To compute the Areas of Triangles.—When two sides and the included angle are known, a and b representing the two sides and θ the included angle,

To find by logarithms the area in acres and decimals of an acre,

When two angles and the included side are known, β and θ being the angles and a the included side,

To find by logarithms the area in acres and decimals of an acre,

When the three sides are known, a b c being the three sides and s their half sum,

To find by logarithms the area in acres and decimals of an acre,

Inclined Measure.

Curvature and Refraction.

INDEX.

• A.
• Angle, to bisect, 16
• ——, to construct, equal to a given angle, 17
• ——, to draw a line making a given, 15
• —— of light in mechanical drawings, 48
• —— —— in topographical drawings, 54
• Arch, Gothic, equilateral, to draw, 23
• ——, —— lancet, to draw, 24
• ——, —— obtuse, to draw, 24
• ——, —— ogee, to draw, 25
• ——, —— Tudor, to draw, 24
• ——, Moorish horse-shoe, to draw, 24
• ——, semi-elliptical, to construct, 23
• Architectural drawings, 121
• Arcs, centres of, to be marked, 10
• Areas to triangles, to compute, 142
• B.
• Bisecting an angle, 16
• Blacklead paper, 8
• Book of reference, 97, 101
• Books for field sketching, 115
• Borders and corners, 69
• Borings, 104
• Bottle indiarubber, 9
• Boundary maps, 104
• Bows, 2
• ——, spring, 2
• Broken lines, 30
• Brushes for tinting, 41
• Buildings—plans, sections, and elevations, position of, on drawing, 125
• C.
• Carbonic paper, 8
• Cartridge paper, 6
• Centre lines, 10
• —— ——, care to be taken in placing correctly, 10
• Centre of circle, to find the, 18
• Centres of arcs to be marked, 10
• Cinquefoil, Gothic, to draw, 26
• Circle, to describe, through three given points, 17
• ——, to draw a tangent to, 17
• ——, to draw radii of, the centre being inaccessible, 18
• ——, to find the centre of, 18
• Circles, concentric drawing, 10
• Cities, to represent size of, 112
• Civil engineers’ plans, 96
• Cleaning drawing pen, 3
• Cleaning off drawings, 9
• Cleanliness, importance of, 9
• ——, precautions to be taken to ensure, 9
• Cloth, tracing, 7
• ——, ——, Sager’s vellum, 7
• ——, ——, sizes of, 7
• Colour for buildings, 47
• —— for cultivated land, 47
• —— for fences, 47
• —— for grass-land, 45
• —— for gravel, 46
• —— for marsh, 45
• —— for mud, 46
• —— for roads, 47
• —— for sand, 46
• —— for streets, 47
• —— for water, 45
• —— for woodland, 46
• —— for uncultivated land, 47
• Colouring cylindrical objects, 124
• —— drawings, 11, 122
• —— rivers and streams, 110
• Colours, 39
• ——, conventional, Table of, 44
• —— for sections, 44
• Compasses, 2
• ——, manner of using, 2
• ——, pencil leg of, 2
• ——, points of, 2
• ——, removing movable leg, 2
• Competition drawings, paper for, 6
• Concentric circles, drawing, 10
• Construction of scales, 11
• Continuous cartridge paper, 6
• —— tracing paper, 7
• Contour lines, 37
• Contours, to plot, 90
• Conventional colours, Table of, 44
• Copying by tracing, 128
• —— by transfer, 129
• —— drawings, 11, 126
• —— from tracing, 11
• Corners and borders, 69
• Cross sections, 98, 102
• Cultivated land, to represent, 32
• Curvature and refraction, Table for correction of, 143
• Curved lines, 29
• —— ——, to draw, 29
• Cutting off drawings, 7, 11, 12
• Cylinders, various methods of shading, 64
• Cylindrical objects, to colour, 124
• —— surfaces, shade lines, 50
• —— ——, shading lines, 51
• Cyma recta, to draw, 25
• —— reversa, to draw, 25
• D.
• Dented drawing-board, to remedy, 14
• Detail plotting, 89
• Dimensions of drawing table, 2
• —— to be written on drawings, 122
• Distances, scales of, 70
• Dividing a line into equal parts, 10
• Dotted lines, 31
• Dotting pen, 31
• ——, regular, to produce, 111
• Drawing, copying and reducing, 126
• ——, inking in to commence from top of, 10
• ——, stretching paper for, 6
• Drawing concentric circles, 10
• —— from copy, 127
• —— lines, 10
• Drawing board, dented, to remedy, 14
• —— office, essentials of, 1
• —— ——, gaslights, 2
• —— ——, position of windows, 1
• —— ——, skylights unsuitable, 1
• —— paper, sectional, 8
• —— ——, to join sheets of, 12
• —— papers, 5
• —— ——, sizes of, 5
• —— pen, 3
• —— ——, cleaning, 3
• —— ——, more than one required, 3
• —— ——, setting, 3
• —— ——, supplying with ink, 3
• —— table, dimensions of, 2
• —— ——, position of, 2
• Drawings, cleaning off, 9
• ——, competition, paper for, 6
• ——, colouring, 11
• ——, cutting off, 7, 11, 12
• ——, ink for, 8
• ——, margin to be left, 11
• ——, mechanical and architectural, 121
• ——, parchment for, 8
• ——, to colour, 122
• ——, to preserve rolled, 12
• ——, to reduce or enlarge, 130
• ——, to remove grease spots from, 10
• ——, to varnish, 14
• —— for lithographers and engravers, 141
• —— for specifications for letters patent, 8
• Dusters, 2
• E.
• Eidograph, 136
• ——, method of setting, 139
• ——, table for setting, 139
• ——, to adjust, 138
• Elevation of trees, 36
• Ellipse, to draw, 21
• Elliptical arch, to construct a semi-, 23
• Encamping grounds, 112
• Engravers, drawings for, 141
• Enlarging by instruments, 131
• —— by scales, 130
• —— by squares, 130
• Equal parts, to divide a line into, 15
• Equidistant and parallel lines, to draw, 28
• Equilateral arch, to draw, 23
• —— triangle, to construct, on a given base, 16
• Erasure of ink lines, 11
• —— of pencil marks, 9
• Error-sheets, 91
• ——, examples of, 92
• Errors, 91
• Essentials of drawing office, 1
• Estate plans, 107
• Examination of maps and plans, 117
• F.
• Ferries, 111
• Field-book, example of, 80
• Field sketching, 114
• Fir-graining, 32
• Flat-tints, 40
• Formulæ, trigonometrical, 142
• G.
• Gaslights in drawing office, 2
• Glass-paper to erase ink lines, 11
• Glue for mounting paper, 6
• Gothic cinquefoil, to draw, 26
• —— equilateral arch, to draw, 23
• —— lancet arch, to draw, 24
• —— obtuse arch, to draw, 24
• —— ogee arch, to draw, 25
• —— quatrefoil, to draw, 26
• —— trefoil, to draw, 25
• —— Tudor arch, to draw, 24
• Gradients, to lay down, 95
• Graining, fir, 32
• ——, oak, 32
• ——, wood, 32
• Grass-land, to represent, 34
• Gravel, to represent, 35
• Grease spot, to remove from drawing, 10
• H.
• Hexagon, to describe a regular, 21
• Hills, representation of, 38
• ——, sand, to represent, 36
• ——, shading, horizontal system, 53
• ——, ——, vertical system, 57
• ——, sketching, shading, and copying, 113
• Horizontal zones, 38
• Horse-shoe arch, to draw, 24
• I.
• Importance of cleanliness, 9
• Inclined measure, Table for correction of, 143
• Indian ink, 8
• —— ——, preparation of, for drawing, 9
• —— ——, quality of, 9
• Indiarubber, native or bottle, 9
• ——, vulcanized, 9
• Ink for drawings, 8
• ——, Indian, 8
• ——, preparation of, 9
• ——, quality of, 9
• —— lines, erasure of, 11
• —— ——, to avoid smearing, 10
• —— slab or saucer, position of, when in use, 10
• Inking in to commence at top of the drawing, 10
• Instruments, 2
• ——, quality of, 2
• Islands, 110
• J.
• Joining sheets of paper, 12, 13
• Jungle, 112
• L.
• Lakes, outline of, 30
• Lancet arch, to draw, 24
• Land, cultivated, to represent, 32
• ——, uncultivated, to represent, 37
• Lead-pencil marks, erasure of, 9
• Lettering, 66, 122
• ——, position of, on plans and maps, 69
• Letters, arrangement of, in titles, &c., 68
• ——, kinds to employ, 67
• ——, mechanical construction of, 66
• ——, size of, 67
• Level-book, example of, 94
• Line, dividing into equal parts, 10
• ——, regular pentagon on a given, 20
• ——, to bisect a given straight, 15
• ——, to construct a square on a given, 19
• ——, to divide a, into equal parts, 15
• ——, to draw a, making a given angle, 15
• ——, to erect a perpendicular to, 15
• Lines, drawing, 10
• ——, broken, 30
• ——, centre, 10, 122
• ——, combinations of, 31
• ——, curved, to draw, 29
• ——, curved and straight, 27
• ——, contour, 37
• ——, dotted, 31
• ——, ink, to avoid smearing, 10
• ——, parallel and equidistant, to draw, 28
• ——, reference, 78
• ——, section, 29
• ——, ——, to draw, 28
• ——, shade, application of, 48
• ——, shading, 50
• ——, ——, in topographical drawings, 52
• ——, straight, difficulties in ruling, 27
• ——, ——, to draw, 27
• ——, wavy, 33
• —— of greatest descent, 57
• —— of uneven thickness, 30
• Lithographers, drawings for, 141
• Local Government Board, regulations of, 104
• M.
• Machine-made paper, 6
• Machinery, rough sketches of, 121
• Manner of using compasses, 2
• Map drawing, 109
• Maps, boundary, 104
• ——, field, examination of, 118
• ——, signs used in, 120
• —— for division into wards, 104
• Margin to drawings, width of, 11
• Marshy ground, to represent, 35
• Mechanical drawings, 121
• Mile stones, 112
• Mining plans, 106
• Moorish horse-shoe arch, to draw, 24
• More than one drawing pen required, 3
• Mountain passes, 111
• Mounting paper, glue for, 6
• —— —— on stretchers, 13
• —— tracings, 129
• Mud in rivers, to represent, 36
• N.
• Native indiarubber, 9
• Needle to erase ink lines, 11
• North points, 69
• Northings and southings, 87
• O.
• Oak-graining, 32
• Obtuse arch, to draw, 24
• Ogee arch, to draw, 25
• Orchards, to represent, 36
• Outline of lakes, 30
• —— of ponds, 30
• —— of rivers, 30
• Oval, to construct, the width being given, 18
• P.
• Pantograph, 131
• ——, methods of setting, 132
• ——, tables for setting, 133, 134
• ——, to use, 134
• Paper, blacklead, 8
• ——, carbonic, 8
• ——, cartridge, 6
• ——, continuous cartridge, 6
• ——, drawing, 5
• ——, ——, to join, 12
• ——, ——, sizes of, 5
• ——, glue for mounting, 6
• ——, machine-made, 6
• ——, sectional, 8
• ——, stretching for drawing, 6
• ——, tracing, 7
• ——, ——, continuous, 7
• ——, ——, preparation of, 7
• ——, ——, sizes of, 7
• ——, ——, to join, 13
• ——, transfer, 8
• ——, ——, preparation of, 129
• ——, to join sheets of, 12
• ——, to mount on stretchers, 13
• —— for competition drawings, 6
• —— for large plans, 6
• Parabola, to draw, base and height being given, 21
• Parallel and equidistant lines, to draw, 28
• Parchment for drawings, 8
• Parliamentary plans and sections, 100
• —— standing orders, 98
• Paste, 14
• Patent, drawings for specifications, 8
• Pathways, 111
• Pen, dotting or wheel, 31
• Pencil marks, erasure of, 9
• —— leg of compasses, 2
• Pencils, 4
• ——, pointing, 4
• —— for field sketching, 115
• Pentagon, to describe, on a given line, 20
• Perpendicular, to erect a, 15
• Plan of trees, 36
• Plans, civil engineers’ and surveyors’, 96
• ——, estate and town, 107
• ——, large, paper for, 6
• ——, mining, 106
• ——, railway, 97
• ——, parliamentary, 100
• Plotting, 77
• —— angular surveys, 81
• —— contours, 90
• —— detail, 89
• —— sounded points in submerged districts, 90
• —— traverse reference lines, 84
• —— vertical sections, 92
• Pointing pencils, 4
• Points of compasses, 2
• Ponds, outline of, 30
• Position of drawing table, 2
• —— of ink slab or saucer when in use, 10
• —— of windows in drawing office, 1
• Precautions to be taken to ensure cleanliness, 9
• Preparation of colours for tinting, 40
• —— of ink for drawing, 9
• —— of stretchers, 13
• —— of tracing paper, 7
• —— of transfer paper, 129
• Preserving drawings, rolled, 12
• Q.
• Quality of Indian ink, 9
• —— of instruments, 2
• Quatrefoil, Gothic, to draw, 26
• R.
• Radii of circle, to draw, the centre being inaccessible, 18
• Railway plans, 97
• —— sections, 102
• —— stations and termini, 112
• Railways, 112
• Rectangle, to construct, similar to a given rectangle, 20
• Rectangular co-ordinates, to plot by, 87
• Reducing and enlarging drawings, 126, 130
• —— by instruments, 131
• —— by scales, 130
• —— by squares, 130
• Reference, book of, 97, 101
• —— lines and points, 78
• —— lines, secondary, 79
• Refraction and curvature, Table for correction of, 143
• Regulations of Local Government Board, 104
• Removing movable leg of compasses, 2
• Rivers, beds of, 110
• ——, mud in, to represent, 36
• ——, outline of, 30
• —— and streams, colouring, 110
• —— ——, inking in, 109
• Roads, 111
• Rolled drawings, to preserve, 12
• Roman cyma recta and cyma reversa, to draw, 25
• Roofs, to draw, 30
• Rough sketches of machinery, 121
• Ruling straight lines, difficulties in, 27
• Running water, to represent, 33
• S.
• Sager’s vellum tracing cloth, 7
• Sand, to represent, 35
• —— banks, 110
• —— hills, to represent, 36
• Scales, 70
• ——, choice of, 72
• ——, construction of, 11, 70, 75, 76
• ——, diagonal, 75
• ——, vernier, 75
• ——, Tables of, 73, 74
• —— of construction, 74
• —— of distances, 70
• —— of shade, English, 59
• —— ——, Lehmann’s, 57
• —— ——, standard, 53
• —— ——, United States’, 59
• Sectional drawing paper, 8
• Section lines, 29
• —— of water, to represent, 30
• Sections, colours for, 44
• ——, cross, 98, 102
• ——, parliamentary, 101
• ——, railway, 102
• ——, to plot, from contour map, 96
• ——, working, 94, 103
• —— of wood, 32
• ——, vertical, to plot, 92
• Semi-elliptical arch, to construct, 23
• Setting drawing pen, 3
• Shade lines, application of, 48
• —— ——, cylindrical surfaces, 50
• Shading, 48
• —— cylinders, various methods, 64
• —— hills, horizontal system, 53
• —— ——, vertical system, 57
• —— ——, rounding curves, 55
• —— lines, 50
• —— ——, cylindrical surfaces, 51
• —— —— in topographical drawings, 52
• —— in colours, 63
• —— ——, cylindrical surfaces, 64
• —— ——, hill slopes, 63
• Sides of triangles, to compute, 142
• Sizes of drawing papers, 5
• —— of tracing cloth, 7
• —— of tracing paper, 7
• Sketches, rough, of machinery, 121
• Sketching, field, 114
• Skylights unsuitable for drawing office, 1
• Sounded points, to plot, 90
• Specifications for letters patent, drawings for, 8
• Spring bows, 2
• Springs, 112
• Square, to construct, equal to ¹⁄₂, ¹⁄₄, &c., of a given square, 19
• ——, to construct, in any proportion to a given square, 20
• ——, to construct, on a given line, 19
• ——, to construct, which shall be a multiple of a given square, 19
• Standing orders of Parliament, 98
• —— water, to represent, 29
• Stations, railway, 112
• ——, telegraph, 112
• Straight-edge, thickness of, 5
• Straight line, to bisect a, 15
• —— lines, difficulties in ruling, 27
• —— ——, to draw, 27
• —— and curved lines, 27
• Stretchers, mounting paper on, 13
• ——, preparation of, 13
• Stretching paper for drawing, 6
• —— ——, glue for, 6
• Supplying drawing pen with ink, 3
• Surveyors’ plans, 96
• Swamps, to represent, 35
• T.
• Table, drawing, position of, 1
• ——, ——, size of, 1
• Table for correction of curvature and refraction, 143
• —— for correction of inclined measure, 143
• —— for setting eidograph, 139
• —— of conventional colours, 44
• Tables for setting pantograph, 133, 134
• Tangent, to draw, to a circle, 17
• Telegraph lines and stations, 112
• Thickness of straight-edge, 5
• Tinting, 39
• Tints, art of applying, 40, 41, 43
• ——, brushes for applying, 41
• ——, double or alternate, 42
• ——, flat, 40
• ——, preparation of, 40
• Toll-gates, 111
• Topographical drawings, shading lines in, 52
• To remove grease spots from drawings, 10
• Town plans, 107
• Towns, to represent size of, 112
• Tracing, copying from, 11
• ——, to copy by, 128
• —— cloth, 7
• —— ——, Sager’s vellum, 7
• —— ——, sizes of, 7
• —-— paper, 7
• —— ——, continuous, 7
• —— ——, preparation of, 7
• —— ——, sizes of, 7
• —— ——, to join sheets of, 13
• Tracings, to mount, 129
• Transfer paper, 8
• —— ——, preparation of, 129
• Transferring, to copy by, 129
• Traverse plotting by rectangular co-ordinates, 87
• —— reference lines, to plot, 84
• Trees in plan, 36
• —— in elevation, 36
• ——, to represent, 36
• Trefoil, Gothic, to draw, 25
• Triangle, equilateral, to construct, 16
• ——, to construct, the length of base and angles at base being given, 17
• ——, to construct, the lengths of the sides being given, 16
• Triangles, primary and secondary, 78
• ——, to compute the areas of, 142
• ——, to compute the sides of, 142
• Trigonometrical formulæ, 142
• Tudor arch, to draw, 24
• U.
• Uncultivated land, to represent, 37
• V.
• Varnishing drawings, 14
• Vellum tracing cloth, Sager’s, 7
• Vertical sections, to plot, 92
• Villages, to represent size of, 112
• Vulcanized indiarubber, 9
• W.
• Washes, art of applying, 40, 41, 43
• ——, brushes for, 41
• ——, double or alternate, 42
• Water, running, to represent, 33
• ——, standing, to represent, 29, 33
• —— in section, to represent, 30
• Wavy lines, 33
• Wells, 112
• Whatman’s drawing papers, 6
• Wheel pen, 31
• Width of margin to drawings, 11
• Windows, position of, in drawing office, 1
• Wood-graining, 32
• Wood sections, 32
• Woodland, to represent, 36
• Working sections, 103
• Z.
• Zones, horizontal, 38