as to injure a casting.
It is therefore that the testing load should never be more than one-
third the breaking load; this will find out the defects, if properly
applied, and more would injure the casting, even if sound.
It is also important to remember that whatever means are employed
to test a girder, it is not sufficient that the pressure just touch and then
be withdrawn; a short time should be allowed to give the pressure time
to come into full operation, and a slight vibration should be given
whilst the beam is loaded.
There are circumstances in which it is advisable not to make the
breaking weight less than six times the load that can be brought
to bear upon the girder, but it is rather exceptional than otherwise.
A well-selected mixture of irons always produces strength, and no
single kind of iron is ever employed, or but very rarely; but the selec-
tion will depend on the part of the country from whence the casting
will come, and sometimes motives of economy will be more potent still.
A heavy casting and a light casting require different kinds of iron,
and there are two kinds of heavy castings; the one may be in a close
CAST AND WROUGHT-IRON GIRDERS.
241
solid mass, when a hard iron should be selected, as it will soften
in cooling in a thick mass; but a long, and proportionately thin casting,
such as a large girder, or a large water-pipe, requires a much more fluid
iron, that it may run freely, and that it may not chill or become too
hard in casting.
It is desirable, in designing cast-iron girders, to bear in mind the
following circumstances: that it is difficult to cast very large castings
from uncertainty of contraction in cooling, and of the regular running
of the metal; such, for instance, as girders of 30 and 40 feet in one
length; that they are awkward to handle, and liable to damage in
transit and erection; that any considerable increase in thickness of the
casting increases the risk from air-holes from the coarse crystalline
texture which large masses of cast-iron assume in cooling; that if in a
casting there are any considerable differences of thickness, danger arises
from corresponding differences or inequalities of contraction in the parts
which are of different thickness.
In Mr. Hodgkinson's work there is a table of fourteen experiments
made on model girders, in which the distance between the bearings
being alike, as also the depths, the proportions of the areas of the top
and bottom flanges vary from equality to 1 to 6, and the strength of
section per square inch is nearly 7 to 12, the total areas of section
being 2.82 and 6.4.
a x d × С.
W =
is the formula from which the constant of trans-
ι
verse strength is deducted, as already shown, so that for every different
form of section the value of the constant C should be different.
In this, as throughout these formulæ, we must repeat to the student
that W is the breaking weight in tons, a the sectional area of the
bottom flange in inches, d the whole depth of the girder in inches, and
7 the length between bearings, also in inches; from the above formula
I W
we obtain
C, which reads, in words, the length multiplied by the
ad
breaking weight, divided by the sectional area of the bottom flange,
multiplied by the depth, equal to the constant C.
A sensible difference is found to exist in the strength of girders
cast erect or cast on the side, the metal being more dense and pure in
242
CAST AND WROUGHT-IRON GIRDERS.
the first, for which the constant, calculated from the breaking weight on
the model above referred to, is 26.8 tons, and for the second it is only 25.7
tons. The latter number is always taken in practice for the greater
security, and almost always the decimal is left out of the calculation.
We must now come to the apportionment of dimensions in cast-iron
girders, and, in calculating this, we must repeat that due regard must
be paid to the fact that considerable difficulty always exists in obtaining
sound castings of large size, and it is almost surprising how very little
neglect, how small an accident will ruin a casting; hence the necessity
of full dimensions in all cast-iron constructions.
It has been experimentally ascertained, that when from one-third
to one-half of the breaking weight at the centre is applied to a cast-iron
beam, a considerable permanent set takes place, denoting that the
clasticity of the metal is affected; and therefore, from twice and a-half
to three times the weight calculated for, applied at the centre, which
about doubles it, is that which we are to consider breaking weight; and
this the more particularly where the girder may be subjected to blows
or jars, as in the case of railway girders. It must not be lost sight of,
that, in proportioning the dimensions of a cast-iron girder, all the con-
ditions to which it may be submitted are to be carefully considered.
In practice it is not always possible to bring the refinements of
science to bear, but where this is possible, even in a slight degree, it
should never be omitted. In Mr. Clarke's History of the Britannia
Bridge, the following remarks are made on cast-iron girders :-
"But for two practical considerations, the best way to arrange the
forms of cast-iron girders would be to consider that the distances from
the neutral line of the upper and lower filaments exposed to com-
pression and tension in the flanges, should be as the capabilities of the
material to bear such strains, and to make the areas of sections from
the bottom of the lower flange to the neutral line, and from the neutral
line to the top of the upper flange, equal as at Fig. 25. The two
considerations which render this inexpedient in practice are, first, the
different thicknesses the section would assume, and which, from the
difference in the contraction in cooling of thick parts and thin parts,
would be unsafe. Secondly, the upper portion, which is exposed to
pressure, is in the position of a column, and consequently more likely
CAST AND WROUGHT-IRON GIRDERS.
243
to give way by bending laterally than by being merely crushed. Owing
to the increase of thickness and breadth hence requisite in the part
exposed to pressure, it is unadvisable in practice that the ratio of the
amount of pressure to that of tension exceed 2 to 1."
Although it is, therefore, inexpedient to give this form of section,
we may obtain an approximation to it as regards the bottom flange, as
in Fig. 25, by making the rise of the step on the bottom flange equal
to about or of an inch.
For railway girders of cast-iron the weight usually calculated for is
2 tons per foot of span for each girder, and more when the span is above
40 feet, and this material is used; which, however, is not expedient, nor
necessary.
For the cast-iron girders of roadways take from 13 to 1.75 tons per
square yard of roadway, which weight may be distributed over 5, 6, or
7 girders, as the case may be, including the outside girders.
then
It has already been pointed out that depth is an important element
in a girder. Depth in a beam increases its rigidity, but lessens the
elasticity. It is also to be observed that depth increases the height of
the column of which we have spoken above, and with the increase of
height the liability to lateral flexure increases also.
From one-twentieth to one-fifteenth of the span is generally taken
for the depth, and more often the latter for railway girders.
As an example, take a railway girder for 30 feet span, or 360 inches.
30 x 2 = 60 tons breaking weight.
d, the depth = 15)360(24;
ΟΙ
600 × a
360
600 a = 21600;
600) 21600 (36 inches for sectional area of bottom flange.
If we take for the width two-thirds of the depth, we shall have 16
inches, but, to avoid fractions, take 18 inches, and we shall have the
bottom flange 18 inches wide and 2 inches thick.
and
= 60;
As regards the top flange and the web, we may consider their
sectional areas together as equal to that of the bottom flange; we have,
244
CAST AND WROUGHT-IRON GIRDERS.
therefore, 36 inches of sectional area to dispose of, and if, for this railway
girder we apportion one-fourth of this amount to the top flange, we may
make it 4 inches by 2 inches=9 inches; this leaves 27 inches for the web,
and if we make this 1½ inch thick it will be near enough for practice.
There is only to add a few remarks as regards the side elevation of
such a girder. When it is not necessary that the flanges should be
parallel, a considerable economy of material may be effected by remem-
bering that a girder of uniform section throughout contains unnecessary
material at all other points, when there is only sufficient at the
centre. A girder may be diminished towards the ends, in the pro-
portion of the rectangles of the segments at every point. If this
diminishing be made in the depth of a girder, the strength decreasing
as the square of the depth, the curve will be in the form of an ellipse.
It is customary to shorten this operation by making the depths at the
ends equal to two-thirds of the depth at the centre, and from these two
ends to pass a curve through the central point-this refers to the top
flange. A similar diminution is often made in the plan of the bottom
flange. In this latter case the tapering towards the ends may assume
the form of a double parabola. The end feathers would be about 2
inches thick, and the intermediate ones about 1 inch thick, and about 3
feet apart. Tie-rods 1½ in diameter are bolted to these, connecting the
girders together, or lugs may be cast in the same horizontal plane as
the bottom flange, and with it, by means of which the same object may
be effected.
The above laws apply generally to the beams for fire-proof floors of
buildings.
At the end of the chapter will be found a table of deflections under
the passage of trains, which, being of a truly practical nature, is not
uninstructive.
Riveted plate girders have almost, if not quite, superseded large
girders of cast-iron, and will probably in most cases take the place of
the latter material altogether. The reliance that may be placed in
wrought-iron, and its high tensile powers, would ensure this.
There are, however, a few subjects in plate girders which require
careful attention and discrimination, the designs of these beams, more
particularly for large spans, being more intricate.
CAST AND WROUGHT-IRON GIRDERS.
245
I
I. Where the top and bottom flanges are both flat, the top flange
requires a sectional area approaching to double that of the bottom flange.
II. In long girders the thin web is subject to lateral flexure and to
buckles, as are all large, thin, flat plates of wrought-iron.
III. Judgment is required as to the riveting the covers and the
angle iron.
With regard to the necessity for making the top flange double in
sectional area that of the bottom flange, this expenditure of material
may be overcome by making the top curved, either semicircular or of
a curvature equal to about the third of a circle in small girders, thereby
offering easier means for the riveting. This system of curving the
top is due to Mr. Brunel. The first announcement of it which the
author met with was in Mr. Clarke's History of the Britannia Bridge,
where a record of the experiments made on such a model will be found.
This is, perhaps, one of the most scientific and elegant adaptations of a
material that we have, for the material exposed to compression is at
once brought to act largely by tension. Reference to Fig. 27 will
explain this, and to this figure the reader is referred for the explanation
of what we have to say about a large plate-girder.
We will now take up the subject of riveting, upon which there are
many different opinions.
In the work already referred to, by Mr. Clarke, we find at page 395
the following remarks
:
"The pin is supposed well fitted in the vertical holes through the
plates. See Fig. 26, by accident marked 20 on diagrams.
"It is therefore only necessary to ascertain the forces requisite for
shearing a single pin of the given section to ascertain the strength of the
whole joint.
"The ultimate resistance to shearing is proportional to the sectional
area of the bar torn asunder.
"And the ultimate resistance of any bar to a shearing strain is nearly
the same as the ultimate resistance of the same bar to a direct longi-
tudinal tensile strain.
7
8
"A mean of four experiments on the single shearing of bars of rivet
iron of inch in diameter was per square inch of section = 24·15
tons.
246
2
CAST AND WROUGHT •
IRON GIRDERS.
"And on a double shearing as above 221 tons.
"The ultimate tensile strength of these bars of rivet iron was found
to be 24 tons per square inch; hence their resistance to single shearing
was nearly the same as their ultimate resistance to a tensile strain.
These experiments were made with a lever to avoid anomalies; by this
means two plates § inch thick were riveted together by a single rivet
inch in diameter, and the rivet was sheared by suspending actual
weights from the plate; the rivet thus sustained 12.267 tons, or 20·4
per square inch.
"Three plates united by a similar rivet, and the rivet sheared in two
places by the centre plate; ultimate weight suspended from the rivet
26·8 tons, or 32·3 per square inch."
In riveting two plates together to resist a tensile strain, the sec-
tional area of the rivets should be equal to that of the plates them-
selves, if we depend solely on the shearing of the rivet; but as rivets
are usually closed in a red-hot state, it is evident that the shortening
of the rivet, as it cools down, must tend to draw together the plates
united, and before they can slip on each other, the friction thus induced
must be overcome simultaneously with the shearing of the rivet itself;
hence the value of the rivet is greater than the value determined above,
by the amount of friction produced by its contraction in cooling.
The contraction of a wrought-iron rod in cooling is about equiva-
lent to 10,000 of its length from a decrease of temperature of 15° Fahr.,
and the strain hus induced is about 1 ton for every square inch of
sectional area the bar. Thus, if a rivet 1 inch in section were
closed at a temperature of 900°, it would, in cooling, decrease of its
length, and, if its elasticity and strength remained perfect, would
produce a tension of 60 tons. The ultimate strength of rivet iron
being, however, only 24 tons, the rivet would, in cooling, be permanently
elongated, and would continue, when cool, to exert a tension of 24 tons,
provided its elasticity remained uninjured by the strain.
Thus if the rivet were not in contact with the plates, excepting at
the head and tail, the plates would be held together by a pressure of
24 tons, and this friction would have to be overcome before the rivet
came into action as a mere pin.
These reasonings were verified by experiments; it is not, therefore,
60
10,000
CAST AND WROUGHT IRON GIRDERS.
247
1
requisite that the area of the rivet should equal that of the plates
united as with a simple loose pin.
This close union of riveted plates is a most important characteristic
of riveted work, the joints being as immovable as the most perfect weld.
Thus also, by judicious riveting, the friction may in many cases be
nearly sufficient to counterbalance the weakening of the plate from the
punching of the holes, so that a riveted joint may be nearly equal in
strength to the solid plates united.
From Mr. Fairbairn's Useful Information for Engineers we extract
the following, which is given after the details of some experiments as
to the strength of riveted joints in the construction of vessels and the
boilers of steam-engines.
General summary of results as obtained from the foregoing experiments.
Cohesive strength of
Plates. Breaking-weight
in lbs. per square inch.
57724
61579
58322
50983
51130
49281
43805
47062
Mean 52486
Strength of single-
riveted joints of equal
section to the plates,
taken through the line
of rivets. Breaking-
weight in lbs. per
square inch.
45743
36606
43141
43515
40249
44715
37161
Double-riveted joint
Single-riveted joint
41590
The relative strengths will therefore be-
For the plate
A
Strength of double-
riveted joints of equal
section to the plates,
taken through the line
of rivets. Breaking-
weight in lbs. per
square inch.
52352
48821
58286
54594
53879
53879
53635
1000
1021
791
248
CAST AND WROUGHT-IRON GIRDERS.
It appears then, when the plates are riveted in this manner, that
the strength of the joints is to the strength of the plates of equal
sections of metal as the numbers
In a former analysis it was
which gives a mean of
1000: 1021 and 791
1000: 933 and 731
1000: 977 and 761
which in practice we may safely assume as the correct value of each.
Exclusive of this difference, we must, however, deduct 30 per cent. in
this particular case for the loss of metal actually punched out for
the reception of the rivets, and the absolute strength of the plates will
then be, to that of the riveted joints, as the numbers 100, 68, and 46.
In some cases, where the rivets are wider apart, the loss sustained is,
however, not so great; but in boilers and similar vessels, where the
rivets require to be close to each other, the edges of the plates are
weakened to that extent.
From Mr. Fairbairn's Work on the Britannia and Conway Bridges
the following extract is made:-" At the commencement it was stipu-
lated that the contractors should use the riveting machine in every
case where it could be applied; and in order still further to enhance the
value of this process, all the parts which could not be reached by the
machine were to be riveted with heavy hammers, for the purpose of
causing the rivets to fill the holes, and otherwise to make the work as
nearly as possible equal to that done by the machine. During the
progress of the construction of the tubes for the Britannia Bridge, the
machine work was found (according to the opinion of Mr. Mare, the con-
tractor), both expensive and inconvenient, on account of the size and
great weight of the plates, and the difficulty of suspending them over
the machine. These drawbacks were not, however, experienced by
Mr. Evans, the contractor for the Conway tubes, who overcame every
difficulty by the introduction of powerful travelling cranes, which
enabled him to rivet the greater part of the bottom and sides of both
tubes by the machine. Mr. Mare, the contractor for the greater
portion of the tubes for the Britannia Bridge, adopted a different
method, and, by the use of heavy hammers, made the work, if not equal
in stability, at least nearly so, to that done by the machine. The
CAST AND WROUGHT-IRON GIRDERS.
249
superior quality of the hand-riveting executed by Mare with the
heavy hammers, imposed the necessity of using the same means in the
hand-work done by the other contractors."
It is now proposed to set out the dimensions of a plate girder for a
span of 100 feet. The greatest load likely to come upon this beam
would be a train of locomotives, which may be taken at 1 ton per foot
this will give 100 tons equally distributed over the girder, which
will be equal to 50 tons in the centre; and if for safety we take three
times this, we shall have 150 tons breaking load in the centre. For a
single line of way on two girders, only half this load would bear on
each girder; but we have the weights of the girder itself, of cross tie-
girders, longitudinal timbers, planking, ballast, rails, &c., so that we
may take out the dimensions of the girder to meet a breaking load at
the centre of 150 tons.
As regards the depth, one-fifteenth of the span is an ordinary rule;
but in wrought-iron girders we may take one-tenth for such a span as
this to obtain rigidity in the beam; this will be 10 feet = 120 inches
=
d, and 7, the length = 100 feet = 1200 inches.
Then by the formula, and taking the constant C at 75 tons, we have
or,
or,
a d C
l
or,
= W =
75 × 120 × a
1200
9000 a
1200
9000 a = 180000;
or,
then, a = 20 square inches in sectional area of the bottom flange, and
also in the top when curved.
= 150;
Such a bridge would, however, but rarely be built for a single line
of way. If we double our former breaking weight, we shall now have
300 tons for W, the breaking weight; but this is in excess, and we may
safely deduct 10 per cent., leaving 270 tons.
We shall now have
75 × 120 a
1200
9000 a
1200
9000 a = 324000;
S
= 150 tons;
= 270;
= 270;
D
250
CAST AND WROUGHT-IRON GIRDERS.
or, a = 36 inches of sectional area in flanges, bottom and top, supposing
the latter to be curved; if flat, we should require a much greater
quantity of material in the top flange.
We have now l, d, and a, the length, the depth, and the sectional area.
For the width of the beam, we should take two-thirds of the depth
but for the following considerations: as these girders must be about
28 feet apart for the double line, unless we have one in the centre,
we must have a number of cross-tie-girders to carry the longitudinal
timbers for the permanent way; these cross girders will have to
be about 5 or 5 feet apart, and will therefore prevent lateral
flexure. If the reader sketches these things as he goes on, it will
make all very clear. As these cross girders will completely prevent
the main girders from bending horizontally in their length, we may
take about one-third of the depth, say 3 feet for the width of the
beam at the bottom flange; this will be 36 inches in width, and,
as we have 36 inches of sectional area, we shall have the bottom
flange 36 inches wide and 1 inch thick, which will be made up of
-inch plates. We now come to the thickness of the web, or central
rib between the top and bottom flanges, and whose function is to keep
these flanges at the greatest possible distance apart under the load. If
we take once and a half the sectional area of the bottom flange for the
sectional area of the web, we shall have th of an inch for the thickness
of the central rib or web. It need hardly be added that a plate th
of an inch thick, and 120 inches, or more correctly 118 inches, in depth,
will require stiffening to prevent all possible lateral flexure, this slender
rib being in the condition of a column. We now come to the top flange.
16
In the Conway Bridge the sectional area of the bottom is 491
square inches, and in the top it is 627. Taking this as a proportion,
we should have nearly 46 square inches for the sectional area of the top
for the beam in question; also it has been shown by several experiments,
that wrought-iron strained by tension beyond 15 tons per square inch,
or compressed beyond 12, is destroyed for all practical purposes.
And,
12:15:36:45.
Then 45 square inches we shall assume for the sectional area of the top
of our beam.
But it is desirable that this extra quantity of material should be as
near the top as possible; 45 - 369, and we shall rivet a strip 9
CAST AND WROUGHT-IRON GIRDERS.
251
inches wide and 1 inch thick along the top of the beam, which will
give the further advantage of continuity in length, as also all the
advantage of double riveting.
Reference to Fig. 27 will give the best explanation.
We have now the sectional areas of the top, of the central rib, and of
the bottom flange, and these must be united by the means of angle-
iron, riveting, and butt plates; the angle-irons will be 4-inch thick, and
the rivets not less than 4 inches apart; butt plates about thick, with
four rows of rivets.
It has already been pointed out that the central rib will require
stiffening, which will be done by Tangle-irons, 5 feet apart, and stay-
ribs, which are shown on the drawing already referred to; there will be
two of these stay-ribs 10 feet apart in the centre, and two the same
distance apart at each end, and two more midway between the centre
and the ends. From the slight dimensions of these stays, they will be
somewhat in the same condition as the central rib itself, and will them-
selves require stiffening by angle-irons. These details, as well as the
means employed for maintaining the top of the girder in its curved
form will be most readily understood by reference to the sketch already
referred to, if the student will work out elevation and plans.
12
For plate girders of a lesser span, as 30 or 40 feet, the same rules
apply, but we should take of the span for the depth of the beam, and
the sectional area of the central rib may be equal to that of the bottom
flange, the width of which will be about of the depth of the beam;
the form of the top will be segmental, about of the circumference
op
of a circle, to admit of greater convenience in riveting; the planking
may be so managed that not more than two stay-plates will be required
at each end, and three girders to form the bridge.
The following are Mr. Hodgkinson's rules for cast-iron columns:-
For solid cylindrical pillars, with ends flat and incapable of motion;
Strength in tons = 44·16 ×
W
44.16
d 3'6
L 17
where 44.16 is the constant, d, the diameter in inches, and L, the length in
feet.
And,
1.7
× L¹7 = d 3°6:
;
s 2
252
TIMBER BRIDGES AND CARPENTRY.
that is, in words-the weight in tons divided by the constant 44.16, and
multiplied by the length raised to power, 17, equal to diameter in inches,
raised to power, 3.6.
For hollow cylindrical pillars, with flat ends and immovable;
And
Strength in tons = 41.3 x
where D is the external diameter in inches, and d the internal diameter
in inches also, and L the length in feet.
In practice, however, perfect fixing is not attainable. For solid
pillars therefore the rule is,
14.9 ×
For hollow pillars,
""
13 ×
D37
d3'6
""
1'7
W
14.9
L
Strength in tons.
Taking wrought-iron at 480 lbs. per cubic foot, the following
practical rules will be found convenient :-
17
× L¹7 = √3'6
d37
D36 - d 3'6
L 17
Strength in tons.
Sectional area in inches x 10 = weight in lbs. for every yard in length.
× length in feet 672 weight in tons.
PART III.
—
TIMBER BRIDGES AND CARPENTRY.
Ir, as there is much reason to anticipate, the patent process of the
Docteur Boucherie of Paris should be as successful in practice as expe-
riments would show, it is probable that the above economical means of
spanning wide chasms will be adopted more commonly than they have
been of late. The decay to which all timber is liable under many
TIMBER BRIDGES AND CARPENTRY.
253
circumstances has not only been the cause of its being much disused,
but also vilified; had strict justice been done, it is not the material that
should have been blamed, but those who put the timbers together.
Many processes have been introduced, which, carried out in their
integrity, would greatly contribute to the preservation of timber; but
rarely has justice been done in these matters, because deception was
comparatively easy. It was but a very few years ago that the writer of
these pages had occasion to see some large and well-designed timber
trusses, on the designs for which the Engineer had evidently bestowed
great pains, and which were to be "Kyanized;" but, alas for human
nature! in this case the timber and Kyan's process had never had the
most remote contact with each other.
In England it is probable that wrought-iron girders will become
more common every year; but English Engineers are all over the
world, and there are still many countries where it is desirable to use
timber, if we can but preserve it from too rapid a decay.
Kyan's process consists in immersing timber in corrosive sublimate,
or bichloride of mercury. Subsequently closed tanks having been sub-
stituted for open ones, and an injecting apparatus with force-pumps, as
well as air-pumps for previous exhaustion, having been added, the solu-
tion was forced into the timber. It is believed that the solution should
not be of less strength than 1 lb. of corrosive sublimate to 9 gallons of
water.
Burnett's process consists in impregnating the timber with a solu-
tion of chloride of zinc.
In Bethell's process, oil of tar, creosote, and pyrolignite of iron,
"which hold more creosote in solution than any other watery men-
struum."
Payne's, by sulphate of iron and muriate of lime.
One of Bethell's processes consists in placing the timber in a strong
iron cylinder, and exhausting the air from it by an air-pump until a
vacuum is created, equal to about 12 lbs. on the square inch; the
creosote is then allowed to flow into the cylinder, and a pressure is put
upon the creosote, by means of a force-pump equal to 150 on the
square inch. The timber has then been prepared. An average of
11 lbs. per cubic foot has been used on the Memel timber at Leith
254
TIMBER BRIDGES AND CARPENTRY.
harbour works. Piles, 14 inches square, of unprepared timber, at
Lowestoft harbour, were shown to have been eaten away to 4 inches
square, in 4 years, while creosoted piles of the same dimensions, drawn
alongside of them, were intact.
We extract the following from the pamphlet circulated by the
Permanent Way Company:-
"The mode hitherto adopted to impregnate trees has been by
saturation only, assisted sometimes by great pressure, and by previously
submitting the timber in cylinders to a vacuum or to heat.
"Dr. Boucherie's process differs entirely, inasmuch as he applies a
moderate pressure, and to one end only of the sap tubes of the tree;
the effect of which is to expel the sap by the preserving liquor, which
takes its place.
(C
By the processes hitherto used, the sap (the formation of which is
admitted to be the cause of decay) is allowed to remain in the tree; in
the Boucherie
process the sap is expelled, and the tubes are thoroughly
cleansed from the fermenting matter."
*
*
*
"Another advantage in Dr. Boucherie's process is derived from the
simplicity and small cost of the apparatus, which for small quantities
will not exceed £10, or £15, and for a railway of 200 miles under £50."
A detailed explanation, with illustrative cuts of the whole process,
will be found in the pamphlet above referred to, as well as a detailed
account of the experiments made. It is very desirable that further
experiments on the transverse and tensile strength of timber so treated
should be made.
WOODEN BRIDGES AND VIADUCTS.
Wood, as a material for the construction of bridges and viaducts,
may be selected in preference to stone or brick, on the score of
economy, and from the comparative rapidity with which such structures
may be erected; but it is of course very inferior to the last-named
materials as regards strength and durability; and in designing and
constructing such works, the inherent defects of wood must as much as
possible be counteracted. Experience has proved that the most simple
TIMBER BRIDGES AND CARPENTRY.
255
combinations of timber are superior, for strength, to complicated
systems; and these have latterly become almost entirely abandoned.
By calculation, a scientifically-framed truss may be made; the almost
impossibility in practice of making such a perfect assemblage of the
timbers as the calculations would have been based upon, renders such
complicated combinations unwise; moreover, to obtain even that degree
of perfection of which practice is capable, we must resort to an excess
of strapping, bolting, keying, morticing, and every description of
jointing, which becomes very expensive, and when we have done all
this, the destructive effects of rain, sun, and wind, increase in the very
proportion of complication introduced in the system of construction;
unavoidably, also, a considerable quantity of material is wasted, which
might be profitably reserved for increase of strength under a more
simple mode of treatment. The intention of a truss, composed of a
multitude of timbers, is not only an equable distribution of the super-
imposed weight, but also a dispersion of the shaking and vibration
resultant from the motion of weight; this, nothing but the most perfect
workmanship could obtain, and all practical men know the extreme
difficulty of obtaining this, however great the expense incurred. In
Colonel Emy's very clever work On Carpentry, and Dempsey's Timber
Bridges, the student will find a variety of systems and combinations;
and several useful trusses, with details, have been given in this work.
For great spans, the laminated arch is unrivalled for strength and
elegance; it is formed of planks laid one upon the other, breaking joint
in length and breadth, and bolted together. Colonel Emy, above-men-
tioned, claims the invention, in 1819. From the tendency of the
planks-which, however, appears to be but small-to spring back to their
original straight line, the thrust of such an arch on piers or abutments
is no greater than that of a single beam. On this description of arch,
originally applied to the construction of roofs, two distinct systems of
bridge arches have been based; the one by the superposition of the
platform on the laminated arch, and the second and best, by suspension
from it. The following note of dimensions of viaducts of this descrip-
tion may not be here out of place.
:
256
TIMBER BRIDGES AND CARPENTRY.
Notes of Dimensions of some Laminated Arches.

Name of Viaduct, or
Bridge.
Ouse Bridge, East
Anglian Railway
Dinting Vale, Shef-
field and Man-
chester.
Wellington, Dean,
Newcastle, North
Shields, and Tyne-
mouth Railway
Ouse Burn, do., do.,
Railway
West Durham
Sechill
-
Newcastle upon -
Tyne and North
Shields
Span in
Name of Engineer. feet and
inches.
J. S. Valentine. 121,6
A. Jee.
J. & B. Green.
The same.
The same.
R. Nicholson.
The same.
125,0
120,0
116,0
Rise in
feet and
inches.
52,6
14,4
25,0
36,0
32,6
79,0 13,0
81,6
8,9
Thick-
ness of
Rib in
feet and
inches.
3,8
4,6
Width
of Rib
in feet
and
inches.
2,9
2,2
2,4
3,9
1,10
3,6 1,10
2,3
1,5
2,3
1,5
7,0 1,9 1,5
In the Sheffield and Manchester, Willington Dean, Ouse Burn, and
West Durham, the platform of the railway is supported by struts
or spurs, which rest upon the laminated ribs, which abut on cast-iron
bed-plates resting on stone piers; there are three ribs in each arch.
In the Sechill and North Shields, in which the laminated arches
form flat segments, the platform is suspended from the arch by wooden
ties strapped to the arch, and braced together laterally; the rib springs
from a joggled cast-iron shoe, resting on the platform which surmounts
stone piers.
In the Ouse Viaduct, on the East Anglian Railway, the platform is
also suspended from the laminated rib; but, most judiciously, the
Engineer has suspended the platform by means of wrought-iron rods.
The drawings, for which we are greatly indebted to Mr. Valentine's
courteous liberality, are far preferable to any description we could give,
TIMBER BRIDGES AND CARPENTRY:
257
and we will close the subject by referring the student to them, and
annexing a few observations which appeared in the Railway Chronicle:-
"The Viaduct over the river Ouse is 150 yards long, and consists
of ten side openings of 30 feet span each, with a single span over the
waterway of 121 feet 6 inches. The method adopted to support the
roadway over this great space is by suspending the platform from three
timber bows, each formed of 3-inch deals, firmly united together by oak
trenails; the suspension rods are of wrought-iron of the very best
material and workmanship; each rod has been proved to be equal to a
strain of 20 tons, and as there are 72 of these rods, the weight they are
capable of supporting is 1440 tons; but the greatest weight which they
will be required to carry will not exceed 310 tons, the platform itself
being 160 tons, and the greatest load that can be placed upon it being
about 150 tons. The piers upon which the superstructure rests are
built of Yorkshire stone, the foundations resting upon the solid gault at
a depth of about 30 feet below the top of the banks. Minute and careful
admeasurements were taken by the Government Inspector to ascertain
the strength of this bridge. Four locomotive engines and tenders, and five
wagons loaded with iron, were placed upon it at the same time; but
scarcely any deflection of the beams was perceptible; and whether the
trains were at rest on the bridge, or passing over it at full speed, there
was not the least perceptible difference."
The drawings of the Ouse Bridge are so perfectly detailed that no
difficulty can occur in setting out any design of this description, by
copying or changing, as future experience may suggest. The above
note of dimensions will also be some guide in deciding on the number
of planks of which the rib is to be composed. At present, as far as we
are aware, 125 feet is the greatest span we have in this description
of arch.
The Ladykirk and Norham Bridge over the Tweed, J. Blackmore,
Engineer, is composed of two arches of 190 feet span each, rise 17 feet.
Each arch consists, first, of a rib of three thicknesses of 6-inch planking
at the crown, and the number of thicknesses is increased one by one
towards the springing, where the thickness of the rib consists of 8
courses of 6-inch planking; above this arch comes the platform, resting
on the summit of the above rib; about 7 feet above the platform comes
258
TIMBER BRIDGES AND CARPENTRY.
another rib, of 110 feet span, and of about 5 feet rise, the springing of
this second arch being over the middle of a centre pier 20 feet thick;
this second rib consists of 7 courses of 6-inch planking at the crown,
diminishing one by one towards the springing, where it consists
of a single plank; the ribs are connected by 14 struts, each strut
strapped at top and bottom to the ribs, and there are 14 braces
connecting the struts; these struts and braces abut both on the upper
and lower ribs at the increase in thickness of planking. This design
possesses the merit of originality, but we have only introduced this
short description of it on account of the great span, and to suggest that
in a similar case the upper rib be brought down and united to the lower
one, and that it be formed of 3 instead of 6-inch thicknesses; the rib,
however, should be made 5 feet 6 inches thick, and 1 foot 6 inches
broad. Where the rise is only one-fifth or less of the span, an increase of
thickness at the springing is unnecessary.
The openings of viaducts are seldom under 30 feet, and as wood is
not used for elegance or durability, but from motives of economy, it is
fortunate that a very simple construction answers every purpose
required; we mean that shown in continuation of the Ouse Bridge. It
has been very extensively used, and experience therefore recommends
its continuance. In the drawings referred to, all that is wanted for the
setting out of working drawings will be found. The reader will
remember that strength of connexion between the trusses transversely
is quite as necessary as the strength required in the form of the truss
itself, and this will be effected by transverse ties and braces.
FIG. 28.
A few words on details may be of some service. Timbers
are connected by various descriptions of joints, the most
simple being generally the best, particularly for our pur-
poses. Fig. 28 shows tenon and mortice; T the tenon,
M the mortice. The thickness of a tenon is made one-
third the thickness of the timber on which it is cut, and
the size of the mortice of course corresponds to the dimen-
sions of the tenon; the depth of a mortice should exceed
a little that of the tenon; as the perfection of the work, so
is the value of the joint; the shoulders of the tenon should
be exactly in one place, and perfectly perpendicular to the
T
M
PR
TIMBER BRIDGES AND CARPENTRY.
259
axis of the timber; where, acting by suspension, little depth is required,
if a strap be added; otherwise an oak trenail should be driven through the
timbers, the holes being bored after the tenon is in the mortice. The
diameter of a trenail should be one-fourth the thickness of the tenon, and
the hole bored for its reception should be at two-thirds from the end of
the tenon, as shown in the figure; but the value, as regards the strength
of a tenon and mortice, should be independent of the trenail. The
above is a rectangular mortice and tenon. Fig. 29 shows an oblique
joint of this description, and it is believed explains itself. The above
description of joint, though common, is not the best of the kind, the
timber T being weak at a, and liable to fly; Fig. 30 is a better system,
FIG. 29.
Милинка
1
FIG. 30.
X
AF
T
M
ww


M
AW
es
where T is partly joggled into M, and s a is made from about one-fifth
to one-fourth of the thickness of the piece M.
In setting out a joint of this kind with a single joggle and no tenon
and mortice, to find the direction of s a, Fig. 31, draw the central axes
of the timbers, and os will give the direction of sa; or divide the
260
TIMBER BRIDGES AND CARPENTRY.
angle as b, and the line sv will give the direction of sa'; or make
s a perpendicular to sb; or from c as a centre with radius c s, describe an
arc, on which set off from one-fourth to one-
fifth of the thickness of the timber M; it
must not be forgotten that too sharp an
angle at a is likely to make M fly at . To
find the direction of s a, in timbers abut-
ting end to end, Fig. 32, divide the angle
a xs, which will give the direction of sæ.
It is always expensive to obtain tim-
bers of large scantlings and great length;
and when a beam beyond 24 feet or there-
abouts is required, we have generally
recourse to scarfing, which, it is unne-
cessary to add, is a joint in which the
ends of the timbers are cut and over-
lapped so as to form one in appearance.
Some persons are partial to complicated
scarfs, but we have no greater faith in
them than in complicated trusses, much
for similar reasons, and because so much
hacking of the timbers must weaken it;
also they become very expensive. In a
scarf, it is evident that the bearing surfaces have to support the
strain, and therefore the greater the quantity of surface the greater
www
чому
I
M
FIG. 31.

xxx
a
1
1
T
a
www.
FIG. 32.

X
1
3
N
the strength, provided the best form be given; therefore, also, a long
scarf is stronger than a short one, for the same reason that any
TIMBER BRIDGES AND CARPENTRY.
261
4
strength at all is gained by a scarf, but a great waste of timber and
much workmanship are involved. One important consideration, and
which should never be lost sight of, is the strain to which a scarf will
be exposed, compression or tension. Scarfs are greatly strengthened by
iron bolts and oak keys. Where the surfaces of the scarfing are square,
iron bolts are preferable to keys, and the contrary where the jointing
surfaces are oblique to the fibres of the wood. Let Fig. 33 be a beam
Ն
FIG. 33.

d
11
π
W
scarfed at W, where it is exposed to a strain from the weight W. The
upper portion of the beam is exposed to compression, the rectangular
bearing a, is therefore the most appropriate, as an acute angle formed
by a line parallel to 6, would, on the beam being compressed, act like a
wedge, and tend to make the upper portion of one beam fly; but this
is reversed at 6, which would tend to open by tension.
Of the keys c
and d, the first would be under compression, and the latter would be
loosened; but being near the neutral line, the tightening and loosening
would be comparatively small, unless the beam were loaded beyond the
bounds of prudence; also c, under compression, would tighten the beam
at a, and though d would not do the same at 6, the bevel joint must pre-
vent any evil results. Whether we have one, two, or more keys, the single
or aggregate depth should not exceed one-third the depth of the beam,
neither should they be too violently tightened when driven. This scarf
is short, and we may add considerable strength by a bolt at W; and it
11
!!
FIG. 34.
a

11
would be better still to place a bolt at c and at d, and the key in the centre,
as at Fig. 34. Fig. 35 is strong enough for most purposes.
It need
262
TIMBER BRIDGES AND CARPENTRY.
scarcely be observed, that the further the scarf may be from the points
of bearing, the greater the strength required; bolts should never be
It
U
6
16
#f
"
FIG. 35.

41
(6
placed too near the end of a beam. Wrought-iron straps are great
auxiliaries of strength, and may be very advantageously used in con-
necting timbers, whatever may be the joint, provided always that tension
be the strain to be resisted. It has been very cleverly remarked, that
a skilful carpenter never employs many straps," &c. ; but however
skilful a carpenter may be, he cannot prevent the effects of atmospheric
influence, neither can he give to comparatively new wood the properties
of well-seasoned timbers. No man who knows anything about design-
ing in wood, would consider straps as principles of strength in his
constructions; but as fastenings, as auxiliaries, they are perfectly
admissible, of course in moderation, and are becoming daily more in
Before use, straps, and indeed all ironwork, should be heated to a
blue heat, and struck over with raw linseed oil; this is far preferable to
paint as preventive to rust, and is in accordance with the practice of
Smeaton. A strap 1 inch wide may be made thick; 13 wide, thick
use.
;
1
4
2 inches wide, thick. Cast-iron plates and shoes are also very useful
to receive or to equalize the thrust from the ends of butting timbers,
the first particularly, where employed as a connecting surface between
the ends of timbers, which, from shrinkage, defect of workmanship, or
otherwise, may come to bear upon opposite angles, instead of the whole
area of their intended connected surfaces.
This subject may now be concluded by practical illustrations of the
rules for ascertaining the strength, or determining the scantlings of
timber.
To ascertain the cohesive strength of timber, or the tension it will
bear, when the weight acts in the direction of the axis of the timber,
multiply the area in inches by the proper tabular number in the table
of specific gravities.
TIMBER BRIDGES AND CARPENTRY.
263
To find the weight that will tear asunder a piece of fir 4" x 4";
we have here 16 square inches, and the tabular number is 9500; then
9500 × 16 = 152,000 lbs., one-fourth of which would be taken in
practice for a perfectly safe load, or 38,000 lbs.
Having the load, to find the scantling, divide the load by the tabular
number; as, let the load be 38,000: 3000 4", for the side of the scantling.
9500
To find the strength of a beam fixed at one end and loaded at the other,
multiply continuously the sectional area by the depth, by the constant
of strength in the same table as the former constant, and divide by the
length, all in inches; if the beam is inclined, the length will be the
horizontal distance between the ends, of course not including the
quantity of bearing, as of tailing into a wall.
To find the strength of a beam of Memel 10 feet long, 5 inches
wide, and 7 inches deep; 5 x 7 = 35 sectional area; 35 x 7 depth
= 245 × 1730, constant of strength = 416850; and this divided by
the length in inches gives 3473 lbs. nearly; but this would be the
breaking weight, only one-third of which should be taken, or 1157 lbs.
as the weight to be borne without straining the timber; and twice this
load may be taken if the weight is to be distributed over the beam.
Given the depth, and length, and the load, to find the breadth; as
above, let the length be 10 feet, the load 1157 lbs., the depth 7; and
the timber of the same description; multiply continuously the weight
by 4, by the length in inches, and divide by 1730, the constant multi-
plied by the depth 7; the product will be the sectional area, which
divide by the depth 7.
=
Given the breadth, the bearing, and the load, to find the depth;
multiply the weight by 4, by the length in inches, and divide the
product by the constant multiplied by the breadth; and the square
root of the quotient will be the depth.
To find the strength of a beam fixed at the ends and loaded in the
middle; multiply continuously the breadth × 6 × the square of the
depth by the constant, and divide by the length; as to find the
strength of a beam of Riga 20 feet long, 13 inches square, we shall
13 × 6 × 132 × 1050 57671
find
=19223 lbs. in the middle, and twice
240
3
this distributed over the beam.
264
AQUEDUCT BRIDGES.
The above rules are for permanent weights.
We may shorten the calculations by dividing any of the constants
by 3, which will save the trouble of reducing the feet to inches; in the
column for constants of elasticity, this has been done; calculations of
this kind are generally made with the constants so reduced.
The above rules are mostly according to Professor Barlow's formulæ ;
and the constants are obtained by the formula
the constant,
Z W
4 b d 2
where 7 is the length in inches,
W the breaking weight,
b the breadth,
d the depth.
7″.
A batten is 2″ ×
A deal is 3″ × 9.
A plank is 3" x 11"; above this size flat timber is termed a slab.
Scantling is a term used to express sectional dimensions of timber;
it is also applied to quartering under 5 inches square.
Logs are about 13" square and under.
A balk is above 13" inches square.
PART IV.
AQUEDUCT BRIDGES.
AMONGST other works of construction connected with railways, the
Engineer has occasionally to design aqueduct bridges, as where the line
of railway crosses under a canal. This style of bridge does not occur
as commonly as other bridges, but requires special precautions, as we
have to make a line of way for water and the passage of boats instead
of carriages or railway trains, and this line of way must not only be
water-tight when the works are completed, but continue so afterwards.
Generally these works are rather more expensive than ordinary
LEGAL REGULATIONS AS TO RAILWAY BRIDGES.
265
bridges; the canal is usually diverted temporarily during the construc-
tion of the bridge; provision has to be made for a towing-path as well
as the waterway of the canal itself; and almost always we are guided as
to dimensions not only by those of the canal as existing before the
passing of the Act, but very often by clauses provided by the special
Act.
It will readily be perceived how necessary it is that an aqueduct
bridge should be water tight, not only as regards the water itself, which
might escape, but also the gradual process of decay in the bridge, which
would ensue from the filtration of water through the materials. Where
the bridge is of brickwork or masonry, it is highly important that
sufficient time be given for the complete settlement of the arch after
the centres are withdrawn, before any other work is commenced.
Plates 17, 17A, 18, 18A and 18в show the working drawings of two
aqueduct bridges; the one in brickwork, the other in cast-iron, for which
wrought-iron may be substituted; the two latter afford the readiest
means of making the bridge water tight.
At the junction of the bridge with the adjoining earth great pre-
cautions are requisite to prevent leakage, which almost always ensues
after settlement; a puddle of fine gravel and lime may be employed to
check this, and will be found to adhere both to the ordinary puddle
and the masonry itself.
PART V.
LEGAL REGULATIONS AS TO RAILWAY BRIDGES.
WE have now gone through the subjects of the arch and of retaining
walls, cast and wrought-iron girders, and timber trusses, and aqueduct
bridges; we have only to add that in getting out working drawings, the
work should be done as if on the ground, and the reader is referred to
the chapter on "setting out works," where it is hoped ample rules will
be .found to meet most cases. No discrepancies would then occur
between the works as designed and as carried out.
T
266
LEGAL REGULATIONS AS TO RAILWAY BRIDGES.
This part of the subject will be concluded by a short abstract of
legal enactments on this part of our subject.
"The width of the arch shall be such as to leave thereunder a clear
space of not less than 35 feet if the arch be over a turnpike road, and of
25 feet if over a public carriage road, and of 12 feet if over a private
road.
"The clear height of the arch from the surface of the road shall not
be less than 16 feet for a space of 12 feet if the arch be over a turnpike
road, and 15 feet for a space of 10 feet if over a public carriage road;
and in each of such cases the clear height at the springing of the arch
shall not be less than 12 feet.
"The clear height of the arch for a space of 9 feet shall not be less
than 14 feet over a private carriage road.
The descent made in the road, in order to carry the same under the
bridge, shall not be more than 1 foot in 30 feet if the bridge be over a
turnpike road, 1 foot in 20 feet if over a public carriage road, and 1 foot
in 16 feet if over a private carriage-road, not being a tramroad or rail-
road, or if the same be a tramroad or railroad, the descent shall not be
greater than the prescribed rate of inclination, and if no rate be pre-
scribed, the same shall not be greater than as it existed at the passing
of the special Act.
"Every bridge erected for carrying any road over the railway shall
(except as otherwise provided by the special act) be built in conformity
with the following regulations :-
"There shall be a good and sufficient fence on each side of the bridge
of not less height than 4 feet, and on each side of the immediate
approaches of such bridge of not less than 3 feet.
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The road over the bridge shall have a clear space between the fences
of 35 feet if the road be a turnpike road, and 25 feet if a public carriage
road, and 12 feet if a private road.
"The ascent shall not be more than 1 foot in 30 feet if the road be a
turnpike road, and 1 foot in 20 feet if a public carriage road, and 1 foot
in 16 feet if a private carriage-road, not being a tramroad or railroad.
"But it is provided, "that in all cases where the average available
width for the passage of carriages of any existing roads, within 50 yards
of the points of crossing the same, is less than the width herein before
LEGAL REGULATIONS AS TO RAILWAY BRIDGES.
267
prescribed for bridges over or under the railway, the width of such
bridges need not be greater than such average available width of such
roads, but so, nevertheless, that such bridges be not of less width, in the
case of a turnpike road or public carriage road, than 20 feet."
SPECIFICATION OF BRIDGE OVER THE RIVER OUSE AT HILGAY.
J. S. VALENTINE, ESQ., C.E.
The foundations for the piers shall be excavated to the depths and
widths shown upon the drawings, or as much lower as the Engineer
may consider necessary from the nature of the ground.
Previous to commencing the foundations, the bottom of the trenches
shall be made perfectly dry and level, for the reception of the planking.
The space around the foundations, to the height of the present
surface of the bed of the river, shall be filled in with sound gault, as
the work proceeds, and well rammed in layers not exceeding 6 inches
in thickness.
thus,
STONE.
The whole of the stone to be used in the piers shall be from
Bramley Fall Quarries, and of the size shown upon the drawings, and
each stone shall be laid upon its natural bed.
The size and bond of the stone in each course are shown with blue
and brown lines in drawing No. 6 d, and this method of laying the
work must be strictly adhered to.
The face of the stone-work, from the surface of the planking to
within 4 inches of the ground line, shall be rough quarry scappled, with
the beds and vertical joints truly worked. Each of the footings shall
be in one thickness of stone, and each course shall not have less than
three bonding stones.
The courses marked in the drawings Nos. 6 a, 66, shall be finished
with their own natural face, and each stone shall have a tooled margin,
worked round the edge 1 inches wide,
3
SUGASIN
ENGHAR
小
​.

3
79
268
LEGAL REGULATIONS AS TO RAILWAY BRIDGES.
The curved part of each of the courses shall be roughly picked and
finished with its own natural face, and each stone shall have a tooled
margin as before described. The courses, marked A and C on the
aforesaid drawings, shall be neatly tooled, care being taken that the
stroke shall be in the direction of the weather current, and not less than
seven strokes in an inch. The centre string and the upper facia shall
be weather throated. The springing course shall be dowelled together
with slate plugs, 7" x 3" x 3" as shown upon the drawing. Two
copper cramps in each joint of the last-named course shall also be
inserted and securely let in with lead.
The cast-iron shoes for the reception of the ends of the bows shall
have their flanges let flush into the cap stones of the piers. They shall
be bedded on lead, and bolted down in the manner shown on the
drawing, and when fixed, the joints round the edges shall be well
caulked with lead.
All the beds and joints of the piers below the ground line shall be
made close, and well flushed in with strong lime grout. The joints
above the ground line shall also be worked close, and shall be laid and
neatly pointed with fine beaten mortar. All bolts and iron work shall
be properly fixed in the manner shown upon the drawings. The lime
to be used shall be fresh-burnt, and of the best quality of water lime
from Stoke or Isleham, or such other place as shall be approved by the
Engineer.
The piers shall, at the completion of the bridge, be neatly and truly
cleaned down, and finished entirely to the satisfaction of the Engineer.
CARPENTRY.
All the timber to be used for these works shall be the very best
Memel or Dantzic fir, free from sap and shakes, large and loose knots,
or any other defects, and shall hold, when finished, the several scantlings
figured on the drawings, and be framed together in the manner thereon
denoted, and the whole of the works shall be executed in accordance
with the Specification for timber bridges generally, hereinafter written.
The arched ribs shall be made to the proper radius. The two
outside ribs shall be 3 feet 8 inches, by 2 feet 2 inches, and
LEGAL REGULATIONS AS TO RAILWAY BRIDGES.
269
the centre rib 3 feet 8 inches, by 2 feet 9 inches, they shall be
formed with Dantzic deals, dressed on the sides and edges, and
in the longest lengths which can be procured. These deals shall be of
the very best quality, perfectly sound and well seasoned, and they shall
be submitted to the Engineer, and approved by him, before they are
used in the work.
thus,
Each deal shall be bent over the one below it in such a manner as
to break joint alternately both ways, and no two end joints shall come
over each other, or within three feet of the joint below it. The first
course shall be three deals in width, and the next two whole deals and
two half deals, and so on till the rib is formed. Each course of deals
shall be covered with a coating of marine glue, which shall be applied
hot, and in such manner as the Engineer shall direct.
The whole of the deals shall be fastened together with the best
compressed oak trenails one inch in diameter, made by Messrs. Ransome
and May, of Ipswich, which shall be placed four feet apart :-
о
O
O
O
с
each trenail shall be of sufficient length to pass through three deals,
and each course shall be trenailed to the two under courses.
The greatest care must be taken in fitting the ends of the deals to
the abutment plates that they fit perfectly close, and true on their ends,
and the ends of all the planks shall abut perfectly square, and true
upon each other throughout the bow.
The longitudinal beams shall be of the lengths shown upon the
drawings, No. 6 c, and scarfed together in the manner shown on
drawing No. 6f. The surface of the beams which are bolted together
shall be wrought perfectly true, and a coating of marine glue shall be
laid between them in the manner described for the bows. The whole
of the diagonal braces shall be accurately cut to the exact length, and
carefully fitted into the iron shoes.
The joists for the roadway shall be 12 inches by 9 inches, and they
shall be each of them in one length, and extend across the whole of the
270
LEGAL REGULATIONS AS TO RAILWAY BRIDGES.
longitudinal beams, upon which they shall be notched, and bolted down
in the manner shown upon the drawing, and the ends shall be neatly
finished to such form as shall be directed. The bearers for the rails
shall be 12 inches by 6 inches, bolted to the joists in the manner shown
upon the drawing, the space between the bearers shall be laid with
Dantzic deals 11 inches by 3 inches, spiked to the transverse beams
with spikes 7 inches long, and inch in diameter; there shall be two
spikes at each joist, and four at the heading joists, and no two heading
joists shall come together on the same joist.
The towing path shall be carried under the centre opening of the
bridge on cast-iron brackets in the manner shown upon the drawings.
The viaduct at each end shall be built in the manner shown upon
the drawings, and of such dimensions as are there given.
IRON WORK.
The whole of the iron to be used in this viaduct shall be of the very
best quality.
Previous to the order for the iron work being given, the Engineer
shall certify his approval of the foundry for the castings, and also the
manufacturer of the whole of the wrought-iron work. The castings
shall be made perfectly true, and of the exact size and dimensions
shown on the drawings. The suspension rods for the platform, together
with the whole of the bolts, straps, spikes, &c., shall be of the very best
quality of scrap iron, and of the dimensions shown upon the drawings,
and each suspension rod shall be tested to a weight of 20 tons. The
thread of the screws of all the bolts shall be engine cut, and of the
very best description of workmanship, which shall have been submitted
to and approved by the Engineer, and all bolts which have screws not
cut perfectly clean and true, will be at once rejected.
The greatest possible care shall be taken that the heads of all the
bolts shall be perfectly sound and true, and of the full dimensions
shown on the drawings. All the iron to be used in this bridge shall
be heated to about a blue heat, and the surface then struck over with
raw and linseed oil to prevent rust.
The Contractor must take upon himself the entire responsibility of
LEGAL REGULATIONS AS TO RAILWAY BRIDGES.
271
the whole of the works during their erection, and must at his own
expense erect good and substantial coffer dams, for the purpose of
getting in the foundations of the piers, which shall effectually keep out
the water from the foundations during the time of their erection, and
after the completion of the work the piles used in forming the coffer
dams shall not be drawn, but shall be cut off at the level of the bed of
the river, if not otherwise directed by the Engineer. All piles which
may be used for the purpose of scaffolding or other temporary works
shall be drawn upon the completion of the works.
The bed of the river shall be excavated to the depth shown upon
the drawings, and to such extent, and in such manner as is stated in the
Act of Parliament for this Railway.
And the barrier banks on each side of the river shall also be
strengthened in accordance with the Act of Parliament. During the
execution of the work the Contractor shall not in any way obstruct or
impede the navigation of the river or the towing paths thereof, but shall
in all respects comply with the several clauses in the Lynn and Ely
Railway Act, for the preservation of the Drainage and Navigation of
the Bedford Level, and all other clauses relating to this river. And he
shall also be responsible to the Engineer who may be appointed by the
Corporation of the Bedford Level to superintend the works for the due
and proper performance of such works, and for complying with the
several clauses above referred to.
A
PART VI.
TABLE I.
OF SPECIFIC GRAVITIES, WEIGHT PER CUBIC FOOT, AND
CUBIC FEET PER TON, OF MATERIALS,
With Cohesive Strength, and Constants of Elasticity and Transverse
Strength. The authorities are G. Rennie, Esq.;
G. Rennie, Esq.; T. Tredgold;
Professor Barlow; J. Bramah; Rondelet, and the Report of the
Commissioners appointed for examining the different Quarries in
England, &c. &c.
NAME OF MATERIAL.
Alder
Ash
Do. dry heart-wood
Basalt
Do.
Beech
Do.
Do.
Birch.
Do.
Bismuth
•P
Boxwood, from
Do.
to
Brass, cast
Do. wire
Brickwork (new)
Do.
(old)
Do.
in cement.
Red Brick
Specific
Gravity.
TABLE OF SPECIFIC GRAVITIES, &c.
Weight
per cubic
foot.
*555
34.68
*758
47.37
•845 52.81
3.000 187.50
2.478
154.87
Cubic feet
per ton.
64.58
47.28
42.51
*854 53.37 41.95
*720 45.00 49°77
*696 43.50 52'18
*720
45'00
*792 49.50 45.25
9.822 613.87
3.64
59.31
*949
1.328 83.00
8.396 524.80
8.544 534.00
1.872 117.00
1.520 95.00
1.920 120.00
2.160 135.00
Cohesion in lbs.
per
square inch.
Tension.
}
15000
11000
19000
18000
Pressure.
82000
Constant of
Elasticity.
205000, or 113
169200, or 92
205000, or 113
!
Const. of
Transv.
Strength.
2020
1560
·
}
REMARKS.
This timber is little used in
carpentry, and unless con-
stantly and perfectly dry decays
rapidly; it is in great demand
among wheelwrights; the total
height of the tree averages 60
and 70 feet.
Beech is very durable if kept
constantly wet, and being also
hard, forms excellent piling;
in building it is not much used;
the average height of the trunk
is 45 feet, and the average
diameter 2 feet.
1928 Birch and Alder are both suit-
able for hydraulic works, but
both decay easily if exposed to
damp, and therefore they are
unsuitable to carpentry.
One cubic yard of brickwork in
cement, may be calculated to
weigh about 3284 lbs. and in
274


Do. common (about)
Do. London stock
Do. Welsh fire.
Chalk.
Do..
Do.
Dorking
Cedar (Indian)
Do. from.
to.
Cement
Clay, from
to
Chestnut (sweet)
Coke
·
Coal, Glasgow.
Do. Kilkenny
Do. Jarrow, Newcastle
Do. Garesfield, do.
Do.Wigham Banks, do.]
Do. Wigan, Lancashire
Do. Cannel Coal, do.
Copper, cast
Do.. wrought
Do.
wire
1.760
110'00
1.840 115.00
2.408 150*50
2.315 144.68 15.41
2'656 166.00 13.49
1.872 117.00
19.14
1.315
82.18
*453
28-31
*753
47.06
1.600. 100.00 22.40
1.920 120.00 18.66
135.00 16.59
2.160
*696 43.50
*755 47.00
1.286
1.526
1.266
80.30
95.30
79.10
80.00
81.37
82.43
79.50
8.800 550'00
8.915
557.20
8.880
555.00
1·280
1.302
1319
1.272
500
1200
500
19000
57000
33000 51000
mortar 2996 lbs. The crush-
ing weight on pale red brick, or
rather soft, is 500 lbs., on hard
red, 807 lbs., on fire-brick
about 1710 per square inch.
The adhesive power of good
cement, when the power tend-
ing to rupture is parallel to the
joint, is about 500 lbs. per
square inch.
This timber was much used some
centuries since, and is very
durable if properly used; the
roof of Westminster Hall and
that of King's College, Cam-
bridge, are constructed with
Chestnut. Average height of
trunk, 40 feet, average diameter
2 feet.
The relative heating powers of
different coals have been pro-
portioned as follows:-
lbs. of water heated from 32°
to 212°.
Name of coal.
Dowlas in Wales.
Newcastle.
72.0
70.0
56.4
64.1
Cannel, Glasgow.
Wigan, Lan-
cashire.
""
275
NAME OF MATERIAL.
Earth, from
to
Ebony, American
Indian
Do.
Elm
Do.
Fir, Christiana
Do. Norway
Do. Memel
Do. American
Do. Riga
Do. Scotch
Glass, from.
to
•
→
V
Specific
Gravity.
*688
•577
*590
*553
1·520 95.00
2.016
1·328
1216
*553
*543
*738
•693
TABLE OF SPECIFIC GRAVITIES, &c.-Continued.
Cohesion in lbs.
per
square inch.
2.824
2.520
Weight
per cubic
foot.
Cubic feet
per tou.
23.57
126.00 17.77
83.00
76.00
34.56 64.93
33.93 66.01
52'09
43.00
36.06
62.09
36.87
53*
34.56
64.71
46.12 48.56
51.72
43.31
187.00
157.50
Tension.
9500
·
Pressure.
1200
1800
Constant of
Elasticity.
87400, or 50
92750, or 5-1
198700, or 115
182000, or 105
200000, or 115
274000, or 158
124000, or 71
108700, or 62
↓
Const. of
Transv.
Strength.
1010
1118
1562
1470
1730
1100
1050
1262
53.2
•
REMARKS.
Lancashire.
The Elm is seldom used in build-
ing, but is noted for its dura-
bility under water; it was used
for the piles of Old London
Bridge; average height of
trunk 44 feet, and diameter 2
feet 8 inches.
There are two sorts of fir, red or
yellow, and white; the red is
the most durable in any situa-
tion, and the best of this kind
is generally from Norway; it is
imported in logs and deals; the
tree (Pinus Sylvestris) seldom
exceeds 18 inches in diameter
from Norway, and 2 feet from
Russia. White Fir (Pinus
Abies) is imported from Chris-
tiana in planks and deals, and
also from America. It was
said by Brindley that Red Riga
would last as long as oak in
any situation.
-
276

Granite, Aberdeen red
× 'do. blue
Do.
Do.
Do.
Do.
Do.
Do.
do. a
do. a
do. a
Do. Blackburn a
Do. Manley a
Do. Tamor a
Do. do. a fine grained
Specimen a
do. grey
Anglesea.
Do. % Dartmoor
Do. Guernsey
Do. × Heytor
Do. Talacre
Do. × Penryn
Do. Peterhead
Gravel
Indigo
Iron, cast
Do. Native
Do. bar
Do. do.
Do. do.
Do. Swedish
Do. Wire
2.643
2.608
2.664
2.704 169.00
2.708
2.708
2.708
2.432
2.256
2.649
165.20 13.55
163.00
13.73
166.50 13.45
13.25
169.25 13.23
169.25
13.23
169.25
13.23
14.73
15.88
165.62 13.23
6.723
7.600
7.787
152.
141*
3.049 190.62 11.75
2.664 166.50 13.45
2.999 187.47 11.96
2.555 159.75 14.02
2.401 150.80 14.85
2.736 171.00 13.10
2.432 152'00 14.73
1.760 110.00
*769 48.10
7.104
444.00
420.18
475*
486.70
5.04
5.33
4.71
4.27
19000
56000
.67600
72000
78000
7100
9200 +
6700
7162 a
11590
9990
6790
4975
2715
5741
11200
7800+
10300 a
8700 +
4700 a
5700 +
7600
14560
2252000, or
1303 a
The numbers under the column
"pressure" are from experi-
ments by G. Rennie, Esq., and
the late J. Bramah, Esq.; a
are the pounds borne, × the
pounds which fractured, and
the others the pounds which
crushed the specimens.
7600a a These constants will of course
be understood to apply to rec-
tangular bars.
According to Duleau, wrought
3333
iron may be extended to of
its length without injuring its
elasticity. Lavoisier and La-
place found by experiments
that wrought-iron at 32° mea-
suring 1 expanded at 212° to
1·00122048; Smeaton found
1001258. For cast-iron, Ge-
neral Boy found 1'0011094.
•
277
278
NAME OF MATERIAL.
Larch
Do.
Lead, cast
Do. milled
Lime
Specific
Gravity.
*522
*560
11.352
11.407
⚫843
TABLE OF SPECIFIC GRAVITIES, &c.-Continued.
Cohesion in lbs.
per
square inch.
Weight
per cubic
foot.
32.62
35.00
·
709 50
712'93
52.68
Cubic feet
per ton.
68.66
64°
3.15
3.14
42.52
Tension.
1782
Pressure.
Constant of
Elasticity.
112000, or 65
131600, or 76
Const. of
Transv.
Strength.
832
1149
1
Larch is a valuable timber, being
strong, hard, and durable; it
has in all ages been much
esteemed, and is one of the
best for hydraulic works; it is
said that the ancient city of
Ravenna was entirely founded
on larch piling; there is no
doubt that it is admirably
adapted for the construction of
wooden bridges and viaducts,
but it has not as yet been
much used for this purpose,
having but lately been grown
to any extent in Britain; it
bears exceeding well the driving
of bolts and spikes; every one
knows how commonly it is used
for railway sleepers.
thick lbs.
1 foot super.milled lead= 3.71
1 = 4·95
ΙΣ
""
""
رد
REMARKS.
""
""
در
""
""
">
23
1
ΤΟ
120~1~||
छ
=
5.93
7.41
9.9
14.85

Limestone, from
Do.
Do. Beer quarry, Devon 2.108
Do. Chilmarks, Wilts.
2.457
Do. Hopton Wood,
Derbyshire
1.856 116.00
2.536 158.50
Do. Seacombe, Dorset 2:416
•
131.75 17.
153.58 14.58
2.536 158.50 14.08
151·00 14.83
35.00
Do. Sutton, Glamor-
ganshire.
2.176 136.00
Mahogany (Spanish). *852 53.00
Do.
Honduras *560
Marble, White, fine
grained, compact
Do. white
2.840 177.50
2.720 170.00
Do. mercury (fluid) 13.568 848·00 2.641
16.47
17300
on com-
pact spe-
cimens.
10080
9680
6058
1
TI
32 feet cube of lime = one
hundred of lime, containing 25
bushels, and the measure is 3
feet square, and 3 deep.
Generally, according to Smeaton,
those limestones, into which
clay enters as a component are
the best adapted for hydraulic
works.
Light brown; friable; chiefly car-
bonate of lime; 6 × 3 × 2.
Light greenish brown; carbo-
nate of lime with a propor-
tion of silica; blocks from
10 cwt. to 3 tons; Salisbury
Cathedral and Wilton Abbey;
generally in excellent condi-
tion.
Warm grey; compact; carbonate
of lime; blocks of 100 feet cube
varying in depth from 3 feet to
10 feet; Belvoir Castle, Chats-
worth, Drayton Manor.
Light brown; semi-compact car-
bonate of lime; 6 × 2 and 4
× 3. Light-houses, piers, and
docks.
-
Light creamy; compact and
highly crystallized carbonate
of lime; blocks of 6 tons and
upwards; thickest bed 12 feet.
In many ancient buildings in
Glamorganshire and the adja-
cent counties.
279
NAME OF MATERIAL.
Mortar, from (old)
to (new)
Magnesian Limestone,
Bolsolver, Derbysh. | 2:427
Do. Brodsworth, Don-
caster, Yorkshire.
2.138
Do. Cadeley, Doncas-
ter, Yorkshire
Do. Huddlestone, Sher-
burne, Yorkshire
Specific
Gravity.
Do. Smawse, Tadcaster,
Yorkshire
1414
1.903
2.025
2.205
Do. Parknook, Yorks. 2140
Do. Roach Abbey, Baw-
try, Yorkshire
2.225
TABLE OF SPECIFIC GRAVITIES, &c.-Continued.
Cohesion in lbs.
per
square inch.
Weight
per cubic
foot.
88:37
118.93
151.70
Cubic feet
per ton.
126.60
14.76
133.63 16.76
17.69
137.68 16.20
133.75 16.75
139.12 16.10
2.040 127.50 17.56
Tension.
Pressure.
6832
6170
Constant of
Elasticity.
Const. of
Transv.
Strength.
REMARKS.
Light yellowish brown; South
well Church, &c.
Light brown; Doncaster Old
Church; Mansion House; thick-
est bed 3 feet 6 inches.
Day and Martin's, Holborn ;
cream colour; the central beds,
which are the best, are 4 feet
thick.
-
Light cream; York Minster;
Selby Cathedral; Westminster
Hall; may be obtained 4 feet
thick.
Whitish cream; very numerous
ancient and modern buildings;
this stone vegetates very rapidly;
it is liable to stun under the
tool; thickest bed 2 feet 6
inches.
Light yellow brown; York Min-
ster, Beverley Minster, Ripon
Minster, &c.; largest blocks
8′ × 3′ × 30', 7d. at quarry.
281
Ո
Oak, fast grown
Do. slow grown
Do.
Do. Canada.
Do. Dantzic
Do. African.
Oolitic Stones, from
to
Do. Ancaster Quarry,
Lincolnshire
Do. Barnack Mill, Nor-
thamptonshire
-
Do. Bath Lodge Hill,
Somerset.
Do. Bath, Baynton,
Somerset.
Do. Drew's
Drew's Quarry
(Bath), Somerset
Do. Cranmore, Wilts.
Do. Haydor, Lincoln-
shire
58.56 38.25
52.87
42.36
*969
60.56
36.98
.872
54.50
*756 47.25 47.40
*993 62.06
2.362 147.66
1·968 123.00
2.228 139.25 16.08
*937
•846
2.188
1.856 116.00
1.968
1.961
2.148
136.75
2.134
16.38
123.00 18.21
122.62 18.26
134.25
133.42 16.78
11000
14000
3800
33
25
193000, or 111
104000, or 60
109000, or 63
268000, or 155
148000, or 86
299500,
1560
1265
1180
1760
1450
2570
"The nearer the magnesian lime-
stones approach to equivalent
proportions of carbonate of
lime, and carbonate of magnesia,
the more crystalline, and the
better they are in every respect."
Hydraulic lime is prepared from
the magnesian limestone.
Loose fibred, porous oak is of
inferior quality; choose close
grained, heavy, and fine pored
specimens: it is principally
used where timber is submitted
to compression, and is in these
days more in use for ship build-
ing than constructive purposes.
Cream colour; fine grained and
compact; Wollaston Hall, and
Belvoir Castle; blocks of 3 and
5 tons in 18 in. thickness.
Whitish brown; often coarsely
laminated; Peterborough Cathe-
dral, and Croyland Abbey, &c.;
beds up to 18 in. thick.
The price of Bath is given at 6d.
and 7d. at quarry.
Light brown; Wells Cathedral;
beds 20 in. thick.
Dark cream colour; Lincoln
Cathedral; blocks 14′ × 3′ × 4′.
NAME OF MATERIAL.
Do. Ketton, Rutland-
shire
Do. Vern Street Quarry,
Portland
Do. Grove Quarry,
Bowes, Portland
Do. Waycroft Quarries,
Portland
Do. Goslings Quarry,
Portland
Specific
Gravity.
2.053
2.153
2.361
2.168
2.028
TABLE OF SPECIFIC GRAVITIES, &c.-Continued.
Cohesion in lbs.
per
square inch.
Weight
per cubic
foot.
128.33
134.62
147.62
best
135.50
126.80
Roach.
Cubic feet
per ton.
17.45
Tension.
Pressure.
4000
6000
Constant of
Elasticity.
Const. of
Transv.
Strength.
REMARKS.
A good lasting stone, much used in ancient and modern
buildings; dark cream colour; the rag stone, 3 feet
6 in. thick.
Whitish brown; may be obtained of any practicable size;
this stone has been employed in various public buildings.
An oolitic carbonate of lime, with numerous fragments
of shells; whitish brown; may be had 9 feet thick; the
lower bed is the best; St. Paul's Cathedral.
Oolitic carbonate of lime, with fragments of shells
whitish brown; depth of freestone 13 feet; Goldsmiths'
Hall and Reform Club House.
Any practicable size, and the same remarks as above.
There are fifty-six quarries in the Island of Portland, and
about 24,000 tons are annually consumed: the top best
is generally the best stone, being fine grained, and free
from defects; in the bottom beds the stone is ill cemented,
and does not stand the weather; in the east cliff quarries
the stone is harder than in the west cliff. Besides the
buildings already mentioned, Somerset House, St.
Martin's-in-the-Fields, and St. Margaret's Tower, Loth-
bury, are built of Portland stone; Westminster Bridge,
and, we believe, Blackfriars, are constructed of Portland
stone; but it is not a lasting material for hydraulic
works. The oolitic formation consists of three strata,
three times repeated; the stone is mostly a carbonate of
282


૧૭
Do. Taynton, Oxon.
Peat, from
to
Pebble
Pewter
Pine, Pitch
Pine, Red
Sand, from
to
Sandstone, from
to
Do. Abercarne, Mon-
mouthshire
Do. Barbadoes, Mon-
mouthshire
Do. Binnie, Linlith-
gowshire
Do. Bolton Quarry,
Yorkshire
-
2.147
1.008
1.472
2.600
7.248
63.00
92.00
163.00
453.00
41.25
41.06
1·440
90.00
1.872 117.00
1.648
103.06
2.687
167.94
2.687 167.94 13.33
2.348 146.75 15.26
2.246 140'06 15.99
126.78 17.66
*660
*657
135.93
2.028
15.74
lime, with shelly fragments, cemented together by a cal-
careous and often argillaceous cement; this bed rests
upon one of argillaceous sand and sandstone, which
reposes on a thick deposit of clay.
Brown; thickest bed 7 feet; Blenheim, and interior of
St. Paul's.
153000, or 88 1630
23000, or 133 1341
We have a great variety of sandstones composed of
quartzose grains principally, united together in most in-
stances by an argillo-silicious cement, with various pro-
portions of mica; the less we find the latter ingredient,
the sounder the stone; we may, perhaps, venture on
dividing the sandstones into four divisions, remembering,
however, that there are a multitude of varieties of each
division:-I. A sandstone of a grey, or bluish grey,
fine, compact, very hard and heavy; this stone is one of
the best, as the Craig Leith, and Abercarne, Elland
Edge, Kentish rag: II. A stone of a coarse grained
nature, as much so in some instances as the coarsest
granite, the grains of which are united by a ferruginous
cement; this second division is also composed of stone,
hard and heavy, and is often the terror of masons from
the quantity of steel "licked off" from their tools; in
mouldings, it disintegrates rapidly from frost and wet,
but for strength it is one of the best building materials,
where, however, fine moulding is not required, as it
pocks very much under the tools; it is commonly called
283
NAME OF MATERIAL.
Do. Bramley Fall,
Yorkshire
Do. Calverley, Tun-
bridge Wells, Kent
Do. Craig-Leith, near
Edinburgh
Do. Crawbank, Lin-
lithgowshire
Do. Duffield Bank,
Derbyshire
•
Specific
Gravity.
2.275
1.388
2·318
2.063
2.125
TABLE OF SPECIFIC GRAVITIES, &c.—Continued.
Cohesion in lbs.
per
square inch.
Weight
per cubic
foot.
Cubic feet
per ton.
142.20 15'75
118.06 19.82
145.90 15.35
129.00 17.44
132.86 16.90
Tension.
Pressure.
·
4000
Constant of
Elasticity.
Const. of
Transv.
Strength.
REMARKS.
by the workmen "bastard granite;" such as the "Bram-
ley Fall," and "Heddon:" III. And next in value, as a
constructive material, we have a stone of a greenish and
greenish brown tint, pretty hard, moderately heavy, but
by no means equal to the former divisions, the disinte-
gration being here much more rapid than in the former
divisions; it also generally contains much more mica:
IV. Division; this latter division consists of a stone of
red, purple, yellowish red, and bright brown colours, and
this last is the worst of the sandstones;-(it will be
understood that these remarks are general and not
special.) In the first two divisions, the stones may be
had of any practicable size, of 4 and 5 feet depths; in
the III. and IV. divisions, the beds are generally much
thinner; the III. division yields the Yorkshire flags and
stones, which may be very advantageously used in the
construction of small arches.
Blocks up to 18 tons; much
used in hydraulic works.
Brownish; beds 3 feet thick.
Fine grained whitish grey; from
6 to 10 feet thick.
Light rusty brown; fine grained;
blocks 10 × 6 × 5.
Light brown; moderately fine.
284
!

285
Do. Duke Quarries,
Derbyshire.
Do. Gatherley Moor,
Yorkshire
Do. Gatton, Surrey
Do. Glamis, Forfar-
shire
Do. Heddon, North-
umberlandshire.
Do. Hollington, Staf-
fordshire
Do. Humbie, Linlith-
gowshire
Do. White Grey
Do. Longannet, Perth-
shire
•
Do. Munlochy, Ross-
shire.
Do. Park Spring, York-
shire
2.312
2.172 135.80
1.646
2.545
2·093
2.128
144.50 15.50
2.243
2.172
16.49
103.00 21.74
161.10 13.90
130.85 17.11
133.00
16.84
140·20 15.97
135.80
16.49
2.107 131.70 17.00
2.569 160.56 13.95
2.416 151'06 14.82
Do. Pensher, Durham 2:418 134.30 16.67
Do. Pyotdykes, Forfar-
shire
2.600
162.50 13.78
5000
1
Red, brown, and grey; rather
coarse; Penitentiary, London;
and partly in filling of Water-
loo Bridge.
Cream colour; moderately fine;
one bed 12 feet thick.
Greenish light brown; blocks
from 35 feet to 60 feet cube;
Hampton Court and Windsor
Castle.
-
Purple grey; moderately fine;
thickest bed 6 feet.
Light brown; coarse; in beds of
4 feet and 12 feet.
Light brown grey; moderately
fine; 30 feet and 40 feet square;
and 8 feet thick; in Stafford-
shire and Derbyshire.
-
Light grey and light brown; 8
feet thickest bed; fine grained.
Light reddish brown; fine
grained; 5 feet for thickest
bed.
Red variegated; fine grained;
beds 2 feet to 6 feet thick.
Light rusty brown; fine grained;
24 feet thickest bed.
Light brown; coarse; thickest
bed 20 feet.
Dark grey; fine grained; 3 feet
to 4 feet thickest bed; Dundee
Harbour.
286
NAME OF MATERIAL,
Do. Ringoodie, Perth-
shire
Do., Scotgate, York-
shire
Do. Stancliff, Derby-
shire
સુ
Teak
Tile, from
to
Tin, cast.
→
hammered
Specific
Gravity.
Do.. Stenton, Durham 2:280
Do. Whitby Company,
Yorkshire
Shingle
Slate, Welsh
Do. Westmoreland,
from
Water, sea
rain
Zinc
2.560
2.371
TABLE OF SPECIFIC GRAVITIES, &C.-Continued.
2.528 158.00
2.028
1.424
2.880
Weight
per cubic
foot.
160.00
to
Do. Anglesea
Do. Cornwall, light blue 2-512
Steel, from
7.840
to
7.776
*745
1.816
113.50
1.856 116.00
7.291 455-70
7.299
456'20
1.027
64.18
1.000
65.50
7.184
449.00
Cubic feet
per ton.
14.00
14.24
148*20 15.11
142:50 15.71
126.80 17.66
89.00
180.00 12:44
2-771 178.00 12.94
2.79:5 174*50
2.876 179.75
157.00
490.00
486.00
46.56 48.11
Cohesion in lbs.
per
square inch.
Tension.
16000
Pressure.
3500
1400
3500
Constant of
Elasticity.
309000, or 178
Const. of
Transv.
Strength.
2460
REMARKS.
Dark grey; fine grained; any
practicable size.
Light greenish grey; moderately
fine; 34 feet thickest bed.
Light rusty brown; moderately
fine; large size blocks.
Light rusty brown; fine grained;
2 feet to 8 feet thick.
Light brown; moderately fine;
large blocks.
1 cubic foot = 6 gallons, 1 pint.

TABLE II.
OF SETS AND DEFLECTIONS ON CAST-IRON GIRDERS
FROM THE PASSAGE OF TRAINS.
1
SECTIONS OF GIRDERS.
SECTION 1.
9
123
<---301-
TABLE OF SETS AND DEFLECTIONS ON CAST-IRON GIRDERS.
No.
1
на со
4
106
7
со сс
9
10
11
12
13
14
15
Bearing in
feet and
inches.
6,10
8,0
8,9
10,0
Breaking
Weight in
tons, ac-
cording to
Formula of
E. Hodg-
kinson, Esq.
43.2
34.8
33.7
29.5
Permanent
Deflections when
tested
in inches.
10 tons in centre.
0.12
0.18
REMARKS.
Deflections in inches under a train of 6 cargs. at 30 m.
[per hour.
K
Do.
0.02
0.03
0.03
0.02
do.
0.01
0.05
0.05
0.04
0.04
Do., 4 luggage wagons.
0.06
0.09
Do., 4 carriages.
0.06
0.12
288


SECTION 4,
SECTION 2.
12-.
SECTION 3,
-1, 6-
-1'. 4-"--------
5:1
of-a
6
-K
H
8'
17
1″
L
3" X 8"
15
"
16
17
18
19
20
21
22
23
24
૨૭ ૨૭
2"
8"
]1玲
​[X];
4310
13z."
81"
Centre.
End.
25
26
27
28
29
3:0
31
32
33
8,0
15
19
37.5
45
34.5
0.15
0.15
0.12
0.16
20 tons in centre.
0.06
0.12
O
●
Deflections under train of 4 cargs., at 30 m. per hour.
0.05
0.06
0.05
0.03
Luggage train, 16 miles per hour.
0.12
Cast flat.
0.12
5 carriages, 33 miles per hour.
0.09
0.67
4
do.
36 miles per hour.
0.09
0.12
0.12
0.09
289


SECTIONS OF GIRDERS.
TABLE OF SETS AND DEFLECTIONS ON CAST-IRON GIRDERS.-Continued.
No.
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
Bearing in
feet and
inches.
19,9
Breaking
Weight in
tons, ac-
cording to
Formula of
E. Hodg-
kinson, Esq.
33.2
Permanent
deflections when
tested
in inches.
•
4 carriages, 40 miles per hour.
0.18
0.18
0.15
0.18
0.15
0.15
0.22
0.13
4
5
REMARKS.
do. 25 miles per hour.
0.12
0.12
0.15
0.12
30 miles per hour.
0.14
0.14
0.21
0.15·
0.15
0.12
0.12
0.21
do.
290

SECTION 5.
2.0
JO"
IN
18"
コイ
​54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
28,0
28,6
30
64.3
63-1
60
,
:
30 tons in centre.
0.68
0.56
0.56
0.53
0.55
0.52
0.50
0.56
0:43
0.56
0-48
0.50
0.62
0.50
30 tons in centre.
0.59
0.56
0.59
0.68
30 tons in centre.
0.45
0.47
0.47
0.54
0.56
0.55
0.50
0.54
0.43
0.56
0.50
Cast on edge.
Cast on edge.
Cast on edge.
291

SECTIONS OF GIRDERS.
SECTION 6.
-1', 8-
SECTION 7.
-2′0.
5
8"
-1
+
t
7" Y. 8"
6
13/15
X₁.
1½"
10"
-10
TABLE OF SETS AND DEFLECTIONS ON CAST-IRON GIRDERS.-Continued.
n
1/
No.
83
84
85
86
87
88
89
90
Bearing in
feet and
inches.
20
20
Breaking
Weight in
tons, ac-
cording to
Formula of
E. Hodg-
kinson, Esq.
50
67.5
Permanent
Deflections when
tested
in inches.
0.50
0.56
0.50
0.62
20 tons in centre.
0.18
0.18
20 tons in centre.
0.12
0.21
REMARKS.
Cast on edge.
Cast flat.
Cast flat.
292


SECTION 8.
SECTION 9.
3,0″.
-->>
-~-~~-~~-~- - - - - - 0 1 2 --
=1ry
84
7"
8"
X
"
3 ±× 4'
1克
​X
14″
10"
14
11+
"
27,"
91
92
93
94
95
96
97
98
99
30
40
60
84.1
30 tons in centre.
0.94
0.94
0.75
1.00
40 tons in centre.
0.87
0.75
0.85
0.87
0.63
Cast flat.
Cast flat.
Another foundry.
293



294
SECTIONS OF GIRDERS.
SECTION 10.
SECTION 10a
2
2
}}
6"
=-12
18″
Centre.
4"
164"
End.
TABLE OF SETS AND DEFLECTIONS ON CAST-IRON GIRDERS.-Continued.
A
2′ 6.
-----བ-----0%------
1
No.
100
101
102
103
104
105
106
107
Bearing in
feet and
inches.
36
42
Breaking
Weight in
tons, ac-
cording to
Formula of
E. Hodg-
kinson, Esq.
←--
62.5
53.5
-
Permanent
Deflections when
tested
in inches.
20 tons in centre.
0.68
0.63
30 tons in centre.]
1.43
1.75
20 tons in centre.
0.94
0.87
1.12
1.13
"/
FO
From end to end 48 feet.
REMARKS.
18
1
·
"



EXPERIMENTS BY GEORGE RENNIE, Esq.
TABLE III.
On the Transverse Strength of Wooden Beams resting on rollers, 3 ft. 9 in.
apart.
Species of Timber.
English Oak.
Ditto
African Oak
Ditto
Ditto
Ditto
Yellow Dantzic Fir .
•
Ash
Beech.
Elm
Yellow Fir
White Deal
295
English Oak.
Ditto
Ditto
African Oak
Ditto
Ditto
Yellow Dantzic Fir.
•
Sectional Breaking
Dimensions.
Weight.
2″ × 2″
""
""
""
""
""
""
1″ × 1″
""
""
""
ور
""
در
1369
1456
1425
1447
1873
1968
999
160
168
193
202
224
224
118
On the Tensile Strength of various Timbers per square inch.
lbs.
12,000
10,500
10,000
9,600
10,000
lbs.
American Oak . 12,200
English Oak
12,000 to 10,500
12,000
Riga Oak
African Oak, from 15,600 to 14,000
On the Tensile Strength of different Metals per quarter of an inch square.
Force in tons
Tensile
force in lbs. per square inch
11662
90***
1218)
Swedish Iron,
English Iron,
296
TABLE IV.
Cast-Iron, horizontal
Cast-Iron, vertical
Cast Steel, tilted
Blister Steel, reduced per hammer
Shear Steel,
Cast Copper
Fine yellow Brass
Cast Tin.
Cast Lead
ditto
ditto
ditto
Brass-hard Gun metal (2 trials)
Wrought Copper, reduced per hammer
. 8391
. 8322
. 7977
. 4504
3492
. 2273
2112
1192
. 1123
296
114
59.94
59.44
52.50
32.17
24.94
16.23
15.08
8.06
8.00
1.60
0.81
On the Transverse Strength of Cast-Iron Beams, for the purpose of deter-
mining the effect of Wrought-Iron, when mixed with Cold-blast
Blaenarvon Cast-Iron in different proportions.
Quality of iron, No. 1, Blaenarvon, unmixed with wrought-iron,
4 ft. 6 in. long between supports, and 1 in. square.
Three bars experimented upon, the average weight of each being
16 lbs. 5 oz.
Average deflection with 506 lbs. in scale, 1.76 in.
Breaking weight . 511 lbs.
* These were unusually strong specimens, but the average of subsequent experi-
ments on various Irons does not give more than 6 tons per square inch.
EXPERIMENTS BY GEORGE RENNIE.
297
Three bars of similar dimensions to the above, with 10 per cent. of
wrought-iron, and weighing upon an average 16 lbs. 9 oz. each;
Average deflection with 611 lbs., 1·50 in.
Breaking weight 625 lbs.
Three bars of similar dimensions to the above, mixed with 20 per
cent. of wrought iron, and weighing upon an average 16 lbs. 10 oz. each :
Average deflection with 628 lbs., 1·58 in.
Breaking weight . 672 lbs.
The results are, that 10 per cent. wrought-iron, with No. 1 Blae-
narvon cast-iron, gives an additional strength of 224 per cent., and with
20 per cent. wrought-iron an additional strength of 31 per cent.
Similar Experiments were made with bars of Blaenarvon Cast-Iron, mixed
with 30, 40, and 50 per cent. of Wrought-Iron respectively.
The results were-
For 30 per cent. wrought-iron, an increase in the
strength of the bar of
For 40 per cent. wrought-iron, an increase of .
For 50 ditto
ditto
.
X
60 per cent.
33
261
""
>>
From which it appears that 30 per cent. of wrought-iron, mixed with
the Blaenarvon, gives the greatest strength.
298
On the Comparative Strength of similar bars of Blaenarvon Cold-blast
Iron in different positions, 1 in. square.
EXPERIMENTS BY GEORGE RENNIE.

In the form of an arch, 4 ft. 6 in.
No. 1. between the abutments; rise or versed
1
sine of chord or span, bore
15
No. 2.
No. 3.
A bar, similar in every respect, but
the arch inverted, bore
and was therefore 31 times weaker
than the former arched beam.
The same with versed sine of
chord or span, bore for the mean of 2
experiments.
from whence it appears that the bar in
this last position was 3.6 times stronger
than the straight bar, and 5 times
stronger than the bar in the form of
an inverted arch of rise.
15
No. 4. Same as above, but reversed.
416
1267lbs

357.lbs

1729. lbs

280.ls.
EXPERIMENTS BY GEORGE RENNIE.
299
On the Transverse Strength of Bars of Blaenarvon Iron, of different Forms,
Depths, and Thicknesses, but of equal Weight with Bars of 1 in, square,
or of 16 lbs. to 17 lbs. each.
Rectangular Bars.
Depth.
in.
2
3
4
Upper side of bar Parabolic.
Side of
cube in
inches.
2
2
2
2
Distance between
supports.
ft. in.
4 6
4
6
4 6
p
4 6
4 6
1 1/1/0
2
4 6
4 6
Weight
of Bars
Manley
Talacre
in lbs.
16 1/1/0
16, 10 oz.
17
12
12
11
11
Upper side of bar Semi-Elliptical.
Designation.
Anglesea Granite
Blackburn ditto .
2
ditto.
ditto.
Anglesea ditto (4 specimens)
Tamur
Ditto
ditto.
ditto (fine grained)
Cornish Heytor (split):
Ditto ditto (crushed)
Dartmoor (10 specimens), sup-
ported without fracture.
Dartmoor (5 specimens)
3
..
Thickness
in.
2
3
Specific
Gravity.
~102 HOHIH
2.704
2.441
2.454
2.419
2.708
2.650
3.050
1105
The permanent deflection varies from to of the breaking weight.
1o8
On the crushing of Stones, 2 specimens of each.
Crushing
Weight
in lbs.
2.626
2.626
14/037/00
2
1/01 -10
247
147
29637
19400
10900
18950
23632
23425
24125
30912
46144
Breaking
Weight
in lbs.
18480
37408
1121
1568
2352
953
1429
950
1450
Crushing
Weight per
cubic inch
in lbs.
3692
2425
1362
2368
2954
2928
3015
3864
5768
4676
The force required to crush a cubic inch of Cast-Iron is 70 tons.
3 2
300
An account of Experiments made on the powers of Stones to resist pressure,
previously to the construction of New London Bridge.
No. of Experi-
ment.
Dimensions
of cube.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
in.
1
/1/1/0
در
""
"}
>>
""
""
>>
""
""
""
""
")
""
""
""
""
""
رو
""
""
EXPERIMENTS BY GEORGE RENNIE.

Name of Granite.
Craig Leith Freestone (white)
Dundee do. (dull grey)
Heytor Granite
Aberdeen, fine grained (yellow
and grey).
do..
Do.
Do.
do. (time 4 hours)
Do. do., inclining to blue
Peterhead (coarse red)
Do.
Granite
Do.
Ditto
Jersey
Do.
Do.
5
3
6 15
5 13
6 3
6 4
7 7
fine grained (reddish) 68
blue kind
7 8
do. duration of
Experiment 50 hours (blue)
Guernsey (2 specimens) Granite.
Cornish, large grained (light grey)
Heytor Granite (another specimen)
Sienite.
Do. (2 specimens)
Aberdeen Granite (red) .
Do.
•
Crushing
Weight.
do.
do. full grained (red)
do.
tus. cwt. qrs. lbs.
4 2 3 19
5 3
0 24
6
9
0 24
6 11
10 7
10 7
6 12
11 2
613
13 7
7 3
8 12
7 3
8 17
0 24
2 12
2 1
3 10
2 23
3 12
0 24
2 12
3 22
3 12
3 3 7
3 7
0 24
0 24
3 24
2 24
3 24
3 12
Crushing
Weight in
lbs.
9287
11560
14448
11560
15188
12657
13870
13967
16560
14360
16644
14778
23280
14857
24864
14920
29904
16100
19320
16100
19920
Average duration of Experiments 10 hours.
A cubic foot of Granite, allowing for every variation, is capable of
sustaining a pressure of from 600 to 700 tons, a stress far beyond any-
thing that can ensue in the boldest arch.
The arches of New London Bridge only give a pressure from 80 to
90 tons per cubic foot.
EXPERIMENTS BY GEORGE RENNIE.
Weights and Dimensions of Arches of London Bridge.
Land Arches .
Second Arches
Middle Arch .
Superficial
Area.
625
785
930
Solidity.
30.000
37.680
44.640
with mortar fresh laid .
26.44°
24°
Tons
Weight.
Angles at which the dressed Voussoirs commenced sliding
without mortar
Ditto
2097.98
2634.99
3121.68
Angles at which various substances stand when dry-
Sand
32° to 33°
Coarse Gravel. 35°
Fine ditto.
. 44°
Fine flour
Wheat, Barley.
Peas.
33°
301
33.30°
25.30°
These experiments on the angles repose of voussoirs made by our
distinguished bridge builder, are particularly valuable, and still more
from the important work in which they were noted. Rondelet, Art de
Batir, Vol. IV., p. 273, says, " It has been found from experiments, that
hard stones laid dry commenced slipping at an angle of 30 degrees, and
with mortar fresh laid at angles of 34 and 36 degrees; and with soft
stones on mortar fresh laid 45 degrees, when the centre of gravity does
not fall without the base." From 34 to 36 degrees is repeated by
Tredgold in Professor Barlow's edition.
302
C
EXPERIMENTS BY GEORGE RENNIE.
ANGLES of EQUILIBRIUM at which various substances stand, as taken
with a Clinometer.
Lime dust, as it falls from a spout
Wheat Flour
do.
Malt do.
do.
Saw Dust
do.
Dry Sand
do.
Ditto, less dry
do.
Wheat Corn, unground do.
Malt do.
do.
do.
Common Mould
Peas
Wet Thames Gravel
Dry Quick Sand from River Thames
Wet
do.
do.
Coarse Gravel Heaps
Common Gravel
Large Flints
Ditto, half the size
Ditto, approaching to sand
do.
do.
Degrees.
45
44
. 40
44
. 40
. 39.16
. 37
37
37
..35
35 to 36
35
. 40
35 to 38
. 35 to 36
40 to 45
35
34 to 35
:

n
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1.5
w
Ir!
40
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6.2
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40
1:1
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to to
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47/x
B
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40
T'S
f
3
1
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1
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6.2
C
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/
3
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15'. 0"..
Fig.14.
40
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:
1
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6.2
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32
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Fig. 7.
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Fig.16.
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Published by Atchley & C° 106 Gt Russell Street, London. April 1857.
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Published by Atchley & Co 106 Gt Russell Street, London. April. 1857.
Fig. 5.
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16
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N
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J.R.Jobbins.
FIG. 11.

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PERMANENT WAY, FORMATION, DRAINS, ETC.
303
CHAPTER X.
PERMANENT WAY, FORMATION, DRAINS, BALLASTING,
LEVELS OF RAILS.
CONNECTED with the permanent way, the four subjects in the heading
of this chapter, come into primary and most important consideration ;
the railways now constructed vary, for the width of formation, from
28 to 31 feet generally; and in order to effect a perfect drainage of this
formation, it is necessary that the centre of the line should be higher
than the sides, and this increase of height varies from 3 to 6 inches;
the heavy traffic occasioned by earthworks will render it very difficult
to maintain this ridge, if the seat of the ballasting is at once formed to
this height; and, as an efficient drainage is indispensable, it is better to
leave a small depth of excess of excavation, and to make the formation
to its proper levels, immediately before the ballast is laid; this subject
will be found to deserve more serious attention than might at first
sight be afforded to it, for if this "formation" be not constructed so as
to effect thoroughly the passage of waters into the "sidings," or side
drains, whatever trouble may be devoted to the maintenance of the
permanent way, will be comparatively lost, as well as the expense
attending it, and this latter very serious consideration will be exactly
in the proportion of neglect with which the permanent way is first
constructed; the Engineer should therefore give strict injunctions to
his inspectors to attend carefully to this, and should direct his personal
attention to it as much as possible. Sub-contractors, to whom the
earthworks are entrusted, will be generally found perfectly indifferent
on this subject, as when once the ballasting is laid there are no means
of detecting slovenly work without taking it up again.
Sidings, or side-drains, form the next subject of consideration. In
a hard solid substance, or in rock, and more especially where great
economy is at first to be of paramount importance, a good ditch may be
304
PERMANENT WAY, FORMATION, DRAINS,
PA
}
cut, with slopes battering in the same ratio as the slopes of the cuttings,
but where the stratification is of a softer nature, where the excavation
is deep, if not in rock, or where the slopes are liable to deterioration,
from atmospheric effects, from rains, soaks, springs, or from the
numerous injuries to which they are constantly liable, it is necessary,
in order to preserve a free and uninterrupted passage for the waters
and debris which accumulate at the foot of the cutting, that side-drains
of rough masonry or brickwork be constructed, and these of sufficient
capacity, by depth and width, to answer the purpose intended. In
passing through marshy soils this capacity will require to be increased,
often considerably, and transverse covered drains leading from the
higher to the lower side of the way, will also be requisite; as, compa-
ratively speaking, the drains have but little strain to resist, they may
be constructed at the least possible cost-rough unhewn stones are all
that is required, and these not of large scantling; of course, we are not
now alluding to drains which are constructed across the formation for
carrying off surface water, accumulating in ditches, and penned up,
which must be disposed of, often by carrying it over the line to a lower
level; specimens of these will be found amongst the examples of drains
and culverts; and Figs. 1, 2, 3, 4, and 5 represent various kinds of
permanent ways.
chess
why
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FIG. 1.

FIG. 2.
ESNEKANA
AUR
20/0
Awaltelli
Sm
196
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The formation having been levelled to the degree of convexity
required, the next operation is the ballasting, which is to form the
20
BALLASTING, LEVELS OF RAILS.
305
foundation for the sleepers, and which must be of such a nature as to
allow water to percolate with the greatest freedom, in order that this
FIG. 3.
Musby Ground
Dry Filling.
A
FIG. 4.
FIG. 5.



Dry Filling
Leat
Peat
foundation be kept perfectly dry, or not only the sleepers will decay, but
they, and consequently the rails, will be in considerable state of motion
at the passage of every train, from a portion of the ballast being reduced
to a soft muddy state. The best ballasting consists of hard broken
stone, but it is expensive; good dry gravel forms excellent ballasting,
and where found in excavations, should, as much as possible, be
306
PERMANENT WAY, FORMATION, DRAINS,
preserved for this purpose; sand, mixed with broken stone, is equally
good. Where these cannot be obtained, we may be satisfied with good
clean cinders, or slag, which also answer the purpose very effectively;
where none of these can be obtained, we may use hard shale, well burnt,
for the upper coating of ballast, though it is rather liable to cake, but
much less, however, than burnt clay, which we have seen used for this
purpose; even the last may be improved by an admixture of sand before
burning. Whether broken stone or gravel be used, care should be
taken that all stones larger than an egg be broken up, and more
particularly for the following reason: should a large stone be placed
under a sleeper, and have an uncertain bearing, or present an angle to
the underside of a sleeper, it will act like a pivot for this latter to move
upon, and at least injure considerably the stability of the rails at this
point, if it does no more. The ballasting will require to be at least 12
inches deep; it should be well levelled and well packed, and any means
that could be used to force it down to a more solid bed would be a great
improvement, as it would tend to lessen the subsidence which ensues
from the first few trains passing over the line; the traffic, however,
which is necessary for completing the works, will tend greatly to
effect this.
On this first bed of ballasting the sleepers are laid; these are
generally of larch fir; they should be sound, free from shakes or signs
of decay, straight, and of good form, as also of the scantlings specified
by the specification, which are generally 8' or 9' x 9" or 10″ × 5″;
besides these, there are the sleepers for the "joint chairs," which should
be 12″ wide and squared; these sleepers should be carefully examined
and measured, as delivered by the Contractor, and all inferior ones
rejected. A broad notch or bed is cut on the upper side of the sleeper
for the seat of the chair; and, as one end of the sleeper will often be
thicker than the other, in consequence of the timber being unsquared,
this stouter end should, on curves, be placed under the outside rail;
attention should be given, that the beds cut for the reception of the
chair be of full size to afford a sufficient seat, and also that the bed be
perfectly flat; on this seat the chairs are fitted, as soon as the sleepers
have been approximatively placed in their places along the line, and the
rails placed in the chairs; the plate layers then commence setting out
BALLASTING, LEVELS OF RAIĻS.
307
the straight lines and curves with reference to the stumps and bed
moulds set out or checked by the Engineer, to which subject we will
return presently, and gradually, by means of boning and guaging, which
is done by means of a standard, measuring exactly the difference between
the rails, the rails are brought to their true position; this being done,
holes are driven in the sleepers for the reception of the spikes on one
side, at each end of every length of rail, and next on the other side, the
greatest care being used to have the guage constantly applied, and the
spikes are driven; a piece of felt is often introduced between the chair
and the sleeper, but vulcanized india-rubber will be found very superior,
the india-rubber occupying a space equal to the seat of the chair, and
the spikes being driven through it; the elastic nature of this substance
tending materially to soften the shock which the wheels meet with as
they successively cross each sleeper, and diminishing the effect of the
vertical motion which the spike must experience in a greater or less
degree in the sleeper. The position of the sleeper, chair, and rail
is then permanently fixed, by the operation of what is termed boxing
up, which is fixing under each sleeper about an inch, more or less, of a
finer description of ballasting, consisting of fine gravel or good sand; by
these means the rail is fixed permanently and correctly, both as regards
the horizontal direction or centre line, and the levels of the gradient.
Ballasting should then be filled up to the upper side of the sleeper.
The guage commonly used by plate layers is an iron rod, of the
shape shown at Fig. 6; the distance between A and B, being the
FIG. 6.
AL
measure from rail to rail, but it meets with so much rough usage, and
is so often bent and straightened again, if the men will take so much
FIG. 7.
B

trouble, that it cannot be depended upon. Fig. 7 shows one of a
superior kind, which should be made of a piece of hard, well-seasoned
3
308
PERMANENT WAY, FORMATION, DRAINS,
wood, and, if varnished, will be less affected by damp; at A, there is a
spirit level, by which the transverse level of the rails may be ascer-
tained; inspectors should be supplied with such a guage, and with it,
check with care the work of the plate layers.
We have alluded to the centre line having to be set out a second,
and often a third and fourth time, in excavations and embankments,
and unless the Engineer, where he has to do this work, takes proper
precautions, he will find it an endless work, or the Contractor will
most likely commit great errors. By referring to the chapters on
earthwork and setting out, the reader will find some advice on this
subject, and we will here add some further instructions, by following
which the work will be found much lessened, enabling therefore the
professional man to attend to other matters requiring his attention.
Where the tangents or straight lines are of any length, marks are always
set up out of the works, by which, of course, this straight line of centre
can always be found; and, by knowing from the section at what
distance on this line the curve was commenced, this point may at any
time be found also, and the curve set out; but on curves of 50 or 60
chains, or where these are numerous, we have pursued the following
plan, by which, at any time, we could find exactly the original site of
centre stumps; Fig. 8 will assist the explanation. Let A B be the
d
À
e.
d
FIG. 8.
•g
b
•h
B
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curve, with the stumps shown by black dots; the straight lines between
these are of course chords; take any two of these stumps-say a b,
produce the line out beyond the edge of the cutting, as at dc, where
drive in a couple of stumps likely to remain; at right angles to this
BALLASTING, LEVELS OF RAILS.
309
line, and in line with a, sight out e a f, and drive in permanent stumps
at each of these also; do the same thing at gb h, and make a note on
the section book for reference hereafter; now at any future time, by
sighting out these lines with accuracy, we find the exact position of a
and 6, by which we may set out the curve; we do this in one or two
places, generally along a curve; by these means there is no difficulty
either in re-setting out or checking; in the outset this may appear
rather long and tedious, but where a cutting of 30 feet or 40 feet deep
is being excavated, and the centres are to be found, it will afford a very
ready way at any time to obtain them; this, and the simple method
already shown, will prevent all difficulties and loss of time; care must
be taken in setting out the permanent centres of an embankment, that
we pass through the centres of bridges and culverts; stumps at every
chain length must be carefully and firmly driven into the top of the
embankment or bottom of the cutting; by these stumps the position of
the rails is fixed, and therefore, the straightness of the line where
straight, and where otherwise, and the regularity of curve, depend on
the position of these stumps.
The levels connected with the height of the permanent rails require
the utmost nicety in the operation of levelling, for although, except in
a few situations, it will be almost impossible, at first, to keep the rails at
the given heights, the bed-moulds remain, if properly fixed, for two or
three years afterwards, for the reference of the plate layers. If the per-
manent way be properly constructed, and these levels accurately set out,
there need not be at any time, after consolidation, any deviation from
the correct height. In cuttings, the bed-moulds,* with very few
exceptions, will remain at the heights to which they are driven at first,
but not so in embankments, on account of the settlement of this latter
construction; but even here we shall have the bridges, on which the
height of rails may be fixed with the utmost accuracy. Having pro-
vided sufficient bed-moulds, commence from a P.P., or B.M., of the
correct height of which there can be no possible doubt, and level from
this to the temporary rails, or any convenient object at a stump or
chain's length, and ascertain the difference of level, and, therefore,
* A bed-mould is a stake of about 2′ × 3" x 3".
310
PERMANENT WAY, FORMATION, DRAINS,
the height of the second object levelled to with regard to datum, and
consequently to formation, as the height we require above datum at
this point will be obtained from the section; say, for instance, that
the height of the P.P. is 302 46 above datum, and the difference
of level between this height and that of the temporary rail or other
object levelled to is 23.10 lower; then we shall have 279.36 for
the height above datum at this point; now refer to your pocket
section, and in doing so be careful of two things:-first, that you
do not mistake one chain stump for another, which would occasion
one great error, and secondly, do not mistake formation for rail height;
to practical men these two last hints may appear puerile, but we do
not profess to write for these; the young practitioner, on the contrary,
from the extreme facility with which either of these errors may be
committed, is very likely to fall into them. To continue, we have
found the height 279.36, and we carefully ascertain that this is at
5 miles 7 chains, where the formation height is 277.06 by the
pocket section; but formation is 2:00 below the level of rails at
every stump; then 277-06 + 200 279'06, which latter is to be rail
height at this point; but 279.36 — 279.06 = 30, therefore, 279.36 is 30
too high, because it is 30 further from datum than 279.06, which is the
correct height, and, consequently, we must have the top of our bed-mould
30 lower than 279.36; we trust this is sufficiently plain. Now, let the
staff be still at 279-36, read off, and see that you read the same height as
before, say 4.20; since it is 30 too high, if we could read off 4.50, the
levelling staff would then be standing on some object at the correct height
of rail, for 4.50 — 4·20
- 4.2030
·30 fall, and 279·36 — ·30 =
30 279.06, which is
rail height; we have, therefore, nothing to do but to drive in a bed-
mould, until the levelling staff being placed upon it, we read off 4·50,
when we shall have rail height at 5 miles 7 chains. We must now
continue driving in these bed-moulds at intervals, a certain number of
chains apart, up or down the line. On a level we should have but to
plant the level midway between the first bed-mould, and the chain
stump where the second would have to be driven; read off the staff on
the first bed-mould, say 4.50; then driving in a bed-mould at any point
along the intended level, until we read off 4:50 again; we should have a
=
-
BALLASTING, LEVELS OF RAILS.
311
·
second bed-mould level with the first, since 4.50 4.50 0.00, or no
difference of level. But say we are going down the line, and that our
gradient is 1 in 150 or 44 per chain; as we are going down we shall
have to drive our bed-moulds lower than the last by a height of 44 ×
the number of chains further on at which the next bed-mould is driven,
that is for 1 chain 44 lower, for 2 chains 44 x 288 lower, 3 chains
44 × 3 = 1.32 lower, and so on; setting out the levels along a straight
line, it will be sufficient, if the bed-moulds be driven at 4 or 5 chains
apart; but on a curve they should not be farther apart thaản 2 or 3
chains' length, and it will be found more likely to keep the work of the
plate layers correct, if these heights be driven on one side and the other
of the line alternately; supposing that we are now setting out the
levels on a straight line and falling gradient, and at 5 chains apart, we
should first plant the level about half-way, the staff remaining on the
bed-mould 279-06; now 44 x 52.20; then at 5 miles 12 chains,
×
rail height will be 2.20 lower than 279 06 or 276 86. Read off the
staff, say 4.80, and then let it be taken down to the bed-mould at 5
miles 12 chains; since the rails at this stump should be 2.20 lower
than at the former stump, we shall have to add this depth to the last
reading of 4.80; and this + 2.20 7.00; and the bed-mould must be
driven until we read off correctly this second reading; for B. S. 7·00 –
F. S. 4·80 = 2.20 fall, and as above, 279.06 2.20 276.86 from
datum. Let us now suppose we are going up the gradient, instead of
adding 44 × 5, we should have to deduct it from the reading required
on the bed-mould, at 5 chains higher up the line, since this would be
·44 × 5 = 2·20 farther from datum since it is a rise; then having again
planted the level midway to obtain this rise, read off the staff on bed-
mould 279.06, say 5·43, then 5·43 — 2·20 = 3·23, which is the reading
we shall require at 5 miles 2 chains; and the bed-mould must be driven
until we have this reading, when the staff is held upon it; for B. S. 5·43
- F. S. 3.23 2.20 rise gradient upon 5 chains, and 279.06 + 2·20
(since we are rising, and, therefore, getting further from datum)=
281.26. On a descending gradient, therefore, the difference of levels
for a certain number of chains must be added to the back sight; and on
a rising gradient this quantity must be deducted from the back sight;
Gagging
=
312
PERMANENT WAY, FORMATION, DRAINS,
in the first case, therefore, it is always +, in the second always - If
we have been minute in explaining this, it is because we have once or
twice found it rather unintelligible at first to beginners, who are apt in
setting out to confuse the datum line with that which corresponds to the
axis of the telescope of the level. Having set out two bed-moulds, we
proceed in the same way if we require a hundred, and we will, there-
fore, only add the farther recommendation, of planting the instrument
about halfway between all the stations; and this more particularly
to avoid the error consequent upon any want of adjustment in the
level, and further, the most indispensable condition, that having set out
the last bed-mould required, we must produce the levels on to the
nearest B.M. for a check on the work, or we can have no assurance of
the accuracy of the levels. On checking up to the B.M., of course the
last height obtained must be that recorded on the pocket section for
the height of the B.M.; any difference found will be so much error.
Proceeding, for instance, as before, suppose we have set out 65 chains
of levels, then 44 × 65 2860, and if we are descending 279 06 –
28.60 250 46 at 5 miles 72 chains; and on levelling up to the B.M.,
which suppose 262.50 we must find a rise of 12.04 between the last
bed-mould set out, and the B.M., because all the levels refer to "Datum"
as well as to "formation height," and "rail height," and from the first
of which the two latter are originally deduced. In conclusion on this
subject, we will add that these bed-moulds should be driven so firmly
into the ground that intentional violence will alone disturb them, and
that they should be so placed as to be out of the way of horses' feet
and waggon wheels.
·
=
On account of the tendency which carriages have to pursue a
straight course when moving along curves, it is necessary to raise the
outer rail, in order to counteract this effort; in the following table will
be found the minima quantities usually allowed for this; for a full
consideration of the subject, we refer the reader to Wood's Treatise on
Railroads, Chap. IV., § 15.
BALLASTING, LEVELS OF RAILS.
313
Radius of Curve in Chains.
10
20 =
14
30 = 9/90
40
60 = $
80 = 1
mile.
""
""
""
""
د.
Rise in Inches.
2.00
1.07
0.71
0.53
0.35
0.25
This difference of level between the two rails on curves is given by
depressing the inner rail, and raising the outer rail one-half the
quantity of difference required.
Professor Barlow, in his Treatise on the Strength of Materials,
speaking of the Manchester and Liverpool railway, says, "I am
disposed to estimate that about one in six of the plain butt joints is as
perfect as can well be desired, and that another one in six is as bad as
bad workmanship and negligence can make it; the remaining two-
thirds varying in character between these two extremes;" this remark,
made some ten or twelve years ago, may, we believe, with perfect
justice be applied to almost every railway constructed; by experiments
then made, Professor Barlow found that the deflection of the rail on a
bad joint was nearly 50 per cent. greater than on a good one; the
writer of these pages has repeatedly noticed one rail to be one-quarter
and nearly one-half inch higher than that at the end of it. What
must be the concussion of a 20 ton locomotive going over such an
obstruction at 30 or 40 miles an hour? Again, the joints are often nearly
an inch wide, where they should not be one-eighth of this width, and
the crushing of the rail at such a joint will be shown by the lamination
after a year's wear. These immense defects result solely from "bad
workmanship and negligence;" and the Engineer in charge of the
construction of a railway should, by the utmost attention on his part,
as well as on that of his inspector, discountenance such shameful
practice. It will be found that plate-layers, when once trained to a
better kind of workmanship, will get on as well with it as with bad,
and the wear and tear of stock, as well as the much less liability to
accident, will amply repay this trouble. The utmost width of joint
Y
314
PERMANENT WAY, FORMATION, DRAINS, ETC.
which should be allowed when the rails are laid in cold weather, is one-
eighth, and in warm weather, one-sixteenth; this, of course, as closely
as can be obtained in practice, for with our utmost care we cannot
obtain perfection. Where the curves are sharp or numerous on a
line of railway, a certain proportion of the lengths of rails should be
made of an increased length to allow for the greater development of
the curve at the outer rail.
By referring back to the articles in this chapter, the reader will
observe, that the perfection of the permanent way consists in the con-
struction of the formation, and an efficient drainage of the same; the
quality of the ballasting and the manner in which it is employed; the
seating of the sleepers and chairs, and the fixing of the rails; the
straightness of the line, or the regularity of the curve; the correctness
of the levels; the fitting of the butting joints, and the transverse
levels of the rails. It will be seen at once, and the more by greater
consideration, that the soundness of the permanent way depends, as
a whole, upon a number of minutiæ, and the expense of its maintenance,
as well as its efficiency, will be exactly in proportion to the degree of
attention given to each and all of these details being practically
carried out.
315
One in
10
11
12
13
14
15
16
17
∞ ∞ ∞
18
przed przed
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
Rise per Chain
in feet.
6.6
6.
5.5
TABLE V.-GRADIENTS.
5'0769
4.7144
4.4
4.1243
3.8823
3.6
3.4736
3.3
3.1427
3.
2.8687
2.7499
2.64
2.5384
2.4437
2.3562
2.2757
2.2
2.1290
2.0625
2.
1.9411
1.8854
1.8333
1.7837
1.7367
1.6923
1.65
1.6097
1.5714
1.5348
1.5
1.4666
1.4347
1·4042
1.375
1.3469
Rise per Furlong
in feet.
66.
60'
55*
50.76
47.14
44.
41.24
38.82
36.
34.73
33.
31.42
30°
28.68
27.49
26.40
25.38
24.43
23.56
22.75
22.
21.29
20.62
20.
19.41
18.85
18.33
17.83
17.36
16.92
16.50
16.09
15.71
15.34
15.
14.66
14.34
14.04
13.75
13.46
Rise
per
in feet.
528'
480.
440°
Mile
406.15
377.14
352'
330'
310.58
288.88
277.89
264*
251*42
240'
229.56
220*
211.20
203.07
195'55
188.57
182.06
176'
170.32
165*
160**
155.29
150 85
146.66
142.70
138.94
135.38
132'
128.78
125.71
122.79
120°
117.33
114.80
112.34
110.
107.75
One in
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
Y 2
316
One in
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
Rise
TABLE OF GRADIENTS.-Continued.
Chain
per
in feet.
1.32
1.2941
1.2692
1.2452
1.2222
1.22
1.1785
1.1578
1.1379
1.1186
1.1
1.0819
1.0645
1.0476
1.0312
1.0152
1.
•9850
•9705
•9565
•9428
•9295
•9166
•9041
•8918
*88*
⚫8684
*8571
•8461
⚫8354
•825
•8148
•8048
*7951
•7857
•7764
•7674
•7586
•75
7415
Rise per Furlong
in feet.
13.20
12.94
12.69
12.45
12.22
12.2
11.78
11:57
11.37
11.18
11.
10.81
10.64
10.47
10.31
10.15
10°
9.85
9.70
9.56
9.42
9.29
9.16
9.04
8.91
8.80
8.68
8.57
8.46
8.35
8.25
8.14
8.04
7.95
7.85
7.76
7.67
7.58
77.5
7.41
Rise
Mile
per
in feet.
105.60
103.52
101.53
99.62
97.77
96.
94.28
92.63
91.37
89.49
88.
.86.55
85.16
83.80
82.50
81.23
80'
78.80
77.64
76.52
75.42
74.36
73.33
72.32
71.35
70.40
69.47
68.57
67.69
66.83
66.
65.18
64.39
63.61
62.85
62.11
61.39
60.69
60.
59.32
One in
50
51
52
53
54
55
56
57
58
59
60
61
62
63
· 64
65
66
67
68
69
70
71
72
73
74
75
76
777
78
79
80
81
82
83
84
85
86
87
88
89
317
One in
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119.
120
121
122
123
124
125
126
127
128
129
Rise per Chain
in feet.
TABLE OF GRADIENTS.-Continued.


*7333
⚫7252
7173
7096
⚫7021
*6947
*6875
'6804
*6734
'6666
'66
*6534
*6470
*6411
*6346
•6285
•6226
6168
•6111
·6055
•
.6
*5945
*5892
•5840
*5789
*5739
:5689
*5641
*5593
*5546
*55
*5454
*5409
*5365
*5322
*528
*5238
*5197
5156
•5116
·
Rise per Furlong
in feet.
7.33
7.25
7.17
7.09
7.02
6.94
6.87
6.80
6.73
6.66
6.60
6.53
6.47
6.41
6.34
6.28
6.22
6.16
6.11
6.05
6°
5.94
5.89
5.84
5.78
5.73
5.68
5.64
5*59
5.51
5.50
5:45
5*40
5.36
5.32
5.28
5.23
5.19
5.15
5.11
Rise per Mile
in feet.
58.66
58.02
57.38
56.77
56.16
55.57
55*
54.43
53.87
53.33
52.80
52.27
51.72
51.26
50.77
50.28
49.81
49.34
48.88
48.44
48°
47.56
47.14
46.72
46.31
45.91
45.51
45.12
44.74
44.37
44°
43.63
43.27
42.92
42.58
42.25
41.92
41.57
41.24
40.92
One in
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
318
One in
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
Rise per Chain
in feet.
TABLE OF GRADIENTS.-Continued.

*5077
*5038
*5
*4963
*4925
*4888
*4852
*4817
*4782
4748
*4714
*4680
*4647
*4615
*4583
•4552
*4520
*4489
*4459
*4429
•44
*4370
*4342
*4312
*4285
*4258
4231
•4204
4178
4152
•
*4126
•4100
*4075
*4049
*4024
*4
*3975
*3952
*3928
·3905
Rise per Furlong
in feet.
5.07
5.03
5'
4'96
4.92
4.88
4.85
4.81
4.78
4.74
4.71
4.68
4.64
4.61
4.58
4.55
4.52
4.48
4.45
4.42
4.40
4.37
4.34
4.31
4.28
425
4.23
4.20
4.17
4.15
4.12
4.10
4.07
4.04
4.02
4*
3.97
3.95
3.92
3.90
Mile
Rise per
in feet.
40'60
40.29
40'
39.70
39'40
39.10
38.81
38.53
38.26
37.98
37.71
37.44
37.16
36.88
36.66
36.42
36.17
35.91
35.66
35.41
35.20
34.96
34.72
34.47
34.28
34.06
33.84
33.62
33.40
33.20
33°
32.79
32.58
32.38
32.18
32.
31.81
31.62
31.43
31.24
One in
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
319
One in
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
TABLE OF GRADIENTS.-Continued.

Rise per chain in
feet.
*3882
*3859
*3836
*3813
*3793
*3770
*3748
*3726
*3705
*3687
*3666
*3646
*3626
*3606
*3586
*3568
*3548
*3529
*3510
*3491
*3473
*3455
*3437
*3419
*3402
*3385
*3368
*3351
•3333
'3316
*33
3284
*3267
*3251
*3235
•3219
*3203
*3187
•3172
•3157
Rise per Furlong
in feet.
3.88
3.86
3.83
3.81
3.79
3.77
3.74
3.72
3.70
3.68
3.66
3.64
3.62
3.60
3.58
3.56
3.54
3.52
3.51
3.49
3.17
3.45
3.43
3.41
3.40
3.38
3.36
3.35
3.33
3.31
3.30
3.28
3.26
3.25
3.23
3.21
3.20
3.18
3.17
3.15
Rise
Mile
per
in feet.
31.05
30.86
30.68
30.51
30:33
30:17
30'
29.83
29.66
29.49
29.33
29.17
29.01
28.85
28.69
28.53
28.37-
28.22
28.07
27.93
27.78
27.64
27.50
27.36
27.22
27.08
26.94
26.80
26.66
26.53
26.40
26.27
26.14
26.01
25.88
25.75
25.62
25.50
25.38
25.26
One in
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
320
One in
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
`214
245
246
247
248
249
Rise per Chain
in feet.
TABLE OF GRADIENTS.-Continued.
•3142
*3127
3113
*3098
•3084
•3069
3055
•3040
•3026
•3013
•
3000
•2986
•2972
*2959
•2946
•2932
•2920
•2907
·2894
•2882
•2869
2856
•2844
•2831
•2819
•2807
*2796
•2784
•2772
•2761
2750
•2738
•2727
2715
2704
*2693
•2682
*2673
2661
2650
Rise per Furlong
in feet.
3.14
3.12
3.11
3.09
3.08
3.06
3.05
3.04
3.02
3.01
3.
2.98
2.97
2.95
2.94
2.93
2.92
2.90
2.89
2.88
2.86
2.85
2.84
2.83
2.81
2.80
2.79
2.78
2.77
2.76
2.75
2.73
2.72
2.71
2.70
2.69
2.68
2.67
2.66
2.65
Rise per Mile
in feet.
25.14
25.02
24.90
24.78
24.66
24.55
24.43
24.32
24.21
24.10
24°
23.90
23.79
23.69
23.58
23.47
23.36
23.26
23.16
23.05
22.95
22.85
22.75
22.65
22.56
22.47
22.37
22.27
22.18
22.09
22.
21.90
21.88
21.77
21.66
21.55
21.46
21.37
21.28
21.20
One in
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
23£
235
236
237
238
239
240
241
242
243
214
245
246
247
248
249
321
1
One in
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
TABLE OF GRADIENTS.-Continued.

Rise per Chain
in feet.
*2640
*2629
•2618
*2609
*2598
2588
*2577
*2567
2559
•2548
2538
*2528
*2519
*2510
•2501
2492
2483
*2475
2466
2453
•2444
2435
*2426
*2417
*2408
*2399
•2390
•2381
*2372
*2363
*2357
2348
*2339
2331
*2323
*2315
*2307
•2299
*2291
2283
Rise per Furlong
in feet.
2.64
2.62
2.61
2.60
2.59
2.58
2.57
2.56
2.55
2.54
2.53
2.52
2.519
2.510
2.50
2.49
2.48
2:47
2.46
2.45
2.44
2.43
2.42
2.41
2:40
2.399
2.390
2.381
2.37
2.36
2.35
2.34
2.339
2.331
2.32
2.31
2:30
2.299
2.291
2.28
Rise per Mile
in feet.
21.12
21.04
20.96
20.87
20.79
20.71
20.63
20.54
20.45
20.38
20.30
20.23
20.15
20.07
19.99
19'92
19.84
19.77
19.70
19.63
19'55
19.48
19.41
19.34
19.27
19°20
19.13
19.06
18.99
18.92
18'85
18.78
18.72
18.66
18.59
18.53
18.44
18.38
18.32
18.26
One in
250
251
252
253
254
255
256
257
258
259
260
261
262
263
261
265
266
267
268
269
270
271
272
273
271
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
322
}
One in
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
TABLE OF GRADIENTS.-Continued.
Rise per Chain
in feet.
*2275
•2268
'2260
•2252
•2244
**2237
*2229
•2222
*2214
*2207
•22
*2192
•2185
•2178
•2171
2164
•2157
•2150
•2143
•2136
•2129
*2123
2116
*2109
*2102
•2095
•2088
•2081
•2074
*2068
•2062
*2055
*2049
•2012
•2036
'2030
*2024
2018
*2012
•2006
•2
Rise per Furlong
in feet.
2.27
2.268
2.260
2.25
2.24
2.23
2.229
2.222
2.21
2.207
2.2
2.19
2.18
2.178
2.171
2.16
2.157
2.15
2.14
2.13
2.129
2.12
2.11
2.109
2.10
2.09
2.088
2.08
2.07
2.068
2.06
2.05
2.049
2.04
2.036
2.03
2.04
2.018
2:01
2.006
2.
Rise per Mile
in feet.
18.20
18.14
18.08
18.02
17.96
17.90
17.84
17.78
17.72
17.66
17.60
17.54
17.48
17.42
17.36
17.30
17.24
17.19
17.13
17.08
17.03
16.97
16.92
16.87
16.81
16.76
16.71
16.66
16.61
16.56
16.50
16.45
16.39
16.34
16.28
16.22
16.18
16.13
16.09
16.04
16'
One in
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
323
TABLE VI.
EXPLANATION OF TABLES.
[L
THE following tables are not intended to be applied in the same way as
Macneill's Tables; they are for the purpose of shortening the calcula-
tions of areas of cross sections, taken at chain stumps. The two cross
sections below will at once explain this. Draw a b parallel to c d, the
formation, scale ef, gh, and at base 30, slopes 1 to 1; opposite the
C
A.
21.75
A.
FIG. 1.

FIG. 2.

g|l5.75
depths we have the areas of A and A, leaving but the triangle and
trapezium to measure by the usual means. The tables are calculated
for Base 17, 20, 28, 30, and 31, and for slopes from 1 to 1 to 3 to 1.
324
Depths.
1.00
2.00
3:00
4.00
1 to 1.
4
17.25
35.00
53.25
72.00
9.00
½ to 1.
17.50
36.00
13.00
13.25
13.50
13.75
55.50
76.00
BASE 17.-Sectional Areas in Feet.
3
4
to 1.
5.00
91.25
97.50
103.75
6.00
120.00 129.00
111·00
7.00 131.25 143.50 155.75
8.00
17.75
37.00
57.75
80.00
10.00
173.25 193.50 213.75
195.00 220.00 245.00
11.00 217.25 247.50 277.75
1 to 1.
18.00
38.00
60.00
84.00
110.00 122.50
138.00
156.00
168.00
192.50
152.00 168.00 184.00 200.00
232.00
1 to 1.
18.50
40.00
64.50
94.00
263.25 305.50 347.75 390.00
400.81
411·74
422.81
14.00
14-25
269.10 312.96 356.92
275.06 320.62 366-18
280.91 328.28 375.55
287.00 336.00 385.00 434.00
293.01 343.78 394.55 445.31
14.50 239.06 351.62 404.19 456.75
14.75 305.03 359.48 413.85 467.21
15.00 311.25 367.50 427.75 480.00
15.25 317.38 375.51 433.67 491.81
15.50 323.56 383.62 443.69 503-75
15.75 329.76 391.78
234.00
274.50 315.00
270.00 320.00 370.00
308.00 368.50 429.00
12.00 240.00 276.00 301·00 348.00 420.00 492.00
2 to 1.
19.00
42.00
532.00
546.84
561.88
576.94
69.00
100.00
135.00
174.00
217.00
264.00
474.50
559.00
488.59
576.37
502.86 593.98
517.34
611.87
630.00
648.37
667.00
685.87
2 to 1.
19.50
44.00
73.50
108.00
147.50
160.00
192.00 210.00
241.50
296.00
3 to 1. Depths.
20.00
46.00
78.00
116.00
643.50
664.08
685.10
706-40
355.50
396.00
420.00 470.00
489.90
550.00
564.00 636.00
266.00
328.00
592.50 705.00
608.09 724.37
623.88 744.00 864.12
453.80 515.81 639.84 763.87
887.90
1.00
2.00
3:00
4.00
5.00
6.00
7:00
8.00
817.50 930.00
840.63 956.93
984.25
1011.93
9.00
10:00
11.00
12.00
728.00 13'00
751.93 13.25
776.22 13.50
800.93 13.75
788.00
826.00 14.00
749.90 851.43 14.25
772.12 877.25 14.50
793.60 903.13 14.75
15.00
15.25
15.50
15.75


325
Depths.
16.00
16.25
16.50
16.75
17'00
17.25
17.50
17.75
to 1.
4 to 1.
400.00
464.00
336.00
342.26
528.00
540.31
408.28
474.30
348.56 416.62 484.69 552.75
354.88 424.91
495.17 565.31
BASE 17.-Sectional Areas in Feet.
361.25 433.50
367.63 441.91
374.00 450.62
380.51
to 1.
1½ to 1.
656.00 784.00
672.34 804.37
688.88 825.00
705.59 845.87
505.75 578.00 722.50
516.39 590.77 739.53
527.19
459.27 538.05
603.75 756.88
616.81
774.34
468.00 549.00
470.78 560.04
485.62 571.19
494.50
582.37
1 to 1.
21.00 467.25 577.50 687.75
21.25 474·14
21.50 480.74
587.03 699.92
596.62 712-18
21.75
488-01 606.28 724.22
630.00
643.31
656.75
670.25
18.00 387.00
18.25 393.51
18.50 400.06
18.75
406.62
19.00 413.25 503.50 593.70 684.00
19.25 419.89 512.53 605.17 697.81
19.50 426.56 521.62 616.69 711.75
19.75 433.26 530.78 628.30
440.00
446.76
20.50 453.56 558.62
20.75 460.38 568.01
20.00
20.25
725.81
540.00 640.00 740.00
549.28 652.80 754.31
663.69
675.67
2 to 1.
2 to 1.
912.00
936.40
961.12
986.13
Depths.
1040·00
16.00
1068.43
16.25
1097.25 16.50
1126·43 16.75
3 to 1.
867.00 1011.50 1156.00 17.00
888.64 1037.40 1185.81 17.25
910.00 1062.12 1216.25 17.50
931-87 1089.39 1246.93 17.75
18.25
18.50
1197.50 1373.25
18.75
792.00 954.00 1116·00 1278.00 18.00
809.84 976.37 1142.90 1309.43
827.88 998.00 1170·12 1341.25
846.00 1021.75
864.50 1045.00
883·09 1068.37
901.88 1092·00
920.84 1115-87
1225.50 1406.00
1253.65 1438.93
1281 121471.25
1310·90 1505.93
19'00
19.25
19.50
19.75
20.00
940.00 1140·00 1340.00 1540.00
959.34 1164-37 1369.40 1574-43 20.25
768.75 978.88 1189.00 1398.12 1509.25 20.50
783.31 998.59 1213.87 1429.13 1644-43 20.75
798.00 1018.50 1239.00 1459.50 1680.00
812.81 1038.59 1264-37 1490·15 1715.93
827.75
1521.12 1752.25 21.50
842.81
1552·40 1788.93 21.75
21.00
21.25
1058.88 1290.00
1079.29 1315.87

326
Depths.
22.00
22.25
22.50
22.75
23.00
23.25
23.50
23.75
24.00
24.25
24.50
24.75
4 to 1.
to 1.
495.00
616.00
502.00 625.78
509.00 635.62
516.14 645.53
523.25 655.50
530.37 665.50
537.56 675.62
544.76 685.78
BASE 17.-Sectional Areas in Feet.
2 to 1.
737·00
748.52
762.19
774.92
787.75
800.67
813.69
826.80
1 to 1.
552.00 696.00
559.26 706.28
566.56 716.62 866.69
573.89 727.03 879.92
1 to 1.
2
840.00
984.00
853.30 1000·31
1016-75
1033.31
2 to 1.
858.00 1100.00 1342.00
873.31 1120-79 1368.37
888.75 1141.88 1395.00
904.31 1163.09 1421.87
920.00 1184.50 1449.00
935.75 1206.09 1476.37
951.75 1227-88 1503.00
971.81
1249.84 1531.87
2 to 1.
Depths.
1584.00 1826.00 22.00
1615.90 1863.43 22.25
1648.12 1901-25 22.50
1680.65 1939-43 22.75
1272.00 1560.00
1294·34 | 1588.37
1316.88
1339.00
3 to 1.
1713.50 1978.00 23.00
1746.62 2016.93 23.25
1780.12 2056.25 23.50
1813.90 2095.93 23.75
1848.00 2136.00
1882-40 2176.43
1617.00 1916.12 2217.25
1645.87 1951.95
2257.43
24.00
24-25
24.50
24.75
25.00 581.25 737.50 893.75 1050.00 1362.50 1675.00 1987 50 2300·00 25.00
25.25 588.64 748.03 907.42 1066.31 1385.50 1704-37 2023.05 2341.93 25.25
25.50 596.06 758.62 921.19 1083.75 1408.88 1734.00 2059.12 2383.25 25.50
25.75 603.31 769.28 934.80 1100.81 1431-79 1763.87 2095*40 2426.93 25.75
26.00 611.00 780.00 949.00 1118.00 1456.00 1794.00 2132.00 2470·00 26.00
26.25 618.51 790.78 963.04 1135.31 1479.84 1824.37 2168.90 2513.43 26.25
26.50 626.06 801.63 977.19 1152.75 1503.87 1855.00 2206-12 2557.25 26.50
26.75 633-44 812.53 991.42 1170-31 1528.09 1885.87 2243.65 2601·43 26.75
27'00 641.25 823.50 1005.75 1188.00
27.25 648.89 834.53 1019.67 1205 51
27.50 656.56 845.62 1034-68 1223.75
27.75 664.26 856.78 1049.29
1241.81
1552.50 1917.00 2281.50 2646.00 27.00
1577.09 1948.37 2319.65 2692.43 27.25
1601-87 1980.00 2358.12 2736.25 27.50
1626.84 2011.87 2396.90 2781.93 27.75
327
Depths.
28.00
28.25
28.50
28.75
to 1.
to 1.
1 to 1.
3 to 1. Depths.
1652.00
868.00 1064.00 1264.00
879-28 1078.79 1278.31 1677-34
890.62 1093.68 1296.75
902-03 1108.67 1315.31
29.00
2044.00 2436·00 2828.00 28.00
2076.37 2475.40 2874-43 28.25
1702-87 2109.00 2515.12 2921.25 28.50
1728.59 2141.87 2555.15 2967.43 28.75
703.25 913.50 1123.75 1334.00 1754.50 2175.00 2595.50 3016·00 29.00
29.25 711·14 924.03 1138.92 1352.81 1780.59 2208.37 2636.15 3063·93 29.25
29.50 719.12 936.62 1156.43 1371.75 1806.87 2243.00 2687.12 3112.25 29.50
29.75 727.01 948.28 1169.54 1390.81 1833.34 2275.87 2718-40 3160.93 29.75
30.00 735.00 960.00 1185.00 1410.00 1860.00 2310.00 2760·00 3210·00 30.00
30.25 743.01 971.78 1200.55 1429.31 1886.84 2344-37 2801.90 3269-43
30.25
30.50 751·12 983.62 1216·19 1444.50 1913.87 2379.00 2843.12 3309.25 30.50
30.75 759.09 995.53 1231.79 1468.31 1940.84 2413.87 2885.40 3358.93 30.75
31.00 767.25 1007·50 1247·25 1488.00 1968.50 2449.00 2929.50 3410:00 31'00
31.25 775.39 1019.53 1263-67 1507.81 1996.09 2484.37 2972.65 3460·93 31.25
31.50 783.56 1031.62 1279:69 1527.75 2023.87 2520.00 3016.12 3512.25 31.50
31.75 791.76 1043-78 1295.80 1547.81 2051.84 2555.87 3059.90 3563.93 31.75
32.00 800.00 1056.00 1312.00 1568.00 2080.00 2592.00 3104.00 3616.00 32.00
32.25 808.26 1068.28 1328.30 1588.31 2108.34 2628.37 3148.40 3668.43 32.25
32.50 816.56 1080.62 1344-68 1608.75 2136.87 2665.00 3193.22 3721.25 32.50
32.75 824.89 1093.00 1360·00 1629.31 2165.09 2701·87 3238.15 3774-43 32.75
33.00 833.25 1105.50 1377.65 1650-00
33.25
841.64 1118.03 1394-42 1670.81
33.50 850.06 1130.62 1411·19 1691.75
33.75 858.51 1143.28 1428.04 1712.81
4
to 1.
BASE 17.-Sectional Areas in Feet.
672.00
679.76
687.56
695.39
1 to 1.
2 to 1.
2 to 1.
2194.50 2739.00 3283.50 3828.00 33.00
2223.59 2776.37 3329.15 3881.93 33.25
2252.88 2814.00 3375.12 3936.25 33.50
2282.34 2851.87 3421·40 3990.93 33.75



328
Depths.
34.00
34.25
34.50
34.75
36.00
36.25
36.50
36.75
1½ to 1.
21 to 1.
Depths.
4046.00
34.00
35.00 901.25 1207.50 1513.75
35.25
35.50
35.75
35.00
35.25
1863.75
1885.81
2493.87 3125.00 3150·62 4386.25 35.50
2524.84 3164.87 3196.15 4441·93 35.75
867.00 1156.00 1445.00 1734.00 2312.00 2890.00 2890.00
875.51 1168.78 1462-04 1755.31 2341.84 2928.37 2932.65 4101·43 34.25
883.06 1181.62 1479.18 1776-75 2371.87 2967.00 2975.62 4157.25 34.50
892.64 1194.53 1496.42 1798.31 2402.09 3005.87 3018.90 4213.43 34.75
1820.00 2432.50 3045.00 3062.50 4270.00
909.39 1220-53 1531·17 1841.81 2463.09 3084.37 3106.40 4326.93
918.56 1234.62 1548.68
926.76 1246·78 1566.29
936.00 1260.00 1584.00 1908.00 2556.00 3204.00 3240.00 4500.00 36.00
944.76 1273.28 1601·79 1930.31 2587.34 3244.37 3285.15 4558.43 36.25
953.56 1286.62 1619.68 1952.75 2618.87 3284.00 3330-62 4617.25
962.39 1300·03 1637.67 1975.31 2650.59 3325.87 3376.40 4676.43
37.00 971.25 1313.50
37.25 980.18 1327.07
37.50
37.75
36.50
36.75
37.00
1655.75 1998.00 2682.50 3367.00 3422.50 4736.00
1673.96 2020.81 2714·63 3408.37 3468.90 4795.93 37.25
989.06 1340.62 1692-18 2043.75 2746.87 3450.00 3515.62 4856.25 37.50
997.76 1353.78 1710.54 2066.81 2779.34 3491-87 3562.65 4916.93 37.75
1007·00 1368.00 1729.00 2090.00 2812.00 3534.00 3610.00 4978.00 38'00
1016.01 1381.78 1747.54 2113.31 2844.84 3576.37 3657.65 5039-43 38.25
1024.56 1395.62 1766.18 2136.75 2877.87 3619.00 3705.62 5101.25 38.50
1034:14 1409.53 1784.80 2160-31 2910.84 3661.87 3753.65 5162.93 38.75
4
to 1.
BASE 17.-Sectional Areas in Feet.
to 1.
4
to 1.
1 to 1.
2 to 1.
3 to 1.
38.00
38.25
38.50
38.75
39.00 1043.25 1423.50 1803.75 2184.00 2944.50 3705.00 3802.50 5226.00
39.25 1052.39 1437.53 1822-42 2207.81 2977.59 3748.37 3851·40 5288.93
39.50 1061.56 1451.62 1841.69 2231.75 3011.87 3792.00 3900.62 5352.25 39.50
39.75 1070-76 1465-78 1860-78 2255.81 3045.84 3835.87 3950.65 5415-03 39.75
39.00
39.25

329

Z
BASE 17.-Sectional Areas in Feet.
Depths.
4 to 1.
to 1.
40.00
1080.00 1483.00 1880.00 2280.00
40.25 1089.26 1494.28 1889.30 2304.31
40.50 1098.56 1508.62 1918.68 2328.75
40.75 1107.89 1523.03 1938.17 2353.31
41'00 1117.25 1537.50 1957.75 2378.00 3218.50 4059.00 4202.50 5740·00 41.00
41.25 1126.64 1552.03 1977-42 2402-81 3253.59 4104-37 4253.90 5805.93 41.25
41.50
1135.06 1566.62 1997.18 2427.75 3288.87 4149.00 4305.62 5872.25 41.50
1145.51 1581.28 2016.80 2452.81 3324.34 4195.87 4357.15 5938.93 41.75
42.00 1155.00 1596.00 2037.00 2478.00 3360.00 4242.00 5124.00 6016-00 42.00
42.25 1164.56 1610.75 2057.04 2503.31 3395.74 4288.37 5180.90 6073-43 42.25
42.50 1174.06 1625.62 2077.18 2528.75
4335.00 5238.12 6141.25 42.50
42.75 1183.63 1640.52 2097.30 2554-30
5295.62 6209.40 42.75
41.75
3431·87
3468-07
4381.87
45.00
45.25
45.50
45.75
3 to 1.
4
1 to 1.
1 to 1.
2 to 1.
3 to 1. Depths.
3080.00 3880.00 4000.00 5480.00 40'00
3114.34 3924.37 4051.15 5544-43 40.25
3148.87 3968.00 4100.62 5609.25 40.50
3183.59 4013.87 4150*40 5674-43 40.75
43'00 1193.25 1655.62 2117.75 2580.00 3504 50 4429.00 5353.50 6278.00 43'00
43.25 1202.89 1670.53 2138.17 2605.81 3541.09 4476.37 5411.65 6346.93 43.25
43.50 1212.56 1685.62 2158.68 2631.75 3577.87 4524.00 5470.12 6416.25 43.50
43.75 1222.26 1700-78 2179.29 2657.81 3614-84 4571-87 5528.90 6485.93 43.75
44.00 1232.00 1716.00 2200.00 2684.00 3652.00 4620.00 5588.00 6556.00 44.00
44.25 1241.71 1731.28 2220.79 2710.31 3689.34 4668.37 5647.40 6626.43 44.25
44.50 1251.56 1746.62 2241.68 2736.75 3726.87 4717.00 5707.12 6697.25 44.50
44.75
1261.39 1762.03 2262.67 2763.31 3764-59 4765.87 5767.15 6768.43 44.75
2 to 1.
1271.25 1775.50 2283.75
1281·14 1743.03 2304.92 2816.81
1291.06 1808.62 2326.18 2843.75
1301.01
1824.28
2347.54
2870.81
2790.00 3802.50 4815.00 5827.50 6840.00 45.00
3840.59 4864-37 5888.15 6911.93 45.25
3878.87
5949.12 6983.25 45.50
3917 34
6010'40
45.75
4914.00
4963-87
•
4963-87 6010
7056.93


330
BASE 17.-Sectional Areas in Feet.
Depths.
to 1.
to 1.
1½ to 1.
2 to 1.
Depths.
6072.00
46'00
to 1.
46.00 1311·00 1840.00 2369.00 2898.00 3956.00 5014.00
7130.00
46.25 1321.01 1855.78 2390.54 2925.31 3994.84 5064.37 6133.90 7203-43 46.25
46.50 1331.06 1871-62 2412-18 2952.75 4033.87 5115·00 | 6195.12 7277.25
46.50
46.75
1341·14 1887.53 2433.92 2980.31 4073.09 5165.87 6268.65 7351.43 46.75
47'00 1351.25 1903.50 2455.75 3008:00 4112.50 5217.00 6321.50 7426.00 47.00
47.25 1361.39 1919.53 2477.67 3035.81 4152.09 5268.37 6384.65 7500.93 47.25
47.50 1371.56 1935.62 2499.68 3063.75 4191.87 5320.00 6448-12 7576-25 47.50
47.75 1381.78 1951.78 2521.79 3091.81 4231.84 5371.87 6511.90 7651.93 47.75
48'00 1392.00 1968.00 2544.00 3120.00 4272.00 5424.00 6576.00 7728.00 48'00
48.25 1402.26 1984.28 2566.29 3148.31 4312.34 5476.37 6640.40 7804-43 48.25
48.50
1412.56 2000.62 2588.68 3176.75 4352.87
48.50
1422.89 2017.03 2611.17 3205.31
48.75
5529.00 6705.12 7881.25
48.75
4393.59
5581.87 6770.15 7958.43
1 to 1.
2 to 1.
3 to 1.
49'00 1433.25 2033.50 2633.75 3234.00 4434.50 5635.00 6835.50 8036.00 49'00
49.25 1443.64 2054.33 2656.42 3262.81 4475.59 5688.37 6901.15 8113.93 49.25
49.50 1454.06 2066·62 2679.18 3291.75 4516.87 5742.00 6967.12 8192.25 49.50
49.75 1464.51 2083.28 2702.05 3320.81 4558.34 5795.87 7033-40 8270.93 49.75
50.00 1475.00 2100.00 2725.00 3350.00 4600.00 5850.00 7100·00 8350.00 50.00
50.25 1485.51 2116.78 2748.04 3379.31 4641.84 5904-37 7166.90 8429.43 50.25
50.50 1496.06 2133.62 2770.87 3408.75 4683.87 5959.00 7234.12 8509.25 50.50
50.75 1506.64 2150.53 2794-42 3438.31 4726.09 6013.87 7301-65 8589-43 50.75
51'00 1517.25 2167.50 2817.75 3468.00 4768.50 6069.00 7369.50 8670.00 51.00
51.25 1527.89 2184.53 2841.17 3497.81 4811:09 6124.37 7437.65 8750·93 51.25
51.50 1538.56 2201·62 2864.68 3527.75 4853.87 6179.00 7506.12 8832.25 51.50
51.75 1548.76 2218.78 2887.79 3557.81 4896.84 6235.87 7574.90 8913.93 51.75


331
Depths.
52.00
52.25
52.50
52.75
BASE 17.-Sectional Areas in Feet.
1 to 1.
4
3 to 1
4
1 to 1.
to 1.
1½ to 1.
2 to 1.
1560.00 2236.00
7644.00
2912.00 3588.00 4940.00 6292.00
1570-76 2253.28 2935.79 3618.31 4983.34 6348.37 7713.40
1581.56 2270.62 2959.68 3648.75
7783.12
7853.15
1592.39 2288.03 2983.77
3689.31
J
2 to 1.
5026.87 6405.00
5070-59 6461·87
53'00
1603.25 2305.50 3007.75 3710·00 5114.50 6519.00
53.25 1614.14 2323.03 3031.92 3740-81 5158.59 6576.37
53.50 1625:06 2340.62 3056.18 3771-75 5202.87 6633.00
1636.01 2358.28 3080.54 3802·81 5247.34 6691.87
54.00 1647.00 2376.00 3105.00 3834.00 5292.00 6750·00
54.25 1658.01 2393.78 3129.54
54.50 1669.06 2411.62 3153.18
54.75 1680.64 2429.53 3179.42 3928.31
53.75
56.00 1736.00 2520.00 3304.00 4088.00
56.25 1747.26 2538.28 3329.29 4120-31
56.50 1758.56 2556.62 3354.68 4152.75
56.75 1769.89 2575.03 3380.17 4185.21
7044-37
55.00 1691.25 2447.50 3203.75 3960.00 5472.50 6985.00
55.25 1702:39 2465.53 3228-67 3991.81 5518.09
55.50 1713.56 2483.62 3253.68 4023.75
55.75 1724.76 2501.78 3278-79 4055.81
5563.87
7104.00
5609-84
7163.87
57'00 1780.25 2592.50 3405·75 | 4217·00
57.25 1791.64 2611.03 3430-42 4249.81
57.50 1803.06 2629.62 3456.18 4282.75
57.75 1814.51 2648.28 3482.04 4315.81
}
8208.00
3865.31 5336.84 6808.37 8279.90
3896.75 5381.87 6867.00 8352.12
5427.09 6925.87 8424.65
:
7893.50
7994.15
8065.12
8136.37
3 to 1. Depths.
8996.00 52.00
9078.43 52.25
9161.25 52.50
9244.43 52.75
·
9328.00 53.00
9411.93 53.25
9496.25 53.50
9580.93 53.75
9666.00 54.00
9751.43 54.25
9837.25 54.50
9923.43 54.75
8497.50 10010.00 55.00
8570 65 10096.93 55.25
8644-12 10184.25 55.50
8718.90 10271.93 55.75
5656.00 7224.00 8792.00 10360.00 56.00
5702-34 | 7284.37 8866.40 10448.43 56.25
5748.87 7345.00
8941-12 10537.25 56.50
5795.59 7405·87 9016 1510625.43 56.75
5841.50 7466·00 9090-50 10715.00 57'00
5888.59 7527.37 9166.15 10804.93 57.25
5935.87 7589.00 9242-12 10895.25 57.50
5983.34 7650.87 9318-40 10985·93 57.75


z 2
332
:
Depths.
1.00
2.00
3.00
4.00
5'00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
1 to 1.
4
20.25
41.00
62.25
84.00
to 1.
20.50
42.00
64.50
88.00
13.00
344.50
302.25
13.25 308.85 352.71
13.50
315.56 361.12
13.75
322.26
369.53
14.00
329.00
14.25 335.76
14.50 342.66
14.75 349.28
BASE 20.-Sectional Areas in Feet.
4
378.00
386.53
395.12
403.73
to 1.
20.75
43.00
66.75
92.00
106.25 112.50 118.75
125.00
129.00 138.00
152.25 164.50
147.00 156.00
176.75 189.00
166.00 192.00 208.00 224.00
386.75
396.67
406.68
416.80
1 to 1.
342.00
200.25 220.50 240.75 261.00 301.50
225.00 250.00 275.00 300.00 350.00 400.00
250.25 280.50 310.75 341.00 401.50 462.00
276.00 312.00 343.00
384.00
456.00
528.00
427.00
437.30
447.69
458.10
21.00
44.00
69.00
96.00
468.75
15.00 356.25 412.50
15.25 363.13 421.26 479.42
15.50 370.06
15.75 377.01
430.12 490.10
439.03 501.05
1 to 1.
21.50
46.00
73.50
104.00
429.00
440.56
452.24
464.06
2 to 1.
2 to 1
22.00
22.50
48.00
50.00
78.00 82.50
112.00
137.50
150.00
174.00 192.00
213.50
238.00
256.00
288.00
513.50
528.34
543.36
558.59
3 to 1 Depths.
23.00
1.00
52.00
2.00
87.00
3.00
120.00 128.00
4.00
162.50
175.00
210.00 228.00
262.50
320.00
382.50 423.00
450.00
500.00
522.00
583.00
600.00
672.00
287.00
352.00
476.00
574.00
672.00
488.06 589.59
770.00
691.12 792.65
710.50
500.25
605.38
815.62
512.46 621.19 730.12 838.85
525.00 637.50 750.00 862.50
537.56 653.84
550.25 670.38
563.07 687.09
598.00
767.00 13.00
682.50
616.12 703.83 791.68 13.25
634.48
725.60 816.72 13.50
747.65 842.18 13.75
653.12
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
868.00 14.00
894.18 14.25
920.75 14.50
947.38
14.75
975.00
770.12 886.38 1002.68
790.50
811.12
15.00
15.25
15.50
910.62 1030.75
935.15 1059.18 15.75

333
Depths.
16.00
16.25
16.50
16.75
1 to 1.
to 1.
384.00
448.00
512.00
391.01 457.03 523.05
396.06 466.12
534.19
405.13 475.26
545.42
18.00
18.25
18.50
18.75
2
to 1.
17.00 412.25 484.50
17.25 419.38 493.76
17.50 426.50 503.12
17.75
432.76 512.52
BASE 20.-Sectional Areas in Feet.
556.75
568.14
579.69
591.30
1 to 1.
576.00
589.06
602.25
615.56
629.00
642.52
656.25
670.06
14 to 1.
704.00
721.09
738.38
755.84
773.50
791.28
809.38
827.59
22 to 1.
3 to 1. Depths.
832.00
960.00
1088.00 16.00
985.15 1117·18 16.25
853.12
874.50
1010.62 1146.75
16.50
896.12 1036.38 1176.68 16.75
2 to 1.
918.00
1060.50 1207.00 17.00
940.39 1089.15 1237-56 17.25
962.50 1115.62 1268.75 17.50
985.12 1142.64
1300.18 17.75
441.00 522.00 603.00
684.00
448.26 531.53 614.79 698.06
455.56 541.12
462.87 550.75
846.00 1008.00 1170.00 1332.00 18.00
864.59 1031.12 1197.65 1364.18 18.25
626.69 712.25 883.38 1054.50 1225.62 1396.75 18.50
638.50 726.50
1078.00 1253.75 1429.50 18.75
19.00 470.25 560.50 650.70
19.25 477.64 570.28 662.92
19.50 485.06 580.12
19.75 492.56 590.03
20.00 500.00 600.00 700.00
20.25 507.51 610.03 712.55
20.50 515.06 620.12 725.19
522.63 630.26 737.92
21.00 530.25 640.50 750.75
21.25 537.89 650.78 763.67
21.50 545.24 661.12 776.68
21.75 553.10 671.53 789.27 908.06 1144-54 1381.12
902.25
741.00 921.00 1102.00 1282.50 1463.00 19.00
756.56 940.84 1126.12 1311.40 1496.68 19.25
675.19 770.25 960.38 1150.50 1340.62 1530.75 19.50
687.55 785.06 980.09 1175-12 1370.15 1565.18 19.75
800.00 1000.00 1200.00 1400.00 1600.00 20.00
815.06 1020.09 1225.12 1430.15 1635.18 20.25
830.25 1040.38 1250.50 1460.62 1670.75 20.50
845.56 1060.84 1276.12 1491.38 1706.68 20.75
861.00 1081.50 1302.00 1522.50 1743.00 21.00
876.56 1102.34 1328.12 1553.90 1779.68 21.25
892.25 1123.38 1354.50 1585.62 1816.75 21.50
1617.65 1854.18 21.75
20.75
334
Depths.
to 1.
22.00
561.00
682.00
22.25 568.76 692.53
22.50 576.50 703.12
22.75 584.30 713.73
4
to 1.
BASE 20.-Sectional Areas in Feet.
3 to 1.
4
803.00
815.27
829.69
843.17
1 to 1.
924.00
940.06
1166.00 1408.00
1187:54 1435.12
956.25 1219.38 1462.50
972.56 1231.34
1 to 1.
23.00 592.25 724.50 856.75 989.00
23.25 600.12 735.25 870.42 1005.56
23.50 608.00 746.12 884.19 1022.25
757.03 898.05 1039.06
23.75 615.89
24.00
624.00
768.00
24.25
632.01
779.03
24.50 640.06 790.12
24.75 648.14 801.28
25.00 656.25 812.50
25.25 664.39 823.78
25.50 672.56 835.12
25.75 680.76 846.53
26.00 689.00 858.00
26.25 697.27 869.53
26.50 705.56 881.13
26.75 713.89 892.78
27.00 722.25 904.50
27.25 730.64 916.28
27.50 739.06 928.12
27.75 747.51 940.03 1132.54
21 to 1.
3 to 1.
1892.00
1650.00
1682.65
1930.18
1715.62 1968.75
1490.12 1748.90 | 2007·68
1253.50 1518.00 1782.50 2047.00
1275.84 1546.12 1816.37 2086.68
1298.38 1574.50 1850.62 2126.75
1321.09 1603.12 1885.15 2167.18
2 to 1.
Depths.
22.00
22.25
22.50
22.75
23.00
23.25
23.50
23.75
912.00 1056.00 1344.00 1632.00 1920.00 2208.00 24.00
926.03 1073.06 1367.09 1661.12 1955.15 2249.18 24.25
940-19 1090.25 1390.38 1690.50 1990.62 2290.75 24.50
954.17 1107.56 1413.34 1720.12 2026.20 2331.68 24.75
1437.50 1750.00 2062.50 2375.00
1461.34 1780.12 2098.80 2417·68 25.25
1160.25 1485.38 1810.50 2135.62 2460.75 25.50
1178.06 1509.09 1841.12 2172.65 2504.18 25.75
25.00
968.75 1125.00
983.17 1142.56
997.69
1012.05
26.00
26.25
1027.00 1196.00 1534.00 1872.00 2210.00 2548·00
1041.70 1214.06 1558.59 1903.12 2247.65 2592.18
1056.59 1232.25 1583.37 1934.50 2285.62 2636.75 26.50
1071.67 1250.56 1608.34 1966.12 2323.90 2681.68 26.75
1086.75 1269.00
1101.42 1287.56
1117.18 1306.25
1325.06
1633.50 1998.00
1998.00 2362.50 2727.00 27.00
1658.84 2030.12 2401·40 2774.18 27.25
1684.37 2062.50 2440.62 2818.75 27.50
1710-09 | 2095-12
2480.15 2865.18 27.75
į
335
BASE 20.-Sectional Areas in Feet.
Depths.
to 1.
1 to 1.
2 to 1.
3 to 1.
Depths.
28'00 756.00
1148.00 1344.00
28.25 764.51
28.50 773.06
28.75
952.00
1736.00 2128.00 2520·00 2912.00 28.00
964.03 1163.54 1363.06 1762.09 2161.12 2560.15 2959.18 28.25
976.12 1179.18 1382.25 1788.37 2194.50 2600.62 3006.75 28.50
781.64 988.28 1194.92 1401.56 1814.84 2228.12 264140 3054.68 28.75
29'00
790.25 1000.50 1210.75 1421.00 1841.50 2262.00 2682.50 3103.00 29.00
29.25 798.89 1012.78 1226.67 1440.56 1868.34 2296.12 2723.90 3151.68 29.25
29.50 807.56 1025.12 1244.93 1460.25 1895.37 2330.50 2765.62 3200.75 29.50
29.75 816.26 1037.53 1258.79 1480.06 1922.59 2365.12 2807.65 3250.18 29.75
30'00 825.00 1050.00 1275.00 1500.00 1950.00 | 2400·00 2850.00 3300.00 30.00
30.25
833.76 1062.53 1291.30 1520.06 1977.59 2435.12 2892.65 3350.18 30.25
842.56 1075.12 1307.69 1540.25 2005.37 2470.50 2935.62 3400.75
851.39 1087.78 1324.04 1560.56 2033.09 2506.12 2978.65 3451.18
30.50
30.50
30.75
30.75
1 to 1.
2
4
to 1.
1 to 1.
33.00 932.25 1204.50 1476.75
33.25 941.39 1217.78 1494.17
33.50 950.56 1231.12 1511.69
33.75 959.76 1244.53 1529.29
2 to 1.
31.00 860.25 1100.50
31.25 869.14
31.50 878.06
31.75 887.01
32.00 896.00 1152.00 1408.00 1664.00
32.25 905.01 1165.03 1425.05 1685.06
32.50 914.06 1178.12 1442.18 1706.25 2234.37 2762.50 3290.62 3818.75 32.50
1340-25 | 1581.00 2061.50 2542.00 3022.50 3503.00 31.00
1113.28 1357.42 1601.56 2089.84 2578.12 3066.40 3554.68 31.25
1126.12 1374.19 1622.25 2118.37 2614.50 3110.62 3606.75 31.50
1139.03 1391.05 1643:06 2147.09 2651.12 3155.15 3669.18 31.75
2176.00 2688.00 3200.00 3712.00 32.00
2205.09 2725.12 3245.15 3765.18 32.25
32.75 923.14 1191.28 1459.17
1727.56 2263.34 2800.12 3336.40 3872.68 32.75
1749.00 2293.50 2838.00 3382.50 3927.00 33.00
1770.56 2323.34 2876.12 3428.90 3981.68 33.25
1792.25 2353.38 2914.50 3475.62 4036.75 33.50
1797.06 2383.59 2953.12 3522.65 4092.18 33.75
336
Depths.
34.00
34.25
34.50
34.75
4
35'00
35.25
35.50
35.75
to 1.
to 1.
BASE 20.-Sectional Areas in Feet.
3 to 1.
4
1 to 1.
969.00 1258.00 1547.00 1836.00
978-26 1271.53 1564.79 1858.06
987.56 1285.12 1582.68 1880.25
996.89 1298.78 1600.67 1902.56
1 to 1.
2
2414.00
2444.59
2475.37
2506.34
23 to 1.
Depths.
2992.00 3570.00 4148.00 34.00
3031.12 3617.65 4204.18 34.25
3070.50 3665.62 4260.75 34.50
3713.90 4317.68 34.75
3110.12
2 to 1.
3 to 1.
3150.00
3150·00
3190.12
1006.25 1312.50 1618.75 1925.00 2537.50
1015.14 1326.28 1636.92 1947.56 2568.84
1025.06 1340.12 1645.18
1034.01 1354.03
35.75
1044.00 1368.00
3762.50 4375.00 35'00
3811.40 4432.68 35.25
1970.25 2600.37 3230.50 3860.62 4490.75 35.50
1673.54 1993.06 2632.09 3271.12 3910.15 4549.18
36'00
1692.00 2016.00 2664.00 3312.00 3960.00 4608.00 36'00
36.25 1053.51 1382.03 1710.54 2039.06 2696.09 3353.12 4010.50 4667.18 36.25
36.50 1063.06 1396.12 1729.18 2062.25 2728.37 3394.50 4060.62 4726.75 36.50
36.75 1072.64 1410.28 1747.92 2085.56 2760.84 3436.12 4111.40 4786.68 36.75
37'00 1082.25 1424.50 1766.75 2109.00 2793.50 3478.00 4162.50 4847.00 37.00
37.25 1091.89 1438.78 1785.67 2132.56 2826.34 3520.12 4213.90 4907.68 37.25
37.50 1101.56 1453.12 1804.68 2156.25 2859.37 3562.50 4265.62 4968.75 37.50
37.75 1111.01 1467.03 1823.79 2180.06 2892.59 3605.12 4317.65 5030.18 37.75
38.00 1121.00 1482.00 1843.00 2204.00 2926.00 3648.00 4370.00 5092.00 38'00
38.25 1130.76 1496.53 1862.29 2228.06 2959.59 3691.12 4422.65 5154.18 38.25
38.50 1140.06 1511.12 1881.68 2252.25 2993.37 3734.50 4475.62 5216.75 38.50
38.75 1150.39 1525.78 1901.05 2276.56 3027.09 3778.12 4529.00 5279.18 38.75
39.00 1160.25 1540·50 1920.75 2301.00 3061.50 3822.00 4582.50 5343.00 39.00
39.25 1170-14 1555.28 1940·17 2325.56 3095.34 3866.12 4636.40 5406.68 39.25
39.50 1180.06 1570.12 1960.19 2350.25 3130.37 3910.50 4690.62 5470.75 39.50
39.75 1190.01 1585.03 1980.03 2375.06 3165.09 3955.12 4745.15 5535.18 39.75
:
337

A A
Depths.
40.00
40.25
40.50
40.75
to 1.
4
•
13 to 1.
21 to 1.
Depths.
41'00
42.50
42.75
1200.25 1600.00 2000·00 2400.00 3200.00 4000.00 4800.00 5600.00 40.00
1215.01 1615.03 2020.05 2425.06 3235·09 4045.12 4855.15 5665.18 40.25
1220.06 1630.12 2040·18 2450.25 3270.37 4090·50 4910.62 5730.75 40.50
1230 14 1645:28 2050.42 2475.56 3305-84 4136·12 4966.40 5796.68 40.75
1240.25 1660.50 2080.75 2501.00 3341.50 4182.00 5022·50 5863.00 41.00
41.25 1250.39 1675-78 2101.17 2526.56 3377.34 4228.12 5078.90 5929.68 41.25
41.50 1260.56 1691.12 2121.68 2552.25 3413.37 4274.50 5135.62 5996.75 41.50
41.75 1270-76 1706.53 2142'05 2578.06 3449.59 4321.12 5192.65 6054.18
41.75
42.00 1281.00 1722.00 2163.00 2604·00 3486.00 4368.00 5250.00 6132.00 42.00
42.25 1291.26 1737.53 2183.79 2630:06 3522.59 4415.12 5307.65 6200.18 42.25
42.50 1301.56 1753.12 2204.68 2656.25 3559.37 4462·50 5365.62 6268.75
42.75 1311.88 1768-77 2225.65 2682.55 3596-32 | 4510·10 5423.87 6377.65
43.00 1322.25 1784.50 2246.75 2709.00 3633.50 4558.00 5482.50 6407.00 43.00
43.25 1332-64 1800-28 2267.92 2735.56 3670.84 4606.12 5541.40 6476.68 43.25
43.50 1343.06 1816.12 2289.18 2762.25 3708.37 4654.50 5600.62 6546.75 43.50
43.75 1353.51 1832.03 2310.54 2789.06 3746-09 4703.12 5660.15 6617.18 43.75
44.00 1364.00 1848.00 2332.00 2816.00 3784.00 4752.00 5720.00 6688.00 44.00
44.25 1374-61 1864-03 2353.54 2843.06 3822.09 4801.12 5780.15 6759.18 44.25
44.50 1385.06 1880.12 2375.18 2870.25 3860.37 4850.50 5840.62 6830.75 44.50
4.4.75 1395'64 1896.28 2396.92 2897.56 3898.84 4900·12 5901.40 6902-68 44.75
45.00 1406.25 1912.50 2418.75 2925.00 3937.50 4950·00 5962.50 6975.00 45'00
45.25 1416.89 1928.78 2440.67 2952.56 3976.34 5000·12 6023·90 7047.68 45.25
45.50 1427.56 1945.12 2462.68 2980.25 4015.37 5050.50 6085.62 7120.75 45.50
45.75 1438·20 1961-53 2484-79 3008-06 4054-59 5101-12 6147.65 7194.18 45.75
to 1.
2
BASE 20.-Sectional Areas in Feet.
3
2 to 1.
4
1 to 1.
2 to 1.
3 to 1.

338
Depths.
46.00
46.25
46.50
46.75
to 1.
4
49.00
49.25
49.50
49.75
BASE 20.-Sectional Areas in Feet.
50.00
50.25
50.50
50.75
1 to 1.
21 to 1.
Depths.
3036.00
3064.06
4094.00
4133.59
5152.00 6210.56 7268.00 46.00
5203.12 6272.65 7342·18 46.25
3092.25 4173.37 5254.50 6335.62 7416.75 46.50
3120.56 4213.34 5306.12 6398:90 7491.68
46.75
to 1.
3 to 1.
1449.00 1978.00 2507·00
1459.75 1994.53 2529.29
1470.56 2011.12 2551.68
1481.39 2027-78 2574-17
47.00 1492.25 2044.50 2596.75 3149.00 4253.50 5358.00 6462.50 7567.00 47'00
47.25 1503.14 2061.28 2619-42 3177:56 4293.84 5410.12 6526.40 7642.68 47.25
47.50 1514.06 2078.12 2642.18 3206.25 4334-37
6590.62 7718.75 47.50
47.75 1525.01 2095'03 2665'04 3235.06 4375.09
6655.15 7795.18 47.75
5462.50
5515.12
1 to 1.
2 to 1.
3 to 1.
48'00 1536.00 2112.00 2688.00 3264.00 4416.00 5568.00 6720.00 7872.00
48.25 1547.01 2129.03 2711·04 3293.06 4457.09 5621.12 6785.15 7949.18
48.50 1558.06 2146.12 2734.18 3322.23 4498.37 5674-50 6850.62 8026.75
48.75 1569·14 2163.28 2757:42 3351.56 4539.84 5728.12 6916.45 8104.68
5782.00 6982.50 8183.00
7048.90 8261.68
49.00
49.25
1580.25 2180.50 2780.75 3381.00 4581.50
1591.39 2197.78 2804.17 3410.56 4623.34 5836.12
1602:56 2215.12 2827.68 3440.25 4665.37 5890.50 7115.62 8340.75 49.50
1613-76 2232.53 2851.29 3470.06 4707.59 5945.12 7182.65 8420.18 49.75
1625·00 2250.00 2875.00 3500.00 4750.00 6000.00 7250.00 8500.00 50.00
1636.26 2267.53 2898-79 3530.06 4792.59 6055.12 7317.65 8580·18 50.25
1647·56 2285.12 2922.68 3562.25 4835.37 6110.56 7385.62 8660.75 50.50
1658.89 2302.78 2946.67 3590.56 4878.34 6166.12 7453.90 8741-68
1670.25 2320.50 2970·00 3621.00 4921.50 6222.00 7522.50 8823.00
1681.64 2338.28 2994.92 3651.56 4964.84 6278-12 7591·40 8904.68
51.50 1693.06 2356.12 3019.18 3682.25
51.75 1704·51 2374.03 3043'04
50.75
51:00
51.00
51.25
51.25
5008.37
5052.09
6334.50 7660.62 8986.75 51.50
6391.12 7730.15 9069.18 51.75
3713.06
48'00
48.25
48.50
48.75
339
to 1.
1 to 1.
5096·00
6448.00
6505.12
1716·00 2392.00 3068.00 3744.00
1727.51 2410.03 3092.54 3775.06 5140.09
1739.06 2428.12 3117.18 3806-25 5184.37 6562.50
1750.64 2446.28 3141.92 3837.56 5228.84 6615.12
BASE 20.-Sectional Areas in Feet.
to 1.
4.
to 1.
Depths.
52.00
52.25
52.50
8082.50
8153.90
52.75
53.00 1762-25 2464.50 3166.75 3869.00 5273.50 6678.00
53.25 1773.89 2482.78 3191.67 3900.56 5318.34 6736.12
53.50 1785.56 2501.12 3216.68 3932.25 5363.37 6794.50 8225.62
53.75 1797.26 2519.53 3241.79 3964.06 5408.59 6853.12 8297.65
54.00 1809.00 2538.00 3267.00 3996.00 5454.00 6912.00
54.25 1820.76 2556.53 3292.29 4028.06 5499.59 6971.12
54.50 1832.56 2575.12 3317.68 4062.25 5545.37 7030.50
54.75 1844.39 2593.78 3343.67 4092.56 5591.34 7090·12
55.00 1856.25 2612.50 3368.75 4125.00 5637.50 7150.00
55.25 1868.14 2631.28 3394.42 4157.56 5683.84 7210.12
55.50 1880.06 2650·12 3420.18 4190.25 5730.37 7270.50
55.75 1892.01 2669.03 3446.04 4223.06 5777·09 7331.12
1 to 1.
2 to 1.
56.00 1904.00 2688.00 3472.00 4256.00 5824.00
56.25 1916.01 2707.03 3498.04 4289.06 5871·09
56.50 1928.06 2726.12 3524-18 4322.25 5918.37
56.75
1940·14 2745*28 3550.42 4355.56 5965-84
57.00 1952.25 2764.50 3576.75 4389.00 6013.50 7638.00
57.25 1964-39 2783.78 3603.17 4422.56 6061.34 7700.12
57.50 1976.56 2803.12 3629.68 4456.25 6109.37 7762.50
57.75 1988.76 2822.53 3656.29 4490·06 6157·59 7825.12
7
7392.00
7453.12
7514-50
7576·12
2 to 1.
7800.00
7870.15
7940.62
8011·40
3 to 1 Depths.
9152.00 52'00
9235.18 52.25
9318.75 52.50
9402.68 52.75
9487.00 53.00
9571.68 53.25
9676.75 53.50
9742.18 53.75
8370.00 9828.00 54.00
8442.65 9914.18 54.25
8515 6210000·75
8588.90 10087·68
54.50
54.75
8662.50 10175.00 55.00
8736-4010262-68 55.25
8810.62 10350-75 55.50
8886-1510439·18 55.75
8960.00 10528.00 56'00
9035 15 10617·18 56.25
9110-62 10706.75 56.50
9186-4010795.68 56.75
9262-50 10887.00 57.00
9338.9010977-68 57.25
9415 62 11068-75 57.50
1160
9492-6511160·18 57.75
340
Depths.
1·00
2.00
3.00
4.00
5.00
6.00
7.00
8:00
1 to 1.
4
28.25
57.00
86.25
116.00
14.50
14.75
2
14.00 .441·00
14.25 449.76
458.56
. 467.28
to 1.
28.50
58.00
88.50
120.00
BASE 28.-Sectional Areas in Feet.
4
to 1.
15.00 476.25 532.50
15.25 485.13 543.26
15.50 494.06 554.12
15.75 503.01
565.03
28.75
59.00
90.75
124.00
146.25 152.50 158.75 165.00
177·00 186.00 195.00 204.00
208.25 220.50
232.75 245.00
240.00
256.00
272.00
1 to 1.
9.00
272.25
292.50
312.75
330.00 355.00
333.00
380.00
368.50 398.75 429.00
439.00 480.00
10.00
305.00
11.00 338.25
12.00 372.00 408.00
13.00 406.25 448.50 490'75 533.00
13.25 414.85 458.71 502.67 546.56
13.50 423.56 469.12 514.68 560.24
13.75 432.26 479.53 526.80 574-06
29.00
60.00
93.00
128.00
490'00 539.00
500.53 551.30
511·12 563.69
521.73
177.50
222.00
269.50
288.00 320.00
1 to 1.
29.50
62.00
97.50
136.00
588.00 686.00
602.06
703.59
616.25
721.38
576.10 630.46
739.19
2 to 1.
30.00
64.00
102.00
144.00
190.00
242.00
294.00
352.00
588.75 645.00
601.42 659.56
614.19 674-25 794.38
627.05
689.06
813.09
373.50 414.00
430.00 480.00 530.00
610.50
489.50 550.00
552.00 624.00
696.00
2 to 1.
30.50
66.00
106.50
152.00
627.50
702.00
786.50
634.34
722.12 809.83
651.36 742.48 833.60
668.59 763.12 857.65
757.50 870.00
775.84 892-12
202.50 215.00
258.00
276.00
318.50
343.00
374.00
416.00
914.50
937.12
784.00 882.00
805.12
826.00
848.12
3 to 1. Depths.
31.00
1.00
68.00
2.00
111.00
3.00
160.00
4.00
454.50 495.00
580.00
671.00
768.00
871.00
897.68
924.72
952.18
5'00
6.00
7.00
8:00
9.00
10.00
11.00
12.00
13.00
13.25
13.50
13.75
980.00
14.00
906.65 1008.18 14.25
931.62 1036.73
14.50
956.85 1065.38
14.75
1008.38
1034 62
1061·15
982.50 1095.00 15.00
1124.68 15.25
1154.75 15.50
1185.18
15.75

½ to 1.
2
to 1.
576.00
512.00
640.00
521.01 587.03 653.05
530.06 598.12 666·19
539.13 609.26
679.42
1 to 1.
BASE 28.-Sectional Areas in Feet.
Depths.
16°00
16.25
16.50
16·75
17.00 548.25 620.50
692.75
17.25 557.38 631.76 706.14
719.69
575.76 654.52
733.30
17.50 566.50 643.12
17.75
18.00 585.00
18.25 594-26
18.50 603.56
18.75
612.87 700.75
666.00 747·00
677.53 760-79
689.12 774.69
788.62
19.00 622.25 712.50
19.25 631.64 724.28
19.50 641.06 736.12
19.75 650.51 748.03
20'00 660.00 760.00
20.25 669.51 772.03
679.06
20.50
784-12
688.63 796.26
21.00 698.25 808.50
21.25 707.89 820.78
21.50 717.24 833.12
21.75 727·10
20.75
1 to 1.
802.70
816.92
831.19
845.55
704.00
719.06
734.25
749.56
765.00
780.52
796.25
812.06
2 to 1.
Depths.
16.00
832.00 960.00 1088.00
851·09 983.12 1115.15
870.381006·50 1142.62 1278.75
1216.00
1247·18 16.25
16.50
889.84 1030.12 1170.38 1310.68 16.75
828.00
909.50 1054.00 1198.50
929.28 1078.39 1227·15
949.38 1102.00 1255.62
969.59 1127.12 1284.64
990.00 1152.00 1314.00 1476·00 18.00
844.06 1010·59 1177.12 1343.65 1510.18 18.25
860.25 1031.38 1202.50 1373.62 1544.75 18.50
876.50 1052:25 1228.00 1403.75 1579.50 18.75
1254.00 1434.50 1615.00 19.00
1280·12
19.25
1465-40 1650.68
1116.38 1306.50 1496.62 1686-75 19.50
1138.09 1333.12 1528.15
19.75
1723.18
860.00 960.00 1160.00 1360.00 1560.00 1760.00 20'00
874.55 977.06 1182.09 1387.12 1592.15 1797.18
994.25 1204.38 1414.50 1624.62 1834-77
903.92 1011·56 1226.84 1442·12 1657.38 1872.68
918.75 1029.00 1249.50 1470·00 1690.50 1911.00
933.67 1046.56 1272.34 1498.12 1723.90 1949.68
948.68 1064.25 1295.38 1526.50 1757.62 1988.75 21.50
845.53 963.27 1082.06 1318.54 1555.12 1791.65 2028.18 21.75
20.25
889.19
21.00
21.25
893.00
909.56
926.25
943.06
1 to 1.
1073.50
1094 84
2 to 1.
·
3 to 1.
1343.00
17.00
17.25
1375.56
1408.75 17.50
1442.18 17.75
20.50
20.75
341

342
BASE 28.-Sectional Areas in Feet.
Depths.
to 1.
1 to 1.
21 to 1.
Depths.
22.00
737·00
22.25
1100.00 1342.00 1584.00 1826.00 2068.00
1118.06 1365.54 1613·12 1860.65 2108.18
1136.25 1389.38 1642.50
1154.56 1413.34 1672.12
22.50
895.78 1025·17
2357.18
•
24.00
24.25
858.00 979.00
22.00
746.76 870.53 993.27
22.25
756.50 S83.12 1009.69
1895.62 2148.75 22.50
22.75 766.39
1930.90 2189.68 22.75
23.00 776.25 908.50 1040-75 1173.00 1437.50
1437.50 1702:00 1966.50 2231.00 23.00
23.25 786·12 921.25 1056-42 1191.56 1461.84 1732-12 2002-37 2272.68 23.25
23.50 796.06 934.12 1063·19 1210.25 1486.38 1762.50 2038.62 2314.75 23.50
23.75
805.89 947.03 1088.05 1229.06 1511.09 1793.12 2075.15
23.75
24.00 816.00 960·00 1104.00 1248.00 1536.00 1824.00 2112.00 2400.00
24.25 826.01 973.03 1120.05 1267.06 1561.09 1855.12 2149.15 2443.18
24.50 836.06 986.12 1136.19 1286.25 1586.38 1886.50 2186.62 2486.75 24.50
24.75 846.14 999.28 1152.17 1305.56 1611·34 1918.12 2224.20 2529.68 24.75
25.00 856.25 1012·50 1168.75 1325.00 1637.50 1950.00 2262.50 2575.00 25.00
25.25 866.39 1025.78 1185.17 1344-56 1663·34 | 1982.12 2300·80 2619.68 25.25
25.50 876.56 1039-12 1201·69 1364.25 1689.38 2014.50 2339.62 2664-75 25.50
25.75 886.76 1052.53 1218.05 1384.06 1715.09 2047.12 2378.65 2710.18 25.75
26'00 897.00 1066.00 1235.00 1404.00 1742.00 2080.00 2418.00 2756·00 26.00
26.25 907.25 1079.53 1251.79 1424.06 1768.59 2113.12 2457.65 2802.18 26.25
26.50 917.56 1093·13 1268.69 1444.25 1795.37 2146.56 2497.62 2848.75 26.50
26.75 927.89 1106.78 1285.67 1464.56
27.00 938.25 1120.50 1302.75
27.25 948.64 1134.28 1319-42
27.50 959.06 1148.12 1337.18
27.75 969.51 1162.03 1354.54
1822.34
2180.12 2537.90 2895.68
26.75
1 to 1.
4
3 to 1.
1 to 1.
2 to 1.
3 to 1.
27.00
1485.00 1849.50 2214.00 2578.50 2943.00
1505.56 1876.84 2248·12 2619.40 2992.18 27.25
1526.25 1904.37 2282.50 2660.62 3038.75 27.50
1547.06 1932.09 2317.12 2702.15 3087·18 27.75
343
BASE 28.-Sectional Areas in Feet.
Depths.
4 to 1.
to 1.
1½ to 1.
28.00
980·00
1176.00
1960.00 2352.00
1372·00 1568.00
1389:54 1589.06 1988-09 2387.12
1407:18 1610.25
1424.92
2016.37
2044.84
30.25
30.50
30.75
2752.12 3224-65 3697·18
28.25 990:51 1190.03
28.50 1001.06 1204.12
28.75 1011.64 1218.28
1631.56
29.00 1022.25 1232.50 1442·75 | 1653·00
29.25 1032.89 1246.78 1460·67 1674.56
29.50 1043.56 1261.12 1480.93 1696.25
29.75 1054.26 1275:53 1496.79 1718.06
30.00 1065.00 1290.00 1515.00 1740·00 2190.00 2640.00 3090.00 3540:00 30'00
30.25 1075.76 1304-53 1533.30 1762.06 2219.59 2677.12 3134.65 3592.18
30.50 1086.50 1319.12 1551.69 1784.25 2249.37 2714.50 3179.62 3644.75
30.75 1097.39 1333.78 1570·04 1806.56 2279.09
31.00 1108.25 1348.50 1588.25 1829.00 2309.50 2790.00 3270.50 3751-00 31.00
31.25 1119·14 1363.28 1607.42 1851.56 2339.84 2828.12 3316.40 3804-68 31.25
31.50 1130.06 1378.12 1626.19 1874.25 2370.37 2866.50 3362.62 3858.75 31.50
31.75 1141.01 1393.03 1645.05 1897.06 2401.09 2905.12 3409.19 3913.18 31.75
32.00 1152.00 1408.00 1664.00 1916.00 2432.00 2944.00 3456:00 3968.00 32.00
32.25 1163.01 1423.03 1683.05 1943.06 2463-09 2983.12 3503.15 4023.18 32.25
32.50 1174.06 1438.12 1702-18 1966.25 2494.37 3022.50 3550.62 4078.75 32.50
32.75 1185.14 1453.28 1721-17 1989.56 2525.34 3062.12 3598.40 4134.68 32.75
33.00 1196.25 1468.50 1740-75 2013·00 2557.50 3102.00 3646·40 4191·00 33.00
33.25 1207.39 1483.78 1760·17 2036.56 2589.34 3142.12 3694.90 4247.68 33.25
1218.56 1499.12 1779.69 2060.25 2621.38 3182.50 3743-624304 75 33.50
1229.76 1514.53 1799.29 2084.06 2653.59 3223·12. 3792.65 4362.18
33.50
33.75
33.75
4
to 1.
1 to 1.
21 to 1.
2744.00
2786.15
2422.50 2828.62
2458.12
2 to 1.
Depths.
3136.00 28.00
3185.18 28.25
3234.75 28.50
28.75
3 to 1.
2871-40 3284-68
29.00
2073.50 2494.00 2914.50 3335.00
2102-34 2530.12 2957.90 3385.68 29.25
2131.37 2566.50 3001.62 3436.75 29.50
2160.59 2603.12 3045.65 3488.18 29.75
344
Depths.
to 1.
13 to 1.
34.00
1241.00 1530.00 1819.00 2108.00 2686.00 3264.00
34.25
1252.26 1545.53 1838.79 2132.06 2718.59 3305.12
34.50
1263.56 1561.12 1858.68 2156.25 2751.37 3346.50
34.75 1274.89 1576.78 1878.67 2180.56 2784.34 3388.12
35'00
1286.25 1592.00 1898.75 2205.00 2817.50 3430.00 4042.50 4655.00 35'00
35.25 1297.14 1608.28 1918.92 2229.56 2850.64 3472.12 4093.40 4714.68 35.25
35.50 1309.06 1624.12 1939.18 2254.25 2884.37 3514.50 4144.62 4774.75 35.50
35.75 1320.01 1640-03 1959.54 2279.06 2918.09 3557.12 4196.15 4835.18
36.00 1332.00 1656.00 1980.00 2304.00 2952.00 3600.00 4248.00 4896.00
36.25 1343.51 1672.03 2000.54 2329.06 2986'09 3643·12 4300.15 4957.18
36.50
1355.06 1688.12 2021.18 2354.25 3020.37 3686.50 4352.62
36.75
1366·64 1704.28 2041.92 2379.56 3054.84 3730.12 4405 40
35.75
36'00
36.25
5018.75 36.50
5080·68 36.75
BASE 28.-Sectional Areas in Fect.
1 to 1.
4
39.00
39.25
39.50
39.75
3 to 1
4
1 to 1.
2 to 1.
2 to 1.
Depths.
3842.00
4420.00
34.00
3891.65
4478.18 34.25
4536.75 34.50
3941-62
3991.90 4595.68 34.75
3 to 1.
4458.50 5143.05 37.00
3818.12 4511.90 5205.68 37.25
3862.50 4565.62 5268.75 37.50
3907.12 4619.65 5332.18 37.75
37.00
1378.25 1720.50 2062.75 2405.00 3089.50 3774.00
37.25 1389.89 1736.78 2083.67 2430.56 3124.34
37.50 1401.56 1753.12 2104.68 2456.25 3159.37
37.75 1413.01 1769.03 2125.79 2482.06 3194.59
38.00 1425.00 1786.00 2147.00 2504.00 3230.00 3952.00 4674.00 5396.00 38'00
38.25 1436.76 1802.53 2168.29 2534.06 3265.59 3997.12 4728.65 5460.18 38.25
38.50 1448.06 1819.12 2189.68 2560.25 3301.37 4042.50 4783.62 5524.75 38.50
38.75 1460.39 1835.78 2211.05 2586.25 3337.09 4088.12 4839.40 5589.18 38.75
1472.25 1852.50 2232.75 2613.00 3373.50 4134.00 4894.50 5655.00 39.00
1484.14 1869.28 2254.17 2639.56 3409.34 4180.12 4950.40 5720.68 39.25
1496.06 1886.12 2276.19 2666.25 3446.37 4226.50 5006.62 5786.75 39.50
1508.01 1903.03 2298.03 2693.06 3483.09 4273.12 5063.15 5853.18 39.75
345
B B
1 to 1.
4
Depths.
2 to 1.
12 to 1.
40'00 1520.00 1920.00 2320.00 2720.00 3520.00
40.25 1532.01 1937.03 2342.05 2747.06 3557.09
40.50 1544.06 1954.12 2364.18 2774.25
40.75 1556.14 1971.28 2386.42 2801.56
3594.37
3631.84
£2
to 1.
`BASE 28.-Sectional Areas in Feet.
1 to 1.
!
3669.50
3707.34
41.00 1568.25 1988.50 2408.75 2829.00
41.25 1580.39 2005.78 2431.17 2856.56
41.50 1592.56 2023.12 2453.68 2884.25
1604.76 2040.53 2476.05 2912.06 3783.59
3745.37
41.75
21 to 1.
3 to 1. Depths.
5920.00
40.00
40.25
5987.18
4320.00 5120.00
4367.12 5177.15
4414.50 5234.62 6054.75 40.50
4462.12 5292.40 6122.68 40.75
2 to 1.
4510.00 5350.50 6191.00 41'00
4558.12 5408.90 6259.68 41.25
4606.50 5467.62 6328.75 41.50
4655.12 5526.65 6398.18 41.75
42.00
42.25
42.50
1617.00 2058.00 2499.00 2940.00 3822.00 4704.00 5586.00 6468.00 42'00
1629.26 2075.53 2521.79 2968.06 3860.59 4753.12 5645.65 6538.18 42.25
1641.56 2093.12 2544.68 2996.25 3899.37 4802.50 5705.62 6608.75
42.75 1653·88 2110.77 2567.65 3024.56 3938.52 4852.10 5765.87 6679.65
42.50
42.75
43'00 1666.25 2128.50 2590.75 3053.00 3977.50 4902-00 5826.50 6751.00 43'00
43.25 1678.64 2146.28 2613.92 3081.56 4016.84 4952.12 5887.40 6822.68 43.25
43.50 1691.06 2164·12 2637.18 3110.25 4056.37 | 5002·50 5948.62 6894.75 43.50
43.75 1703.51 2182.03 2660.54 3139.06 4096.09 5053.12 6010.15 6967.18 43.75
44.00 1716.00 2200.00 2684.00 3168.00 4136.00 5104.00 6072.00 7040·00 44:00
44.25 1728.51 2218.03 2707.54 3197.06 4176.09 5155.12 6134.15 7113.18 44.25
44.50 1741.06 2236.12 2731·18 3226.25 4216.37 5206.50 6196.62 7186.75 44.50
44.75 1753.64 2254.28 2754.92 3255.56 4256.84 5258.12 6259.40 7260.68 44.75
45.00 1766.25 2272.50 2778.75 3285.00 4297.50 5310.00 6322.50 7335.00 45.00
45.25 1778.89 2290.78 2802.67 3314.56 4338.34 5362.12 6385.90 7409.68 45.25
45.50 1791.56 2309.12 2826.68 3344.25 4379.37 5414.50 6449.62 7484.75 45.50
45.75 1804.26 2327.53 2850.79 3374.06 4420.59 5467.12 6513.65 7560.18 45.75
1 to 1.
4.
Depths.
12 to 1.
46.00
4462.00
5520.00
46.25
1817.00 2346.00 2875.00 3404.00
1829.76 2364.53 2899.29 3434.06 4503.59 5573.12 6642.65
46.50 1842.56 2383.12 2923.68 3464.25 4545.37
4587.34
46.75 1855.39 2401.78 2948.17 3494.56
BASE 28.-Sectional Areas in Feet.
1 to 1.
2
3 to 1.
4
1 to 1.
3525.00 4629.50
1881.14 2439.28 2997.42 3555.56 4671.84
1894.06 2458.12 3022.18 3586.25
1907.01 2477.03 3047-04 3617.06
4714.37
4757.09
2 to 1.
3 to 1. Depths.
6578.00 7636.00 46'00
7712.18 46.25
5626.50 6707.62 7788.75 46.50
5680.12 6772.90 7865.68 46.75
5734.00 6838.50 7943.00 47.00
5788.12 6904.40 8020.68 47.25
6970.62 8098.75 47.50
7037.15 8177.18 47.75
5842.50
5897.12
2 to 1.
47'00 1868.25 2420.50 2972.75
47.25
47.50
47.75
48'00 1920.00 2496.00 3072.00 3648·00 4800.00 5952.00
48.25 1933.01 2515.03 3097.04 3679.06 4843.09 6007.12
48.50 1946.06 2534.12 3122.18 3710.25 4886.37 6062.50
48.75 1959.14 2553.28 3147.42 3741.56 4929.84 6118.12
49'00 1972.25 2572.50 3172.75 3773.00 4973.50 6174.00 7374.50 8575.00 49'00
49.25 1985.39 2591.78 3198.17 3804.56 5017.34 6230.12 7442.90 8655.68 49.25
49.50 1998.56 2611.12 3223.68 3836.25 5061.37 6286.50 7511.62 8736.75 49.50
49.75 2011.76 2630.53 3249.29 3868.06 5105.59 6343.12 7580.65 8818.18 49.75
50.00 2025.00 2650.00 3275.00 3900.00 5150.00 6400.00 7650.00 8900.00 50.00
50.25 2038.26 2669.53 3300.79 3932.06 5194.59 6457.12 7719.65 8982.18 50.25
50.50 2051.56 2689.12 3326.68 3964.25 5239.37 6514.50 7789.62 9064.75 50.50
50.75 2064.89 2708.78 3352.67 3996.56 5284.34 6572.12 7859.90 9147.68
51'00 2078.25 2728.50 3378.75 4029.00
51.25 2091.64 2748.28 3404.92 4061.56
51.50 2105.06 2768.12 3431.18 4094.25
2118.51 2788.03 3457-04 4127-06
50.75
5329.50 6630.00 7930.50 9231.00 51.00
5374.84 6688.12 8001.40 9314.68 51.25
5420.37 6746.50 8072.62 9398.75 51.50
5466.09 6805.12 8144.15 9483.18 51.75
51.75
7104.00 8256.00
7171.15 8335.18
7238.62 8414.75
7306.40 8494.68
48'00
48.25
48.50
48.75
346
347
Depths.
to 1.
1 to 1.
2 to 1.
5512.00 6864.00 8216.00
5558.09 6923.12 8288.15
6982.50 8360.62
7042.12 8433.40
52.00 2132.00 2808.00 3484.00 4160.00
52.25 2145.51 2828.03 3510.54 4193.06
52.50 2159.06 2848.12 3537.18 4226.25 5604.37
52.75 2172.64 2868.28 3563.92 4259.56 5650.84
53.00 2186.25 2888.50 3590.75 4293.00 5697.50 7102.00 8506.50
53.25 2199.89 2908.78 3617.67 4326.56 5744-34 7162.12 8579.90
9913.00 53'00
9997.68 53.25
53.50 2213.56 2929.12 3644.68 4360.25 5791.37 7222.50 8653.62 10084.75 53.50
53.75 2227.26 2949.53 3671.79 4394.06 5838.59 7283.12 8727.65 10162.18 53.75
54.00 2241.00 2970.00 3699.00 4428.00 5886.00 7344.00
54.25 2254.76 2990.53 3726.29 4462.06 5933.59 7405.12
54.50 2268.56 3011.12 3753.68 4496.25 5981.37
54.75 2282.39 3031.78 3781.67 4530.56 6029.34
7466.50
7528.12
2
to 1.
BASE 28.-Sectional Areas in Feet.
4
to 1.
1 to 1.
2 to 1.
3 to 1.
Depths.
9568.00 52.00
9653.18 52.25
9738.75 52.50
9824.68 52.75
8802.00 10260.00 54.00
8876.6510348·18 54.25
8951.62 10436.75 54.50
9026.90 10525.68 54.75
55.00 2296.25 3052.50 3808.75 4565.00 6077.50 7590.00 9102.50 10615.00 55.00
55.25 2310.14 3073·28 3836.42 4599.56 6125.84 7652.12 9178.40 10704.68 55.25
55.50 2324.06 3094.12 3864.18 4634.25 6174.37 7714.50 9254.62 10794.75 55.50
55.75 2338.01 3115.03 3892.04 4669.06 6223.09 7777.12 9332.15 10885.18 55.75
56.00 2352.00 3136.00 3920.00 4704.00 6272.00 7840.00 9408.00 10976.00 56.00
56.25 2366.01 3157.03 3948·04 4739.06 6321.09 7903.12 9485.1511067.18 56.25
56.50 2380.06 3178.12 3976.18 4774.25 6370.37 7966.50
56.50
56.75 2394.14 3199.28 4004·42 | 4809.56 6419.84 8030·12 9640.40 11249.68 56.75
57.00 2408.25 3220.50 4032.75 4835.00 6469.50 8094.00
57.25 2422.39 3241.78 4061.17 4880.56 6519.34 8158.12
57.50 2436.56 3263.12 4089.68 4916.25 6569.37 8222.50
57.75 2450.76 3284.53 4118.29 4952.06 6619.59 8287.12
9562-6211158.75
9718.50 11342.00 57'00
9796.90 11435.68 57.25
9875.6211528.75 57.50
11622∙18
9954-6511622.18 57.75
348
Depths.
1.00
2.00
3.00
4.00
1 to 1.
4.
9.00
30.25
61.00
92.25
124.00
5.00
6.00
7.00 222.25
8.00
256.00
1 to 1.
14:00
469.00
14.25 478.26
14.50 487.56
14.75 496.78
BASE 30.-Sectional Areas in Feet.
15.00 506.25
15.25
15.50
15.75
3 to 1.
30.50
62.00
94.00
128.00 132.00
30.75
63.00
99.75
562.50
515.63 573.76
585.12
525.06
534.51 596.53
1 to 1.
10.00
11.00 360.25 390.50 420.75 451.00
12.00 396.00 432.00 463.00 504.00
31.00
64.00
99.00
136.00
156.25
162.50 168.75
189.00 198.00 207.00
234.50
272.00
290.25 310.50
325.00 350.00 375.00 400.00 450.00
330.75 351:00 391.50
511.50
576.00
175.00
216.00
246.75 259.00
288.00 304.00
13.00 432.25 474.50 516.75 559.00
13.25 441.35 485.21 529.17
13.50 450.56 496.12 541.68
13.75 459.76 506.03 554.30
618.75
631.92
645.19
658.55
518.00
528.03
567.00 616.00
579.80 630.56
540.12 592.69 645.25
551.23
605.60
659.96
1 to 1.
2
31.50
66.00
103.50
144.00
2 to 1.
187.50 200.00
234.00 252.00
283.50
308.00
336.00
368.00
32.00
68.00
108.00
152.00
643.50 728.00
573.06 660.84 748.62
587.24 678.36 769.48
696.09 790.62
601.56
675.00
787.50
690.06 806.34
705.25
720.56
432.00
500.00
572.00
648.00
714.00 812.00
731.09 833.62
750.38 855.50
768.69 877.62
900.00
922.62
825.38 945.50
844.59
968.62
i
2 to 1.
32.50
70.00
112.50
160.00
212.50
270.00
332.50
400.00
3 to 1.
33.00
72.00
117.00
168.00
860.60
885.15
225.00
288.00
357.00
432.00
472.50 513.00
550.00 600.00
632.50
720.00
693.00
792.00
Depths.
1.00
2.00
3.00
4.00
5°00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
897.00 13.00
812.50
836.33 924.18 13.25
951.62 13.50
979.78 13.75
910.00 1008.00 14.00
935.15 1036.68 14.25
960.62 1065.75 14.50
986.35 1094.88 14.75
1012.50 1125.00 15.00
1038.88 1155.18 15.25
1065.62 1185.75 15.50
1092.65 1216.68 15.75
349
Depths.
to 1.
16.00
544.00 608.00
16.25 553.51 619.53
16.50 563.06 631.12
16.75 572.63 642.76
4
to 1.
17.00 582.25
654.50
17.25 591.88 666.26
17.50 601.50 678.12
17.75 611.26 690.02
18.00 621.00 702.00
18.25
630.76 714.03
18.50
640.56
726.12
18.75
650.37
738.25
4
BASE 30.-Sectional Areas in Feet.
to 1
1 to 1.
672.00 736.00
685.55 751.56
699.19
767.25
712.92
783.06
783.00
797.29
811.69
826.12
726.75
799.00
740.64 815.02
754.69 831.25
768.80 847.56
1 to 1.
2 to 1.
Depths.
1248.00
16.00
864.00 992.00 1120.00
883.59 1015.62 2147.65 1279.68 16.25
903.38 1039.50 1175.62 1311.75 16.50
923.34 1063.62 1203.88 1344.18 16.75
2 to 1.
17.25
943.50 1088.00 1232.50 1377.00 17:00
963.78 1112.89 1261.65 1410.06
984.38 1137.50 1290.62 1443.75 17.50
1005.09 1162.62 1320.14 1477.68 17.75
864.00 1026.00 1188.00 1350.00 1512.00 18.00
880.56 1046.09 1213.62 1380.15 1546.68
18.25
897.25 1068.38 1239.38 1410.62 1581.75
914.00 1089.75 1265.50 1441.25 1617.00
18.50
18.75
3 to 1.
884.05
840.70 931.00 1111.50 1292.00 1472.50 1653.00 19.00
855.42 948.06 1133.34 1318.62 1503.90 1689.18 19.25
870.19 965.25 1155.38 1345.50 1535.62 1725.75 19.50
982.56 1177.59 1372.62 1567.65 1752.68 19.75
1000.00 1200.00 1400.00 1600.00 1800.00 20.00
914.05 1017.56 1222.59 1427.62 1632.65 1837.68 20.25
930.19 1035.25 1255.38 1455.50 1665.62 1875.75 20.50
945.42 1052.06 1268.34 1483.62 1698.88 1914.18 20.75
900.00
19.00 660.25 750.50
19.25 670.14 762.78
19.50 680.06 775.12
19.75 690.01 787.53
20'00 700.00 800.00
20.25 710.01 812.53
20.50 720.06 826.12
20.75 730.13 837.76
21.00 740.25 850.50
21.25 750.39 863.28
21.50 760.24 876.12
960.75 1071.00 1291.50 1512.00 1732.50 1953.00 21.00
976.17 1089.05 1314.84 1540.62 1766.40 1992.18 21.25
991.68 1107.25 1338.38 1569.50 1800.62 2031.75 21.50
21.75 770.60 888.03 1006.77 1125.56 1362.04 1598.62 1835.15 2071.68 21.75
→
350
1
Depths.
22.00
22.25
22.50
22.75
1 to 1.
2 to 1.
21 to 1.
781.00
791.26
902.00
914.03
1905.15
1940.62
1023.00 1144.00 1386.00 1628·00 1870.00
1037.77 1162.56 1410'04 1657.62
1054-69 1181.25 1434-38 1687.50
801.50 928-12
811.89 940.28 1070·67 1200'06 1458.84 1717.62 1976:40
822.25 954.50 1086.75 1219.00 1483.50 1748.00 2012.50
832.62 967.75 1102.92 1238.06 1508.34 1778.62 2048-87
843.00 981.12 1119.19 1257.25 1533.38 1809.50 2085.62
853.39 994.53 1135.55 1276.56 1558.59 1840-62
2277·00 23.00
2319.18 23.25
2361.75 23.50
2122.65 2404.68 23.75
24.00 864.00 1008.00 1152.00 1296·00 1584.00 1872.00 2160.00 2448.00 24.00
24.25 874.51 1021.53 1168.55 1315.56 1609.59 1903.62 2197.65 2491.68 24.25
24.50 885.06 1035·12 1185-19 1335.25 1635.38 1935.50 2235.62 2535.75 24.50
24.75 895.64 1048.78 1201·67 1355.06 1660.84 1967.62 2273.70 2580.18 24.75
25.00 906.25 1062.50 1218.75 1375.00 1687.50 2000.00 2312.50 2625.00 25.00
25.25 916.89 1076.28 1235.67 1395.06 1713.84 2032.12 2351.30 2670.18 25.25
25.50 927.56 1090.12 1252.69 1415.25 1740.38 2065.50 2390.62 2715.75 25.50
25.75 938.26 1104.03 1269.55 1435.56 1766.59 2098.62 2430.15 2761.68 25.75
26'00 949.00 1118.00
26.25
26.50
1287.00 1456.00 1794.00 2132.00 2470·00 2808.00 26.00
959.76 1132.03 1304.29 1476.56 1821.09 2165.62 2510.15
970.56 1146.13 1321.69 1497.25 1848.37 2199.50 2550.62
981.39 1160.28 1339·17 1518.06 1875.84 2233.62 2591.40
26.75
992.25
2854.68 26.25
2901.75 26.50
2949.18 26.75
1174.50 1356.75 1539.00 1903.50 2268.00 2632.50 2997.00 27.00
1188.78 1373.92 1560.06 1931.34 2302.62 2673.90 3046.68 27.25
1203.12 1392.18
1959.37 2337.50 2715.62 3093.75 27.50
1025.01 1217.53 1410.04
1987.59 2372-62 2757.65 3142.68 27.75
1003 14
1014.06
1581.25
1602.56
23.00
23.25
23.50
23.75
27.00
27.25
27.50
27.75
1 to 1.
4
BASE 30.-Sectional Areas in Feet,
to 1.
4
to 1.
1 to 1.
3 to 1. Depths.
2112.00 22.00
2152.68 22.25
2193.75 22.50
2235.18 22.75
"
351
Depths.
1 to 1.
2 to 1.
Depths.
28'00 1036·00 1232.00
28.25 1047.01 1246.53
1428.00 1624.00 2016·00 | 2408·00 2800.00 3192.00 28.00
1446.04 1645.56 2044.59 2443.62 2842.65 3241.68 28.25
28.50 1058.06 1261.12 1464-18 1667.25 2073.37 2479.50 2885.62 3291.75 28.50
28.75 1069.14 1275.28 1482-42 1688.56 2101.84 2515.62 2928.90 3341-68 28.75
29.00 1080.25 1290.50 1500.75 1711.00 2131.50 2552.00 2972.50 3393.00 29.00
29.25 1091.39 1305.28 1519·17 1733.06 2160.84 2588.62 3016:40 3444.18 29.25
29.50 1102.56 1320.12 1539.93 1755.25 2190.37 2655.50 3060.62 3495.75 29.50
29.75 1113-76 1345.03 1556.29 1777.56 2220.09 2662.62 3105.15 3547.68 29.75
30.00 1125.00 1350.00 1575.00 1800.00 2250·00 2700·00 3150.00 3600.00 30.00
30.25 1136.26 1365.03 1593.80 1822.56 2280·09 2737.62 3195.15 3652.68 30.25
30.50 1147.56 1380.12 1612.69 1845.25 2310.37 2775.50 3240.62 3705-75
1158.89 1395.28 1631.54 1868.06 2340·59 2813.62 3286.15 3758.68 30.75
1170-25 1410.50 1650.25 1891.00 2371·50
2371-50 2852.00 3332.50 3813.00 31.00
1181.64 1425.78
1914.06 2402.34 2890.62 3378.90 3867.18 31.25
1937·25 2433.37 2929.50 3425.62 3921.75 31.50
1960-56 2464-59 2968.62 3472.65 3976.68 31.75
30.50
30.75
1669.92
1193.06 1441·12
1204.51 1456.53
31.00
31.25
31.50
31.75
to 1.
1
2
BASE 30.-Sectional Areas in Feet.
to 1.
3
to 1.
1689 19
1708.55
1 to 1.
2 to 1.
3 to 1.
32.00 1216·00 1472.00 1728.00 1984.00 2496.00 3008.00 3520.00 4032.00 32.00
32.25 1227.51 1487.53 1747.55 2007.56 2527.59 3047.62 3567.65 4087.68 32.25
32.50 1239.06 1503.12 1767.18 2031.25 2559.37 3087.50 3615.62 4143.75 32.50
32.75 1250·64 1518.78 1786-67 2055'06 2590.84
4199.18 32.75
3127.62 3663.90
33.00 1262.25 1534.50 1806.75 2079.00 2623.50 3168.00
33.25 1273.89 1550.28 1826.67
33.50 1285.56 1566·12 1846.69
33.75 1297.26 1582.03 1866.79
3712.50 4257.00 33.00
2103.06 2655.84 3208.62 3761.40 4314.18 33.25
2127·25 2688.38 3249.50 3810.62 4371·75 33.50
2151.56 2721·09 3290.62 3860.15 4429.68 33.75
352
Depths.
to 1.
to 1.
1 to 1.
3 to 1 Depths.
2754.00
3332.00
35.00
35.25
34.00 1309.00 1598.00 1887.00 2171.00
3910.00 4488.00 34.00
34.25 1320-76 1614.03 1907.29 2200.56 2787.09 3373.62 3960.15 4546.68 34.25
34.50 1332.56 1630.12 1927.68 2225.25 2820.37 3415.50 4010.62 4605.75 34.50
34.75 1344·39 1646.28 1948.17 2250.06 2853.84 3457.62 4061.40 4665'18 34.75
35'00 1356.25 1662.50 1968.75 2275.00 2887.50 3500.00 4112.50 4725.00
35.25 1367·64 1678.78 1989-42 2300.06 2921.34 3542.62 4163.90 4785.18
35.50 1380.06 1695.12 2010.18 2325.25 2955.37 3585.50 4215.62 4845.75 35.50
35.75 1391·51 1711-53 2031.04 2351.56 2989.59 3628.62 4267.65 4906.68 35.75
36'00 1404.00 1728.00 2052.00 2376.00 3024.00 3672.00 4320.00 4968.00 36.00
36.25 1416.01 174453 2073-04 2401.56 3058.59 3715.62 4372-65 5029.68
36.25
36.50
36.75
36.50 1428.06 1761.12 2094·18 2427.25 3093.37 3759.50 4425.62 5091.75
36.75 1440·14 1777-78 2115.42 2453.06 3128.34 3803.62 4478.90 5154.18
37.00 1452.25 1794.50 2136.75 2479.00 3163.50 3848.00 4532.50 5217.00 37.00
37.25 1464.39 1811.28 2158.17 2505.06 3198.84 3892.62 4586.40 5280.18 3.7.25
37.50 1476.56 1828.12 2179.68 2531.27 3234.37 3937.50 4640-62 5343.75 37.50
37.75 1488.51 1844-53 2201·29 2557.56 3270.09 3982.62 4695.15 5407.68 37.75
38.00 1501.00 1862.00 2223.00 2584.00 3306.00 4028.00 4750.00 5472.00 38.00
38.25 1513.26 1879.03 2244.79 2610.56 3342-09 4073.62 4805.15 5536.68 38.25
38.50 1525.06 1896.12 2266.68 2637.25 3378-37 4119.50 4860.62 5601.75 38.50
38.75 1537.89 1913.28 2288.55 2664.06 3414.59 4165.62 4916.50 5666.68 38.75
1550.25 1930.50 2310.75 2691.00 3451.50 4212.00 4972.50 5733.00 39.00
1562-64 1947.78 2332.67 2718.06 3487.84 4258.62 5038.90 5799-18 39.25
1575.06 1965.12 2355.19 2745.25 3525.37 4305.50 5085.62 5865-75 39.50
1587.51 1982.53 2377.53 2772.56 3562.59 4352.62 5142.65 5932.68 39.75

39.00
39.25
39.50
39.75
BASE 30.-Sectional Areas in Feet,
4
to 1.
1 to 1.
2 to 1.
2 to 1.
C C
Depths.
4 to 1.
1/2 to 1.
1½ to 1.
22 to 1.
Depths.
40.50
40.25
6135.75 40.50
6204.18 40.75
40.75
41.00
40'00 1600.00 200.000 2400.00 2800.00 3600.00 4400.00 5200.00 6000.00 40*00
40.25 1612.51 2017.53 2422.55 2827.56 3637.59 4447.62 5257.15 6067.68
1625'06 2035.12 2445·18 2855.25 3675.37 4495.50 5315.62
1637-64 2052-78 2467.92 2883.06 3713:34 4543.62 5373.90
1650.25 2070.50 2490.75 2911·00 3751.50 4592.00 5432.50
41.25 1662.89 2088.28 2513.67 2939.06 3789.84 4640.62 5490-40
41.50 1675.56 2106.12 2536-68 2967.25 3828.37 4689.50 5550·62
41.75 1688.26 2124.03 2559.55 2995.56 3867-09 4738.62 5609.15
42.00 1701·00 2142.00 2583.00 3024.00 3906.00 4788.00 5670.00 6552.00 42.00
42.25 1713.76 2160.03 2606.29 3052.56 3945.09 4837.62 5730.15 6622.68
42.25
42.50 1726.56 2178.12 2629.68 3081.25 3984-37 4887.50 5790.62 6693.75 42.50
42.75 1739.38 2206.27 2653.15 3110.05 4023.82 4937.62 5851.37 6765.15
43.00 1752.25 2214-50 2676.75 3139.00 4063.50 4988.00 5912.50 6837·00 43.00
43.25 1765.14 2232.78 2700.42 3168.06 4103.34 5038.62 5973.90 6909.18 43.25
43.50 1778.06 2251.12 2724-18
3197.25 4143.37 5089.50 6035.62 6981.75 43.50
43.75 1791-01 2269.53 2748.04 3226.56 4183.59 5140.62 6097.65 7054-68 43.75
44.00 1804.00 2288.00 2772.00 3256.00 4224.00
44.25 1817-01 2306.53 2795.04 3285.56
1830.06 2325.12
1843 14 2343-78
42.75
4264-59
44.50
4305.37
2820.18 3315.25
2844-42 3345.06
44.75
1856.25 2362.50
2868.75 3375.00
1869.39 2381.28 2893.17 3405.06
4346 34
4387.50
4429.84
1882.56 2400.12 2917.68 3435.25 4470.37
1895.76 2419.03 294229 3465.56 4512.09
45.00
45.25
45.50
45.75
BASE 30.-Sectional Areas in Feet.
·
0^3+
to 1.
1 to 1.
2 to 1.
3 to 1.
6273.00 41.00
6342-18 41.25
6411.75 41.50
6481.68 41.75
5192.00 6160.00 7128.00 44.00
5243.62 6222.65 7201.68 44.25
5295.50 6285.62 7275.75 44.50
5347.62 6348.90 7350·18 44.75
5400.00 6412.56 7425.00 45.00
5452.62 6476·40 7500·18 45.25
5505.50 6540-62 7575-75 45.50
5558.62 6605.15 7651.68 45.75
353


354
¿
½ t
BASE 30.-Sectional Areas in Feet.
to 1.
Depths.
4 to 1.
1 to 1.
2 to 1.
2 to 1.
Depths.
46°00
46.50
46.75
6048.00 7200.00 8352.00 48'00
6103.62 7267.65 8431.68 48.25
46.00 1909.00 2438.00 2967.00 3496.00 4554.00 5612.00 6670.00 7728.00
46.25 1922.26 2457.03 2991.79 3526.56 4596.09 5665.62 6735.15 7804.68 46.25
46.50 1935.56 2476.12 3016.68 3557.25 4638.37 5719.50 6800.62 7881.75
46.75 1948.89 2495.28 3041.67 3588.06 4680.84 5773-62 6860.40 7959.18
47'00 1962.25 2514.50 3066.75 3619.00 4723.50
47.25 1975.64 2533.78 3091.92 3650.06 4766.34
47.50 1989.06 2553.12 3117.18 3681.25 4809.37
47.75 2002.51 2572.53 3142.54 3712.56 4852.59
48.00 2016:00 2592.00 3168·00 3744.00 4896.00
48.25 2029.51 2611.53 3193.54 3775.56 4939.59
48.50 2043.06 2631.12 3219.18 3807.25 4983.37 6159.50 7335.62 8511.75 48.50
48.75 2056.64 2650-78 3244.92 3839.06 5027.34 6215.62 7403.90 8592.18 48.75
49.00 2070-25 2670.50 3270.75 3871.00 5071.50 6272.00 7472.50 8673.00 49.00
49.25 2083.89 2690.28 3296.67 3903.06 5115.84 6328.62 7541·40 8753.18 49.25
49.50 2097.56 2710.12 3322.68 3935.25 5160.37 6385.50 7610-62 8835.75 49.50
49.75 2111·26 2730.03 3348.79 3967-56 5205.09 6442.62 7680.15 8917.68 49.75
50.00 2125.00 2750.00 3375.00 4000.00 5250.00 6500.00 7750·00 9000.00 50.00
50.25 2138.76 2770.03 3401.29 4032.56 5295.09 6557.62 7820.15 9082.68 50.25
50.50 2152.56 2790.12 3427.68 4065.25 5340.37 6615.50 7890.62 9165.75 50.50
50.75 2166.39 2810.28 3454-17 4098.06 5385.84 6673.62 7961.40 9249.18 50.75
51.00 2180.25 2830.50 3480.75 4131.00 5431.50 6732.00 8032.50 9333.00 51.00
51.25 2194.14 2850-78 3507.42 4164.06 5477.34 6790.62 8103.90 9417.18 51.25
51.50 2208.06 2871·12 3534.18 4197.25 5523.37 6849.50 8175.62 9501.75 51.50
51.75 2222.01 2891.53 3560.54 4230.56 5569.59 6908.62 8247.65 9586.68 51.75
4
to 1.
1 to 1.
3 to 1.
5828.00 6932.50 8037.00 47.00
5882-62 6998'90 8115.18 47.25
5937.50 7065.62 8193.75 47.50
5992.62 7132.65 8272.68 47.75
355

Depths.
52.00
52.25
52.50
52.75
BASE 30.-Sectional Areas in Feet.
56.00
56.25
56.50
56.75
to 1.
to 1.
to 1.
2236.00 2912.00 3588.00 4264.00
2250.61 2932.53 3615.04 4297.56
2264-06 2953.12
2278.14 2973.78
1½ to 1.
| 2 to 1.
5616.00 6968.00
5662.59 7027.62
3642.18 4331.25 5709.37
3669.42 4365'06
7087.50
7147.62
5756.34
1 to 1.
3696.75 4399.00
4433.06
3751.68
3751-68 4467.25
3779.29 4501.56
5803.50 7208.00
5850.84
7268.62
5898.37
7329.50
5946.09
7390.62
53.00
2292.25 2994.50
2306.39 3015.28 3724.17
5994.00
7452.00
53.25
53.50 2320.56 3036·12
53.75 2334·76 3057.03
54.00 2349.00 3078.00 3807.00 4536.00
54.25 2363.26 3099.03 3834-79 4570.56 6042.09 7513.62
54.50 2377.56 3120.12 3862.68 4605.25 6090.37 7575.50
54.75 2391.89 3141.28 3891.17 4640.06 6138.84 7637.62
55.00 2406.25 3162.50 3918.75
55.25 2420-64 3183.78
55.50 2435.06 3205.12
55.75 2449.51 3226.53
4675.00 6187.50 7700.00
3946.92 4710.06 6236.34 7762.62
3975.18 4745.25 6285.37 7825.50
4003 54 4780-56 6334.59 7888.62
4032.00
2478.51 3269.53 4060.54
2493.06 3291.12 4089.18 4887.25
2507.64 3312-78 4117.92 4923.06
2464.00 3248.00
4816.00
4851.56
6384.00 7952.00
6433.59 8015.62
6483.37 8079.50
6533.34 8143.62
57.00 2522.25 3334.50 4146.75 4959.00 6583.50 8208.00
57.25 2536.89 3356.28 4176.67 4995.06 6633.84 8272.62
6684-37 8337.50
6735.09 8402-62
57.50 2551.56 3378.12 4204.68 5031.25
57.75 2566.26 3400-03 4233.79 5067.56
21 to 1.
Depths.
8320.00 9672.00 52.00
8392.65 9767.68 52.25
8465:62 9843.75 52.50
8538.90 9930.18 52.75
3 to 1.
•
8612.50 10017·00 53.00
53.25
8686 40 10104.18
8760-62 10191.75 53.50
8835.15 10279.68 53.75
8910.00 10368.00 54.00
8985-15 10456-68
54.25
54.50
9060-62 10545-75
9136-40 | 10635·18
54.75
9212-5010725.00
9288.90 10815.18
9365.62 | 10905·75
9443.65 10996.68
9520-0011088·00
9597·6511179-68
9675-62 11271-75
9753.90 11363.18
55.00
55.25
55.50
55.75
56.00
56.25
56.50
56.75
57.00
57.25
9832.50 11457·00
9910-40 11550-18
9990-62 11643.75
10070·15
10070-15 | 11737.68 57.75
57.50

c c 2
356

1
Depths.
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9:00
1 to 1.
4
13'00
13.25
13.50
13.75
31.25
63.00
95.25
128.00
161.25
195.00
to 1.
31.50
64.00
97.50
132.00
BASE 31.-Sectional Areas in Feet.
4
to 1.
167.50
173.75
204.00 213.00
229.25 241.50 253.75
264.00 280.00 296.00
299.25
319.50 339-75
360.00
10:00
335.00 360.00 385.00 410.00
11.00 371.25 401.50 431.75
12.00 408.00 444.00 475.00
462.00
516.00
31.75
65.00
99.75
136.00
445.25 487.50 529.75
454.60 498.46 542.42
464.06 509.62 555.18
473.51 520-78 568.05
483.00 532.00 581.00
492.51 543.28 594.05
502.06 554.62 607.19
511.53 565.98 620.35
1 to 1.
14.00
14.25
14.50
14.75
15.00 521.25 577.50 633.75
15.25 530.88 589.01 647.17
15.50 540.56 600.62 660.59
15.75 550.26 612-28 674.30
32.00
66.00
102.00
140.00
180.00
222.00
266.00
312.00
572.00
586.31
600.74
615.31
1 to 1.
32.50
68.00
106.50
148.00
192.50
240.00
290.50
344.00
400.50
460.00
522.50
588.00
2 to 1.
630.00
728.00
644.81 746.34
659-75
764.88
674.71
783.44
33.00
70.00
111.00
156.00
205.00
258·00
315.00
376.00
441.00
510.00
583.00
660.00
656.50 741.00
674.09
761.87
691.86
709.84
782.98
804.37
826.00
847.87
870·00
892.37
2 to 1.
33.50
72.00
115.50
164.00
3 to 1.
34.00
74.00
120.00
172.00
Depths.
1.00
2.00
3:00
4.00
217.50
230.00 5.00
276.00
294.00
6.00
339.50 364.00
7:00
408.00 440.00
8.00
481-50 522.00
560.00
610.00
643.00 704.00
732.00 S04:00
9'00
10.00
11.00
12.00
825.50
910.00 13'00
849.58
937.43 13.25
874.10 965.22 13.50
898.90 993.43 13.75
924.00 1022.00 14.00
949.40 1050.93 14.25
975.12 1080.25 14.50
1001.10 1109.63 14.75
15.00
690.00 802·50 915.00 1027.50 1140.00
705.31 821.59 937.87 1054.13 1170·43 15.25
720:75 840.88 961.00 1081.12 1201.25 15.50
736.61 860.34 984.37 1108.40 1232.43 15.75


357
Depths.
16.00
16.25
16.50
16.75
17.00
17.25
17.50
17.75
18.00
18.25
18.50
18.75
BASE 31.-Sectional Areas in Feet.
to 1.
to 1.
14 to 1.
560.00 624.00
688.00 752.00 880.00
569.76 635.78 701.80 767.81 899.84
579.56 647.62 715.69 783.75 919.88
589.38 659.51 729.67
799.81
599.25 671.50
609.13 683.51
619.06 695.62
629.01 707.77
3 to 1.
4
1 to 1.
743.75 816.00
757.89
832.27
772-19
848.75
786.55
865.31
2 to 1.
1008.00
1031-87
1056.00
940.09 1080.37
920·00 1020·00
935.30 1037.81
950.69 1055.75
966.17 1073.81
21 to 1.
1136.00
1163.90
1192 12
1220.63
Depths.
1264.00
16.00
1295.93
16.25
16.50
1328.25
1360.93 16.75
3 to 1.
1394.00 17.00
1427.31 17.25
17.50
1337.89 1495'43 17.75
960.50 1105.00 1249.50
981.03 1130.14 1278.90
1001.88 1155.00 1308.12 1461.25
1022.84 1180·37
639.00 720.00 801.00 882.00 1044-00 1206.00
649.01 732.28 815.54 898.81 1065.34 1231.87
830.19 915.75 1086.88 1258.00
844.87 932.75 1108.50 1284.25
950·00 1130.50 1311.00 1491.50 1672.00 19'00
967-31 1152.59 1337.87 1523.15 1708:43 19.25
889.69 984.75 1174-88 1365.00 1555.12 1745.25 19.50
904.80 1002.31 1197.34 1392.37 1587·40 1782-43 19.75
659.06 744.62
669.12
757·00
769.50 859.70
689.39 782.03 874-67
699.56 794.62
709-76 807.28
1368.00 1530.00 18.00
1398.40 1564.93 18.25
1429.12 1600.25 18.50
1460.00 1635·75 18.75
19.00 679.25
19.25
19.50
19.75
20.00 720.00 820.00
20.25 730.26 832.78
740.56 845.62
20.50
750.88 858.51
1220.00 1420.00 1620.00 1820.00 20.00
1242.84 1447·87 1652.90 1857.93 20.25
1265.88 1475.00 1686-12 1896.25 20.50
20.75
1289.00 1504-37 1719.63 1934.93 20.75
21'00 761.25 871.50 981.75 1092.00 1312.50 1533.00 1753.50 1974-00 21.00
21.25 771.64 884.53 997.42 1110.31 1336.09 1561.87 1787.65 2013·43 21.25
781-74 897.62 1013·18 1128.75 1359.88 1591.00 1822.12 2053.25 21.50
792.35 910.78 1028.52 1147-31 1383.79 1620:37 1856.90 2093.43 21.75
21.50
21.75
358
Depths.
22.00
22.25
22.50
22.75
4
1/2 to 1.
21 to 1.
Depths.
22.75
23.50
24.00
24.25
24.50
24.75
2298.45 2603.93 24.75
803.00 924.00 1045.00 1166.00 1408.00 1650.00 1892.00 2134.00 22.00
814-51 938.28 1061.02 1185.81 1433.29 1680.87 1928.40 2175.93 22.25
825.00 951.62 1078.19 1204.75 1457.88 1711.00 1964.12 2217.25 22.50
835.64 965.03 1094:42 1223.81 1482.59 1741·37 2000·15 2258.93
23.00 846.25 978.50 1110-75 1243.00 1507.50 1772.00 2036.50 2301.00
23.25 856.87 992.00 1127·17 1262.31 1532.59 1802.87 2073-13 2343 43
867.50 1005.62 1143.69 1281.75 1557.88 1834.00 2110.12 2386.25
23.75 877.26 1018.28 1159.30 1300.31 1582.34 1864.37 2146-40 2428-43
24.00 888.00 1032.00 1176.00 1320.00 1608.00 1896.00 2184.00 2472.00
24.25 898.76 1045.78 1192.80 1339.81 1633.84 1927.87 2221.90 2515.93
24.50 909.56 1059.62 1209.69 1359.75 1659.88 1960.00 2260.12 2560.25
920.39 1073.53 1226.42 1379.81 1685.59 1992-37
25.00 931.25 1087.50 1243.75 1400.00 1712.50 2025.00 2337.50 2650-00 25.00
942.14 1101.53 1260.92 1420.31 1739-09 2057.87 2376.55 2695.43 25.25
25.50 953.06 1115.62 1278.19 1440.75 1765.88 2090·00 2416.12 2741.25 25.50
25.75
964.01 1129.78 1295.30 1461.31 1792.34 2124.37 2455-90 2787-43 25.75
26.00 975.00 1144.00 1313.00 1482-00 1820·00 2158.00 2496.00 2834.00 26.00
26.25 986.01 1158.28 1330.54 1502.81 1847.34 2191.87 2536.40 2880.93 26.25
26.50 987.06 1172.63 1348.19 1523.75 1874-87 2226.00 2577.12 2928.25 26.50
26.75 1008.14 1187.03 1365.92 1544-81 1902.59 2260.37 2618.15 2975.93
27.00 1019.25 1201·50 1383.75
27.25 1030.39 1216.03 1401·17
27.50 1041.56 1230.62 1419.68
27.75 1052.76 1245.28 1437.79
25.25
26.75
1930.50 2295.00 2659.50 3024.00 27.00
1958.59 2329.87 2701.15 3073.93 27.25
1986-87 2365.00 2743.12 3121.25 27.50
2015 34 2400·37 2785·30 3170-43 27.75
BASE 31.-Sectional Areas in Feet,
to 1.
*/**
4
to 1.
1 to 1.
1566.00
1587.31
1608.75
1630.31
1 to 1.
1
2 to 1.
3 to 1.
23.00
23.25
23.50
23.75
359
Depths.
28.00
28.25
28.50
28.75
•
4 to 1.
to 1.
to 1.
1 to 1.
1492-68
1511·17
1064-00 1260.00 1456·00 1652.00 2044-00 2436.00
1075.26 1274-78 1474-29 1673·81 2072-84 2471.87
1086.56 1289.62
1695.75 2101.87 2508.00 2914.12
1717·81 2131.09 2544.37 2957.65
1097-89 | 1304·53
BASE 31.-Sectional Areas in Fect.
"
1 to 1.
2 to 1.
1
2 to 1.
Depths.
2828.00 3220.00 28.00
2870.90 3269.93 28.25
3320-25 28.50
3370.93 28.75
1740·00 2160.50 2581.00 3001.50
2190·09 2617.87 3045.65
2219.87 2655.00 3090.12
2249.84 2692.37
3 to 1.
29.00 1109.25 | 1319.50 1529.75
29.25 1120-64 1334.53 1548.42 1762.31
29.50 1132.06 1349.62 1567·40 1784-75
29.75 1143.51 1364-78 1586.04 1807-31
30.00 1155.00 1380.00 1605·00 1830.00
30.25 1166.51 1395.28 1624.05 1852.81
30.50 1178·06 1410.62
30.75 1189.64 1426.03
2280.00 2730.00 3180.00 3630.00 30.00
2310.34 2767.87 3225.40 3682.93 30.25
1643.19 1875.75 2340.87 2806.00 3271.12 3736.25 30.50
1662.29 1898.81 2371·34 2844-37 3316.90 3789.43 30.75
31.00 1201.25 1441.50 1681.25 1922.00 2402-50 2883.00 3363.50 3844.00 31:00
31.25 1212.89 1457.03 1701·17 1945.31 2433.59 2921.87
31.50 1224.56 1472-62 1720-69
31.75 1236.26 1488.28 1740·30
32.00 1248.00 1504.00 1760.00 2016.00 2528.00
32.25 1259.76 1519.78 1779.80 2039.81 2559-84
32.50 1271.56 1535.62 1799.68 2063.75 2591.87
32.75 1283.39 1551-53 1819.42 2087.81 2623.59
3410.15 3898.44 31.25
3457.12 3953.25 31.50
3504-40 4008.43 31.75
3040·00 3552.00 4064.00 32.00
3079.87 3599.90 4119.93 32.25
3120·00 | 3648·12 4176.25 32.50
3160.37 3696.65 4232.93 32.75
33.00
1968·75 2464.87 2961.00
1992-31 2496.34 3000·37
33.00 1295.25 1567.50 1839.75 2112.00 2656.50 3201.00 3745.50 4290.00
33.25 1307.14 1583.53 1859.92 2136.31 2689.09 3241.87 3794.65 4347.43 33.25
33.50 1319.06 1599.62 1880-19 2160.75 2721.88 3283.00 3844.12 4405.25 33.50
33.75 1331.01 1615.78 1900.54 2185.31 2754.84 3324.37 3893.90 4463.43 33.75
3422.00 29.00
3473.43 29.25
3525.25 29.50
3134.90 3577-43 29.75
360
&
Depths.
to 1.
to 1.
1 to 1.
2 to 1.
3 to 1 Depths.
34.00
34.25
2788.00 3366.00 3944.00 4522.00 34.00
2821.34 3407.87 3994:60 4580.93 34.25
2259.75 2854.87 3450.00 4045'12 4640-25
2888.59 3492.37
1343.00 1632.00 1921.00 2210.00
1355·01 1648.28 1941-54 2234.81
34.50 1367.06 1664-62 1962.18
34.50
34.75 1379:14 1681.03 1982.92 2284.81
4096.15 4699.93 34.75
35'00 1391.25 1697.00 2003.75 2310.00 2922.50 3535.00 4147.50 4760:00 35'00
35.25 1402.89 1714-03 2024.67 2335.31 2956.59 3577.87 4199.15 4820:43 35.25
35.50 1415-56 1730.62 2045.68 2360.75 2990.87 3621.00 4251.12 4881.25 35.50
35.75 1427.26 1747.28 2066.79 2386.31 3025.34 3664-37 4303.40 4942.32 35.75
2412:00 3060.00 3708.00 4356·00
2437.81 3094:84 3751.87 4408.90
2463.75 3129.87 3796·00 | 4462·12
2489.81 3165.09 3840.37 4515.65
BASE 31.-Sectional Areas in Feet.
36'00
36.25
36.50
36.75
38'00
38.25
38.50
38.75
$ to 1.
4
1 to 1.
1440·00 1764·00
5004.00 36.00
36.25
37.00
2088.00
1452.26 1780.78 2109:29
5065.93
1464-56 1797.62 2130.68
5128.25 36.50
1476·89 1814.53 2152·17
5190.93 36.75
37.00 1489.25 1831.50 2173.75 2516.00 3201·00 3885.00 4569.50 5254.00
37.25 1501.64 1848.53 2195.42 2542.31 3236.09 3929-87 4623.65 5317-43 37.25
37.50 1514-06 1865.62 2217.18 2568.75 3271.87 3975.00 4678.12 5381.25 37.50
37.75 1526 26 1882-28. 2239.04
4020-37 4732.90 5445-43 37.75
1539-00 1900.00 2261.00
1551·51 1917.28 2283.04
1563.56 1934.62 2305.18
1576-64 1952-03 2327.30
2595·31 3307·84
2622.00 3344.00 4066.00 4788.00 5510.00
2648.81 3380.34 4111.87 4843.40 5574-93
2675.75 3416.87 4158.00 4899.12 5640.25
2702·81 3453.34 4204.37 4955.25 5705-43
39.00 1589.25 1969.50 2349.75 2730.00 3490.50 4251.00 5011.50 5772.00
39.25 1601-89 1987.03 2371.92 2757-31 3527-09 4297.87 5068.15 5838-43
39.50 1614-56 2004-62 2394.69 2784-75 3564.87 4345.00 5125.12 5905.25
39.75 1627.26 2022.28 2417·28 2812.31 3602·34 4392.37 5182.40 5972.43 39.75
39.50
2 to 1.
38.00
38.25
38.50
38.75
39°00
39.25
361
1 to 1.
4
Depths.
to 1.
to 1.
1½ to 1.
2 to 1.
40'00
1640.00
1652.76
2040.50 2440.00 2840.00 3640.00 4440·00 5240.00
40.25
2057-78 2462.80 2867.81 3677.84 4487.87 5297.97
40:50 1665.56 2075.62 2485.68 2895.75 3715.87 4536.00 5356.12
40.75 1678-39 2093 53 2508-67 2923:81 375409 4584-37 5414-65
BASE 31.-Sectional Areas in Feet.
?
1 to 1.
2 to 1.
3 to 1.
6040.00
6107.93
6176.25
6244.93
Depths.
40.00
40.25
40-50
40.75
41.00 1691.25 2111.50 2531.75 2952.00 3792.50 4633.00 5473.50 6314.00 41'00
41.25 1704-14 2129.53 2554.92
41.25
41.50 1717.06 2147.62 2578.18
41.75 1730.01 2165.78 2601.30
42.25
42.75
2980.31 3831·09 4681.87 5532.65 6383.43
3008.75 3869-87 4731.00 5592.12 6453.25 41.50
3037.31 3908-84 4780.37 5651.90 6523.43 41.75
42.00 1743·00 2184.00 2625.00 3066.00 3948·00 | 4830·00 5712.00 6594.00 42.00
42.25 1756·01 2202.28 2648.54 3094.81 3987.34 4879.87 5772-40 6664.93
42.50
1769-06 2220.62 2672.18 3123.75 4026.87 4930.00 5833.12 6736.25 42.50
1782.13 2239.02 2695.90 3152.80 4066.57 4980.35 5894.12 6807.90 42.75
43'00
1795.25 2257.50 2719.75 3182.00 4106.50 5031.00 5955'50 6880.00 43'00
43.25 1808.39 2276:03 2743.67 3211.31 4146.59 5081-87 6017.15 6952.43 43.25
43.50 1821.56 2294.62 2767.68 3240.75 4186.87 5133.00 6079.12 7025.25 43.50
43.75 1834.76 2313.28 2791.79 3270-31 4227.34 5184.37 614140 7098·43 43.75
44.00 1848.00 2332.00 2816.00 3300.00 4268.00 5236.00 6204.00 7172.00 44.00
44.25 1861.26 2350.78 2840.29 3329.81 4308.84 5287.87 6266.90 7245.93 44.25
44.50 1874.56 2369.62 2864.68 3359.75 4349.87 5340.00 6330.12 7320:25 44:50
44-75 1887-89 2388.53 2888.17 3389.81 4391·09 5392.37 6393.65 7394.93 44.75
45.00 1901·25 2407.50 2913.75 3420.00 4432.50 5446.00 6457.50 7470.00 45.00
45.25
1914.64 2426.53 2938.42 3450.31 4474-09 5497.87 6521.65 7545-43 45.25
45.50 1928.06 2445.62 2963.18 3480.75 4515-87 5550.00 6585.12 7621.25 45.50
45.75 1941.51 2464-78 2988.04 3511-31 4557.84 5604-37 6650·99 7697.43 45.75
362
Depths.
46'00
46.25
46.50
46.75
1 to 1.
4
BASE 31.-Sectional Areas in Feet.
to 1.
1 to 1.
2 to 1.
Depths.
1955.00 2484.00
5658.00
3542.00 4600.00
3572-81 4642.34
3013:00
6716.00 7774.00 46.00
1968.51 2503.28 3038·04
5711.87 6781.40 7850.93 46.25
1982.06 2522-62 3063.18 3603.75 4684-87 5766.00 6847.12 7928.25 46.50
1995'64 2542.03 3088-42 3634.81 4727-59 | 5820.37 6913.15 8005.93 46.75
47.00 2009.25 2561.50 3113.75 3666.00 4770·50 5875.00 6979.50 8084.00 47'00
47.25 2022.89 2581.03 3139.17 3697.31 4813.59 5929.87 7046.15 8162.43 47.25
47.50 2036.56 2600.62 3164.68 3728.75 4856.87 5985.00 7113.12 8241.25 47.50
47.75 2050.26 2620-28 3190.29 3760:31 4900·34 | 6040·37 7180.40 8320.43 47.75
48'00 2064.00 2640.00 3216.00 3792.00 4944.00 6096.00 7248.00 8400.00
48.25 2077.76 2659.78 3241.79 3823.81 4987.84 6151.87 7315.90 8479.93
48:50 2091.56 2679.62 3267.68 3855.75 5031-87
7384.12 8560.25
7452.65 8640.93
48.75 2105.39 2699.53 3293.67
6208.00
3887.81 5076.09 6264-37
49'00 2119.25 2719.50 3319.75 3920.00 5120.50 6321.00 7521.50 8722.00 49'00
49.25 2133.14 2739.53 3345.92 3952.31 5165.09 6377.87 7590.65 8803-43 49.25
49.50 2147.06 2759.62 3372.18 3984-75 5209.87 6435'00 7660·12 8884.25 49.50
49.75 2161.01 2779.78 3398.54 4017.31 5254.84 6492.37 7729.90 8967.43 49.75
50.00 2175.00 2800.00 3425.00 4050.00 5300.00 6550.00 7800.00 9050.00 50.00
50.25 2189.01 2820.28 3451.54 4082.81 5345.34 6607:87 7870-40 9132.93 50.25
50.50 2203.06 2840.62 3478.18 4115.75 5390.87 6666.00 7941.12 9216.25 50.50
50.75 2217·14 2861.03 3504.92 4148.81 5436.59 6724-37 8012.15 9299·93 50.75
51.00 2231.25 2881.50 3531.75 4182.00 5482.50
9384.00 51'00
51.25 2245.39 2902.03 3558.67 4215.31 5528.59 6841.87 8155.15 9468.43 51.25
51.50 2259.56 2922.62 3585.68 4248.75 5574-87 6901·00 8227.12 9553.25 51.50
51.75 2273.76 2943.28 3612.29 4282.81 5621.34 6960.37 8299.40 9638.43 51.75
4
to 1.
1 to 1.
2 to 1.
6783.008083.50
3 to 1.
48'00
48.25
48.50
48.75



363
Depths.
52.00
52.25
52.50
52.75
53'00
53.25
53.50
53.75
1
4
to 1.
2288.00
2302.26
2964.00 3640.00 4316.00
2984.78 3667.29 4349.81
2316.56 3005.62 3694.68 4383.75
2330.89 3026.53 3722.17 4417.81
BASE 31.-Sectional Areas in Feet.
to 1.
3
to 1.
1 to 1.
1½ to 1.
2 to 1.
Depths.
5668.00
5714.84
7020.00 8372.00 9724.00 52.00
7079.87 8444.90 9809.93 52.25
5761.87 7140.00 8518.12 9896.25 52.50
5809.09 7200.37
8591.65 9982.93 52.75
2345.25
7261.00
7321.87
3047.50 3749.75 4452.00 5856.50
2359 64 3068.53 3777-42 4486.31 5904-09
2374.06 3089.62 3805-18 4520.75 5951.87
2388.51 3110.78 3833.04 4555.31
7383.00
5999.84 7444.37
6048.00 7506.00
6096.34 7567.87
6144-87 7629.00
6193.59 7692.37
55'00 2461.25 3217.50 3973.75 4730·00 6242.50 7755.00
55.25 2475.89 3239.03 4002.17 4765.31 6291.59 7817.87
55.50 2490.56 3260-62 4030.68 4800.75 6340.87 7881.00
55.75 2505.26 3282.28 4059.29 4836.31 6390.34 7944-37
54.00
2403·00 3132.00 3861.00 4590.00
54.25 2417.51 3153.28 3889.04 4624.81
54.50 2432.06 3174.62 3917-18 4659.75
54.75 2446.64 3196.03 3945.92 4694-81
2 to 1.
3 to 1.
8665.50 10070·00 53.00
8739.65 10157.43 53.25
8814-12 10245.25 53.50
8888.90 10333:43 53.75
54.00
54.25
8964-00 10422:00
9039-40 10510.93
9115 12 10600.25 54.50
9191-15 10689.93 54.75
9267.50 10780.00
9344-15 10870.43
9421-12 10961.25
9499-40 11052 43
9576.00 11144.00 56.00
9653.90 11235.93 56.25
9732-12 11328.25 56.50
9810-65 11419.93 56.75
9889.50 11514.00
56.00
56.25
2520.00 3304.00 4088.00 4872.00 6440.00 8008.00
2534-76 3325.78 4116.79 4907.81 6489.84 8071.87
56.50 2549.56 3347.62 4145.68 4943.75 6539-87 8136.00
56.75 2564.39 3369.53 4174-67 4979-81 6590·09 8200.37
57.00 2579.25 3391.50 4203.75 5016:00 6640.50 8265.00
57.25 2594·14 3413.53 4232.92 5052.31 6691.09 8329.87
57.50 2609.06 3435.62 4262.18 5088-75 6741.87 8395.00 10048·12 11701·25
57.75 2624.01 3457.78 4291.54 5125.31 6792.84 8460-37 | 10127-90 | 11795 43
9968.6511607·43
55.00
55.25
55.50
55.75
57'00
57.25
57.50
57.75

INDEX.
ABUTMENTS, 220, 222
Accidents in Boring, 35, 37
Alluvial deposits, 52
Angle of deflexion, 6
friction, 209
""
>>
>>
Arch, applied theory of the arch, 203
backing to, 153, 172
brick, 153, 173
>>
""
33
>>
""
35
""
""
""
39
35
"
stone, 176
""
Ashlar, 174, 223
Asphalte for arches, 177
Auger, 20
>>
>>
39
">
BACKING to arch, 177
""
>>
Ballasting, 156
Beton, 190
Boring, 19
>>
??
limiting angle of resistance, 209
tangential, 3
"
A.
with stone quoins, 227
elliptic arch, to draw, 229
>>
laminated, specification for, 267
segmental arch, to find radius, 230
length of, 231
""
"
to find number of voussoirs, 232
worm, 21
valve, 24
B.
"
tar for, 177
to retaining walls, 143
accidents in, 35
auger, 20
claw, 26
crab engine-stand, 32
jumpers, 21
valve, 24
note-book, 39
piping, 33
""
head-piece, 25
lengthening-rods, 25
Boring, piping, insertion and extraction of, 37
platform, 27
plotting, 39
pricker, 25
>>
""
>>
""
""
""
>>
""
worm, 21
""
auger, 21
Bricks, 152
Brick arch-See arch
Brickwork, 152, 172, 225
Bridges, legal regulations as to, 265
aqueduct, 264
brick, 201-226
timber, 254
"1
""
>>
11
"
CARPENTRY, 154-180, 258-268
Cast-iron, 240
93
2)
""
""
>"
Centres for arches, 234
Chalk, 42
""
""
Chert, 45
"S
sample bags, 19
spring bar, 31
""
triangle, 27
widening tools, 34
19
Clay, 43, 185
fire, 44
""
""
girders, 241
rules for calculating strength
of, 243
getting out working draw-
ings, 244
, in foundations, 197
13
""
C.
soft, or upper, 43
grey, or lower, 43
THERE ARE
iron-stone, 44
London, 44
Oxford, 43
plastic, 41
yellow, 44
slate, 47
slopes, 44
puddle, 195
366
Clay in embankments, 128
Concrete, 154
""
""
135
""
""
""
""
""
""
Cop, 168
Coping, 178
Cross sections, 55, 78
Culverts, specifications, 179
353
""
""
setting out in sidelong ground, 116
Curves, ranging curves-Chapter I., 1
to set out tangent to two straight
lines, 2
tangential angle, 3, 6
finding commencement and end of, 3—7
inaccessible lengths in setting out, 5-8
intersection of tangents inaccessible, 4
various cases of, 5
to set out by the tangential angle, 4
curves of similar flexure but different
radius, 6
straight tangent between curves of
contrary flexure, 6
having the deflection angle and the
length of curve, to find the tangential
angle and the radius, 6
obstructions in setting out, 8
ranging short lengths by offsets, 11—12
در
""
""
دو
""
""
""
353
13
""
""
composition of, 187
specification for, 176
expansion and contraction of, 188
gravel in, 176
lime in, 176, 189
sand in, 188
mixing, 189
wheeling away and shooting, 190
setting out without theodolite, 13
of wing walls, 101
Cuttings-See Excavations
""
315
""
DEFLEXIONS on cast-iron girders, 288
Deposits, alluvial, 52
diluvial, 52
""
Deviations from plans and sections, 1
Diluvial deposits, 52
Ditch, 168
Dressing stone-See Masonry.
EARTHWORK-Chapter VI., 119, 149
D.
slopes, 120
slips, 120
INDEX.
E.
Ellipse, 229
Embankments, 128, 149
Embankments, sand in, 49, 128
clay, 128
""
""
settlement of, 89
Energetic-application of this term as regards
the composition of mortars and cements, 193
Excavations-Chapter VI., 119, 141
""
""
""
""
""
""
""
""
""
""
Extraction of boring rods, 35
pipes, 37
""
FELSPAR, 52
Fencing-specifications, 142, 147, 167
wall, 167
""
Filling in of foundations, 180
over arches, 139-177
Foundations, 151, 197
"J
clay, 185
levels of, 92
""
""
99
GATES, 168
""
39
precautions in forming, 129
seat of, 129, 131
""
Gneiss, 47
Gradients, 82
Granite, 46
sand, 49
sandstone rock, 49
management of, 123, 127, 132
to spoil banks, 126
for foundations, 151.
occupation, 148
"J
for level crossings, 148
General clauses in specifications, 135
Girders, cast-iron, 237
"
Gravel, 45
F.
excavations for, 151, 180
cast-iron in, 197
concrete in-See concrete
wrought-iron, 237
Cornish, 46
Irish, 47
Scotch, 47
Greywacke, 47
Gullet, 123
Gypsum, 52
G.
H.
HEAD-PIECE in boring tackle-See Boring
Hornblende, 53
Hydraulic limes, 192
ļ
""
Pierpoint, 175
Piping See Boring
INERT-application of term in composition of Plate laying, 307
mortars and cements, 193
Iron, 240
Pocket section, 65
Portland stone, 48
Post and rail fencing, 167
Pozzuolanas, 193
Puddle, 195
Purbeck, 54
55
""
cast-See cast-iron girders
wrought-See wrought-iron ditto
LAND plans, 63
Legal enactments for the construction of rail-
ways, 265
Lengthening rods in boring, 25
Levels, setting out, 83
99
""
of rails, 309
bridges, 103
Level crossings, gates for, 148
Lias, 53
Limestone, 48
·Loam, 53
""
"
MAGNESIAN limestone, 47
Marl, 53
33
Masonry, 155, 224, 227
ashlar, 174, 223
block in course, 174, 225
pierpoints, 175
""
35
I.
""
""
L.
""
M.
""
""
Metalling for roads, 155
Millstone grit, 53
Mortar, 153, 175
""
rubble, 157, 225
dressing blocks, 224
mortar in, 224
technical terms, 227
NICKING out, 17
Note-book, or register for borings, 39
for setting out slopes, 62
N.
OOLITIC formation, 48
0.
PEAT, 53
Permanent fencing, 147, 167
posts for B.Ms., 55
way, 157
INDEX.
P.
RANGING, 1
Register for boring, 39
Riveting, 245-247
Road, form of, 170
Roads, temporary, 172
>>
"
legal enactments, 265
Rubble masonry, 175
backing, 174
SAND, 49
"
>"
"
Sandstone, 49
""
""
""
3
19
35
in concrete-See Concrete
in mortar-See Mortar
>>
""
ور
""
**
""
35
35
دو
R.
""
setting out slopes, 62
>>
55
S.
""
""
Yorkshire, 51
Scarfing-See Carpentry
Schist, 54
Schorl; 54
Derbyshire, 49
Dumbartonshire, 50
Durham, 50
Edinburghshire, 50
Gloucestershire, 50
Kentish, 50
Lanarkshire, 50
Linlithgowshire, 50
Monmouthshire, 50
Seat of embankment, 129-131
Section, working, 55, 65
Septaria, 54
Serpentine, 54
Setting out curves 2,
Northumberland, 51
Nottinghamshire, 51
Perthshire, 51
Rossshire, 51
Shropshire, 51
Staffordshire, 51
Wiltshire, 51
a bridge in a cutting, 102
foundations, 78
gradients, 83
367
368
INDEX.
Setting out levels, 78, 80, 90
of rails, 309
""
""
""
""
""
"3
45
در
21
""
slopes, 56
on the square, 93
on the skew, 104, 110
springers, 117
viaduct on a curve, 113, 115
""
""
Side-cutting, 127, 129
Side drains 121
Slips in cuttings, 120
Slopes, soiling, 169
wing-walls, 98, 101
of earthwork, 120
gravel, 45
Specifications-Chapter VII., 134
on the skew, 112
slope of, 117
general clauses, 135, 161
"J
Spoil banks, 126, 127
Straps, wrought-iron, 155-262
Stripping soil, 119
Surface draining, 122
TABLES, 315-322, 324-363
""
of skew lengths, 108
Talc, 54
Tangents, 2
Tar, or asphalte for arches, 177
Timber, 152
";
""
THE END.
T.
""
details of timber work, 158
Transverse strength, 237
rules for calculating strength, 262
constructions, 154
V.
VIADUCTS, setting out on curve, 113, 115
levels, 72, 90
""
19
W.
Woodwork, 154
Working section, 65
Wrought-iron, 244
10.0″.
11.0
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Published by Atchley & Co 106 Gt Russell Street, London. April 1857.
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Section through Tunnel Front.
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Published by Atchley &C. 106 Gt Russell Street, London. April 1857.
Section through Pilaster.
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Half Longitudinal Section.
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Angle of Skew 75+
Half Plan above Footings
23
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Scale 10 Feet
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Rails
of Railway
E/
A
B
Pl. Vill.

Section at R.
C
D
Line

Line


J.R.Jobbins
хо
Sq u ar e
14:
Piles
18
O
EI.
D
口
​C la p
-*
D
el v natio
ひ
​7'8
Ꮽ v Z
ם
口
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PL
ם
D
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D
-
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12
X
10
O
Ra
40
+X+0
10
'x
TRUSS FOR A 30 FEET SPAN.
I
LII
6x4
in
50
6.9
b
1
D
Skew span 33 feet & 30 feet on the square
675-
Strut
☐
ם
Transvere Section on the Square
Elevation

ם
0x
LI
26' é
12
6' ő
planking
A NA ZS
0
T
-
|
X
5 0
D
ם
12
X
10
6.9
ច
Try
Published by Atchley & C° 106 Gt Russell Street, London April 1857
10
m
کہ
D
ធ
D
ㅁ
​1
☐
X
O
D
口
​ப
ם
wh
ㅁ
​+
11
f
J.R.Jobbins
!

•
•
Enlarged view of Scarfing & c.
14
12
10
k
Op
34.
J
t
1
T
12
14
دگی
11.
Pile 14 Square
TT
t
+
bolt
Cast Iron Work at b.
+
I
1
1
12
3 4"
Fig 4.
1
1
l' pins
→→
**2
DI
13 long between
Read & Bur
1
holes dram?
10
1
!
1
Details of wrought Iron Strap at Foot of Struts marked (a)
NB The dotted lines represent the Strap for the Struts marked b
13
薯
​I
•
I
t
!
1
Axx cx_
1
3
Strut a
<***
、
ה!
badad
諗
​Published by Atchley & C° 106 Gt Russell Street, London April 1857
*
ܗܘ ܗܘ ܗܘ
-=-=-=-=-
Scale 6 Ft-1 Inch.
17
#1
U
གནས་གས་ ་ ་ གས་ ་ མ་་ ་ ས་
----K
PI. 9a


JR Jobbins.
13 -13
1/2 Bolt
= =>
13
10
Bolts 1/2
x-
·
1
13- ×-13-
A
BERERE DE
40 Feet
B
"
"
}}
Scale 4 Feet - 1 Inch
40 FEET TRUSS.
Elevation
1
}}
Published by Atchley & (°106 Gt Russell Street, London April 1857
C
D
208
↑
-ই
Pl 10

Cantlevers to be
foced on the head of
the piles by 5 spikes
12 long to each.
JR Jobbins
<-
سے
13
"1
12
"
Level
13 × 6½
12 × 6
Section at A.B.
14′ 6″
of
#1
13
O
13
5x0
ㅁ
​イグ
​170
14
}
}
}
1
1
↓
1
20 3
Section at C.D.
14 6
Ravls
13 × 6/2
#1
13
2. Š
O
13
ㅁ
​[
13
x
La
12
+92
12
Scale 4 Feet to one Inch
Published by Atchley & C° 106 Gt Russell Street, London April 1857
13
->
-
ㅁ
​12
Pl. 10 a

91
16″ 6:
Casting
× 15
12
12
12
5
at B.
Scale 4 inches 1 Foot
.
Enlargements at
xx 15
16"
7'
at A & B
16' .
"1
16
TRUSS FOR A 40 FEET SPAN.
x 15"
A
,
16" x 16'
☐
}
1
{
}
}
ㅁ
​TOT
向
​I U
"1
16"-
x 15
14
16°
× 16"
Transverse Section.
15' 0"
ㅁ
​C
B
Irne
Elevation.
Published by Atchley & C° 106 Gt Russell Street, London April 1857
10' 6
of
40
Scale 10 Ft = 1 inch
16'
0"
16".
B
Rails
16".
JA
1'. 5'
•
A
Casting
A
at A
Scale 4 inches = 1 Foot
Scale 1/4 of an Inch - 1 Foot
w
Pl 11






JR Jobbins
The
←
Straps 3x72
#
1
I e v
Joist notched on
2
"/
е
6
7
10 6
"}
15 x 9"
Cast Iron Shoes 1/2 thick
12 6
15 × g
乙
​#
to the
Sectio I
→→
f
Principal
15" x 9
15 × 9
X
X
× 4
R
a
i
4 × 7/8
xo
Z
S
26..
15 x 9
15 × 9
1
146
I
e
15 × 9
15×9″
4.4
TRUSS FOR A 44 FEET SPAN.
7
Elevation.
Tumbers in parapeb 4" square
Board ½ thick
Board 1% thick
Cast Iron Shoes
Wrot› Iron plate 12″× 9"x1/2″ 15×9″
Key holes 34x1"
5 of Iron below Keyholes
〃
Scale 5 Feet = 1 Inch
Published by Atchley & C° 106 Gt Russell Street, London April 1857
-- 5' 6
6 Ő
6.6
6.0
S
xx
I e vel
Ashlar
2' 0"
19"
"
Cross Section
16.
12
イグオ
​of
15" x 4
17" x 9
"
12 × 12
18′ 9″
R a i l s
19
Ashlar
D
Pl. 12.


JR Jobbins
·
·
❤
19½ botts
#1
4 x 4"
"
}
Τι
пе
1
Details
6
Q O
1.
20
at A .
of
I
'5″.
77
LO
·1.2 - - - - - 6
1
1
6
!
1
4″ × 4″
Rails
1
Scale ½ an Inch to one Foot.
Published by Atchley & C° 106 Gt Russell Street, London April 1857
1.0
-1.2-.
7/
4
X
4"
K--
12″.
10"
12" × 12"
42
--1.2.
Pl.13.

·
J.R.Jobbins.
1
12" × 12"
4'x4'
Details
I i ne
-XO,
IX W
10-
If bolts-
12
0
171
"/
at B
2 5
f=
#
5
1
کا
چاه
1.0.
q Y
"1
6
O
Q
O
4"x 4"
Παντς "
↓
H Z ine
D
B
17700
4.4″
Elevation
50 feet
Scale 12 Feet - 1 Inch.
- -5′3″
J
1
Raits.
~Let
F
Half Transverse Section
QUUUUUL
If½ bolts
Ꮮ
Z
6 ó
12″ × 12
"/
ވ
1
at C.D.
n
е
For details - Scale 1/2
TRUSS FOR A 50 FEET SPAN.
an Inch - 1 Foot
Published by Atchley & C°106 Gt Russell Street, London April 1857
1
1
о
f
1
250
4 8
Half Transverse Section at E.F
R
8″ x 8″
a
z
"
=∞0×80
14'
Z
1 ½ ----16
10
1
1.2.
ហ
14
3 6
-1
1
- 12″
6"
{
1
1
1
1
40.
6
br
اور
Ht
12
Batter in 30
JR Jobbins
PI 132

1
"
#
पद
1276
12×12
16×8
16×8″
6 × 4
Level
12×12
"
× Co
カメヤ
​16×8
}}
16x8
tal
ם
ㅁ
​#1
12
X 11
12
O
O
14×8″
#
1
I
#4+4
е
Half
ν
е
N° 3.
Transverse Section
Z
14 × 4/2
12 × 2
12 × 6
12 × 6
12* × 6
0
14 × 8″
X
8' x 5
No 2.
f
12 × 6
Elevation of Inner Rib
of
K 14
X
0 4
Scale 4 Feet - 1 Inch
=
•x
.::5
--ribe
R
5 × 3
11
a
-
O
A
}}
12
X 11
12
[O
14" x 8
z z
//
7 x 4
Published by Atchley & C° 106 Gt Russell Street, London April 1857
||
イメーズ
​16x 8″
S
11
6 x 4
1
1
Ra v l s
12×2
Fi. 14 d


JR Jobbins.
C
Stone Step
W
по
O
N
Akan mulan Mudge
TIMBER FOOT BRIDGE WITH CORRUGATED IRON SCREEN.
"
Note. Wrought Iron Straps 2½ x 1/4" and 3/4″ Bolts.
X
n
3′0″
THE TWO TRUSSES ARE 8 FT APART.
Cor
wg
Elevation.
z e d
I ever
of
I ron
15
t
12"x
8 × 4
r e e n
Ra v l s
Published by Atchley & C° 106 Gt Russell Street, London April 1857
พ
S
› by man
Z
JURNA
↑
Scale 10 Feet
es
1 Inch.
7"
Pl lb.

J.R Jobbins
N


↓
ax 8.
12
X
1236
1 2 × 1 2
Cast Iron Boxes for receiving the ends of the principal Rafters.
4X4
1
}}
16×8
16x8
1846
12×12
12
X
161
TRUSS FOR A 50 FEET SPAN
1
Elevati on
Scale 1 Foot -1 Inch for Nos ja 2ª & 3 a
Scale 10 Feet - 1 Inch.
50 Feet
Sect 1 on
6 x 4"
N° la
No 2a
Plan
I
►
N° 1
Enlarged
Half Elevation of Outer Ribs
14 × 7
е
乙
​14 x 8'
=20
diam!
12½
25′ 8.
Scale 4 Feet - 1 Inch
0
f
14
ገባ
5x
Published by Atchley & Co 106 Gt Russell Street, London April 1857
7*4
12″ × 7
6x4 V
"} "1
16×8
No 3 a
Enlargement at A
し
​S
| | 12 × 2
TR b
}



1
}
+
6 x 6
3/20x
** 9
Two 1/2 bolts
st one
-3′ 18¾½ -
}
+4/2x4/2
1
Rise 1 in 5
472 472
36 0
$7/2
X
Half Elevation.
12″ × 6″
6. Ő
TIMBER FOOT BRIDGE
68
Scale 4 Feet - 1 Inch.
6 x 41/2
Q
*
Four/%" bolts
Ú is
34¾½--
!
C
1
12′ Ő
t
VA
}
--
6.0.
Published by Atchley & Co 106 Gt Russell Street, London. April 1857
I e
1
V
e v
6.0
18.Ő
D
16.34
of
B a l a n c e
C
6.0
R a i l s
I i n e
15 0
"
·4 ő-
S t o n Ø
-
JR.Jobbins.
Pl. 16



3.6
Towin
33.0
26′. Ő
t
1
1
1
}
I
!
1
1
Į
Cross Section of Bridge
Surface
P w
d
of
G
1
1
}
}
1
1
1
|
1
I
!
44.0
I
I
1
Present Surface of Ground
Į
Water
d i e
Path
Scale 10 Feet
1 Inch
Published by Atchley & Co 106 Gt Russell Street, London. April 1857.
///
I
Mattel M
¡
i
!
IKE
Half
Elevation.
12.0
AQUEDUCT BRIDGE
I o
!
w i n g
I
1
1
(
1
1
1
59′. Ő
C
e
Pa
n
+
Sadaka pa v kad ga v s m
J
Mad Maga
Pla
TITI
z h
tr
1.6
L
То
33.0
li
W
11
59'.
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ļ
I
N
9
2
f
0:9
F
↑
1
I
I
1
1
Po a
I
¡
!
Ե
i a
h
N
Ő
153
773)
Surface of Rails
a l
32′.0"
JR Jobbins.
Pl.17.
33
33
Surface
atat
09
of Rails
Half
החזות
7
Surface of
Longitudinal
P
C o n c rete
C e
W
d
32 Ő
Water
TV t r
Ե
33 ő
ď
Z
е
@
9 ና
40 &
I
I
}
11 Ő
I
I
Section
All the Fe
AQUEDUCT BRIDGE.
Fekk == q + + F F F
A++ #++ = = x + Haq x <-
10.0.
Plan
o f
32' Ö
Scale 10 Feet - 1 Inch
26
Published by Atchley & C° 106 Gt Russell Street, London April 1857
<
с
Section at A.B.
1
I
I
33′ 0″
1
1
1
!
I
1
I
1
#
!
I
I
a
5'0
59' 0"
TV
4'6
ου
Z
B
A
59' 0"
Pl.17.

A
187
JR Jobbins
*
}
Level of Towong Path
Slope
of
Embankment
Foot of Slope
02
看看
​19--
5.7%
-23..
1
1
I
I
16 Ő
1
1
I
I
I
I
I
•
I
1
1
0
1
!
1
1
I
t
1
I
I
J
7
|
..b
2
co
Half Elevation
53
e_
Į
!
1
CAST IRON AQUEDUCT BRIDGE.
10
41
T o w v n g
e......
1
P r c po s e d
3
Path
56
v r d er
>
10
||||||||||
[m]
I o w i n
P-
Gur der
To
V e ve l
I
Section at gh
Pat h
for
Scale 4 Feet = 1 Inch.
K
Ro a d
Published by Atchley & Co 106 Gt Russell Street, London April 1857
1
{
ļ
"
Half Section.
36.
////////
/ / / / / / / //
6 6.
///////////
/ / / / // ///////,
////////
Towing Path
/ / / / / / / // ////////
Pl 18

JR Jobbins

pal, legat dan vande de alta
cara prin allega
dad de la p
dar village had to add to t
Gurder a
W
27
I
8
I
=m
I
}
I
1
1
1
1
}
1
|
I
1
1
1
#
16′ Ó
1
1
1
1
I
·
1
1
1
Water
1
}
Section at ef
< 14/16
F
www.
Bottom
0,2
L e ve l
- Nac
Plates
Top of
Counterforts
7
Section at ef
TÓ
P u d d l e
Present
H
of
O
{
Surface
Level of Water
Canal
in
A q u e d u c t
P
Abutment Plate at x.
}
1
I
I
I
5′ 6″
✰
14″
Ο
4
O
I
TH
1
12
1
[
Firefor
tore forest
Level
Plan of underside of Bottom
Plates of Aqueduct.
Scale 4 Feet
1 Inch
Scale to Enlarged Parts 2 Feet 1 Inch
Section at ab
O
of
5
Published by Atchley & C° 106 Gt Russell Street, London April 1857
Cover u n gi∞
6' 8
I o w v n g
9
10
!
1
P l a b e
Section at c d
6' ő
Towing
Path.
།།
Path
12 X
Level of Water
1
I
Bottom of Canal
Section
at c d
Level of Towing Path
<
0 +
I
-
K
[
1/2
10″
12
< 2½ >
JR Jobbins
6
09
1
I
C
t
19.
721/20
-→
I
1
ľ
4' ő
80
3 ő
g
✨ 2 ő
2 Ő ×
1
Iine of Foot of Towong Path Wall
Iine of Towing Path Wall(Coping)
4'. 9
I o w v n g
4' 9
=
X.
.-5′-6″--
OC
Path
A q w
1
Dobbet Wo
LE
e dz
c t
A q w e d w cz
5' 6
-5-6-
h
Centre
Plat
33 9
Plate
1
e s
I
Plan.
I v ne
S
I
t
t
Covering Plates
0
1
I
1
31
of
of Towung
Canal
A
15 0°
31.1
d
Path
G i
r der
G v r d e r
i
Scale 4 Feet
35′ 9″
1 Inch
X
4′ 3/4-
X
4 34
Gurder
G v r der
}
G r r d er
Published by Atchley & C° 106 Gt Russell Street, London April 1857
Fo
\\\\\\\\\\\\\
\……………\……….
2.0″
f
1
+4
<
-
20
L
A
F
Pl 18 b

HHHHHH
JR.Jobbins
M
↓
Vegetable Soil
Turf Moor
Sand
Gault
}
1
Sood
1
I
!
.. 30 0´.....
F
}
凹
​30'0
FF
lowing
1
6'0..
THE
Path
KIM
O
16
.
口 ​O 口 ​♫
D
O a
Half Plan of Bridge Complete
V
♫
TO
Le ve l
ሩ
1
يام
10′0″
a.
12'. É
of
Elevation
30
Բ
W a te p
+40
•
DKI DK
Scale of Feet
O
D
པ
51
•
•
DIKI
KILL
▸
33
BRIDGE OVER THE RIVER OUSE AT HILGAY, DESIGNED BY J S VALENTINE CE 1847.
Q
DK CRICK
•
Published by Atchley & C° 106 Gt Russell Street Londor Apri 185
•
MIM
Half Plan of Tumbers
A p
XK
DAK
KILIKI
2
15
O
K
O
Ill
→
Q
ミ
​Two thicknesses of 4% Fir Planking
O
GO
>
O
Q
DE
NE
•
13
O
미
​ե
C
1
30′ 0″
•
Peet
Gault
13
O
}
•
......
.30.0
་
{
I
I
HT
→
•
Pl 19


Section of Capping on Bow
Section shewing Abutment Plates to Struts
and Plate to suspending Rod
co.
36
"
2
BRIDGE OVER THE RIVER OUSE AT HIL GAY
I S Valentine Engineer
5 Ó
12'× 9*
K
1---
I
12inch
5
14/17
O
4/2
6
K--
O
O
7
Scarf to Beams of Bridge" full Size
+
Cross Section.
Scale 4 Feet = I Inch
10
1
26 ő
1
910
Suspending
U
O
5 t
I
I
1
t
↓
I
Scale of Inches and Feet
Q
O
+
1
f
J
[
1
Rod
O
O
↓ T
D
L=d
5 0
12 × 9"
X
Published by Atchley & C° 106 Gt Russell Street, London April 1857
, о оч
O
O
1
I
¦
1_
5 Feet
-X-
20.
36
PARVAN
ļ
Pl 19a


JR Jobbins
12
Plan of Abutment Plate for Struts
6
O
2 2*
1
ช่ 2.
CONS
Elevation of D°
-
14/2
3%
ड
8
Double
End view of Abutment Plate
with Struts fixed
=10
--
2/17/1
Plate on Bow for Suspendmg Rods
"
2 2
End view of Shoe
12
Scale 1/2 Inch to 1 Foot
2
?
º
24
♡
个
​2 2
Suspending Rods
-
イイ
​51
22
Plate under Tie Beams for
Susponding Rods
.
#
2
2 6
1+
Abutment
6 Fb
160
24/4A 2
ng
for Outer Bow
BRIDGE OVER THE RIVER OUSE AT HIL GAY
DETAILS OF IRON WORK.
I S Valentne Engineer
Elevation
6
1
Xó
ģ ..
for Inner Bow
O
--
'
A=
2.2
Plan of Covering Plates.
5
22
12
30 In
Ө
O
1/4 130U
5
* 9
10
62
"
ข
Section at a b
Publihed by Atchley & C° 106 Gt Russell Street, London April 1857
Will
of Shoe
O
O
1
Į
Plate
- 3 - -
A
2 2
22
Plan of Shoe
о
20
19
2
•
I
t
督
​10
10
End view of Shoe with Section of The Beam
Pl 19b


JR Jobbins
2 FEET CULVERT
9
Section
Gravel
Elevation
16.
1'6'
2 ő
on edge
16
FOUR
Longitudmal Section
"
8′ 0″
--
16
in Cement
Section 1½ B
←
FEET
B
3131/18
40
3.0-
I
1
+
1
29.
York
B
-17/2--
2 É -
V B
/
#
16
BAR
>
CULVERT
B
17/2
Plan
B
1½
}
1
1
}
I
1
Į
I
Cross Section
4.0
0,2
7%B
Longitudinal Section
1% B
16
d
1
8 0
H
Scale 4 Feet
Plan
со
1 Inch
FRAMHER
Bala
5
3 B-
FEET
of Entrance
ź 6.
3' 6'----
Published by Atchley & C° 106 Gt Russell Street, London April 1857
1
?
1
CULVERT
on edge vn
1
..2 6
Elevation
vn Cement
A
Cross Section
Elevation
104
on edge in Cement
3 ö
Batter i'th per Foot
2 6
13
Pl 20










JR Jobbins
f
28
3.
B
* 12.0"
Q
Plan.
12.0.
Slope 1½ bo 1
6
}
2.3.
<--
FEET
1/2 B
H
3 B
E m b a n k m e n t
Cement
#
65. Ő
0
128'. Ő
I
3:0
I
+
1
i
į
CULVERT..
Elevation.
!
on edge
την
2.
B
1/2
6.6.
6.0
Cement
Cross Sections.
6
1
1
D
20
blad
3.0
ސ
12′.0″
BB
Scale 4 Feet
1 Inch
Published by Atchley & C° 106 Gt Russell Street, London. April 1857.
|
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J.R.Jobbins.
Slope's in 20
10
0
#
Surface of Ground
Scale 6 Feet = 1 Inch
q f
птолет
похолат
1
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C
10
←
10
51
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EX
GATE FOR
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1
LEVEL
Fransverse Section
5.4
MĚZAVAZÁVAVAŽNA
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Y
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Published by Atchley & C° 106 Gt Russell Street, London April 1857
*
allas
•
8' Ő
0
0
0
D
--
68
- Road Material
| 1 3
4 ģ
20-28
1
↓
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Surface of Roadway
20110
15′ Ö
Pl 21



JR Jobbins
10
X
10
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94 bolts
TURNPIKE AND PUBLIC ROADS. GATES FOR LEVEL CROSSINGS.
Elevation
25 6
A
1
F
I
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1
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1
I
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|
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4 × 3″
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1
Rivets
Details A and B. Scale 1 Inch - 1 Foot
cox
O
Published by Atchley & C° 106 Gt Russell Street, London April 1857
Plan
25' Ő
B
1
I
1
B
1
1
1
1
I
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2"
F
1
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1
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JR Jobbins
A
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↓
3′. Ő
ott &
1
JR Jabbins
12
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12
"1
12
12
12 Pin
7/2 ×
***
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4.6
O
4 x 3
3 × 1/4
O
Iron 2½ × 3/8″
B
3×17/4
X
3 × 11/4
OCCUPATION
#7
34 bolts
Plan.
11.0″.
4.3.
Elevation
15
6.3.
•
ROADS
10.
3x3
3
xQ
Published by Atchley & C° 106 Gt Russell Street, Lordon April 1857
9°
9
Level
of
Ravi s
Scale 2 Feet = 1 Inch.
W
Pl. 22 a
+

+
96
!
1
1
1
+
1
}
1
O
O
Rails
Scale 10 Feet = 1 Inch
Elevation.
O
O
10' 0
4'6
f
O
Scale 2 Feet - 1 Inch.
Plan.
10 × 10
O
A pin
174
1
Ο
4
GATES FOR LEVEL CROSSING
O
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1
1
1
Q
O
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XRT
FIELD
5.4
4.8
9,1
2. Ő
ROAD.
3/2½ x 1/2
Slope 2 to
4/12
X
Published by Atchley & C° 106 Gt Russell Street, London. April 1857
The width of the Top of the Embank must in all
cases be 6 Feet more than the width of the Bridge
within the Parapets
of
Road wa
Metallumq
min
Faggots от
1
1
1
t
董
​Section of an approach to a Bridge
Scale 1/4 Inch = 1 Foot
}
3/2 × 1
3 1/2 x 1
Scale 5 Feet 1 Inch
3/2 × 1
X
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Brushwood
N
J
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3 × 3
3
Slope 2 to
Pl. 23

JR Jobbus
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Pubnshed by Atchley & C° 106 Gt Russell Street, London April 1857
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Published by Atchley & C° 106 Gt Russell Street London April 1857
JR Jobbir
небритые мон
A..
4 Tive Drain
Porch
..
2.10
I
5 11½
}
4. 9/2
4.
3.3
4 Tile Drain
2.1
1.8/2.
1
N
N
2.3
1.2
Inch proper ledged Door
with rounded linings
both sides, Thumb Latch
316
7.4
3.3
Living
12′.8"
4.0
9" Quarry Paving in
beaten Mortar.
♡
ROADSIDE STATION.
Booking
12.6
12′. Ó
4 Quarter Partition
2.6
RooI
Counter
Ground Plan.

ģ
m
Office
gő
11/4 Yellow Deal Floor
128.
上し​ap
2.3
5.8
Bay Window
1
2.12.
4.6
York Paving
1
3.Ö
4.0%--
Inch proper ledgedi Door with
and rounded lining next Closet
Architraves next living Room
3.Ő
4.Ö
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+
1
1.6
I
1
1
1
Cast Iron
Oven
1.6
4.4.
·3" York Step
1.1ő¼‰
Copper
1.2.1.6
42 Quarter
filled in with
4 Tile Drain
3.3
3. 2¾½ --
Inch proper ledged
Door rounded linings
both sides 6 Fron Lock
8.0
Washhouse
Brick on Edge Paving
Sink
2′. 9"
Published by Atchley & Co 106 Gt Russell Street, London. April 1857.
partition
Brick nogging
Pantry
Brick on Edge Paving
D
I
3'.9
1
=00
-4/4/
2.3
!
..B
4" Tove Drain
Scale 4 Feet = 1 Inch.
4" Tile Drain
T
TR Jobbins.
Rainwater pipe
Pla i n
Tiling
6.6
#
I
t
Chamber
3.2%
Inch deal Folding Floor
Quarter partition Sill 4 × 4
x
Quarter partition Sill 9 × 4
?
:
molded
Į.
Plan
Inch deal Folding Floor
3.2/2..
Zinc Gutter
2.5
NV
1.619
1.2
SW. Lead Hips
flashing to ridge •
N.S
g
ROADSIDE STATION.
Coping Bricks in Cement
5.5½.
Y
Rain water pipe
}
6 Cou
•
P l a i
1
I i l i n g
22 Courses
р
Door Frame 5 × 4
Scale 4 Feet
Sof
22 Cast Iron
Rainwater pipe
Gutter
4½ Cast Iron Eaves
X
Posts 4/2 × 4
Purlin 5×4
Z
Rafters 4x
1 Inch.
Head 4% × 6
leiting Torst 5
Head 4/2×4
Brick on Edge
:00
18 Courses
*13 Courses.
Wall Plate 6x51
returned all round
the Walls
2.3
Published by Atchley & Co 106 Gt Russell Street, London.. April 1857.
I
1
!
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Veiling
9
Section at A. B.
z ž
Wal plate 4x3
returned all round
the Walls
Common Rafters 4/½,
-Ridge 9″ × 1½
Collar है x 3
Ter
Ceiling Jousts 3 × 2
X
8.0
Posts 4×4
Quarter 4 × 2
Principal
Kink
Head of Partition 6 × 4
Spiked to principal Rafters
FoÿSV-7332" -Strwbted
-7332″-
Rafters
Q ua
Sill 9 × 4/2
Zdr
1
4 x
Postis
Purlin 6x4
+
a v in g
39 Courses
12 Courses
40 Courses
I
Pl. 25 a

J.R: Jobbins.
}
#
1
5.0
Cesspool
2 Fork Stone
1
1
1
I
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f
7.6
1
1
↑
7
C
A.
群
​2 3
2
1
in Brick
!
Note The Walls and Ceiling of the Kitchen Staircase Living Room and two
Bed Rooms to be plastered three Coats the Walls to be twice colored
the Ceiling to be bwice Lime washed.
5'. 1
9'Barrel Drain Iron Grating
3'. 6
Wood
.2.0..
3.3
Inch Deal Floor
Inch Deal
Shelkon
proper bearers
House
Brick on Edge
panng in Mortar
Small
Cesspool
GATE
2.10 …..
Oak Sill
Inch proper ledged
Door thumb Latch
3 and small Bolt
7'. 3
7. 6
1
I
I
I
}
Pantry
in
9° Quarry Paving
1.2
1. 17/4 × 1.37/2
Ground
KEEPER S
4 Tile Drain
1.6
"
17 Gatton
Copper
1.6
Cast Iron
Oven
1.1½-
Tooled Hearth
3'. Ő
ME
§
3.9°
York Paving
1.2
Plan.
LODGE.
4" File Drain
.3.5%
Sunk Stone
Sink
Inch proper leadged Door with
Architrave. mouldings inside
8 stock Lock's and 2 Barrel
bolts ornamental latch
Kitche 1
9" Quarry Paving
in beaten Mortar
Cement Skirting,
Living
12.0°
1
3.0
Deal rounded handrail turned newel
and square bar Bannisters inch
partition to enclose Stairs
K
:
9' Quarry Paving in beaten Mortar
Inch Deal Square Skirting
9 Inches high
Room
3.22.....
Ledged Door
with Closet
4.9
прот
1
·
12.Ő
:
f
:
:
17
!
:
Bay Window
3 tooled Door
Step
Published by Atchley & Co 106 Gt Russell Street, London. April 1857.
3.3
|
t
1
W`6
5.11
4 Tile Drain
B
Scale 4 Feet 1 Inch.
Pl. 26.

2/½ Cast Iron
Rain water Pipe
Coping Bricks in Cement
I i ṛ v n g
Pla i n
Coping Bricks in Cement
不
​2.3
4. 6
Chamber Plan.
- i Ñ ½ G
1.2.2
1.2
прит ч
2.3
11/2-7
Tooled Hearth
Back
Bed
Room
Inch Deal Folding Floor
Inch Square Skirting Thigh
2 Inch Rubbed
York Hearth
2.67%
4" quarter partition, the heads spiked to
Front
the principals of Roof and the Sill dovetailed Inch Ledge Door
at each end to the Wall Plates
Bed
Inch Ledge Door
Thamblatch
__ï.6½-
Inch Deal Folding Floor
Inch Square Skirting 7" high
& Barrel Bolt
Room
I
I
1
+
Thumb Latch &
Barrel Bolt
GATE KEEPERS LODGE.
2 Inch Cast Iron
Rain Water Pipe
and Rage
Plain
T i l i n g
amu ng
Courses→
1
I
15 Courses
5 lb.milled Lead stepped
flashings next Wall
Parlin 5x4.
Rafters Pe
Plate 4x3
Window Bond / × 3
9 Quarry
Scale 4 Feet = 1 Inch.
*
I
1
1
18 Courses
Courses
Plate 4 x 3
Brick on Edge
in Cement
Section on Line A.B.
lating Joists 3 x
Bond 4 × 3
X
Paring
Published by Atchley & Co 106 Gt Russell Street, London. April 1857.
Bracke
2 x 8.
۱۲
3 York: Step
-
26 2
eft x n
1. #
-J
·
Plate 5×4″
1
I
Common Rafters
ist
Wall plate 4.3
returned all round
the Walls
47/2 × 2
Iv ne
·
"
tett 6 x 3
ar ex
Ceiling Jousts X
Head of Partition 6× 4
spiked to Principal Rafter
दिना
Ridge 91%
Shutt ve
Sill 9x7
Yellow
Joists
Principal Rafters
9x6
Brick
Deal
5 × 2
Bench 8×3.
Post 4 × 4°
Floor
Fo o t i n g s
Purlins 6x4
x 3
T
29 Courses
Coursesx-
39 Courses
t
Plates 65 to be
returned round the Gables
bur
4½ Cast Iron Eaves Gutter
40 Courses
I
PI. 26a


[
J.R.Jobbins.
6″ x 6″
1
1
S t at e
5
===<#
4
X
2. 6°
Plan.
19'. Q."
·2.6^
S la te
t
J
t
f
I
I
+
1
Ø
^
6
U
N A L S
Elevation
R
I
.2′. 6′
5' x 4"
I
1
Published by Atchley & Co 106 Gt Russell Street, London. April. 1857.
= Loxt
5
4
#1
4 x 2
H
11/4 Boarding
#
6
X
6
"
A+G
4
6′.0"
↓
အများအာ
O
O
Section.
Scale 2 Feet 1 Inch
1
+
2'.0"
s i a z e
"Cox*
5
X 11
4
12" x
4
ก
ון
=c++
X
Pl. 27.

C
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J.R.Jobbins.
Framing of the Arm
A
B
O
O
Q
O
O
O
O
O
O
10
O
O
000000000000
O
O
3
O
7
2'. 0
The Zinc Plate is Rivetted to this Framing
thaig
$
1
I
I
།
O!
1
[
1
1
O
O
10
3
O
O
O
O
O
Onderde
O
O
O
O
O
Elevation.
1 x 27/2
Wear Rod
:
:
Staple
**
O
Staplę
000000000000
Pin to Stop
the Lever
1 dram
8/2
SIGNAL

1/2 2 13¾4 2 12 1½
"
可
​2
9°¾/4
93/4
Ź
93/4
1/2+
1 ½ ½ 2 2 × 2 ¾
4 2 221%2
1
і гипогру
Side Elevation
C
D
ㅁ
​¿
Published by Atchley & Co 106 Gt Russell Street, London. April 1857.
1
1
$
Rest Stop
Rod #diam?
A
Section at A
H
Rod ½ diam
1
1
Section at B.
Caution Stop
1
Rod 1/2 diam.
Indo
·Danger Stop
Ad Post
General Drawings Scale 2 feet = 1 Inch
Details.
Scales full size
•
--
7/26
I
0
!
1
1
Pl. 28.
I
•
2
I
i
¿
Date Due

}

I
1
Transportation
Library
TF
200
H37
v.2
Haskoll,W.D.
Railway construct-
lion

意​!
5
浙
​1
*
3.1