  Line 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 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 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 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. 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 Fig. 79. Larger illustration (19 kB). The total length of the scale will be determined by the greatest length which it is required to read off at once, and in the following manner. Thus, let it be required to construct a scale of 1/24, = 1/2 inch to Amongst Continental nations, decimal scales are usually employed, which are far more convenient in practice than those involving the awkward ratios of miles, furlongs, chains, yards, feet, and inches. The decimal scale has also been adopted for the United States’ Coast Survey, the smallest publication scale of which is 1/30000; this is also the scale of the new map of France. In choosing a scale, regard must be had alike to the purposes for which the drawing is intended, and to the nature and the amount of detail required to be shown. Thus a larger scale is required in plans of towns than in those of the open country; and the smaller and more intricate the buildings, the larger should the scale be. Also a plan to be used for the setting out of works should be to a larger scale than one made for parliamentary purposes. The following Tables, given by Rankine in his ‘Civil Engineering,’ enumerate some of the scales for plans most commonly used in Britain, together with a statement of the purposes to which they are best adapted.
The vertical scale, or scale of heights, is always much greater than the horizontal scale or scale of distances, and the proportion in which the vertical scale is greater than the horizontal, is called the exaggeration of the scale. This exaggeration is necessary, because the differences of elevation between points on the ground are in general much smaller than their distances apart, and would therefore, without exaggeration, be unapparent, and also because, in the execution of engineering works, accuracy in levels is of more importance than accuracy in horizontal positions. Scales of Construction.—Scales of construction are intended to afford means of measuring more minute quantities than scales of distances. Of the former there are two kinds, known respectively as the Diagonal and the Vernier scale. The diagonal is the more frequently employed. Its construction involves no peculiar difficulty, as it consists simply of an ordinary scale of distances, with the addition of a number of parallel lines crossed by other parallel lines drawn diagonally from the smaller points of division. An example will best show the construction and mode of using this scale. Suppose it to be required to construct a scale of 10 miles to the inch, showing furlongs diagonally; the scale to measure 50 miles. Here 1: 10:: x: 50, whence x = 5 inches. Divide this length of 5 inches into five equal parts, and the first part into tenths to show miles, in the manner already described for scales of distances. Then, since it is required to Fig. 80. Larger illustration (31 kB). To use this scale, suppose a length of 24 miles 5 furlongs is required. Place one leg of the dividers upon the point in which the fourth diagonal intersects the fifth parallel, and extend the other to the point in which the primary division marked 20 intersects the same parallel. In like manner, if the distance required be 33 miles 3 furlongs, it must be taken from the intersection of the third diagonal with the third parallel, to the intersection of the primary division marked 30 with the same parallel. It is obvious that if a scale of feet showing inches diagonally be required, twelve equidistant parallel lines must be drawn instead of eight as in the foregoing example where furlongs are required. The diagonal scale possesses the important advantages of accuracy and distinctness of division which render it very suitable as a scale of construction. Another practical advantage is that it is less rapidly defaced by use than the other kinds, in consequence of the measurements being taken on so many different lines. The construction of the vernier scale is similar to that of the Fig. 81. Larger illustration (23 kB). To show how the foregoing principle is applied in practice, we will take an example. It is required to construct a scale of 1/100 to show feet and tenths of a foot. Construct a scale in the ordinary way, and subdivide it throughout its whole length, as shown in Fig. 81; then each division will show one foot. Above the first primary division, draw a line parallel to the scale and terminating at the zero point. From the zero point, set off on this line towards the left a distance equal to eleven subdivisions, and divide this distance into ten equal parts. Now, as eleven divisions of the plain scale have been divided into ten equal parts on the vernier, each division on the latter will represent 11/10 = 1·1 of that on the former; and as the divisions of the plain scale represent feet, those of the vernier will represent 1·1 foot. Consequently, the distances from the zero of the scale to the successive divisions The mode of using this scale will be seen from the following example. Let it be required to take off a distance of 26·7 feet. From zero to the 7th division of the vernier is, as we have seen, 7·7 feet. Therefore, to ascertain how far to the right of zero we must go to obtain the distance of 26·7 feet, we must subtract 7·7 from that distance, which gives 19. Thus to take off the distance, one leg of the dividers must be placed on the 7th division of the vernier, and the other on the 19th division of the plain scale. If the distance to be taken were 27·6 feet, one leg of the dividers would have to be placed on the 6th division of the vernier, and the other on the (27·6) - (6·6) = 21st division of the plain scale. To construct a scale to show feet and inches, make the vernier equal to thirteen divisions of the plain scale and divide it into twelve equal parts. Each of these divisions will then represent 13/12 = 11/12 of a foot. Scales of construction may be purchased upon box-wood or ivory, but where great accuracy is important, it is best to lay down the scale upon some part of the drawing, as in such a case it expands and contracts with the drawing under the influence of moisture. Examples of scales of distances will be found on Plates 8 and 9. Section III.—Plotting.The transference of the measurements determined by the survey from the field-book to the paper is termed plotting. The operations of plotting are very simple, and the ability to perform them properly may be acquired with a little practice. But their due performance demands the same extreme care and attention as that of the operations in the field, for it is obvious that the precautions taken to ensure accuracy in the latter may be rendered nugatory by inaccurate Reference Lines and Points.—The lines chained over in a survey and recorded in the field-book are not usually the actual lines existing on the ground, but imaginary straight lines chosen for the purpose of referring other lines and points to them. They are, therefore, appropriately termed reference lines, and all points situate in them to which other lines are referred, in other words, all points in a reference line in which other reference lines intersect it, are termed reference points. Reference lines are generally made to form triangles for facility of computation, and these triangles enclose the area to be surveyed. But to determine the details included within them, it is necessary to form other and smaller triangles within the larger ones first laid down. The latter are, therefore, distinguished as Primary and the former as Secondary triangles, and the lines of which they are composed are called primary and secondary reference lines. Plotted Points.—In laying down a line of definite length upon paper, the positions of its extremities are determined and marked by pencil dots; such dots, or rather the points indicated by such dots, are termed plotted points. The line is drawn by joining the plotted points. To Plot Reference Lines and Points.—To plot a reference line of a given length when the position of neither of its extremities is given, a light dot must be made upon the paper in a convenient part to indicate the position of one extremity. The pencil-point mark should be as light and well defined as possible, and hence it is essential that the pencil used should be hard, and always kept pared to a fine To plot secondary reference lines, as, for example, a number of offset lines, apply the scale so that its edge may be parallel to and almost over the pencil trace of the primary line and its zero point coincident with the point at which the line begins. Care must always be taken to place the zero of the scale at the beginning of the line, and not at the end of it. At the distances recorded in the field-book as those at which the offsets were taken, plot upon the line, in the manner described above, the points indicating the extremities of the offset lines. All other points, such as stations and intersection of fences, roads, and streams, should be plotted at the same time. Around all stations, a light, hand-drawn circle should be placed, and intersections marked by small cross lines. This being done, place the offset scale so that the zero may coincide with the plotted point in the reference line and the edge be perpendicular to the line. To bring the edge into this position, the end of the scale should be placed parallel to the reference line; this is, of course, assuming the scale to be perfectly rectangular, as it ought to be. The other extremities of the lines may then be plotted in the same manner as those of the primary lines. To illustrate the foregoing remarks, let it be required to plot the following portion of a field-book.
Having laid down in a convenient part of the paper the beginning of Line 1, place the edge of the scale so that the zero may coincide with the plotted point and the edge be parallel to one of the meridians. Holding the scale firmly in this position, plot the distance 2504 links, and join the plotted points. Then, without removing the scale, plot upon this reference line the distances at which the secondary or offset lines were taken, that is at 420, 850, 1220, 1440, 1610, 1790, and 2000 links. In this case we have nothing but offsets; had there been stations or intersections of fences, roads, or streams, these would have had to be plotted at the same time, and distinguished by an appropriate mark. Line 2 begins at the end of Line 1, and returns on the left at an acute angle, as indicated by the arrow in the field-book. But as the magnitude of this angle is not known, the survey having been taken with the chain alone, the exact direction of Line 2 must be ascertained in the following manner. Take the length of the line in the compasses, and with this distance as a radius, strike an arc from the end of Line 1. Also with the length of Line 3 as a radius, strike an arc from the beginning of Line 1, at which point Line 3 closes, intersecting the former. The point of intersection will be the end of When the survey has been made with the aid of an angular instrument, the method of plotting the primary reference lines differs somewhat from the foregoing. In this case, the paper should be first covered with a number of parallel straight lines ruled about an inch and a half apart to represent magnetic meridians. The first station may then be marked upon one of these meridians in a convenient part of the paper. To lay down the first reference line, apply the protractor to this meridian with its centre point coincident with the plotted point, and from the bearing recorded in the field-book, lay off the given angle. Join the two plotted points and produce the line indefinitely; and upon this line lay off a distance equal to the length of the measured line. The second reference line must be drawn in the same manner, from the end of the first, by laying off from that point Fig. 82. To lay down Fig. 82 in this manner, having fixed the first station A, the length of the first primary reference line AB may be laid off upon the meridian, because in this case the bearing being due north, the reference line will Angles may be more accurately laid down by means of a table of natural sines and cosines and a linear scale than by means of a protractor. This is especially true when the angles are subtended by long lines, as, for example, lines of 3, 4, and even 6 feet. In such cases, a protractor is of little use. This mode of laying down angles is also convenient in some cases where angles have been taken, but some of the sides not measured. In using the table, it must be remembered that the radius of the sines and cosines is taken as unity; therefore, to find the sine and cosine for any other radius, the sine and cosine in the tables must be multiplied by that radius. To lay down the angle ABC in Fig. 82, the reduced cosine of the angle should be plotted from B in the point a, according to some scale. The scale length of the reduced sine should then be scribed from a, and the scale length of the radius scribed from B. A line drawn from B through the point of intersection of the scribes will lay down the angle corresponding to the sine and cosine in the table. Suppose the radius chosen to be 5 chains, the angle being 32° 30'. The cosine of 32° 30' is ·8434, which multiplied by 5, the assumed radius, = 4·2170. Lay off this distance from B on the base AB. The sine of 32° 30' is ·5373, which multiplied by 5, = 2·6865. From the point a, which is distant 4·2170 chains from B, with a radius equal to 2·6865 chains, describe an arc; and from the point B, with a radius equal to 5 chains, describe another arc. From B draw a line through the intersection of these arcs, and lay off upon it the measured length of 1946 links as recorded in the field-book. If only the length of the base AB and the magnitudes of the angles ABC and BAC were given, the lengths of the sides BC and AC would have to be calculated by trigonometrical formulÆ. This method of calculating the lengths of the sides of triangles and plotting them with the beam compasses, like chained triangles, is the most accurate for laying down the great or primary triangles of a survey. When it is required to plot according to this principle a solitary angle, as, for example, that between a station line and the meridian, a circle should be drawn with as large a radius as practicable round the station at which the angle is to be laid down. The distance between the points at which the two lines enclosing the angle cut that circle is then found by multiplying the radius by the chord of the angle, that is, by twice the sine of half the angle. It sometimes happens, particularly in extensive surveys, that all the angular points of some triangles cannot be plotted upon the same sheet of paper. In such cases, the plot of the outlying points and the sides of the triangles may be laid down in the following manner. Plot the intersected triangles independently and trace them on tracing paper. Then, having drawn a fine line upon both sheets to represent the sheet edge, lay the points on the trace corresponding to those already plotted on the first sheet down upon, and make them to coincide with, the latter. Secure the trace in this position and trace the sheet edge line upon it. The intersected lines may now be plotted on the fair sheet with a pricker at points outside the sheet edge line. Next apply the trace to the second sheet and make the sheet edge lines coincide. Having secured the trace in this position, the points and the intersected lines on this second sheet may be plotted upon the fair paper by means of the pricker. To Plot Traverse Reference Lines.—In plotting a traverse survey in which the angles have been measured from a fixed line of direction, the magnetic meridian, the direction of the lines may be all laid down at the first angular point. An example will best show the method employed in this case. It is required to lay down the traverse shown in Fig. 83. Fig. 83. Larger illustration (75 kB). In a convenient part of the paper draw the straight line NS to represent the magnetic meridian, and plot upon it the first station A. Set the protractor with its centre accurately placed over this point and its 360th and 180th divisions coinciding with the meridian. Holding the instrument securely in this position, lay off around it all the bearings as entered in the field-book, numbering them in the order in which they were taken. Against each of these numbers it is well to place the page of the field-book on which the measurement of the angle and the survey of the line are entered. The plotting must now be commenced by laying down the first line through the first bearing Fig. 84. The degree of accuracy to be attained will depend in a great measure upon the extent of the traverse. With long lines the difficulties increase, and with a great number of angles the chances of error are multiplied. If the angles are carefully taken, it is probable that seconds have been read off in several instances, and these if neglected, especially upon long chain lines, may lead to an error of some importance. Also when the lines are long, the parallel ruler becomes practically useless, and some other system has to be adopted. One way of overcoming these difficulties is to draw a parallel to the first meridian through every third or fourth angle; in such a case, great care must be observed in drawing the parallels. A more easily practicable method, however, is to use the T-square in the manner already described. If the left-hand edge of the drawing board be made the north, the blade will determine meridional lines, and by The most accurate method of plotting a traverse is by rectangular co-ordinates, or, as it is usually termed, Northings, Southings, Eastings, and Westings, because the position of each station is plotted independently, and is not affected by the errors committed in plotting previous stations. This method consists in assuming two fixed lines or axes crossing each other at right angles at a fixed point, computing the perpendicular distances or co-ordinates of each station from those two axes, and plotting the position of each station by means of the T and set squares and a linear scale. The meridian is usually made to represent one of the axes, and in this case the co-ordinates parallel to one axis will be the distances of the stations to the north or south of the fixed point, and those parallel to the other axis will be their distances to the east or west of the same point. Let NS, Fig. 84, represent the meridian, and AB the first bearing taken, and the first line measured. The angle in this case is NAB = ?. If ? is an acute angle, the second station B is to the north of the first station A; if it is an obtuse angle, B is to the south of A. If the angle ? lies to the right of the meridian, B is to the east of A; if to the left, to the west. Thus it will be seen that if the northernly and easternly directions are considered positive, the southernly and westernly directions will be negative. From the foregoing it is manifest that the co-ordinates of B are as follows:— Northing A a = b B (or if negative, southing) = AB × cos. ?. To plot the point B, draw through the point A, with the aid of the T-square, a horizontal line. Multiply the chained length of the line AB by the sine of the angle NAB as entered in the field-book, and set off this distance along the horizontal line. From the point thus determined, erect, with the aid of the set square, a perpendicular, which will be parallel to the meridian. Multiply the chained length of AB by the cosine of the angle NAB, and set off this distance along the perpendicular line. The point thus determined will be the position of the second station B, which may then be joined to A by a straight line. Fig. 85. The mode of laying down the survey in Fig. 85 will now be obvious. Having determined the position of the second station B in the manner just described, draw a horizontal line through B and determine the third station C in the same way. The fourth station D being to the left of the meridian passing through C, c d is a westing and is to be considered as negative. Therefore the horizontal line through C must be drawn to the left of that station, and the station D determined in the same manner as the preceding stations. The results of all these calculations should be entered in a book, Let it be observed that both ? and sin. ? are positive or negative according as that angle lies to the east or to the west of the meridian; and that the cosines of obtuse angles are negative. To Plot Detail.—By “detail” is meant outlines or objects whether natural or artificial, such as fences, walls, rivers, canals, roads, lakes, water margins, beach marks, seas, or imaginary boundary lines. In plotting from the entries of measurements for detail, these measurements should be laid down upon the paper in the order and manner indicated in the field-book. The mode of plotting the perpendicular reference lines by means of which the position of the detail is fixed has already been fully described and illustrated. The proper connections for detail, as shown by the field-book, should be made by drawing a firm pencil line through the detail points with the aid of an offset scale adjusted successively to the adjacent points. All such connections should be clearly and elegantly made. When all boundaries, roads, and streams have been drawn and inked in, tracings should be taken in small portions of all that has been laid down for the use of the “examiner.” The duties of the examiner are to make on the ground the necessary corrections for omissions and detail in error; to give, in position and character, woods, water, marsh, commons, vegetable and geological features, and permanent artificial structures; and to furnish the descriptive names of places and things, or any other desirable information. The topographical character of mountains, marshes, bogs, rough pasture, woods and water, should be drawn in character To Plot Contours.—The student who has made himself familiar with the methods of laying down angles, and plotting reference lines and points, will find no difficulty in laying down contour traces. When the contour points have been surveyed with the chain, the contour is obtained by drawing a free line of feature through the plotted points. But when the contour points have been surveyed by measuring magnetic angles to known points, such angles must be laid down at these points, and produced to meet in the contour point. The drawing of contours differs from the drawing of ordinary detail insomuch as each contour point is shown by a small dot, and each carrying point by a similar dot surrounded by a small hand-drawn circle to distinguish it. The former should be so plotted as to be distinguishable in the trace or contour line, which should be readily traceable, but not conspicuous. The line joining adjacent points should be true lines of feature. Colour is usually employed for these lines, and it is well to give them a broken or somewhat undefined character. When the French system is adopted, contour lines are drawn continuous, a broad but faint line of colour. To Plot Sounded Points in Submerged Districts.—When the angles have been measured on dry land with the theodolite, these angles should be laid down at the dry-land points, and the lines produced to meet in the sounded point. But when the angles have been measured on the water with a sextant, a station pointer is required. The arcs of the pointer should be adjusted to read the measured angles, and the instrument applied to the plotted points of the observed objects so as to bring the hair lines accurately to their respective object points. The sounded point may then be correctly plotted through the centre of the pointer. If the angles have been measured by the magnetic compass, that is, if the angles are those made with the magnetic meridian, the angles should be laid down at the plotted points of the The sounded point determined by angles measured with the sextant may also be plotted by describing circles on the land-object lines as chords, to contain segmental angles equal to the measured angles. Such circles will intersect in the common land-object point and the sounded point. To plot the sounded point in this manner, requires the solution by construction of the problem, “to describe on a given line a segment of a circle that shall contain a given angle.” But this method is generally found too tedious in practice. Errors and Error-sheets.—There is a tendency, as we have previously remarked, for the measured lengths of lines to be a little too long, by reason of the irregularities of the surface. It is usual to allow for this source of error 1 in 1000 in fair open country, and 11/2 in 1000 in close country. When the measurements differ by an amount exceeding these limits, the pencil trace should not be drawn between the reference points, but the line should be entered on an “office error-sheet.” The error-sheet should show the number of the plot-sheet, the triangle, the book and page in which the measurements are entered, and the scale and measured lengths of the line. To ascertain the source of the error, other lines referenced to the reference point or points of the line in error should be plotted, and the apparent source should be entered on the error-sheet. If the lines referred to the same point be found to plot to another point in the reference line, the scale measurement of this point should also be entered. And if the reference point in error be not directly surveyed in the survey of their respective lines, the measurements for reference and the arithmetical reductions will have to be examined. Besides the office error-sheet, there should Office Error-sheet.
Field Error-sheet.
To Plot Vertical Sections.—In plotting a vertical section, a fine and firm horizontal line is first drawn to represent the datum line. The reference points are then plotted upon this line from the level-book by
Fig. 86. Larger illustration (54 kB). Draw the datum line DL, Fig. 86, and set off along it the distances 230, 465, 640, 794, &c., links; these points will be the reference points for the perpendiculars. Erect a perpendicular from each of these points, and lay off, to a suitable scale, upon these lines successively the vertical heights 100, 107·04, 115·97, 113·03, 107·03, &c. The points thus determined will be the surface detail points, and by joining these we shall obtain the surface line. Then will ADLB represent a section of the ground between A and B. A description of objects on the surface worthy of notice should be written over such objects. In working sections, where great accuracy is required, larger scales are employed, and the levels are taken at more frequent intervals. Sections, especially working sections, are usually drawn upon ruled, or, as it is called, “section” paper, the nature of which we have already described. This method, which was introduced by Mr. Brunel, possesses many practical advantages, inasmuch as it obviates the necessity of plotting the “distances” and erecting perpendiculars, the latter already existing. It also greatly facilitates the computation of the contents of a given section. Its chief defect lies in the difficulty of making the horizontal lines coincide when joining the sheets end to end. Of course scales are not required upon section paper. To lay down Gradients.—The method of laying down the gradients of railways and roads usually adopted in practice consists in applying one end of an extended silken thread to the section at the point in which the road commences, and the other end in such a position that the thread may cut the profile of the earth’s surface so as to leave equal portions of space above and below the thread, as nearly as can be judged by the eye. The cuttings from the parts above the thread will then furnish sufficient materials to form the embankments in the spaces below. This is called “balancing” the cuttings and embankments. When the first gradient has been determined in this way, it may be found unfavourable to the second in respect to the extent of cuttings and embankments; in such a case it must be modified to suit the requirements of the latter. In this way the gradients must be modified successively until the compound result evidently gives a minimum of cuttings and embankments, due regard, of course, being had to the limits imposed by the nature of the case, both with respect to the ruling gradient and the proper heights for bridges. To Plot a Section from a Contour Map.—The mode of plotting a section from a contoured plan was explained when treating of contour lines. The contour map used for this purpose should give the features of the surface configuration in sufficient detail without serious error. Having drawn a line of section on the map and a datum line upon the fair paper for the vertical section, the points in which the section line intersects the contours should be measured on the scale of the map from a zero point in that line, and the measurements plotted upon the datum line. Perpendiculars should then be drawn through these plotted points, and on these perpendiculars the reduced altitudes of their respective contour points should be plotted. A line drawn through these surface plotted points will be the surface line. When the horizontal scales of the map and the section are the same, the contour plane lines may be drawn on the paper for the section parallel to the section line on the map, and perpendiculars raised to intersect them from the points on the map in which the section line intersects the contours, in the manner previously described. The points of intersection with the parallel lines will be the surface contour points in the vertical section. For practical purposes, the parallel lines and the perpendiculars are only temporarily drawn in pencil until the surface trace shall have been obtained and drawn in ink, with the datum line. Section IV.—Civil Engineers’ and Surveyors’ Plans.In the preceding Sections the manner of laying down plans has been fully described and the principles involved in the operations minutely explained. It now only remains, therefore, to direct attention to certain matters relating to the preparation of plans, which are necessitated by the circumstances of particular cases. Civil engineers’ plans usually consist, if we except harbour surveys, of a representation, to a rather large scale, of long and The section should be drawn to the same horizontal scale as the plan, and the exaggeration of the vertical scale should be such as to To distinguish the nature of the soils passed through, sections are frequently coloured, as shown in Plate 21. The information given by this means concerning the character of the strata is of very great value to the engineer or to the contractor, inasmuch as it enables them to predicate with some degree of certainty the amount of labour that will be required in executing the proposed work. It is, therefore, highly important that the draughtsman correctly represent the character of the strata. The conventional modes of representing these features are shown on Plate 20, which should be carefully studied and copied. It is necessary that the engineering draughtsman should be acquainted with the “Standing Orders” of Parliament relating to the preparation of plans and sections, in order that he may fulfil the conditions therein laid down. And as most of the important details involved by the exigencies of practice in the preparation of such plans and sections are prescribed by these Standing Orders, we will give so much of them as relates directly to the matters under consideration; by so doing, the details will be clearly and fully described, and the requirements of the law concerning them authoritatively made known. Nature of the Documents required.—“In cases of bills relating to engineering works, a plan and also a duplicate thereof, together with a book of reference thereto, and a section and also a duplicate thereof, as hereinafter described, shall be deposited for public inspection at the office of the clerk of the peace for every county, riding or division in England or Ireland, or in the office of the principal sheriff clerk of every county in Scotland, and where any county in Scotland is divided into districts or divisions, then also in the office of the principal sheriff clerk in or for each district or division in or through which the work is proposed to be made, maintained, varied, extended or enlarged, or in which such lands or houses are situate, on or before the 30th day of November immediately preceding the application for the bill.” “In the case of railway bills, the ordnance map, on the scale of one inch to a mile, or where there is no ordnance map, a published map, to a scale of not less than half an inch to a mile, or in Ireland, to a scale of not less than a quarter of an inch to a mile, with the line of railway delineated thereon, so as to show its general course and direction, shall, on or before the 30th day of November, be deposited at the office of the clerk of the peace, or sheriff clerk, together with the plans, sections, and book of reference.” “In cases where the work shall be situate on tidal lands within the ordinary spring tides, a copy of the plans and sections shall, on or before the 30th day of November, be deposited at the office of the Harbour Department, Board of Trade, marked ‘Tidal Waters,’ and on such copy all tidal waters shall be coloured blue, and if the plans include any bridge across tidal waters the dimensions as regards span and headway of the nearest bridge, if any, above and below the proposed new bridge, shall be marked thereon, and in all such cases such plans and sections shall be accompanied by a published map or ordnance sheet of the country, over which the works are proposed to extend, or are to be carried, with their position and extent, or route accurately laid down thereon.” “In the case of railway bills, a copy of all plans, sections, and books of reference, and the aforementioned published map with the line Plans.—“Every plan required to be deposited shall be drawn to a scale of not less than four inches to a mile, and shall describe the line or situation of the whole of the work (no alternative line or work being in any case permitted), and the lands in or through which it is to be made, maintained, varied, extended or enlarged, or through which every communication to or from the work shall be made; and where it is the intention of the parties to apply for powers to make any lateral deviation from the line of the proposed work, the limits of such deviation shall be defined upon the plan, and all lands included within such limits shall be marked thereon; and unless the whole of such plan shall be upon a scale of not less than a quarter of an inch to every one hundred feet, an enlarged plan shall be added of any buildings, yard, courtyard or land within the curtilage of any building, or of any ground cultivated as a garden, either in the line of the proposed work or included within the limits of the said deviation, upon a scale of not less than a quarter of an inch to every one hundred feet.” “In all cases where it is proposed to make, vary, extend or enlarge any cut, canal, reservoir, aqueduct or navigation, the plan shall describe the brooks and streams to be directly diverted into such intended cut, canal, reservoir, aqueduct or navigation, or into any “In all cases where it is proposed to make, vary, extend or enlarge any railway, the plan shall exhibit thereon the distances in miles and furlongs from one of the termini; and a memorandum of the radius of every curve not exceeding one mile in length shall be noted on the plan in furlongs and chains; and where tunnelling as a substitute for open cutting is intended, such tunnelling shall be marked by a dotted line on the plan.” “If it is intended to divert, widen or narrow any turnpike road, public carriage road, navigable river, canal or railway, the course of such diversion, and the extent of such widening or narrowing shall be marked upon the plan.” “When a railway is intended to form a junction with an existing or authorized line of railway, the course of such existing or authorized line of railway shall be shown on the deposited plan for a distance of eight hundred yards on either side of the proposed junction, on a scale of not less than four inches to a mile.” Book of Reference.—“The book of reference to every such plan shall contain the names of the owners or reputed owners, lessees or reputed lessees, and occupiers of all lands and houses in the line of the proposed work, or within the limits of deviation as defined upon the plan, and shall describe such lands and houses respectively.” Sections.—“The section shall be drawn to the same horizontal scale as the plan, and to a vertical scale of not less than one inch to every one hundred feet, and shall show the surface of the ground marked on the plan, the intended level of the proposed work, the height of every embankment and the depth of every cutting, and a datum horizontal line, which shall be the same throughout the whole length of the work, or any branch thereof respectively, and shall be referred to some fixed point (stated in writing on the section), near some portion of such work, and in the case of a canal, cut, navigation, turnpike or other carriage road or railway, near either of the termini.” “In cases of bills for improving the navigation of any river, “In every section of a railway, the line of the railway marked thereon shall correspond with the upper surface of the rails.” “Distances on the datum line shall be marked in miles and furlongs, to correspond with those on the plan; a vertical measure from the datum line to the line of the railway shall be marked in feet and inches, or decimal parts of a foot, at each change of the gradient or inclination; and the proportion or rate of inclination between each such change shall also be marked.” “Wherever the line of the railway is intended to cross any turnpike road, public carriage road, navigable river, canal or railway, the height of the railway over or depth under the surface thereof, and the height and span of every arch of all bridges and viaducts by which the railway will be carried over the same, shall be marked in figures at every crossing thereof; and where the roadway will be carried across any such turnpike road, public carriage road or railway, on the level thereof, such crossing shall be so described on the section; and it shall also be stated if such level will be unaltered.” “If any alterations be intended in the water level of any canal, or in the level or rate of inclination of any turnpike road, public carriage road or railway, which will be crossed by the line of railway, then the same shall be stated on the said section, and each alteration shall be numbered; and cross sections in reference to the said numbers, on a horizontal scale of not less than one inch to every three hundred and thirty feet, and on a vertical scale of not less than one inch to every forty feet, shall be added, which shall show the present surface of such canal, road or railway, and the intended surface thereof when altered; and the greatest of the present and intended rates of inclination of such road or railway shall also be marked in figures thereon; and where any public carriage road is crossed on the level, a cross section of such road shall also be added; and all such “Wherever the extreme height of any embankment, or the extreme depth of any cutting, shall exceed five feet, the extreme height over or depth under the surface of the ground shall be marked in figures upon the section; and if any bridge or viaduct of more than three arches shall intervene in any embankment, or if any tunnel shall intervene in any cutting, the extreme height or depth shall be marked in figures on each of the parts into which such embankment or cutting shall be divided by such bridge, viaduct or tunnel.” “Where tunnelling, as a substitute for open cutting, or a viaduct as a substitute for solid embankment, is intended, the same shall be marked on the section.” “When a railway is intended to form a junction with an existing or authorized line of railway, the gradient of such existing or authorized line of railway shall be shown on the deposited section, and in connection therewith, and on the same scale as the general section, for a distance of eight hundred yards on either side of the point of junction.” Besides the information thus written on the plan, it is useful to the engineer, though not prescribed, to have the levels of important points either written or shown by means of contour lines, especially when the plan is to be used in selecting a line of railway. The results of trial pits and borings may also be written on the plan, and the estimated cost of each part of the work placed opposite to its position on the paper. Working Sections.—For working sections the horizontal scale adopted is usually three or four chains to the inch, and the vertical scale 30 or 40 feet to the inch. A working section should show the level of the ground, the level of the proposed work, and the height of embankment or depth of cutting at every point of the ground where the level has been taken, these quantities being found by calculation, not by measurement on the paper. The position and levels of all “bench marks” should also be clearly indicated. At every crossing Besides an acquaintance with the “Standing Orders,” the engineering and surveyor’s draughtsman should possess a knowledge of the Regulations of the Local Government Board, for these have to be complied with in the preparation of plans relative to main sewerage, drainage, and water-supply. These Regulations are as follows. Boundary Maps.—In cases in which a special district is proposed to be formed for the adoption of the Local Government Act, a map must be submitted, accompanied by a written description of the proposed boundary, designated by letters from point to point, commencing from a fully and clearly defined point on the north side of the map marked by the letter A and a written description, then proceeding eastward by natural or other well-defined features, until the description closes upon the point started from. The name of the proposed district must be printed on the map, with the area in acres. The population and the number of houses, with the rate of increase as ascertained at the two last decennial periods upon which the census was taken, must be given, and a duplicate or tracing of the map furnished. Maps for Division into Wards.—A map of the entire district must, in this case, be submitted, with the main boundary distinctly defined, Plans of Proposed Works.—It is in all cases necessary, upon application being made by Local Boards for the Secretary of State’s sanction to a loan for the execution of works, that plans, sections, detailed estimates, and specifications be submitted with the application, accompanied with the information relative to area, population, number of houses, and rateable value of the district required for boundary maps. Tracings of such plans and sections, and copies of the estimates and specifications must be sent in for filing at the Local Government Act Office. General Plan.—A general plan exhibiting the area which will be affected by the proposed works must be laid down to a scale of not less than two feet to a mile. It should have figured upon it the levels of the centres of all the streets and roads at their intersections and angles, and at every change of inclination; also, where a district is near the sea, it should show the high and the low tide level of the sea, and where there is a river, the summer and the flood-water levels should be recorded. Permanent bench marks having reference to the surface levels should be cut on public buildings, or other permanent and suitable objects, throughout the district, and clearly marked on the plan. Sections should accompany this plan, upon which the levels of the cellars should be shown. Such a plan may be used for showing the lines of main-sewers and drains, lines of water-pipes, and gas-mains. The lines of main-sewers and drains should have the cross-sectional dimensions and the gradients distinctly marked upon them. Detailed Plan.—A detailed plan for the purposes of house-drainage, paving, the sale and purchase of property, or other purposes of a like character, must be constructed to a scale of not less than ten feet to a mile. Upon this plan must be exhibited all houses and other buildings, bench marks, the levels of streets and roads, of cellars, of the sea at high and low tide level, and the summer and the flood level of rivers. Three feet by two feet will be a convenient size for the sheets of this plan, and by representing the marginal lines of the sheets upon the general plan, and numbering the sheets to correspond, the general plan will become a very useful index. As it may occasionally be desired to carry out works piecemeal, with a view to save the time which would be occupied in the preparation of a complete plan from actual survey, it is sufficient in the first instance to furnish a general plan of streets and roads only, with the surface levels and those of the deepest cellars, and the proposed scheme of works shown thereon, after which the works can proceed in sections. But with each separate application for sanction to a loan, a correct plan and section or sections should be submitted, accompanied by detailed estimates and specifications. It must, however, be understood that the complete plan of the entire district must be proceeded with, so that, when the works are finished, the Local Board and the office of the Local Government Act may possess a proper record. Mining Plans.—The plotting of mining surveys is performed in the same manner as the surface traverse surveys already described. Before proceeding to lay down the plan, it is well to divide the paper into squares of 10 chains side, or 10 acres area, by two sets of lines crossing each other at right angles, one of which sets should represent meridians. This operation should be performed with scrupulous care; and to ensure accuracy, beam compasses should be used to lay off the divisions. The lines should be finely drawn in colour to distinguish them from other lines to be put upon the drawing. Care must be taken to get the plan fairly upon the paper, so that the conformation By reason of the variations of the magnetic meridian, the date of a survey should always be written on the plan; and as the plan of underground workings is laid down piecemeal as the workings progress, often extending over a period of many years, care must be taken to reduce all bearings to the original meridian. Unless these matters are strictly observed, serious errors may result. When two or more veins of mineral are being worked one above the other, and are placed upon the same plan, they are distinguished by means of colour. It matters not what colours are employed for the several separate workings so long as they are distinct from each other. Also the mode of applying the colour, whether with the brush or with the pen, is entirely a question of taste. It may, however, be observed that as mining plans are constantly being added to, it is very difficult to avoid a patchy appearance when the colour is laid on with the brush. Plate 33 shows the manner in which mining plans are got up. Estate and Town Plans.—Plans of estates and towns, including as they do only a limited area and requiring great distinctness of detail, are laid down to a large scale; for the form and character of the detail are, on such plans, of equal importance with its position. With such a scale as is required in these cases, it is possible, not only to clearly distinguish natural and artificial features, but to introduce means of The manner of showing the various kinds of fences has been already described. Trees are usually shown in elevation for the sake of artistic effect; but care must be taken to give them such dimensions as will accord with the scale of the drawing. Houses and other buildings are shown in plan of the correct form, and washed for distinction in light red for dwelling-houses, dark grey for outhouses, and light grey for public buildings. Dark grey is also used for all wooden and iron buildings to distinguish them from those constructed of the ordinary materials, brick and stone. But besides such distinctions, others are needed to indicate the character of natural features and artificial constructions. These are obtained either by showing the object roughly in elevation, or by some purely conventional means. The signs of this character that are likely to be frequently required on estate plans are shown on Plate 15. The manner of representing water, which has been described in a preceding Section, will be found illustrated in detail on Plate 11. Plates 10 and 14 show various kinds of trees; in this form they may be introduced very effectively into plans of estates. The several stages which a plan passes through in the office are shown on Plate 2. If the plan is to be coloured, the colouring must be done before the lettering is put on. Plate 3 shows a plan lightly coloured, as used by surveyors, solicitors, and others; and Plate 17 shows a finished plan in colour. The methods of laying on the colours and the principles involved in the operations have been fully described and explained in a former Section. In Plate 13 is given a town plan showing a proposed street improvement. Such a plan must be laid down to a large scale, and the details in and near the part affected must be drawn in clearly and accurately. The uncoloured portion represents the plan as prepared for lithographing. When pink colour is used to show the proposed street, the buildings should be coloured in black by a light wash of Indian ink. Yellow or The Plates relating to this Section are Nos. 2, 3, 10, 11, 13, 14, 15, 17, 19, 20, 21, and 33. Section V.—Map Drawing.The principles and practice of map drawing, being in the main identical with those of ordinary plan drawing, have been generally explained and described in the preceding Sections. In the present Section, therefore, we have only to direct attention to such details as belong especially to the former class of topographical representations. These details relate chiefly to the selecting of objects and features on the surface of the ground whose character entitles them to special notice, and therefore to distinct delineation; to the practical methods of sketching such objects and features in the field, and to the means and the manner of reproducing them on the finished map. The first and the last of these questions have been treated by Mr. James in his Handbook of Topography, and the second by Lieut. R. S. Smith of the United States’ Army, in so concise and yet so complete a manner that we have not hesitated to avail ourselves of their labours rather than attempt to offer any instructions of our own. The following is, therefore, worthy of respectful attention. Single Stroke Streams.—In inking in streams, begin at the source and draw downwards towards yourself, increasing the pressure on the pen as you descend. The use of the steel pen in drawing single stroke streams is very objectionable. Even soft steel pens are apt to cut the surface of the paper, and in sharp bends it is quite impossible to ensure an even width of line with the best yet made; by re-inking, much time is lost, and frequently a rough jagged line is the result. The common quill pen finely pointed will work well on any sort of paper. Double Line Streams and Rivers.—In maps of a small scale from 8 to 32 miles to the inch, it is usual to darken the north-western bank, supposing the light to fall from the N.W. corner of the map; but on maps of a large scale it is usual to attend strictly to the height of the banks, and the draughtsman should carefully represent the exact nature of each bank on his field-sketch or plane-table sheet. Colouring Streams or Rivers.—Single stroke streams may be inked in with either a dark line of Prussian blue, or a light line in Indian ink may first be drawn and a streak of Prussian blue or cobalt run neatly along it. Cobalt is much used both in single and double stroke streams—it is certainly the prettiest and most lasting blue we have, and the preference should be given it, as it imparts a high finish to MS. maps. In maps which contain much hilly ground, the streams should be drawn in with light ink and a very fine pen at first, and be re-drawn with dark ink or dark blue after the shading of the hills. Large rivers on all maps published in England are now coloured with a flat-wash of cobalt or Prussian blue. Some draughtsmen prefer shading rivers according to bends, and keeping the shade as falling from the N.W., but this system cannot be carried out on maps of a large scale, where the height of the bank is correctly represented. Islands and Sand-banks, Sandy and Pebbly Beds of Rivers.—Islands which are only visible at low water, on well-coloured maps, are usually first washed over with a light shade of burnt or raw sienna, or a mixture of raw sienna and light red; the last-mentioned colour does not easily mix with water, and should not be used if any other can be substituted. After the tint is dry, dot finely with light Indian ink or dark burnt sienna. Sand-banks are coloured in the same way. Sandy beds may be similarly treated, omitting the dotting if pressed for time. Pebbly beds should first be tinted with a mixture of burnt or raw sienna, then dip into a dark shade of burnt sienna any coarse camel-hair brush, and splitting the brush by drawing it between the forefinger and thumb, dot in the tinted portions. Care must be taken to avoid having Another very easy and successful method of dotting in sand or pebbly beds is with a tooth-brush. First, on tracing or any other thin paper, trace out exactly the limit of the tinted portion requiring dotting, cut out these portions from the trace and place it correctly over the original, dip a tooth-brush lightly into a saucer of colour of the required depth of tint, and holding it in the left hand over the uncovered portions, with the forefinger of the right hand or the blade of a pen-knife, gently splutter the colour from the brush; when it is necessary to cover a large space with dots, this will be found the simplest and most speedy way of doing it. Roads and Pathways.—The main or trunk roads in any country should be very distinctly represented by double and perfectly parallel ink lines, coloured between the lines with lake or carmine. District roads metalled, or those made between chief towns, should be shown by a single line coloured with lake or carmine. Unmetalled roads and paths by only a single line in burnt sienna. The same system should be carried out in roads in a mountainous country, and the draughtsman should give, either on the map or in the column of remarks, such information regarding roads as is likely to be useful to travellers or military authorities. Mountain Passes.—On large scale maps these should be distinctly marked, and the windings of the road correctly shown. Along the Pass, write the name in small lettering, and state whether it is practicable for horses, or fit only for men on foot. On maps of a small scale, it will be sufficient to show the pass by a zigzag line across the hollow, with a note as above. Fords and Ferries, Toll-gates.—Fords should be carefully noted and the name and depth of water during the rainy and dry seasons given, if possible. The number of boats at every ferry should be correctly ascertained, and noted on the map. Toll-gates may be shown on roads with a light line drawn across the road, and the words “Toll-gate” be clearly written on the side of the road. Encamping Grounds, Mile Stones, Wells, Springs and Tanks, should be correctly shown and named on all maps. Telegraph Lines and Stationsmust be shown on all maps drawn to a scale of four miles to an inch and upwards, by the usual symbol. On maps of a small scale, show by dots or a thin line of yellow, giving a reference under the title. The Stations are of the first importance, and should be represented by the symbol. Railways, Stations, and Termini.—Railways are represented by a strong black line, with or without thin lines drawn at right angles to the main line. They should of course be very carefully and accurately laid down, as they form the chief feature in any country. Stations are shown by well-defined circles, and the name given in plain lettering. Termini are best shown by blocks representing the size of the buildings according to the scale of the map. Except on maps of a very large scale, jungle should not be shown over hilly ground. Representing such objects as trees, jungle or brushwood, over plains or flat lands, on all ordinary scale maps, is very necessary, and the exact limits of the jungle or waste should be surveyed and correctly given by a dotted line, but over hilly ground it would be impossible to do so without impairing the beauty and hiding the features of the hill drawing. If it is actually necessary to make it known that the hills have jungle on them, let a foot-note to the effect be inserted amongst the remarks or under the title of the map. Under the head of remarks or notes, it is always very necessary to state the kind of jungle which exists in the surveyed tracts, for the information of speculators and timber merchants, and for the guidance of the lithographer or engraver. Notes on maps, whether statistical or geographical, can never be too full; they are useful in supplying at once information which could be obtained only from reading reports, and frequently they render topographical details intelligible where there might otherwise be doubt or misconception. They can be recorded in any spare corner or blank space on the map. Size of Cities, Towns and Villages, and the different ways of representing them.—It is of the utmost importance that all maps of a large Sketching, Shading, and Copying Hills.—In sketching hills, always begin by fixing—1st. The drainage; 2nd. Those features which are most prominent, such as peaks, rocks, ledges of rock running with the strata of the hills, trees remarkable for some peculiarity in shape or size so as to be recognized from various positions, and any other objects likely to help the eye in filling in the details; and lastly, sketch the details, beginning always with the ground nearest yourself. Endeavour to portray your ground faithfully—1st. By preserving the direction and bend of streams as in nature; 2nd. By giving the run of the ridges correctly; 3rd. By fixing the peaks, ledges of rock, precipitous falls and flats carefully; 4th. By showing the saddles or depressions between peaks, which can only be done by giving the peaks on either side sufficient relief in shading; 5th. By attending strictly to the true breadth of valleys; 6th. By suppressing all hollows with a suitable depth of tint; 7th. By careful representation of the banks of streams in the valleys; and lastly, by finishing shades and touches, in which is comprehended the retouching with brush or pen work the entire piece, strengthening the shade of the higher ridges and peaks to show their relative heights, and suppressing the white tint along the ridges. Many excellent draughtsmen are in the habit of leaving the ridge of mountain ranges quite white; this is evidently a mistake, for, unless the ridge of any range of hills is of one uniform height from end to end, it cannot correctly be left white. Thus a wrong impression is conveyed of the surface of the ridge, the white streaks look harsh and are displeasing to the eye, and a stiff and unartistic look is given to the finish of the drawing. The means of communication, whether by roads or minor tracks, are important, both for civil and military purposes, and should be carefully inserted in the map. This can generally be done with facility in a hilly country, as the fixed marks will be visible in sufficient Field Sketching.—Field sketches are made with the lead pencil, and may be drawn upon every page of the compass-book, or upon the alternate pages, at the option of the topographer. In the former case, the bearings and distances are recorded upon the drawing; in the latter, the record occupies the left-hand page, and the sketch the opposite one. The page for sketching should be ruled in squares, with blue or red ink, forming thus an indeterminate scale, the length of the sides of the squares being assumed at pleasure, according to the nature of the ground. Both the record and the sketch are read from the bottom of the page upward. Suppose the stations of the survey to be 100 feet apart; then, assuming the side of the square to be 100 feet, commence the sketch at the bottom of the page—in the centre, if the survey promises to be tolerably straight; if otherwise, at some point to the right or left of the centre, the reason for which will be explained directly. Let the bearing from the first station, the starting point or zero, be N. 10° E. Draw a line from the bottom of the page upward; the side of the square being assumed 100 feet, number the stations upon the squares as far as the line is run, say 325 feet, and write the compass angle down along this line. Let the bearing from the second station, or No. 1, be N. 1° W.; draw a line, making, as nearly as can be judged by the eye, the proper angle with the last bearing, and proceed as before. When the page is exhausted, commence with a vertical line at the bottom of the next one, marking upon it the remainder of the old bearing, and making, by the eye, a new series of approximate protractions as before. If it can be foreseen, as in most cases it can, that the line of survey will be very crooked, bending, for example, from left to right, then commence the bearing at Thus far we have supposed a measured line upon the ground, to which the situation and dimensions of objects might be referred. It is much more difficult to embody the relative positions and dimensions, where all is left to the eye. Here a cultivated judgment is of the greatest value. Practice alone can make a good sketcher under such It is easy thus to make a sketch of a single hill, but when there are many, and the general face of the country is sloping also, the difficulties of representing the connection of the different hills at their bases are considerable. In such cases the direction and lengths of the valleys, or water-courses if there are any, must first be noted, bearing in mind the illusions of perspective in both its effects, previously mentioned. Then establish the positions of the different summits, marking down their relative heights, after which put in the other objects to be represented, such as roads, trees, buildings, &c., referring their positions to each other, and correcting them where they are found to disagree. Horizontal curves present the readiest means to the beginner in sketching declivities. When, after some practice, the form of a body suggests, as it always will, its horizontal sections, then it will be time to resort at once to the lines of greatest descent. The greatest difficulties to be overcome in the practice of eye-sketching are, 1st, that of converting a perspective view into a plan, in all its true proportions; and 2nd, in forming a just conception of the intersections of different slopes at their bases. Hence the rule, to project first upon the sketch, all the lowest lines, or water-courses, and then the highest parts or summits. Then the middle lines and objects may be placed, and the sketch filled up by referring all others to those three groups which may be regarded as determined. The lead pencil for field drawing should be moderately hard, and the general tone of the drawing should be rather light. The shading of slopes ought not to overpower by its depth the distinctness of other objects, and the pencil should be so used and of such a quality as not to be easily defaced by rubbing. We have already described some of the duties of the “examiner” in verifying and supplying detail in the field. The following fuller exposition of those duties and the methods of performing them is taken from an excellent little treatise on Land Surveying, by John A. Smith, C.E. Examination of Maps in the Field.—For the purpose of the examination, the “examiner” should be furnished with an elegant and accurate trace, ink copy, of the plotted detail of the district, and he should be provided with a suitable sketch case, lined with prepared ass skin, pencil, linear scale, chain, &c., and labourers. The trace copy, in one sheet, should be in extent not more than can be conveniently secured in the sketch case. It is desirable that the marginal detail on the trace copy shall be common to the adjoining sheets for examination. If the district be extensive, and if there be no more than one examiner engaged on the examination, adjoining sheets should not be given to the same examiner, that the character of the examiner’s work may be ascertained by independent examinations of the same marginal detail. In the examination of the detail representation on a map the “examiner” should be mainly guided by a few leading considerations; these are:— 1. The position of a straight line, or detail, on the map will be correct when its actual and plotted position on the ground and map makes equal angles with another known line and intersects it in a known point, the position of which line and point on the ground has been previously ascertained to be correctly represented on the map. 2. The line, or detail, will be correctly laid down—given in magnitude and position—when its position and length on the ground and map are ascertained to correspond accurately. From 1 and 2 it will be seen— a. That the point of intersection of two given straight lines on the ground, and the corresponding point on the map, will be a given point on the map, if the corresponding lines on the map be ascertained to be correctly laid down in position. And, b. That any two points being given or correctly determined, the straight line terminating in them will be a given line. Further, c. That a straight line traced or drawn through given points, is given in position. It should be kept in view that lines may be more accurately traced, and to a greater distance, with the naked eye, when the party tracing is rather above than below the level of the field on which the trace shall be made. It may be also seen that a point on the map which is the common point of intersection of three straight lines drawn through well-defined points in the detail will be a given point, if lines traced through the corresponding detail points on the ground be found to have a common point of intersection. And further, that the correct determination of two such points on the map determines, as already stated, the position of a straight line through these points. The determination, in the above manner, of three such common points of intersection correctly determines the representation of a given triangle. In the examination the sides of the triangle determined by intersections, as above, should be measured on the ground, to ascertain and verify the accuracy of the determinations of the angular points on the trace or map. The production of detail lines, and lines traced through plotted points, should be taken up in the chain measurements of the sides of this triangle. Through these verified points straight lines should be traced, and drawn in pencil, to well-defined points in the detail, such as the buttals of fences, the corners of houses and walls, gate piers, &c. On these lines the intersected and neighbouring detail should be examined by chain and scale measurements. In the measurement of the lines the internal and adjacent external detail should be very carefully examined, and corrected on the map where found in error. The examination of the detail should be carried forward by the production and intersection of given lines, and also by chain measurements from given points, to verify the position of the detail or other points on the map. This examination should be continued to the limits of the trace sheet. In remote parts of the trace and district, lines of verification should be drawn, traced on the ground and measured with the chain to verify the scale measurements by the examination. These lines should be long, and in situations affording few facilities for the accurate determination on the map of the position of the plotted detail by other modes of examination. The straight line passing through the extremities, or other well-defined points in curved detail, should be regarded as a detail line, and the position of the intermediate curved detail verified by ordinates Among the Plates appended to this work will be found several examples of map drawing suitable for reference. Plate 16 shows the signs used on ordinary maps and charts. Plates 29 and 30 contain signs used chiefly upon Indian and colonial maps; and Plates 31 and 32 give the signs employed upon military maps, with a section and a plan of fortifications. These signs should be neatly drawn and their dimensions suited to the scale of the map, the same remark applying to these as to trees in elevation. Plate 1 is a plan showing the principal characters of work used in mapping. This plan has been very carefully compiled and drawn to render it suitable as a plan of reference. Plate 12 illustrates the construction and colouring of hills according to the several methods described in the preceding Sections. Other examples, with rocky cliffs, will be found on Plate 14. Plate 18 contains a piece of the Ordnance map drawn to a scale of one inch to the mile, and furnishes an example of finished work. Upon the same Plate will be found a piece of chart showing soundings, intended as a reference for hydrographers and others engaged in marine surveys. And Plate 28 shows the manner in which geological maps are prepared. The whole of these examples will be found worthy of careful study as specimens of the draughtsman’s art. The Plates relating to this Section are Nos. 1, 10, 12, 14, 18, 28, 29, 30, 31, and 32. Section VI.—Mechanical and Architectural Drawings.It is not within the scope of the present work to explain and to illustrate the principles according to which mechanical drawings are executed. These must be studied in special treatises on Projection. The several methods of giving expression and embellishment to this class of drawings have, however, been fully described, and the principles upon which these methods are founded carefully explained. It now remains for us to add a few general remarks and some detailed instructions on the practical application of these principles and methods. Before commencing the delineation of any machine, the draughtsman should make himself thoroughly acquainted with its character; that is, he should ascertain the nature of the work it is designed to perform, the means by which it performs that work, and the manner of its construction. This preliminary study is necessary to enable him to obtain a good general idea of the more important parts, which he will have to give prominence to in the drawing, and to understand the nature of the various connections between the numerous pieces of which the machine is composed. The dimensions of the several parts must be carefully taken, and when drawing from actual machinery, rough sketches should be made to serve as a guide in getting out the complete drawing. The dimensions should be clearly marked upon such sketches. As a general rule, it is best to begin with the ground line and position of main driving shafts, from which dimensions may be taken in every direction. The manner of writing the dimensions, whether upon the rough sketch or upon the complete drawing, should always be thus dimension for lateral, and thus dimension for vertical dimensions. To enable the draughtsman to take these with accuracy, he should be provided with a pair of callipers for measuring the diameters of shafts, a plumb-line for obtaining lateral distances when the objects are not in the same horizontal plane, and a two-foot rule. The chief point to be attended to in commencing the drawing of a machine is to obtain the correct positions of the centre lines of its principal component parts, especial regard being had to the centres of motion. These centre lines have been explained in a former Section. Having laid down these lines accurately in their relative positions, separate sketches may be made on a large scale of each part of the machine, and the details of each part constructed upon each corresponding centre line in succession, until the whole machine is built up. The centre lines should be drawn in red, and the dimensions should be laid off on each side of them. It will frequently be necessary to take a careful section, to obtain sufficient information from which to draw the plan and the elevation. With respect to the written dimensions on a drawing, it may be remarked that they cannot be too full or too numerous. Indeed, without complete written dimensions a drawing is almost useless; for though a scale may and should in all cases be attached, great labour would be required to make use of the drawing by means of the scale only. Every dimension which an engineer is likely to require to know should, therefore, be plainly written. Nor is it sufficient to give a dimension once only, as on the plan, for example, and to omit it on the elevation or on the section. It should never be necessary to refer to another drawing to find a dimension. The lettering should be clearly executed, and the direction of the lettering should be the same as that of the figuring, an example of which has been given; that is, it should read from the front or from the right-hand side of the drawing. If a drawing is to be coloured, the lettering, and all dark lines, such as shade lines, must be left till after the colour has been applied. On all coloured drawings the draughtsman should endeavour to obtain a bright, clear tint by repeating the washes a sufficient number of times. In preparing a flat-wash the tint should be mixed up slightly darker than is required, and the solid colouring matter allowed to settle before using. The solution, being poured off without disturbing the sediment, will give a perfectly clear and pure tint. Tints for colouring perspective drawings should always be prepared in this A means of adding considerably to the definiteness of a coloured mechanical drawing, and of promoting, in a remarkable degree, its effective appearance, is obtained by leaving a very narrow margin of light on the edges of all surfaces, no matter what may be the angles they form with the surfaces that join them. This should be done invariably; we do not even except those edges which happen to have shadows falling upon them. In such cases, however, this margin, instead of being left quite white, should be slightly subdued. The difficulty of achieving this effect of imparting a clear, regular, unbroken appearance to these lines of light seems very formidable, and, indeed, almost insuperable. The hand of the colourist may be as steady and confident as a hand can be, and yet fail to guide the brush, at an almost inappreciable distance from a straight or a circular line, with that precision and sharpness so requisite for the production of this beautiful effect. We shall, however, explain a novel and an effective method of arriving at this most desirable result. Suppose the object about to receive the colour to be the elevation of a long flat rod or lever, on the edge of which a line of light is to be left. Fill the drawing pen, as full as it will conveniently hold, with tint, and draw a broad line just within, but not touching, the edge of the lever exposed to the light. As it is essential to the successful accomplishment of the operation that this line of colour should not dry, even partially, before the tint on the whole side of the lever has been laid on, it will be well to draw the pen a second time very lightly along the line, so as to deposit as much tint as possible. Immediately this has been done, the brush, filled with the same tint, should be passed along so as to join the inner edge of this line of colour and the whole surface of the lever to be filled in. By this means a distinct and regular line of light is obtained without sacrifice of time. A still more expeditious way of colouring such The line of light upon cylindrical objects may be beautifully produced by the same means. To indicate this line with perfect regularity is highly important, for if strict uniformity be not maintained throughout its length, the object will appear crooked or distorted. Having marked in pencil the position of the light, and filled the drawing pen with a just perceptible tint, draw a line of colour on one side of the line of light. Then, with the brush filled with the same tint, fill up the space unoccupied by the shade tint, within which the very light colour in the brush will disappear. The portion of the surface on the other side of the line of light being treated in the same way, the desired effect, of a stream of light, clear and mathematically regular, will be obtained. The effectiveness and expeditiousness of this method will be most noticeable on long circular rods of small diameter, where a want of accuracy is more immediately perceptible. The extreme depth of shade, as well as the line of light, may, on such rods, be marked by filling the pen with dark shade tint, and drawing it exactly over the line representing the deepest part of the shade. On either side, and joining this strip of dark colour, another, composed of lighter tint, is to be drawn. Others successively For the correct representation of a building, plans, sections, and elevations are required. The plan is usually a horizontal section of the building close above the ground floor. The position and the dimensions of the walls and the rooms of a house are shown by this means. As the walls are shown in section in the plan, sections of the various walls must, of course, be supplied before the plan can be drawn. It is usual to colour the section of the walls in a ground plan; but not unfrequently a dark wash of Indian ink is preferred to colour. The number of sections required will depend upon the regularity of the building; but generally it will be found that two half-sections are sufficient. These two half-sections are usually placed side by side, separated by a single line. The lines on which they are constructed must be drawn distinctly on the plan, and lettered. The section is then described as “Section” or “Half-section” on AB, &c. Usually the line of section is broken in plan, and the section is then said to be on AB, CD, one half being on AB and the other half on CD. Separate sections to larger scales are required for the details of construction, such as joints of rafters, mouldings to windows, and other parts needing distinct representation. Elevations generally represent the whole of one side of the building, and every side that differs from the rest must have its own elevation. Such elevations are termed Front, Back, and End Elevations, or North, South, East, and West Elevations. In order to show the foundations, a section of the ground is sometimes given with an elevation; in such a case the level of the ground should be shown by a distinct line. Sometimes the portions of the structure below the ground are shown by dotted lines. Such portions should not be coloured. In getting out the drawings the plan should first be drawn, then the sections, and finally In the accompanying Plates will be found examples of colouring mechanical and architectural drawings. These should be studied in conjunction with the Section on colouring in the first part of this work. Plate 22 shows a piece of marine engine carefully coloured to indicate the material of which the several parts are made, and Plate 23 contains a piece of permanent way, consisting of wrought-iron rail and bolt, cast-iron chair and wooden sleeper and block, and an elevation of a skew bridge, accurately coloured and shaded in accordance with the principles already explained. It is not within the scope of this work to treat the subject of projection, whether orthographic, isometrical, or perspective; but we have given examples of each of these for the purpose of illustrating the remarks and instructions on colouring given in the Section referred to above. Thus Plate 24 is a perspective drawing, such as are frequently made by architects, requiring a high degree of skill and taste on the part of the colourist. And Plate 27 contains two isometrical views of a building. These examples are intended to serve as models of finished colouring. The Plates relating to this Section are Nos. 22, 23, 24, and 27. Section VII.—Copying and Reducing.Duplicates of drawings are very frequently required; so frequently, indeed, and in such numbers, that their production constitutes a large portion of the work executed in every drawing office. Generally, these duplicates are required to the same scale as the original drawing; but often it becomes necessary to reduce or to enlarge the scale to render the drawing suitable to the purpose for which it is intended. The various means and methods by which such duplicates are produced are, therefore, important matters to the draughtsman, Drawing from Copy.—Drawing from copy is rarely resorted to for the purpose of obtaining duplicates, the process being too slow for practical requirements. But it constitutes the principal means, after the study of projection, by which pupils in the office are initiated into the art of producing drawings. A few hints concerning the best modes of proceeding in these operations will, therefore, be serviceable, both to the instructor and the instructed. First draw a horizontal and a vertical line through the middle, each way, of the sheet upon which the copy is to be made; draw also similar lines upon the copy. As these lines divide the paper equally, they may, for the sake of distinction, be called “divisional lines.” If the centre lines are not shown on the copy, these must next be drawn in lightly with the pencil, great care being taken to place them correctly. The position of these centre lines relatively to the divisional lines may then be transferred by means of the dividers from the copy to the fair sheet, upon which they must be drawn finely but distinctly. Sometimes it will be necessary to draw other lines upon the copy, and to transfer them in like manner to the fair sheet. The details may then be drawn in upon these centre lines, by transferring to them the measurements taken from the centre lines of the copy. In taking measurements from a centre line through an object that has both sides alike, the dividers should be turned over to ascertain whether the distance on the other side of the centre line is the same, so as to prove the accuracy of the drawing with respect to the centre line. All measurements must be taken in the exact direction of the distance to be measured, and be transferred in the same direction, or an obviously incorrect distance will be the result. In making the mark, the point of the dividers should not be pushed into the paper, a just visible mark being all that is required; care must also be taken, when using the compasses, not to press the leg into the paper, as the holes thus made render circles and arcs inaccurate, are unsightly at all times, and When two or more views of the same objects are given, they should be worked upon simultaneously; because, having once drawn in the centre lines, one measurement may be applied to the corresponding part in each view, and so time and trouble saved. In copying maps and plans by this method of drawing from copy, both the copy and the fair sheets are divided up into small squares, by drawing a number of other lines parallel to the divisional lines described above. The intersection of detail with these lines may then be readily and correctly transferred from the copy to the fair sheet. Copying by Tracing.—Tracing furnishes the most expeditious means of multiplying drawings. When a tracing is required in outline only, the usual way is to fasten the sheet of tracing paper with ordinary drawing pins over the drawing to be traced; the sheet of tracing paper should be sufficiently large to allow the pins to be clear of the drawing. If the sheet is not large enough for this, strips of thin paper, with one edge gummed to the tracing paper and the other to the board, may be used. When this method is not practicable, the pin holes may be effaced to some extent by turning the drawing upside down, and pressing back the edges of the holes with the flat end of a pencil, after the tracing has been removed. If the tracing is to be coloured, it must be stretched on the board, or it will never lie flat after being moistened; and if the colouring is to be applied before the tracing is removed from the drawing, it is essential that the tracing paper be larger than the drawing, so that it may be cut off without injury to the latter. When there is not sufficient time to stretch the tracing paper, the tendency to buckle up when drying may be greatly lessened by placing weights around any part immediately after the colouring has been laid on. If the tracing is to be mounted, the In performing the stretching process, the sponge must not be applied directly to the tracing paper, but to a piece of clean white paper laid over it; sufficient moisture will pass through to the tracing paper in a few seconds. Sometimes, when the sheet is small, merely breathing upon it will be found sufficiently effective. As tracing paper is thus greatly affected by the breath, it has been recommended to entirely finish both circles and lines within a small area at a time, when copying a drawing, as if all the circles were put in first, as on a drawing, many of them might be out of position before the lines could be drawn. This recommendation is, however, of doubtful value. When tracing from another tracing, a piece of white paper should be placed beneath the copy to render the lines distinct. A tracing may be made upon ordinary drawing paper by means of the glass drawing board. This consists of a sheet of plate glass let into a wooden frame about 3 inches wide flush with the face, the inner edges of the frame being rebated for this purpose. This copying board is placed on a table in front of a window, and supported at an angle of about 25°, so as to get a strong light beneath, which light may be increased by placing a sheet of white paper upon the table to reflect upwards. The original drawing being pinned down to this board with a sheet of drawing paper or parchment over it, the finest lines will be plainly visible, and the drawing may be traced in the same manner as upon tracing paper. To alter the light, the angle of the board may be changed. This method, which is coming extensively into use, is a very convenient one for copying plans and maps. Copying by Transfer.—Copying by transfer has superseded the method already described as “drawing from copy.” Transfer paper, as employed for this purpose, may be made in the following manner. Take half an imperial sheet of very thin paper, such as tissue paper, and having stretched it upon a board, rub some common blacklead To transfer a drawing, the sheet of transfer paper is laid with its prepared face upon the paper which is to receive the drawing, and over this is placed a tracing of the drawing to be copied, carefully pinned down. The straight lines of the tracing may then be transferred to the drawing paper below by going over them with a style or other pointed instrument that will not cut the tracing. For the regular curves and circles, it will be sufficient to mark the centres by a small cross, thus, ×, and the radii by short lines. Other curves may be transferred by means of the French curve. By this means a copy of the original drawing is obtained in black or red lines, which may be afterwards inked in. Though three distinct operations are required in this process, making the tracing, transferring, and inking in, a drawing can be much more rapidly copied by means of it, than by measuring off with the dividers, as in drawing from copy. Reducing and Enlarging.—It is evident that in drawing from copy, the drawing may be reduced or enlarged at pleasure, since it is only necessary to take half or twice the dimensions as required. Usually proportional compasses are employed for this purpose. When reducing by scales, it is obviously not essential to use the same scale as that to which the original is made; the dimensions on one scale may be readily transferred to any other, and the student will do well to make himself familiar with the operation. For reducing or enlarging plans, several means are employed: one of these is known as the method of squares, and is illustrated on Plate 26. In the preceding remarks on drawing from copy, it was shown how in copying to the same scale, both the copy and the fair sheet were divided into squares of equal size, and how the intersections of the detail with the lines forming these squares on the copy were Drawings may also be rapidly reduced or enlarged by means of instruments called the Pantograph and the Eidograph. Both of these instruments are shown on Plate 26. The following very complete description of the pantograph and the eidograph is given in an excellent work on ‘Mathematical Drawing Instruments,’ by W. F. Stouley, of Holborn, London. “The pantograph, as represented on the plate, consists of four rules of stout brass, which are jointed together in pairs, one pair of rules being about double the length of the other. The free ends of the shorter pair are again jointed to the longer in about the centre. It is important that the distance of the joints on each of the short rules should exactly correspond with the distance of the joints on the opposite longer rules, so that the inscribed space should be a true parallelogram. To enable the instrument to work freely and correctly, all the joints should be perfectly vertical, and with double axes. Under the joints casters are placed to support the instrument, and to allow it to move lightly over the paper. One of the long rules has a socket fixed near the end, which carries a tracing point when the instrument is used for reducing. The other long rule, and one of the shorter rules, have each a sliding head fitted upon it, which is similar to one of the heads of a pair of beam compasses. Each head has a screw to clamp it in any part of the rule, and carries a perpendicular socket, which is placed over the edge of the rule in a true line with the joints. Each socket is adapted to hold either a pencil holder, tracing point, or fulcrum pin, as may be required. The rules upon which the heads slide are divided with a scale of proportions: “A loaded brass weight, which firmly supports a pin that fits exactly into either of the sockets, forms the fulcrum upon which the whole instrument moves when in use. “The pencil holder is constructed with a small cup at the top, which may be loaded with coin or shot to cause the pencil to mark with the required distinctness. “Arrangement is made to raise the pencil holder off the drawing. This is effected by a groove down one side of the pencil holder, in which a cord is fixed, passing from the pencil along the rules, turning the angles over small pulleys, and reaching the tracing point, where it may be readily pulled by the hand to raise the pencil. This will be found especially convenient when the pencil is required to pass over any part of the copy not intended to be reproduced. “The pantograph is set to reduce drawings in two ways, termed technically the erect manner and the reverse manner. It will be necessary to give full details of each manner, particularly in relation to the scales engraved upon the instrument, which are not very intelligible; indeed comparatively few professional men are sufficiently acquainted with them to avail themselves of their full value. “By the erect manner of setting the pantograph, the reduced copy will appear erect; that is, the same way as in the original. The general position of the parts of the instrument set in this manner is shown in the plate, where it will be seen that the fulcrum pin is placed in the socket of the sliding head upon the outside long rule, and the pencil holder in the socket upon the short central rule. By this method of setting the instrument, it will reduce in any of the given proportions not exceeding half-size, technically from 1—2. The scales engraved upon the rules that accord with the erect manner of setting are those which have 1 for the first proportion; as 1—2, Table of Reductions by the Pantograph in the Erect Manner, the Fulcrum being placed in the Socket upon the Outside Rule, and the Pencil upon the Central Rule.
“In the above Table the readings which are given with the proportions are given to show clearly which proportions agree with the erect scales; many of those that do not agree with the reading are very useful, as 2—3, which is often required to reduce a drawing from a scale of 20 to one of 50. “In the reverse manner of setting the pantograph, the reduced copy appears reversed, or upside down, to the original. The fulcrum pin is placed in the socket upon the short central rule, and the pencil holder is placed in the socket upon the outside rule. This is generally the most convenient way of using the pantograph for large drawings, as the original and copy come edge to edge, and need not overlap each other, which is often compulsory in the erect manner; the range of scale is also much greater, as the proportions include the unit proportions of the erect scale, and continue in ratios up to full size. “The following Table will give the readings of the instrument Table of Reductions by the Pantograph in the Reverse manner, the Fulcrum being placed in the Socket on the Central Rule, and the Pencil in the Socket upon the Outside Rule.
“The above Table and the previous one give the proportions for reductions, the tracing point being in every instance considered upon the outside rule. If it were required to produce an enlarged copy, which the pantograph will do but very imperfectly, the pencil and tracer would have to change places; the proportions of course would read the same. “In using the pantograph some care is required in setting the fulcrum weight in the best position to allow easy action of the instrument over the space required. It should always be roughly tried over the boundary before commencing the copy. “The ordinary pantograph will in no instance work over a large drawing at one operation, but it may be shifted about as required, using care, and testing the copy after the fulcrum is moved, to see that the tracer and pencil correspond in those parts already produced, that the pantograph will reach in its shifted position. The fulcrum weight being generally made with needle points to attach it to the drawing will be found very difficult to shift so short a distance as is frequently required. This may be easily remedied by attaching with gum a piece of indiarubber over each of the sharp points, when it is “In copying the buildings which frequently occur in plans of estates, &c., a straight slip of transparent horn will be found very convenient to guide the tracing point. Some draughtsmen have the horn cut with an internal angle, by which one side and one end of a building may be traced without shifting the horn. “Architects and mechanical engineers seldom use the pantograph; however, it may perhaps be sometimes used with advantage for tracing in the most difficult and tedious parts of a drawing with a precision impossible by hand. This applies particularly to such parts as are frequently repeated, as capitals, trusses, bosses, tracery, &c., upon drawings to very small scales. In these instances it is only necessary to make a detail sketch, say six times the size required, and to place the fulcrum weight in such position that the pencil will pass over the parts required to be filled in, the tracer at the same time resting on a corresponding part of the detail sketch, which may be placed in position under the tracing point, and be held sufficiently by two lead weights. For a second ornament on the same drawing, the detail may be shifted without moving the fulcrum. “To follow the outline of any object of the ornamental class, or for the reduction of mechanical drawings to a size suitable for wood or other engravings, the strip of horn will be found particularly useful; indeed, to obtain any degree of precision, it will be better, generally, to let the tracer follow a guiding edge placed over the original for that purpose. French curves are particularly useful, although perhaps only a small piece may be available at once. The tracer may rest on the surface until another part of the curve is found to correspond with the continuation of the line. “In some old pantographs a guide is fixed to the tracing point. The guide is a kind of handle similar to a drawing pencil, the point of which is hinged to the point of the tracer. This gives a convenient and firm hold of the point, and appears to the author a useful appendage. “Pantographs have been made in many shapes unnecessary to describe, as they are all of one principle—that of a parallelogram jointed at the four corners; the principal difference being in the position of the points and fulcrum in relation to the parallelogram. One thing is essential in every construction,—that is, that the fulcrum, tracer, and pencil should always be in a true line when the instrument is set for use. The parallelogram may be in any position on the instrument, to the fancy of the maker. “The Eidograph was invented by Professor Willis in 1821. It is a most ingenious and exact instrument, for many purposes superior to the pantograph, within the range of its working powers, which, however, may be considered to be limited to reducing or copying off, between the full size of the original and one-third of the size; for greater reductions, the balance of the various parts is thrown so far out that it appears clumsy to use, and is really inferior to the pantograph. The great merit of the eidograph is, that within its range it reduces conveniently and exactly in all proportions; for instance, we may reduce in the proportion of 9 to 25 as readily as 1 to 2. It is also in every way superior to the pantograph in freedom of action, there being no sensible friction on the single fulcrum of support, and in its movement it covers a greater surface of reduction. “It is somewhat curious that an instrument of such great merit should be little known in the profession, where its uses would be so constantly convenient. This may partly be attributed to the very few published descriptions which are to be found in works treating on mathematical instruments. It is not intended, however, to infer that there are not many eidographs in use, but that the writer presumes they are comparatively little known, from his personal acquaintance with professional men, and from the number of large pantographs that are made and sold to perform work that could be done so much more exactly and conveniently by the eidograph. This remark will not apply to the small pantograph, which is less expensive than a small eidograph, and answers perfectly for the reduction of small plans—as, for instance, those frequently attached to leases and conveyances. “The details of the construction of the eidograph are as follows:—The point of support is a heavy, solid, leaden weight, which is entirely covered with brass; from the under side of the weight three or four needle points project, to keep it in firm contact with the drawing. Upon the upper side of the weight a pin, termed a fulcrum, is erected, upon which the whole instrument moves. A socket is ground accurately to fit the fulcrum, and attached to a sliding box, which fits and slides upon the centre beam of the instrument. The sliding box may be clamped to any part of the beam by a clamping screw attached. Under the ends of the beam are placed a pair of pulley wheels, which should be of exactly equal diameter; the centre pins of these revolve in deep socket fittings upon the ends of the beam. The action of the two wheels is so connected as to give them exact and simultaneous motion. This is effected by means of two steel bands, which are attached to the wheels. The bands have screw adjustment to shorten or lengthen them, or to bring them to any degree of tension. Upon the under side of each of the pulley wheels is fixed a box, through which one of the arms of the instrument slides, and is clamped where required. At the end of one of the arms a socket is fixed to carry a tracing point, at the end of the other arm a similar socket is fixed for a pencil. The pencil socket may be raised by a lever attached to a cord, which passes over the centres of the instrument to the tracing point. The two arms and beam are generally made of square brass tubes, and are divided exactly alike into 200 equal parts, which are figured so as to read 100 each way from the centre, or by the vernier cut in the boxes through which the arms and beam slide they may be read to 1000. “There is a loose leaden weight which fits upon any part of the centre beam, packed in the box with the instrument. The weight is used to keep the instrument in pleasant balance when it is set to proportions which would otherwise tend to overbalance the fulcrum weight. “In the above details it will be particularly observed that the pulley wheels must be of exactly equal diameters. It is upon this that “From the details just given, the general principle of the eidograph may be easily comprehended. Thus, the wheels at each end of the beam being of equal size, the steel bands connecting them being adjustable, so as to bring the wheels into any required relative position, it follows, that if the arms fixed to the wheels be brought into exact parallelism, they will remain parallel through all the evolutions or movements of the wheels upon their centres; consequently, if the ends of the arms be set at similar distances from the centres of the wheels, any motion or figure traced by the end of one arm will be communicated to the end of the other, provided the fulcrum of support be placed also at a similar distance from the centre of one of the wheels. “To adjust, or ascertain if the eidograph is in adjustment, is very simple, from the reason that when the arms are parallel the adjustment is perfect for all proportions. The manner of ascertaining this is as follows: place all the verniers at zero, which will bring them to the exact centres of the arms and the beam, place the arms at about right angles with the beam, then mark simultaneously with the tracer and pencil point, turn the instrument round upon its fulcrum, so that the pencil point be brought into the mark made by the tracer; then, if the tracer fall into the mark made by the pencil the instrument is in adjustment. If it should not fall into the same mark, the difference should be bisected, and the adjusting screws on the bands should be moved until the tracer fall exactly into the bisection, which will be perfect adjustment. “When the eidograph is in adjustment, if the three verniers be set to the same reading on any part of their scale, the pencil point, “The divisions upon the eidograph do not positively indicate the reductions required to be performed by the instrument, but merely give a scale, which, with the assistance of the vernier, divides the beam and arms into 1000 parts. To obtain the quantity to which the verniers are to be set, it is necessary either to apply to a table of proportions relative to divisions, or to simple arithmetic, as will be shown. A printed table is very generally placed inside the lid of the box in which the instrument is packed, which contains part of the following proportions: Table for Reducing or Enlarging Proportions.
“The table here given answers for the general purposes of reducing, such as the bringing of a plan from one chain scale to another, the quantities of which are found by the following rule: “To find the quantity equal to any given proportion for the setting of the eidograph.—Subtract one sum of the proportion from the other, and multiply this difference by 100 for a dividend; add the two sums of the proportion together for a divisor: the quotient from the working of this will give the number to which the arms and beam are to be set. “For instance, let it be required to reduce a drawing in the proportion of 3 to 5.
“The centre beam is to be set to 25 on the side nearest the pencil point, the pencil arm is also set to the 25 nearest the pencil point, and the tracer arm is set to the 25 farthest from the trace. If it were required to enlarge in the same proportion, each side would have to be set at the opposite 25. “To clearly illustrate the subject, it may be well to give another example. Let it be required to reduce an ordnance plan of five feet to the mile to a scale of three chains to the inch. First, we must have like terms, therefore to reduce both proportions to feet to the inch will, in this instance, be the most simple way; thus:
“If the slides of the instrument be set to 38·46, it will be, practically, sufficiently near.” Photography is also frequently resorted to for the purpose of reducing and enlarging drawings. The results are satisfactory within certain limits of size; for it is obvious that when the drawing is large, the parallel lines will converge in the photograph, for reasons which will be understood from the laws of perspective. For enlarging small and intricate drawings, photography is very useful. In preparing drawings for reduction by this process, all lines and shadows should be put in in Indian ink only. For optical reasons, colour cannot be reproduced by photography, and as certain colours produce an effect which might not be anticipated by the inexperienced, it will be well to warn such against these effects, to prevent disappointment at the results obtained. Thus blue, for instance, shows Drawings for Lithographers and Engravers.—The drawings required by the lithographic draughtsman are simply outline drawings or tracings, with the shaded drawing for reference when such is required. The shaded drawing should be traced when in outline only with a fine-pointed pencil, not too hard. The engraver prefers such a tracing to the drawing itself, unless he can have the latter before it is shaded. He will, however, require the shaded drawing as a guide in copying in the shadows. As the drawing always gets soiled under such circumstances, unless protected, it is prudent to place it upon a board of the exact size, with a glass over it to fit, the glass being kept in its place by a strip of paper pasted round the edge. The drawing will not be required at all if only an outline engraving is to be made. In that case, the lines that are to be shade lines must be indicated on the pencil tracing; a dot in red ink on each of such lines will be sufficient. A scale should always be put upon lithographs and engravings, instead of merely stating that it is drawn to some particular scale, because the paper just before receiving the impression is damped, and consequently expands. For this reason, no engraving is of the same size as the original drawing; and as the degree of moisture varies, no two engravings from the same plate ever are exactly equal in size. Hence the necessity for drawing the scale is obvious. The Plate relating to this Section is No. 26. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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