Acute angled triangle, 2.
Angle, definition of, 1; measure of an, 3;
to measure an, contained by two straight
lines, 7; to set off an, to contain a given
number of degrees, 7.

Angle, acute, 1; obtuse, 1; right, 1.
Angles vertically opposite are equal: the-
orem, 8.

Barometer, levelling by the, 157.
Beam compasses described, 64.
Bench mark defined, 138.
Bletchingly tunnel, 191.

Box sextant, 71; method of using, 72;
elimination of the parallax, 73; for lay-
ing off long offsets from a station line,
74; to obtain the angle subtended by
two objects in the same horizontal
plane, 73; to obtain the angle subtended
by two objects in the same vertical
plane, 73.

Box tunnel, 190.

Brick and stone viaducts, 215; brick via-
duct at Maidenhead, 215; London and
Greenwich Railway, 215; Ouse Valley
viaduct, 215; Quaker's Yard viaduct,
215; South-Western Extension Rail-
way, 215; stone viaduct over the Ouse,
215; Vale Royal stone viaduct, 215.
Bridge Britannia, 212; Conway suspen-
sion, 214, Gainsborough, 214.
Bridges, Irón tubular girder, 214; lattice,
217; oblique, or skew, 216; railway,
212; tubular, and other girder, 212;
wooden, 217.

Britannia bridge, description and dimen-
sions, 212.

Casting, computation of area by, 38.
Centrifugal force of trains in railway
curves, 209.

Chain described, 9; Gunter's, 9.
Chain, surveying with the, 32; to survey
four-sided fields, 40; to survey fields
having more than four sides, 42; ex-
amples, 43; defects of the common

method, 45; to survey lakes, 48; to
survey large estates by the, 58; to
survey parishes with the, 58; to sur-
vey swampy ground, 48; to survey tri-
angular fields, 35; to find the area of
triangular fields, from the three sides,
36; to find the area of triangular fields
by casting, 38; to survey woods with
the, 48; method of measuring hilly
ground, 52; examples, 53; to erect a
perpendicular with the, 32; to find the
width of a river that the chain will not
reach across, 35; to measure a line im-
peded by an object not obstructing the
sight, 33; to measure a line impeded
by an object obstructing the sight, 33;
table showing the reduction in links,
&c., upon every 100 links, for every half
degree of inclination, 52.

Chain and cross, to survey with the, 15;
to survey fields included by any number
of crooked or curved sides, 24; to sur-
vey fields contained by more than four
si les, 20, examples, 21; to survey fields
in the form of trapeziums, 18; to survey
square and rectangular fields, 15; ex-
amples, 16; to survey triangular fields,
17; examples, 18; to measure a line
across a wide river, 31, to find the area
of a piece of land, the dimensions being
given, 30; to find the area of a segment
of a circle or any other curvilineal
figure, 29.

Chord defined, 3.

Circle, definition of a, 3; chord, 3; cir
cumference, 3; divisions of a, 3; radius,
3; sector, 3; segment, 3.

Circular protractor, 13; described, 79;
method of using, 80.

Circumference defined, 3.

Compass, prismatic, described, 69.
Compasses, beam, 64; drawing, 11; hair,

11.

Conway suspension bridge, 214; tubular
bridge, 214.

Copying, methods of, 07.

Copying by squares, 68.

Crooked fences, use of parallel rules in
reducing to straight ones, 54.

Cross defined, 9.

Curvature, correction for, 131.
Curve rulers, 158.

Curves, railway, examples of the ex-
pensive severance of property by im-
properly setting out, 176; laying out,
158; limits of, 159 (see also Railway
Curves).

Cuttings, railway, setting out, 181; level
book used in setting out, 186.
Cutting, railway, to find the surface
width of a, when the ground is very
uneven, 185; to set out the width of a,
when the surface is laterally level, and
at a given height above the formation
level, 181; to set out the width of a,
when the ground is laterally sloping,
182; to set out the width when it con-
sists partly of a cutting and partly
of an embankment, 184; to find the
contents of a, 192; tables for finding
the contents of, described, 192; to find
the contents of, the areas, its length,
bottom, width, and ratio of the slopes
being given, 196; to find the content
of, when the ratio of the slopes of the
two sides are given, 199; to find the
content of, when each of the sides
have two different ratios of slope, 198;
to find the content in cubic yards, the
depths, width, and ratio of slopes being
given, 194; to find the quantity of a
cutting of a tunnel, 199.

Datum line defined, 136.
Degrees defined, 3.

Diameter of a circle defined, 3.

Division of land (see Land, laying out and
dividing).

Drawing compasses, 11.

Equilateral triangle, 2.

Engineering surveying, 126; levelling,

126; method of laying out gradients,
153; method of laying out railway
curves on the ground, 158; methods of
finding the contents of railway cut-
tings, 192; on setting out the surface
width of railways, 181; tunnelling, 188;
problems and formula of utility in,
204.
Engineering surveys by the theodolite,
89; to survey woods, lakes, harbours,
&c., 90; method of taking the angles,
91; planning and proving the work, 92;
to survey roads and rivers, 93; to sur-
vey a town, 95.

Estates, method of surveying large, by
the chain, 58.

Fences, use of the parallel ruler in re-

ducing crooked to straight ones, 54.
Field book, description and use, 14; Rod-
ham's improved, 81.
Figure, quadrilateral, 2.

Lakes, method of surveying, 48, 93.
Land, to calculate the, required for a
railway, 187; division of, 225; Acts
of Parliament relating to the division
of, 125; division of among various
claimants, 112; to divide a rectangular
piece of ground among any number
of claimants, 112; examples, 113; to
divide a triangle equally or unequally,
113; example, 114; to divide an ir-
regular field among sundry claimants,
115; to set out from a field a quantity
of land that shall have a given value,
117; to divide a common of uniform
value, 122; to divide a common of
variable value, 123; method of setting
out roads, quarries, &c., previous to
enclosing commons, &c., 123; method
of dividing the remaining part of the
common, 124; to divide from a field or
common any quantity of land, 110; to
divide a quantity of land from a tri-
angle, 108.

Land, laying out, 100; to lay out a given
quantity in a circular form, 106; ex-
amples, 106; to lay out a given quan-
tity in the form of an ellipse, 107; to
lay off any quantity from an irregular
field, 108; examples, 109; to lay out
a proposed quantity in the form of
a rectangle, 101; to lay out a given
quantity in the form of a rectangle,
the length of which shall have a
given proportion to its breadth, 102;
to lay out a given quantity in a regular
polygon, 105; examples, 106; to lay
out a rhomboid of given area, 104;
examples, 105; to lay out a given
quantity of land in the form of a
square, 100; examples, 101; to lay out
a trapezium of a given area, 104; to
lay out a triargle of given area and
base, 104.

Land surveying, 1; instruments used
in, 9, 62; methods of dividing land,
112; methods of laying out land, 100;
railway surveys, 88; to survey with
chain and cross, 15; to survey with
chain alone, 32; to survey with the
theodolite, 89; problems and formulæ
of utility in, 204.
Lattice bridges, 217.

Laying out and dividing land (see Land,
laying out and dividing).

Level book, examples of, 145, 148, and 153;
examples of, for running or check levels,
142; practical, 137; used in setting out
curves, 186.
Levelling defined, 126; by the barometer,
157; cross levels, 148; example of level
book, 148; datum line defined, 136;
example of level book, 136; levels for
the formation of a section, 144; ex-
ample of level book for plotting the
section, 145; levels for the formation
of a section: to draw the section,
147; operation of levelling, 139; par-
liamentary plans and sections, 149;
practical level book, example of, 137;
principles of levelling, 133; to find the
difference of levels of several points,
133; examples, 134; to draw a sectional
line in the earth's surface, the levels
of which have been taken, 135; run-
ning a check level, 138; example of
level book for ditto, 142; working sec-
tion, 149; example of level book for
plotting the working section, 153; con-
tour levelling, on, 220.

Levelling instruments described, 126.
Levelling staves, 131.

Levelling with the theodolite, 156.
Levels, Gravatt's, 129; Troughton's, 128;
water, 130; Y, 126.

Line defined, 1; a right line cutting two
parallel right lines, make the alternate
angle equal: theorem, 8.
Linear measures, table of, 15.
Lines on the ground, directions for mea-
suring, 10.

Lines, parallel, defined, 1.

Lodsworth, method of surveying the
parish of, 61.

Parallel lines defined, 1.
Parallel ruler, use of the, 54; to draw an
equalising line through a crooked fence,
57; to reduce a curved offset piece to a
right-angled triangle, 55; to reduce an
offset piece to a right-angled triangle,
54; to reduce an irregular field to a
trapezium, 56.

Parallelogram having a given length and
breadth, to describe a, 6.

Parishes, method of surveying with the
chain, 58.

Pentagon defined, 3.

Plane defined, 1.

Plane triangle defined, 2.

Planning extensive surveys, general di-
rections for, 80.
Planning surveys, 14.

Plans, description of, 86.

Plotting scales, description and use, 12
Plotting surveys, instruments for, 11.
Ponds, method of surveying, 93.

Point defined, 1; from a given point to
let fall a perpendicular, 5.
Polygons described, 3.

Practical geometry, problems in, 4.
Prismatic compass described, 69.
Protractor, description and use, 13.
Protractor, circular, 13.

Quadrant, 3.

Quadrilateral figure, 2.

Radius of a circle, 3.

Railway, to calculate the land required
for a, 187.

Railway bridges, 212.

Railway curves, 158; examples of ex-
pensive severance of property by im-
properly setting out curves, 176; form
of, 158; limit of, 159; mechanical,
158; method of laying out, 158; neces-
sity of, 158; practice of engineers in
the adoption of, 178; table of offsets
for, 218; table of radii of, on the Taff
Vale Railway, 179; use of curves to
avoid valuable property, 179; the posi-
tion of two straight portions of a rail-
way being given to determine the
radius of the curve that joins them,
160; method of laying out a curve by
tangential angles, 161; given the ra-
dius to find the tangential angle for
a chord of one chain, 162; second
method of ascertaining the tangential
angle, 162; to find the length of the
tangent, the radius and angle of inter-
section being given, 163; to find the
angle of intersection when the point of
intersection of the tangents falls into a
sheet of water, &c., 163; to find the
length of a curve, the angle of inter-
section and the tangential angle being
given, 163; to lay out a curve on the
ground with the chain only by equi-
distant offsets from its tangents, 164;
to lay out the curve by offsets from its
chord or chords wher obstructions occur

11