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THE
DRAUGHTSMAN’S HANDBOOK
OF
PLAN AND MAP DRAWING.
[Illustration: PLATE 1.
=PLAN= SHEWING PRINCIPAL CHARACTERS OF WORK USED IN MAPPING.
_B. Alexander, Lith._
E. & F. N. Spon. London & New York.]
THE
DRAUGHTSMAN’S HANDBOOK
OF
PLAN AND MAP DRAWING,
INCLUDING INSTRUCTIONS FOR THE PREPARATION OF
ENGINEERING, ARCHITECTURAL, AND MECHANICAL
DRAWINGS.
~With Numerous Illustrations and Coloured Examples.~
BY
GEORGE G. ANDRÉ, C.E., M.S.E.
[Illustration]
LONDON:
E. & F. N. SPON, 48, CHARING CROSS.
NEW YORK:
446, BROOME STREET.
1874.
PREFACE.
The main purpose of the present work is to be a handy book of reference
for draughtsmen engaged chiefly in Topographical Drawings. But to have
limited its use to one class of draughtsmen, and especially to the
skilled members of that class, would have necessitated the discovery of
more cogent reasons for its publication than its author has yet been
able to adduce. Works of such a character exist already, and though
their imperfections are numerous, they fulfil their purpose in a fairly
satisfactory manner. But had the field been clear in this direction, it
is so restricted in extent that to have entered upon it would have been
to undertake a labour that promised little fruit, for such a work could
be only of small utility even to those for whom it was specially
intended. It was, therefore, determined to make the present handbook
_generally_ useful by giving it a much wider scope. And hence, if the
intention has been efficiently carried out, it may claim a place in
every drawing office, be it that of the Topographer, the Hydrographer,
the Surveyor, the Military, Civil, or Mechanical Engineer, or the
Architect. Whether or not this degree of success has been achieved, is
not for the author to judge. But should he have failed to reach the high
mark at which he has aimed, he hopes, with some degree of confidence,
that he has at least succeeded in producing a book which the experienced
draughtsman will find valuable as a book of reference, and which the
pupil may constantly consult with profit. A want has long been felt by
draughtsmen for some work of this kind to which they might refer their
pupils in the office, and it may not be presumptive to suppose that the
present work has supplied that want. To render it convenient for this
twofold purpose, it has been divided into two parts. In the first part
the principles and practices of the art have been clearly but briefly
explained and illustrated; while in the second part, the application of
the principles previously learned has been treated of, and such
information given as relates directly to the duties of the practitioner.
Of course, in a work of the present character, originality in the matter
is neither to be expected nor desired; enough if the manner shows some
novelty, and is such as to add value to the matter.
Although the preparation of maps and plans has received the chief share
of attention, engineering, architectural, and mechanical drawings have
been largely treated of. Projection, orthographic, isometric and
perspective, has been altogether omitted as beyond the scope of the
work; but Colouring and Shading have been fully considered and profusely
illustrated.
The Plates appended as examples for reference are numerous and varied in
character; they have been specially prepared by B. Alexander, to whom
the author offers his warmest thanks for the truly admirable manner in
which he has executed the work entrusted to him.
16, CRAVEN STREET, CHARING CROSS,
_September 7th, 1874_.
CONTENTS.
PART I.--THE ESSENTIAL ELEMENTS.
SECTION I.--THE DRAWING OFFICE AND ITS FURNISHINGS.
PAGE
The Drawing Office 1
Instruments 2
Materials 5
Precautions and Remarks 9
SECTION II.--GEOMETRICAL PROBLEMS. 15
SECTION III.--LINES, DOTS, AND THEIR COMBINATIONS.
Straight and Curved Lines 27
Lines of uneven thickness 30
The Broken Line 30
The Dotted Line 31
Combinations of Straight, Broken, and Dotted Lines 31
The Wavy Line 33
Grass-land 34
Swamps and Marshy Ground 35
Sand and Gravel 35
Woodland 36
Uncultivated Land 37
Contour Lines 37
SECTION IV.--COLOURS.
Flat-tints 40
Conventional Colours 44
Water 45
Grass-land 45
Marsh 45
Sand and Gravel 46
Mud 46
Woodland 46
Cultivated Land 47
Uncultivated Land 47
Buildings 47
Roads and Streets 47
Fences 47
SECTION V.--SHADING.
Application of Shade Lines 48
Cylindrical Surfaces 50
Shading Lines 50
Shading Lines on Cylindrical Surfaces 51
Shading Lines in Topographical Drawings 52
The Vertical System of Shading 57
Shading in Colours 63
Hill Slopes 63
Cylindrical Surfaces in Mechanical Drawings 64
PART II.--APPLICATIONS.
SECTION I.--LETTERING, BORDERING, AND NORTH POINTS.
Lettering 66
Borders 69
North Points 69
SECTION II.--SCALES.
Scales of Distances 70
Scales of Construction 74
SECTION III.--PLOTTING.
Reference Lines and Points 78
Plotted Points 78
To Plot Reference Lines and Points 78
To Plot Traverse Reference Lines 84
To Plot Detail 89
To Plot Contours 90
To Plot Sounded Points in Submerged Districts 90
Errors and Error-sheets 91
To Plot Vertical Sections 92
To lay down Gradients 95
To Plot a Section from a Contour Map 96
SECTION IV.--CIVIL ENGINEERS’ AND SURVEYORS’ PLANS.
Standing Orders of Parliament 98
„ „ „ Documents required 99
„ „ „ Plans 100
„ „ „ Book of Reference 101
„ „ „ Sections 101
Working Sections 103
_Regulations of Local Government Board_:--
Boundary Maps 104
Maps for Division into Wards 104
Plans of Proposed Works 105
General Plan 105
Detailed Plan 106
Mining Plans 106
Estate and Town Plans 107
SECTION V.--MAP DRAWING.
Single Stroke Streams 109
Double Line Streams and Rivers 110
Colouring Streams or Rivers 110
Islands and Sand-banks, Sandy and Pebbly Beds of Rivers 110
Roads and Pathways 111
Mountain Passes 111
Fords and Ferries, Toll-gates 111
Telegraph Lines and Stations 112
Railways, Stations, and Termini 112
Size of Cities, Towns, and Villages 112
Sketching, Shading, and Copying Hills 113
Field Sketching 114
Examination of Maps in the Field 118
SECTION VI.--MECHANICAL AND ARCHITECTURAL DRAWINGS. 121
SECTION VII.--COPYING AND REDUCING.
Drawing from Copy 127
Copying by Tracing 128
Copying by Transfer 129
Reducing and Enlarging 130
The Pantograph 131
The Eidograph 136
Drawings for Lithographers and Engravers 141
TRIGONOMETRICAL FORMULÆ 142
INCLINED MEASURE 143
CURVATURE AND REFRACTION 143
INDEX 144
LIST OF ILLUSTRATIONS.
--------------------------------------+-------------+---------------
| Page. | Plate.
+-------------+---------------
ALPHABETS, examples of | .. | 4, 5, 6
Angle, to bisect | 16 | ..
Angles, to construct | 16, 17 | ..
Arch, equilateral | 23 | ..
----, horse-shoe | 24 | ..
----, lancet | 24 | ..
----, obtuse | 24 | ..
----, ogee | 25 | ..
----, semi-elliptical | 23 | ..
----, Tudor | 24 | ..
Architectural drawings, colouring of. | .. | 24
| |
BORDERS | .. | 1, 3, 8, 9, 13
Boundaries, parish, &c. | .. | 3, 15
| |
CANAL LOCKS | .. | 1, 11
Chart, example of | .. | 18
Cinquefoil, Gothic | 26 | ..
Circle, to describe through | 17 | ..
given points. | |
----, to find the centre of | 18 | ..
Cliffs | .. | 1, 11, 14
Colouring architectural drawings. | .. | 24
---- maps and plans | .. | 1, 3, 13,
| | 17, 28, 33
---- mechanical drawings | .. | 22, 23, 27
Copse | .. | 1, 10
Corners | .. | 1, 3, 8, 9, 13
Cylinders shaded | 51, 52 | ..
Cyma recta | 25 | ..
---- reversa | 25 | ..
| |
DOCKS | .. | 1, 11
Drawings, architectural, colouring of.| .. | 24
----, isometrical | .. | 27
----, mechanical, colouring of. | .. | 22, 23, 27
| |
EIDOGRAPH | .. | 26
Ellipse, to draw | 22 | ..
Equilateral triangle, to construct. | 16 | ..
| |
FLOURISHES | .. | 25
Fortifications, plans | .. | 32
----, sections | .. | 31
| |
GEOLOGICAL MAPS | .. | 28
---- sections, coloured | .. | 20, 21
Grass | 34 | 1, 17
Gravel | 35 | 1
| |
HARBOURS | .. | 11
Hexagon, to describe | 21 | ..
Hill shading | 53, 55, 56, | ..
| 58, 61, 62, |
| 63 |
Hills | .. | 1, 12, 14, 17
---- in colour | .. | 12, 14
| |
ISOMETRICAL DRAWINGS | .. | 27
| |
LAKES | .. | 1, 3, 11, 17
Land, cultivated | 32 | 1, 13
----, uncultivated | 37 | ..
Lettering, examples of | .. | 4, 5, 6, 7, 8,
| | 25
Line, to divide into equal parts. | 15 | ..
Lines, broken | 30 | ..
----, contour | 37 | ..
----, dotted | 31 | ..
----, section | 29 | ..
----, shade | 49 | ..
----, to bisect | 15 | ..
| |
MAPS, geological | .. | 28
----, Ordnance, example of. | .. | 18
---- and plans, colouring of. | .. | 1, 3, 13,
| | 17, 28, 33
Marsh | 35 | 1, 10, 11
Mechanical drawings, colouring of. | .. | 22, 23, 27
Mining plans | .. | 33
| |
NORTH POINTS | .. | 9
| |
OVAL, to construct | 18 | ..
| |
PANTOGRAPH | .. | 26
Parabola, to draw | 21 | ..
Pentagon, to describe | 20 | ..
Perpendicular, to erect | 15 | ..
Plans, estate | .. | 3, 17
----, fortifications | .. | 32
----, mining | .. | 33
----, office | .. | 2
----, parliamentary | .. | 13, 19
----, reducing or enlarging | .. | 26
----, town improvements | .. | 13
---- and maps, colouring of. | .. | 1, 3, 13, 17,
| | 28, 33
Plotting, examples of | 82, 85, 86, | ..
| 88, 93 |
| |
QUARRIES | .. | 1
Quatrefoil, Gothic | 26 | ..
| |
RADII OF CIRCLE, to draw | 18 | ..
Railways | .. | 1, 3
Rectangles, similar, to construct | 20 | ..
Rivers | .. | 1, 11, 12, 17
----, outlines of | 30 | ..
Roads | .. | 1, 3, 12, 17
Rocks | .. | 1, 11
Roofs | 30 | ..
| |
SAND | 35 | 1
---- banks | .. | 1, 11
Scales | 71, 75, 76 | 2, 3, 8, 9, 13
Section plotting, example of | 93 | ..
Sections, fortifications | .. | 31
----, parliamentary | .. | 19, 21
---- of strata, examples of colouring.| .. | 20, 21
Shade, scales of, for hills | 53, 58 | ..
Signs, various, used in Indian and | .. | 29, 30
Colonial maps. | |
----, ----, used in maps, plans, &c. | .. | 15, 16
----, ----, used in military maps and | .. | 31, 32
fortifications. | |
Soundings | .. | 11, 18
Square, to construct | 19 | ..
----, multiple of, to construct. | 19 | ..
Squares, proportional, to construct. | 19, 20 | ..
Swamps and marshy ground. | 35 | 1, 10
| |
TANGENT, to draw | 18 | ..
Titles, examples of | .. | 3, 7, 8
Towns | .. | 1, 3, 11, 13
Traverse plotting, example of. | 85, 86, 88 | ..
Trees | 36 | 1, 3, 10, 13,
| | 17
Trefoil, Gothic | 25 | ..
Triangles, to construct | 16, 17 | ..
| |
VILLAGES | .. | 1
| |
WATER, flowing | 33 | 11
----, standing | 29 | 1, 11
---- in section | 30 | ..
Wood-graining | 32 | ..
Wood in section | 32 | ..
Woods | 36 | 1, 3, 10, 17
--------------------------------------+-------------+---------------
PLAN AND MAP DRAWING.
PART I.--THE ESSENTIAL ELEMENTS.
SECTION I.--THE DRAWING OFFICE AND ITS FURNISHINGS.
There are few occupations so dependent for their correct performance
upon minute matters of detail as that of the draughtsman. Things
apparently the most trivial are sufficient to render inaccurate or to
mar the appearance of the otherwise most carefully and skilfully
executed design, and as the value of a drawing depends wholly upon its
accuracy and its appearance, it is obvious that such matters of detail,
however trivial they may be in themselves, demand careful attention. We
have, therefore, deemed it desirable to preface our remarks on Plan and
Map Drawing with a brief description of the instruments and materials
required, and of the mode of using them which experience has shown to be
the best.
_The Drawing Office._--The first essentials of a room for drawing in
are--that it shall be quite free from damp and be well lighted. The
position of the windows is a matter of some importance, and though
persons have largely to accommodate themselves to circumstances in this
respect, it is desirable to know what are the most suitable conditions,
in order that they may be complied with as far as circumstances permit.
Skylights are unsuitable, because the light entering from above is
liable to be intercepted by the body, and especially by the hands of the
draughtsman; besides which, the light from a skylight is seldom
sufficient. For the same reasons, a window placed very high in the room
is objectionable. When possible, a western aspect is to be preferred, as
the light from this direction is less variable and lasts later in the
day than from other directions. Blinds of some kind are necessary to
modify the light when the sun shines directly upon the window. Gaslights
should be situate about 3 feet above the drawing table, and there should
be two burners, placed not less than 2 feet apart, as otherwise the
hands and the instruments will cast shadows which will prevent fine
lines and points from being seen.
The drawing table should be placed under the window; it should have a
breadth of about 2 feet 6 inches, and its height should be 3 feet 8
inches at the back and 3 feet 6 inches at the front. The front edge
should be rounded over.
Dusters and means for washing the hands must also be provided, as it is
requisite to frequently dust the paper and the instruments, and to keep
the hands perfectly clean.
_Instruments._--All drawing instruments should be of the best
workmanship, for it is impossible to obtain accuracy with imperfect
tools, and they must be kept in order by careful handling. For all kinds
of drawing, compasses of three sizes are required, the ordinary compass,
the bows, and the spring bows. The best compasses are those which are
sector-jointed. The points should be kept sufficiently sharp not to slip
on the paper, but not so sharp as to readily penetrate it. It is also
important that the points be thin and round, as otherwise, when several
arcs have to be struck from the same centre, the compass leg is apt to
make a large hole, which is utterly destructive of accuracy. The pencil
leg should be kept exactly equal in length to the steel leg, for true
circles cannot be drawn when one leg is shorter than the other. In
removing the movable leg, care should be taken to draw it straight out,
as nothing spoils the instrument so soon as wrenching the leg from side
to side. In using the compasses, the instrument should be held lightly
between the thumb and the forefinger only. It should not be pressed upon
the paper; but it should rest equally upon both points. If the weight of
the hand be thrown upon the instrument the points will penetrate the
paper. Care should also be taken to bend the joints so as to keep both
legs perpendicular to the paper. If attention be not given to this
matter, the steel leg will make a large hole in the paper, and the ink
leg will make a ragged line, because only one of the nibs will touch.
Next in importance to the compass, and of more frequent use, is the
drawing pen. The draughtsman should possess at least two of these
instruments, one for fine, and another for medium lines. When the proper
opening of the nibs for fine lines has once been obtained, it is
desirable not to change it; the pen can always be cleaned by passing a
piece of drawing paper between the nibs. The cleaning of the pen should
be carefully attended to; it should never be put away without having
every particle of dried ink removed from it; and frequently, while in
use, it should be wiped out to remove the dust, which is constantly
settling in it, as well as the particles of lead that are taken up from
the paper. The ink is supplied by breathing between the nibs and dipping
them in the liquid, or by means of a camel’s hair brush. When the latter
method is adopted, care should be taken to protect the brush from the
dust floating in the atmosphere of the room.
After considerable wear, the drawing pen will require setting. The
operation of setting requires some judgment and considerable practice,
and is one of those mechanical niceties which it is difficult to
describe. Generally it will be found advantageous to have the pen set by
an instrument maker. As, however, this resource is not always at hand,
it is desirable that the draughtsman should be able to set his own pen.
The following description of the operation given by W. Binns, in his
admirable work on Projection, is the best we have seen. “The nibs must
be precisely of the same length, rounded in two directions, and as sharp
as it is possible to make them without producing to the touch a
sensation of cutting, and without scratching the surface of the paper
when drawing a line, which is generally the case when one nib is longer
than the other. This irregularity may be detected by placing
alternately the sides of the pen at an acute angle with the forefinger,
and slipping the edge of the nail over the point, when the difference in
length will be at once perceived; and it may be reduced by drawing a few
lines, as it were, on a turkey stone, with the pen applied to the edge
of a set square in the same manner as if drawing lines upon paper, but
with this difference, that during the longitudinal motion of the pen the
handle must be turned over in a circular manner, so as to give a rounded
form to the point of the pen. If the pen be now held with the point
directed towards the eye, and gently moved about so as to catch the
angle of reflexion, a bright speck on one or both nibs will be observed,
which must be reduced by rubbing the pen to and fro upon the stone,
giving at the same time a slight rotary motion to the handle, which must
be held at an angle of about 20° with the face of the stone: the point
of the pen being examined from time to time, and the process of reducing
the bright specks continued until the point is as fine as can be used
without cutting or scratching the paper. If at this stage the two nibs
are of the same length, a perfectly solid and fine line can be drawn.
The beginner, however, must not be disappointed if sixty minutes are
thus expended before he can produce a satisfactory result; whereas two
minutes in the hands of a practitioner would suffice.”
The instrument most frequently in the hands of the draughtsman is the
lead pencil. These are required of various degrees of hardness, but for
lines that are to be ruled an H H is the best. The most suitable
qualities of lead are those which are the most easily rubbed out; these
qualities are sometimes gritty, but this defect is more than compensated
by the facility with which a line may be removed from the paper. There
is some art in cutting a pencil properly. If the point is intended for
sketching, it should be cut equally from all sides, so as to produce a
perfectly acute cone. But for line-drawing a flat or chisel point should
always be used. This point is much stronger, and will last much longer
than the cone point. To produce the chisel point, first cut the pencil
from two sides only with a long slope, and afterwards cut the other
sides away only just sufficiently to round the first edge a little.
This side wood is needed both to afford a support to the lead, and to
show in what direction the point stands. To avoid breaking the lead, the
knife should be held at an acute angle with it. A point cut in this
manner may be kept in order for some time by rubbing it upon a fine file
or upon a piece of glass-paper or fine sandstone.
Of the other instruments used in drawing, nothing need be said in this
work, as their use presents no difficulties. It may, however, be well to
remark that no straight-edge employed for ruling lines should be less
than a fourteenth of an inch thick, for if the edge be very thin, it
will be impossible to prevent the ink from escaping from the pen on to
it.
_Materials._--The drawing papers known as Whatman’s are the best
prepared of any obtainable, and they are almost universally employed. Of
these there are two kinds, the smooth and the rough; the former is
technically called _not_ paper, and is the more suitable for mechanical
and architectural drawings; the rough is more effective for perspectives
and Gothic elevations. A third kind is known as the _hot-pressed_, but
as it does not take colour so well as the not and the rough, it is not
often used. The various sizes are indicated by their names, which are
the following:--
Antiquarian 53 × 31 inches.
Atlas 34 × 26 „
Columbier 34¹⁄₂ × 23¹⁄₂ „
Demy 20 × 15 „
Double Elephant 40 × 26³⁄₄ „
Elephant 28 × 23 „
Emperor 68 × 48 „
Imperial 30 × 22 „
Medium 22³⁄₄ × 17 „
Royal 24 × 19¹⁄₄ „
Super Royal 27¹⁄₂ × 19¹⁄₄ „
The sizes considered best, and almost universally used for engineering
and architectural drawings, are the elephant, the double elephant, and
the imperial. If smaller sizes are required, the half or quarter sheet
is used. Antiquarian has generally a good surface to draw upon, and it
is preferred by some architects. The atlas is also a very good paper.
Besides the foregoing, there is the machine-made or cartridge paper,
which is very commonly employed for detail drawings. It has not so good
a surface as the other kinds, nor is it so white; its chief advantage is
found in its dimensions, it being made uniformly 53 inches wide and
continuous. Hence the exact length required may be obtained. For large
plans and competition drawings, either cartridge or emperor paper is
used.
Paper that is to receive an elaborate drawing must be stretched and
glued to the board. This operation is one requiring a little skill and
some practice to perform successfully. The following is the best manner
of proceeding. The sheet to be strained is laid face upward upon the
board, and a wet sponge is passed rapidly along the margins, and then
across the face, including the margins, until the whole surface is
sufficiently and uniformly wetted. The object of wetting the margins
first is to prevent cockling by allowing them a longer time to expand in
than the middle of the paper. The sheet must now be left for about ten
minutes, or until the wet gloss has entirely disappeared. The process of
glueing to the board is as follows. A straight-edge is laid along one
end of the sheet, and about ³⁄₈ of an inch of the margin is turned up
against it, and glued by means of a brush. The margin is then turned
down and rubbed quickly with a knife-handle or, still better, a
paper-knife. The opposite end of the sheet is next pulled outwards and
glued in the same way, and the same method is afterwards applied to the
top and bottom margins. Some draughtsmen prefer to glue down the
_adjoining_ edges, but generally it will be found that laying down
successively _opposite_ edges will give more satisfactory results. The
contraction of the paper in drying should leave the face quite flat and
solid. During the process of drying, it is important to keep the board
in a perfectly horizontal position, as otherwise the water will
gravitate towards the lower side and soften the glue, and as the sheet
will dry unequally, the lower edge will break away.
The thinner the glue used the better, and for this reason the best
quality should be obtained, and care should be taken to keep the water
supplied that is lost by evaporation. When it becomes necessary to
replenish the glue-pot, the cake should be soaked in cold water for at
least eight hours.
The removal of a drawing from the board presents no difficulty. A pencil
line is drawn along the margin at a sufficient distance from the edge to
be clear of the glue, and a pen-knife is guided along this line by a
straight-edge not used for drawing.
As duplicates of drawings, especially if they be working drawings, are
usually tracings, tracing paper is an important material in every
drawing office. It is too well known to need a description. It is sold
in various sizes, and of various prices, but the most usual sizes are 30
× 20 inches, and 40 × 30 inches, the price of the former being 3_d._ and
that of the latter 6_d._ a sheet. It may also be purchased in continuous
lengths of 24 yards, 42 inches wide, for about 8_s._, or if extra stout,
16_s._ A much less expensive mode of obtaining tracing paper is to make
it one’s self. Common silk or _tissue_ paper may be purchased in
quantities at less than a halfpenny a sheet of the ordinary size. This
may be prepared by placing a single sheet at a time flat upon a board or
other smooth horizontal surface, and applying a mixture of boiled
linseed oil and turpentine. This mixture should be composed of one part
of oil to five of turpentine, and it should be applied with a small
sponge. One coating is sufficient, and it should not be put on too
thickly. Each sheet as prepared should be hung over a string stretched
across the room to dry, and when all the clear oily marks have entirely
disappeared, it will be ready for use. Five gills of turpentine and one
of oil is enough for two quires of double-crown tissue paper. That
tracing paper is best which is toughest, most transparent, and most free
from greasiness. The continuous papers are more economical than those in
sheets, because just the quantity required can always be taken from the
roll. For durability, tracing cloth is to be recommended; it is sold in
continuous lengths of 24 yards, and it may be had from 18 inches to 41
inches in width. That known as “Sager’s vellum cloth” is of excellent
quality, both for transparency and strength.
Some kinds of drawings, such as specifications for Letters Patent, plans
upon deeds, &c., have frequently to be made upon parchment. Special
kinds of parchment can be obtained for these purposes. There is a kind
made which is quite transparent, and which can be purchased cut to the
Patent Office regulation size. As parchment has always a more or less
greasy surface, before commencing to ink or to colour, it should be
pounced over with pouncet of finely-powdered French chalk. Besides this
precaution, it will be necessary to add a little ox-gall to the ink or
colour.
Blacklead and carbonic paper are used to transfer a drawing. The former
is prepared by rubbing thin paper over with a soft block of Cumberland
lead; the latter by painting one side of the paper with lamp-black
ground to perfect fineness in slow drying oil. Carbonic paper is used
for coarser work than blacklead paper. Both may be purchased, properly
prepared, at a trifling cost. The drawing to be copied is laid over the
sheet of paper which is to receive the copy, with a sheet of the
blacklead or carbonic paper interposed, and a tracer is passed with a
light pressure over the lines. This method is mostly used to reproduce a
drawing from a tracing, to obtain a finished copy from a rough draught
that has become soiled and marked in designing, or to avoid errors or
small alterations in the first drawing.
A very convenient kind of paper for small working drawings, or for
sketching to scale, is that known as sectional paper. This is paper
ruled into small squares to a given scale with pale ink. The spaces in
ordinary use are ¹⁄₁₀, ¹⁄₈, ¹⁄₆, ¹⁄₅, and ¹⁄₄ inch. Thicker lines are
drawn either to mark off the inches or to count the spaces in tens. With
this paper, the scale may be dispensed with, as the eye is capable of
subdividing the spaces with sufficient accuracy for practical purposes.
Sectional paper is much used for sections of railway cuttings and
embankments, as it affords a ready means of calculating the contents. It
is also made up into sketching books and architects’ pocket-books, for
which purposes it is peculiarly convenient.
Indian ink is used for all kinds of geometrical drawings. Being free
from acid, it does not corrode the steel points of the instruments, and
it preserves its colour unchanged. It is difficult to get the genuine
ink, but even that, as it is imported from China, varies considerably in
quality. For line-drawing, that is the best quality which will wash up
least when other colours are passed over it. This quality is ascertained
in the trade, though not with absolute certainty, by breaking off a
small portion. If it be of the right quality, it will show a very bright
and almost prismatic-coloured fracture.
The ink is prepared for use by rubbing it with water on a slab or in a
saucer. The saucer should be quite smooth inside, so as not to abrade
the ink. When mixed to the requisite thickness, which may be ascertained
by drawing a line with a common pen, it should be covered to protect it
from the particles of dust floating about the room. Ink should be rubbed
up perfectly black, for pale ink makes the boldest drawing look weak.
But after it has become black, any further mixing will only injure it by
rendering it viscid. It is best to use it immediately after it is mixed,
for if re-dissolved, it becomes cloudy and irregular in tone. The
addition of a little ox-gall will make it flow more freely from the pen.
For erasing Cumberland lead-pencil marks, native or bottle indiarubber
is sufficient; but for other kinds of pencils, fine vulcanized
indiarubber is better. This, besides being a more powerful eraser,
possesses the important quality of keeping clean, as it frets away with
the friction of rubbing, and thus presents a continually renewed
surface. Vulcanized rubber is also very useful for cleaning off
drawings.
_Precautions and Remarks._--It is essential to the good appearance of a
drawing that the paper be preserved perfectly clean. The hands
especially should be kept as much as possible from resting on it, as the
perspiration makes it greasy, and when once it has acquired this defect,
clear, sharp lines become impossible. A sheet of clean paper should be
constantly interposed between the draughtsman’s hands and the drawing
upon which he is working. Brown or printed paper is unfit for this
purpose, as the former is either greasy or tarry, and the latter is apt
to soil from the printed matter. White paper can be had of large size,
or, if necessary, several sheets may be pasted together.
To prevent risk of smearing the lines when inking in, it is well to
begin at the top of the drawing and to work downwards, also from the
right to the left for vertical lines. The ink slab or saucer should be
kept on one side and never in front of the drawing. Should a drawing get
a grease spot, it may be removed by the application of a hot smoothing
iron to a piece of clean blotting-paper laid over the spot, but not
sufficiently to be coloured over.
Great care should be taken to correctly place the centre lines of a
drawing; these lines should be drawn very fine and distinct. In working
drawings the centre lines are of great importance, as the dimensions are
always measured from them; in such cases it is customary to draw them in
red or blue colour. In all cases where a plane figure is symmetrical
with respect to a given line, whether the line exists in the figure or
may be considered as existing in it, that line should be drawn first,
and such a line is known as a centre line.
The centres of all arcs should be marked for the ink compasses at the
time the arc is struck by the pencil, by placing a small hand-drawn
circle around it. It is also necessary to mark distinctly by short
intersecting straight lines the exact points at which the arc begins and
ends. When a number of concentric circles have to be struck, the smaller
ones should be struck first, as it is more difficult when the hole in
the paper becomes enlarged to draw a small circle than a large one.
Whenever it is practicable, lines should be drawn _from_ a given point
rather than _to_ it; and if there are several points in one of which two
or more lines meet, the lines should be drawn from that one to the
others; thus, for example, radii should be drawn from the centre to the
points in the circumference of a circle. When a point has to be
determined by the intersection of circular arcs or straight lines, these
should not meet at an angle less than 30°. In dividing a line into a
number of parts, instead of setting off the part repeatedly along the
line, it is better to set off a convenient multiple of the given part,
and subdivide it; that is, to work from the whole to the parts, rather
than from the parts to the whole. This is an important principle in
surveying as well as in plan drawing, and in the construction of scales
it ought always to be observed.
Ink lines should never be erased with a knife, nor should an ink-eraser
be used, especially if the drawing is to be coloured. A needle point
will take out a short line in a way that leaves little trace of the
error. A very good means of taking out a line is furnished by a piece of
Oakey’s No. 1 glass-paper folded several times until it presents a round
edge; the application of this leaves the surface of the paper in a much
better condition for drawing upon than it is left in by the knife. When
the drawing is to be coloured, it is best to wash out a wrong line with
a small hard brush, and to slightly sponge over the place through a hole
of the requisite size cut in a scrap of drawing paper, to save the other
parts of the drawing. When a line has been drawn a little beyond the
point at which it should terminate, it will generally be found better to
avoid erasure by laying a little Chinese white over the line with a fine
sable-brush. Sometimes, when erasures are unavoidable upon a drawing
that is to be coloured, it will be found expedient to take the surface
off the whole of the paper with glass-paper, the colour will then flow
equally.
In copying from a tracing, it is well to put a sheet of drawing paper
underneath the tracing, for it not only shows up the lines more
distinctly, but it prevents the dividers from tearing the drawing while
taking off measurements.
Before commencing a drawing, a cutting-off line should be drawn all
round the sheet clear of the glued portion. The portions outside of this
line are useful to try the drawing pen upon before drawing a line, or
for trying a tint when colouring. Care should be taken not to leave too
narrow a margin, for nothing detracts more from the appearance of a good
drawing. For a drawing occupying a space of 1 foot or 15 inches square
over all, there should be a margin of at least 5 inches all round, with
the border line from 1¹⁄₂ to 2 inches from the cut-off line. Other
sizes should be in proportion. This rule is given by Maxton in his
‘Engineering Drawing,’ who also has the following remarks on cutting off
and preserving drawings. “The opposite side should never be cut first,
for if so cut, upon nearly completing the cutting of the third side the
paper undergoes contraction, and the fourth side pulling against it, is
apt to snap off the remaining inch or so, and generally in towards the
sheet, seldom in the margin on the outside of the cutting-off line. The
sheet should be cut off all round, taking care, by applying the
knife-blade under the edge of the sheet, that it is free from the board
before proceeding to cut off the side or end adjoining. When the sheet
has been removed, the strips of drawing paper left on the board should
be simply sponged over two or three times, and they will peel off
easily.
“For preserving a rolled drawing, a common substitute for string, and
one less likely to crease the drawing, is made as follows:--Take a strip
of drawing paper from 1¹⁄₂ to 2 inches wide and an inch longer than the
circumference of the rolled drawing. About half an inch from each end
make incisions, at one end in the middle and one-third of the breadth
across, and at the other end at the sides, each one-third of the breadth
across. Fold in these sides, so that they may pass through the incision
in the opposite end of the strip; on being opened again after they have
passed through, the whole will form a hoop, which, when slipped over the
drawing, will keep it secure.”
As cartridge paper is not always suitable, it sometimes becomes
necessary to join the smaller sizes end to end. To do this neatly the
edges should be cut straight, and a straight-edge laid upon the paper,
allowing ³⁄₈ inch to project beneath it. This portion of the paper
should then be rubbed down with sand or glass-paper until the outer edge
is quite thin. The edges of both sheets to be joined must be treated in
this way, and covered with a thin coating of gum. Having placed these
edges in contact, a strip of paper 1¹⁄₂ or 2 inches wide should be laid
upon the joint, and well rubbed with the handle of a paper-knife. If the
paper thus joined has afterwards to be stretched on a board, it should
be done while the joint is damp. In sponging the paper, care must be
taken not to go over the joint.
In joining sheets of tracing paper, the joint should never be made more
than ¹⁄₄ inch broad. The gum used for this purpose should be very thin,
and a strip of drawing paper should be placed upon each side of the
joint until it is quite dry. It is a good plan to roll the joined sheet
upon a roller with the joint in a line with the roller and the strips
infolded over the joint. When left to dry in this position, the joint
will be perfectly smooth.
Drawings have frequently to be mounted on stretchers, and the operation
of mounting is one requiring some care and practice. Generally it will
be found more convenient to purchase the stretcher ready made complete;
but when this is not done, care must be taken to have the frame made of
sufficient strength to resist the tension of the paper when dry. The
sides and the ends of a stretcher, 8 or 9 feet long, should be 4 inches
broad and not less than ⁷⁄₈ inch thick, and for any length above 18
inches there should be one or more bars across. A frame 6 feet long
should have two cross-bars dividing the length into three equal parts,
and they should be of such a thickness as not to come up flush with the
sides and ends by about ¹⁄₈ inch. The inner edges on the face of the
latter should be rounded down to the level of the cross-bars, and the
same degree of rounding should be given to the edges of the cross-bars
themselves. This is necessary to prevent the edges from showing a soiled
mark on the paper. When the frame has been thus prepared, the linen or
calico should be spread out on some flat surface and the frame laid upon
it face downwards. The ends of the linen should then be pulled over and
nailed to the back; next, the middle of the sides should be pulled over
and fixed in the same way. The intermediate spaces are afterwards tacked
down by placing a tack alternately on opposite sides, care being taken
to pull the linen tight and smooth before inserting the tack. It is a
good plan to fold the edge, as the double thickness will hold the
tacking better than if single.
To mount the paper on the stretcher, it should be laid face downwards
upon a clean flat surface, which will be all the better if covered with
a clean cloth, and sponged with clean water. When the water has soaked
in, apply with a flat brush some cold flour paste, and, if necessary,
remove all knots or particles of gritty matter, as these would prevent
the paper from lying close to the linen. The addition of a little alum
to the paste improves its adhesive property, and also tends to make the
drawing less stiff when dry. When a good coating of paste has been well
distributed over the paper, place the stretcher upon the paper and rub
the back of the linen well; then turn the stretcher over and rub down
the edges of the paper. Air-bubbles between the linen and the paper may
be got rid of by puncturing the spot with a fine needle and rubbing it
down. Paper thus mounted may be drawn upon nearly as well as when
stretched on a board. To give an edge for the [T]-square, a strip of
wood with parallel edges may be temporarily nailed on.
Some drawings, such as large plans of estates, have frequently to be
varnished. This operation requires some skill, and can be satisfactorily
accomplished only by a practised hand. The process generally adopted is
to stretch the drawing upon a frame, and to give it three or four coats
of isinglass size with a flat broad brush, taking care to well cover it
each time, and to allow it time to dry between each coat. The best
varnish is Canada balsam, diluted in oil of turpentine. This requires to
be put on evenly in a flowing coat with a fine flat brush, and to be
left in a warm room free from dust until it is thoroughly dry. The
drawing must be in a perfectly horizontal position while the size and
the varnish are being applied. In drawings to be varnished, thick lines,
such as shade lines, and chalky colours should never be put on before
sizing, as they are apt to blot during the process.
Should a fir drawing-board get accidentally dented, an application of
water to the part will, within certain limits, bring it up to its proper
level.
SECTION II.--GEOMETRICAL PROBLEMS.
_To bisect a given Straight Line._--Let A B (Fig. 1) be the given line.
From A and B, with any radius greater than ¹⁄₂ A B, draw arcs cutting
each other in C and D; then the line joining C D will bisect the line
A B as at E.
[Illustration: FIG. 1.]
[Illustration: FIG. 2.]
_To erect a Perpendicular to a given Straight Line._--Let it be required
to erect a line perpendicular to the point B (Fig. 2) in the line A B.
From any point C above the line, with radius B C, describe an arc as
A B D; join A C and produce the line until it cuts the arc in D, and
join D B; then will D B be perpendicular to A B.
[Illustration: FIG. 3.]
_To divide a Line into any number of equal parts._--Let it be required
to divide the line A B (Fig. 3) into five equal parts. From B, at any
angle, draw B C, and on the line B C lay off five equal parts, 1, 2, 3,
4, 5; then take a set square E, and make one of the sides containing the
right angle coincide with the points A and 5, and to the other side
apply a straight-edge D; then by passing the set square along the edge
of the straight-edge and drawing lines from the points 4, 3, 2, 1,
through the line A B, we shall have the line A B divided into five equal
parts through the points 1′, 2′, 3′, 4′.
_To draw a Line making, with another line, a given Angle._--Let it be
required to draw a line making with the line A B (Fig. 4) an angle of
35°. From a scale of _chords_, which will be found on most scales
supplied with a set of instruments, take off 60°; from the point A, with
this distance for radius, describe an arc C D; lay off on this arc the
distance of 35° taken from the same scale of chords; from A draw a line
through this point. Then will the line A E make with the line A B an
angle of 35°. The same result may be more readily arrived at by means of
a protractor. If the centre point of the protractor be placed on the
point A and its base made to coincide with the line A B, we can from its
circumference prick off the distance of 35°, and a line drawn from A
through the point thus found will make, with the line A B, the required
angle of 35°.
[Illustration: FIG. 4.]
[Illustration: FIG. 5.]
_To bisect an Angle._--Let B A C (Fig. 5) be the angle which it is
required to bisect. From A, with any radius, describe an arc cutting the
lines A B and A C in D and E; from D and E, with the same or any other
radius, describe arcs cutting each other in F, and from A draw a line
through F; this line will bisect the angle as required.
[Illustration: FIG. 6.]
[Illustration: FIG. 7.]
_To construct an Equilateral Triangle on a given base._--Let A B (Fig.
6) be the given base. From A and B, with radius A B, describe arcs
cutting each other in C; join A C and C B, which will complete the
required triangle.
_To construct a Triangle, the lengths of the Sides being given._--Let it
be required to construct a triangle whose sides shall be equal
respectively to 6, 5, and 4. Lay down the base A B (Fig. 7), making it
equal to 6 divisions of the scale; from A with radius equal to 4
divisions, and from B with radius of 5 divisions of the scale describe
arcs cutting each other in C; join A C and C B, which will complete the
required triangle.
[Illustration: FIG. 8.]
_To construct an Angle equal to a given angle._--It is required to draw
a line making with the line D E (Fig. 8) an angle equal to that
contained by the lines B A C. From A, with any radius, draw an arc F G,
and from D, with the same radius, draw the arc H I, and make H I equal
F G; then a line drawn from D through I will make, with the line D E, an
angle equal to the angle B A C.
[Illustration: FIG. 9.]
_To construct a Triangle, the length of the base and the angles at the
base being given._--It is required to construct a triangle whose base
shall equal 1 inch, and the angles at the base be 30° and 45°
respectively. Having made the base A B (Fig. 9) of the required length,
make the angles at A and B of the required magnitude in the manner
already described (see Fig. 4), and the continuation of these lines
meeting in the point G will complete the construction of the required
triangle.
[Illustration: FIG. 10.]
_To describe a Circle which shall pass through three given points._--Let
A B C (Fig. 10) be the points through which it is required to draw the
circle. From each of these points, with any radius, describe arcs
cutting each other in D and E; join the points D and E, and the point
where these lines intersect will be the centre from which to describe
the circle which will pass through the points A B C as required.
[Illustration: FIG. 11.]
_To draw a Tangent to a circle._--I. Let B (Fig. 11) be the point from
which it is required to draw the tangent. Draw the radius O B, and at B
erect a perpendicular (see Fig. 2); then will the line B D be a tangent
to the circle. II. It is required to draw a tangent from the point E in
the same circle. Draw the radius O E extending beyond the circumference
to F, and make E G equal to E F. From F and G, with any radius, describe
arcs cutting each other in H and I; then a line drawn through these
points will be a tangent to the circumference at E.
[Illustration: FIG. 12.]
_To find the Centre of a circle._--From any point in the circumference,
as B, (Fig. 12), describe an arc cutting the circumference in A and C,
and from A and C, with the same radius, describe arcs cutting the first
arc in two points; through the points of intersection draw lines to the
interior of the circle, and the point O where these lines intersect will
be the centre of the circle.
[Illustration: FIG. 13.]
_To draw lines which shall be Radii of a circle, the centre being
inaccessible._--Having laid off on the circumference of the arc, the
distances apart of the radii, as A, B, C, &c. (Fig. 13), from each of
these points, with radius greater than a division, describe arcs cutting
each other as at _a_, _b_, _c_, &c., join A _a_, B _b_, C _c_, &c., and
the lines so drawn will be radii of the circle as required.
[Illustration: FIG. 14.]
_To construct an Oval, the width being given._--Draw the line A B (Fig.
14) equal to the width, and bisect A B by C D (see Fig. 1). From the
point of intersection E, with radius E A or E B, describe the circle
A C B F, and from A and B through F, draw the lines A G and B H. From
A, with radius A B, describe the arc B G, and from B, with the same
radius, describe the arc A H; also from F, with radius F G or F H,
describe the arc G D H, which will complete the required oval.
[Illustration: FIG. 15.]
_To construct a Square on a given line._--Let A B (Fig. 15) be the given
line. At A erect a perpendicular (see Fig. 2), and from A, with radius
A B, describe an arc cutting the perpendicular in C; also from B and C,
with the same radius, describe arcs cutting each other in D; join C D
and B D, which will complete the required square.
[Illustration: FIG. 16.]
_To construct a square that shall be a Multiple of any given
square._--Let A B C D (Fig. 16) be the given square, and let it be
required to construct a square that shall contain 2, 3, 4, &c., times
its surface. Draw the diagonal B C, then the square described on B C
will be double the square A B C D. Lay off D E, equal to B C, and draw
C E; then the square described on C E will be three times the square
A B C D. In the same manner lay off D F, equal to C E, and the square
described on C F will be four times the square A B C D; and so for any
multiple of the square A B C D.
[Illustration: FIG. 17.]
_To construct a square that shall be equal to ¹⁄₂, ¹⁄₄, &c., of any
given square._--Let A B C D (Fig. 17) be the given square. On A B, as a
diameter, describe the semicircle A G B, and erect at the centre E the
perpendicular E G. Draw G B, which will be the side of a square equal to
one-half of A B C D. Lay off B F, equal to one-fourth of A B, and erect
the perpendicular F H; then the square described upon H B will be equal
to one-fourth of A B C D. In the same manner a square may be constructed
equal to _any_ part of A B C D.
[Illustration: FIG. 18.]
_To construct a square that shall be in any Proportion to a given
square._--Let A B C D (Fig. 18) be the given square. It is required to
construct a square which shall be to A B C D as 2 is to 5. Upon the side
A B as a diameter describe the semicircle A F B, and divide the line A B
into five equal parts. At the second point of division erect the
perpendicular E F and join A F; the square described upon A F will be to
the given square A B C D as 2 is to 5.
[Illustration: FIG. 19.]
_To construct, upon a given base, a Rectangle, which shall be similar to
a given rectangle._--Let A E F G (Fig. 19) be the given rectangle. It is
required to construct upon the base A B, one that shall be similar to
A E F G. Produce A E and lay off the given base from A to B; draw the
diagonal A G and produce it indefinitely. Erect a perpendicular to A B
at B, and from the point D where it intersects the diagonal produced,
draw D C perpendicular to A F produced. Then A B C D will be similar to
A E F G. All rectangles having their diagonals in the same line are
similar.
[Illustration: FIG. 20.]
_To describe a regular Pentagon on a given line._--Let A B (Fig. 20) be
the given line. Bisect A B at C, draw C F perpendicular to A B, and make
C D equal to A B. Draw A D and produce it indefinitely; make D E equal
to half A B. From A as a centre, with A E as a radius, describe an arc
cutting the perpendicular C D in F; and from A F and B as centres, with
radius A B, describe arcs cutting each other in G and H; join A G, B H,
F G and F H; then A G F H B will be the pentagon required.
[Illustration: FIG. 21.]
_To describe a regular Hexagon._--With a radius equal to the length of
one side of the required hexagon, describe a circle (Fig. 21), and set
off the same radius round the circumference of the circle, which will be
thus divided into six equal parts. Join the points thus found, and the
required hexagon will be completed as A B C D E F.
[Illustration: FIG. 22.]
_To draw a Parabola, the base and height being given._--Let C A (Fig.
22) equal half the base, and C D the height. From the point D draw D E
parallel and equal to A C, and from the point A draw A E parallel and
equal to C D. Divide D E and A E similarly, making the end E of A E
correspond to the end D of E D. Through 1, 2, &c., in DE draw 1, 1; 2,
2, &c., parallel to D C. Join D to the several points 1′, 2′, &c., in
A E. The parabola will pass through the points of intersections of these
lines with the verticals drawn from D E to C A.
[Illustration: FIG. 23.]
[Illustration: FIG. 24.]
[Illustration: FIG. 25 _a_.]
[Illustration: FIG. 25 _b_.]
_To draw an Ellipse._--I. By means of a piece of string and pins. Place
the diameters A B and C D (Fig. 23) at right angles to each other, and
set off from C half the major axis at E and F; then will E and F be the
two foci in the ellipse. Fix a pin at E and another at F; take an
endless string equal in length to the three sides of the triangle E F C
and pass it round the pins, stretch the string with a pencil G, which
will then describe the required ellipse. II. From the centre O (Fig. 24)
describe a circle of the diameter of the minor axis of the required
ellipse. From the same centre, describe another circle with a diameter
equal to its major axis. Divide the inner circle into any number of
equal parts as 1, 2, &c., and through these points draw radii cutting
the outer circle in 4, 3, &c. From 1, 2, &c., draw horizontals, and from
3, 4, &c., draw perpendiculars cutting each other in E F, &c.; the curve
traced from C through the points C E F A, &c., will complete the curve
of the required ellipse. III. Let A B (Fig. 25 _a_) be the major and C D
the minor axis of the required ellipse. On any convenient part of the
paper draw two lines F G, F H (Fig. 25 _b_) at any angle with each
other. From F with the distance E C or E D, the semi-axis minor,
describe an arc cutting the lines F G, F H, in I and K; and from F with
the distance E A or E B, the semi-axis major, describe the arc L M. Join
I M, and from L and K draw lines parallel to I M, cutting F G, F H, in N
and O. From A and B (Fig. 25 _a_) set off the distance F N (Fig. 25 _b_)
in points N′, and from these points as centres, with F N as radius,
describe an arc of about 15° on each side of the major axis. From C and
D (Fig. 25 _a_) set off on the minor axial line the distance FO (Fig.
25 _b_) in points O′, and from these points as centres, with radius FO,
describe arcs of about 15° on each side of the axis C D. To obtain any
number of intermediate points take a slip of paper (Fig. 25 _a_) and
mark upon one edge, with a sharp-pointed pencil, 1, 3, equal to the
semi-axis major, and 2, 3, equal to the semi-axis minor. If the slip of
paper be now applied to the figure and moved over it in such a manner
that the point 2 is always in contact with the major axis, and the point
1 in contact with the minor axis, the outer point 3 will describe a
perfect ellipse, any number of points in which can be marked off as the
“trammel” is moved into successive positions.
For this last method, which in practice is by far the best, we are
indebted to Binns’ ‘Orthographic Projection.’
[Illustration: FIG. 26.]
_To construct a Semi-Elliptical Arch._--The span A B (Fig. 26) and rise
C D being given, divide C A and C B into any number of equal parts.
Through the point D, draw E F parallel to A B, and from the points A and
B erect the perpendiculars A E and B F. Divide A E and B F similarly to
C A and C B. Produce C D and make C G equal C D. From D draw lines to
the points 1, 2, 3, &c., in the lines A E and B F; also from G draw
lines through the points 1, 2, 3, &c., in the line A B, and produce
these lines until they cut those drawn from D to the corresponding
numbers in A E and B F. Through the points thus obtained draw the curve
of the ellipse.
[Illustration: FIG. 27.]
_To draw the Gothic Equilateral Arch._--From the points A and B (Fig.
27), with radius A B equal to the span, describe the arcs B C and A C.
By joining C to A and B we obtain an equilateral triangle from which
this arch derives its name.
[Illustration: FIG. 28.]
_To draw the Gothic Lancet Arch._--In this arch, the centres E and D
(Fig. 28) from which the arcs are struck, are situate outside of and in
a line with the points of springing A and B; thus it is constructed on
an acute-angled triangle, as will be seen by joining C to A and B.
[Illustration: FIG. 29.]
_To draw the Gothic Obtuse Arch._--This arch, called sometimes the
Drop-Arch, is constructed on an obtuse-angled triangle; the centres E
and D (Fig. 29) being situate below and within the points of springing A
and B.
[Illustration: FIG. 30.]
_To draw the Gothic Tudor Arch._--On the line of springing A B (Fig.
30), take any two points as F and G, so that A F is equal to G B. Draw
F E and G D cutting each other on the bisecting line through C; from F
and G, with radius F A or G B, describe the short arcs, and from E and
D, with radius E C or D C, describe the arcs meeting in C.
[Illustration: FIG. 31.]
_To draw the Moorish Horse-Shoe Arch._--The centres E and D (Fig. 31)
from which the arcs forming this arch are struck, are situate above and
within the points of springing A and B. One of the most graceful forms
of this arch is obtained when the height of the points E and D above the
line of springing and their distance from the bisecting line through C
are equal to one-third of the span A B.
[Illustration: FIG. 32.]
_To draw the Gothic Ogee Arch._--The most pleasing form of this arch is
that constructed on an equilateral triangle, in the following manner.
Having drawn the equilateral triangle A B C (Fig. 32), draw F G parallel
to A B. Bisect the sides A C and C B and produce the bisecting lines to
F G and H, which will complete the triangle F G H similar and equal to
the triangle A B C. From H, with radius H A or H B, describe the arcs A
E and B D, and from F and G, with the same radius, describe the arcs E C
and C D.
[Illustration: FIG. 33.]
[Illustration: FIG. 34.]
_To draw the Roman Cyma Recta and Cyma Reversa._--Join A B (Fig. 33) and
bisect A B in C. From the points C and B, with the distance B C,
describe arcs cutting each other in E; and from A and C, with the same
radius, describe arcs cutting each other in D; from D, with the same
radius, describe the arc A C, and from E describe the arc C B. The
projection of the upper end of the curve over the under, as F B, is
generally equal to the height, A F, of the moulding. The same
description applies to the Cyma Reversa (Fig. 34) letter for letter.
[Illustration: FIG. 35.]
_To draw the Gothic Trefoil._--Having drawn the equilateral triangle
A B C (Fig. 35), bisect the angles and produce the bisecting lines
D E F which will bisect the sides of the triangle in G H I. From A B and
C as centres, with radius A H or A I, equal to half the side of the
triangle, describe the arcs K L M, and those concentric with them, and
from the centre O of the triangle describe the outer circles and
concentric arcs, which will complete the figure.
[Illustration: FIG. 36.]
_To draw the Gothic Quatrefoil._--Draw the square A B C D (Fig. 36);
bisect the sides of the square at I K L M and produce the bisecting
lines to E F G H. From the angles A B C D of the square as centres, with
radius A I or A M equal to half the side of the square, describe the
arcs P N R S, and draw the outer concentric arcs. The circles,
completing the figure, are drawn from the centre O of the square.
[Illustration: FIG. 37.]
_To construct the Gothic Cinquefoil._--Having drawn the regular pentagon
A B C D E (Fig. 37), bisect the angles and produce the bisecting lines
to F G H I K, which will cut the sides of the pentagon in _a_, _b_, _c_,
_d_, _e_. From A B C D and E as centres, with radius A _a_ or A _b_,
equal to one-half of the side of the pentagon, describe the arcs
L M N P R, and draw the outer concentric arcs and those concentric with
them. The circles are drawn from the centre O of the pentagon, as in the
preceding example.
SECTION III.--LINES, DOTS, AND THEIR COMBINATIONS.
All kinds of drawings are made up of lines and dots; these are the
constituent parts, the materials which the draughtsman has to employ. It
is therefore essential that he should make himself acquainted with their
various forms and uses, and familiar with those means of producing them
which experience has shown to be the best, before commencing the study
of the principles by which the representation of an object is
delineated. And moreover, it is desirable that he should acquire a
familiarity with the operations required in the delineation of isolated
objects, previously to making any attempt to place them in combination
for the purpose of producing a complete drawing. The student will,
therefore, do well to study carefully and to practise diligently the
forms and examples given in this Section.
_Straight and Curved Lines._--All straight lines, however short, should
be ruled, whether they be drawn with the pencil or the pen. Pencil
lines, which are intended to serve merely as guides to the pen, should
be drawn lightly, as otherwise it will be difficult to rub them out
without injuring the ink. They should also be drawn a little beyond the
point at which the line is required to terminate, because the
intersection of the lines at that point makes it more distinctly
visible, and there is, consequently, less danger of passing beyond that
point or of stopping short of it when inking in. It is very important
not to stop short of the required length when ruling a straight line
with a pen, for it is extremely difficult to lengthen the line
subsequently without leaving the join visible. An accurate line cannot
be drawn unless the point of the pencil or the pen be kept close up to
the rule, and to do this the top should be inclined a little outward.
Before inking in a line that has been drawn in pencil, the indiarubber
should be passed lightly over it, to remove the particles of lead
adhering to the paper, for if these particles are allowed to remain,
they get between the nibs of the pen and prevent the ink from flowing
freely. The chief difficulties in ruling a straight line with the pen
are, to keep it of a regular thickness throughout, and, when numerous
parallel lines have to be drawn, to keep them at equal distances apart.
To draw an even line, a first requisite is that the pen be in good
condition. Frequently it will be found when drawing fine lines that the
pen ceases to mark before the end of the line is reached, and as we have
already said, it is very difficult to join a line without leaving
visible traces of the operation. To remedy this defect, the pen must be
reset as described in Section I. If a very hard pencil has been used, or
if the pencil has been pressed heavily upon the paper, the pencil line
will lie in a groove in the paper, and as the nib of the pen will not
touch the bottom of this groove, the line drawn will be ragged. Another
cause of unevenness is unduly pressing the pen against the rule; this
pressure closes the nibs, and besides producing an irregularity in the
thickness of the line, is very apt to cause a blot by forcing out the
ink, which adheres to the rule when brought into contact with it. To
prevent this, care should be taken to press the pen very lightly against
the edge of the rule. A pen is manufactured by Stanley, of Holborn,
London, which has the back nib much stiffer than the other, so that all
danger of defect from this cause is removed by the construction of the
instrument. To ensure a good line, the pen should rest lightly upon the
paper, and the handle of the pen should make the same angle with the
paper from the beginning to the end of the line. A considerable amount
of practice is required to accomplish this, and to acquire the habit,
the same attention should be given to the pencil as to the pen. The
ability to draw a number of parallel lines at equal distances apart
without measuring requires considerable training of the eye, and this
training can be obtained from practice alone. This ability must be
acquired before anything further is attempted, and the student who
spends a good deal of time in its acquisition may have the satisfaction
of knowing that while he is going through this somewhat monotonous
practice, besides exercising himself in drawing accurate lines, he is
acquiring a correctness of eye and a power of hand that will be of
incalculable service to him later.
The straight line, besides being used for the outlines of regular
objects, is employed conventionally for various purposes. When it is
required to show an object in section, the part in section is covered
with straight and parallel lines drawn at an angle of 45° and at equal
distances apart, as in Fig. 38. To represent standing water, as ponds
and lakes, horizontal straight lines are drawn parallel to each other
and at equal distances apart over the surface, as shown in Fig. 39.
[Illustration: FIG. 38.]
[Illustration: FIG. 39.]
Curved lines, when arcs of circles, are drawn by the compasses. Other
curves are drawn by hand through points previously found. To draw the
curve correctly through these points, unless they be very numerous, a
knowledge of the nature of the curve is necessary, which the draughtsman
should in all cases endeavour to obtain. When the curved line is long,
it is usually inked in with the drawing pen, with the aid of an
instrument called the French curve, or cardboard moulds cut for the
purpose; but for short lines an ordinary fine-pointed steel-pen point,
or better, a good quill is used. In general, all lines drawn by hand
should be drawn _towards the body_, as a better command of the pen can
be obtained in that direction than in any other. In inking in curves by
this means, the draughtsman should proceed continuously along the
pencil-drawn line by partly repeated touches with the pen point, so held
that the divided points of the pen may follow partly in the same track.
Each touch should be made about one-thirtieth of an inch in length, and
it should begin and end fine. Each succeeding touch must begin half its
length back, so that the line is advanced by one-sixtieth of an inch. In
map drawing all irregular lines are drawn in this way. Tracing maps
will afford the student excellent practice in this mode of using the
pen.
[Illustration: FIG. 40.]
_Lines of uneven thickness._--Though generally a line is required to be
of even thickness throughout, cases sometimes occur in which a variation
in the thickness may be made to express some feature or quality of the
landscape. The usual application of this kind of line is to mark the
outline of rivers, lakes, and ponds, as shown in Fig. 40. The drawing of
such a line presents no difficulty; the increased thickness is produced
by going over those parts of the line again with the pen. Care must,
however, be taken not to make a sudden increase in the breadth of the
line, but to begin and end imperceptibly.
[Illustration: FIG. 41.]
[Illustration: FIG. 42.]
[Illustration: FIG. 43.]
_The Broken Line._--The broken line, shown in Fig. 41, is of frequent
occurrence in all kinds of drawings. In architectural and engineering
drawings it is usually employed in roofs, as in Fig. 42, and for water
in sections, as in Fig. 43. It is also used in combination with other
lines for various purposes. In drawing a succession of broken lines,
care must be taken not to allow the break in one line to be immediately
over that in another. The effect may be varied considerably by
increasing or diminishing the extent of the break. As in section lining,
the lines should be at regular intervals apart, and be all of the same
degree of fineness. Broken lines are sometimes used upon the face of
stone buildings, instead of marking in the joints and etching or
colouring. In such a case the breaks are long, and the lines widely
spaced.
[Illustration: FIG. 44.]
_The Dotted Line._--Of still more frequent occurrence is the dotted
line. There are two kinds of dotted lines, distinguished by the shape of
the dot, and known as the _long_ and the _round_ dotted line. These are
shown in Fig. 44, as well as a combination of the two.
The round dotted line is of very general application. In architectural
and mechanical drawings, it is used to distinguish hidden parts, and to
mark the path of a moving piece in a machine. In plans, it is used to
show the position of proposed works, to denote the walks through
pleasure grounds and gardens, to indicate lines chained over in
surveying, and frequently for other purposes, at the pleasure of the
draughtsman. The long dotted line is employed to mark the boundaries of
a township, the navigable channel of a river or creek, and in
large-scale maps to show farm and bridle roads, footpaths, and the
divisions of land among different tenants. The combination of the long
and round dotted lines is used for the boundaries of a parish. Another
combination of two round and one long dots, or sometimes of three round
and one long, is used to denote proposed railways, canals, roads, and
other similar works.
To draw a good dotted line requires some care. The difficulty lies in
keeping the dots at equal distances apart, and in making them equal in
size; and unless both these conditions are fulfilled, the line will not
present a pleasing appearance. To obviate this difficulty, an instrument
is sold by mathematical instrument makers, called the dotting or wheel
pen. But it requires very great care in using, as otherwise it
frequently happens that the ink escapes from it and spoils the drawing.
For this reason, its use has been generally abandoned by draughtsmen.
But if the instrument were better constructed and carefully handled, it
might be made to do good service.
[Illustration: FIG. 45.]
[Illustration: FIG. 46.]
[Illustration: FIG. 47.]
[Illustration: FIG. 48.]
[Illustration: FIG. 49.]
_Combinations of Straight, Broken, and Dotted Lines._--Combinations of
the foregoing lines are used for various purposes. Some draughtsmen
employ alternate, full, and dotted lines, to denote wood in section, as
in Figs. 45 and 46; when wood is used in combination with iron or other
metal, this is a very good way of distinguishing it. Wood-graining,
though not made up of straight, broken, or dotted lines, yet partakes
somewhat of the nature of all three kinds, and may therefore be
introduced here. Oak-graining is shown in Fig. 47, and fir-graining in
Fig. 48. The former is executed with the drawing pen, and requires some
care and practice; the latter is most readily done with a common pen or
a crow-quill. End wood is grained as shown in Fig. 49. The spring bows
are very suitable for drawing in the circles, as a certain degree of
turn to the nut will open the ink leg to the required distance after
drawing each circle. A few broken wavy lines, called _shakes_, radiating
from the centre, produce a good effect. When several pieces of end wood
come together, the centres in each should not be in the same relative
position.
[Illustration: FIG. 50.]
Cultivated land is represented by alternate broken and dotted lines,
suggesting furrows, as shown in Fig. 50. For the sake of variety, these
lines are put in in sets, and in different directions, one set being
usually parallel to one side of the enclosure. The lines are first ruled
in continuously with the pencil, and the broken and dotted lines
afterwards drawn in over them by hand. The portions of the broken lines
must in this case be short, and the breaks still shorter. The dots must
be fine and close together; they are made by touching the paper with
the point of the pen, and immediately lifting it off without _dragging_
it over the paper. All round dots must be made in this way.
_The Wavy Line._--The wavy line is very important in topographical
drawings, as it is employed to represent running water, and frequently
large bodies of standing water to which motion is communicated by the
wind, as lakes and the sea. These rippled lines are intended to
represent the ripples in the water, a purpose which they fulfil in a
very pleasing manner. They must, however, be well executed, or the
pleasing effect will not be produced. The operation of drawing these
lines is usually regarded by the draughtsman as a tedious and an
uninteresting one. But such ought not to be the case, for there is ample
scope in it for the exercise of the taste and the judgment, and in
proportion to the taste displayed and the judgment exercised, will be
the effect of the work when executed.
[Illustration: FIG. 51.]
Fig. 51 shows the manner of employing these lines. In representing water
by this means, the lines should be drawn from the shores towards the
middle of the stream or lake, and never from the middle outwards, for if
the latter mode of proceeding be adopted, the proper graduation of the
spaces between the lines becomes impossible. The shore line, or outline
of the water, should be a moderately thick line, and of uniform
thickness throughout. The first shading line may be of nearly the same
thickness as the shore line, and it must be drawn as near to it as
possible. Also this shade line, as well as all subsequent ones, must
follow exactly all the windings of the shore line; this is essential to
a correct expression. To effect this with accuracy, care should be taken
to make the space between the shore and the shade line a fine _white
line_. The second shade line must be drawn a little finer than the
first, and at a slightly increased distance from it. This gradual
diminution of the thickness of the lines, and increase of the spaces,
must be continued to the middle of the current. The last line in the
middle of a piece of water must always return to itself. When the
shading lines meet the margin of the drawing, they should terminate in
it, that is, they should be drawn out to the margin as though they had
been continued beyond and cut off.
These lines require to be drawn clean, and to do this the hand must be
kept steady. This steadiness may be obtained by taking a very short hold
of the pen, and resting the middle finger upon the paper. The lines, as
we have already said, should be drawn towards the body, the drawing
being turned about as required to facilitate this, and the last line
drawn must be always kept on the left of the one being drawn. By this
means the last line and the point of the pen are kept constantly in
sight. It is also important that the lines should be completed
successively, rather than that several should be carried on at once,
because if the latter mode of working be adopted, the eye is apt to
become confused by the different intervals, and an uneven distribution
of the lines is the result. A principle to be attended to is that every
line shall return to itself, spirals being altogether inadmissible. The
distance of the lines apart and their thickness are expressive of the
character of the object; thus, in a small pond, for example, they will
be fine and close together; in a large pond or a lake they will be
thicker and more widely spaced; and in the open sea they will be made to
present a bold appearance by increasing still more their thickness and
the distance between them.
[Illustration: FIG. 52.]
_Grass-land._--Various combinations of lines and dots are used,
conventionally, to represent certain natural features of common
occurrence. As far as convenient execution will allow, these signs are
made to resemble the objects denoted. Thus the sign for grass-land
consists of groups of short lines, arranged like tufts of herbage, as
shown in Fig. 52. Each tuft is composed of five or seven lines
converging towards a point situate below the base, the middle line being
the longest, and the outside ones mere dots. In drawing these groups,
the base must be kept quite straight, and parallel to the base of the
drawing whatever the shape of the enclosure may be. Beginners usually
experience considerable difficulty in keeping the base straight, the
tendency being to make it curved. Great care is needed to distribute the
groups evenly over the paper, and to avoid the appearance of being in
rows, for the latter arrangement is destructive of that natural aspect
which this sign otherwise possesses.
[Illustration: FIG. 53.]
_Swamps and Marshy Ground._--As the surface of marshy ground consists of
water and grass, a combination of the signs for these objects is
employed to represent it. An illustration of this is given in Fig. 53.
The lines representing the water should always be ruled parallel to the
base of the drawing, and they should be grouped in an irregular manner
so as to leave small islands interspersed throughout the locality. These
islands should be covered with grass, and to show them out more
distinctly, there should be nothing but water immediately around them.
The division between the land and the water should be sketched in
lightly before proceeding to rule in the lines. Sometimes dotted lines
are used for the water, but full lines are to be preferred. The addition
of a tree here and there improves the appearance of a drawing. A
distinction is frequently made between a swamp and a marsh by watering
the former more extensively than the latter. In drawing in marsh land,
care should be taken to make the fineness of the lines in accordance
with the scale of the map, as otherwise an offensive appearance will be
produced. This caution applies equally to all signs.
[Illustration: FIG. 54.]
_Sand and Gravel._--Sand and gravel are represented by dots, the dots
being made larger for the latter than for the former, as shown in Fig.
54. Simple as the operation of filling in these dots is, it is one that
requires some degree of care. Beginners are apt to mar the appearance
of their drawings by inattention in this respect. The dots should be
made in the manner already described when speaking of the dotted line,
that is, the point of the pen should be brought slowly down upon the
paper, and lifted without dragging it; and no dot should be made without
a deliberate intention respecting its position. All arrangement in rows
must be carefully avoided. In sand-hills, the slopes should be made
darker than the level parts by placing the dots closer together. Mud in
tidal rivers may be represented by very fine dots placed close together.
[Illustration: FIG. 55.]
[Illustration: FIG. 56.]
_Woodland._--Trees are generally shown in plan (as in Fig. 55). The
outline is circular in character, and, to have a good effect, it should
be made up of simple curves firmly drawn; small indentations should be
avoided as bad. A few touches of the pen are given on the interior and
towards the shadow. The latter is cast by parallel rays of light
inclined 45° to the horizon, and is detached from the outline of the
tree. When the scale is large, the shadow will be elliptical in form,
but in small scales it will become a simple circle. In representing
woodland, the trees and masses of trees should be disposed in every
possible variety of position, care being taken, however, to avoid all
regular figures and arrangements in lines. In parks and gardens, where
the arrangement of the trees is artificial, it is usual to represent a
grove in a rectangular form. Orchards are shown by placing single trees
with their shadows at the points of intersection of two sets of
equidistant parallel lines drawn at right angles to each other. These
lines are drawn in pencil and afterwards erased. Some draughtsmen prefer
to draw trees in elevation, as shown in Fig. 56. This method allows the
various kinds of trees to be distinguished on the plan, and gives scope
to artistic skill.
[Illustration: FIG. 57.]
_Uncultivated Land._--Uncultivated land, other than woodland, is
represented by drawing bushes in plan, similar to trees, but of smaller
dimensions, and mixing tufts of grass with them, as shown in Fig. 57.
[Illustration: FIG. 58.]
_Contour Lines._--Suppose a cone A B C (Fig. 58) cut at regular vertical
intervals apart by a series of horizontal planes 1, 2, 3. The
intersections of these planes with the surface of the cone will give
lines upon that surface; and it is obvious that the cone may be
represented in plan by the projection of these lines, as shown in the
figure. To obtain this projection, draw the horizontal line D E, and
from the apex of the cone and from the intersections of the cutting
planes let fall vertical lines. From the point where the line from the
apex meets the line D E as a centre, with radii equal to the distances
from this point to those where the lines from the sections meet D E,
describe circles. These circles will be the horizontal projections of
the lines on the surface of the cone produced by the cutting planes; and
these lines are called _contour lines_. Also it is obvious that, from
the plan of the cone so obtained, we may as readily project the
elevation, provided we know the vertical distance apart of the sections
denoted by the contour lines. To obtain the elevation, we have only to
draw horizontal lines at the given distance apart, and from the points
in D E erect perpendiculars to meet them. Lines drawn through the points
of intersection will give the elevation of the cone. To find the
inclination of the surface of the cone, upon _a b_, a portion of the
normal D E, as a base, erect a perpendicular _b c_, equal in height to
the distance of the sections apart, and join _a c_. The hypothenuse _a
c_ then represents that portion of the surface of the cone which is
included between the two contour lines, and of which the angle of
inclination is _b a c_. The space between two contour lines is called a
horizontal zone.
The cone being a regular figure, its contour lines are circles. For
irregular figures, the contour lines will be irregular curves. The
regular inclination of the surface of the cone causes the projections of
the contour lines to be at equal horizontal distances apart. But when
the inclination varies, the horizontal distance between the contour
lines also varies, the distance decreasing as the inclination increases.
Thus the method of representing objects in plan by contour lines, not
only gives the correct form of the object, but shows the relative
inclination of every portion of its surface. This may be clearly seen in
Figs. 59 and 60, the former of which is a representation in plan by
contour lines of an irregularly shaped object, and the latter an
elevation of the same object projected from the plan.
[Illustration: FIG. 59.]
[Illustration: FIG. 60.]
The system of representation by contour lines is generally adopted by
topographers to distinguish and define the variation of the surface of
the ground in regard to hill, valley, and plain. By intersecting a
mountain, for example, by a sufficient number of horizontal planes, its
correct form may be delineated, and the declivity of its surface
accurately shown. The relative declivity of any portion of its surface
is indicated by the difference in the horizontal distance of the curves
apart; and by constructing a triangle upon a normal to the upper curve
in the manner already described for the cone, the absolute slope at any
point between any two curves may be readily determined. The ground is
supposed to slope uniformly from one curve or contour line to the next.
Such, however, is rarely the case; but provided the curves are taken at
frequent intervals, the error is of no practical importance. Hollows are
represented in the same way; and whether the representation is that of a
hill or a hollow, is known from the other parts of the map. Thus, if
Fig. 59 represent a hill, the vertical projection will be as shown in
Fig. 60; but if it denote a hollow, the outer curve must be projected
highest, and the vertical section will be Fig. 60 inverted. In practice
the contour lines are numbered, the number of any contour indicating its
height above a plane of reference called a datum plane. The vertical
distance of the contour lines apart varies with the character of the
ground and the object of the survey; but it is seldom less than 25 feet.
The lines are obtained by the surveyor by fixing a number of points on
the same level by means of instruments.
SECTION IV.--COLOURS.
The preceding Section treats exclusively of representation by lines and
dots, or that mode of delineating objects and natural features known as
line or pen drawing. There is, however, another mode of representation
by means of colours that is fast coming into general use. This latter
mode is far more expressive than the former, and, besides affording a
wider scope for artistic effect, shows with greater distinctness and
precision the character of the object represented. For these reasons it
is almost always adopted for plans of estates and geological sections,
and also very frequently for other kinds of topographical as well as for
engineering and mechanical drawings. The colours used for this purpose
are not applied in the way the artist applies them; but they are laid on
in thin washes to produce a faint tint rather than a body of colour. The
process is called tinting or flat-washing, and though it cannot be
described as a work of art, considerable practice and skill are
requisite to execute it properly.
_Flat-tints._--A drawing to be coloured must be previously stretched and
gummed to the board, in the manner described in Section I. Unless the
paper be prepared in this way, it will remain blistered after being
wetted by the laying on of the tints. The lines of the drawing must be
very fine, and the ink, though black, should not be thick. Great care
should be exercised in drawing in the outlines, that there be always a
piece of clean paper between the hand and the drawing, for the least
degree of greasiness will prevent the colours from working freely.
Should the surface of the paper, however, from inattention to this
matter, or from accident, become slightly greasy, the defect may be
partially remedied by adding a little prepared ox-gall to the water with
which the colours are mixed. When all the outlines have been drawn in
and the pencil lines erased, the drawing is prepared for the colouring
by being _washed_. The washing is effected by passing a soft sponge well
saturated with clean water gently and rapidly over the surface. The
purpose of this washing is twofold; first, to remove those portions of
the ink which a wet brush would detach from the paper in laying on the
colours, and which, by becoming mixed with the tint, would injure its
purity; and second, to damp the surface of the paper in order to prevent
the colour from drying too rapidly. The latter is an important matter,
for if the tint which is being applied dries quickly, it is impossible
to unite the edges properly, and the tint, especially if the surface be
large, will have a cloudy and blotchy appearance. As the operation of
washing renders the paper too wet to immediately receive the colour, it
must be allowed to remain in a perfectly horizontal position for a short
time to dry, and during this time any tendency to dry unequally must be
corrected by means of blotting-paper. While the paper is drying, the
tints may be prepared.
To ensure satisfactory results, care must be taken in the preparation
and preservation of the tints. They should never be made by artificial
light, and a sufficient quantity should be made at first to cover all
the portions required, as it is very difficult to match a tint exactly.
When a drawing is several days in hand, it is best to prepare a fresh
tint for every coat, for the colours will change in the course of a day
or two, even if protected from the light. A few drops of water should be
added now and then, to make up for the loss by evaporation, especially
in warm weather. Tints left to dry upon the palette should never be wet
up again for use, but they should be washed clean out and a fresh tint
made; if this precaution be not attended to, the colour will not be
pure. When a tint is to be mixed, the end of the cake of colour should
be moistened and allowed to soften for a minute or two, as this will
cause it to rub smooth and free from fragments. The palette should then
be moistened and the end of the cake rubbed gently and evenly upon it
till a sufficient quantity of colour has been obtained, which may be
added to the requisite quantity of water by means of a brush. A
precaution necessary to be observed is never to rub one colour down upon
another, as it will probably be laid aside to dry with the other colour
on it. The brush used should be as large as the nature of the work will
allow, and it should be of the best sable hair; the quality is judged by
the length of the hair, the longest and stiffest being the best.
Draughtsmen frequently do all their work with a couple of sable brushes
attached to one holder, one being for colour and the other for water; in
this case the brushes should be of different colours to prevent
mistakes.
The art of laying on a flat-tint consists in allowing the coloured water
to flow equally over the paper, which thus becomes uniformly tinged. To
facilitate this, the surface of the drawing should be inclined towards
the draughtsman at an angle of about five degrees during the process of
laying on the colour. Having taken as much colour on the brush as it
will safely carry without dropping, the operation of applying it should
be begun in the upper left-hand corner, the brush being carried along
towards the right, so as to make the colour lie neatly along the upper
outline. The brush should then be struck unhesitatingly from right to
left and from left to right alternately, so as to bring the colour down
in horizontal bands or stripes, taking care not to pass the brush a
second time over the same surface during the same wash, and to control
it neatly within the proper limits. If the surface of the paper be in
this way kept well wetted with the colour, or if, in other words, a flow
of colour be kept in motion with the point of the brush, the tint can be
carried on with perfect continuity. It is important to keep as nearly as
possible the same quantity of colour in the brush until the lower
outline is nearly reached, when the quantity must be diminished so as to
finish at the lower outline without a great excess of tint, for the
excess must be taken up by a damp brush. No accumulations should be
allowed to take place anywhere, as on drying, these places would show a
darker tint. When the colour has once flowed over the surface, the tint
is finished, and must not, as we have said, be touched a second time,
for any attempt to remedy defects while the colour is drying will only
make them worse. Generally it will be found that the more quickly a tint
is laid on, the better is its appearance. A little practice will enable
the student to lay on a wash in the proper manner, but to keep within
the outlines is a matter of greater difficulty and one that requires
some dexterity in the handling of the brush. If the boundary should be
exceeded, a finger of the left hand should be instantly applied to brush
the colour back. Though the foregoing directions can be followed
strictly only on large surfaces, the principles involved in them must in
every case be observed.
The alternate or double tint consists of two colours applied
alternately, their edges being made to blend into each other. The
application of the double tint involves no particular difficulty. Having
prepared two tints of equal intensity and provided a brush for each, lay
on one of the colours at the upper outline of the figure, and before
this dries, take the brush charged with the other colour, and run round
its edge, allowing them to blend together. Repeat the first tint in the
same manner, and continue the tints alternately till the surface is
covered. The forms of the masses of each colour should be varied, and
not made in stripes or spots, but irregularly clouded.
All flat-tints should be made very light, and intensity of colour should
be produced by repeating the wash. As every surface looks better with
two washes than with only one, the strength of the tint should be such
as to allow two coats to be laid over the lightest parts. If the colours
have been laid on too dark, or the general effect be uneven and
disagreeable, the defect may be remedied by sponging. This operation
should be performed with a close-grained 6-inch sponge, and be commenced
at the upper end of the inclined board. A basin of clean water having
been provided, and an empty basin to receive the dirty water from the
sponge, first moisten all the white surface of the paper to prevent the
tint taken off by the sponge from adhering to it; then, having filled
the sponge with water, pass it gently to and fro across the sheet. Press
out the dirty water into the basin, refill the sponge, and repeat the
operation until hardly any tint comes off. Sponging after five or six
coats have been laid on generally improves the appearance of a drawing;
it softens down asperities, and makes the tints blend into each other;
the surface of the paper also takes the tints more readily after
sponging.
Small defects may frequently be remedied by a process called stippling.
This consists in making a number of dots with the point of a brush
containing an almost imperceptible quantity of colour. The process,
though a tedious one, produces a very beautiful effect, similar to that
of dotted engravings. Excesses beyond the boundary lines may be washed
out with the water-brush, and the stains removed by a piece of clean
blotting-paper. White spots left in a tint may be filled up, after the
tint is dry, with the point of the brush; but care must be taken not to
touch beyond the edges of the tint, as that would double the intensity
at the edges and produce a ring.
All flat surfaces in a drawing should be lighter or darker, in
accordance with their distance from the eye. In laying on flat-tints
when the surface is not in shade, it must be borne in mind (1) that all
surfaces which are parallel to the plane of the picture, and therefore
equally distant from the eye, should receive a tint of uniform
intensity; (2) that those surfaces which are farthest from the eye
should receive the darkest tint; and (3) that surfaces which are
inclined to the plane of the drawing should receive a tint of varying
intensity, the depth of the tint increasing as the surface recedes from
the eye. When the surfaces are in shade, the converse of these rules
holds good.
_Conventional Colours._--In representing objects by means of colours,
the natural colours of the objects are in some cases adhered to; and in
others, for the sake of greater distinctness, a conventional colour is
adopted. In engineering, architectural, and mechanical drawings, the
latter mode is nearly always resorted to, while in plans of estates the
former is very frequently employed. Unfortunately, practice is not
uniform among draughtsmen in the conventional use of colours; but the
following Table shows the colours mostly employed, and represents the
general practice.
Carmine or crimson lake For brickwork in plan or section to be
executed.
Prussian blue Flintwork, lead, or parts of brickwork to
be removed by alterations.
Venetian red Brickwork in elevation.
Violet carmine Granite.
Raw sienna English timber, not oak.
Burnt sienna Oak, teak.
Indian yellow Fir timber.
Indian red Mahogany.
Sepia Concrete works, stone.
Burnt umber Clay, earth.
Payne’s grey Cast iron, rough wrought iron.
Dark cadmium or orange Gun metal.
Gamboge Brass.
Indigo Wrought iron--bright.
Indigo, with a little lake Steel--bright.
Hooker’s green Meadow land.
Cobalt blue Sky effects.
And some few others occasionally for special purpose.
Sections are represented either by lines of the colour drawn with the
pen or the point of the brush, or by a darker shade of the colour. In
mechanical drawings, sections are frequently shown by ink lines drawn
over the colour.
In plans and maps, as we have said, some attempt is made to give the
true appearance of things. As this--which may be called the natural mode
of representation--allows more scope for artistic skill than the
conventional, a great deal must be left to the judgment and the taste of
the draughtsman. But there are general principles and features that may
be laid down and described, and such are the following:--
_Water._--For water, a flat-tint of pure indigo is used. To produce the
clear, transparent effect of water, there should be two coats of the
tint, which, to allow of this, must be very light coloured.
_Grass-land._--For grass or cleared land, a flat-tint of green is
employed. This tint is composed of indigo and gamboge, and should be of
a lively hue, which may be produced by giving predominance to the
gamboge. Care must always be taken in preparing greens for maps and
plans, that the blue be kept subordinate to the yellow; for a
predominance of the former colour produces a _cold_ quality, which is
utterly destructive of that _natural_ appearance it is intended to give.
The intensity of the tint for this and for other purposes should be such
as to distinguish it clearly from others, and to allow somewhat for
fading, without masking any of the details of the drawing; and it must
be clear and transparent. We may here remark that all tints which are
much extended should be _balanced_, that is, no one should obtrude
itself upon the eye by its relatively too great intensity.
_Marsh._--Marsh and swamp are represented, as in line drawing, by a
combination of the signs for water and grass-land. The tints are laid on
horizontally, that is, parallel to the base of the drawing. They are
not, however, laid on in bands or strips across the drawing, but are
made to project in irregular points from each side, with here and there
a long and narrow patch to represent an island. The land should cover a
larger portion of the space than the water, and it should be washed in
first, care being taken to make the white spaces left for the blue
colour resemble the green in form, which spaces should project their
horizontal points into the green as the latter projects its points into
the white. The outer limits of a marsh should consist of an outline of
projecting green points. The land portion of the marsh is finished by
drawing a light shading line of indigo and burnt sienna along the lower
edge of the green. This line must be drawn _upon_ the edge and not
_against_ it upon the white space. In washing in the water, care must be
taken not to overlay the edges of the green. A good effect is produced
by introducing a tree here and there upon the land.
_Sand and Gravel._--Sand is shown by a flat-tint of yellow ochre. Sand
and gravel are represented by dotting the flat-tint with burnt sienna by
means of the point of the brush held in a vertical position. Stones and
rocks in sand should be first outlined with the pen in burnt sienna and
sepia in equal proportions, and afterwards filled in with the brush with
the same colour.
_Mud._--In the survey of rivers, creeks, and coasts, it frequently
becomes necessary to show tracts of mud between the lines of high and
low water. For this purpose a flat-wash of sepia or Indian ink may be
used dotted with Indian ink of greater intensity. The dots in this case
must be very minute and thinly placed, and they should be evenly
distributed. A fine-pointed pen will be found more effective in putting
in these dots than the point of the brush.
_Woodland._--To represent woodland, a flat-tint of green is first laid
over the ground, as for grass-land. The groups and masses of trees are
next drawn in outline, in the manner described in the last Section, with
a hard and sharp lead pencil, or with a pen and pale ink. To fill in
these outlines, a colour made up of indigo and gamboge in the same
proportions as the ground tint, but of greater intensity, is laid on the
lower and right-hand portion of each tree and mass of foliage, so as to
occupy about two-thirds of the figure. The remaining portion, which will
be the side towards the light, is then touched with an orange tint
composed of gamboge and burnt sienna. It only remains to add the shadow.
As the light is supposed to enter the drawing in parallel rays from the
upper left-hand corner, the shadow of every object will surround its
lower and right-hand outlines. It is laid close up to the outline in
masses of foliage; but for single trees, as in orchards, it is detached.
The form of the shadow was described in the last Section. To produce the
shadow, the same tint is used as for the ground, two or three successive
applications being sufficient to increase the intensity to the requisite
degree; or a neutral tint may be used, composed of indigo, burnt sienna,
and a little lake. After the shadow has been put in, the outlines on
that side should be strengthened by going over them again with the pen.
By drawing the trees in elevation, an opportunity is afforded for the
display of artistic skill far greater than the foregoing method admits
of. When drawn in this way, the work partakes somewhat of the nature of
landscape painting.
_Cultivated Land._--Cultivated land is represented by a flat-tint of
burnt sienna.
_Uncultivated Land._--Uncultivated land or brushwood is represented by a
double tint of green, as for grass-land, and burnt sienna, as for
cultivated land, laid on in the manner already described for the double
tint. As this is the only double tint used, it may be made, if thought
desirable, with alternate green and crimson lake.
_Buildings._--Buildings, including all structures of masonry, as
bridges, locks, walls, and such like, are coloured with crimson lake,
and shadowed with a neutral tint composed of indigo, burnt sienna, and a
little lake, as given above for forest land.
_Roads and Streets._--Roads and streets, and generally all those
portions of a drawing not particularly described, are tinted with yellow
ochre.
_Fences._--Hedges are represented by green dots, varied in size for
bushes; stone or brick walls, by a line ruled in red; and wooden fences
by lines of neutral tint, either ruled or drawn in by hand, according as
the line is to be straight or otherwise. In every case the shadow must
be put in.
In determining the intensity of the various tints employed on a
topographical drawing, care must be taken that everything be “in
keeping.” A cardinal rule of art is that nothing shall unduly obtrude
itself; and in a coloured plan, _spottiness_, as it is called, should be
studiously avoided. Forest, brushwood, and cultivated land, should be
represented by tints of about equal intensity, and the same equality may
be observed for grass-land, marsh, water, and sand, but the intensity
should be less than in the former case. Tints that are of small extent
may be a little exaggerated in intensity for the purpose of giving them
greater distinctness, especially when the object represented is a
building. Gardens and orchards require a little exaggeration in depth of
tint, to distinguish them from the surrounding country; but care must be
taken not to make the distinction too marked. It will generally be found
conducive to a maintenance of “keeping,” to lay the lightest tints on
first.
SECTION V.--SHADING.
In mechanical and architectural drawings, shade lines must be considered
rather as embellishments than constituent parts of the drawing. They
are, however, frequently employed; and as their incorrect use may
deceive the eye with respect to the intention of the designer, it
becomes an important matter to know when to apply them with propriety.
[Illustration: FIG. 61.]
[Illustration: FIG. 62.]
_Application of Shade Lines._--As we have already explained, the light
is supposed to fall upon the objects in a drawing in parallel rays from
the upper left-hand corner for elevations, and from the lower left-hand
corner for plans. To determine whether or not a given line should be a
shade line, we have only to ascertain whether or not the light,
introduced in such a manner, falls upon that edge of the object which
the line represents. All those parts of a body upon which the rays of
light fall directly, are said to be _in light_; all those parts upon
which the rays of light do not fall directly, are said to be _in shade_;
and those parts of a surface which are deprived of light by another body
intercepting the rays, are said to be _in shadow_. These definitions
should be borne in mind. Lines representing the boundaries of surfaces
in light should be fine lines, and lines representing the boundaries of
surfaces in shade should be thick or shade lines. Let it be required,
for example, to determine the shade lines of the cube shown in elevation
in Fig. 61. The extreme rays of light falling upon the cube meet the
edges in _b_ and _c_; hence the surfaces _a b_, _a c_, are in light, and
the surfaces _d b_, _d c_, are in shade. The foregoing rule will thus
make _a b_ and _a c_ fine lines, and _d b_ and _d c_ shade lines. If the
cube were turned so that _a b_ should be at right angles to the rays of
light, the extreme rays would fall on the edges _a_ and _b_, and the
middle ray which now falls on _a_ would fall on the middle of the line
_a b_. The rays immediately beyond those which are arrested by the edges
_a_ and _b_, may be considered to pass along in contact with the
surfaces _a c_ and _b d_; and these surfaces must, therefore, be
regarded as in light. Thus we shall have in this case the lines _a b_,
_a c_, and _b d_, fine lines, and the line _c d_ a shade line. It is the
practice of some draughtsmen to make _a c_ and _b d_ in such cases a
medium line, and the practice has propriety to recommend it. The
foregoing explanations of the shade lines in the elevation of the cube,
render any further remarks concerning those in the plan, Fig. 62,
unnecessary. In practice, whether or not a surface is in light may be
determined by placing the set square of 45° against it.
[Illustration: FIG. 63.]
[Illustration: FIG. 64.]
The same principles are observed in the end elevation of the hollow
cylinder, shown in Fig. 63. The extreme rays meet the circumference in
the points _a_ and _b_; consequently the surface _a c b_ is in light,
and the surface _a d b_ is in shade. The middle ray meets the surface
perpendicularly at the point _c_, which will be the lightest part of
that surface; similarly, _d_ will be the darkest part. To show this, the
shade line must be gradually increased in thickness towards the point
_d_. The shading of the inner circle will be the converse of the outer.
Fig. 64 shows a plan of the same object.
[Illustration: FIG. 65.]
_Cylindrical Surfaces._--Let _a b c d_, Fig. 65, be a plan, and _k l n
m_ an elevation of a cylinder. The portion _a c b_ is in light, and the
portion _a d b_ is in shade, of which latter portion _a_ and _b_ are the
edges. From the points _a_ and _c_ draw vertical lines _e f_, _g h_.
Then will _e f_ be that part of the cylinder upon which the light falls
perpendicularly, or the lightest part, and _g h_ the edge of the surface
in shade, or that portion of the surface of the cylinder that would cast
a shadow upon the plane of projection. Hence this will be the darkest
part, and consequently it is obviously improper to make the line _k l_ a
shade line. This demonstration, which is given by Binns, shows that
shade lines must never be applied to cylindrical surfaces. If this
principle be observed, cylindrical may be readily distinguished from
flat surfaces.
[Illustration: FIG. 66.]
_Shading Lines._--Shade lines are applied only to the edges or
boundaries of surfaces; when lines are put upon a surface to show the
effects of light and shade, they are called shading lines. The use of
the latter is determined by the same principles as that of the former;
indeed, a shade line may be practically considered as an end view of a
number of shading lines. In Fig. 66, which is an elevation of a hexagon,
the surface _c_ is in shade, and to represent this surface correctly, it
must be made darker than the others. This darkening of the surface is
effected by drawing the shading lines heavier or closer together, or by
both of these means combined. The surface _b_ is in light, but the rays
fall upon it obliquely; the shading lines on this surface will therefore
be lighter and more widely spaced than on _c_. The surface _a_ is also
in light, and receives the rays normally, that is, the direction of the
rays is normal to the surface. Hence this surface will reflect most, or,
in other words, will be the lightest. This is shown by making the
shading lines still lighter, and spacing them still more widely than
those on _b_. The greatest care is needed in applying shading lines to
keep their thickness and the spacing regular, as an error in these
respects will frequently produce an effect quite opposed to what is
intended.
[Illustration: FIG. 67.]
_Shading Lines on Cylindrical Surfaces._--If the demonstration
previously given concerning shade lines on cylindrical surfaces be
understood, the application of shading lines to these surfaces will
present no difficulty. The darkest and the lightest part of the cylinder
having been determined, and in practice this can be accomplished with
sufficient exactness by the eye, the shading lines are applied according
to the principles explained above with respect to the hexagon. The first
shading line is drawn upon the darkest part; and each successive line on
each side of this first line is drawn lighter and spaced more widely
than the preceding. At the lightest part, a clear space is left to
represent the reflexion of the rays that occurs strongly there, and
beyond this part the shading is made equal to that of the corresponding
part on the other side. The thickening of the lines is effected by going
over them a sufficient number of times. Fig. 67 shows a vertical and a
horizontal cylinder shaded in this manner. In outline drawings of
machinery, this mode of shading with parallel lines is frequently
resorted to.
[Illustration: FIG. 68.]
[Illustration: FIG. 69.]
[Illustration: FIG. 70.]
[Illustration: FIG. 71.]
It will be evident, on reflection, that when the cylindrical body stands
parallel with the direction of the rays of light, as shown in Fig. 68,
the lightest part will be in the middle, and the shade will increase in
intensity as it approaches the edges. The shading of the interior of a
cylinder is, as we have already remarked when treating of shade lines,
the converse of that of the exterior. This is shown in the sectional
elevation, Fig. 69. When parallel with the direction of the rays of
light, as in Fig. 70, the internal shading is the same as the external.
On bright circular surfaces, such as that of a circular saw, or the
polished end of a shaft, the light is radiated from the centre, as shown
in Fig. 71. This mode of shading is strictly in accordance with the
appearance presented by such surfaces. It may be remarked here, that if,
through inadvertence, any part should be made too dark, the error may be
corrected by darkening all the other parts in a corresponding degree.
[Illustration: FIG. 72.]
_Shading Lines in Topographical Drawings._--The shading lines put upon
mechanical drawings are merely accessories used for purposes of
embellishment. But in topographical drawings, shading lines are applied
to give expression, and they constitute an essential element in the
representation. We have shown how undulations of the ground,
constituting hill and valley, are represented by contour lines. But it
is obvious that these lines furnish information respecting the
character of the surface only at those points through which they pass.
Thus we are necessarily left in ignorance of the irregularities existing
between any two successive contours. To supply this information which
the contours fail to give, shading is resorted to. Another important
object of hill shading is to represent the surface of the ground
conventionally in a manner that will immediately afford an idea of its
character without the aid of regular contours. The method adopted
consists in employing lines varying in their thickness and in their
intervals apart according to the slope of the ground to be represented.
This method is based upon the principle of the horizontal contours,
which is to give to the same vertical interval the same absolute amount
of shade, whatever the inclination of the ground may be. The shading
lines are used, as we have said, to fill in the features of the ground
between contours already fixed; and to ensure accuracy and uniformity in
the representation, a “scale of shade” is employed. The accompanying
Fig. 72 shows the standard scale of shade adopted by the Council of
Military Education, and made use of for all the Government surveys. The
second and the fifth columns of this scale show the spacing of the
hachures and their thickness for different angles of slope, while the
first and the last columns show the number of hachures to be
interpolated between contours at every 25 feet vertical intervals,
supposing the slope to be uniform. The slope is denoted both by the
number of degrees in the angle it makes with the horizontal, and by a
fraction showing the ratio of the vertical height to the base in a
right-angled triangle, the hypothenuse of which is the slope in
question.
The scale of shade is constructed for a horizontal scale of six inches
to the mile, and the amount of shade has been chosen with a view of
producing the best possible artistic effect. Of course, the most
satisfactory results, both artistically and practically, will be
obtained when the ground is delineated to this scale, but it can be
readily applied to any other scale. For example, the horizontal interval
for a slope of ¹⁄₂₀, corresponding to a vertical interval of 25 feet,
will be 20 × 25 = 500 feet, which, on a scale of six inches to a mile,
will be represented by a length equal to ⁵⁰⁰⁄₅₂₈₀ × 6 = 0·566 inches. In
this case, therefore, supposing the slope of the ground to be uniform
between two given contours 25 feet apart, we should represent it by
means of the hachures shown opposite a slope of ¹⁄₂₀, continued over a
space of 0·566 inch.
[Illustration: FIG. 73.]
In topographical drawings, the light is supposed to fall vertically upon
the surface; hence a level surface will reflect all the light that falls
upon it, while one of 45° will not reflect any.
The drawing of the hachures presents certain difficulties of execution
that can be overcome only by continued practice and careful attention to
the modes of proceeding which experience has proved to be the most
effectual. Thus an important rule is always to draw “from left to right
and downwards.” To allow this to be done, the drawing must be placed
with the summit of the hill to the left hand, and be turned round as the
work progresses. The hachures should always be commenced at the crest of
the hill, working outwards towards the foot of the slope. They should be
drawn firmly, and of a length varying from ¹⁄₄ inch to ³⁄₄ inch,
according to the width of the zone, that is, according to the greater or
less degree of the slope, as shown in Fig. 73, at _a_, _b_, _c_, _d_.
When the hill is steep, the lines are made short and thick, and when the
declivity is less, they are made longer and lighter, becoming fine and
clean as the level is approximated to. A difficulty with beginners is
to press upon the pen equally from the beginning to the end of the
stroke, the tendency being to press more heavily towards the end, thus
producing a whip-like appearance quite opposed to artistic effect, and
conveying a false impression of the character of the ground. A good
effect is produced by imparting a slightly tremulous motion to the pen
when drawing the hachures. The form of the hill being accurately defined
by the pencil contour lines, it is not necessary that the accessory
curves formed by the shading lines should be rigorously continuous, and
indeed a much better effect, artistically, is gained by avoiding such a
manner of drawing them. The various sets of lines must be placed
together, end to end, in such a way that the groups or sets shall not be
separated by a vacant space, nor overlap each other. Care must be taken
that the junctions of sets in two contiguous zones do not form a
continuous line from one zone to the other, but everywhere “break
joint.” Each zone must be filled in before the next lower one is
commenced, the drawing being turned as the work progresses to allow the
rule enunciated above of “from left to right and downwards” to be
complied with. The distance between the shading lines must be increased
or diminished according as the width of the zone varies, so as to divide
the space equally; and on reaching the part where the lines were begun,
the ends must be brought neatly together. As this can be most
satisfactorily accomplished where the lines come close together, it is
best to begin at the steepest part of the slope.
In taking a set of hachures round a sharp bend, as in the case of a spur
or a ravine, a practical difficulty occurs, which difficulty is
increased as the angle becomes more acute. The most effective way of
overcoming this difficulty is to draw a pencil line down the spur or
re-entering angle, as shown at A B and C D in Fig. 74, and to mark off
on this line, at the proper intervals, small arcs of the same radius, as
near as can be judged by the eye, as the curve of the contour line. The
sets of hachures on each side may then be drawn to these arcs. Guiding
lines, as _a b_, _c d_, _e f_, and _g h_, should be drawn at right
angles to the general direction of the contours to ensure the hachures
being correctly placed before and after rounding the angle. For this
method of carrying a set of hachures round a sharp curve, we are mainly
indebted to Lieut. R. Pulford’s ‘Theory and Practice of Drawing.’ When
this method is not employed, the hachures must be drawn on each side of
the angle first, and those for the angle filled in separately.
[Illustration: FIG. 74.]
Great care must be taken in filling in the zones formed by the contour
lines, that the drawing when finished do not present the appearance of
separate layers or bands; for such an appearance is not only quite
opposed to artistic effect, but it conveys a false notion of the
character of the ground. The successive zones are not separate portions
of the surface, but each is a continuation of the one adjoining it. The
great principle to be observed in this, as in all matters of hill
shading, is that changes of slope are gradual. When the contours are
only pencilled in as guide lines to be afterwards erased, the
above-mentioned defect may be avoided by drawing the hachures over them,
without reference to exact spacing. But when, as is usually the case in
regular surveys, the contours are inked in in dotted lines, the only
means of avoiding it is to space the hachures on each side of a contour
line at the same distance apart.
The student of map drawing should practise assiduously this system of
shading in detached portions before undertaking the delineation of a
complete hill. For such exercises, either a soft, medium-pointed steel
pen, or a quill may be used.
_The Vertical System of Shading._--The foregoing system of shading is
known as the _Horizontal_, and is now generally employed in this country
for all kinds of surveys. There is, however, another system much used
abroad, and frequently adopted here for engraved maps. In this system,
which is known as the _vertical_, the shading lines are made to radiate
from or converge into the curved parts of a hill, according as they
project or re-enter. Such lines are called _lines of greatest descent_;
they are supposed to describe the same course that water would describe
if allowed to trickle in streams down the slopes, and hence they exhibit
both the _direction_ and the _degree_ of the slope. Having the
horizontal sections given, we may obtain a complete knowledge of the
direction in which the ground slopes by drawing perpendicular to them
any number of lines of greatest descent; the degree of declivity is
expressed by purely conventional means. The means adopted for this
purpose are of two kinds. One depends upon the principle of vertical
illumination, in which the maximum quantity of light is reflected
upwards to the eye by a horizontal surface, and a minimum by a surface
inclined 45° to the horizon. This is the English and German convention,
and it lays more stress upon the proportions of black to white in
indicating the degree of slope, than upon the distance between the
shading lines. The other convention, which is the French, on the
contrary, makes its expression depend more upon the distance between the
lines of greatest descent than upon the shade of colour produced, though
in this also the tint is graduated from dark to light, according to the
degree of declivity.
A scale of shade is used for this system, founded upon the same
principles as that already given for the horizontal system. The scale
adopted is due originally to Major Lehmann, of the Saxon Infantry; but
it has received some modification to adapt it to the requirements of
practice. Fig. 75 shows Lehmann’s scale. It is constructed for every 5°,
from a level up to a slope of 45°, which is the steepest slope at which
earth will stand. Each division of the scale corresponding to a given
slope is subdivided into nine parts, to show the proportions of black to
white. For a level, the whole of these spaces are left white; for a
slope of 5°, the proportion is one black to eight white; for a slope of
10°, two black to seven white; and so on up to 45°, for which slope we
have all black. The longitudinal divisions of the scale below that
against the outer edge A B contain the same proportions of black to
white, but equally distributed to show the mode of applying it. Thus, in
the division _o p r s_, corresponding to a slope of 5°, the single black
space is, in E F G H, divided into two equal parts and distributed; in
G H I K, these two parts are again equally divided and distributed; and
so on throughout the other longitudinal divisions. If now the scale be
cut off along the line L M, the part L M C D will constitute a scale,
the graduated edge L M of which will furnish us with a means of marking
off the distance between the centres of the shading lines.
[Illustration: FIG. 75.
LEHMANN’S SCALE OF SHADE.]
To find the proportion of black to white in the foregoing scale for any
given slope:--Subtract the given inclination from 45° for a denominator,
and put the given inclination for a numerator. In the scale, as drawn in
the figure, the variations are by 5°; but it is obvious that a scale may
be drawn in the same manner to mark smaller variations, if thought
desirable.
In applying this method in the United States’ Coast Survey, it was
remarked that “this scale of shade does not represent slopes greater
than 45°, thereby limiting the graphic capabilities and effect of the
map. It also makes the slopes too dark as they approach the inclination
of 45°, and does not well represent slopes of less than 5°, which latter
it is often desirable and necessary to express distinctly.” The
following modification was therefore made:--
-----------------+-------------
|Proportion of
Slope. +------+------
|Black.|White.
-----------------+------+------
2¹⁄₂° or 2³⁄₄° | 1 | 10
5° „ 6° | 2 | 9
10° „ 11° | 3 | 8
15° „ 16° | 4 | 7
25° „ 26° | 5 | 6
35° | 6 | 5
45° | 7 | 4
60° | 8 | 3
75° | 9 | 2
-----------------+------+------
By this scale, the slighter slopes are represented distinctly. For
slopes less than 16°, the shades are darker than in Lehmann’s scale;
this makes their difference more noticeable. Above 25° the shades are
lighter.
A further modification, which for ordinary purposes possesses the
advantages of simplicity and facility of application, has been made in
England, and very generally adopted. This modification consists in
fixing with accuracy only three proportions of black to white for three
medium slopes, as follows:--
-------+-------------
|Proportion of
Slope.+------+------
|Black.|White.
-------+------+------
Level | .. | all
15° | 1 | 2
22¹⁄₂° | 1 | 1
30° | 2 | 1
45° | all | ..
-------+------+------
A scale of shade may at once be constructed from this Table, by assuming
the thickness of the shading line for the medium slope of 22¹⁄₂°, which
thickness must be suited to the scale, and to the degree of fineness and
finish it is intended to give the drawing. Generally, if the lines have
such a relation to the scale of the drawing as to present a
well-connected appearance, it will be found that fewer shading lines and
a rather coarse texture will conduce more to clearness of expression
than a finer texture, which tends to produce a dryness of style. In
shading to this scale, it should be applied to the drawing wherever the
slope corresponds to one of the three on the scale. Intermediate slopes
are indicated by graduating the thickness of the shading lines. In all
cases a good deal must be left to correctness of eye and skill of hand.
In the French method, as we have said, the inclination is expressed by
the distances between the centres of the lines of greatest descent. The
limits of the slopes that can be represented by this method are, ¹⁄₁ or
45° for the greatest and ¹⁄₆₄ or 0° 53′ 43″ for the smallest. The
largest scale that will admit of conveniently drawing the lines of
greatest descent is ¹⁄₆₀₀ full size, or about 8³⁄₄ feet to a mile. The
vertical distance between the horizontal sections is generally taken as
1 yard. Hence to a scale of ¹⁄₆₀₀ the least width of zone will be ⁶⁄₁₀₀
inch, and the greatest ⁶⁄₁₀₀ × 64 = 3⁸⁴⁄₁₀₀ inches.
The distance between the shading lines is reckoned from centre to
centre, and is determined by the rule:--To the distance between the
upper and the lower curves of any zone add ³⁄₁₀ of an inch; a sixteenth
part of this sum will be the proper interval for the shading lines. The
distance is measured along the line of greatest descent. Thus, if the
inclination be ¹⁄₆₀ and the scale ¹⁄₆₀₀, the width of zone will be ·06 ×
60 = 3·60 inches, and by the rule we have
3·60 + ·3 3·9
--------- = --- = 0·244 inch.
16 16
Another rule is:--To a fourth of the distance between the upper and the
lower curves of any zone, add ⁷⁵⁄₁₀₀₀ of an inch; a fourth part of the
sum will be equal to the interval.
The thickness or breadth of the lines is made to vary directly as the
inclination to assist in expressing the declivity. This thickness is
determined by the following rule. For a slope of ¹⁄₁ the thickness of
the shading lines is equal to ²⁄₃ of the distance between their
centres, and this thickness will diminish with the inclination down to
¹⁄₆₄, where the lines will be as fine as they can be drawn. In a slope
of ¹⁄₁ this rule will always make the breadth of the shading lines twice
that of the white space contained between them.
To represent declivities by the vertical system of shading a
considerable amount of practice is required. This practice should be
commenced by drawing repeatedly the scale of shade, and gradually
applied, as proficiency is attained, to the varying inclinations of a
hillside. Having the horizontal sections of the hill given, the degree
of slope should be written upon it in pencil in as many places as is
necessary. The distances between the centres of the shading lines may
then be marked off upon the upper curve of the zone from the scale of
shade, and the lines of greatest descent drawn through the points thus
determined. The exact proportion of black to white being then adopted,
the colour will express the degree of the slope, and the line of
greatest descent will show its direction.
The principle of making the shading lines longer on a gentle slope than
on a steep one should be adhered to generally; but in this matter much
must be left to the judgment and the skill of the draughtsman.
Frequently on slight inclinations it will be desirable to divide and
subdivide the zone by medial lines, as shown in Fig. 76, and on very
steep slopes the shading lines may be drawn over two or more zones. For
ordinary scales the extremes of length may be fixed at ¹⁄₆ of an inch on
the steepest slopes, and ³⁄₄ of an inch on the gentlest.
[Illustration: FIG. 76.]
It is not necessary to repeat the process of construction for every
line, such a mode of proceeding would be too laborious and slow. It will
be sufficient to determine the lines in this exact manner at those parts
where the greatest changes of slope occur. Thus a group should be
constructed in each zone where the slope is greatest and another where
it is least, after which a few intermediate ones may be put in. The
vacancies may then be filled in, taking care to graduate the changes in
passing from group to group. By this means we do not, of course, get a
mathematically exact representation of the surface, but it is
sufficiently accurate for practical purposes.
When the preparatory pencil lines have been drawn in and the spaces for
the shading lines laid off by dots, the shading should be commenced at
the steepest part of the upper zone. The lines should be drawn firmly
from curve to curve, taking care to make each row terminate evenly at
the lower edge; they must always be drawn downwards and from left to
right, proceeding in this direction round the zone till the point of
setting out is reached, where the joining must be carefully effected.
This can always be done most neatly where the lines are thickest, as we
have previously pointed out. The succeeding zones should be filled up in
the same manner. As changes must be gradual in every direction, care
must be taken to make the contiguous zones blend into each other. When
it is required to pass from a light zone to a darker one beneath it, the
lower ends of the lines in the light zone should be thickened a little,
so as to meet the upper ends of the lines in the dark zone with nearly
the same colour. The upper ends of these latter lines should also be
slightly lightened. The lines of one zone must not be continued into
those of the next. Even on a uniform slope such a prolongation of the
lines would produce a hard appearance, which should be avoided. But in
the case of a conical hill, like that shown in Fig. 77, it would give
rise to an error in principle; for soon after leaving the summit we
should have too few lines of descent. When the hill has been covered
with shading lines, the base and the summit must be softened off by
tapering the lower end of each line at the base, and the upper end of
each line at the summit. To give the taper to the latter, the drawing
should be turned upside down.
[Illustration: FIG. 77.]
When the curves are parallel or nearly so, the shading lines are
straight, and also nearly parallel. But when the curves depart widely
from each other, the shading lines will themselves have a slight
curvature, for being lines of greatest descent, they must be normal to
the curves. In such cases, a number of normals should be put in at short
distances with the pencil, as shown in Fig. 78, to serve as guides to
the shading lines. The foregoing directions for shading a hill apply
equally to the shading of a hollow, the shading lines in which are
converging.
[Illustration: FIG. 78.]
Occasionally short slopes steeper than the “natural slope” of 45° will
be met with. Such being exceptions to the law of slopes, are marked in
an exceptional manner. When the surfaces of these slopes are of earth,
they are shown by black lines drawn parallel to the horizontal curves,
and when of rock, by black lines drawn in all directions, not
intersecting, but abutting abruptly upon each other in short heavy
masses, as shown in Fig. 78.
_Shading in Colours._--Frequently in topographical drawings, and still
more frequently in mechanical drawings, colour is resorted to to produce
the effect of shading lines. As the principles according to which colour
is applied for this purpose are the same as those which determine the
use of shading lines, there remains little to be said on this matter
beyond describing the modes of applying the colour.
_Hill Slopes._--In representing slopes, the tint employed to give the
effect of that produced by the ink lines already described is composed
of indigo and burnt sienna, and is applied as a flat-wash. A little lake
is added to neutralize the greenish hue of this tint when it is to be
laid over sand or cultivated ground. The different degrees of intensity
required to express the inclination are produced by repeating the wash
over those parts which are darker than the rest. To accomplish this
neatly, the darker portions must be washed in first, so that the final
washings may cover the whole surface, and the edges of each successive
wash must be softened off or blended into the next with a brush and
clean water. In shading hills, the paper along the crest of the slope
should be first moistened with the water-brush, and before it dries, the
laying on of the colour should be begun on the moistened part, and
proceeded with down the slope. The effect of representing hills by this
method, which is a very expeditious one, is much improved by adding
light shading lines with the pen, either in pale ink, or a mixture of
indigo and burnt sienna. The ground is always covered with its
appropriate sign before the shading tint is laid on.
_Cylindrical Surfaces in Mechanical Drawings._--In shading cylindrical
surfaces and drawings generally, three methods are employed. One of
these is known as _softening off_, and is employed on finished drawings
of machinery. For shading by this method, a brush called a softener is
required; this has a brush at each end of the handle, one being larger
than the other. Having moistened the paper, and filled the smaller brush
with colour and the larger one with water, a narrow strip of colour is
laid along the darkest part of the cylinder, and immediately after,
while the colour is quite moist, the water-brush is drawn along one edge
of the strip and then in like manner along the other, so as to cause the
colour to flow over that portion of the surface which has been damped.
The brush is then wiped upon a cloth and drawn lightly down the edge to
take up the superfluous water. The colour should be light to begin with,
and the quantity to be taken in the brush must be determined by
experience. The same remark applies to the water-brush, for if too
little be used the colour will not spread sufficiently, and if too much,
the colour will be diluted and rendered uneven. These operations of
laying on the colour and softening off are continued until the
cylindrical appearance has been produced. Each succeeding coat should be
laid on before the preceding one is quite dry, as the colour will spread
more evenly over a damp surface. The previously applied coat must,
however, have been sufficiently absorbed not to wash up, or a clouded
appearance will be the result.
Another method, known as the French, consists in applying a narrow strip
of colour to the darkest part, and overlaying this with other strips,
each wider than the one previously laid on. To regulate the breadth of
the strips, a number of meridian lines are drawn upon the cylinder. When
shaded in this manner, the cylinder presents the appearance of a polygon
rather than that of a cylinder.
The third method, by reason of the facility it affords of producing
effect, is very suitable for large drawings and diagrams for
illustrating papers and lectures. In shading according to this method, a
thick line or a narrow strip of very thick and black Indian ink is laid
on the darkest part of the cylinder with the point of the brush. The
breadth of the strip will be regulated by the diameter of the object,
and it should be previously lined out in pencil. When dry, a damp brush
is passed over it so as to remove the sharp edges of the strip, and to
cause the ink to run slightly over the moistened surface of the paper.
The flat colour washes are then applied as required, the washes being
carried over the black strips, which will be further reduced in tone by
a portion of the ink mixing with the colour.
In shading, it will be found convenient to keep the light side of the
object next to the operator, as it is easier to wash towards the body
than from it with the water-brush. The brush should be held in as nearly
a vertical position as possible, as it is more easy, when that position
is observed, to keep within the boundary lines.
PART II.--APPLICATIONS.
SECTION I.--LETTERING, BORDERING, AND NORTH POINTS.
_Lettering._--The lettering of a plan, map, or drawing of any kind,
occupies a prominent and conspicuous position, and may be considered as
forming an essential part of the drawing. It is, therefore, obvious that
the character of the lettering, and the degree of finish introduced into
its execution, will have an important influence on the general
appearance of the drawing. Nothing detracts more from the value of a
map, considered as a work of art, than a bad style of lettering, while,
on the other hand, a well-chosen and well-executed style is both
pleasing to the eye, and produces on the mind an impression of accuracy
in the more important features of the work. Hence it is not merely
desirable, but necessary, that the draughtsman should acquire the
ability to form letters correctly and neatly, especially if he be
engaged on topographical drawings, into which lettering enters very
largely.
The formation of letters requires great attention and long practice. It
is not a matter in which much assistance is to be derived from
descriptions or written instructions of any kind; practice alone from
good models will give the requisite skill. The difficulty of forming the
letters correctly and of uniform dimensions may, however, be
considerably lessened by using guide lines drawn in pencil, to be
afterwards erased. Such lines are called _construction lines_, and the
mode of employing them is shown in Plate 4. A careful study of this
Plate will give the student a clear understanding of the use of these
lines, which could not be imparted by pages of description. A reference
to the letters B, E, and T, in connection with the construction lines
will show most readily the nature and the degree of assistance afforded
by the latter.
In making capitals, each letter must be sketched in pencil; the outline
must then be drawn in ink with a firm and steady line, and afterwards
filled up with the pen. In forming the small roman and italic letters,
three construction lines are drawn, the lower two to limit the height of
the ordinary letters, and the upper one to limit the height of such
letters as _d_ and _l_, and the capitals. The heavy parts of these
letters are made at once by a bold pressure of the pen. The curved
portions should be carefully distinguished from the straight. The
letters _a_, _c_, _g_, _o_, _s_, &c., for example, are composed wholly
of curved lines. They should be drawn symmetrically, and their width
should be only a little less than their height. The round portion of the
_g_ should not quite reach to the lower line. A perfect regularity
should be maintained throughout the letters, as the beauty of their
appearance depends greatly on this. Care must also be taken, in italic
writing, to keep the inclination the same everywhere. Manuscript
lettering should be more extended than the clear roman or italic type,
for crowding greatly mars its appearance.
The character of the letters employed should be in accordance with that
of the drawing upon which they are to appear. Thus for engineering and
mechanical drawings, there is nothing more suitable generally than the
plain block letter. But on drawings of a more artistic and ornamental
character, a more elaborate form of letter may and should be used. And
of these elaborate forms, there will always be one more suitable than
the rest to the particular character of the drawing. The choice of this
form is a matter to be left entirely to the judgment and the taste of
the draughtsman.
Another matter on which the draughtsman will have to exercise his
judgment is the _size_ of the letters employed. This must manifestly be
in accordance, first, with the character of the object denoted, and,
second, with the scale of the drawing. With regard to the former of
these conditions, it is obvious that propriety will demand a larger
letter for the city than the town, for the town than the village, for
the village than the farm, and for the mansion than the gate-lodge. This
propriety of relative importance must be everywhere observed. The
different types of lettering are arranged in the order of importance as
follows:--1, The upright capital; 2, the inclined capital; 3, the
upright roman, or ordinary small type; and 4, the small italic. The
draughtsman will have to exercise his judgment in suiting the size to
the scale of the map, but the following Table may be taken as a general
guide:--
--------------+----------------------+-----------------------------
Scale. | Height of Upright | Height of Small Roman.
| Capitals. |
--------------+----------------------+-----------------------------
¹⁄₆₀₀, or one | |
inch to fifty | |
feet. |Six-tenths of an inch.|Twelve-hundredths of an inch.
¹⁄₂₆₄₀, or two| |
feet to a | |
mile. |Four „ „ |Eight „ „
¹⁄₅₂₈₀, or one| |
foot to a | |
mile. |Three „ „ |Six „ „
¹⁄₁₀₅₆₀, or | |
four inches | |
to a mile. |Two „ „ |Four „ „
--------------+----------------------+-----------------------------
The thickness of the capital should be one-seventh of the height.
As far as practicable, the lines of lettering should be parallel to the
base of the drawing. Frequently, however, cases will occur in which it
will be desirable to letter in other directions and in curved lines. In
writing along a curved or very irregular outline, the course of a river
or the boundary of an estate, for example, an agreeable effect is
produced by making the lines of lettering conform in some degree with
the outlines against which they are written.
The arrangement of the letters in titles and the effective disposition
of the words are also matters requiring great care and some taste. The
design and the execution of the title afford another opportunity of
enhancing the beauty of a drawing by a display of striking arrangement
and appropriate ornamentation. Plates 7 and 8 show some useful models
for plans, and Plate 25 contains some specimens of flourishes which may
frequently be introduced with pleasing effect. The form which the title
shall assume and the space which it shall occupy must be determined
before beginning to put it upon the drawing. To avoid erasures, it is
well to sketch roughly upon a piece of paper, a trial title, emendations
in which can be easily made. When found satisfactory, draw a vertical
centre line, which should pass through the middle letter of each line.
Apply this centre line to the centre line of the title on the drawing,
and lightly mark in with the pencil the position of each letter. When
this method is not adopted, the middle letters should be put in first
upon the centre line, and the others afterwards inserted from left to
right, and from right to left.
In maps, the title may be placed outside the border if it consist of one
line only, but if it occupy more than one line, it should be placed
within the border. Generally, it should be placed in one of the corners
of the map, and its size should bear some proportion to that of the map.
The letters composing the name of the locality, which is usually the
most important word, should not exceed in height three-hundredths of the
length of the short side of the border. The letters of the other words
will vary in size according to their relative importance.
_Borders._--Plain borders usually consist of two lines, the outer one
heavy, and the inner one light. The heavy line should be equal in
breadth to the blank space between it and the light line, and the total
breadth of the border, that is, of the two lines and the space between
them, should be one hundredth part of the length of the shorter side.
Ornamental corners may be made to embellish a drawing considerably, and
they afford some scope to the fancy and the taste of the draughtsman.
Several examples of borders and ornamental corners will be found in the
accompanying Plates.
_North Points._--The meridian or north and south line is an
indispensable adjunct to every topographical drawing. When the extent of
country represented is considerable, it is usual to make the top of the
map the north, and in such a case the side border lines are meridian
lines. Frequently, however, in plans, the shape of the ground does not
admit of this arrangement, and then it becomes necessary to mark a
meridian on some part of the map. This line is usually made a
conspicuous one, and its north extremity is often ornamented with some
fanciful device. The ornamentation of the meridian line should be in
keeping with the rest of the map. Plate 9 contains several examples
which may be adopted or modified as deemed desirable.