Land surveying, 92; ditches, method of
measuring, 95; ponds and rivers,
method of measuring, 94; boundaries,
94; field book described, 96; instru-
ments described, 92, 95; method of
measuring lines on the ground, 93;
planning survey, described, 96.
Land surveying with chain and cross, 87;
triangular fields, 98; fields in the form
of trapeziums, 99; four-sided fields,
100; fields contained by more than
four sides, 101; field, included by curved
sides, 104; to measure a line across a
river, 107.

Land surveying with chain only, 108;
triangular fields, 108; four-sided fields,
111; with more than four sides, 111;
parishes and large estates, 113.
Level book, examples of, 122, 123, and
125.

Levelling, term defined, 115; instru-

ments described, staves described, 118;
use of, described, 120; practice of, de-
scribed, 120; to find the differences of
levels of several points, 120; to draw a
sectional line of several in the earth's
surface, the levels of which have been
taken, 121.

Levelling, practice of, levels for the for-
mation of a section, 124; example of
level book, 125.

Line defined, 1; datum described, 122;
right definition of, 1; straight, defined,

1.
Lines, mensuration of, 19; application of,
19; parallel, described, 1.

Linear measure, table of, 19, 97.

Lune, to find the area of a, 47; exam-
ples, 48.

Masons' work, method of measuring, 82;
examples, 83.

Mensuration described, 1; of lines, ap-
plication of, 19.

Mensuration, problems, 19; of solids,
52; of surfaces, 34.
Minute, defined, 3.

Miscellaneous exercises, 52.
Multiplication, symbol for, described, 18.

Oblique prism defined, 53; pyramid de-
fined, 53.

Obtuse angle defined, 1; angled triangle,
definition of, 2.

Octagon described, 3.

Octagon, problems relating to the:-to

make an, on a given line, 9; to de-
scribe an, in or about a given circle, 12.
Octahedron described, 54.

Offset-staff, described, 54; method of
using, 94.

Painters' work, method of measuring, 88;
exercises, 88.

Parabola, to describe or construct a, 15;
Parabola, problems relating to the:-any
two of the following parts being given
to find the third: the parameter, the ab-

scissa, and the ordinate, 33; formule
and examples, 33; to find the area of a,
49; formulæ and examples, 49; to find
the length of an arc of a, its ordinate
and abscissa being given, 33; formulæ
and examples, 33.

Parabolic frustrum, to find the area of a,
49; formulæ and examples, 49.
Paraboloid, to find the solidity of a, 72;
examples, 72.

Paraboloid, frustrum of a, to find the soli-
dity of, 72; examples, 72.
Parallel lines defined, 1.

Parallelogram described, 2.

Parallelogram, problems relating to:-to
describe a rectangled, having a given
length and breadth, 6; to find the area
of a, 34; formulæ and examples, 34.
Parallelopipedon described, 53; to find
the solidity of a, 55; formulæ and ex-
amples, 56.

Parishes, method of surveying, with
chain, described, 113.

Paviors' work, method of measuring, 89;
examples, 89.

Pentagon described, 3.

Pentagon, problems relating to:-to make
a regular, on a given line, 9; to in-
scribe a, in a given circle, 13; example,

13.

Pentagonal prism defined, 52.

Plane, term defined, 1; triangle, defined, 2.
Planning surveys described, 96.
Plasterers' work, method of measuring,
87; examples, 87.

Plotting scales, described, 95.

Plumbers' work, method of measuring,
89; examples, 90.
Point, term defined, 1.
Polygons described, 3.

Polygons, problems relating to;-to make
a, on a given line, 9; to inscribe a, in
a given circle, 10; to circumscribe a,
about a circle, 10; to find the angles of,
10; to find the centre of a, or the
centre of its inscribed or circumscribed
circle, 11; irregular, to find the area of,
40; examples, 40; regular, to find the
area of, 41; formulæ and examples, 41;
regular, being given, to find the radii of
its inscribed and circumscribed circle,
24; formulæ, 24; examples, 25; tables
of, 10, 24.

Practical geometry, problems in, 4.
Prism, definition of, 52; oblique, defined,
53; pentagonal, defined, 52; right, de-
fined, 53; square, defined, 52; triangu-
lar, defined, 52; to find the solidity of
any, 57; formule and examples, 57; to
find the area of the surface of a, 57.
Prismoid defined, 64; to find the con-
tent, 64; formulæ and examples, 64.
Promiscuous exercises, 52.
Proportion, symbol for, 18.
Pyramid, definition of, 53; axis of, de-
fined, 53; frustrum of, defined, 54;
height of, described, 54; irregular, de-
scribed, 54; oblique, defined, 53; regu
lar, defined, 54; right, described, 53

segment of a, described, 54; vertex of
a, defined, 53.
Pyramid, problems relating to the-to
find the solidity of a, 58; examples, 58;
to find the slant surface of a right, 58;
formulæ and examples, 58; frustrum of
a, to find the solidity of a, 60; formulæ
and exercises, 61; frustrum of a, having
its ends polygons, to find the contents,
60; formulæ, 60; examples, 61; frus-
trum of a, to find the slant surface, 61.

Quadrant, term defined, 3.
Quadrilateral figure described, 2.

Radius of a circle defined, 3.
Railway curves, method of laying out,
described, 127; forms of curve de-
scribed, 127; to lay out a curve by
the common method, 127; examples,
128; to lay out a curve by offsets from
its tangents, 129:-(1.) When the
length of the curve does exceed of its
radius, 129; example, 130. (2.) To
lay out a curve when it is any required
length, 130; table of offsets to, 138.
Railway cuttings, to find the contents of,
130; earthwork tables described, 130;
to take the dimensions, 131; to find the
content from the depth, 132; to find
the content from sectional areas, 133;
example, 134.

Rectangle described, 2.

Refraction, correction for, explained, 119;
table of corrections for, 138.
Regular body defined, 54.
Regular pyramid defined, 54.
Rhomboid described, 2.
Rhombus, definition of, 2.
Right angle defined, 1.

Right angled triangle defined, 2; line de-
fined, 2; a line, cutting two parallel
lines, makes the alternate angle: theo-
rem, 17; pyramid, defined, 53; prism,
definition of a, 53.

Ring, to find the area of a circular, 47;
formulæ and examples, 47; cylindrical,
to find the solidity of a, 70: to find the
surface of a, 70; formulæ and examples,
70.

River, to measure a line across a, with

chain and cross, described, 107.
Roofs, to find the concave surface of
arched and vaulted, 90; examples, 90;
to find the solid contents of materials,
90; examples, 90.

Scales, plotting, described, 95.
Seconds defined, 3.

Sector of a circle, definition of the term,
3; to find the area of, 43; formulæ and
examples, 43.

Segment of a circle, term defined, 3.
Semicircle, definition of, 3.

Slaters' work, method of measuring, 86;
examples, 86.

Sliding rule, see Carpenters'.

Solid, term defined, 52; axis of, defined,

53; faces of, described, 54; measure,

table of, 54; segment of, described, 54;
frustrum of, defined, 54.

Solidity, to find the, of any regular body,
72; examples, 73.

Solidities of regular bodies, table of, 72.
Solids all similar are like to one another,

as the cubes of their like linear dimen-
sions: theorem, 17; general rule for
finding the contents of, 135; Gompertz's
investigation of the above rule, 135;
examples, 136; mensuration of, 52.
Specific gravity, term defined, 91; table
of, 91; to find the weight of a body
from its bulk, 92; examples, 92; to find
the magnitude of a body from its
weight, 92; examples, 92.

Sphere, definition of, 53; axis of, defined,
53; segment of, described, 54.
Sphere, problems relating to the :-to find
the solid content of a, 65; examples,
66; to find the convex surface, 67; for-
mulæ and examples, 68; frustrum of a
defined, 54; sector of, defined, 54;
zone defined, 54; segment or zone, to
find the convex surface, 67; formulæ
and examples, 68.

Spherical frustrum, to find the solid con-
tents, 67; formule and examples, 67;
segment, to find the solidity of a, 66;
examples, 66.

Spheriod, to find the solidity, 70; formulæ
and examples, 71; middle zone of a, to
find the content, the ends being circu-
lar, 71; examples, 71.

Spindle, circular, defined, 54.
Spindle, problems relating to the:-to find
the solidity of a, 68; formulæ and ex-
amples, 68; to find the contents of the
middle zone, 69; to find the convex
surface, 69; examples, 70.

Spindle, circular, problems on:-to find
the convex surface of any segment or
zone, 69; examples, 70.
Square, definition of a, 2.

Square, problems relating to the:-to de-
scribe a, whose side shall be of a given
length, 6; to describe a circle in, or a
given square, 11; examples, 12; to de-
scribe a, in or about a given circle, 12;
to make a, equal to two given, 14; to
make a, equal to the difference between
two given, 14; to make a, equal to the
sum of any number of squares taken
together, 14.

Square measure, tables of, 34, 97; prism,
definition of, 52; root, symbol of, 18.
Staff, offset described, 93; method of
using, 94.

Straight line, definition of, 1.

Straight line, problems on the :-to divide
a given, into two parts, 4; to draw a,
at a given distance, parallel to a given
line, 4; through a given point to draw
a straight line parallel to a given
straight line, 4; from a given point in
a straight line to erect a perpendicular,

4.

Subtraction, symbol for, 18.
Surface, definition of, 1.

Surfaces of regular bodies, table of, 72.
Superfices, mensuration of, 72; of regu-
lar bodies, to find the, 72; examples,
73.
Surveys, planning, described, 96.
Surveying, see Land Surveying and
Engineering Surveying.

Tables, earthwork described, 130; of
areas of segments of circles, 137; of
corrections for curvature and refrac-
tion, 138; of linear measure, 19, 97; of
offsets for railway curves, 138; of poly-
gons, 10, 24; of solid measure, 54; of
specific gravity, 91; of square measure,
34, 97; of surfaces of regular bodies,
72; for measuring timber, 139.
Tangent, to draw a, through a given point
to a circle, 8.
Tetrahedron defined, 54.
Theorems, geometrical, 16.

Tilers' work, method of measuring, 86;
examples, 86.

Timber measuring, 75; to find the area
or content of a plank, 75; examples,
76; to find the area or content by the
sliding rule, 76; examples, 76; to
find the solid content of squared
timber, 76; examples, 77; by sliding
rule, 76; example, 77; to find the solid
content of unsquared timber, 78; ex-
amples, 78; by sliding rule, 78; exam-
ples, 79; table, 139.
Trapezoid, definition of, 3.
Trapezoid, problems relating to the:-the
base and two perpendiculars being
given, to construct a, 6; to find the area
of a, 37; examples, 37.
Trapezium, definition of, 2; diagonal de-
scribed, 2; to find the area of a, (1.)
For any trapezium, 38. (2.) When
two opposite angle are supplements of
each other, 38; examples, 38; to mea-
sure with chain and cross, field in the
form of a, 99; to find the content, 99;
examples, 99.

Triangle, acute angled, defined, 3; equi-
lateral, defined, 2; isosceles, defined, 2;
obtuse angled, define, 2; plane, defi-
nition of, 2; right angled, defined, 2.
Triangle, problems relating to the-to
construct a, with three given right lines,
any two of which must be greater than
the third, 5; given the base and per-

pendicular, with the place of the latter,
to construct the triangle, 5; to con-
struct a right angled, having a given
base and perpendicular, and to find the
hypothenuse, 6; given the base and
hypothenuse, to construct the right
angled triangle, and find the perpen-
dicular, 7; to inscribe a circle in a
given, 11; examples, 11; about a, to
circumscribe a circle, 11; examples,
11; to make a, similar to a given, 13;
examples, 13; to find one side of a
right angled, two being given, 19; for-
mulæ and examples, 20; two sides and
base being given, to find the perpen-
dicular, 23; formulæ and examples,
23; to find the area of a, 36; formulæ
and examples, 36; to find the area of
a, by the chain, 109; the greatest side
of
every, is opposite the greatest angle:
theorem, 17; any two angles being
given, the, becomes known: theorem,
17; similar, are to one another in the
duplicate ratio of their homologous
sides: theorem, 17.

Triangular prism, definition of, 52.
Triangular fields, method of surveying
with chain and cross, 98; construction,
98; to find the content, 98; examples,

98.

Triangular field, method of surveying
with chain, 108; examples, 108.
Trigon, to describe a, in a given circle, 12.

Vaulted roofs, to find the concave surface
of, 90; examples, 90; to find the con-
tent of the materials, 90; examples,

90.

Wedge, to find the solidity of a, 63; for-
mulæ and examples, 63.

Y-level, construction described, 115; ad-
justments described for parallax and
collimation, 116; of buble tube, 117;
of the axis, perpendicular to the vertical
axis, 117.

Zone, circular, to find the diameter of a,
its parallel chords and its breadth being
given, 30; formulæ and examples, 30;
circular, to find the area of a, 46; ex-
amples, 46.