Fig. 86.
Larger illustration (54 kB).
Draw the datum line D L, 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 A D L B 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. Thus, in a railway working section, for example, the levels are taken at every chain’s length, and also over every little undulation in the surface of the ground. In preparing such sections, vertical lines are drawn in blue at every chain’s length up to the surface of the ground from the datum line, and on each vertical is written the reduced height above datum from the column of reduced levels in the level-book.
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.
—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.
—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.
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 narrow tracts of country through which it is proposed to construct a means of communication, such as a railway, a road, or a canal. They do not differ essentially from other plans, the survey being taken in the ordinary way, and the plan laid down according to one or other of the methods described in the preceding Section. The width of railway surveys varies from five to twenty chains, at the option of the engineer. An important matter demanding careful attention is to survey, plot, and number all fields and other enclosures, houses and other buildings situate within the limits of deviation, that is, the boundaries of the space beyond which it is not proposed to deviate the line of railway. The object of numbering every separate enclosure, road, building, or other object on the plan, is that they may be the more readily described in a book prepared for that purpose and called the Reference Book. Parish and county boundaries are shown by dotted lines, as explained in a former Section. Frequently it is necessary, in consequence of the smallness of the scale adopted for the plan, to give enlarged drawings of certain portions. In these cases, whenever practicable, the enlarged plan should be placed directly under or over the small plan to which it refers, as such an arrangement is not only more pleasing to the eye, but is far more convenient for reference than one in which there is no relation of position between the two plans. The proposed railway should be represented by a full and heavy line, and the limits of deviation shown by strong dotted lines. The names of the different parishes through which the line passes should be conspicuously written, and the name of the county placed at the top of each sheet; the sheets also should be distinctly numbered. It is not usual to distinguish different kinds of fences on plans of engineering projects, as on estate plans to a large scale; on the former it is sufficient to distinguish between fenced and unfenced lines of division of land, marking the former by plain, and the latter by dotted lines. It is almost needless to remark that a scale of distances should accompany every plan.
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 show distinctly the irregularities of the surface. The horizontal datum line of the section should have marked on it a scale of distances corresponding with those marked along the centre line of the plan, in order that corresponding points on the plan and the section may be readily found, and great care should be taken that horizontal distances on the plan and on the section exactly agree. Cross sections are longitudinal sections of existing lines of communication which the proposed work will cross; they may cross the centre line of the proposed work either at right angles or obliquely. Cross sections may also be required where the ground slopes sideways; in general they should be ranged accurately at right angles to the centre line, and they should be plotted without exaggeration, that is, their vertical and horizontal scales should be the same as the vertical scale of the longitudinal section. All cross sections should be plotted as seen by looking forward towards them along the centre line.
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.
—“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 of railway delineated thereon so as to show its general course and direction, is required to be deposited at the office of the Board of Trade, and at the Private Bill Office of the Houses of Parliament; and in cases where any portion of the work is situate within the limits of the Metropolis, a copy of so much of the plans and sections as relates to such portion of the work is required to be deposited at the office of the Metropolitan Board of Works. Also a copy of so much of the plans and sections as relates to each parish in or through which the work is intended to be made, or in which any lands or houses intended to be taken are situate, together with a copy of so much of the book of reference as relates to such parish, is required to be deposited with the parish clerk of each such parish in England, with the school-master of each such parish in Scotland, and with the clerk of the union within which such parish is included in Ireland.”
—“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 variation, extension or enlargement thereof respectively, for supplying the same with water.”
“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.”
—“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.”
—“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, there shall be a section which shall specify the levels of both banks of such river; and where any alteration is intended to be made therein, it shall describe the same by feet and inches, or decimal parts of a foot.”
“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 cross sections shall extend for two hundred yards on each side of the centre line of the railway.”
“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.
—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 of road, river or stream of any kind, should be inserted some remark respecting the work to be constructed, with a reference to the number of the working drawing prepared. The latter may be a special drawing, as for a bridge, or a general drawing, as for a level crossing and gates. The results of boring should also be shown on the working section. As soon as the works of construction have been determined upon, notes should be inserted from the working drawings, or other sources, of the angles of skew at which the line crosses roads or streams, the spans of arches on the square and on the skew, the rise of the arch, the depth of the arch stones, and of the puddle, if any be used, and, if the works be on an inclined plane, the rise or fall from centre to centre of the piers. Similar memoranda should also be made of girder bridges, culverts, and other works occurring along the line. To all working drawings the acting engineer always affixes his signature.
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.
—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.
—A map of the entire district must, in this case, be submitted, with the main boundary distinctly defined, and the name of the district clearly printed thereon. The proposed division into wards must be by lines, clearly defined on the map of the district; brooks, roads, footwalks, streets, fences, or other easily recognizable lines of division may be adopted. Such lines must be defined on the map by a margin of colour. The proposed boundary-lines must be described in the same manner as in the boundary map, and the name or number of the ward, with the relative areas, population, and rateable value must be given. A duplicate map or a tracing must be deposited at the Local Government Act Office for future reference.
—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.
—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. The dimensions of water and gas pipes should also be shown in figures or in writing.
—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.
—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 of the outline or boundary to the edges of the paper may have a pleasing effect to the eye; and the direction of the meridians must be determined according to this condition. By having the plan thus divided into squares of 10 acres each, the quantity of ground worked out may be approximatively estimated at any time by inspection, and the total quantity may be readily computed in the same manner. Besides dividing the plan itself in this way, it will be found extremely useful to have a sheet of tracing paper, or better, tracing cloth, divided into squares of 316·228 links side, or 1 acre area, in black lines; each of such squares being subdivided into 4 by lines in colour, to show quarters of an acre. To find the area of any portion of exhausted or of unworked ground, it is only necessary to lay this divided sheet over such portion and to count the squares and quarters included in it.
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.
—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 producing pictorial effect into their representation. The nature of these means may be seen in the examples of plans appended to this work.
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 any other bright tint may be used for the proposed street, the object being merely to distinguish it clearly. Existing streets should be coloured in yellow ochre, except when that colour is used for the proposed street, in which case burnt sienna may be used.
The Plates relating to this Section are Nos. 2, 3, 10, 11, 13, 14, 15, 17, 19, 20, 21, and 33.
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.
—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.
—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.
—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 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 too much colour in the brush, or the dots will run into each other and make ugly daubs.
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.
—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.
—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 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.
, should be correctly shown and named on all maps.
must 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 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.
—It is of the utmost importance that all maps of a large scale should show the size accurately of cities, towns and villages. If the scale admits of it, the several blocks or groups of houses with the roads between them should be correctly drawn.
—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 number along the road, so that the latter may be drawn in at once by plane-table operations along the line of communication to be surveyed. In flat countries, or where the view is circumscribed, it may be necessary to resort to measurements and plotting; but should any case occur where the fixed points of reference are far apart, the traverse system must be resorted to, and the road should be plotted from computed co-ordinates.
—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 the bottom of the page accordingly, beginning at a point on the extreme right, and running it diagonally to the left, so as to make due allowance for the great deflection anticipated in the next bearing. Such cases may be foreseen in running around an inclosure, or in following a curving stream or ridge. The advantages of the system of squares in sketch books completely overbalance the one disadvantage, which is, that the diagonal bearings will not make exact distances upon the squares, while the vertical and horizontal ones will. It will be remembered that the surveying book is designed to be exact only in its record and the general features of the ground, and that a slight change of scale is not material, as it can be made exact when the survey is protracted upon the map. By these approximate protractions, any page of the book of survey conveys a very just notion of the bearings and distances, and of the relative positions of the general features of the ground. The first station being at the bottom of the page, note down, in the space between it and the second one, all the features of the ground passed over by the line of survey; as to whether it is cultivated, forest, marsh, &c.; whether it is crossed by streams, ditches, &c., and their width; if it rises or falls; about what degree of slope, &c. On both sides of the line introduce, according to the scale, and their distances, as judged by the eye, all topographical objects within sight, such as buildings, roads, streams, hills, &c., &c., drawing them to the scale if possible, and if they cannot be got upon the page, describing briefly their nature and position. In sketching hills endeavour to project as many horizontal curves as possible, which should be lightly put in, and then the shading lines may be drawn over them. The degree of slope should be frequently written down in numbers upon the sketch. The names of localities, streams, hills, farms, &c., should also be entered.
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 circumstances. Rules must, from the nature of the case, be few and general. In the first place, all objects within the field of vision are presented to the eye in perspective, whereas the sketch is to be a plan. The apparent diminution of dimensions in distant objects must therefore be corrected on the plan. For example, the windings of a crooked stream, or a road, in perspective, are much exaggerated in retiring into the distance; they must therefore be straightened out in the sketch more and more, as they are more removed. 2nd. In looking at variously placed hills from a somewhat elevated station, the eye will in some cases look directly, or perpendicularly, at the face of some slopes, while in others, the surface of the slope, if prolonged, will pass through the eye, and will not be seen in its true dimensions, though its inclination may be judged. In sketching the shapes of hills, bodies of water, masses of forest, &c., these facts must be taken into consideration, and to ensure skill, eye sketches of a small portion of ground having well-marked features must be frequently made, and compared with measurements of the same features. In sketching a single hill, the best station is at the summit. First endeavour to represent the lowest horizontal curve of its surface; then a medial one; then the form of the level space at the summit, or the highest horizontal curve. Others may then be introduced between these, until the ground is sufficiently expressed. The angles of inclination should be frequently noted down in numbers; all accidents of ground, such as ravines, rocks, &c., should be carefully placed, and all other objects, such as houses, fences, trees, &c., should be put down in their proper relative positions and dimensions. Having thus prepared a skeleton of horizontal curves, numbered as to inclination and heights, the sketch will always serve a useful purpose without any lines of greatest descent. After sufficient practice in this method, the eye will become so cultivated as to enable the draughtsman to express the form of ground by lines of descent at once, the mind conceiving the position of the horizontal curves, and thus supplying the necessary data for the shading lines, the relative thickness and length of which for the different slopes is a matter very easy of acquirement. But this should not be attempted until the method by horizontal sections is thoroughly mastered.
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.
—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 or tangents. Buildings and adjacent detail should be carefully examined by productions, &c., because of the greater difficulties these details usually present to the surveyor and plotter, and the consequent liability to small errors in the position of some of the plotted points, which affect the direction of lines determined on them.
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.
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 manner. The methods of laying on flat-washes and of shading by colours have been described in former Sections. The following additional remarks on colour shading are taken from Worthen’s ‘Cyclopædia of Drawing.’
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 surfaces is to draw a second line of colour along and in contact with the opposite edge of the lever or other object, and to fill in the intermediate space between the two wet lines with the brush. In this way a clear, uniform outline to the tint is obtained. The blades of the drawing pen must not be sharp, and care must be taken not to press heavily upon it, as otherwise the blades will leave their course visible—an unsightly betrayal of mechanical means to obtain such regularity in the colouring. Flat circular surfaces may be treated in the same way, by using the pen compass instead of the drawing pen. When such surfaces are large it will be judicious to colour them in halves or in quadrantal spaces, but great care must be taken to join the parts neatly. The lines of junction may be obliterated by slightly washing them, or by laying a very light tint over the whole surface, taking care in crossing the lines of junction to rub them lightly with the brush.
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 lighter should follow, until, on one side, the line of the rod is joined, and, on the other, the lightest part of the rod is nearly reached. The line of light is then to be shown, and the faint tint used at this part of the operation spread with the brush lightly over the whole of that portion of the rod situate on either side of this line, thus blending into smooth rotundity the graduated strips of tint drawn with the pen.