The Draughtsman's Handbook of Plan and Map Drawing / Including instructions for the preparation of engineering, architectural, and mechanical drawings.

by George G. André

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].

Fig. 38.

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.

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.

Fig. 41.

Fig. 42.

Fig. 41.

Fig. 42.

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.

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.

Fig. 45.

Fig. 46.

Fig. 45.

Fig. 46.

Fig. 47.

Fig. 48.

Fig. 49.

Fig. 48.

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.

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.

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.

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.

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.

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.

Fig. 55.

Fig. 56.

Fig. 55.

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.

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].

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.

Fig. 59.

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.

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