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.
Section II.—Scales.
To all drawings which do not show the full size of the objects represented, it is necessary to affix the scale according to which the objects are drawn. Such a scale is called a scale of lengths or distances, because, by means of it, the distance from one point to another is ascertained. The scale of distances does not contain very minute subdivisions, and consequently is not suitable for use in constructing the drawing. For the latter purpose, another scale, similarly but more minutely divided, is employed, and is known as the scale of construction. A familiarity with the modes of constructing both of these scales should be early acquired by the young draughtsman.
Scales of Distances.
—One means of denoting the scale of a drawing is furnished by what is called its representative fraction, the denominator of which shows how many times greater the actual length is than that in the drawing. Thus a scale of 1⁄24 shows that 1 inch on the drawing represents 24 inches on the object; in other words, that the object is twenty-four times larger than the drawing. But in addition to this representative fraction, it is usual to affix a graduated straight line, termed a scale, for the purpose of conveniently measuring distances upon it. It is manifest that the unit of length in this scale must bear the same ratio to the real unit of length that a line in the drawing bears to the line which it represents. Thus if the representative fraction be 1⁄24, 1 inch on the scale will represent 2 feet.
Scales of distances are usually of such a length as to be a multiple of 10 linear units of some kind, as 100 miles, 50 chains, 20 feet; and this length should also be such as to allow of long lines being taken off at one measurement. To construct the scale, two light lines should be drawn at a suitable distance apart, and below the lower of these lines and at a distance from it equal to one-third of the space between them, a third and heavy line should be drawn. The primary divisions may then be made with the compasses in the following manner. Supposing the number of divisions to be five, open the dividers to what appears to be the fifth part of the line, and step this distance along the line; if the fifth step exceed or fall short of the end of the line, close or open the dividers 1⁄5 of the distance, and repeat the trial. This is the quickest and, for large divisions, the most accurate method of dividing a line. To render the divisions more distinct, draw a heavy line between the two light lines in alternate divisions. The left-hand division must be subdivided into the units or lesser measures of which it is made up. For example, if the primary divisions are each of 10 feet, the subdivisions will be feet; if they represent feet, the subdivisions will be inches, and so on. The subdividing should be performed in the following manner. Having erected a perpendicular of indefinite length from the left-hand extremity of the scale, take with the compasses from any scale the number of divisions into which it is required to divide the part. With this distance in the compasses, strike, from the first primary or zero division, an arc cutting the perpendicular, and join the point of intersection to the centre from which the arc is struck. Thus we shall have a right-angled triangle formed of the first primary division of the scale, the perpendicular and the radius, the latter being the hypothenuse (see [Fig. 79]). Mark on the hypothenuse the divisions to which it was made equal, and from the points of division let fall perpendicular lines upon the scale. These will divide the latter into the required number of equal parts. The length of the hypothenuse should be so chosen as to make an angle not greater than 50° with the base.