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.

Fig. 61.

Fig. 62.

Fig. 61.

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.

Fig. 63.

Fig. 64.

Fig. 63.

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.

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.

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.

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.

Fig. 68.

Fig. 69.

Fig. 70.

Fig. 71.

Fig. 68.

Fig. 69.

Fig. 70.

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.

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.

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.

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.

Fig. 75.
Lehmann’s Scale of Shade.

[Larger illustration] (48 kB).

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:—

Slope.Proportion of
Black.White.
21⁄2°or23⁄4°110
5°„6°29
10°„11°38
15°„16°47
25°„26°56
35°65
45°74
60°83
75°92

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:—

Slope.Proportion of
Black.White.
Level..all
15°12
221⁄2°11
30°21
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 + ·316 = 3·916 = 0·244 inch. 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.

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.

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.

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.