.REESE LIBRARY PRELIMINARY SURVEY PRINTED BY SPOTTISVYOODE AND CO., NEW-STREET SQUARE LONDON PRELIMINARY SURVEY AND ESTIMATES BY THEODORE GRAHAM GRIBBLE CIVIL ENGINEER t. L JTY LONDON LONGMANS, GREEN, AND CO, AND NEW YORK : 15 EAST i6' h STREET 1891 A // rights reserved s INTRODUCTION THE Anglo-Saxon race, in sundry climates and conditions, and under divers forms of government, is unquestionably pre-eminent to-day in the civilisation of the world. It is not alone beca'tis^e they are the greatest traders, but because they are at the same time the greatest navigators and engineers of the world that the English-speaking nations hold the proud primacy of race. Whether it be at the first appearance of railways upon the Eastern hemisphere, or the first cable-knot between the old world and the new, or the development of virgin continents, and the carrying of a luxurious civilisation into the heart of nature's wilderness, the Anglo-Saxon is always at the front. The strengthening of the Anglo-Saxon bond from year to year is more attributable to improved means of com- munication than to sentiment. The constantly conflicting interests of commerce, the intense rivalries of handicrafts, the minor jealousies of social life, fostered by selfish iso- lation, produce barriers which would increase and gulfs which would widen ; but the iron horse, the ocean grey- hound, and the subtler electric fluid are for ever making the men who speak the same tongue shake hands again. To the pioneer surveyor, however, the field available for TI Preliminary Survey new enterprise is rapidly becoming less, whilst the number of surveyors increases. It becomes, therefore, more and more important for those who leave our shores to possess the handiest and most efficient instruments, to know the best and most rapid methods of using them, and to understand the diverse conditions of the countries to which they go. The members' list of the British Institution of Civil Engineers has now reached the colossal total of about six thousand. These figures alone would serve to show the extent of the demand for foreign employment, for certainly there is not enough home work to go round so many ; but, especially in the department of surveying, the Institution list gives but little idea of the number of young men who are issuing year by year from pupilage or college with their eye on our distant dependencies. It is furthermore a noteworthy fact that, especially for surveyors, although the field of engineering enterprise is be- coming greater and greater, the colonial door is closed to young Englishmen, just as soon as men can be trained abroad. Both in Canada and Australia, a diploma is needed to qualify a man to practise as a land-surveyor ; the studies for which cannot be easily pursued in England. In the case of India the Government have met the difficulty by giving their men the special training needed for that country at Cooper's Hill College, but the door is closed to others. In the Colonies the reason of this is because in the first place Australians are independent in their ideas, but also very much because the young English surveyor is too often an importer of instruments of which he knows little into a country of which he knows less, so they prefer to educate their engineers on the spot. Introduction vii Things have changed for the better, no doubt, but about twenty years ago it seemed as if the English engineer were educated as much as possible in things he could not use, and as little as possible in things which would be needed by him in a new country. The writer enjoyed the last two years of the lectures of one of the most celebrated professors of engineering of his day, and purchased the whole of that scientist's textbooks ; but it is a significant fact that one of the former students earned his living by explaining after the lecture what the professor had meant to convey to his hearers. Finding a year or two afterwards that he could get the kind of information he wanted in a smaller compass and simpler language the writer parted with his little library of textbooks. The same drawbacks attended the pupil in the engineer's office as the student in the university. Men were not then made to keep their levels in adjust- ment, but allowed to run to the nearest instrument-maker. They were never taught the American method of levelling or curve-ranging, and the road and railway making which they learned was that which was suitable to a country like England, but of little use for the Colonies. The con- sequence has been that when they arrived there they were thrown upon their own ingenuity, and produced a conglome- rate of different types of construction upon different gauges, which has been the reverse of profitable to the investors and without reflecting much credit upon themselves. On the Canadian Pacific Railway the writer rarely met a young engineer fresh from England who could quickly adjust his level or theodolite or who knew anything of the American system of curve-ranging or had the least notion of telemetry. viii Preliminary Survey It has been the fashion to criticise America for her cheap railways, her numerous gauges, her erroneous curve-ranging, and in fact everything that was not the way we do it in England. This has been the language of those who have either not been there or who have not understood the methods adopted there when casually observing them with a biassed judgment on a passing visit. The American is just an Anglo-Saxon like ourselves, only with a little more liberty and a great deal more scope. He is not at all ashamed to come and learn from the old country what age and experience have qualified her to teach him, but in the handling of a virgin colony, with great undeveloped resources, we may do well to learn of him. In simplicity of survey practice, uniformity of gauge, types of bridges and of rolling stock, the American engi- neer may be profitably (though not slavishly) imitated in the work of opening out a new sphere of enterprise such as our recently acquired colonies, and it is to be hoped that, profiting by past experience, English engineers will fuse their ideas into something like uniformity and produce a harmonious construction. The methods of surveying considered in the following pages are by no means exclusively American. In the class of work formerly called telemetry, but now tacheo- metry, we have to go to Italians, French, and Germans for most of the original conceptions and the best modern developments. Comparatively few English engineers really practise these methods unless they have learned them abroad, although some are thoroughly proficient in them. The title of this book, ' Preliminary Survey,' is American, and answers somewhat to our ' Parliamentary Work ; ' but it covers a wider range, in fact the whole science of surveying Introduction ix in condensed form with the exception of those minute details where very great accuracy is needed. The object in view has been to present to the young engineer going abroad a handy vade-mecum which with the necessary tables will enable him to carry out a survey in a new country rapidly, correctly, and according to the ideas and requirements of the people. It has also been sought to furnish in the first and third chapters an aide-memoire to the expe- rienced surveyor for his assistance in roughly estimating the cost of the proposed works, and so to guide his decision in the case of alternative routes and situations. Considerable use has been made of standard authorities on both sides of the Atlantic, but the subject matter is in the main the result of actual experience. The necessary compactness of such a work has made it eclectic. Some methods have been passed over with slender comment, although occupying much space in other textbooks. On the other hand such subjects as tacheometry, computation by diagram and slide-rule, signalling, &c., which are as yet hardly known to the general public except in pamphlet form, are here treated of at considerable length. An attempt has been made to explain the elements of astronomy, as far as they are needed in the simple problems used by the surveyor, in such a manner as will be understood by those having no previous knowledge of the subject, and a great many of the definitions which take up much space in ordinary textbooks have been placed in a glossary. No tables are given which are to be found in the Nautical Almanac or in ordinary mathematical tables, as these have to form part of the surveyor's impedimenta. The following extract from the statute book of the Dominion of Canada will give a fair idea of what the x Preliminary Sutvey pioneer surveyor in any of the colonies should know, both in theory and practice. Both in Australia and India survey practice is carried on very much in the American manner. The subjects enumerated in the Canadian statute are not treated so much in detail in this work, in order to leave space for other subjects, such as tacheometry and curve- ranging, which are equally useful to the railway man. The author desires to express his acknowledgments for a great deal of useful material to the following gentlemen who have kindly given their courteous permission to use tables, maps, diagrams, and formulae in works of which they are either the authors or custodians : James Forrest, Esq., Secretary Inst. C.E. and editor of ' Minutes of Proceedings.' Captain Wharton, Hydrographer to the Navy, and author of ' Hydrography.' A. M. Wellington, Esq., C.E., editor of 'Engineering News,' New York, and author of standard works referred t'o in the text. John C. Trautwine, Esq. (jun.), editor of Trautwine's < Pocket Book.' Other authorities on different subjects have been also referred to, and acknowledged in different parts of the book. The calculations in chapters three and eight have been very kindly checked by an old friend, Mr. William T. Olive, Resident Engineer on the Manchester Main Drainage ; most of the other figures have been checked in one way or another, but it is possible in a first edition that errors may still remain undetected, and any information as to mistakes in the text, figures, or diagrams will be gladly welcomed by the author. Introduction xi QUALIFICATIONS OF THE DOMINION LAND AND TOPOGRAPHICAL SURVEYOR Excerpt. 49 Victoria, Chapter 17. Royal assent, May 25, 1883. (Dominion of Canada.} 99. No person shall receive a commission from the Board of Examiners authorising him to practise as a Dominion land surveyor until he has attained the full age of twenty- one years, and has passed a satisfactory examination before the said Board on the following subjects ; that is to say : Euclid first four books, and propositions first to twenty-first of the sixth book ; plane trigonometry, so far as it includes solution of triangles ; the use of logarithms, mensuration of superficies, including the calculation of the area of right-lined figures by latitude and departure, and the dividing or laying off of land ; a knowledge of the rules for the solution of spherical triangles, and of their use in the application to surveying of the following elementary problems of practical astronomy. 1. To ascertain the latitude of a place from an observa- tion of a meridian altitude of the sun or of a star. 2. To obtain the local time and the azimuth from an observed altitude of the sun or a star. From an observed azimuth of a circumpolar star, when at its greatest elongation from the meridian, to ascertain the direction of the latter. He must be practically familiar with surveying opera- tions, and capable of intelligently reporting thereon, and be conversant with the keeping of field notes, their plotting and representation on plans of survey, the describing of land by metes and bounds for title, and with the adjust- xii Preliminary Survey ments and methods of use of ordinary surveying instruments, and must also be perfectly conversant with the system of survey as embodied in this Act, and with the manual of standing instructions and regulations published by the authority of the Minister of the Interior from time to time for the guidance of Dominion land surveyors. 102. Any person entitled to receive, or already possess- ing a commission as Dominion land surveyor, and having previously given the notice prescribed in clause 98 of this Act, may be examined as to the knowledge he may possess of the following subjects relating to the higher surveying, qualifying him, in addition to the performance of the duties declared by this Act to be within the competence of Dominion land surveyors, for the prosecution of extensive geodetic or topographic surveys, or those of geographic exploration, that is to say : 1. Algebra, including 'quadratic equations, series, and calculation of logarithms. 2. The analytic deduction of formulas of plane and spherical trigonometry. 3. The plane co-ordinate geometry of the point, straight line, the circle, and ellipse, transformation of co-ordinates, and the determination, either geometrically or analytically, of the radius of curvature at any point in an ellipse. 4. Projections : the theory of those usually employed in the delineation of spheric surfaces. 5. Method of trigonometric surveying : of observing the angles and calculating the sides of large triangles on the earth's surface, and of obtaining the differences of latitude and longitude of points in a series of such triangles, having regard to the effect of the figure of the earth. 6. The portion of the theory of practical astronomy Introduction xiii relating to the determination of the geographic position of points on the earth's surface, and the direction of lines on the same, that is to say : Methods of determining latitude. a. By circum-meridian altitudes. b. By differences of meridional zenith distance (Talcott's method). c. By transits across prime vertical. Determination of azimuth. a. By extra-meridional observations. b. By meridian transits. Determination of time. a. By equal altitudes. b. By meridian transits. Determination of differences of longitude. a. By electric telegraph. b. By moon-culminating stars. 7. The theory of the instruments used in connection with the foregoing, that is to say, the sextant or reflecting circle, altitude and azimuth instrument, astronomic transit, zenith telescope, and the management of chronometers ; also of the ordinary meteorological instruments, barometer (mercury and aneroid), thermometers, ordinary and self- registering, anemometer, and rain gauges, and on his know- ledge of the use of the same. 15 GREAT GEORGE STREET, LONDON, S.W., 1890. CONTENTS INTRODUCTION PAGB Extent of the demand for surveyors. Necessity for adaptation to the requirements of a new country. Objects aimed at in the present work. Statutory qualifications of the land and topo- graphical surveyor for the Dominion of Canada v CHAPTER I GENERAL CONSIDERATIONS Qualifications of the pioneer surveyor. Subject matter of a pre- liminary report. Extent to which general considerations affect the location. Tables of resistance to traction from gradients and curvature. Abt system. Cape railways. Rule for finding amount of traffic necessary to pay a given dividend. Maximum amount of business with a single line. Arrangement of curves and gradients. Tables of ditto on American and Australian railways. Rough estimates for railways, highways, and tram- ways. Cost of plant ........ i CHAPTER II ROUTE-SURVEYING OR RECONNAISSANCE Pioneering for railway location in America. Methods suit- able to different circumstances. Sketching. Photography. The plane-table and prismatic compass. The meridian by the plane-table. Traversing with plane-table and stadia. Traverse with passometer, aneroid, and pocket altazimuth- Profile and xvi Preliminary Survey PAGE contours by ditto. Surveying with the sextant. Range-finding with a two-foot rule. Distance-measurement by time, by horses' and camels' gait, by patent log, by revolutions of the propeller. Mapping by plane-construction, by conical projec- tion, by stereographic projection. Mercator's projection. . 30 CHAPTER III HYDROGRAPHY AND HYDRAULICS Coast-lining. Boat-survey. Running survey from the ship. Distance-measurement by gun-fire. Gnomonic projection. Symbols in charting. Sun -signalling. Flag-signalling. The Morse code. Tides and currents. Hydraulics. Kutter's formula and diagram. Discharge from tanks, cisterns, and weirs. Diagram for ditto. Trautwine's approximate rule for discharge of pipes under pressure. Ditto for discharge over weirs. Horse-power of falling water. Efficiency of water- wheels. Horse-power of a running stream. Hydrostatic pres- sure and diagram. Notes on dredging, dredging plant, boring, concrete and dock work . . . . . . .81 CHAPTER IV GEODETIC ASTRONOMY Compared with nautical astronomy. General principles. ' Gain- ing or losing a day.' Classification of methods. Observations for determining the meridian. By equal altitudes. By cir- cumpolar stars in same vertical. By time interval of culmina- tion of circumpolar stars. By pole star at elongation. By solar azimuth. Observations for local mean time and longi- tude. Table for reducing arc to time, and vice versd. Time by solar transit. By solar hour-angle. Sidereal hour-angle. Absolute methods ' of determining the longitude. Jupiter's satellites. Lunar occultation. Lunar distance. Terrestrial difference of longitude. Moon- culminating stars. Observa- tions for latitude. Rules for different cases in both hemispheres. By circumpolar stars. By meridional altitude of a fixed star. By meridional altitude of the sun. By an altitude of the sun cut of the meridian. By two altitudes of the snn or a star. Graphic latitude . . . . . . . . .116 Contents xvii CHAPTER V TACHEOMETRY PAGE Derivation. Definitions. History and first principles of stadia measurement. Method of putting in stadia-hairs to any required reading. Analogy of tacheometry with celestial parallax. Limits of error. Different types of telescope. Different methods of holding the stadia- staff. Comparison of results. Surveying with the tacheometer. Auxiliary work to ditto. Description of the author's methods in the Sandwich Islands. Reduction of the traverse to difference of latitude and departure. Ditto to longitude and latitude. Levelling with the tacheometer. Contouring. Plotting the profile. Sketch of a Hawaiian ravine with part of a horse-shoe curve and contours. Tacheometric curve-ranging. Mr. Lyman's conclusions on stadia-telescopes. The plane-table and stadia. Time occupied in tacheometric survey . . . . .15^ CHAPTER VI CHAIN-SURVEYING Application to preliminary survey. Chaining. Sources of error. Setting out a square. Deflection distance. Surveying with chain only. With chain and cross-staff. Fieldbook. Areas. Traverse with transit and chain. Different methods of fieldbook. Curve-ranging with the chain only. Krohnke's tangential system. Jackson's six-point equidistant system. Kennedy and Hackwood's method. Method by offsets without a table . 194 CHAPTER VII CURVE-RANGING WITH TRANSIT AND CHAIN Properties of the circle and general nomenclature. Confusion arising from diversity of terms. Advantages of decimal gradua- tion. Fundamental problems. Different methods of keeping the fieldbook and specimens. Curve-ranging by tangential angles. Dalrymple-Hay's curve-ranger. Parallel tangents. a xviii Preliminary Survey PAGK Reverse curves. Turn-outs. Transition curves. The ' tramway ' spiral. The ' horse-shoe ' spiral. The 'mountain ' spiral. The ' trunk-line ' spiral ........ 209 CHAPTER VIII GRAPHIC CALCULATION FOR PRELIMINARY ESTIMATES Objects of preliminary measurement for estimates. Use of diagrams. The slide-rule for ordinary arithmetic. Proportion. Multiplication. Division. Involution and evolution. The slide-rule as a universal decimal scale. Calculation of slopes and gradients with tables and slide-rule. Table of squares and square- roots. Table of railway sleepers for all gauges. Measurement of earthwork by diagram and slide-rule. Measure- ment of iron bridges by diagram and slide-rule. Stone and brick bridges by diagram and slide-rule. Service diagram for railways and tramways. Centrifugal force. Reduction of thermometer scales. The slide-rule as a universal measurer. Circles. Areas. Volumes. Weights and measures, with tables. Tree-timber. Permanent way. Angle and tee iron. Round and square iron. The slide-rule as a ready reckoner. Wages table. British and foreign money . . . .241 CHAPTER IX INSTRUMENTS Levels and their adjustment. Levelling. Level-staves. Theo- dolites. The ' Ideal ' tacheometer. The sketch-board plane- table. Pocket altazimuths. Passometers and pedometers. Sextants. The solar compass. The heliostat and heliograph. Principles of telemeters. Eckhold's omnimeter. The Wagner- Fennel tacheometer. The Dredge-Steward omni-telemeter. The Weldon range-finder. The simplex range-finder. The Bate range-finder. The aneroid barometer. The boiling-point thermometer. Hypsometry and diagram. Drawing instru- ments. The slide-rule. The protracting tee-square. Im- provised protractors. The eidograph and pantagraph. The planimeter. Stanley's computing scales. The station-pointer. Books. Mathematical tables. Field and MS. books. Stationery . ' ". ;..-., . . . . . 286 Contents xix APPENDIX PAGJt Functions of right-angled plane triangles. Functions of oblique plane triangles. Functions of right-angled spherical triangles. Functions of oblique spherical triangles. Tables for azimuth by circumpolar stars. Table for transition curves Tables of specific gravity 373 GLOSSARY .......... 391 INDEX . 416 LIST OF PLATES PLATE I. FIG. 26, KUTTER'S FORMULA . . . To face page 100 II. FIGS. 28, 29, THEORETICAL VELOCITY IN FEET PER SECOND, MILES PER HOUR DUE TO GIVEN HEAD . . ,, ,, IO6 III. FIG. 30, COEFFICIENT in IN TRAUTVVINE'S FORMULA FOR FLOW IN PIPES . ,, ,, 108 FIG. 31, COEFFICIENT r IN TRAUTVVINE FOR FLOW OVER WEIRS . . . . ,, ,, 108 IV. FIG. 32, HYDROSTATIC PRESSURE . ,, ,, no V. FIGS. 75, 76, EARTHWORK . . . . ,, ,, 252 VI. FIGS. 80, 81, IRON BRIDGES . . . ,, ,, 256 VII. STONE ARCHES ,, ,, 258 VIII. TIMBER TRESTLES 259 FIG. 82, SERVICE DIAGRAM FOR TRAMWAYS On ,, 261 FIG. 83, ,, ,, RAILWAYS ,, ,, 262 IX. FIGS, no, iii, BAROMETRICAL PRESSURE . To face ., 350 PRELIMINARY SURVEY AND ESTIMATES CHAPTER I GENERAL CONSIDERATIONS THE following remarks will be more applicable to railway reconnaissance, though much of the principle contained in them is also that which guides the surveyor for trunk roads for military or commercial transportation. QUALIFICATIONS OF THE SURVEYOR The man who is first in the field should be a man of wide range of experience rather than a minute technologist. He is usually given much discretionary power as to his location. He has also advisory powers, or rather duties, which are great responsibilities. He is called upon to report upon the scheme from a bare possibility down to a desirable investment. Before engaging his services, the promoters have generally made up their minds that there must be * money in it,' and they want, like most other people, to obtain a maximum of good showing for a minimum amount of outlay. The surveyor is generally disposed to favour a new 2 Preliminary Survey undertaking, because, however much or little money there may be in it for him, there is likely .to be ' work in it,' and he has often to resist the natural tendency to make too good a showing. There are several considerations which likewise influence him in this direction. Shareholders always expect a sanguine report, and take discount off it in any case ; so that a mode- rate report is to them a bad one. There is a moral certainty that, however carefully a walk-over survey may be made, a revised location will show a material improvement in the line of economy or efficiency, or both, and therefore the surveyor is tempted to make allowance for this in his trial profile. He is, perhaps, well aware that the nearer his profile resembles the surface of a billiard table the better he will please his employers. When the country is so rough that chaining is out of the question unless he is able to adopt one of the rapid methods to which these pages are meant to draw attention a large element of conjecture enters into his calculations, and he is naturally disposed to conjecture favourably rather than critically. SUBJECT MATTER OF A RAILWAY REPORT The surveyor is generally called upon to advise his promoters 1. Whether any kind of line is feasible. 2. Whether it is likely to be profitable. 3. What type of railway would be most suitable, and what style of rolling-stock. 4. He is to furnish a plan, profile, and estimate of one or more routes which he considers eligible. All these points are closely connected. One kind of line is feasible where another is wholly impracticable ; a light, cheap railway will often yield a handsome dividend where a heavy line would never emerge from the hands of a receiver. General Considerations 3 On the other hand, a light railway built to carry heavy traffic will probably be wedged out of existence by a higher-class competing line. The style of rolling-stock procurable to handle the business often regulates the location as much as the location rules the rolling-stock. The route is dependent on the topography to a great extent, but the situation of towns with which communication is necessary often overrides the consideration of topography. It is only experience which can enable an engineer to form rapidly and correctly the general idea of the class of line suited to the circumstances. If, as is often the case, gauge and rolling-stock are fixed factors in the problem, there remain the questions of grades and curves, which must be to a large extent dependent upon the topography, and it is there that the judgment of the surveyor is most needed, both in the limiting and the arrangement of these vital elements of a railway. With regard to the first point of feasibility. This has almost dropped out of the reckoning of to-day. It may be taken for granted that a railway can be constructed nearly anywhere. The only insurmountable difficulties to railway projects are, first, lack of funds ; second, opposition of vested interests. It is another thing when we come to the question of Whether it will pay. Here the engineer has to study, i. What the existing traffic of the district is, and how it would be likely to be affected by the introduction of a rail- way. 2. What is the probability of the traffic being handled by some other means of transit in competition. 3. What rates can be commanded, and whether it will be in the main a through or a local traffic. 4. What is the outlook for development of the business, with any possibly counteracting causes. 5. Probabilities of another competing railway in the future. All these subjects dovetail themselves into the actual reconnaissance of the route ; engineering difficulties give B 2 4 Preliminary Survey way to commercial exigencies and vice versa, until the sur- veyor has evolved his ideas of a line with maximum efficiency at minimum cost which will command the maximum amount of business. The climate in which the undertaking is to be carried on is a very important consideration. In tropical climates the use of timber is to be avoided where possible, on account of predatory insects and the rapid decay produced by alter- nations of hot sun and heavy rains. The rainy season regularly changes the trickling rivulet into the mighty river, and these actions of the weather greatly affect the construction of culverts and bridges, and therefore, indirectly, the location. In some places streams are turned into tunnels to save build- ing culverts, and an overflow channel provided at the junction of an embankment and side-hill for abnormal freshets. In cold climates snowsheds are a very costly item, and the study of the principles of drifting snow will often modify the location. The general topography also radically affects the location. It rules both gradients and curvature and the type both of gauge and equipment. If the land falls toward the seaboard, with a heavier export than import trade such as a mineral railway which only takes back lumber, agricultural produce, and so forth the gradients can be steeper than would be otherwise permis- sible ; the rule being then to adopt that which can be sur- mounted as a contrary grade by the light traffic. The method of ' bunching,' or concentrating the severe gradients in order to handle them specially, is a very im- portant one. The best policy for a new country is to carry long trains as far as possible with one engine, and then to divide them on a turn-out and take them over the climb in sections, or else to provide an assistant engine for the district. The following table (No. XXIV. of Mr. Wellington's standard work on American ' Railway Location ') shows the General Considerations engine ton-mileage required to move i ton of net load (ex. engine) .TOO miles on a level, except for a rise of 2,400 feet on different grades, worked with assistant engines : according to the average daily experience of American railways. TABLE I. Traction on Grades. Engine ton-mileage per ton of Rate of Length Length of net load moved 100 miles incline incline track While on While on incline level track \ feet per mile miles miles 24 IOO 1-056 056 30 60 40 0-862 O'2IO '072 80 30 70 0760 0-369 -129 100 2 4 7 6 0755 0-400 T55 120 20 80 0-766 0-42I -187 150 16 84 0-803 0-442 1-245 2OO 12 88 0-900 0-463 1-363 ' It would be seen that the rate of incline had an incon- siderable influence on the motive power required, for the reason, largely, that the length of the run on which large power was required decreased paripassu with the increase of rate, which was not the case with through grades. ' In this table moreover it was assumed that the total length of the road remained uniform at 100 miles, whatever the rate of grade adopted for the high-grade section. This is ordinarily quite out of the question, the lower grade being usually attainable only by adding so much further develop- ment within an approximately uniform air-line distance. 4 Assuming, for example, that in the above table eighty miles of level track was essential in any case, and that in the remaining air- line distance of twenty miles, any one of the above rates of pusher-grades from twenty-four to 200 feet per mile was obtainable, but only by development a rather extreme assumption, but sufficient for illustration the table would thus read : ' Preliminary Survey TABLE II. Traction on Grades. Rate of Length Engine ton-mileage per ton of net load moved between the incline grade. Incline Level TO- rasr While on level track Total ft. per mile miles miles miles 24 IOO 80 1 80 I-056 0-421 '477 30 60 80 140 0-862 0-421 283 80 30 80 110 0760 O'42I 181 IOO 24 80 IO4 0755 0-421 176 1 2O 2O 80 IOO 0766 0-42I 187 150 16 84 IOO 0-803 0-442 245 2OO 12 88 IOO O-QOO 0-463 363 TABLE III. Adjustment of Gradients for Assistant Engines, according to the Average Daily Performance on American Railways. (H. M. Wellington. ) \ Grade at which the same train can be drawn by the aid of Ruling grade One assistant engine Two assistant engines worked by one engine in feet Heavier by Of equal ' Ofeaual Heavier by per mile weight on drivers 20 P er 40 per , weight on drivers 20 per 40 per | cent. cent. cent. cent. 1 level 24 29 33 46 54 62 IO 42 48 53 70 80 90 20 59 66 72 92 104 116 30 76 84 91 "3 126 138 40 92 101 109 133 147 1 60 fo 107 122 117 126 133 142 152 169 167 185 180 199 70 136 148 158 185 201 2l6 80 15 162 173 201 217 232 90 164 176 187 216 232 247 IOO 177 189 201 230 247 26l no 190 202 214 120 203 215 227 I 3 215 227 239 , I4O 227 239 251 'SO 238 250 262 - General Considerations 7 Caution. In calculating the increase of motive power due to severe gradients, the wear and tear on locomotives, such as the ' thrashing ' of an engine up a steep incline by an inexperienced driver, is an item which, though difficult to calculate, should be allowed for by a large margin. The assumptions in the above table are that the rolling friction on the level is 10 Ibs. per ton ; for lower frictions the gradients are proportionally lessened. The gradients are compensated for curvature. A good method of overcoming steep gradients is by the Abt rack system. The special feature about it is that sections of mountain line can be worked thus without changing gauge or altering the rolling stock. The loco- motives do not depend on adhesion, therefore they can be much lighter just where the construction of bridges is the most serious item. The Abt system is also specially adapted to short branch mountain lines. The notes and memoranda that the surveyor wants are to give him a general but accurate idea of the alternative advantages of the different schemes that arise, and it is with that object that the chapter on Graphic Calculation has been added ; condensed to its utmost limit. In selecting a route and deciding upon the class of line for a railway scheme it should be considered First: If a competing line, how to obtain a pronounced superiority to the existing one, either on the score of efficiency or economy. Second : If the first in the district, how without wasteful expenditure to secure primacy. That is to obtain a line which will so handle the existing and prospective business as to hold its own, and that the best, of the business. In order to ensure that his line will be suitable to the future mode of working it, the surveyor should be acquainted both with the ordinary and the special types of rolling-stock that are to be used. In new countries it is essential to 8 Preliminary Survey economy that the engines and cars should be flexible, not only as regards side-play, but also, if one may coin the term, ' up and down ' play. It is furthermore necessary that level crossings should be permitted over all country highways, and, when on the level prairie, over existing railways also. Station buildings should be very primitive, and the booking performed on the train. It was stated by Mr. J. C. Mackay at the Institution of Civil Engineers in 1886, that 'the present railways of the Cape Colony had been constructed on a lavish scale with rails weighing 60 Ibs. per yard, and expensive stations, some of them costing over 2o,ooo/., while the railways alone had cost 8,ooo/. per mile. This great expenditure had been incurred for the sake of conveying one tram per day, in some cases only one train every other day, and the consequence was that the revenue did not pay one half the interest on the loan, after deducting working expenses, and the working of these lines was obliged to be carried on in such a manner that the bullock waggon competed successfully with the rail- ways. 'At Kimberley, with its 1,500 passengers and 350 tons of goods per mile of railway per annum, a line with rails of 60 Ibs. per yard, and expensive rolling-stock and stations, had been adopted.' The writer is not in a position to verify at the moment the accuracy of these figures, nor to state to what extent they may be modified by subsequent development of the districts ; but as they stand, reflecting most adversely upon the judgment of the promoters and the engineers, it should be added as a qualification that they only serve to show one side of the question, but that which needs to be most emphasised for a new country the danger of put- ting old-country ideas upon young-country shoulders. The counter-evil of putting down poor lines where there is busi- ness for good ones, probably to pad the promoters' pockets, General Considerations g has plenty of illustrations both at home and abroad, and the engineer is too often compelled against his judgment to make both his location and construction suit the ' spirit of the times.' The former evil of wasteful or even premature expendi- ture is one which greatly checks the inflow of fresh capital into a country. A receiver is a perfect scarecrow to fresh enterprise. Purely speculative railway-making is as great a hindrance to bona fide undertakings as jerry-building in its smaller sphere ; whether it come in the form of too good or too bad a line of railway. A single line with properly arranged passing places, rails 30 to 40 Ibs. per yard, engines of 15 to 20 tons, in easy country, can be built for 4,ooo/. per mile, including the equipment, in almost all parts of the globe ; provided that the line starts from the seaboard, or from a place in rail- connection with the seaboard. This line, properly located, is capable of handling 1,000 tons of freight per day, and is, therefore, even with low rates, in a position to yield a handsome profit to the investors. Putting net receipts at \d, per ton-mile, it would return 9 \ per cent, on the cost of construction with that volume of business. APPROXIMATE RULE FOR FINDING THE AMOUNT OF TRAFFIC REQUIRED TO PAY FIVE PER CENT. ON THE COST OF CONSTRUCTION OF A RAILWAY. Assumptions. Tariff, 75^. per ton-mile for passengers and freight. Passengers reckoned at two tons each. Expenses -50^. per ton-mile. Net receipts, -25^. per ton- mile. 365 days to the working year. Traffic in tons per diem = cost in per mile x '1315. Example : On a road costing 4,ooo/. per mile, the traffic needed in tons per diem=4,ooo x '1315 = 526. The amount of traffic required varies inversely as the net value of the receipts per ton-mile. io Preliminary Survey Therefore for any other net value such as -53^. per ton- mile, the amount of traffic is found by the slide-rule in the following manner : Place the given value -53^. on the upper scale of the slide under the '25 on the rule. Find the required multiplier 0-62 on the rule opposite to the 1315 on the slide. Leave the brass marker at 62 on the rule, and make a i of the slide coincide with it. Then the result, 248 tons, will be found on the rule opposite to 4,000!. cost, or 186 tons opposite to 3,ooo/. cost and so on. CONVERSE RULE To find the percentage on cost of construction when the argument is : 1. The tonnage of freight per day (average of 365 days). 2. The net profit per ton-mile in decimals of a penny. 3. The cost of construction of one mile in sterling. Multiply the tonnage by the profit. Divide the product by the cost of construction. Multiply the quotient by 152-1. Result is the percentage. Example. Data are : Daily tonnage . . . .542 Net receipts per ton-mile . -47^. Cost of construction per mile . 46507. BY SLIDE-RULE, USING LOWER SCALES OF SLIDE AND RULE Place a i of the slide over the 542 (tonnage) on the rule. Place the brass marker at 47 (receipts) on the slide. Place 465 (cost) on the slide at the marker. Place the marker at the right-hand i of the slide. Place the left-hand i of the slide at the brass marker. Read the percentage General Considerations II 8-34 on the rule opposite to the constant 152-1 on the slide. 1 (The operation can be done in about 35 seconds.) Mr. Robert Gordon in his paper on Economic Construc- tion of Railways, ' Min. Proc. Inst C.E.,' gives a note on the problem of the maximum capacity of a single track, quoting from Mr. Thompson of the New York, Pennsylvania, and Ohio Railroad ('Railway Gazette,' 1884, 1-43). He says that for trains running an average of twenty miles per hour, the most economical speed for freight, the maximum is reached with stations 37 miles apart, when with an allowance of six minutes' detention for each train crossed, and eight minutes extra for each passenger train passed, it is found that the limit is reached when the time of detention equals that of running in the 24 hours, which gives sixty trains per day both ways. For fifty trains and over, the track should be doubled between the termini and the next stations. In practice it is found that grades limit the number of cars run in a train, so that, if forty loaded cars be the ordinary number on the level, only twenty are taken over an undulating country by a single engine. Actually, on Mr. Thompson's division, 98 miles in length, the Standard engine takes nineteen cars, the Mogul twenty- three cars, and the Consolidation thirty-three cars each per train. 2 The type of railway is affected first of all by grade. There 1 For the explanation of the principle of the slide-rule see pp> 242, &c., also 361, &c. 2 The total annual expenses on railroads in the United States usu- ally range between 65 and 130 cents (2s. %\d. and $s. $d.} per train- mile, that is, per mile actually run by trains. Also between I and 2 cents (| and id.} per ton of freight and per passenger carried one mile. When a road does a very large business, and of such a character that the trains may be heavy and the cars full (as in coal-carrying roads), the expense per train-mile becomes large, but that per ton or passenger small ; and vice versa, although on coal-roads half the train-miles are with empty cars. Trautwine's ' Engineer Pocket Book. ' , See also, at p. 21, Table of ' Earnings of American Railways. ' 1.2 Preliminary Survey can be no question that there are many light narrow-gauge railways which are earning a good return on the capital which could not have kept their heads above water as standard- gauge railways. It is true, on the other hand, that a very large mileage of narrow gauge is every year being converted into standard gauge, in order to avoid breaking bulk. Surveyors are not gifted with prophecy to know what the changes of the next fifty years will be, but a fair amount of experience will enable them to tell whether the line will always remain a feeder, or whether it is likely to form part of a trunk line. The narrow gauge enables the engineer to adopt curves of very small radius, but then he must keep to a flexible type of locomotive and car which involves lighter loads and less speed ; consequently, less business done for the same labour and superintendence. A theoretically perfect railway is an air-line on a dead level between two points, and yet, apart from its cost, in nine cases out of ten it would not be the best line. A great deal of the sinuosity of a well laid-out railway in a new country is productive. It carries the trains to where the business is or where it is going to be. Sometimes the local traffic is the major part of the busi- ness. It generally commands a higher rate than through traffic, and it would be a serious mistake to straighten a line to catch through traffic of small bulk carried at cut-rates and by so doing to lose a steady monopoly of a lucrative local business. Bad gradients are worse than sharp curves ; the latter can be to a great extent mitigated in their discomfort by well-made carriages ; in their resistance by flexible locomo- tive frames ; and in their danger by careful signalling. But gravity no skill can dispose of, and bad gradients have killed many a promising line. Considerable opportunity exists in every line ot railway for arrangement of the curves and gradients so as to make General Considerations them as little objectionable as possible. The first question for the surveyor is whether or not the construction is to be homogeneous. If, for instance, he has to traverse level prairie for fifty miles, then cross a range of hills 3,000 feet high within an air-distance of another fifty miles, then another stretch of prairie of fifty miles, he has to consider whether it would be advisable to develop his mountain section for better gradients or whether he should arrange the line for a different class of locomotives in the three sections. "All this affects the location. The two main points to be borne in mind with regard to curvature are the speed at which trains will have to run and the kind of rolling-stock which will have to be carried. The following Tables IV. to IX. from Mr. Wellington's book already referred to will be found useful in fixing the limit of curvature and gradient to be adopted on a new line. The American curve-nomenclature is explained in Chapter VII. TABLE IV. Resistance on Curves. Length of wheelbase Resistance on 4 curve at 10 miles per hour Type of engine Weight Rigid Total Total Ibs. per ton Ibs. per degree American 101,000 7' 6" 21' I0f" 1963 39-0 975 Ten-wheel . 123,000 12' 5 " 23' 8" 175 28-4 7-1 Consolidation 136,000 H' 6| 21' I" 1850 2O 'O 5'o Note. Consolidation engines are made to run round a Wye (see p. 240) with curves of 136 feet radius without any trouble. Curvature per mile on some of the Railways in the Rocky Mountains. Average degree per mile 34 Name of Railway Colorado Central . Virginia, Truckee . Union Pacific Texas Central Southern Pacific , Length of section. miles 22 65 H3 142 420 278 59 247 63-6 1.4 Preliminary Survey TABLE V. Curvature and Grades on Sections of Eastern Trunk-roads. Name of road Miles Curvature per mile Per cent, curved Degrees per mile Per cent, level o. w |1 Rise and fall per mile Ruling Grades New York Central 296-6 0-78 ig'8 iS'i ,4-8 1-8 3 '8 21-23 Boston and Albany 202 'o 1*55 56'o 72-5 o'o 9'3 T 3'7 So Concord and Ports mouth .... 4o'o 1-41 37 '2 3'8 19*0 i5'3 80 Ulster and Delaware Montrose Penna . Summary of N. East ern States . . 73 '2 27-2 5,372 3'6o 6 '35 i'88 41-0 49-0 35'5 80-5 24*1 55*9 13-6 3 '9 22-8 24'! 4'7 ji'6 9-6 13*0 160-142 95-74 The column ' Rise per mile ' gives the average excess of rise over the fall in one mile. The next column gives the feet of rise and fall. Thus, if a road rose 500 feet and fell 200 in 100 miles, it would be given above : Rise per mile 3*0, Rise and fall 2-0. The first quantity is an unavoidable necessity, due to difference of level at the termini. From the same work, on the authority of Mr. M. N. Forney, locomotive expert, it is stated that : (> , TABLE VI. Curve Limits far faced Wheel Bases. Feet rad. Axles 3 feet apart will roll in a curve of 67 ,, 4 >- . 91$ ,, 5 M 'S3 ,,6 174.1 ,, 7' ., M 251 8 ,, ,, ,, 337 ,, 9 479 10 ,, 6 43 | CENTRIFUGAL FORCE On any three curves having radii as i, 2, 3, the centri- fugal force at any given velocity is as 3, 2, i ; but the coefficient of safety against overturning or disagreeable effect is as v/3, ^2, V 1 = 173, 1-41, roo. General Considerations TABLE VII. Giving for various curves the inferior and superior limits of speed within which the centrifugal force is more or less objection- able or dangerous. Curve Maximum and minimum limits of speed in miles per hour Degree Minimum. Having Radius in feet no disagreeable effect Maximum. On the point of overturning the vehicle 2 2,865 41-39 130-89 4 i433 29-27 92-55 6 955 23-90 75*57 8 717 2070 65-44 10 574 18-51 5 8 -54 12 478 16-90 53-43 14 410 15-64 49'47 16 359 14-63 46-28 18 3i9 1378 43^ 20 288 13*09 41'39 22 262 12-48 39-46 24 240 "95 3778 26 222 11-61 36-72 28 2O7 1 1 -06 34-98 3 193 10-69 33-80 40 146 9-25 29-27 50 "5 8-28 26-lS 60 96 7-56 23-90 Rule. For the centrifugal force in Ibs. per ton of 2,000 Ibs. C= -02 3348 V 2 D, where C= centrifugal force in Ibs. per ton, V= velocity in miles per hour, and D= degree of curvature from which the following table is made. TABLE VIII. Curve Limits at Different Speeds. Speed in miles per Degree of curvature hour l0 5 10 15 20 10 2-33 11-67 23-35 35*02 46-70 2O 9-34 4670 93*39 140-09 18678 30 2I'OI I05-07 210-13 315-20 420-26 40 g 60 37-36 58-37 84*05 18678 291 "85 42O'26 373-57 583-70 840-53 560-35 875-55 1,260-8 747-14 I,l67-4 1,681-1 70 II4-4 572-03 1,144-05 1,706-08 2,288-1 1 6 Preliminary Survey The centrifugal force varies directly as the degree of curvature. The heavy division lines mark the assumed maximum limit of speed for safety, when the centrifugal force is=W. On the 4 per cent, grades of the Mexican Railway, re- versed curves of 150 feet radius were worked for a year with ordinary locomotives. Narrow-gauge railways have rarely been constructed with curves sharper than 24 in the United States, but there are a few as sharp as 30 in Colorado. In the writer's location of 3 ft. gauge railways in the Sandwich Islands ; curves of 40 (146 '2 ft. radii) were the minimum, but many of them were more than a semicircle ; previous railways had been constructed with 75 ft. radii in that district, but in most cases without necessity. The trains run at ten miles an hour with perfect safety, though it can hardly be called comfortable. There is practically no danger of the trains overturning because the loss of speed due to curvature keeps them well within the limits of safety. For rules on the same subject applicable either to feet or Gunter's chains, see p. 264. There is chronic trouble to railway managers from curves of unnecessary sharpness, put in either to save the trouble of a second revision, or from lack of experience on the part of the surveyor. It is true that rolling-stock can be made to go round almost anything, but not without suffering from it. It is a curious fact that single-line railways which have DOWN Vj, >- UP FIG. i. their crossing stations arranged in the usual way, as Fig. i, wear the locomotive wheels more on one side than the General Considerations 17 other. This arises from the trains always entering the stations faster than they leave them. Probably, if the crossing stations were made as shown in Fig. 2 this would not take place. It is a preferable arrangement, except DOWN vm => FIG. 2. where the through express trains run past the station with- out stopping, in which case the usual arrangement is to be preferred unless very flat curves are used in the switch on Fig. 2. EFFECT OF INCREASED DISTANCE FROM DEVELOPMENT, AND OF CURVATURE UPON WORKING EXPENSES The following notes and Table IX. are from Mr. Welling- ton's book, being deduced from extensive American statistics. Fractional changes of distance increase or decrease expenses by only 25 to 40 per cent, of the average cost of operating an equal distance. 600 degrees of curvature will waste about 50 per cent, as much fuel as the average burned per mile run. The lowest probable limit of curve-resistance at ordinary speeds in ordinary curves is about Ib. per ton per degree of curvature. With worn rails and rough track it may be as high as f Ib. per ton. Curve-resistance per degree of curve is very much greater on easy than on sharp curves, so that when, for ex- ample, the resistance is i Ib. per ton on a i curve, it may be 6 Ibs. to 8 Ibs. per ton on a 10 curve, and not more than 15 to 18 Ibs. on a 40 or 50 curve. The almost uniform increase in cost in the first three main divisions of the line is principally due to grades and curves, which get worse as the line stretches inland. c 1 8 Preliminary Survey TABLE IX. Running Expenses on Pennsylvania Railroad affected by Cuivattire. Average cost per train mile in cents Repairs Fuel Stores Total Eastern division . 6-42 6-93 i -ic 14-50 Middle division . j 8-87 7-00 1-07 16-94 Western division . 9*25 7-59 I'39 18-23 Mountain and Tyrone ... 6-60 7-04 0-83 J 4'47 COMPENSATION FOR CURVES Some of the various rules used in compensating steep gradients for curvature are given by Mr. Robert Gordon in ' Min. Proc. Inst. C.E.,' vol. Ixxxv. : 'The best American practice invariably allows com- pensation when the curve falls on a gradient by lessening the inclination as the sharpness of the curve increases. Some difference of opinion exists amongst the authorities as to the amount of reduction required, but the average given is 0*05 per i oo ft. per degree of curvature. 'This practice varies, however, and Mr. A. A. Robinson, , who has had great experience on steep gradients, gives as follows : TABLE X. Compensation for Curves. Per 100 feet per degree * Rate of maximum grade o to i in 166-0 compensation 0-06 ,, ,, ,, i in 166 to i in 62-5 ,, 0-05 ,, ,, iin62'5toiin 33-5 ,, 0-04 * Mr. Blinkensdorfer gives 0*03 to 0-07 in the same limits ; while Mr. Wellington allows 0*06 on all maximum curves. The practice also of widening the gauge on curves varies much. Some engineers allow only the same play of \ inch that is given on straight lines ; while others increase it \ inch and more on curves. But opinion is unanimous in requiring a tangent between reverse curves, and sharp General Considerations curves are eased off at both ends. In some cases gradients also are eased at the approaches.' The following tables are taken from Mr. Trautwine's ' Pocket- Book : ' TABLE XI. ; spine United States Railroads. \ .'-. Name of company Per mile of road Per train mile Per cent, of receipts $ cents Lehigh Valley, 1872 . 6 5| Pennsylvania Central, 1869 32,000 Philadelphia and Reading, 1859 . 54i 1868. 17,200 144 Connecticut, average of all the R. R., t 1861 \ 3,7Sl 95 57 Massachusetts, average of all the \ R. R., 1861 J 3,785 85 60 * New York State, average of all the ) R. R., 1867 1 13,856 76 New York Central, average of all the ) R. R., 1867 ) 15,620 170 77^ English R. R., averages for 1856-7-8 66 50 Scotch ,, ,, ,, 56 44 Irish ,, ,, ,, 5 2 40 TABLE XII. Statistics of several United States Narroiv-gauge Railroads for 1884. (Poor's Manual. ) ] Rolling-stock "B _ | ' .> oad and eq t per mile mual earni lile of road 1 penses -f- s earnings o o o 1 8! ra *- S3 3 e C t, MP ** PH fei o 6 V: a %& M 3 O Bridgton & Saco | Riv., Me. . . [ 2 16 2 2 i 16 $ 12,167 $ I,Tt2 $ 834 '75 Profile and Fran- ) conia, N. H. . f 3 H 3 7 6 15,43 1,346 640 48 Catnden and Mt. | Ephraim, N. J. f Bradford and ) Kinzua, Pa. . j 3 3 6 39 5 5 2 6q 13,645 14,922 2,868 i,793 2,642 r,7i7 92 '96 Denver and Rio ) Grande . . . J 3 1,685 239 "5 7- 5,676 35,ooo 3,519 2,573 '73 C 2 .20 Preliminary Survey TABLE XIII. Items of Total Annual Expenses for Maintenance and Operation of all the Railroads of the United States in 1880. (Poor's Manual. ) $ Per cent, per mile total Percent, of earnings Repairs of road, bed, and track 451 1 1 -23 6-82 Renewals of rails .... 197 4-89 2-97 Renewals of ties .... 122 3 '04 i-85 Repairs of bridges .... 102 i 2-55 i-55 Repairs of buildings 87 2-17 1-32 Repairs of fences, crossings, &c. Telegraph expenses 17 -42 41 i "oi 25 62 Taxes ...... 152 3-77 2-29 Maintenance of road and real i estate ' 1,169 29-08 17-67 Repairs, c. of locomotives 249 6-19 376 Repairs, &c. of passenger, baggage, j_ and mail cars . . . . J 120 2'99 1-82 Repairs, c. of freight cars 257 6-40 3-89 Repairs, c. of rolling-stock \ (including renewals and addi- 1 627 I5-58 9 '47 tions) . . . . . J Passenger train expenses . 137 2-07 Freight train expenses 330 8-21 4'99 Fuel for locomotives 374 9-31 5-66 Water-supply, oil, and waste . 70 1-74 i -06 Wages of locomotive runners and ) firemen . . . . . i" 310 772 4-69 Agents, and station service and ) supplies . . . . . ) 45i 11-23 6-82 Salaries of officers and clerks . 139 3-46 2-10 Advertising, insurance, legal ex- ) 6 1-8*7 penses, stationery and printing . J 123 3 1 07 Damages to persons and property 40 98 60 Sundries ..... 250 6-22 378 Running and general expenses 2,224 55'34 33-64 Aggregate annual expenses 4,019 lOO'OO 6078 General Considerations 21 TABLE XIV. Gross Annual Earnings per Mile, per Passenger Mile, and per Ton Mile, of some of the Principal United States Railways in 1880. _ Length in miles From passen- gers per mile of From passen- gers per passen- From freight per mile _r From freight per ton road ger mile ot road mile Pennsylvania R. R. 1,806 4,700 $ 0242 $ 15.615 0089 New York Central 994 6,651 O2OO 21,794 0086 Central Pacific . 2,447 2,237 0303 4,577 0249 Chicago, Burl., and Quincey. 1,805 i i,532 O24O 7,202 -on i Philadelphia and Reading . 780 3,429 O2OI 17,200! 'Oi6i Union Pacific 1,215 2,624 0320 ! 7,154 0199 Atchison, Topeka, and \ Santa Fe . . .1" i,398 1,144 0606 3,974 0209 Average of United States 87,801 1,641 0251 4,740 -0129 TABLE XV. Annual Earnings and Expenses of the above roads in 1880. Length in miles Gross earn- ings per mile Expenses per mile Expenses -r- gross earnings Pennsylvania R.R. . . . 1, 806 $ 20,315 $ 12,267 585 New York Central . . . 994 28,445 17,969 609 Central Pacific .... 2,447 6,814 3,340 470 Chicago, Burlington, & Qu. Philadelphia and Reading . 1,805 780 8,734 20,629 4,454 n,754 497 568 Union Pacific I 21 S q,778 4, CQ7 426 Atchison, Topeka, & Santa ) Fe 1" 1,398 5,n8 2,408 458 Total United States . . . 87,801 6,611 4,019 608 ESTIMATES A few estimates of roads, railways, and tramways, will now be given, which will to some extent fix the ideas on what must necessarily be subject to very great diversity, according to the circumstances of each case. The surveyor would do well to make rough shots at his estimate on his first walk-over, so as to guide him in his 22 Preliminary Survey choice of alternative routes, and even the most approximate ' aide-memoires ' are often of great service. The tendency of even experienced men is to over-esti- mate rough country and under-estimate easy country. A big gulch or canon is apt to scare most men, and swaggering viaducts float across their mind's eye, which often by patient reconnaissance melt down to one or two reverse curves and a ' bit of a trestle.' An ordinary American railway of about 100 miles in length in moderately easy country will require about 15,000 cubic yards of earthwork per mile. Mr. Trautwine's estimate, made quite a number of years ago, is near enough for a rough shot to-day. It is as follows for a single line in United States : Gauge 4' 81". Labour $\ 75 = js. per day. Grubbing and clearing (average of entire road) 3 acres $ at $50 150 Grading 20,000 cubic yards of earth at 35 cents . 7,000 Ditto 2,000 cubic yards of rock at $i . . 2,000 Masonry of culverts, drains, abutments of small bridges, retaining walls, 400 cubic yards at $8 . 3,200' Ballast 3,000 cubic yards broken stone at $i . . 3,000 Cross-ties 2,640 at 60 cents delivered . . . 1,584 Rails (60 Ibs. to a yard) 96 tons at $30 delivered . 2,880 Spikes 150 Rail-joints ........ 300 Subdelivery of material along the line . . . 300 Laying track 600 Fencing (average of entire road) supposing only one half of its length to be fenced . . . . 450 Small wooden bridges, trestles, sidings, road -crossings, cattle-guards, &c. ...... 1,000 Land damages 1,000 'Engineering, superintendence, officers of Co., sta- tionery, instruments, rents, printing, law expenses, and other incidentals ..... 2,386 ' 26,000 This amount is only extended to units to bring the total to a lump General Considerations 23 Add for depots, shops, engine-houses, passenger and freight stations, platforms, wood sheds, water stations with their tanks and pumps, telegraph, engine-cars, weigh scales, tools, &c. ; also for large bridges, tunnels, turnouts, &c. (Trautwine.) Mr. R. C. Rapier, of the well-known firm of Ransomes and Rapier, in his 4 Remunerative Railways ' gives an estimate for the equipment of a metre-gauge single- line railway, 40 miles long, including 40 Ib. rails, wooden sleepers, seven engines weighing 15 tons each on six wheels, turn tables, tanks, water-cranes, weigh-bridges, sheerlegs, signals, 35 passenger carriages and brake vans, 150 freight waggons of different kinds, workshop-fittings, and stores. The total for 40 miles 86,7087., or for i mile 2,i68/. The same author gives another estimate for the equip- ment of a forty-mile 3 ft. 6 inch gauge-railway with 45 Ib. rails, eight engines weighing 18 tons on six wheels, and a similar list of materials to the metre-gauge, somewhat in- creased. The total for forty miles 98,8407., or for one mile 2,47 1/. Where it is necessary, as in England, to put up gate- keepers' houses, and sometimes signal-interlocking gates at level crossings, it is often as cheap, having regard to future expenses of operating the line, to go over or under the road. Gatekeepers house. s. d. Wages 15^. per week = 5 per cent, on capital ot 780 o o House ........ 220 o o ;i,ooo o o Even where there is no help from the ground the earth- work can generally be got under 20,000 cubic yards. A Iter native bridge. s. d. 20,000 cubic yards earthwork at ga. . . 750 o o One bridge ..*.... 250 o o ;i,ooo o o * - B| o\ k ca ^ 1 ^ vo" tC * ^ ^ VO g tx % CO *cj f^. ^ CO t 1 *-. O o H H 1 q Os g CO & ll Ii 21 a| S2 f* 1 tt H-i ^o " S C tr! 3 -0 o ri oji.S c-G 3 General Considerations 25 A railway 87 miles long was completed for the Nizam of Hyderabad about the year 1885, for under 6,ooo/. per mile. It was promoted by the Indian Government, and built under the supervision of the Government engineer. The gauge was 5 ft. 6 inches, the rails were 66^ Ibs. per yard, of steel, and the sleepers steel also. The price included equipment and fencing. ROADS The Grand Trunk carriage road of the Bengal Presi- dency cost approximately 5007. per mile. The work was done mainly by starving poor during famine time, under the administration of Lord William Bentinck about 1835. The width was 40 feet, metalled in the centre 16 feet wide with either broken stone or a natural concretion of carbonate of lime, called ' Kunkur,' rammed by hand (there being no steam rollers in those days). The cost of laying the metal at an average lead of one mile was i62/. 6s. od. per mile, and cost of repairs and maintenance of ditto 337. i2s. od. per annum. Total cost of maintenance was 5 640 i 9 i W. Spire of Hockley Parish Church 1 A, Clump of Beeches near Hockley ray on A. The compass-box is placed on its delineated position on the paper, and if the sight-rule has been cor- rectly adjusted, and there be no local magnetic deviation or sufficient diurnal variation to account for it, the needle will still be at rest at the centre of its run. If not, its position should be measured by the graduation on the compass-box as an addition to or deduction from the initial variation, and an entry made of the variation at B. In selecting the next base C by intersection of two rays from A and B, a point should be chosen which, in addition to advantages of commanding position, should form as nearly as possible with AB an equilateral triangle ; the reason being that in any triangulation the more acute the angles, the less reliable must of necessity their intersections be. and an equilateral triangle is the only one in which no included angle is less than 60. When primary points have thus been located all over the map, the filling in of roads and other detail is done either with the prismatic compass and passometer, as shown in the example on p. 54, or, if more accuracy is required, with compass and tape. This subsidiary survey is plotted on tracing paper, and pricked through on to the map. This method is preferable to traversing in the detail with the plane-table itself as described on p. 41 because it saves the map from getting soiled, and is an independent check' (when the tape is used) upon the other work. Route- Survey ing 39 The main practical points to be observed in using the table are to set it up firmly upon its tripod ; to level it per- fectly true with a circular bubble ; to be very exact with its setting in meridian ; to keep the pencil finely pointed ; to draw the rays with the utmost nicety, and above all things not to get hurried. ROAD AND RAILWAY WORK The work required for preliminary road and railway survey resolves itself into two classes : the first a reconnais- sance of such rapidity that even stadia measurements take too long, and, except at intervals, there has to be as little time as possible devoted to erecting, levelling, and adjusting of instruments of any kind ; the second, a telemetric location survey, which will give the levels sufficiently close to plot a profile from them, and this is quicker and better done by the transit-telemeter than by the plane-table. The 'Verner' sketch-board is described on p. 318, to which the reader's careful attention is directed; its use will be first explained when accompanied by a prismatic compass on reconnaissance, and then some few further illustrations will be given of its more extended application when en- larged and developed into the regular surveying plane-table for the sake of those who may wish to make the most of it. VARIATION OF THE COMPASS BY THE PLANE-TABLE Before starting, the variation of the compass should be ascertained either by an observation of the solar azimuth, as explained on p. 132, or, failing suitable instruments for that purpose, by equilinear shadows on the sketch-board, as shown by Fig. 5. Erect the instrument on its wooden tripod, having the roll of mapping paper tightened up into its place. Fix the brass stile in the hole provided for it near the compass-box, and adjust the board level and stile vertical by the clino- Preliminary Survey S Q QS meter or otherwise. Draw the centre line of the table across the paper from headpiece to tailpiece, and ' set ' the table so that the needle shall be at rest in line with this centre line. Check once more the adjust- ments by clinometer, and the instrument is ready. About an hour or two before noon place a mark with a pencil at the extremity of the shadow cast by the stile, and from the base of the stile as a centre and with a radius equal to the length of the shadow describe a circle right round the board. When the sun begins to drop again in the afternoon, watch the shadow until it once more touches the circle. Mark it, and bisect the chord drawn between the two shadow-points in the circle, and draw a line to the base of the stile from the centre of the chord. This will be very nearly the astronomical meridian, and the angle between it and the centre-line will be the variation of the compass. The error, as explained on p. 135, arises from the altered declination of the sun during the lapsed time, which varies from o to i angular minute per hour. The error may at all times be neglected for this class of work. When the weather is uncertain it is best to take two or three points, say at 2 hours, ij hours, and i hour before the meridional passage, in order to ensure getting the sun in the afternoon again. FIG. 5. Route- Surveying 1 4 1 SKETCHING AND PLANE-TABLING The sketch-board is used upon two distinct principles. When buckled on to the wrist, the correctness of the align- ment depends on the little compass in the head-piece, checked as much as possible by bearings taken with the prismatic com- pass. No back and forward rays can, of course, be taken. The board has to be ' set ' at every point of observation by the 'working meridian,' which is a line drawn across the compass- box with an index at its end, by which the compass-box can be turned in any direction. The circle round the compass is graduated into divisions of ten degrees each, and the index is placed in such a position that when the needle is under it the board will be directed in the general line of route. When once fixed the index is never touched unless the survey begins to run off the paper. It is a fiducial line by which to adjust or ' set ' the board whenever a sight is taken ; and considerable practice is required to hold the board steady on the wrist with the needle truly under the index whilst the sight is being taken. It is also quite an awkward business to keep the edge of an ordinary sight-rule or ruler at the station- point whilst it is being rotated to take a sight. It was to meet this difficulty that the needle-point sight-rule, described in Chap. IX., was contrived, which has proved a great convenience, and much better than merely sticking a needle in the station. Most surveyors use elastic bands for keeping the ruler in position, but a thin string with a spring under- neath is neater. The ' working meridian ' is fixed upon before starting by means of any existing map, or, failing all such data, by inspection of the ground. For instance, if a route-survey be required from London to Birmingham we draw a pencil line between the two cities upon an ordinary atlas, and, running up the line to the intersection of a parallel, we find the astronomical bearing to be roughly 50 N.W. Supposing also that the variation of the compass has been just deter- 42 Preliminary Survey mined, as already described, to be 20 W., the magnetic bearing of the air-line between the two cities will be 30 N. W. This is called the c Line of Direction,' and is marked as such on the headpiece, corresponding with the direction in which the paper has to be fed forward upon the rollers. The words * Line of correspond with a due northerly direction ; that is to say, when the index is placed in line with the ' Line of FIG. 6. Direction,' and the needle is brought under it with its north pole towards the words ' Line of,' the board will be held in position for running due north. We want to run a course of 30 N.W., and therefore fix the index 30, that is, three divisions to the right of the words * Line of,' so when the needle is brought to rest under the index, the ' Line of Direction ' will point to Birmingham. The width of the paper being ten inches, it will take in Route- Survey ing 43 20 miles on either side of the air-line to a scale of four miles to the inch, and this would take in the whole map if we were following one of the main highways. If the line should run off the paper a ' cut-line ' must be drawn and a fresh start made in the middle of the paper with the same line of direction. This method of using the sketch- board is illustrated by Fig. 6. The magnetic bearing of the line of direction should be written up before commencing, so that the index, if accidentally shifted, may be replaced. The prismatic compass is of great use in checking the angles taken in this manner with the sketching-board. The bearings of at least the main lines of the traverse can be taken, and whenever important intersections are wanted upon salient points they should be likewise checked with the pris- matic compass. It is quite possible to have too many instru- ments, but a compass clinometer, as described in Chap. IX., is no inconvenience and most valuable. However skilfully the board is held in line, the slightest jog to the arm may, imperceptibly to the sketcher, twist the table several degrees. The value of the sketching-board is not lessened, but on the contrary much enhanced, by assisting it with the prismatic compass. The same amount of detail can be filled in, but with increased accuracy. SKETCHING WITH THE AID OF MAPS Where existing maps of any kind are available, they should be made all possible use of. An enlargement from an atlas, however imperfect, should be laid down to scale, and unless the map is thoroughly reliable, like an Ordnance map, it is best to draw the enlargement in pencil, and to plot in ink, or vice versa, so that the divergences may be at once apparent. To copy detail from the existing map would only confuse, but a check of alignment and distances is of great assistance. It frequently happens that during a rapid traverse a case 44 Preliminary Survey arises demanding more careful treatment than can be given with the board on the wrist. A metallic telescoping tripod is buckled to the bag of the sketch-board, or, when riding, is attached to the saddle. It is only sixteen inches long when shut up, and gives no trouble. By it the sketch-board can be used as an ordinary plane-table, but being light and vibratory it is only used in emergencies ; for continuous plane-tabling the wooden tripod should always be employed. In this form, the work can be done in fairly easy country at the rate of twenty miles a day. It is something more than a sketch and something less than a survey, but seeing that it takes hardly any more time to a practised man than if he simply took notes, it has the great advantage of graphic representation over mere literary description. ACCURATE PLANE-TABLING The second method of using the sketch-board mounted on its wooden tripod differs in no way from the ordinary plane-table except that the instrument is smaller. The principle of this kind of surveying is the geometrical law of similar figures, by which when a single side is known all the rest are determined by their positions in the figure. It is a graphic triangulation resting on the same mathe- matical theory as telemetry. The method of setting up the table has been already explained. The U.S. Geological and Coast Survey have covered immense tracts of country with plane-table work and use instruments of large size 24 inches by 30 is the maximum. They are fitted with elaborate joints for levelling them true, and furnished with sight-rules carrying stadia telescopes with vertical arcs for measuring angles of inclination. The figure on p. 42 of a traverse by the first method will also serve for the second. The preliminaries are all the same, the only difference being that the board is ' set ' at each new station by a backsight on the previous station with the sight- Route- Surveying 45 rule. The precision attainable in this way is very great. Check angles should still be taken with the prismatic compass, especially where the bases are short, but the rays are gene- rally more accurate than the compass-bearings, particularly so if there is local attraction to the needle. The compass- bearings, both with the needle in the headpiece (which is set to the * working meridian ' precisely as before) and those by the prismatic compass, are simply checks and nothing more. In taking a sight, the ray should be projected at the edge of the paper about half an inch long ; it should be marked with the signs of the back and fore station thus : A/B if taken from one main station to another, or B/B t &c. if taken from a main station to some outside point. The signs should FIG. 7. also be entered in a book of description (see p. 38) specify- ing what the points represent, and accompanied by little sketches, especially when the points are not very sharply defined, such as distant villages, hill-peaks, or river-bends, so that when arriving at the next station and taking the backsights of intersection, the memory may be assisted as to the precise spot viewed on from the last station. These little sketches are sometimes made upon the map, but it is not such a good plan, as they are liable to come in the way of succeeding rays. The flag on Fig. 6, p. 42, is shown as an out-station, but the board can be moved to its vicinity and backsights taken to all the previous stations on flag poles. The coincidence of 46 Preliminary Survey these rays with the foresight will prove the accuracy of the work and close the traverse. The whole principle of plane-tabling is here embodied. The stadia work, levelling and contouring, which are added by means of the accessory instruments to the larger tables, do not form an essential part of the instrument itself, and will be treated of under telemetry. AUXILIARY PLANE-TABLING The method of using the plane-table as an adjunct to the tacheometer for filling in detail will be next described. In Fig. 7 a tacheometer traverse is being carried along a main road, and a building with enclosure is proposed to be filled in with the plane-table, being situated upon a cross road, and it being desired to avoid a deviation with the tacheometer. A point E l is fixed in the vicinity of the building by a sight with the tacheometer, if possible, within 100 feet of the further corners. The plane-table, worked by an assistant, is then set up at B t , and aligned by a ray on B. The line BB L is then laid down on the paper without any reference to the compass. The distance BBj is not absolutely necessary, but, being known, it is better to plot it, and so locate B on the paper to enable a checksight to be taken upon it if the table has to be moved to another sub- station. If all the corners are within 100 feet, they can be taped without moving the table and laid off to scale on rays taken with the sight-rule. If the table has to be moved to another sub-station in order to command the whole of the detail, it can be triangulated as already described, but it is generally quicker to locate several points with the tacheometer as plane-table stations than to sub-triangulate with the plane-table. LOCATION OF THE INSTRUMENT The subject must not be dismissed without touching upon the well-known three-point problem for locating the Route- Survey ing 47 instrument, although it should not be used when a more direct method is possible. It frequently happens that, when surveying with the aid of a map, it becomes necessary to determine the position of the instrument on the ground from one or more points indicated on the map and transferred from it to the plot. If only one or two points are known, the problem cannot be solved without the compass. Case i. When one point is known. Maps are generally constructed having the astronomical north at the top of the sheet. Ordnance maps and ordinary atlases are made thus, but not so the parish maps. When this is not the case, the .- position of the astronomical or magnetic meridian or both must first be determined on the ground from the known point in the manner already described. When the geographical alignment of the map is known, and the variation of the compass has been ascertained, the magnetic meridian should be marked on the map at the known point, a bearing taken to it with the prismatic compass, and plotted backwards from it, i.e. 1 80 bearing. A base line is then run at right angles if possible, but if the ground will not admit of it, as nearly square as possible, and the bearing taken. The base line is measured, and from its extremity another bearing is taken to the known point. 48 Preliminary Survey Then laying down the two bearings from the point towards the observer's position on the plot, take the measured distance by scale and place it with the dividers, in its proper bearing, where the extremities will coincide with the two rays from the known point. If the base cannot be run square, the bearing of the base has to be run out with a parallel ruler. It is also convenient to lay off the base in an even number of feet or yards as 100 or 1,000, for then the distance can be read off from a table of tangents. Case 2. When two points are known, the prismatic compass is used in the same way, but a base is dispensed with. The two known points are plotted from the map in their proper position upon the plane-table, their bearings A 'a FIG. 9. taken and plotted backwards as before from magnetic meridians drawn through the known points. Their inter- section is the locus of the instrument. Case 3. When three points are known the plane-table can be located by the sight-rule alone. Let A, B, C be the three known points and #, 6, c their position on the plot. It is required to locate upon the plot the point of observation and to set the table so that the plot shall have its lines parallel to those in nature, or, as it is termed, the table be ' in meridian.' It is obvious that rays through A, B^, or Cc will intersect somewhere, and by Euc. vi. 2 we know that in any triangle, #AB, #BC, or rAC, when the sides AB, ab ; AC, ac ; BC, be, are proportional they are parallel. Therefore, if by adjustment Route- Surveying 49 of the table we find the position in which the three rays Aa, B<, Gr, intersect in one point, the plot will be parallel and the table in meridian, and the point of observation correctly located on the plot. When the instrument is not c in meridian,' a ' triangle of error ' is formed as shown on the figure, the elimination of which adjusts the table. There is one exception, when the of error FIG. 10. point of observation is situated in the circumference of a circle described about the three known points, the triangle of error disappears for any position in that arc. This is at once seen by being able to rotate the table without causing any error, and some other point must be chosen from which when located the required point can be determined. See more on the three-point problem by station-pointer in Chapter IX. THE PLANE-TABLE AS A RANGE-FINDER Fig. 8, p. 47, illustrates the principle of range-finding described on p. 338. The plane-table will, carefully handled, determine this range or distance of an object with as great accuracy as with some optical range-finders. Military engi- neers do not use it for this purpose because the enemy is fond of making a target of it. E 5o Preliminary Survey MEASUREMENTS OF DISTANCE Setting aside the chain, the methods available for deter- mining the distances upon route survey are of three kinds. Firs^ mere judging by the eye and hand, for which some data will be presently given of value to the sketcher. Secondly ', the ancient method of pace-counting, to which may be added the trocheometer for wheeled vehicles, the time-measure- ment of horses' gait, and the patent-log records combined with time measurement when steaming on a river. Thirdly ', the telemetric or optical measurement of distance, which, including the subject of military range-finding, is treated of in the chapter on Tacheometry, also in the chapter on Instruments. It belongs in its practice more to the route survey, though in principle it is to be classed with tacheometry. First. Judging by the eye is a faculty which is an im- portant part of the capabilities of the sketcher. A good shot will sometimes come pretty near the distance by look- ing at it as a range for a fowling-piece ; a cricketer by the distance he can throw a ball. By holding the hand across the field of view at arm's length, so as to cover the height of a man, a horse, or a man on horseback either with the palm or with one or more fingers, we have a measurement some- what on the stadia principle and of some assistance in guessing. The second method, of pace-counting &c., may be brought to a very fair degree of accuracy for the purpose of reconnaissance, and we will first touch upon the passometer or pace-measurer. It is in appearance like a watch, the mechanism consisting of an escapement carried by a loaded lever, which is shaken by the shock of the step and returns by means of a light spring ; the escape- ment actuates a train of wheelwork, and moves an index on the dial to record either the number of paces or the actual Route- Surveying 51 mileage. If the latter, an adjustment is provided to make the index read correctly to any given length of pace and instrument is called a pedometer. For long bases, the mileage indicator is as useful as the other; but for short distances, and varying inclinations, the counting index is preferable as no instrumental adjustment is needed, but scales of paces are drawn upon the board to their ascer- tained value under different conditions of travel, with their respective designations. The needle-point sight-rule is provided with a broad chamfered edge upon which, when using only one or two scales of paces, they can be gummed with stamp-margins so as to have the working- scale at all times on the paper and avoid dividers. This is dispensed with by using the Mannheim slide-rule as sight- rule and scale : see p. 245. The passometer does nothing more than count the paces ; the accuracy of the measurement depends upon the regularity with which the walker can pace. A course of training in this is indispensable, but can be easily gained during times of recreation. The chief points are to walk naturally without trying to step yards or any other specified dis- tance, to hold the body erect, and to maintain the same speed. The best way to arrive at reliable data of pacing is to walk over a piece of road where the mile-stones are cor- rectly indicated. A piece of railway will do very well for flat walking if the sleepers and ballast are avoided, keeping to the side of the bank or cutting. A turnpike road is better. For hill walking a six-inch Ordnance map will give the contour lines crossing the public roads, from which the gradients can be calculated. The time of one's walk has a great deal to do with the length of step. By educating oneself into the same rate of time uphill or downhill, fresh or tired the length of pace will be much more uniform than it is ordinarily. Gradients as steep as i in 40 do not then make any differ- ence on the average length. E 2 Preliminary Survey The following trials were made up and down a road varying from i in 20 to level, but all uphill one way, and down the other. Dis- tance, feet Number of paces Value in feet of 100 paces Uphill A to B . B to C . C to D . 2,900 2,080 820 ist time 1,091 783 284 and time 1,161 705 285 3rd time ^IS 2 ist time 266 266 289 2nd time 268 295 287 3rd time 2 5 6 285 291 Total 5,800 2,158 2,151 2,144 284 741 1,163 269 269-5 271 Downhill D to C . C to B . B to A . 820 2,080 2,900 286 726 1,156 296 725 1,121 287 287 251 277 287 26l 288 28l 249 Total 5,800 2,168 2,142 2,188 267 270-5 26 S Average of the three times . Range of one time from average . Maximum range of shortest distance) from average .... I 2-687 fe et per pace i -4 per cent. 10-9 per cent. These trials were under unfavourable conditions as regards gradient, and are given to show results attainable by an unpractised walker. See also closing error on p. 55. They demonstrate very clearly the tendency of pacing towards uniformity over long distances even when there may be great variations over short lengths. The distance was only a little over a mile, but this fact becomes more apparent on daily journeys of ten to twenty miles, in which the total error can easily be kept within from i to 2 per cent. When particular exactness is needed, and an assistant is present, it is advisable every two or three miles to check the rate by taping a stretch of 300 paces or so, in order to detect changes due to fatigue, rough or slippery roads, c. Route- Surveying 5 3 A series of scales may be constructed for use on various gradients, but it is less confusing to work to one scale and make a marginal note in the fieldbook to guide in making the corrections when plotting, or calculating the latitude and departure. The plotting may be done by the protractor, but the principle of working to latitude and departure is more exact, and the calculations are done as quickly with the slide-rule as if the angles were laid off with the protractor. There is a harmony, moreover, between this process and the daily astronomical observations, both being a reference to rect- angular co-ordinates. The analogy of traversing with navigation should be thoroughly studied ; even down to curve-ranging as will be shown later on. In the traverse for route-survey the work is nothing more than the dead-reckoning ; only instead of suffering from liability to error in under-currents, slip of screw, and what not, it is troubled with magnetic aberra- tion, irregularities of pace, and 'personal error.' The astronomical observation comes in to help out the land surveyor with the addition of the frequent sighting of landmarks whose geographical position is known, and the number of which becomes every year greater and greater. The astronomical work is sometimes performed with the Hadley's sextant, but the surveyor finds a greater range of usefulness in the transit theodolite. SURVEYING WITH THE SEXTANT The Hadley's sextant is a favourite instrument with travellers, who learn its use from one of the ship's officers when getting to their destination, and then employ it for traversing on land. It will not take angles any more correctly than they can be plotted direct upon a plane- table ; it is necessary to correct the angles when they are taken between points at considerable difference of level, whereas the plane-table gives the horizontal projection at 54 Preliminary Survey once. It is much slower in sighting, and needs careful sketches and entries in the fieldbook to avoid mistakes. Its great advantage is its portability, and an immense deal of good work may be done with it, but only the principles of adjusting it are given in the chapter on instruments, its use being very simple. CLOSED PASSOMETER TRAVERSE In order to exhibit the degree of accuracy attainable with the passometer and prismatic compass alone, the closed traverse illustrated by Figs. IT, 12, was made in the course of Scale of Feet 1000 3000 R- FIG. ii. daily walks and visits to friends, and without making correc- tions for sloping ground. It has to be remembered that not only does the pace vary in length according to the slope, Route- Surveying 55 but a deduction has to be made for the horizontal projec- tion of the distance. As going uphill tends to shorten the step, and increase the number of them to the mile, the error is aggravated by the projection. Going downhill it is diminished. The table for deductions due to projection is L - ~^\\Ciosing error 25 /& JUICES . FIG. 12. given in the chapter on chaining, but the pedestrian must make his own table of pace-variation from actual experi- ment. The roads of Sevenoaks are both hilly and tortuous, and therefore represent an unfavourable case for a route-survey. 56 Preliminary Survey Hardly any check angles could be taken on account of the obstructions to view. It will serve to show a degree of accuracy which can be at least equalled in more favour- able situations. The 'closing error' of 25 J- paces has been purposely left in the plot, and the process by which it should be distributed over the bases is placed upon a separate figure. The closing error does not represent the maximum error j it is an average one, arising in large measure from the sloping ground ; but there is also a slight twist in the plot, so that in one place where both pace and angle error assist one another, there is a divergence of fifty paces from the truth in the neighbourhood of one of the cross roads. The total closing error amounts to J per cent, of the periphery, the maximum error to about \\ per cent. On a day's march of twenty miles, the error at the next solar observation would be barely detected ; but as each observa- tion is independent, cumulative error of pace-measurement is removed within the instrumental limits of about \ mile of latitude, or, supposing an exact chronometer, of longitude either, but failing the chronometer, the error in longitude may be much more, as already explained in Chapter I. DISTRIBUTION OF CLOSING ERROR This must not be confounded with fudging, which means correcting by guesswork. Distribution of error is to a great extent dissipation of its amount all over the plot. The process is almost self-explanatory on Fig. 12. The total periphery is laid out on a straight line marking each station, and an ordinate is laid off at the extremity equal to the closing error. The extremity of this ordinate being con- nected with the other end of the line, a triangle is formed the ordinates to which at every station represent (on the assump- tion of the error being gradually cumulative) the correction to be applied at each point in a direction parallel to that of the line between the two divergent ends of the traverse. Route- Survey ing 57 Where the error is small in proportion to the total periphery this process reduces it to an unscaleable quantity on any single base line. SCALE OF PACES The construction of a scale of paces is as follows. Let us suppose that we wish to produce a map upon a scale of six inches to the mile. A chained base of 1,000 feet is paced and repaced until the average has been found to be for instance 357 paces. We then lay down our scale of miles, say three inches for half a mile, in furlongs and chains, and calculate by slide-rule the value of 1,000 paces in furlongs and chains. 1 Taking this amount from the mile scale we lay it down as our scale of 1,000 paces and subdivide it as follows : (Fig. 1 3, p. 59). From one end of it, we erect a perpendicular, and selecting some convenient decimal boxwood scale such as a i oft. to the inch, we adjust it so that one end is at the extremity of the pace-scale, and some multiple of ten (in this case the 40) on the perpendicular ; we then draw a line form- ing the hypotenuse of a triangle and tick off every four divisions of the boxwood scale so that we have subdivided our hypotenuse into ten equal parts. All we have to do 1 The two proportions are as follows : Let x be the number of paces in a mile, and y the number of chains in i ,000 paces. 1,000 : 5,280 :: 357 : x; or* - 357 x 5,280 x: 80:: 1,000 : y- Q iy = .to_2LL. Using the lower scales of rule and slide. Place the right-hand i of the slide over the 528 of the" rule. Place the brass marker at the 357 on the slide. Without displacing the marker, bring the 80 of the slide to the marker and read off the result, 42 ch. 44 links, on the slide oppo- site the left-hand i of the rule. a * C/3 1 *H Scale of Paces . 1000-4? 44 Chains 00 * 500 '* oa fttj.9 < ' _^ 0' I t ""--., \ f ''--. \ t " ~ -i. __ J / ' 4 ) ^ ~ - M S; "*--.., ! ; SCALES TO FIG. 13. then is to rule down perpendiculars to the pace-scale and it will be divided into spaces of 100 paces each. See also direct scaling by slide-rule, p. 245. FIELDBOOK The fieldbook, on opposite page, requires but a very brief explanation. The backsights are taken to equalise minute errors of observation, to locate and remove them when important, and to detect magnetic deviation. To reduce the meridional bearings to azimuths from north or south point, the following table may be used. TABLE XVII. Reduction of Azimuths From o to 90, azim. = bearing unaltered : N. E. From 90 to 180, azim. = 180 bearing: S. E. From 1 80 to 270, azim. = bearing- 1 80 : S.W. From 270 to 360, azim. = bearing 360 : N. W. [The author's pocket altazimuth has both graduations. See Chapter IX. ] The error at closing is seen to be 2 2 paces to the north and 13 to the west. We will represent it thus '\T7\ Then (i) to find the direction and magnitude of the line itself we have tangent angle d = ^. By slide-rule as before = '591. 6o Preliminary Survey Keeping the brass marker at the '591 we shift the tangent scale to its initial position and find under the marker the angle 30 35' N. W. (2) To find the length of the closing error L= v/22 2 +i3' 2 For 22 2 bring the brass marker to 22 on the lower scale of this rule, the upper index will then correspond with 484 on the upper scale. Similarly with the lower index at 1 3, the square 169 is found on the upper scale. Adding the two together =65 3 ; direct the upper index to 653 on the upper scale and the square root 25-5 is read off from the lower. It will be seen that involution and evolution are performed by simple inspection without using the slide, and this forms one of the most important uses of the slide-rule. l (3) To get latitude and departure. Place the right hand extremity of the sine-scale of the slide under the distance, and read off the latitude from the rule above the com- plement of the angle, and the departure opposite the angle itself. Thus in the first entry the distance=7o. Place the extremity of the sine-scale opposite a 7 on the upper scale of the rule. The reduced bearing is 19!, of which the complement is 70^ ; opposite these two angles on the slide we shall find the departure and latitude respectively. Check-sights are very useful in such work as this to correct twists The house shown on the plot was filled in entirely by angles. When engaged in filling in new roads to an old but accurately triangulated map such as an old Ordnance Survey the errors are localised by first plotting the work in the usual way and then superimposing a tracing of it upon the Ordnance Map ; the errors of the new work are thus narrowed within the limits of the nearest reliable points and the whole made very nearly as correct as the rest of the Ordnance Map. 1 This operation can be also performed by placing the sine-scale with the angle 30 35' under the 13 of the rule, and the answer will be found opposite the right-hand I of the slide. Route- Surveying 6 1 PROFILE The profile or section is produced from readings of the aneroid barometer at every station. The distances are laid off and the heights ruled up as in ordinary levelling. In the case of a closed traverse, there will generally be a ' closing error' of levels which has to be equalised or distributed similarly to the closing error of the traverse. Some of the sources of error are explained in the chapter on instruments, but they are usually cumulative and approximately uniform. They can only be treated as such, and the total periphery of the base being laid off upon a horizontal line representing the true datum, the amount of the closing error is laid off on a perpendicular at its extremity either above or below according as the last reading is less or greater than it ought to be. A ' false datum ' is then drawn from the starting point at the end of the perpendicular, and the levels are scaled from the false datum, which is afterwards erased. CONTOURS The contours are laid on by the pocket-altazimuth, check- angles being taken along the bases and in other directions. The pocket altazimuth is fully explained in Chapter IX. When we know the elevation of the point of observation and the slope of the ground in any direction we can plot the contours from the cotangent of the angle (that is the tangent of the complement) which represents the horizontal distance, corresponding to one foot of difference of level. Thus let the slope be 10 of depression. To find cot 10. Place the tangent-scale in its initial position and brass marker at 10. Reverse the slide and place the right-hand i of the slide at the index. Read the answer 5-67 on the slide opposite the left-hand i of the rule. If we want contours at every 10 feet the horizontal equivalent will be ten times this, i.e. 56*7 feet. Inasmuch as the aneroid readings are in 62 Preliminary Survey feet it is best to have a feet scale upon the plot as well as the two already mentioned for setting out the contours. This is by no means the only way of contouring. The contours of the Ordnance Survey are taken with the level, and dots are placed on the map where the staff was held. They are either plotted from cross sections or from field 400 30Q 200 IQOO 675 320300 oFeet DatuMWFttabotvOniJJat.- _StatK>n4 32 \ For Plan see Fig. II froftle of &John*s Road Jfor : Scale 6 Inches =On& MIL& Vert, Scale 1O0F*-OneMite FIG. 14 tracings on which the location of the level points are estab- lished by tape measurements from hedges, buildings, &c. The cross section is the most laborious and hardly the more exact method of the two. If the contours are needed before the plan is plotted, it is unavoidable, but when the principal contours are at a hundred or even fifty feet interval it be- Route- Surveying 6 3 comes a very tedious operation in hilly country. By the second process, the level is kept at nearly the same collima- tion going round the hill until it comes round to the same point again, or leaves the region of the survey. Telemetric contouring with the level (for which see p. 197) is suffi- ciently accurate for all ordinary purposes and is indepen- dent of any plan. Hill-sketching is often done in the form of contours by the eye, instead of hachures, which convey but little idea of the topography ; such contours by being close or far apart show at once the relative steepness or flatness of the ground. The examples of profile and contouring given, Figs. 14, 15, and 16, with the fieldbook are, one from the traverse, Fig. n, the other from a walk through Knole Park. The instruments used were the aneroid barometer, pocket altazimuth, and passometer. The aneroid was first examined between Ordnance bench- marks, with results as follows : Ordnance Aneroid Ordnance Benchmark at ' The Vine ' to Ordnance Benchmark Railway Bridge London, Chatham, and Dover Railway 187-8 185 Ordnance Benchmark at ' The Vine ' to Ordnance Benchmark Railway Tavern 2OO'8 205 Ordnance Benchmark at Railway Bridge to Ordnance Benchmark at Railway Tavern 13-8 20 On the profile, the discrepancies between the aneroid readings and the elevations calculated by the altazimuth were so small that they were not distributed. In the con- touring, on the other hand, the aneroid had to be used with less time allowance for settling, and needed considerable correction from the altazimuth. The profile was taken whilst walking up the hill with a friend without detaining him beyond two or three minutes. The only entries made in the fieldbook at the time were the station column, vertical angle, pedometer, aneroid, and remarks. 6 4 Preliminary Survey If a cumulative error of the aneroid is discovered from benchmarks, or from returning to the starting point on a closed traverse, it must be eliminated as already described before entering its readings in the column provided for the purpose. When in the field its readings can be entered in Feet Horizontal iqoo ' . w Feet Vertical FIG. 16. the column for remarks. When this is done, the aneroid levels rule the profile ; the altazimuth angles are only relied upon for the portion of profile between the aneroid readings. The advantage of using a clinometer or altazimuth in conjunction with thejaneroid, especially in the form recom- -sSsl-sl^^ 1 w taXllll's^ 1 VH 0) en J- *^> & - r^ ^ rS ctf ^ c us V g ^ -I -d i 8 . g - w ' & ttJ rt C >. ; ,. ftgfcol^ 8 ^ | 1 K 'rt 1 g2a<^SH.,o^ | ^ 3 O ^ ^ u < S tt< "2 ^1 aj & i ' i * Iu~) ON 10 IO O 1 a 1 1 1 M ^ 00 co H 1 $ 2-B : |I u S ON ^ N -^- "4- oo c co ' H CO ~v K^ 'sjs 1 % _ -V 2 v 10 ( 1 & 8 + j\ co - 5; g I G 4> V % \r> i o t u V N ) 1 "rt . h O O O 'O O r O w O c VO VO ^ ^ j M ! -1 M "^ .48 4J O O O '0 XO I O g S| 1 O 0) IO CO ( H ON O CJ _