B M M=ifl 37fl TT"^ iiTTSTj.itfjssrjWHmyi'"' ''"■■'■ REESE T LIBRARY UNIVERSITY OF CALIFORNIA Icccssions No.^/^OO Shelf No. Ci ^o fl^ TREATISE MARINE SURVEYING & HYDROMETRY. XTNIVEliiSIT- IIF TUK FROM Ljyf'AXTF.X TO /}J,AA'A'^J>t THE PROPOSED IMPROVEMENTS reference: s. TlicLmemims 'L Lit' rV/i / %'r.f Sa/td laj ks ^o Juw \Sater s OwH rnmaP hUbhcd Plan or (beTo m T/iepcats coloured /i^d to hoDredtfcd- Lonciitiiduial SecUm onj^Biyerlune W the^ew Bridge tx> CoOewe^' shm'u^ Oied^th required to beExcavcUal , o' ^ at the ditreimt rords to oGmin W feet up to Lancaster at E.WofordiTwrj Sprmp '/ides. ^ A* Enffrox-ed by permission of the C ofS^Omrgcs Qui^ rhr Stevc/ison's Ti-eatise on. Afaruie Sunr // TREATISE ON THE APPLICATION OF MARINE SURVEYING & HYDROMETRY TO THE PRACTICE OF CIVIL ENGINEERING, BY DAVID STEVENSON, CIVIL ENGINEER, AUTHOR OF A SKETCH OF THE CIVIL ENGINEERING OF NORTH AMERICA, &C. ADAM & CHARLES BLACK, EDINBURGH; LONGMAN & CO., AND J. WEALE. LONDON. MDCCCXLII. WART fH' Till-: Vll ILWlfl FROM OPOSED IMPROVEMENTS E NAVIGATION ■n:\j:xsn.\ a- soxs /■: V(if.\ /■:/■:// s I W ,- i\ Lomiiludinal Seclum ot the River Lane tn at the din'm-nt fords to o/> Engraved by permission or the Comnu / / TREATISE ON THE APPLICATION OF MARINE SURVEYING & HYDROMETRY TO THE PRACTICE OF CIVIL ENGINEERINCx. BY DAVID STEVENSON, CIVIL ENGINEER, AUTHOR OF A SKETCH OP THE CIVIL ENGINEERING OF NORTH AMERICA, &C. ADAM & CHARLES BLACK, EDINBURGH; LONGMAN & CO., AND J. WEALE, LONDON. MDCCCXLII. 3 y <5<5 / ^// PREFACE. The following Treatise is intended to afford a plain and detailed description of the " Application of Marine Survey- ing and Hydrometry to the practice of Civil Engineering," on which, it is believed, no work has hitherto appeared. I have endeavoured to confine myself strictly to the con- sideration of the subject which is set forth in the title, with- out entering on an exposition of the principles on which the art of surveying is based, or giving a description of the con- struction and methods of adjusting and using surveying in- struments, as these subjects have been already so fully treated of by others as to render any remarks on them quite superfluous. The necessity of having accurate data on which to form designs for harbour and river improvements, or other hy- draulic works, as well as to estimate their expense, will be readily admitted by all Engineers. It is, therefore, of great importance that those engaged in such inquiries, although ri PREFACE. they do not actually conduct the operations of surveyings should be thoroughly acquainted both with the principles in- volved in them, and their practical application, so as to be able, not only to direct the attention of others to the best method of procuring the data required for Engineering in- vestigations, but, if necessary, to acquire them for them- selves. There are many works which treat most fully and satis- factorily of the theory of surveying, but they appear to be generally wanting in directions for its practical applica- tion. On some departments of the art, such as making tidal observations, soundings, sections and borings, and conduct- ino- hydrometrical investigations, all of which are of the highest importance in Engineering inquiries, the works with which I am acquainted are either altogether silent or very inexplicit. The present treatise has been written in the hope that it may tend, in some measure, to supply this want ; and I have endeavoured to make it intelligible to those who are engaged in the study of the profession, as it is at an early stage of their progress that a knowledge of the subject treated of can be best obtained. It is to be observed, however, that the reader is supposed to be already familiar with the art of surveying as generally taught, and with the use of the theodolite, sextant, and level, PREFACE. vii which are the instruments employed. If information on these points be required, he is referred to any of the nu- merous published works on Trigonometry and Surveying, and, in particular, for a description of the instruments, to the very excellent treatise on that subject by Mr Simms. The series of operations necessary in surveying a river embraces almost every point required in making any ma- rine survey for Engineering purposes, and if all the steps of a river survey be thoroughly understood, no difficulty will be found in applying the system recommended in the fol- lowing pages to a harbour survey including part of a line of coast, or to any similar case. I have, therefore, in order to simplify the subject, confined my observations principally to the details of river surveying, noticing, as they occur, such points as require further explanation with reference to the survey of a harbour, or of a line of coast. As it is dif- ficult, however, to find any one case in which good illustra- tions of all the different departments of surveying are com- bined, the examples given are selected from the surveys of different rivers, according as they seemed best adapted to the object in view. I have also made some observations on the manner of protracting the field work, and given an example of a finish- ed plan, which may prove useful to the reader. It may be proper to state, that the observations contained viii PREFACE. in the following chapters have been thrown together, at in- tervals of leisnre from more urgent duties, and are chiefly the result of a pretty extensive experience obtained in the course of surveys which were either at an early pe- riod conducted by myself, or have latterly been made under my directions. I take this opportunity of expressing my obligations to Richard Ellison of Sudbrooke Holme, Esq., for his kind permission to refer to the Fossdyke navigation ; and for similar favours I am indebted to the liberaUty of the Perth Harbour Commissioners, the Directors of the Ribble Navigation Company, and the Commissioners of St George's Quay, Lancaster. DAVID STEVENSON. Edinburgh, Feb. 1842. CONTENTS. CHAPTER I. TRIAXGULATION. Selection of Stations — Conditions required to constitute a good Triangu- lation — Difficulties in selecting Stations — Poles — Flags — Arrange- ment of Colours of Flags, &c., for distinction — Reference to the Magnetic North — Local variation — Examples of local variation in Surveys — Its eiFect — Construction of a Compass for the plan — Se- lection of the Stations from which to determine the Magnetic North — Points to he kept in view in adjusting the Theodolite for ohservation — Mode of observing and registering the Bearings — Example of Field Book — Rule for adjusting Instriunent at the succeeding Stations — Parallelism of the same Bearings at different Stations — Reverse Readings — Rule for reducing reverse Bearings, CHAPTER II. BASE LINE. Most desirable Length for a Base Line — Requirements for insuring an accurate Measurement — Process of Measuring — Methods of deter- mining the Extremities of the Base — Three cases described, first, when the Line extends between two Triangulation Stations ; se- cond, when it is an independent Line, but connected with the Tri- angulation by a back Bearing ; third, when it is measured on a sand bank and unconnected with the Triangulation — Methods to be pursued in these different cases described, . . . . 21 X CONTENTS. CHAPTER III. TIDE OBSERVATIONS. Remarks on the Tides of Rivers — Variations in the Tidal Lines — Pro- fessor Robison's remarks as to the anomalies of River Tides — Ex- planation of the exact nature of the inquiry into the Tides which is to be instituted — Selection of Stations for Tide Observations — Agents which produce disturbance in the Parallelism of the Tidal Lines — Description of Tide Gauges to be used — Points to be kept in view in fixing them — Method of fixing them on sloping Beaches — Method of keeping the Time — Method of making Observations — Form for registering Observations — Description of Form — As- certaining the relative Levels of the Gauges — Points to be kept in view in levelling for this purpose, ..... 30 CHAPTER IV. SOUNDINGS. Nature of the Variations on the Tidal Lines explained — Examples of the Variations on the Dee in Cheshire — The Lune in Lancashire — The Forth in Stirlingshire — Manner in which these Variations af- fect the Soimdings — Reference of Soundings to one Datum Line explained — Half Tide Level not applicable in the case of Rivers — High AVater of a certain Tide adopted — Use made of the Tide Gauges in reducing Soundings to the Datiun — Formula for their reduction — Example — Formula only true on the supposition of the Lines being parallel to High Water — Example in the case of the Dee — Results aflfected by the erroneous supjiosition — Mode of avoidmg this by increasing the number of Tide Stations — But this not always attainable — General Rules for taking Soundings to ap- proximate to accuracy — Method of taking Soimdings described — Equal Distribution of Soundings over Area of River — Observa- tions for fixing their positions, ...... 46 CHAPTER V. LOW WATER SURVEY. Objects of the Low Water Survey — Difficulties encoimtered in makiiig it — Surveys situated on the coast and in rivers — Use made of the CONTENTS. Triangulation Stations — Observations for lixing positions of points in Survey — Changes on Sand Banks produced by spring tides, high winds, &c. — Different methods of keeping Field Book — Examples — Method of executing the field work — Dangers to be avoided in making Low Water Survey — Means for averting them — Dangers in consequence of anomalous flow of Tides — Example of this on the Dee — Cause of the phenomenon, ..... CHAPTER VI. SURVEY OF HIGH WATER MARGIN. Objects of the Survey of the High Water Margin — Two systems of Surveying employed for this purpose — Chain and Traverse Survey- ing — Use made of the Triangulation Stations — Description of the process of Traverse Surveying — Directions for adjusting the Theo- dolite — Reverse Bearings — Method of keeping Field Book — Ex- ample from Survey of the Tay — Checks on the accuracy of the field work — Method of surveying outlines of extensive tide covered marshes, .......... CHAPTER VII. CROSS SECTIONS AND BORINGS. Uses of the Cross Sections and Borings — Situations in which they are required — Reference of Sections and Borings to Datum Line of Survey — Directions for making Sections — Description of Appara- tus employed, and its application — Directions for making Borings — Description of Apparatus, and its application — Method of keep- ing Field Book — Importance of this dejiartment of the Survey, as affecting designs for works — Example of this in the case of the river Ribble, in Lancashire, and the Fossdyke, in Lincolnshire, 92 CHAPTER VIII. HYDROMETRICAL OBSERVATIONS. Application of Hydrometrical Observations to Engineering — Discharge of Rivers — Making of Cross Section —Determining the Velocity — Instruments for measuring the Velocity — Floats — Objections to CONTENTS. Floats for this purpose — The Tachometer of Woltmann — Descrip- tion of instrument, and its application — Adjustment of Scale of Tachometer for observation — Formula for reducing the Surface to Mean Velocity — Table of Mean Velocities — Instrument for deter- mining Velocities of Currents in the sea — Floats — Massey's Log — Instruments for measuring Under Currents — The Tachometer — The Under Current Float — Instruments for ascertaining the Direc- tions of Currents at sea — Obtaining specimens of water from dif- ferent depths for the purpose of analysis — The Hydrophore — Varieties of construction — Manner of using them, . . 105 CHAPTER IX. PROTRACTION OF THE TRIANGULATION, BASE LINE AND TRAVERSE SURVEY. Methods of Protracting Triangulation — By the calculated sides of the Triangles — By the Bearings — Principle on which Protraction by the Bearings is based — Protractors used — Drawing Protractor on the paper — Method of dividing it — Method of transferring Bear- ings to diiFerent parts of the paper — Protraction of Base Line, 1st, When it lies between two Triangulation Stations ; 2d, When it does not extend between Triangulation Stations, but is neverthe- less connected with the Triangulation by Bearings ; 3d, When the Base is not connected with the Triangulation — Trigonometrical calculation for solving third case — Method of Protracting Tri- angulation before laying down Base Line — Objections to this mode — Correction of the measured length of the Base necessary — Pro- traction of the Survey of the High Water Margin when the sys- tem of Chain or Traverse Surveying is employed — Checking accu- racy of the measurement of the Survey Lines, . . . 126 CHAPTER X. PROTRACTION OF LOW WATER SURVEY AND SOUNDINGS. Protracting Sextant Observations for fixing Positions of Points — The Station Pointer — Protracting them by Construction — Ordinary rule for this — Improved method — Solution of the problem on which the method is based — Practical application of the principle — Objec- CONTENTS. xiii tions to Protracting by Construction— Protracting the Outlines of Low Water Channel and Sand Banks — Protraction of Soundings — High Water Soundings — Low Water Soundings — Formula for ascertaining the Rise of Tide and the Heights of the Sand Banks above Low Water — Method of Protracting a Longitudinal Sec- tion, 143 Note relative to the Chart of the River Lune, . . . 154 Appendix, .......... 159 Index, ........... 167 PLATES CHART OF THE Lune to face Title-Page. PLATE I. II. III. IV. V. VI. VII. VIII. IX. X. XL XII. XIII. Page 1 19 48 48 52 52 53 53 54 75 103 ^vil""»"' \-- i/l. -/ TREATISE. CHAPTER I. TRIANGULATION. Selection of Stations — Conditions required to constitute a good Triangulation — Difficulties in selecting Stations — Poles — Flags — Arrangement of Colours of Flags, &c. for distinction — Reference to the Magnetic North — Local variation — Examples of local variation in Surveys — Its effect — Construction of a Compass for the plan — Selection of the Stations from which to determine the Magnetic North — Points to be kept in view in adjusting the Theodolite for observation — Mode of observiag and regis- tering the Bearings — Example of Field Book — Rule for adjusting Instru- ment at the succeeding Stations — ^Parallelism of the same Bearings at different Stations — Reverse Readings — Rule for reducing reverse Bear- ings. The triangulation is tlie first operation to be performed in making the survey of a river ; of which, indeed, it may- be said to form the groundwork. It consists, as is no doubt already known to most of our readers, in the selection of certain well defined points on the banks of the river, called Stations, and the determination of the relative positions of those points by angular observations. Considerable judg- ment is necessary in selecting these stations ; and the bear- ings by which their positions are determined must be taken TREATISE, CHAPTER I. TRIANGULATION. Selection of Stations — Conditions required to constitute a good Triangulation — Difficulties in selecting Stations — Poles — Flags — Arrangement of Colours of Flags, &c. for distinction — Reference to the Magnetic North — Local variation — Examples of local variation in Surveys — Its effect — Construction of a Compass for the plan — Selection of the Stations from which to determine the Magnetic North — Points to be kept in view in adjusting the Theodolite for observation — Mode of observing and regis- tering the Bearings — Example of Field Book — Rule for adjusting Instru- ment at the succeeding Stations — Parallelism of the same Bearings at different Stations — Reverse Readings — Rule for reducing reverse Bear- ings. The triangulation is tlie first operation to be performed in making the survey of a river ; of which, indeed, it may be said to form the groundwork. It consists, as is no doubt already known to most of our readers, in the selection of certain well defined points on the banks of the river, called Stations, and the determination of the relative positions of those points by angular observations. Considerable judg- ment is necessary in selecting these stations ; and the bear- ings by which their positions are determined must be taken A 2 TRIANGULATION. with great accuracy, more particularly as they are after- wards to be employed as objects for observation in laying dovm. the positions of sunken rocks, sand banks, and sound- ings of the depth of water, and in making the survey of the margin or banks of the river ; departments of the field work which will be more particularly explained hereafter, when the various uses to which the triangulation stations are to be applied will be fully illustrated. Before attempting to fix the positions of any of the sta- tions, the observer should walk along the whole extent of the river to be surveyed, examining first the one bank, and then the other. The object of this perambulatory survey is to make himself master of the general configuration of the shores or banks of the river, that he may be the better able, from actual knowledge of the ground, to fix the sta- tions so as best to fulfil the several conditions required to constitute a good triangulation ; on which, as may be infer- red from what has already been said, the accuracy of the other departments of the survey, as well as the ease with which they are made, chiefly depend. The conditions re- ferred to are. Firsts That the triangles formed by the imaginary straight lines joining the adjacent and opposite stations be as nearly as possible equilateral. Second^ That from each station there shall be visible as much of the ground to be surveyed, and as many of the other stations, as possible. Thirds That the stations be not so far distant from each other as to render it inconvenient to employ them as points of observation in determining the positions of the sand- TRIANGULATION. 3 banks, rocks, soundings, or other objects which require to be laid down. Fourth, That the stations be as few in number as pos- sible, consistently with the foregoing conditions. And, Fifth, That each station be so chosen as to allow the theodolite, or other angular instrument, to be placed in correct adjustment over the spot occupied by the station- pole ; which, as will be afterwards seen, must admit of re- moval for that purpose. The fulfilment of these conditions may appear, at first sight, to be no very difficult task, for, in viewing the out- line of a river as laid down in a chart or plan, the difficul- ties which have, in many situations, to be encountered, are not in their full extent discernible ; but in practice, many obstacles present themselves, which experience alone ena- bles the surveyor to overcome, and these impediments to the operations render the proper selection of the stations for the triangiilation a work in which both care and judg- ment are required. Inequalities in the level of the banks of rivers, for example, often give rise to great inconvenience in selecting the stations. In some situations, the banks suddenly rise from a low flat to an abrupt head, having a considerable elevation, and projecting from the general line of the shore. When a corresponding elevation and projec- tion take place in the opposite bank, producing a sudden contraction in the bed of the river (a formation of country not uncommonly met with), the triangulation may be said to be divided into two compartments, one on either side of the projecting heads ; and it is often very difficult, in such a case, even by the best possible arrangement of the stations, 4 TRIANGULATION. to connect these cunipartments in a satisfactory manner, cither for want of a sufficient number of observations, or iVoin the too great acuteness of the angles formed by the bearings taken from different points, by the intersections of Avhich, the positions of the stations are determined. Again, when the river is broad, and the banks in the foreground are uniformly flat, with hills rising in the distance, much trouble often arises, in observing with the theodolite, from the dif- ficulty of "picking up" the stations, if their positions are not selected and the colours of the flags arranged with re- ference to the circumstances and appearance of the back- ground. The confiji'uration of the shores or banks of no two rivers being exactly the same in these respects, it is evident that no two triangidations, arranged in reference to particular cases, can be found exactly to agree, each being made to suit the peculiarities of the situation for which it was in- tended ; and, therefore, no specific rules for the direction of the surveyor in the selection or arrangement of the stations can be given. In deciding on these matters, he must be guided by his own judgment, always keeping in view the five conditions already mentioned, and endeavouring, as far as possible, to fulfil them. I cannot pass from this part of the subject without remarking, that those who are inexpe- rienced in surveying are very apt, in attempting to obviate some of the difficulties alluded to, to overlook the second last of the conditions to which I directed attention, and to adopt too many stations for their triangulation. This error should be carefully guarded against ; for although the diffi- culties encountered may appear, at first sight, to be satis- TRIANGULATION. 5 factorily overcome by increasing the nnmber of stations, it will generally be fonnd in the end tliat this desirable result cannot be obtained by resorting to such a measure. The adoption of this plan of overcoming obstacles, while it does not serve the purpose intended, introduces many serious evils ; for not only is there a loss of time in fixing and making observations from each superfluous station, but, what is of much greater consequence, error and confusion, both in makino- the trian^ulation, and afterwards in fixino- the low water lines and soundings, may be caused by the observer mistaking one station for another when they are thus injudiciously placed too near each other. The truth of these remarks will be known to the expe- rienced surveyor, who is alive to the importance of reducing the chances of error in his work ; an object which must be the aim of all who would survey well. For it must be re- membered, that in very few cases is it convenient to pro- tract more than a very small part of the field work while a survey is in progress ; and, therefore, it is proper that the surveyor should, in every step of his proceedings, pursue that course which insures the greatest chance of accuracy, that he may not have to go over any of the field work a second time ; and, in compliance with this view, all his ob- servations should be registered, and his field books kept in such a manner, that any one acquainted with this sort of work may be able to protract the survey from them. When the river has been fully inspected, and the positions for the stations, after due consideration, determined on, the station poles are to be erected. The poles used in all the surveys with which I have been connected, were tapered 6 TRIANGULATION. spars, of natural growth, measuring 4 to 5 inclies in dia- meter at the large end, and from 15 to 25 feet in length, according to the situations for which they were intend- ed. Flags of white or red cotton cloth, about 3 feet 6 inches in breadth, and from 3 to 5 feet in length, were fix- ed to the tops of the poles, for the purpose of rendering the stations more conspicuous. The poles were then firmly placed in a vertical position, their ends being sunk three or four feet into the soil, and a small mound of earth or stones heaped round them to keep them steady. In compliance with the last condition which was stated, care should be taken to place the poles so that, when removed in the course of the triangTilation, the theodolite may be easily set with its vertical axis directly over the spot occupied by the pole. I am particular in directing attention to this point, hav- ing, on more than one occasion, seen a pole inadvertently placed in so injudicious a manner that it was quite im- possible to adjust the instrument accurately, on its removal for that purpose. If any of the stations are situated near dwelling-houses, it is advisable to place them under the charge of the inmates, when they are disposed to take this trouble, as great inconvenience is often occasioned by their being carried off or destroyed by mischievous persons. Generally speaking, one wbite flag is fixed to each of the poles, but sometimes two white flags, or a red and a white one, or two red ones, are placed on them, for the purpose of distinguishing them, when it is feared, from the direc- tion in which they are to be viewed, or from any other cause, that the stations may be mistaken for one another. This precaution is often necessary, and I have in nianv cases found TRIANGULATION. 7 it to be indispensable. The most secure way of fixing the flags to the poles, is to have a piece of stout cord doubled and strongly sewed into one end of the flag, so much of the cord being left extending beyond the edges as is necessary for tying the flag to the pole. The upper part of the pole, for the dis- tance of 6 or 7 feet from the top, ought to be cleared from protuberances and smoothed, to prevent the flag from being- caught by it during high winds and torn. For the same reason, the cloth of which the flag is composed must be firmly hemmed^ otherwise it will be gradually wasted away by every successive breeze of wind, until nothing but its ragged end, and the cord by which it is attached, are left on the bare pole. Objections have occasionally been raised to the use of flags for the purpose of distinguishing stations, owing to their being invisible when the wind blows in the line of the observer's vision. I certainly have, on some oc- casions, experienced inconvenience from this cause ; but, on the whole, I have no hesitation in saying that the method of distinguishing the stations which has just been described is the best and most convenient I have yet tried. Baskets of wicker-work painted diff'erent colours, and other marks of a similar description, fixed on the poles, are recommended in preference by some. These I have tried, and where placed between the observer's eye and the sky, they are as well seen as flags, provided they present the same surface : but if the station be in a place where hills, or trees, or any other objects rise behind it, I have found no distinguishing mark equal to a flag, the motion of which in the air can be detected when all still bodies appear to be blended into one general mass. The use of a pocket telescope ^ill be found 8 TRIANGULATION. of great service in assisting the observer to " pick up" the stations when any difficulty exists, especially if the theodo- lite be not furnished with a detached telescope, which in the instruments generally employed for ordinary surveying is seldom the case. These different points may, perhaps, be considered by some as too insignificant to be mentioned ; but it is of the greatest advantage to attend particularly to such minutiae ; and those only who have once or twice lost a day's work from not doing so can fully estimate their importance. There are few things more annoying than to find that a day's work is lost owing to a flag on a principal station having been car- ried away, or to its injudicious colour or position having rendered it invisible ; and if this be occasioned by the ne- glect of some of these seeming minutiae, the annoyance is doubly harassing. When the station poles have been set up, the observations of their bearings are next to be taken with the theodolite, or other angular instrumemt employed. That this may be done in a satisfactory manner, fine weather is necessary ; if it blows hard, it is only a loss of time to attempt the ope- ration, but there ought to be a light breeze, sufficient to blow out the flags so as to make them " shew," and also to carry away the slight haze which almost invariably accompanies calm weather. Bright sunshine is, generally speaking, by no means so favourable for the operation as a sky some- what cloudy. If the weather should not be favourable for this purpose, some other part of the survey may be pro- ceeded with ; for the poles being fixed, the triangulation may be co!n[>lete(i at any future time when most convenient. TRIANGULATION. 9 But I shall follow out what may be considered the natural order, and describe what is necessary for completing the tri- angulation, before entering on any of the other departments of the survey. The magnetic ueedle, independently of those changes which are ascertained to be constantly going on in its direc- tion and dip, to which the term " variation" has been applied, is subject to other variations occasioned by local attraction, in consequence of which, it has, under certain circumstances, been found, that, in surveys even of limited extent, the mag- netic north, as indicated by the needle, varies in its direc- tion to a very appreciable amount at different stations. The causes of these variations are in some cases very apparent, but in others they are not so easily discovered, and there- fore cannot be so well guarded against. I have met with many instances of errors in observations produced by local variation, some of which have given rise to considerable trouble, before the cause from which they proceeded could be detected. On the river Tay, for example, I found the vari- ation on one occasion to amount to 2° 30' in a distance of about a quarter of a mile. The first of the series of obser- vations by which this local variation of the needle was dis- covered, was made on the top of a high bank, about 50 feet above the level of the water, and the second on a low tide- covered sand bank in the middle of the river ; but the at- tracting influence could not, in this case, be satisfactorily ascertained. On another occasion, an error, amounting to no less than 7°, was introduced into the bearings of a sur- vey, in consequence of certain observations which had been referred to the magnetic north having been made in the 10 TRIANGULATION. vicinity of a large steam engine boiler, which lay concealed from view in a warehouse, close to which the instrument had been set, and the influence of this mass of iron on the data of the survey could not, at the time the observations were made, be avoided. In another instance an error of 2° was in like manner introduced into a harbour survey, owing to the instrument having been inadvertently set too near a cast iron mooring pall which was fixed on one of the quays. These facts seem sufficient to warrant the general conclusion, that the magnetic north, as indicated by the needle, should never be employed in surveying, as a check on the accuracy of the bearings of stations or objects ; because its direction cannot be relied on as unalterable ; and in accordance with this view the needle will be found to act a very subordinate part in the system of surveying which I have attempted to describe in this treatise. It is absolutely necessary, however, that the positions of the stations in reference to the magnetic north should be determined as accurately as possible, in order that a mag- netic meridian line may be applied to the survey from which a compass may be constructed, for, without this, the utility and value of the chart or plan to be made would, of course, be greatly diminished. In order to insure this, it is only requisite, in beginning the survey, to assume the magnetic north as indicated by the needle attached to the instrument, as the zero of the observations ; and it is well to note the bearing of the magnetic north at the first three or four sta- tions of the triangulation, for, in this way, any great local variation, similar to that in the cases already alluded to, which may happen to exist at any of the stations, will be TRIANGULATION. 11 less likely to pass undetected. If tlie bearings of the north line are very nearly the same at all the stations at which it has been observed, the mean may be adopted as the mag- netic meridian for the survey. It is proper that the true as well as the magnetic north should be shewn on the plan ; but as the variation of the compass for almost every place in this country is known and has been ascertained far more accurately than can possibly be accomplished by any obser- vations made by an engineer in the course of his investi- gations with an ordinary surveying theodolite, it is un- necessary in this place to describe the manner of determin- ing it with that instrument. The compass constructed on the magnetic bearing taken in the manner described as a basis, with the line of true north, at the nearest place for which it has been determined, applied to it, is sufficiently accurate for all marine surveys made in the practice of civil engineering to which the system of surveying described in this treatise, as explained in the preface, is strictly limited. The station at which the observations of the triangula- tion are commenced should be such that an extended view may be had, including distant objects within its range ; for if it be selected in a contracted part of the river where the distance between the different objects to be observed is in- considerable, there is much less probability of making so near an approximation to the truth in determining the exact position of the line of the magnetic north in reference to the survey. As an illustration of this, let us suppose that in the bisection of a station pole at a short distance, say 220 yards from the point of observation, an error of 2 inches has been made, arising partly from the poles not having been 12 TRI ANGULATION. placed perfectly perpendicular, and ]mrtly from the difficulty of effecting its accurate bisection. If the imaginary lines representing the true and the observed directions were pro- duced beyond the observed station at which the error had been made, they would evidently continue to diverge, and the error would be gradually increased in direct proportion to the distance ; and at the distance of say 6 miles, it would be found, in the case I have mentioned, to have increased from 2 inches to 8 feet. Now a space of 8 feet, which is nearly double the whole length of the flag attached to the poles, when viewed with a good instrument and under fa- vourable circumstances at the distance of 6 miles, is a much more appreciable quantity in attempting to bisect a pole of say 4 inches in diameter, than a space of 2 inches, viewed under the same advantages, at the distance of 220 yards ; and hence an observation made to a distant station is more likely to give a correct result in obtaining the magnetic line for the survey than one taken to a near object. The way in which this angular divergence affects the results of a survey is obvious, for in the case of commencing the tri- angidation at the broadest part of the river any error made in the angular observations may be said to be the maximum error of the survey, its effect in throwing the points out of their true position being gradually decreased as the distances between the stations decrease ; but if the triangulation be begun at the narrowest part of the river, any error that is made may in that case be called the minimum error of the survey, and will be gradually increasing as the survey ex- tends, so that at the broadest part of the river the amount of angular divergence from the true line may, as already shewn, TRIANGULATION. 13 be very great. This cause of inaccuracy, which is so easily obviated, should be strictly guarded against in surveying ; for if an error be found to exist in the direction of the mag- netic meridian, it is imjDossible to decide whether it is due to the cause I have endeavoured to explain, or is to be im- puted to variation produced by local attraction ; a doubt which, of course, precludes correction. The only other consideration to be attended to in the se- lection of the stations from which to observe and determine the magnetic north is, that they shall be free, so far as can be ascertained, from the agents which cause local attraction ; a remark, the force of which will be apparent to all from what has been already said on that subject. Sometimes, no doubt, these sources of error, as has been shewn, exist in forms which prevent their presence from being readily dis- covered, and for this the surveyor has no remedy ; but still stations which present apparent agents, such as the imme- diate vicinity of an iron work or steam engine, or even a mass of trap rock, ought to be avoided. I have throughout supposed the reader to be familiar with the use of surveying instruments, and therefore I shall only make three remarks regarding the adjustment of the theo- dolite for observation, with reference to points, which some, who are able to use the instrument, are apt to overlook. In the first place, the station pole ought invariably to be removed from its place to make room for the instrument. It is not sufficient to push it to one side, as is sometimes done. In the second place, the instrument should be set exactly over the spot which the pole occupied, and by the help of the adjusting plummet attached to the theodolite, 14 TRIANGULATION. its axis will be easily made very nearly to coincide with what was formerly the axis of the station pole. And, in the third place, the instrument should be very carefully levelled before beginning to observe, and care taken that the level- ling plate screws are not again touched till the observations are completed. All of these remarks being kept in view, and the instrument having been adjusted with 360° bearing north, as indicated by the needle, the observations may be commenced. The observer ought then to take the bearings of all the stations within view, as well as of all conspicuous marks on the banks of the river, such as spires, chimneys, or any pro- minent and well defined objects, which may afterwards be useful, as points for observation, in laying down the positions of the soundings and sand banks. In taking these observa- tions, he should begin at zero or 360° (which are identical), and go regularly round the horizon. It is proper to take the objects to be observed in regTilar succession as they come into view, that none of them may be omitted, and that there may be as little occasion as possible for moving the instru- ment. When the observations have been completed, a bear- ing should again be taken to the first station observed, to ascertain whether the reading be the same as that registered in the field book ; and if this is found to be the case, the lower limb of the instrument may be presumed to have re- mained stationary during the operation, and the observa- tions may be held as accurate. The theodolites used for such surveys as I am describing have generally two verniers, placed at opposite points of the horizontal limb. At these the angles maybe read off only TRIANGULATION. 15 to degrees and minutes, smaller angular quantities being disregarded. If an instrument reading to seconds be em- ployed, the exact bearing may be noted, as it will be use- ful if any of the triangles are to be calculated ; but for ordinary surveys this refinement is unnecessary, as angidar quantities, which are smaller than one minute, cannot be appreciated in protracting the work. It is proper, how- ever, in all cases, to read off and register the bearings gi- ven by both verniers, as the one reading serves as a check on the other. They will occasionally be found to differ a minute in the reading, and in that case the mean maj be taken as the true bearing, if great accuracy is required ; but this, as will afterwards appear, is of no practical consequence in protracting the work. The following is the manner in which the observations ought to be registered, and, like all the other examples I have given, the angles are taken from the field book of an actual survey. Angles at Balmerino Station, River Tay, 8th Aiigust 1833. Vernier Vernier A B o / North magnetic, . 360 b 180 West chimney of Birkhill House, 80 40 260 40 Flisk station, , 90 4 270 4 Randerston station. . . 101 20 281 21 Errol Church spire, . 105 23 285 23 Seaside station. . 110 56 290 57 End of red-tiled house. Powgavie, : 117 24 297 23 Powgavie station, . . 128 46 308 46 End of plantation. . 141 32 321 31 Monorgan station, . . . 148 20 328 20 Invergowrie station, . 189 34 9 34 190 30 10 31 233 26 53 26 246 51 66 52 268 58 88 59 274 12 94 12 283 30 103 30 360 180 16 TRI ANGULATION. Invergowrie cliiinney, Dundee Law, Dundee Church Tower, Ferry ness, Newport Inn, Small house in Wormwort Bay, Magnetic north, The positions of most of these stations will be seen on referring to Plate I., which is a sketch shewing a small part of the triangulation of the river Tay, in which they occur. When the bearings have been taken, the station pole is again erected in its place and carefully plumbed, and the observa- tions from the other stations may then be proceeded with. Referring to the same example, we shall suppose that the next station from which observations are to be made is Flisk. The field book must then be consulted to ascertain what was the bearing of Flisk from Balmerino. It is found to be registered on the other page under vernier A as 90° 4'. That vernier is then set and clamped at 90° 4', and the instrument having been directed to Balmerino station, the observations are taken and registered as follows : — Angles taken at Flisk Station, River Tay, 8th August 1833. Balmerino station, East Balmbrich station, Balmbrich Castle, River Earn station, Mugdrum Island station. West Port Allen station, Vernier Vernier A B 90 4 270 4 270 14 90 13 268 30 88 30 276 9 96 9 273 30 93 30 278 53 98 54 TRIANGULATION. 17 East Port Allen station, Randerston station, Church of Errol, Seaside station, End of red house, Port Allen, End of plantation, Monorgan station, Invergowrie station, Dundee Law, Dundee Church Tower, BirkhilL Vernier Vernier A B o ' o ' 283 40 103 40 296 25 116 26 299 57 119 57 330 26 160 29 348 56 168 57 30 4 210 4 37 40 217 40 55 20 235 21 70 14 250 15 77 57 257 58 96 14 276 13 We shall suppose the next place from which observations are to be taken to be Seaside. In adjusting the theodolite at this station, the surveyor has a choice of adopting either the bearing from Balmerino or from Flisk, as that to which he is to set the vernier. In the event of adopting Bal- merino, the vernier would be set at 110° 5& (the bearing of Seaside from that station), and the instrument directed to Balmerino. In adopting Flisk it would be set at 330° 26', the instrument being directed to that place ; and in either case the bearings would be taken in the manner al- ready explained. In this way the angular bearings to prominent objects from all the triangulation stations on the river are to be carefully taken and registered. The following general rule may be given for adjusting the theodolite, as shewn practically in the foregoing ex- amples : Suppose the observations are to be taken from a station which we may call z, the surveyor may adopt, as the primary bearing for setting the instrument, the angle 18 TRIANGULATION. which z bore from any other station in the survey, as w, x, or y, from which z had previously been observed (provided the situations of those stations render them equally appli- cable), the theodolite being, in every instance, directed to the station the bearing of which has been used. By following the system which has been described, it is obvious that all the corresponding bearings throughout the whole of the triangulation will be parallel to each other, whatever be the position of the station from which they are taken. For example, the lines bearing 360°, 45°, 90°, and 135°, or N., NE., E., and S.E. by compass, at all the differ- ent stations, will be parallel to each other, and of course all the intermediate bearings of the same name will be parallel also. This may perhaps be rendered more clear by a reference to Plate II., in which the irregular dotted lines are supposed to represent the outline of a river, and A, B, C, D, E, F and G, stations placed on its banks ; the circles representing, on an exaggerated scale, the horizontal limb of the theodolite, when adjusted at the different points. At station A, 360° is set at the magnetic north, as indicated by the needle. The bearing of B from A is then found to be 45°, and in setting the instrument at B, the station A is made to bear 45° from it also. In like manner the bearing of C from B is 180°, and that of B from C is made the same. The reader will trace this throughout the whole of the sta- tions to G. A simple examination of the diagram will shew, that if the triangulation is correctly constructed in accord- ance with the rules laid down, the corresponding bearings throughout the whole, as already stated, will be parallel to each other. I TRIANGULATION. 19 One point has still to be noticed. It will be observed that the bearing from A to G is 135°, but that the bear- ing from G to A is 315". This, although a different read- ing, is actually the same bearing, as appears very obviously from the diagram, the variation in the reading being occa- sioned by the limb of the instrument having been turned round 180°. Every bearing may, in this way, be said to have two readings at opposite points on the limb of the theo- dolite ; and the original and its opposite bearing are read alternately. Thus, if we represent the stations of a trian- gulation by the letter A, affixing numbers in the order in which the observations were made at them, calling the first Aj, it will be found that all those having even numbers as A2, A4, Ae, Ag &c., will give the same bearings to station Aj, as those taken from it, and all those having odd num- bers, such as A3, A5, A7, A9 &c., will give the opposite bear- ings to Ap In checking the bearings of different stations to ascertain whether the work has been accurately done, some difficulty may arise to the inexperienced, especially if the theodolite has only one vernier, by finding this variation from a bearing formerly taken and registered. If the instrument has two verniers A and B, and if the reading vernier A does not indicate the same bearing as that formerly registered, the original bearing will be found on examining the vernier B. But if there be not two verniers, the rule for discovering whether the work be right is easily applied, and is as follows. Suppose a reading, as from G to A, plate II, does not cor- respond with the bearing taken on a former occasion from A to G, then if the angle read is above 180° deduct 180° from it, and it will give the former bearing; if it be 180° or 20 TRIANGULATION. below 180° add 180° to it, and the same result will be ob- tained. Thus the bearing from G to A = 315° - 180** = 135° = the bearing from A to G ; and again, the bearing from A to E is 63° 20' + 180° = 243° 20' = the bearing from E to A. It will be obvious to all, that the foregoing observations have reference to an instrument whose reading limb is di- vided into 360° and not into twice 180°, the former division being preferable, and now almost universally adopted. ( 21 ) CHAPTER II. BASE LINE. Most desirable Length for a Base Line — Requirements for insuring an accu- rate measurement — Process of Measuring — Methods of determining the extremities of the Base — Three cases described, first when the Line ex- tends between two triangulation stations ; second, when it is an inde- pendent Line but connected with the triangulation by a back bearing ; third, when it is measured on a sand bank and unconnected with the triangulation — Methods to be pursued in these different cases described. The process described in the former chapter is entirely one of angular not of linear measurement ; and although it affords the data for determining the relative positions of the different stations and objects on the river, it does not give the means of ascertaining the linear distances between them in terms of any measure, as yards or miles. It furnishes, in fact, merely a representation or map of the relative po- sitions of the objects, intersected by the lines of observation, without affording a scale, which can be determined only by the actual measurement on the ground of a base line ; an operation which forms the subject of the present chapter. The actual measurement of ^the fundamental base line, and the observations for the determination of its length in reference to the distances between the triangulation stations, 22 BASE LINE. cannot occupy too much care and attention, as the accuracy of the scale of the survey, and consequently of all the linear dimensions on the plan to be constructed, depends entirely on the correct execution of these important operations. Most of our readers are, no doubt, aware of the extreme care and labour which have been bestowed on the operation of measuring the great fundamental base lines for the tri- gonometrical survey of the country, a subject which has given rise to much practical and theoretical discussion ; and although, in surveying for engineering purposes generally, the same degree of accuracy is not required, and is indeed quite inappropriate, as well from the time which must be devoted to it as from the means employed in its attainment, still the surveyor, bearing in mind the importance that is attached to this department in surveys of greater extent, ought, in his own practice, to use every means in his power to make as near an approximation to the truth as possible. The length of the base line to be adopted is the first con- sideration to which the attention of the surveyor ought to be directed. In deciding on this point, he must be regu- lated partly by the extent of the survey to be made, and partly by the formation of the country. A line extending from three quarters of a mile to a mile and a quarter in length will be found sufficient for most engineering surveys. But, it may be stated as a general rule, that it is advan- tageous to adopt as long a base line as the circumstances of the situation will admit of, taking care, however, that the limits I have mentioned be ,not greatly exceeded, and, at the same time, keeping in view that the angles from the extre- mities of the base to the other stations may be favourable BASE LINE. 23 for connecting it with the survey. It is often only with great difficulty, however, that even this limit in regard to the length of the base line is attained, and it can very rarely be exceeded in ordinary river surveying, owing to the diffi- culty, in most situations, of obtaining a stretch of ground of sufficient extent possessing all the necessary requirements to insure accuracy in the measurement. The requirements alluded to may be comprehended under three heads, all of which the surveyor ought to keep in view in selecting the situation for the base line. In the first place, the surface of the ground ought to be smooth, and without inequalities, so as to admit of the mea- suring chain being fully and properly stretched, on which the accuracy of the result may be said chiefly to depend. Secondly, although the base may be measured on regularly rising gTOund, which, in conformity with the first require- ment, has a smooth surface, still it is more desirable that the site of the line should be as nearly level as possible : for if one extremity of the base is on a much higher level than the other, it is necessary that the difference of height be accurately ascertained by the spirit-level, in order that a correction may be applied for the error in actual horizontal length, produced by measm'ing along the hypothenuse in- stead of the base of a right angled triangle. This operation involves a considerable consumption of time, and ought, il' possible, to be avoided, by selecting a level line. It is very seldom necessary, however, to resort to it in surveying a river ; for if the formation of its margin should be such as to preclude the possibility of selecting a situation on the land free from the disadvantage of an irregularity in its 24 BASE LINE. level, a nearly horizontal plane, of sufficient extent, is, in most cases, afforded at low water by some of the sand banks in its bed or estuary. Thirdly, the two poles used for mark- ing the extremities of the base ought, if it can possibly be attained, to be visible from every point of the line, as this greatly conduces to the ease and accuracy with which the work is done, saving the trouble of putting in intermediate poles, and the chance^ of error in consequence. This re- quirement is generally easily attained wiien the site of the base is on a sand bank ; but when it extends along the margin of the river, fences and other obstructions occasion- ally intervene, and cause much trouble in effecting an ac- curate measurement. I mention this circumstance as the evil may often be avoided, by using a little care in selecting the site. When a situation for the measurement of the line, ful- filling these three requirements, and extending between two of the triangulation stations, can be obtained, it should at once be adopted, as both the field work and the protraction are thereby greatly facilitated ; and although, in order to simplify the subject, the attainment of this desirable object was not introduced in the preceding Chapter as one of the conditions necessary for making a good triangulation, yet it should not be overlooked in fixing on the sites of the trian- gulation stations. It is often, however, no doubt, very diffi- cult to pitch upon two points possessing the necessary re- quirements for good triangulation stations, and at the same time having a clear stretch of ground extending between them, in all respects suitable for making an accurate mea- surement ; and when this union of qualities cannot be pro- BASE LINE. 25 cured, the base line may be placed, as already tinted, either on a level sand bank or marsh, so situated that favour- able angles may be obtained from the principal stations on the river for fixing its extremities with accuracy, and con- necting the measured distance with the triangulation of the survey. The nature of the observations required for this purpose merits a little attention, and will be noticed here- after. In the mean time it may be remarked in reference to any situation that may be adopted, that the method of procedure in measuring the line is the same in all cases. Rods formed of wood, glass, and other materials, as well as chains of a peculiar construction, are employed in the measurement of base lines when a very near approximation to the truth is required ; but for surveys of the kind described in this treatise the measure or rule employed is the common sur- veying chain of 100 feet in length. The chain of 66 feet, although exceedingly useful, and even indispensable, in land- surveying, from its being divided into links, is, from this very circumstance, by no means so convenient as the 100 feet chain for engineering surveys, in which the whole of the dimensions are referred to a scale of feet. From the nature of its construction, the chain, on being stretched, is very liable to yield to a small extent at the junction of each link, and its length is thus often gradually increased by use. It should, therefore, be carefully compared with some known standard, and, if necessary, properly adjusted before being employed in the measurement of the base line. But if this be inconvenient, it will answer equally well to compare it with the standard, after the operation has been completed, 26 BASE LINE. and before it has been used for any other purpose, and if found too long, an addition, proportional to the amount of error, must be made to the length of the base. The persons employed in measuring the line ought to have some experience in the use of the chain. Care should be taken that it be properly stretched, and that the marking pins be placed with exactness by those who " drive" and " lead " it. It is also of importance that the exact line of direction be kept with the greatest possible accuracy, as any variation from it causes an increase in the measured length. The distance should be ascertained at least three times, or oftener if necessary, otherwise no check on its accuracy is obtained ; and the person who " drove " the chain during the first measurement, ought to " lead " it during the se- cond. If the maximum difference between the results be found not to exceed 3 feet, the third measurement being intermediate between the other two, the operation may be considered as sufficiently accurate for ordinary purposes, and the mean of the three results should in that case be adopted as the length of the base line of the survey. When the base line extends between two of the triangu- lation stations, which, as already noticed, is the most con- venient situation that can be adopted, the points referred to in the foregoing remarks are all that demand particular attention ; but in reference to those cases where the line is situated on a marsh or sand bank, some remarks are still necessary relative to the observations which are required for fixing the positions of the extremities of the base, and connecting the measured distance with the triangidation of the survey. BASE LINE. 27 . The surfaces of marshes and sand banks are, in general, smooth and flat, without any great diversity of level, and are, on this account, very favourable for making an accu- rate measurement ; but as they are generally covered by the tide at high water, it is often difficult, and sometimes impossible, if they are on a very low level, to complete the whole operation of measuring the line, and taking the ob- servations for fixing its extremities in one tide ; which, if it can be accomplished, is, for many reasons, desirable. When the marsh or sand bank on which the measurement is to be made has been selected, and the situation of the line, in reference to the triangulation stations, has been duly considered and fixed on, a small surveying pole, having a flag attached to it, should be placed at one extremity of the base ; and a similar pole should be set uj^ in the direction in which the measurement is to be made, and at such a dis- tance from the first as may be considered a proper length for the line. The distance between the poles should then be ascertained in the manner already described ; and as it will, in all probability, prove to be a quantity which is not easily divisible, a correction to convert it into an easily divisible quantity may be made in a very simple manner. Thus, if the length be 8007 feet, a quantity into which it would be difficult to divide any given space, one of the poles should be moved back 7 feet, and the length of the line reduced to 8000 feet ; a quantity into which any space on a plan may, if necessary, be easily and accurately divided for the purpose of making a scale. The utility of this cor- rection will be better understood when we come to treat of the protraction, to facilitate which it is intended. 28 basp: line. It is evident tliat if an observation be taken from one of the triangnlation stations to tbe pole at either of the extre- mities of the base line, and if this observation be used as the primary bearing in taking the angles for ascertaining the position of the line, the bearings so taken will accord in parallelism with those of the triangnlation ; and the site of the base line might thus be laid down by the means em- ployed in protracting the triangulation itself, which will be particularly described hereafter. When the base line poles, therefore, are so situated that they may be allowed to re- main for some time, even though exposed on a marsh or sand bank, without danger of being carried away by the tide, and all traces of their positions lost, it is proper that the observations for determining their positions should be made in this way. But it is sometimes necessary, and has indeed happened in my own experience, that in order to obtain a proper base line, they must be placed on a low- sand bank, covered to a considerable depth at high water, and situated in the midde of a channel or estuary, perhaps 5 or 6 miles in breadth, where it would not be safe to allow the stations to be overflowed, with the expectation of their remaining unchanged ; and, therefore, as the whole opera- tion connected with the measurement has to be completed in one tide, there is not, in such circumstances, sufficient time for ascertaining the bearing of the poles from any of the triangulation stations. If there wera no local attrac- tion, the magnetic needle might, in this case, be again re- ferred to. But, from what has already been said on this subject, it will be seen that its direction cannot be relied on. Indeed, the first instance of variation, mentioned at page 9, BASE LINE. 29 occurred on a sand bank in attempting to make observations for fixing the extremities of a base line in tbis manner, being quite analogous to the case at present under consider- ation. One of the stations of the triangTilation ought, therefore, to be taken as zero ; and the theodolite should be set, and the observations made, in the following manner. The instrument being clamped at 360°, the telescope is to be directed to the station which has been assumed as zero ; after which, the bearings of all the stations within view are to be taken and registered ; and the same operation having been repeated at the other end of the base line, it will be found that sufficient data have been obtained for accurately determining its position, as will appear more evidently here- after in treating of the Protraction. f/X^ OF THE '^ ( 30 ) CHAPTER III. TIDE OBSERVATIONS. Remarks on the Tides of Rivers — "Variations in the Tidal Lines — Professor Robison's remarks as to the anomalies of River Tides — Explanation of the exact nature of the inquiry into the Tides which is to be instituted — Selection of Stations for Tide Observations — Agents which produce dis- turbance in the parallelism of the Tidal Lines — Description of Tide- Gauges to be used — Points to be kept in view in fixing them — Method of fixing them on Sloping Beaches — Method of keeping the Time — Method of making Observations — Form for registering Observations — Description of Form — Ascertaining the relative Levels of the Gauges — Points to be kept in view in levelling for this purpose. The tides of rivers are influenced partly by the circum- stances under whicli the great tidal waves of the ocean enter their mouths or estuaries, and partly by the size of the streams and the configuration of the beds and banks of the rivers themselves, all of which have a share in modifying the free flow of the tidal currents along their channels. As no rivers are to be met with whose communication with the sea, and the course and strength of whose streams are in all respects similar, corresponding dissimilarities naturally occur in the circumstances attending the rise and fall of river tides. A thorough and accurate investigation of this TIDE OBSERVATIONS. 31 subject forms a very important part of the marine depart- ment of a river survey ; and tlie method of conducting it, as a^Dplicable to the object of engineering surveying, will now be described. The observations contained in the pre- ceding chapters may be said to apply to the art of survey- ing generally ; but many of the remarks to be made regard- ing tidal ohservations, soundings and sections, refer solely to such investigations as are instituted in reference to purely engineering questions, and are consequently inapplicable to other purposes. If it were correct to assume that the high water mark of each tide, at any given number of points in a river's course, stood invariably on the same level,— that the times of high water at these points were the same, — and that the progres- sive rise and fall of the tides were uniform and equal at every point, — or, in other words, that the lines formed by the surface of the water at all periods of flood and ebb, which we shall in future denominate the tidal lines of the river, were parallel to the line of high water, — the work of the surveyor would be greatly simplified. But if the engi- neer were to make such an assumption the groundwork on which to found his opinions and frame his designs, his con- clusions would almost invariably be formed on erroneous data; and in many instances the consequences might be very serious. In no river, so far as I am aware, are the high water lines of every tide perfectly level, or the tidal lines invaria- bly parallel ; and observations made in reference to these points, in some situations, give results which are very ano- malous, and which would very materially affect the accu- 32 TIDE OBSERVATIONS. racy of the soundings and sections of a river, if they were not distinctly ascertained, and the necessary precautions taken to avoid the errors to which they would inevitably lead. The following remarks by the late eminent Professor Robison,* illustrative of the causes of some of the anoma- lies in river tides, are interesting in connection with this subject. Regarding one of the anomalies to which I have alluded^ namely, the rise or inclination which often occurs in the high water line, from the entrance of a river upwards, the Professor makes the following observations : — " When a wave of a certain magnitude enters a channel, it has a cer- tain quantity of motion, measured by the quantity of water and its velocity. If the channel, keeping the same depth, contract its width, the water, keeping for a while its mo- mentum, must increase its velocity or its depth, or both, and thus it may happen, that, although the greatest eleva- tion produced by the joint action of the sun and moon in the open sea does not exceed 8 or 9 feet, the tide in some singular situations may mount considerably higher. It seems to be owing to this that the high water of the Atlantic Ocean, which at St Helena does not exceed 4 or 5 feet, setting in obliquely on the coast of North America, ranges along that coast in a channel, gradually narrowing till it is stopped in the Bay of Fundy as a hook, and there it heaps up to an astonishing degree." Again, as to the variation in the times of high water at different points, and the non-paral- lelism of the tidal lines, the same eminent individual makes * Robison's Mechanical Philosophy (Brewster's Edition), vol. iii. p. 353. TIDE OBSERVATIONS. 33 the following remarks : — " Suppose a great navigable river, running nearly in a meridional direction, and falling into the sea in a southern coast. The high water of the ocean reaches the mouth of the river (we may suppose) when the sun and moon are together in the meridian. It is there- fore a spring tide high water at the mouth of the river at noon. This checks the stream at the mouth of the river, and causes it to deepen. This again checks the current farther up the river, and it deepens there also, because there is always the same quantity of land water pouring into it. The stream is not perhaps stopped, but only retarded. But this cannot happen without its growing deeper. This is propagated farther and farther up the stream, and it is perceived at a great distance up the river. But this re- quires a considerable time. We may suppose it just a lu- nar day before it arrives at a certain wharf up the river. The moon at the end of the day is again on the meridian, as it was when it was spring tide at the mouth of the river, the day before. But in this interval there has been another high water at the mouth of the river, at the preceding mid- night, and there has just been a third high water about 15 minutes before the moon came to the meridian, and 35 minutes after the sun has passed it. There must have been two low waters in the interval at the mouth of the river. Now, in the same way that the tide of yesterday noon is propagated up the stream, the tide of midnight has also proceeded upwards, and thus there are three co-existent high waters in the river. One of them is a spring tide, and it is far up at the wharf above mentioned. The second, or the midnight tide, must be half way up the river, and the c 34 TIDE OBSERVATIONS. third is at the mouth of the river. And there must be two low waters intervening. The low water, that is, a state of the river below its natural level, is produced by the passing low water of the ocean, in the same way that the high wa- ter was. For when the ocean falls below its natural level at the mouth of the river, it occasions a greater declivity of the issuing stream of the river. This must augment its velocity ; this abstracts more water from the stream above ; and that part also sinks below its natural level, and gives a greater declivity to the waters behind it. And thus the stream is accelerated, and the depth is lessened in suc- cession, in the same way as the opposite effects were pro- duced. We have a low water at different wharfs in succes- sion just as we had the high waters." " This state of things, which must be familiarly known to all who have paid any attention to these matters, being- seen in almost every river that opens into a tide way, gives us the most distinct notion of the mechanism of the tides. It is a great mistake to ima^ne that we cannot have high wa- ter at London Bridge (for example), unless the water be raised to that level all the way from the mouth of the Thames. In many places that are far from the sea, the stream at the moment of high water is down the river, and sometimes it is considerable. At Quebec it runs downwards at least 3 miles per hour. Therefore the water is not heaped up to a level, for there is no stream without a declivity." In the river Amazon, the tide is said to ascend against the stream, in the manner described, for several days, and to penetrate to the distance of 200 leagues from its mouth, seven or eight tides, with intermediate low waters, following TIDE OBSERVATIONS. 35 each other in succession ;* and in the Thames we find a similar tidal succession, but not to so great an extent, and arising, according to Mr "Whewell, " from the peculiar cir- cumstance of the river's having a tide compounded of two tides arriving by different roads, after journeys of different lenglhs," in allusion to the two branches into which the tidal wave is divided on reaching the British shores, one of which flows up the English Channel, while the other pro- ceeds along the west and northern coast of the country, and flowing down the east coast, again joins the other branch. Such variations on the tidal lines as those described in the quotations from works of Professor Robison, would no doubt be found to exist in every situation, if the rise of tide and the capacity of the river or estuary were sufficiently great to admit of their full development, and if the obser- vations made were of sufficient extent to include them with- in their range. But from the smallness of our rivers, which flow from a comparatively narrow and contracted country, the ordinary surveys made for engineering purposes in Bri- tain very rarely embrace so great a field of observations as to include the range of more than one tide, nevertheless, even in this country, such irregularities are found to exist on the tidal lines as to require careful investigation to insure accu- racy, especially in situations where the rise of tide is great. Before entering fully on the explanation of the diff'erent steps to be taken in making a correct series of tidal obser- vations, by which alone the anomalies I have alluded to can be discovered, some preliminary remarks, in explanation of the exact nature of the inquiry to be instituted, appear ne- cessary to the proper understanding of what is to follow. " Encyclopedia Britamiica, art. River 36 TIDE OBSERVATIONS. If the tidal lines of a river were level and parallel, a se- ries of observations on the progressive rise and fall of the tides (made in the manner described hereafter), at a single oraduated gauge placed in any part of its course, at which the whole of the tidal rise and fall is developed, would af- ford sufficient data for obtaining a survey in all respects correct. If, on the other hand, the lines had a certain in- clination, but were nevertheless parallel to each other, the single series of observations alluded to, would still be suffi- cient for obtaining the correct depths at high water, and consequently an accurate profile of the bed of the river, ex- hibiting all its inequalities ; but it is evident that the incli- nation of the tidal lines, and, what is of more importance, the true position of the bed of the river in reference to the datum line of the section, could not be ascertained by this means. Thus let the lines a h and c d represent the high Fig. 1. water line and the bed of a river respectively, and let there be a rise of 1 foot 6 inches in both of them in the distance represented in the cut. If one tide gauge only were used, suppose at the lower extremity of the river, the section, when protracted, would assume the form represented by the dotted lines x b and ^ d, in which the high water line and bottom of the river are shewn as being level, whereas their TIDE OBSERVATIONS. 37 correct positions in reference to the level line a e, whicli we may suppose to be the datum line of the section, are those represented by the lines a h and c d, on each of which there is a rise of 1 foot 6 inches. The inclination of the bed forms an important element in all questions relative to the navigation of rivers, and pro- per means must be adopted for its determination before any design of improvement can be formed. In order to ascer- tain this, it is obvious that at least two tide gauges must be used, one at either extremity of the river ; and farther, that their relative levels must be accurately ascertained. Now, if the high water line in the case referred to in fig. 1. should stand at 10 feet on the lower gauge, it will, if their zeroes are at the same level, stand at 11 feet 6 inches on the upper one at the same moment, thus indicating the dif- ference of level. In this way not only are the data for as- certaining the correct depths at high water afforded, but a proper section of the river can be made, its tidal lines and bed being represented in their true positions in reference to the datum line. From what has already been said, however, regarding the anomalies of the tides, it will readily be seen that it would be improper to assume that the tidal lines are paral- lel during the whole period of flood and ebb ; and there- fore it is necessary, in surveying, to provide for this, by adopting intermediate stations for tide observations, and by taking the soundings of the river at particular periods when the deviation from parallelism in the tidal lines is at its minimum, as will be more particularly noticed hereafter. In determining the number and selecting the sites of 38 TIDE OBSERVATIONS. the stations at which tide observations are to be made, the engineer ought to be regulated by the amount of tidal rise and the configuration of the banks of the river. In rivers where the rise of tide is small, and the tidal currents are very languid, fewer places of observation are required than in situations where there is a great rise of tide, accompa- nied by rapid currents, as the parallelism of the tidal lines, on which the correctness of the soundings depends, is less apt to be disturbed in the former than in the latter case. It may be stated as a general rule, that the more numerous the tide stations are, the nearer will the results obtained approximate to the exact line of the tidal wave at any par- ticular moment of flood or ebb, and the less chance will there be of error in reducing the depths of the soundings. As, however, every additional station involves additional trouble and expense, and as great difficulty is often expe- rienced in finding persons properly qualified to make the observations, it is generally necessary, in ordinary survey- ing, to reduce this part of the establishment as much as possible, and often to a greater extent than could be wished, adopting, in preference, the precaution of taking the sound- ings at those periods of tide when the deviation from paral- lelism is ascertained to be small, and in this way the want of a more extended system of observations is of less con- sequence. The only matter of regret in pursuing this course is, that so near an approximation cannot be obtained to the forms assumed by the tidal wave during flood and ebb, which is in itself a subject of great interest. Whether an extended or limited series of observations is to be adopted, it is necessary, while selecting the sites for TIDE OBSERVATIONS. 39 the stations, to have due regard to the agents most likely to produce disturbance in the parallelism of the tidal lines. The most powerful of these agents are, abrupt turns or bends, and sudden enlargements or contractions in the transverse sectional areas of rivers. The irregularities which exist in the declivities of the beds of most rivers do not necessarily affect the parallelism of the tidal lines, and need not there- fore, unless they are abrupt a.nd high, influence the survey- or in selecting the stations, their only effect being to alter the vertical amount of tidal rise at the places where they occur. When the sites of the stations have been finally deter- mined on, which should be done at an early stag^e of the survey, the tide gauges ought to be erected, and the obser- vations at the different places commenced without loss of time, in order that they may embrace as great a range of tides as possible, as the correctness of the results deduced from the observations of course depends on their number. The gauges should be made of plank, and ought to mea- sure about 7 inches in breadth and IJ inch in ^'^- -• thickness, their length depending on the rise of ~5 tide. They should be accurately graduated to feet, 6 inches, and 3 inches, in the manner shewn in the diagram. It is unnecessary to graduate the inter- mediate inches, which may be easily measured by the €ye; and when marked, introduce a needless complexity of gi'aduation, apt to puzzle rather than to assist the ordinary class of observers. The gauges should be of a length sufficient to include the whole range of the highest tide from low to high water, 40 TIDE OBSERVATIONS. and should be so placed as to be easily seen at all times by tlie person who is to make the observations. The first of these desiderata can be best attained by making the gauge a few feet longer than the reputed maximum rise of tide at the station where it is to be fixed, and by placing 2 or 3 feet of it below the supposed low water line, it being a matter of no consequence at what point on the staff the low water stands. The second is often very easily accomplished by fix- ing the gauge beside a quay wall or an abruptly rising bank. But difficulty sometimes occurs when it is necessary to erect it on a gently sloping beach, where the surface, covered by the rise of tide, is so great as to render the figuring of the gauge, if placed at the low water line, indistinct, or perhaps altogether illegible, when viewed from the high water mark. I have on more than one occasion, under such circumstances, found it very convenient to divide the gauge into pieces, and to fix them in the manner shewn in fig. 3. The rise of tide is here represented as being 19 feet; and the gauge is divided into four pieces, the upper mark of each being placed on the same level as the corresponding mark at the bottom of the piece above it. It is better to employ this TIDE OBSERVATIONS. 41 simple arrangement when it can possibly be done, than to put up the gauge in one piece, which, in such a situation as that alluded to, not only requires a very strong frame- work properly guyed for its support, but is liable to be car- ried away by the tide, while recourse must be had to the inconvenient method of using a telescope, in order to read the figures. The gauges having been adjusted, the observations on the progressive rise and fall of the tide should be commenced. The persons employed to make them must be furnished with watches. It is difficult entirely to avoid variation in time at the different stations, and the only remedy for this is to visit the observers as often as possible, and, if necessary, to correct their time by reference to a pocket chronometer ; the amount of error and the time when the correction was made being noted in the tide book. In this way the neces- sary allowance may be made for difference of time in com- paring the observations at different stations, and in reducing the depths of the soundings. The observations should be made at intervals of not less than ten minutes, and should extend from six in the morning till six in the evening at least, and earlier or later when soundings are to be taken before or after these hours. It will be found to be a great convenience to employ printed forms for registering the ob- servations of both the tides and soundings, and indeed of all the observations in surveying to which they can be applied. Annexed is a copy of the form I have been in the habit of using for registering those of the tides, which will best ex- plain the mode of doing it. The example is taken from the lliver Lune. 42 TIDE OBSERVATIONS. REGISTER OF TIDES AT OLASSON PIER Time. 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 10 20 Height. Rejiarks Wuid Time. 10 11 12 30 40 50 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 Height. 24 22 10 17 15 14 1 ■.; .12 U Remarks. TidebL-,n, ) to appear, j NTj- — The zero of the tide gauge in this example was placed TIDE OBSERVATIONS. 43 STATION, KIVEE LUNE, Ctii SErxKMnEn 183,1. Time. Height. Time. Height. Remarks. Remarks. H. M. Ft. In. H. M. Ft. In. 1 10 20 .1 11 5 30 40 50 -- 10 1 1 30 4 i 6 '■■■ •■ 40 4 10 10 •2:; 50 ■■) IJ 20 •2>> 2 <-! (> 30 2S i) 10 - (3 40 23 10 Wind ) SW. { light r 20 (i 50 23 11 30 [) G 7 2;> 11 hroer.o. 1 40 10 6 10 50 11 6 20 3 10 20 12 13 14 (i 5 2 30 40 50 30 40 lo 15 (1 9 II RESULTS, 50 1(3 7 Greatest depth, 24 ft. 3 in. 4 IT y Greatest height, 8 10 18 o Whole rise, 23 7 20 19 () Began to rise at 9 h. 5 m. 30 19 (> High Water at 12h.lOiii. 40 20 1 50 21 5 10 20 -21 !) above the level of high water, so that the gauge reads downwards. 44 TIDE OBSERVATIONS. Tho/>\s-^ column contains the time ; the second, the height at which the water stood on the gauge ; the third, is for re- marks, and at the end are the results of the day's observa- tion. The figures in black are those of the printed form, and those in red correspond to the figures entered by the observer. It may be proper to mention, before leaving the subject of the apparatus employed, that, in river surveys I have never found it necessary to use glass tubes in making the observa- tions, as the water has generally been comparatively calm ; but in surveying exposed places, such as parts of the coast, in reference to harbours, I have found it indispensably ne- cessary to employ this apparatus, to counteract the disturb- ing eflPect of the undulation of the surface of the sea, even in moderate states of the weather. The next process to which I shall advert, is that of as- certaining the relative levels of the different gauges, for the purpose of determining the form assumed by the tidal lines. Advanta;ge should be taken of calm weather for this pur- pose ; and although it is only an ordinary levelling operation, yet, like everything else in which accuracy is indispensable, it requires attention, often absorbs a great deal of time, and probably ends in error if not conducted in a systematic manner. It is a nice operation to transfer a level accurately for a distance, varying perhaps from 6 to 30 miles or more, according to the extent of the survey ; and while it is inex- pedient to introduce too many refinements in performing the operation, it is necessary to insure expedition and accuracy that the following particulars be attended to. In i\\Q first place the whole distance must be levelled at least twice, and TIDE OBSERVATIONS. 45 any part of it that may be found erroneous, of course oftener. Secondly, the distance to be levelled should be divided into compartments of such lengths that each of them may be gone over twice in one day ; and, in addition to this, bench- marks should be fixed at convenient intervals. Thirdly, a tripod, or, what answers the same purpose, a small peg of wood driven a few inches into the ground, on which to rest the levelling rod, should invariably be used where the soil is soft ; and,ybwr/A/y, the distance at which the rod is placed from the instrument should be as nearly as possible the same in taking the fore and back sights, so as to neutralize the ejQPect of the earth's curvature, and should not exceed 350 paces. By attending to these directions, the work will be gTeatly simplified ; but it is nevertheless a tedious opera- tion, and every improvement on the instruments used, or the system of levelling adopted, deserves attention. The latest improvements on the instruments of which I am aware, are those suggested by Mr Thomas Stevenson, who, in addition to the parallel plate screws, has introduced a ball and socket jomt, and a small circular level, to facilitate the adjustment of the instrument, and certain screws for moving and clamp- ing the vane of the levelling rod. By means of these im- provements, as tested by experiment, a very great saving in the time at present consumed in adjusting the instrument is effected, and greater nicety in bringing the centre of the vane to coincide with the cross hairs of the instrument is obtained. ( 46 ) CHAPTER IV. SOUNDINGS. Nature of the variations on the Tidal Lines explained — Examples of the variations on the Dee in Cheshire— The Lune in Lancashire — The Forth in Stirlingshire — Manner in which these variations atFect the Soundings — Reference of Soundings to one Datum Line explained — Half Tide Level not applicable in the case of Rivers — High Water of a certain Tide adopted — Use made of the Tide Gauges in reducing Soundings to the datum — Formula for their reduction — Example — Formula only true on the supposition of the Lines being parallel to High Vfater — Example in the case of the Dee — Results aifected by the erroneous supposition — Mode of avoiding this by increasing the number of Tide Stations — but this not always attainable — General Rules for taking Soundings to ap- proximate to accuracy — Method of taking Soundings described — Equal Distribution of Soundings over area of River — Observations for fixing their positions. That any directions as to the best metliod of taking soundings, and avoiding inaccuracy in reducing tliem to high or low water, arising from the non-parallelism of the tidal lines, may be clearly understood and duly appreciated, it is necessary that the reader should know distinctly the nature of the variations adverted to, which are determined by means of the observations treated of in the preceding chap- ter ; and also that he should be fully aware of the manner in which they affect the accuracy of the soundings, and the SOUNDINGS. 47 extent of error that may, under certain circumstances, be occasioned by tlieni. I shall, therefore, before entering upon what is, strictly speaking, the subject of this chapter, lay before the reader the results actually obtained by me in making some surveys for engineering purposes, as they will afford distinct practical information on the points al- luded to, and, at the same time, be useful in conveying a correct idea of the nature of the data required in producing a complete marine survey. The results which I shall state, in the first place, were obtained from observations made during the months of May and June 1839, in surveying the river Dee in North Wales, with reference to the improvement of its navigation. In making the survey of that river, which extended from the Bridge of Chester to Flint, three series of simultaneous tide observations were instituted, one at Chester, another at a small village called Connah's Quay, and a third at Flint. The following were the results obtained from the survey. The distance from Chester to Connah's Quay is 7 J miles, and that from Connah's Quay to Flint 3|- miles ; the whole distance from Chester to Flint being 11 miles. The part of the river which extends from Flint to Connah's Quay may be said to be an open estuary ; and the upper part, extending from Connah's Quay to Chester, is an artificial tidal canal, having an unobstructed water-way of about 500 feet in breadth at high, and 250 feet at low, water.*' * It was in this straight reach that Mr J. S. Russell made certain obser- vations on the " Tide Wave of the Dee," the result of which he reported to the British Association in 1837. 48 SOUNDINGS. The high water line was found, by an average of twenty- four observations, to rise 2 inches from Flint to Connah's Quay; and from Connah's Quay to Chester the rise was found to vary from 4 inches at neap to 14 inches at spring tides, giving, as the result of twenty four observations, an average rise of 6 inches. The whole average rise on the high water line from Flint to Chester is therefore 8 inches. The difference between the times of high water at the different stations was found to vary very much, and appeared to be more affected by the state of the winds, or some other cause unknown, than by the circumstance of the tides being neap or spring ; but the average of the observations gave the time of high water at Flint twenty minutes earlier than at Connah's Quay, and that of high water at Connah's Quay thirty minutes earlier than at Chester ; the whole average difference in time between high water at Flint and at Chester being fifty minutes. The average level of the low water line at Connah's Quay is 2 feet 6 inches below that at Chester, giving on the dis- tance of 7-J miles an average fall of 4.09 inches per mile, and the level of the low water at Flint is 7 feet 6 inches below that at Connah's Quay, giving on a distance of of miles an average fall of 24.54 inches per mile. The total fall from Chester to Flint is 10 feet, being an average fall on the dis- tance of 11 miles of 10.9 inches per mile. When the rise of tide, as indicated by the Liverpool tide table, is 18 feet on the Dock sill at Liverpool, the rise in the Dee is 20 feet 10 inches at Flint, 13 feet 8 inches at Connah's Quay, and 11 feet 5 inches at Chester. Plates III. and IV. represent approximately the forms Sqaaaci 6 6 6 6 6 U - 5 5 u < ^^ O S - o ^> 1^1 i-l fil i?!l iFil a iS l ^^1 PI |2| ,131 ^1 ipl fi[ JHH i lr-IHrl T;i Pgrww^inipr^5n r%r''^ra '^^i '^i '^^i 'si '4 i?l^^;l^i^^i_^ SOUNDINGS. 49 assumed by the tidal lines of the river, to which the atten- tion of the reader is particularly directed. It is much to be regretted that in this case, as well as in the generality of surveys for engineering purposes, a greater range of tide- observations could not be obtained, and a nearer approach to their actual form could not be made, for the reasons stated in page 38. Plate III. represents the flood lines of a tide rising 19 feet 8 inches at Flint. In this, as well as in the other diagrams illustrative of the rise or fall of the tides, the perpendicular lines shew the relative positions of the stations, and are graduated in the same way as the tide gauges. On the horizontal line at the top of the diagrams, the relative distances between the stations are marked in miles, and at the right side of the plates, the time corre- sponding to the level of the tide is expressed in hours and minutes. The hard diverging lines are drawn through the points at which the tide stood at the different stations, as ascertained by observation, and represent the tidal lines of the river. Those which are dotted shew the probable di- rection of those lines, when their forms could not, for want of additional data, be more accurately determined. The tide, as will appear from an inspection of Plate III., began to rise at Flint at 8 hours 40 minutes ; at 10 hours 15 minutes it had risen 12 feet 8 inches, and at that time had just appeared at Connah's Quay, the surface of the water at Flint being 5 feet 4 inches above that at Connah's Quay. At 11 hours 20 minutes the tide had risen 18 feet 4 inches at Flint, and was 1 foot above the level of the water at Connah's Quay, and 7 feet 10 inches above that at Chester, at which place the tide had just begun to appear. Thus, 50 SOUNDINGS. while at low water there is a fall of 11 feet from Chester to Flint, there was at the time above mentioned a fall of no less than 7 feet 10 inches on the surface of the water from Flint to Chester. At 12 hours 10 minutes it was high- water at Flint, and at that time there was a fall of 1 foot 7 inches to Chester ; but the high water at Chester did not occur till one o'clock, by which time the water at Flint had fallen 2 feet 2 inches, and the fall on the surface of the water from Chester to Flint was 3 feet 1 inch. On refer- ring to plate IV., which shews the lines of ebb tide on the same day, it will be found that the water subsides gradually, and that the tidal lines approach much more nearly to parallelism and horizontality than during flood tide. The upper line of this diagram corresponds with the tidal line when it is high water at Chester. A similar series of facts obtained in surveying the River Lune ill Lancashire, in reference to the improvement of its navigation, will be found to corroborate the general results deducible from those made at the Dee, although the two cases are very diff*erent, as regards both the extent of the surveys and the configuration of the countries in which they were made. The observations at the Lune were taken during the months of August and September 1838 at three parts of the river, namely, Glasson Dock, Heaton Point, and Lancaster Quays. The distance from Glasson to Heaton is 3J miles, and that from Heaton to Lancaster 2J miles, making the whole dis- tance from Glasson to Lancaster 5^ miles. The high water lino at Glasson, Heaton, and Lancaster, was found occasionally to stand exactly at the same height; SOUNDINGS. 51 but the average difference of level gave a fall of 1 inch from Glasson to Heaton, and a rise of 3 inches from Heaton to Lancaster, the surface of the water at Heaton being slightly- depressed, and a small degree of concavity on the high wa- ter line observable. The occurrence of this irregTilarity may be accounted for by the configuration of the estuary of the river, which is shewn in the chart of the Lune appended to this treatise. A great contraction of the space between the banks occurs at Glasson, which checks the free flow of the tidal wav , and consequently raises its level at that place. After passing this contraction, however, the water flows into the large tidal basin or area in which the Heaton tide gauge was placed, extending from Glasson towards Lancaster, and here the tide level again falls, owing to the much larger sur- face over which the water is distributed. The time of high water was found, on eight occasions out of twenty four, to be exactly the same at Glasson, Heaton, and Lancaster. The difference of time, however, between Glasson and Lancaster varied from to 10 minutes, and the average of the observations gave the time of high water at Glasson 3f minutes earlier than at Lancaster ; but this dif- ference in time seemed to depend entirely on the wind or state of the weather, and not on the circumstance of the tide being spring or neap. The average level of the low water at Glasson is 7 feet 3 inches below that at Heaton, giving, in a distance of 3J miles, an average fall of 26.76 inches per mile ; and the average level of the low water at Heaton is 3 feet 9 inches below that at Lancaster, giving, on the distance of 2^ miles, an average fall of 20 inches per mile. The level of the low 52 SOUNDINGS. water at Glasson is, therefore, 11 feet below that at Lancas- ter, giving, on the whole distance of 5J miles, a fall on the low water line of 24 inches per mile between the two places. When the rise of tide, as indicated by the Liverpool tide table, is 18 feet above the dock sill, the rise of tide in the Lnne is 21 feet 1 inch at Glasson, 13 feet 10 inches at Heaton, and 10 feet 2 inches at Lancaster. Plates V. and VI. represent the forms assumed by the tidal lines of the Lnne during a spring tide which rose 23 feet 4 inches at Glasson. The tide, as will appear from ajn inspection of Plate V., began to rise at Glasson at 9 hours ; at 10 hours 5 minutes it had risen 11 feet 4 inches, and at that time had just appeared at Heaton ; the surface of the water at Glasson being 4 feet 3 inches above that at Heaton. At 10 hours 40 minutes the tide had risen 15 feet 6 inches at Glasson, and was 1 feet 9 inches above the level of the water at Heaton, and 4 feet 4 inches above that at Lancaster, at which place the tide had just begun to appear. Thus, while at low water there is a fall of 11 feet from Lancaster to Glasson, there was at the time men- tioned a fall of 4 feet 4 inches on the surface of the water from Glasson to Lancaster. At 12 hours 20 minutes it was high water at Glasson, Heaton, and Lancaster, and at that time there was a fall of a few inches both from Lancaster and from Glasson to the intermediate station at Heaton, producing the concavity of the high water line already al- luded to. On referring to Plate VI. which shews the lines of ebb tide on the same day, it will be found that the water sub- sides gradually, a slight degree. of concavity on the surface ■ ;l4^'.i!glk'H|i3lF-ll!l/-IHHHH7T7r ^;^° l ^ 'si 'gj .^1 'al N 'si 'd '2l 'si '3| 'al M 'm i2[ Iq^I ^ 'H '-H '^H H H 'H '4 cc < ^° - Q OC O o ,^^ . Q ui I- bJ Q. Q < u UJ < > i^ ~ o SOUNDINGS. 53 being discernible for an hour and a half after high water ; and during the whole of the ebb tide, as in the former case, the lines approach much more nearly to parallelism and ho- rizontality than during flood tide. The upper tidal line of this diagram corresponds with that of high water. I have found in all rivers whose tides I have examined with this object in view, that, on comparing the lines formed during spring with those formed during neap tides, the lat- ter are invariably more nearly parallel to the line of high water ; the deviation from parallelism decreasing in propor- tion to the decrease in the rise of tide. For the purpose of illustrating this, I have given, in Plates VII. and VIII., an example of the lines formed by the flood of a neap tide on the Lune, and the ebb of a neap tide on the Dee, which, when compared with the examples of the spring tides of these rivers already given, will be found to approach much more nearly to horizontality and parallelism. A farther illustration of this is presented in the following tabular views of the maximum difference of level between the sur- face of the water at Flint and Chester on the Dee, and at Glasson and Lancaster on the Lune, during the flow of tides of various amounts of vertical rise. RIVER DEE Date. Rise of Tide at Fli.vt. Maximum Fall from Flint to Chester. 1839. feet. In. Feet. In. May 21. 14 3 8 ... 23. 15 6 4 5 ... 25. 16 4 5 8 ... 29. 18 6 6 June 10. 19 8 7 10 54 SOUxNDINGS. UIVER LUNE. Date. Rise of Tide at Gl.\sso\. aiaximum Fall from Glasson to Lancaster. 1839. Aug. 29. ... 31. Feet. III. 12 1 12 9 Feet. In. 1 1 1 6 Sept. 1. 3. 15 4 19 8 2 2 10 5. 23 2 3 2 6. 23 6 4 4 I shall only refer to another example which is chiefly in- teresting, as shewing the undulating lines of the tide wave in its passage up the narrow channel of a winding river. I allude to the Forth in Stirlingshire, in which, from its tor- tuous course, the tides are somewhat remarkable. To give an idea of the Avindings of this river, it may be stated that the distance in a straight line between the towns of Alloa and Stirling, both of which are situated on its banks, is 5 miles ; while that by the river's course is no less than 10-| miles. The tides, however, in the Forth, are not so rapid as those to which I have been referring, otherwise the de- viations in the tidal lines would doubtless have been much greater than they were found in reality to be. The tide observations on this river were made under the direction of my father in the year 1825, and from the wind- ing nature- of the stream, it was found necessary to have four stations, namely, at Alloa, Tillibody, Powishole, and Stir- ling. ■ The deviation in the lines will be seen by reference to the diagrams in Plate IX., Avhich arc constructed nearly SOUNDINGS. 55 in the same manner as those already described, and repre- sent the forms assumed by the surface of the water during flood and ebb, at the end of every successive half hour. The most anomalous result of this investigation occurs at Pow- ishole, where the undulating surface of the water was found to rise higher than at any other point on the river, either above or below it. Although many other series of observations affording si- milar results might be given, it seems unnecessary to enter upon them ; my only object being to enable the reader to form distinct ideas as to the nature of the deviations in the tidal lines, and the several investigations that require to be instituted in making a correct survey. The examples I have given, it is presumed, afford sufficient information for that purpose. I shall, therefore, proceed to shew in what man- ner and to what extent the accuracy of the soundings may be affected by the nonparallelism of the tidal lines to the line of high water ; and, that the observations to be made may be clearly understood, I shall, in the first place, offer a few remarks on the datum to which the soundings should be reduced, and also on the nature and use of the reference which is made to the tide gauges, in the reduction of their depths to that datum. It is evident that all soundings must be reduced or re- ferred to one datum line, before a correct notion can be formed of the depths of water at the places where they were taken. Different opinions have been advanced as to the most convenient datum to be used for this purpose. When the whole rise of the tide can be observed, which is the case in harbour surveys situated on the coast, the " half tido 56 SOUNDINGS. mark," or that central point from which the high and low water levels of every tide are very nearly equidistant, is a convenient point for referring to. The existence of such a point " equidistant from the high and low water of any one tide and on the same level, or coinciding with, the points half way between high and low water of every other tide," has been determined by observations made in several situa- tions. It is behoved to have been first detected in 1830 by my father while surveying the Dornoch Frith in reference to a salmon fishing question, and is particularly alluded to in his report to the Court of Session on that subject, dated 31st January 1831. In 1833 it was found to exist in the Frith of Forth in making the tide observations for a harbour survey; and in 1834, in surveying the Skerryvore Rocks on the west coast of Scotland, with a view to the erection of the Skerryvore Lighthouse. In 1835, I ob- tained the same results at the Isle of Man ; and in the same year Captain Denham brought a similar result, ob- tained from extensive observations made at Liverpool, be- fore the meeting of the British Association held at Dub- lin. The agreement of these different series of observa- tions made at points so far distant from each other seems to prove the universality of the phenomenon, at least on the shores of this country. It is evident, however, that this datum is only applicable to situations where the whole rise of tide can be observed, which, in river surveys, is rarely the case, even at a single station, the bottom of the gauges, owing to the rise on the bed of the river, being generally above the low water line of the ocean. The datum line assumed in such surveys is therefore that SOCNDINGS. 57 of blgli water of an ordinary spring tide. This, however, is an indefinite datum, unless the rise of that which has been assumed as the ordinary spring tide be distinctly specified, in which case it is quite explicit, and is found perfectly to answer the object intended; for if we are told that the soundings on any river are reduced to high water of an ordinary spring tide, rising 16, 18, or 20 feet, as the case may be, at a certain point in the river which must be men- tioned, then the depths in reference to the high water of any other tide can, with this information, be easily ascertained. In order to explain the use of the reference which is made to the tide gauges, in reducing the soundings, we shall sup- pose that a depth was taken in the middle of an estuary, and that the observer, at the time he made the observation, had not any means of ascertaining the state of the tide. Such an observation would evidently be of no practical use, from the circumstance of its being impossible to ascertain whether the tide had still to rise, had attained its full height, or had lallen a certain number of feet at the moment it was made, without a distinct and accurate knowledge of which, the depth could not be reduced to the 1-evel of the high water of any particular tide. If all the depths were taken exactly at the time of high water of the tide to which they were to be referred, they would not require any correction ; but it is obvious that in practice this could not be done ; and re- course is consequently had to the tide observations, by means of which the reduction is easily effected. All that is neces- sary for this purpose, is to note the time at which the sound- ing is taken, in order that the height of the tide at the near- est gauge corresponding to that time may be afterwards as- 58 [FOUNDINGS. certained. The method of obtaining the corrected depth resolves itself into one of three cases, depending on the time oi tide at which the observation was made. It is as follows : — Let a represent the depth of sounding made at a certain hour. /9 the height at which the water stood on the tide gauge at the same hour. 7 the height to which high water of ordinary spring tides rises on the gauge, — -which will be ascertained while the survey is in progress by the series of tide observations made in the manner already explained ; and S the depth of the sounding reduced to high water. Now, in the first case, if ^ is below the level of y, then ^ = «+ (7-/5). In the second case, if (3 is on the same level as y, then d = a; And in the third case, which may happen in a high spring or equinoctial tide, if (3 is above the level of 7, then ^ = «- (^- 7). These formulee would give the true corrections of the soundings, however far removed from the tide gauge their positions might be, if the lines formed by the tidal wave were parallel to that of high water at all times of tide, as in that case the vertical spaces 7^^ or /3 — 7, intercepted between the high water line, and the other tidal lines, would be equal throughout the whole of the tidal area of the river or estuary. But it has been shewn that the tidal lines are not parallel, and the formulee I have given may therefore^ under certain circumstances, lead to error. As an example of this, I shall take one of the tide lines of the Dee from Plate III. SOUNDINGS Fig. 4. 69 Let F and C, fig. 4., represent tlie positions of Flint and Connali's Qnay tide gauges, and the intermediate point z the place at which the sounding was taken. Let F C repre- sent the line of high water to which it is wished to reduce the sounding, a h the bed of the river, c d the low water line, and e d the tidal line which existed when the obser- vation was made, which is not imaginary, but will be found to correspond with that at 10 hours 15 minutes, as re- presented in Plate III. Further, let the sounding x y =% feet. Let the depth at high water z y 2ii the position of the sounding, as measured on the diagram, =17 feet 4 inches. Let the rise of tide at Connah's Quay g d = 12 feet 5 inches, the rise of tide at Flint c/= 19 feet 8 inches, and the height at which the water had risen on the Flint gauge, when the sounding was made, e c— 12 feet 8 inches. Now, suppose the sounding is to be reduced by a reference to Connah's Quay ; according to the foregoing formula we should have zy=xy + {gd-{)) = 8^+(12'.5-.0=20 feet 5 inches, GO SOUNDINGS. the depth at high water, instead of 17 feet 4 Inches, giving 3 feet 1 inch more than the actual depth, an error which might lead to unpleasant consequences, both as regards the navigation of the river and the framing of an estimate of works for its improvement. Again, if reference were to be made to Flint, we should have zi/=aj^+/c-ec = 8f. + (19^8-12^8)=15 feet, the depth at high water, instead of 17 feet 4 inches, being an error of 2 feet 4 inches. Now, the case that has been taken, which, in any view of the subject, would involve an error in the depth, either of 3 feet 1 inch, or 2 feet 4 inches, is not the worst that may be cited, for, under certain circumstances, and in certain situations, the error would be considerably greater. Nor, indeed, are the high water depths the only results that would be affected. The section of the bed of the river, the depths of the soundings when reduced to low water, and the heights of the sand banks above the low water line, the correctness of which, as will be explained in Chap. X., de- pends entirely on the accuracy of the high water depths, would all be equally erroneous. It is obviously of great importance, therefore, that the engineer should not only be fully aware of the cause of these errors, and the extent to which the results of a survey may be affected by them, but also that he should know, and be able to apply where neces- t^ary, the means by which they may be neutrahzed. It has been shewn that the erroneous results alluded to arise from the nonparallelism of the tidal lines to the line of the high water to which the soundings are to be reduced, and it has been stated that the most effectual means of avoiding SOUNDINGS. 01 inaccuracy, from this causo, is to increase the number of gauges ; but even this precaution, unless carried to an ex- tent which may, in ordinary practice, he safely regarded as quite unattainable, would not produce the desired effect. The only really practicable cure which can be applied, is that of taking the soundings when the lines are most nearly parallel to the line of high water. That there are not only certain tides, but also certain periods of every tide, when this approach to parallelism is much more near, than at other times, has, it is presumed, been clearly established; and in accordance with this view of the subject, I shall give five rules for direction, in making the soundings, the correctness of which I have had repeated opportunities of practically testing. First, Soundings made in the immediate vicinity of the gauge, by a reference to which they are to be corrected, are not appreciably affected by deviations from parallelism, and may be taken at any time of tide, and under any circum- stances. Second, The farther distant the positions of the sound- ings are from the gauge, by a reference to which they are to be corrected, the greater is the chance and the amount of error which may arise from nonparallelism. Third, Soundings should be made during neap in pre- ference to spring tides.* Fourth, Soundings should be made in ebb in preference to flood tides. * The strong currents, during spring tides, are unfavourable for the pur- pose of sounding, independently of the greater deviation from parallelism in the lines. r>2 SOUNDINGS. Fifths Soiindino'S to be taken in flood tides, especially during springs, slionld not be made till within about an hour of high water. If these precautionary rules be kept in view, they will be found to counteract in so great a measure the effects of non- parallelism, as to insure, in most cases, sufficient accuracy for all practical purposes, in reducing the observations. They apply most particularly to rivers in which the rise of tide is great, and the currents are strong ; but they may be ' said to be applicable, in a greater or less degree, to all si- tuations. A compliance with them may, at first sight, appear to be difficult, and to entail great loss of time in making the marine department of the survey, but the object to be attain- ed is very important, and well worthy of some sacrifice of time; and if calm weather must be chosen for making the tri- angulation and taking the levels of the tide gauges, there is no reason why favourable tides should not be chosen for tak- ing the soundings. The rules I have o o Ttl r-< CC C> lO CO <5 fl" cq O uc o o CO o o o o -* O O rl CO ■"^ T' -■ -' -■ — • — ■— - _- o : ; t^ 02 aj ■ : xn '^oj • ■Xj -Ssii xn 1^ •5?t) ■ j 05 St 11^ cc 111 \ 111 ^cS^ i ^sSt : ^c^ Il3 \ IP : JfS 6s< 5 :3W< i aiS^ : '3S^ : 6^< SOUNDINGS. 71 . :> • J CO CO (N CO o5 .0 O O CD O O O CD O -^ r^ r-" 4~- O O O CO o i^OTtH-^TJ^COCOCOCOOCOO^COOOiO <^ r/> q -Ti T? rt rf '/i -n CO ~1 fc > o CJ r-< o 1^ < CQ 02 ^, OJ o *? ^ ^. ^ u J ^ S Ph ^-.i) t^ ( 72 ) CHAPTER V. LOW WATER SURVEY. Objects of the low water survey — DiiRculties encountered in making it — Sur- veys situated on the coast and in rivers — Use made of the triangulation stations — Observations for fixing positions of points in survey — Changes on sandbanks produced by spring tides, high winds, &c. — Different me- thods of keeping field book — Examples — Method of executing the field work — Dangers to be avoided in making low water survey — Means for averting them — Dangers in consequence of anomalous flow of tides — Example of this on the Dee — Cause of the phenomenon. The low water survey of the tidal area of the river is the operation to be explained in the present chapter. The points to be determined in this important department are the direction of the low water channels, the ontlines of the banks of sand or gravel which form the bed of the estuary, and the positions of all rocks, shoals, or other obstructions to navigation ; and although the case of a river survey has been taken for the sake of illustrating the method to be pursued, it is to be understood, as explained in the Preface, that the following remarks apply with equal propriety to any marine survey made for engineering purposes. LOW WATER SURVEY. 73 When the estuary to bo surveyed is broad, and the river, as often happens, is divided into two or three low water channels, and seeks its way to the sea by numerous wind- ings among extensive sand banks intersected in all direc- tions by sleeves of water, the delineation of the low water lines is often attended with mncli trouble, if not with danger, and even in the most favourable situations it will generally be found that the satisfactory execution of this department is the most difficult part of the survey. This difficulty may be attributed to two causes ; the flat- ness of the surface to be surveyed, which prevents a full view of the windings of the river from beinfj obtained, and the shortness of the time that can be devoted to it on any one day, which, from the nature of the investigation, is necessa- rily limited to the duration of low w^ater. Advantage should therefore be taken of every means by which its execution may be facilitated ; and, for this purpose, if there be any high ground on the shore of the estuary, the river should be viewed from it during low water, and a sketch from such a point of view made either by the hand, or with the camera lucida, or any other suitable instrument, will, in many cases, be found a great assistance in enabling the surveyor to trace the windings of the channel, when otherwise he would be involved in doubt and difficulty. The surveys of the low w^ater lines of beaches, banks, or rocks, which are situated in the sea, and are made in refer- ence to harbour improvements, should be conducted only during low water of spring tides, as it is at such periods of the tide alone that a correct view of the bottom can be ob- tained. If this be overlooked, numerous omissions and er- E 74 LOW WATER SURVEY. rors may be introduced into the survey, as there are many banks and rocks which, during neap tides, are covered to the depth of 2 or 3 feet, and consequently invisible, and lia- ble to escape notice, but which are left quite dry, and can be easily and accurately surveyed at low water of springs. But in rivers and estuaries, the levels of whose beds are above the level of low water of neap tides, it is of no im- portance whether the survey be made during neaps or springs, as the former will evidently ebb sufficiently far to leave the whole of them dry, so as to admit of their accurate delinea- tion. It is in the department of the survey of which we are now treating, that the stations and points fixed by the tri- angulation will be found most serviceable ; for although a surveyor, unacquainted with the use of the sextant, may fix the positions of the soundings, as explained in the preceding chapter, by observations made from theodolites placed on the shore, that method of observing could not be applied on a large scale to surveying the sand banks. Nor is the system of traverse surveying with the chain and theo- dolite, as recommended for the banks of the river above high water, and described hereafter, in any way better adapt- ed for that purpose. There is only one mode of proceed- ing with which I am acquainted that can be advantageously adopted for this part of the work, and that is, to traverse the whole of the low water lines of the river, taking angles with the sextant at every prominent point or bend, to at least three known objects on the shore, in the manner al- ready explained for determining the positions of the sound- ings ; the spaces between the points of observation being FIELD BOOK IHTEM IDllE. FJ.ATEX ^fry^)i3J?. 9 3 '2/' 9^, a. ^<^^^,^',^//<,. s9'ij' ' "J9 YSya^, Ah5 LOW WATER SURVEY. 75 sketched in by the hand as the survey proceeds with as much accuracy as possible. It may be conceived that this mode of surveying is not sufficiently detailed for the im- portant part of the survey to which it is applied ; but it must be kept in mind that the outlines of the sand banks and the low water channels of all rivers and estuaries are liable to constant changes produced by spring tides, high winds and land floods, and therefore, (considering the short- ness of the time that can be devoted to this department), a more minute or detailed survey than that alluded to would be needless. This system of surveying will be best understood, and the method of registering the observations most easily ex- plained, by a reference to Plate X., whicli is part of a field book, shewing the survey of a sand bank in the river Dee. It will generally be found advisable to make the sketch on a larger scale than is shewn in the plate, the ex- ample given, having, for convenience, been somewhat redu- ced from the original. A quarto field book has the form and size of page on which the work can be most conveniently registered. Referring to Plate X., we shall suppose that the survey of the bank commenced at the point marked a. The ob- server in this case, standing close to the edge of the water, took three observations, in the manner described at p. ^o^ to four points on the river, whose positions were known, name- ly, " Red Rock Tower" (which, to save time and room in registering, is marked R. R. T.), " Lower Barrel Perch," ("L. B. R") "Middle Barrel Perch" (" M. B. P."), and " Quarryhouse," which were sufficient for determining the 76 LOW WATER SURVEY. position where he stood. He then proceeded along the edge of the bank until he came to b, a projecting point, where he took a second series of angles, in order to fix its po- sition. In this case the line of bank between the two points a and h was nearly regular, and is so sketched in the field book. He next proceeded to c, but between b and c it will be observed that there are two small indentations from the straight line joining b and c, which are marked 10 feet and 15 feet respectively. The exact positions and amounts of these indentations could have been determined by taking angles with the sextant to known points on the shore at the places w^here they occurred, as in laying down the more pro- minent points of the bank ; but in order to save time, they are sketched in the field book in the manner shewn, and the dimensions paced, or more generally, for small distances, measured only by the eye, approximations which are suffi- ciently accurate for all practical purposes, owing to the va- riations to which the outlines of the banks are subject, from the causes already alluded to. In this way the whole out- line of the bank was traversed, and the field book made out as shewn in the plate. When the lines to be surveyed in this manner are intri- cate, and the observations to be made very numerous, it is sometimes found convenient, in order to prevent confu- sion, to keep the field book in a form which diff'ers some- what from that shewn in the plate, and may be used on all occasions, if found more convenient. A sketch of the bank which is surveyed, is made on one page of the field book, and all the points on the sketch at which angles are taken are numbered 1, 2, 3, 4, &c. The andes taken at LOW WATER SURVEY. 77 tlie different points are entered on the opposite page, every series of angles having the nnmber of the point at which they were taken placed opposite to it ; and in this way, while no mistake as to the positions of the angles can be made, all confusion is avoided, and ample room left in the field book for sketching and remarks. It is proper that the day and the time when the observa- tions were taken, as shewn in the example given, should be noted in the field book, and thus the observer is enabled to make any correction that may be required to compensate for tide or flood in the river, which may be so gradual in their rise as to be imperceptible at the bank to be sur- veyed, but would nevertheless be easily detected by refer- ring to the tide gauges. From the example of the field book that has been given, and the explanation that has been made regarding this mode of surveying in laying down sand banks, its application to any other purpose, such as surveying the low water lines or the outlines of rocks, cannot fail to be readily understood, and it is therefore conceived to be unnecessary to give any farther examples in illustration of it. Two persons, one to take the angles, and another to re- gister them and make the sketches of the banks, are requir- ed for the proper performance of this system of surveying. But in the survey of low flat banks, which are dry only during a very short time, it is sometimes convenient, in or- der to expedite the work, to employ two or even three ob- servers with their assistants, who ought to proceed to dif- ferent points with their sextants, and thus, by dividing the duty, the survey of the whole bank may be completed in one 78 LOW WATER SURVEY. tide. A boat and crew must also be in constant attendance, not only for carrying the observers across the channel when necessary, but for the more important purpose of prevent- ing the serious consequences that might ensue from their being surrounded by the tide, without the means of extri- cating themselves. In situations where the tide is rapid and comes in with a head or hore^ this should be particularly attended to, care being taken to arrange the work so that the observers may be in the immediate vicinity of the boat (from which, in the course of the survey, they must often be far removed) about the time when the tide may be expected to make its appear- ance. I have seen instances in which serious results might have ensued, had a boat not been in immediate attendance at the coming of the tide. One great cause of danger on such occasions arises from the difficulty of knowing from what direction the flood tide will first make its appearance. It does not, as might natu- rally be looked for, invariably ascend the low water channel of the river, although its bed is always on a lower level than the banks on either side ; but in some situations first appears by flowing over the sand banks into the regular channel of the river, where it joins the downward current of fresh water, and, along with it, continues to flow toward the sea, until their joint eff'ect is neutralized by meeting that branch of the tide which forces its way up the proper chan- nel. The branch of tide which first makes its appearance in the manner described therefore undergoes certain changes in the direction of its motion, which are somewhat curious. The direction imparted to it before leaving the great tidal LOW WATER SURVEY. 79 wave of the ocean is first wholly reversed, for it flows toward the sea along with the fresh water of the river, and this new motion is next completely checked, and again reversed, by the same tidal wave from which it emanated, and of which it may be said to form a part. The flow of the tide is in this respect occasionally attended by very unexpected circumstances, and as these may some- times come under the notice of the engineer in the practice of marine surveying, it may not be uninteresting or unin- structive to give an example of these apparent anomalies, with an explanation of what appears to be the cause of their occurrence. The most remarkable one with which I am acquainted occurred to myself on the river Dee, near Flint, where the estuary is about 3^ miles in breadth, and the low water channel, which winds through a large extent of sand bank, is very tortuous. In the accompanying diagram, fig. 5., the Fig. 5. letters abed represent the low water channel, the direction of the current being shewn by the arrows. In examining 80 LOW WATER SURVEY. minutely tlie Avindings of the stream in reference to certain investigations, it was necessary to walk down the right bank of the river at low water, close to the edge of the channel. While so engaged, I crossed, at the point &, a hollow or depression in the sand bank, which, though sunk below the general level of the bank, was nevertheless quite dry, the lowest part of it being raised considerably above the level of the water in the river opposite to it. I had only advanced a very few steps after crossing this hollow, when I heard the rushing noise of the approaching tide, which, as it was at the height of springs, was expected to come in with great rapidity. Expecting to meet the tide forcing its way up the channel of the river, I continued to walk on, but see- ing no appearance of it, and hearing the noise gradually in- creasing, and apparently coming from behind me, I began to suspect that all was not right, and on turning round per- ceived, to my great surprise, a rapid run of water flowing (in the direction shewn by the arrows in the cut) through the hollow which I had just crossed, and joining the river at b. I immediately hastened back towards the boat, which wait- ed for me a little higher up the river, and after having waded through the newly formed stream, which had attain- ed a depth of 6 or 8 inches by the time I crossed it, I stood on the upper side of it to see the result of this unlooked for inroad. The water continued to rush through the hollow, rapidly gaining breadth and depth, and at last, after an interval of probably two or two and a half minutes from the time at which the noise was first heard, the tide ap- peared forcing its way up the channel of the river, and, join- ing the current which rushed through the hollow d 6, the . LOW WATER SURVEY. 81 sand bank h c d was soon encircled by a broad and deep boundary of water, renderinn- all access to it or egress from it quite impracticable unless by a boat. This, it is believed, is only one of many instances of such a precursor of the regular tide which are to be found in situ- ations where the flood sets in rapidly, and it shews with how much caution those engaged in this sort of sm-veying ought to conduct their operations. An explanation of the cause of this phenomenon may be found in the circumstances attending the rise of the tide, as illustrated in the several diagrams of the tidal lines already given and described in the preceding chapter. It will be recollected, that, at some periods of flood tide, the level of the water was considerably higher in the lower than in the upper parts of the navigation. In the case of the Dee, in- deed, where the peculiarity in the flow of the tide for which we are attempting to account occurred, the level of the wa- ter at Flint was found on one occasion during flood tide to be 7 feet 10 inches above that at Chester, the surface of the river thus forming an inclined plane from the sea down- wards. Now this inverted order of things would naturally exist during certain states of the tide at the part of the river at which the phenomenon I have described was observed, or, in other words, the level of the water at d in the diaoyam, would be above that of the water at h. Without observa- tions made for the special purpose of ascertaining the fact, it is impossible to say what the maximum difference of level during flood tide might be ; but on the supposition that the distance by the channel dch was a mile, we may infer from an examination of the diagram of the tidal lines already al- 82 LOW WATER SURVEY. luded to, that the difference in height between the two points would be considerable. We shall suppose, then, that the tide, on arriving at the point d, divides into two branches or currents, and that one proceeds up the channel of the river towards c, while the other flows into the hollow in the sand bank at d towards e. Now, as the level of the water at d rises, the stream which has flowed into the hollow in the sand bank gradually rises higher and higher upon the bank, until it surmounts the summit level, which we may suppose to be at e, after which it rushes from eioh with- out obstruction. In the mean time, the other branch of the tide is forcing its way against the stream of the river by the long circuitous channel d ch having a greater distance, more friction, and the current of the fresh water to contend with ; and before it reaches 6, the water at d has attained a much higher level than that at 6, and has even overtopped the summit level of the sand bank at e, and is flowing with- out obstruction into the channel of the river in the manner represented to have taken place on the Dee. Thus, in all cases where the retarding influences which exist in the re- gular channel of the river exceed the retarding influences in any hack lake or swash wdy^ the tide will flow through the latter sooner than the former, and give rise to an ano- maly such as I have described. ( 83 ) CHAPTER VI. SURVEY OF HIGH WATER MARGIN. Objects of the survey of the high water margin — Two systems of surveying employed for this purpose — Chain and traverse surveying — Use made of the triangulation stations — Description of the process of traverse sur- veying — Directions for adjusting the theodolite — Reverse bearings — Method of keeping field book — Example from survey of the Tay — Checks on the accuracy of the field work — Method of surveying outlines of ex- tensive tide covered marshes. It is generally necessary that the high water margin of a river or an estuary should be distinctly defined, in order that the conservators of the navigation may know the boundaries to which the powers granted by their acts of parliament ex- tend. These powers are occasionally brought into action for the purpose of preventing the proprietors of the sur- rounding land from erecting works within the high water mark, in order to extend the limits of their property, es- pecially when these works prove injurious to the navigation, either by curtailing the tidal capacity of the river to a serious extent or interfering with the fair-way. In other cases, again, land may be reclaimed without impairing to a hurtful de- 84 SURVEY OF THE gree the tidal capacity of a river, or injuring its navigation ; and in sucli situations, works, erected expressly for its im- provement, often have a direct tendency, by encouraging the depositation of silt and mud to hasten the process of " land makinaf." But as the conservators of the river in these cases have generally power by their act of parliament to make certain claims on the proprietors, for all the land that has been taken from the bed of the river and added to their property in consequence of such operations, the means of de- termininix the extent of land that has been rcjlaimed must be afforded. In all cases where land is reclaimed, the high water mar- gin is of course changed both in its form and position. It is therefore necessary for the settlement of questions rela- tive to land that the whole of the shores be accurately survey- ed in such a manner that the original marginal line of the ri- ver may, at any period, be traced by reference to fixed objects on the banks, whose relative positions cannot vary. When the survey has been completed and the poles removed, stone marks should therefore be sunk in the ground at the sites of the different triangulatioa stations, so that their positions may at any future period be easily discovered ; and the sur- vey of the margin of the river, which is the subject to be treated of in the present chapter, should, in accordance with these views, be made to embrace all houses or other remark- able objects whose positions are not likely to be changed, and which lie within 200 yards of the high water mark. Two different systems of surveying may be employed for delineathio- the maroin of tlie river. The one is that of " chain surveying," which is adopted by land surveyors, and HIGH WATER MARGIN. 85 being founded entirely on measurements made with tlie chain, is best suited to situations where the distances ])e- tween the triangulation stations are not very great. The other is that which is called " traverse surveying," a system in which the lengths of the lines are measured by the chain, and checked by angular observation, and their directions are determined by means of the theodolite. In either case, the stations of the trianoulation oncfht to be regarded as points whose positions have been finally determined, and the survey of the banks should be divided into a series of smaller surveys or compartments quite independent of each other, and extending between the different triangidation sta- tions. If an error happens to be made in the field work, its effect is, by this arrangement, confined to that compartment of the survey in which it was committed, and does not ex- tend beyond the fixed points by which it is limited. As little more than the mere outline of the shore of a river requires to be represented, the system of traverse sur- veying is most applicable for that purpose. When compared to the method pursued by land surveyors, it saves time and insures greater accuracy, especially when the distances between the triangulation stations are considerable. It is often convenient, however, for the engineer to confine his operations to the triangulation, and the survey and sound- ings of the tidal area within high water mark, leaving to land surveyors the survey of the margin of the river ex- tending between the different stations. In that case, the land surveyors of course adopt the systems they have been in the habit of using, but where they are not employed, and the survey is to be made by the engineer's own assistants, 86 SURVEY OF THE it is believed it will be found most convenient to employ the system of traverse surveying, on which I shall therefore make a few remarks. This method of surveying, as is generally known, con- sists in measuring a series of straight lines along the mar- gin of the shore to be delineated, in determining the direc- tions of these lines, and in obtaining data for checking their lengths by angular observations. Offsets taken with a tape- line from the lines so measured and determined, to all pro- minent points, give their exact positions. The survey may be commenced at any of the triangida- tion stations ; and that the bearings to be taken may be con- nected with the triangulation itself, the instrument should be adjusted so that, when directed to any of the other sta- tions, the bearing indicated by the reading vernier shall be the same as that originally obtained from the same point, when the triangulation was made. While the instrument is being thus adjusted at the triangulation station, an assist- ant should be sent forward to fix a surveying pole (which, in explaining the system, we shall call station a) in the di- rection in which the first line of the survey is to be measured. He should take care to place it in such a situation that as long a line as possible may be obtained from station a to the next station, which may be called b. When the pole has been adjusted, an observation must be taken to it with the theodolite and registered in the* field book. The measure- ment of the line and offsets is then commenced, a sketch of the outline of the shore or bank being made, and all the distances carefully marked on it as the survey proceeds. On arriving at station a, the whole length of the measured HIGH WATER MARGIN. 87 line ouglit to be registered in the field book under the bear- ing. To prevent confusion, it is advisable to number the lines in regular order as they occur, and to attach letters of the alphabet at each extremity, the letter (as a') which stoo d at the end of one line being placed in an accented form (of) at the beginning of that which succeeds it. In order to adjust the instrument at a (the point at the termination of the first measured line), it ought to be set at the angle which the survey line bore, and directed back to the triangulation station from which the survey commenced. Bearings should then be taken to any of the triangulation stations within view, for the purpose of checking the mea- surement of the distance. While these observations are being made, an assistant advances in the direction in which the next line is to be measured, and fixes the station pole, which may be called &, in the same way as has already been noticed. The bearing of 6 is then taken and noted down, and the measurement of the line commenced. A station pole must be left at a to mark its position, as the back bearing must be set to it from the point 6, before the bear- ing of the next line, which would be to station c, can be taken. It seems almost unnecessary to say that it is of much im- portance in this, as well as in all departments of surveying, to be able to keep a distinct field book, as it insures great facility as well as accuracy in the protraction of the work. But exactness in this respect can be attained only by prac- tice. The sketching necessary for this purpose is of quite a diff'erent nature from that of which a knowledge is re- quired in landscape drawing or painting, for the representa- 88 SURVEY OF THE tioii of tlic surface of the ground is not laid down in pro- portion 1>Y the surveyor ; the size of the offsets, or, in other words, the breadths being greatly exaggerated in comparison to the lengths. The tendency which beginners have to keep up the proportions of length and breadth as they appear to the eye, is the great difficulty to be overcome in attempting to keep a good field book. I have given an example of a field book of part of the river Tay, to shew in what way it should be kept, and a re- ference to it will perhaps serve to render more intelligible the explanation of this system of surveying which I have attempted to give. Plate XI. represents a page of the field book, and contains two short survey lines. The first is marked line No. I. in the corner of the field book, and com- mences at Balhepburn, one of the stations of the triangula- tion. The theodolite on this occasion was directed to Middle Pow, another of the triangulation stations, set at the angle of 126° 12', which in this case was adopted as the primary bearing of the survey. The bearing to a 128° 9' was then taken and registered, after which the line was measured, and its whole length, 266 feet, also registered. No offsets required to be measured on this short line, which extended between the station and the edge of the river. At a' (Plate XI.) the theodolite was set back on Balhepburn station with a bearing of 128° 9'. The bearing of h 169° 8' was then taken and registered, and the length measured. Offsets were taken to all remarkable points, the distances at which they occurred being noted on the dotted line in the field book, which represents that measured on the ground. On arriving MLLU DUUIV. ri^rs XT Ii7f.e II -r ^^^ J^' ^^^\\\ )\flnmim'iiiii»iii!>»liiiiiiiiiii , ^ u>-> 111.. ; ftW y^T e I /^ |;- ■ -^^ -'L^i" k:tv"I^" C^^^ ^i?^,^f-.&«/ c?/^ J/ze/' ^OA J'^'//J3. FIELD BOOK MYEM TAT. PZATHXa ^j:fiG eld ^i^U. Ditch S ^.tt. Jffytvi cK,n7r.Trven/j /•" HIGH WATER MARGIN. 89 at b tlie termination of tlie line, tlie whole measured distance 2037 feet was registered. I now refer to plate XII, in which ¥ at the commencement corresj3onds with b at the termina- tion of the last line in Plate XT., both of the letters represent- ing the same point on the ground. The theodolite, with the bearing of the last line, viz., 169°.8, was then set back upon a', the surveying pole having been left standing for that purpose, and angles were taken, as shewn in the plate, to Middle pow 146° 46', and Kirpow 155° 44', two stations of the triangula- tion, in order to give the means of checking the measured distance in protracting. In conclusion, the bearing of the next line or the pole at c was taken and registered as 324° 39'. This line was then measured, and offsets taken as formerly, the distance being registered at 1774 feet. It is to be observed, that when a line is very long, or where its intricacy renders it necessary to shew it on a very large scale, one page of the field book may not be sufficient to contain the whole of it ; and in that case, it is carried to another page, and noted as a continuation of the preceding line. The whole coast of the river is surveyed in the manner described, the lines following the contour of the shore, the straightness or crookedness of which determines their num- ber and lengths, until another triangulation station is reached, at which point the accuracy of the angular part of the sur- vey may be tested. It will be observed that the method of using the back bearing in traverse surveying is simply an extension of the same system which is practised in making the triangulation, in which, as explained in Chap. I., the corresponding bearings at different stations are parallel to each other ; and, consequently, if the primary bearing of the F 90 SURVF.Y OF HIGH traverse survey at the first or starting station be made to coincide with the same bearing in the triangulation, it is evident, that, when the instrument has been adjusted on arrivino- at a second triangiilation station, the bearing taken from it to any third one, will, if the woi'k be right, be either the same bearing as that formerly observed, or the one on the opposite side of the horizontal limb. If this be not the case, it may be inferred that some error in the observation has been made, and the angles must be observed again. To permit this to be done, it is a necessary precau- tion to place a mark, such as a peg of wood, in the hole formed by every setting of the surveying pole, which may remain until the angles have been checked in the manner explained. In conformity to the same principle, namely, that of the parallelism of the corresponding bearings, it is evident that the direction of the magnetic needle, under the limitations for variation mentioned in Chap. I., may be used at the different stations, to ascertain whether any great mistake has been committed ; for, if the work be cor- rect, the needle, if unaffected by local attraction, will point to 360°, or 180°, at every station when the instrument has been adjusted for observation, and the vernier set at 360° on the horizntal limb. In situations where the margin of the sea or of the river has a large tract of tide covered marsh land in front of it, whose level is but a few inches below that of high water, a forma- tion often met with, the system of surveying recommended for laying down the sand banks may be advantageously combined with that of the traverse surveying which has been described. I have known cases where such marshes, WATER MARGIN. 91 covered only at very high tides, and often affording excel- lent pasturage, extended upwards of a mile from what might be termed the high w^ater mark of the river. Such tracts of land, although only occasionally covered by the tide, ought, nevertheless, to be included in the survey of the mar- gin of the shore. But as it would be unnecessary, as well as inconvenient, to employ the same minute mode of survey- ing in the delineation of their variable outlines, as in that of the more permanent margin of the river, it is better to combine the two systems, applying, to what may be con- sidered the permanent margin, the mode of traverse survey- ing, as explained in the present chapter, and laying down the outlines of the marshes as the traverse survey proceeds, by sextant observations, in the manner already explained in treating of the surveys of sand banks. The determina- tion of the cases in which the one or other, or a combination of both of these systems of surveying is most applicable, must be left to the discrimination of the surveyor. ( 92 ) CHAPTER VIL CROSS SECTIONS AND BORINGS. Uses of the Cross Sections and Borings — Situations in whicli fhey are re- quired — Reference of Sections and Borings to datum liue of survey — Directions for making Sections — Description of apparatus employed, and its application — Directions for making Borings — Description of appara- tus, and its application — Method of keeping Field book — Importance of this department of the survey, as affecting designs for works — Ex- ample of this in the case of the river Ribble, in Lancashire, and the Fossdyke, in Lincolnshire. The department of the field work to be next noticed, is that of making sections and borings, which are indispen- sably necessary in all cases where hydraulic works are to be executed. In deepening a navigation, or the entrance to a harbour, for example, these operations furnish the data for ascertaining the quantity and quality of the materials to be removed, in order to obtain a certain depth of water, while, by discovering the composition and form of the bottom, they enable the engineer to select the most eligible site for excavating a navigable channel, founding a pier or break- water, or any other hydraulic work. In surveys of rivers, made expressly with reference to the improvement of their navigation, sections and borings are, in general, required only at those parts of the channel CKOSS SECTIONS AND BORINGS. 93 where fords or shoals occur, or any obstructions which need to be removed, no intermediate observations being neces- sary. But where rock is found at intervals in a river's course, in some places quite bare and exposed to the run of the water, and in others covered to a considerable depth with gravel, sand or any other deposit, it is necessary to make the sections and borings at shorter intervals, in order that the formation of the bed may be ascertained with suf- ficient accuracy to enable the engineer to form designs for works, and estimates of their expense, with either advantage or precision. Much time may be lost in making the sections and bor- ings, and erroneous data may be obtained, if the operation be not gone about in a proper manner ; and I conceive that this treatise would be incomplete, were I to omit offering a few remarks on what I have found, in practice, to be the best system in conducting this very important depart- ment of an engineer's survey. In the first place it may be stated, that it is advisable carefully to examine the whole course of the river, and to select the places at which sections and borings are re- quired, before commencing to make any of them. In mak- ing this selection, the engineer can be guided only by the object of the investigation and the formation of the river's course. If there be fords or shoals in the bottom which occasion obstructions to the navigation, and require to be removed, one or more lines of section may be fixed on at each shoal, according to its extent, and the positions of the lines selected should be marked by wooden stakes di'iven into either bank of the river. Where, as sometimes happens, 94 CROSS SECTIONS AND BORINGS. the channel is irregular, or lias rock occurring at various points, it is often necessary to obtain, by means of nume- rous cross sections, an exact survey of the whole, or at least of a great part of the bed, before any distinct plan of operations can be formed; and in that case, a series of stakes must be fixed on the margin of the river, at equal distances of 100 feet or 200 feet apart, according to the minuteness of the investigation to be made. In every case the stakes employed to indicate the positions of the sections should be regularly numbered with a marking iron, in the order in which they occur in the river, to prevent the possibility of one section being mistaken for another ; an accident which is not unlikely to occur when the breadth of the river is pretty regular and the banks do not present prominent objects, by a reference to which the positions of the lines may be determined. The stakes so fixed should be noticed in making the traverse survey of the banks, and in this way their sites may afterwards be correctly protracted on the plan. That the depths of the sections and borings may be re- ferred to the same datum as the soundings of the depths of water treated of in Chapter IV., the levels of the wooden stakes which mark the positions of the lines in which they are to be made, should be fixed in reference to that datum. To save time and a multiplication of observations, it ought to be done while the levels for ascertaining the relative heights of the tide gauges are being taken ; but if this ar- rangement be not convenient, a separate series of observa- tions must be made with this object specially in view. I shall now suppose that the positions of the difi'erent CROSS SECTIONS AND BORINGS. 95 lines of section and boring have been selected and marked by stakes, and that the levels of these stakes, in reference to some datum line have been ascertained, and shall proceed to offer a few remarks on the method of conducting the ope- ration of making the sections and borings themselves. The most favourable time for making both the sections and the borings is during lovir water, when there is no land flood, or, in other words, when the river is at its " summer water level." It will invariably be found that the appara- tus employed can be much more easily used, and the results obtained in a more satisfactory manner, under these circum- stances, than when the river is increased in breadth and depth, or the velocity of its current augmented, by either the tide or land floods. When the breadth of the stream exceeds 200 or 250 feet, and the soil in the bottom is sufficiently soft to admit of it, one or more iron bars (according to the breadth of the stream) about fths of an inch in diameter, and 14 or 15 feet long,* should be fixed upright at convenient intervals in the bed of the river in the line in which the section is to be made. A strong cord gTaduated at every 10 feet with lea- ther marks, having the figures distinctly shemi on them, should then be stretched across the river ; one end of the cord being made fast to the section stake, and the other to an iron rod, or some such fixture, driven into the opposite bank of the river. When the line has been extended be- * Rods, measuring 15 feet, are generally sufficiently long for the low wa- ter depths of our rivers, especially when it is considered that the sections, to which I am at present alluding, are made only at the shallowest parts where obstructions to the navigation occur. 96 CROSS SECTIONS AND BORINGS. tweeii these two j^oints, and liauled as tight as seems con- sistent witli its strength, it should be raised and secured to the several iron bars that have been fixed in the bed of the river, at as great a height above the surface of the water as can be conveniently reached from the boat. The intermediate supports thus produced are for the purpose of shortening the points of suspension, and preventing the cord from floating on the surface of the water ; for the marks cannot be distinctly seen when it is in that situa- tion, and if it remains for any length of time so immersed, the current gradually stretches the line, altering both the direction and the distances, and occasioning great inconve- nience. Doubts may exist in the minds of some as to the sufficient accuracy of the graduation of a line which has to undergo the repeated alternations of wetness and dryness thus produced, and which is so frequently stretched ; and objections to the method of tying it up to the iron rods may be started, on the ground of its forming a series of curves in- stead of a straight line. But such doubts and objections refer to quantities of comparatively small importance, and may, I am convinced from experience, be safely disregarded in practice, which is the chief object to be kept in view in the present inquiry. I have made many sections in the manner described, varying from 100 to 800 feet in length, and in no case have I met with any practical error or difficulty in consequence of the length of the section line diff'ering materially from the breadth of the river, as ob- tained trigonometrically in the course of the survey. It is advisable, however, that the cord to be used should be properly wetted and stretched before being graduated ; and CROSS SECTIONS AND BORING S. 97 its length should likewise be occasionally checked in the course of a survey of long duration. The cord having been adjusted in the manner described, a section of the bank of the river extending from the stake . which marks the position of the section line to the edge of the water should be made with the spirit level and rod in the usual way ; the stake being taken as the datum for the levels, and the zero for the distances. When this has been completed, soundings are to be taken with a sound- ing rod across the river, from bank to bank, at intervals of 10 feet, as marked on the graduated cord, after which a section, or, more strictly speaking, a continuation of that already made on the opposite bank of the river, is to be ex- tended from the edge of the water to the high water mark, or as much farther as may be considered necessary. By these processes sufhcient data are obtained, pro- vided the water has not altered its level while they were in progress, for laying down an exact section of the bed of the river in reference to the stake on the bank. But should the flow of the tide happen to commence while the soundings are being taken, or should the survey be proceeding either during flood or ebb tide, the results obtained would evidently be inaccurate, and require correction in consequence of the change of level which would, in the cases mentioned, take place on the surface of the water. In order to enable the observer to know when a change of level occurs, and to cor- rect his observations according to the amount of that change, it is obvious that he must be able, at any particular moment, to ascertain the height of the water as compared with what it was at the commencement of the soundings when the 98 CROSS SECTIONS AND BORINGS. level of its surface was fixed in reference to the datum line. For this purpose it is necessary, as soon as the sec- tion of the bank has been carried to the water's edge, and before the soundings have been commenced, to drive a short graduated tide gauge into the bank of the river, with its zero, or some known point, at the level of the water. In this way, if the water either rises or falls, the amount of difference in level can at once be discovered, and the depths of the soundings corrected by referring to the gauge. The borings, or more properly speaking, probings to which I shall now allude, though of great importance, are of a com- paratively superficial nature, being confined to the depth be- low the bottom to which the intended operations are likely to extend. This, in ordinary cases, is very limited. They are made with iron rods about 18 feet in length, and one eighth of an inch in diameter, steeled at the points, and graduated to feet and half feet with chisel marks. If more extended observations are required in this department of the survey, which is sometimes the case, they must, of course, be made with boring rods by persons qualified to execute such work, the nature of which it is unnecessary to enter on in this place. The borings with which we have to do, however, although superficial, generally occupy much more time than the sec- tion ; and it is advisable, that while one party has been making the preliminary arrangements and observations, and taking the soundings and levels for the section, in the man- ner already explained, another party should be going on with the borings. For this purpose, it is necessary to de- termine at what intervals they are to be taken, and to in- struct the person who is to take charge of the boring de- CROSS SECTIONS AND BORINGS. 99 partment accordingly. When rock occnrs within the depth to which the operations may be expected to extend, the in- tervals between the borings should not exceed 10 feet ; but in other situations, every 30 or 40 feet may be sufficient, according to the nature of the bed of the river. The person who makes the borings must register the distance of each, as indicated by the graduated cord, and the depth to which it extends below the bed of the river. This may readily be ascertained by deducting the depth of water at the spot from the whole depth indicated by the graduation on the boring rod, before it is withdrawn from the bore. The nature of the stuff as to hardness or softness should also be re- gistered, with any other remarks, bearing on the investi- gation, that may suggest themselves. The boring rods are jumped into the bed of the river by men working from boats ; and when the stuff is too hard to admit of this, they are driven by blows from a light hammer. In the latter case, difficulty sometimes arises in drawing them, especially from tenacious marl or clay ; but they can always be raised with a little trouble, by means of a purchase applied from the boat, after being started by the blow of a hammer. Rods of this kind are exceedingly convenient ; and for the com- paratively superficial, though highly important, examina- tion referred to, are the simplest and best adapted apparatus I have ever used. For further illustrating the operation which I have at- tempted to describe, I add a page of a field book, contain- ing the notes of observations taken in making a line of sec- tion and borings on the river Ribble. The first table marked No. 1. is the register of the levels 100 CROSS SECTIONS AND BORINGS. on one side of the river, and contains the sights from the section stake to the water's edge. By this it appears that the fall from the section stake to the surface of the water is 7.30 feet. To this fall there is added 1.78 foot, the fall from the datum line to the stake, which is ascertained in the manner alluded to in page 94 ; the total fall from the datum line to the surface of the water being 9.08 feet. The fourth column of this table contains the distances, and the last, remarks. The table marked No. 2. refers entirely to the sections and borings of the bottom of the river. The figures in the first, third, and fifth columns, are filled in on the ground. Those in the second and fourth columns represent the depths redu- ced to the datum. This is done by adding to the depths of the soundings and borings, the fall from the datum line to the surface of the water. In this case the fall, as shewn by table No. 1., is 9.08 feet; but in making the corrections, the decimal part .08 is rejected, and 9 feet assumed as the constant quantity to be added to all the depths. The pro- tracted field work of this line of section and borings is re- presented in Plate XIII. fig. 2, to which the reader is refer- red for a farther explanation of the subject. CROSS SECTIONS AND BORINGS. 101 FIELD-BOOK. No. 1. Cross Section of River Rihhle, at Stake No. 15, 25th July 1838. LEVELS. Sights. Rise. FaU. Distance. Remarks. 2.68 3.84 1.16 35 On Stake No. 15. 3.84 9.98 6.14 92 At edge of water. Add fall from da- tum line to stake, 7.30 1.70 Surface Surface of water below stake, of water below datum. 9.08 No. 2. SOUNDINGS AND BORINGS. Corrected Corrected Depth of Water. Depth of Water be- low datum. Distance. Depth of Boring be- low datum. Depth of Boring below Bed of River. Feet. in. Feet. in. Feet. in. 9 9 9 100 19 9 10 feet through sand and gravel to rock. 3 6 12 6 110 19 6.6 do. do. 3 9 12 9 120 17 3 4.6 do. do. 3 9 12 9 130 16 6 3.9 do. do. 3 12 140 16 2 4.2 do. do. 3 12 150 16 3 4.3 do. do. 3 3 12 3 160 15 9 3.6 do. do. 3 6 12 6 170 14 6 2.0 do. do. 4 6 13 6 180 15 1.6 do. do. 4 6 13 6 190 14 0.6 do. do. 3 7 12 7 200 Bare Kock. 2 6 11 6 210 Do. do. 2 9 11 9 220 Do. do. 2 6 11 6 230 Do. do. 2 3 11 3 240 Do. do. 2 11 250 Do. do. 2 11 260 Do. do. 2 3 11 3 270 Do. do. 2 2 11 2 280 Do. do. 2 11 290 Do. do. 1 9 10 9 300 Do. do. 5 3 14 3 303 ... Do. do. 5 14 310 Do. do. 5 14 320 Do. do. 4 9 13 9 330 Do. do. 4 9 13 9 340 Do. do. 4 9 13 9 350 ... Do. do. 4 6 13 6 360 Do. do. 3 9 12 9 370 Do. do. 3 6 12 6 380 Do. do. 1 3 10 3 385 Do. do. at Quay Wall, 6 ft. high. 102 CROSS SECTIONS AND BORINGS The use of the cross sections and borings is to furnish data on which designs of improvements and estimates of their expense can be founded ; and the correctness of an opi- nion, either as to the practicabihty or efficiency of a work, or as to the probable expense of its execution, may be said to depend, in almost all cases, on the minuteness and accu- racy with which they are made. As this department of the survey is of great importance, I may be excused for going into some detail regarding it ; and I shall therefore, before concluding, endeavour to illus- trate, by a reference to practice, the necessity of conducting it with care and accuracy. The example to which I shall refer is taken from the case of the river Ribble in Lancashire. The upper part of this river flows in a bed composed of successive patches of solid sandstone rock, compact gravel and loose sand, the irregu- larity of which rendered an extensive series of cross sections and borings absolutely necessary before any design for the improvement of the navigation could be devised, or any esti- mate of its expense formed. These lines of section and bor- ing, which were made throughout the whole of the upper part of the river, at distances of 100 feet apart, varied much in their character ; some giving a bottom composed of sand, and others of hard gi-avel, while in certain places the bottom was found to consist of rock, quite exposed, or covered with a deposit of mud or gravel, varying from a few inches to several feet in depth. I have shewn two of these sections in Plate XIII. figs. 1. and 2., which, although made at the distance of only 100 yards apart, fully illustrate the va- riety in the results obtained, and shew the importance •S .'2? « \: "^-s -i: ^ \i ' %i % •=>,i! % \ %g %. ■?. > "^ « "V ■'^,- -- \ - :- v "^'1 % " oNmoa % - ;! ; 1 2 ■ - 2 -r ? ^ o ; "H ■t*^ % < ■ 1 ■^<- -■^ •] '■<> -, Ji^ % -. ■■■/■ -"H -.-. /g f- a V g-g ,^, \ - ss. % \| - ifl ^ % o o ""'V ; s -SJ. - c 1 \. ■■Vl - S '^ J \ .J? — >£ \ ' % --. 1 °^ o / *S r ^\? f 1 Y- 1 y s : ° s{ ■" ■<• o CROSS SECTIONS AND BORINGS. 103 of these inquiries in forming designs and estimates of such works. In the first of these sections, it will be seen that the bot- tom of the river consists of gravel and sand, witli rock un- derneath, at depths varying from 5 to 12 feet below the bed ; in the second, on the other hand, the bottom is on as high a level as the first, and is composed of bare rock, with- out any deposit on it. The new navigable channel, which has been excavated since the survey was made, is shewn on the sections in dot- ted lines ; and, from an examination of the Plate, any one at all acquainted with engineering will at once perceive the great difference, as regards both expense and diflftculty, which attended the execution of the work at the two places. In fig. 1 the operation consisted simply of dredging in sand and gTavel, and was easily and cheaply accomplished by a dredging machine of the ordinary construction. In fig. 2 it consisted entirely of excavation in solid rock permanent- ly under water. This excavation, which varied from a few inches to 13 feet 6 inches in depth at the deepest place, and amounted to 30,793 cubic yards, was executed by means of a series of cofferdams of peculiar construction, which were kept dry by a pumping apparatus worked by a steam enoine,* a mode of excavating attended with very gi'eat ex- pense when compared to the simple process of dredging re- quired for forming the channel in section No. 1. These * I have given an account of the details of this work, and the construction of the cofferdams designed for executing it, in a communication which was read before the Institution of Civil Engineers in 1841, and is printed in the Transactions of that body, vol. iii. p. 377. 104 CROSS SECTIONS AND BORINGS. widely different operations, however, occurred on the same river, at a distance of only 100 yards apart, and it is very obvious that, without a series of such sections, it would be impossible to form any opinion as to either the nature of the operations or the amount of outlay required for improv- ing- the naviojation of such a river as that alluded to. Many examples of a similar kind might be given, but it seems unnecessary to enter on them. I shall therefore close this chapter by referring to the accompanying cut (fig. 7.), which represents a cross section of the Fossdyke navigation in Lincolnshire in its former state, and also a view of the condition in which it is proposed to be placed by the operations at present in progress. Fig. 7. The dotted line represents the cross sectional area of the canal and banks in its unimproved state. The hard lines shew its enlarged limits, which at some places have been already attained. This example, as in the former case, tends to shew the necessity of minute and accurate sections, on which to base all calculations as to the extent and cost of the work to be execnted. ( 105 ) CHAPTER VIIL HYDROMETRICAL OBSERVATIONS. Application of hydrometrical observations to engineering — Discbarge of rivers — Making of cross section — Determining the velocity — Instruments for measuring the velocity — Floats — Objections to floats for this purpose — The tachometer of Woltmann — Description of instrument and its appli- cation — Adjustment of scale of tachometer for observation — Formula for reducing the surface to mean velocity — Table of mean velocities — Instrument for determining velocities of currents in the sea — Floats — • Massey's log — Instruments for measuring under currents — The tacho- meter — The under current float — Instruments for ascertaining the di- rections of currents at sea — Obtaining specimens of water from differ- ent depths for the purpose of analysis — The Hydrophore — Varieties of construction — Manner of using them. The preceding chapters refer to the different depart- ments of the field work, by which data are obtained for constructing a plan or chart, and forming designs and esti mates of works to be executed. Certain hydrometrical operations have now to be noticed in connection with the subject of marine surveying, which, though not required in making designs and estimates, must nevertheless be occasionally performed by the civil engineer in determining particular points relative to the improvement of juivigations, the construction of harbours, or the adjustment 10(? IIYDROMETKICAL OBSERVATIONS. of the ri"lits of neiglibouring land owners in reference to salmon fisheries. The last of these subjects, although com- paratively unknown in England, has, for a great length of time, occupied much attention in the Scotch courts of law, some of the cases involving intricate physical questions, the solution of which is, in many instances, effected wholly or in part by means of the data afforded by hydrometrical observations. It is unnecessary in this place to enter into any detail re- garding the nature of the various questions for the deci- sion of which hydrometrical observations may be required.* It seems sufficient simply to narrate the different investiga- tions in which the engineer may be engaged, and to describe the apparatus employed, and the method of conducting them. I shall, therefore, without farther remark, observe, that it is often necessary in the course of the practice of engi- neering to determine the discharge of rivers, the velocity and direction of surface and under currents, and the quality of water taken from various depths and at different times of tide, as well with regard to the proportions of sea and fresh water which constitute the mixture, as to the quantity of solid materials, such as sand or mud, held in mechanical suspension. A few brief remarks on the mode of conducting these in- vestigations and the apparatus employed, will form the sub- ject of this chapter. * For further information on this subject, the reader is referred to the Reports to the British Association on " The Progress and Present State of our Knowledge of Hydraulics as a branch of Engineering," by George Ron- nie, Civil Engineer. London, 1835. HYDROMETRICAL OBSERVATIONS. 107 The discharge of a stream is ascertained by multiply iiig i ts mean velocity by its area ; and in gauging a river with this object in view, it is necessary, first, to determine accurately its sectional area in a plane as nearly as possible at right angles to the direction of the current, and immediately thereafter to make the observations for the measurement of its velocity before any change in the level and consequent al- teration of the area obtained, has taken place. A part of the river having been selected for this purpose, where the banks are regular and the stream tranquil, a graduated cord should be stretched across as nearly as possible at right angles to the direction of the current. The depths of water should then be carefully taken, with a rod graduated to feet and inches, or decimals, at every 5 or 10 feet (as indicated by the marks on the cord), according to the minuteness of the inquiry to be instituted, or the irregu- larity of the river's bed. This process being conducted in the same way as that already described at page 95, re- quires no further explanation. It seems only necessary to remark that the nature of this investigation renders an exact measurement of the breadth of greater importance than in the case referred to in Chap. VII., and that, as suggested by my friend Professor Gordon, a cord of brass wire, which, from its unyielding nature, would unquestionably form a more accurate measure, might be substituted with advan- tage for one' made of hemp. Having obtained an exact cross sectional area of the stream, the next point is to determine the velocity of the current passing through it. This, however, varies, gradu- ally decreasing from the fair-way of the river towards the 108 I[YDROMETRICAL OBSERVATIONS sides, and from the surface towards the bottom ; and there- fore, for the purpose of calculation, the mean velocity must be determined. This is done by ascertaining the surface velo- city in the middle of each of the compartments into which the transverse section of the river is divided, by the sound- ings made, as already explained, and from these surface velocities, by a simple formula, the mean velocity of each of the compartments can be obtained, and the mean of these will be the required mean velocity of the river. For the purpose of ascertaining the surface velocities, various methods may be employed. The most common, but by no means the most satisfactory, mode of proceeding, is to throw into the water a float com- posed of some small body (whose specific gravity is merely great enough to sink it to a level with the surface), at a point about 30 or 40 feet above the line of section, so as to insure its acquiring the full velocity of the current before it reaches the eord. An observer, stationed at the cord, notes exactly the moment at which the float passes, and follows it down the stream till he reaches the line of two poles, which have been fixed in reference to the obser- vations, when he again notes the exact moment of its transit at the lower station. The elapsed time between the two transits is then noted in the book, along with the distance between the two places of observation, which, owing to the irregularity of most rivers, with regard to width, depth, and velocity, can seldom be got to exceed 100 feet. This operation has, of course, to be repeated for every compartment of the cross section. Certain disadvantages attend this metliod, which render IIYDROMETRICAL OBSERVATIONS. lOD it not generally applicable. For example, it is only adapt- ed to rivers of limited breadth, owing to the ini[)0ssibility of an observer being able to discover with sufficient accu- racy when the float passes the station lines, if it be viewed from a distance, as from the bank of a broad river. There are, however, greater objections than this, which, when pointed out, will be sufficiently obvious to every one. In any part of the river passe-d over by the floats, the slightest irregularity of the bottom produces a disturb- ance in the motion of the stream, and alters the velocity of the current, so that the result indicated by the elapsed time is more or less vitiated, and the mean velocity deduced from such data, is not, in almost any case, that which exists at the line of cross section. It is also impossible, by this method, to obtain a sufficient number of distinct and independent ob- servations, applicable to each division of the stream, as the eddies and irregularities of the current which exist in all rivers, generally cause the lines passed over by the floats to cross and interfere with each other in such a man- ner as to destroy all connection between any given series of observations, and the several compartments of the river, whose mean velocity they were intended to ascertain. The superiority of the method which I am about to de- scribe, consists in ascertaining the velocity of each portion of the stream, in the exact line in which the cross sectional area is taken. The instrument employed for this purpose is a mo- dification of the tachometer of Woltmann, which is in general use in France and Germany, both as an anemometer, and a hydrometer, being made of the degree of delicacy suited to the purpose to which it is to be apphed. In this instrument 110 HYDROMETRICAL OBSERVATIONS the velocity is measured by tlie current impinging on a vane and causing it to revolve, tlie number of revolutions made by tlie vane being registered on an index, wliicli is acted on by a set of tootbed wbeels. The construction of this beautiful instrument, and the manner in which it acts, will be best described by a refe- rence to the accompanying cut, fig. 7., which is taken from Fig. 7. a tachometer or stream gauge made by Mr Robinson, opti- cian, London, and is drawn to a scale of one third of the full size. In this view, /y represents what may be termed the driving vane, which is acted on by the stream, and of which ^ is a plan. The plane of this vane is twisted as represented by the dark shading in the cut, so as to present, not a knife- IIYDROMETRICAL OBSERVATIONS. Ill edge, but an oblique face to tlie action of the current, wLlcb, by impinging on it, causes it to revolve exactly in the same way that the wind propels the sails of a windmill. On the spindle or shaft of this vane, an endless screw is fixed at e, which works in the teeth of the first registering wheel, and causes It to revolve, when the vane is in motion and the screw in gear. Letters a and h represent a bar of brass, to which the pivots on which the registering wheels revoh^e, are attached. This bar Is moveable on a joint at h ; and at the point «, a cord, « c is fixed, by pulling which the bar and wheels can be raised, and on releasing it they are again depressed by a spring at d. When the bar is raised, the teeth of the wheel are taken out of gear with tlie endless screw, and the vane is then left at liberty to revolve, the number of its revolutions being unregistered ; but when the cord is released, the spring forces down the wheels, and immediately puts the registering train into gear, in which state it is represented in the cut. Letter A is a stationary vane (which is shewn broken off, but measures about 9 inches in length) for keeping the plane in which the driving vane revolves, at right angles to the direction of the current, and k is the end of a wooden rod to which the tachometer is attached when used. The different parts of the instru- ment Itself are made of brass. The moveable bar for the registering wheels and the aj)- plicatlon of the cord and spring which have been described, afford the means of observing with great accuracy in the following manner. The instrument having been adjusted by sett'ug the registering wheels at zero, or noting ni the field book the figure at which they stand, the cord Is pulled 112 IIYDROMETRICAL OBSERVATIONS. tiglit so ;is to i-alse tliem out of gear, and tlie instru- ment is then immersed in the water. The vane imme- diately begins to revolve from the action of the current, and is permitted to move freely round until it has attained the full velocity due to the stream. When this is supposed to be the case, a signal is given by the person who observes the time, and the registering wheels are at that moment thrown into gear by letting the cord slip. At the end of a minute another signal is given, when the cord is again drawn and the wheels taken out of gear, and on raising the in- strument from the water, the number of revolutions in the elapsed time is read off. This operation being completed in the centre of each division of the cord, the number of re- volutions due to the velocity at each part of the very line where the cross section is taken, is at once obtained. Before using the tachometer, it is obvious that the value of a revolution of the vane must be ascertained ; and although this is done by the manufacturers, it is proper that the scale of each instrument should be determined by the person who uses it, and that it be tested if the instru- ment has been out of use for some time, before being again employed in making observations. A scale sufficiently ac- curate for most hydrometrical purposes (though not for the instrument when used as an anemometer) may be obtained by applying it to some regular channel, such as a mill lead formed of masonry, timber, or iron, where the velocity is nearly the same throughout, and noting the number of re- volutions performed during the passage of a float over a given number of feet, measured on the bank. In this way, it was found, by the mean of 62 observations, that each re^ HYDROMETRICAL OBSERVATIONS. 113 volution of tlie vane in tlio iiistrLunout of which a drawiiio- has been given, indicated the passage of the water over 46 inches. The number of revolutions at several parts of the stream was ascertained to be the same in equal times, at both the commencement and the end of the experiments. This number, therefore, becomes in the instrument alluded to, a constant multiplier of the number of revolutions indi- cated by the vane ; and hence, the number of feet passed over by the water in the given interval of time is ascertained. Having thus by means of the tachometer determined the surface velocity of the river at each of the divisions of the extended cord, the next step is the reduction of the ob- served surface to those of mean velocities, which will be readily done by the following rule of De Buat. If unity he taken from the square root of the surface ve- locity expressed in inches, the square of the remainder is the velocity at the bottom, and the mean velocity is the half sum of these two. Thus, let « = the observed surface velocity, i^ = the bottom velocity, and 7 = the mean velocity. + /5. = ^V a - 1 ) and 7 and hence, the mean velocity is directly deducible from the surface velocity by the following formula. 2 * The following table of surface, bottom, and mean veloci- ties may be useful in saving the trouble of calculation in cases where a great many observations have to be reduced. 114 HYDROMETRICAL OBSERVATIONS. TABLE OF SURFACE, BOTTOM, AND MEAN VELOCITIES. Vki.ocity I-\ I.N CUES. Velocity in I> (■iip:.s. Surface. Bottom. Mean. Surface. Bottom. Mean. 1 0.000 0.5 51 37.717 44.358 2 0.172 1.086 52 38577 45.288 3 0.537 1.768 53 39.439 46 219 4 1.000 2.500 54 40.303 47.151 5 1.527 3.263 55 41.167 48.083 6 2.101 4.050 56 42033 49.016 7 2.706 4.853 57 42.900 49.950 8 :^.343 5.671 58 43.768 50.884 9 4.000 6.500 59 44.637 51.818 10 4.G75 7.337 60 45.508 52.754 11 5.364 8.182 61 46.379 53.689 12 6.071 9.035 62 47.252 54.626 13 6.788 9.894 63 48.125 55.562 14 7.516 10.758 64 49.000 56.437 15 8.254 1L627 65 49.875 57.436 IG 9.000 12.500 C6 50.751 58.375 17 9.754 13.377 67 61.623 59 314 18 10.514 14.257 68 52.507 60.253 19 11.283 15.141 69 53.386 61.193 20 12055 16.027 70 64.266 62.133 21 12.835 16.917 71 55.147 63.073 22 13.619 17.809 72 50.029 64.014 23 14.408 18,704 73 56 912 64.956 24 15.202 19.601 74 57.795 65.897 25 16.000 20.500 75 58.079 66.839 26 16.802 21.401 76 59.564 67.782 27 17.607 22.303 77 60.450 68.725 28 18.417 23.208 78 61.336 69.668 29 19.230 24.115 79 62.223 70.611 30 20.045 25.022 80 63111 71.555 31 20.864 25.932 81 64.000 72.500 32 21.695 26.847 82 64.889 73.444 33 22.511 27.755 83 65.779 74.389 34 23.3:58 28.669 84 66.670 75.335 35 24.167 29.583 85 67.561 76.280 36 25.000 30.500 86 68.453 77.226 37 25834 31.417 87 69.358 78.179 38 26.671 32.335 88 70.238 79.119 39 27.510 33.250 89 71.132 80.013 40 28.350 34.175 m 72.026 81.006 41 29.193 35.096 91 72.921 81.960 42 30.038 36.019 92 73.818 82.909 43 30.885 36.942 93 74.713 83.856 44 31.733 37.806 94 75.609 84.804 45 32.583 38.791 95 76.506 85.753 46 33.435 39.717 96 77.404 86.702 47 34.288 40.644 97 78.302 87.651 48 35.049 41.524 98 79.201 88.600 49 36.000 42.500 99 80.100 89.550 50 36.857 43.428 100 81.000 90.-^00 HYDROMETllICAL OBSERVATIONS. 115 Tlie mean velocities obtained, either Ly calculation or the use of tables, are to be multiplied into the a^-ea of the spaces in the centres of which the observations were made, in order to obtain the cubic contents of water discharged in each division; and to obtain the whole discharge, it is only necessary to add together the results of the ob- servations made in all the different compartments. The apportioning of the stream into different parts, and treat- ing each as a separate channel, appears to insure a much greater probability of a correct measurement than any method which depends upon assigning to the whole area a common velocity ; and it is obvious that this method can be effectually followed only by the use of the tacho- meter described, or of some similar instrument (such as Pitot's tube), which possesses the advantage of confining its indications to the spot where the sectional area of the river is actually measured. Wherever, as will frequently happen in regular streams, the velocity of several compart- ments, as ascertained by the stream gauge, are found to be the same, the areas of these compartments may be added into one sum and multiplied by the common velocity. It seems necessary to observe that velocities exceeding 3 miles an hour are apt to injure an instrument of the size and proportions shewn in the cut, and that in gauging more rapid rivers, an instrument on the same principle, but of stronger make, should be employed. Great convenience in this as in other departments of sur- veying and observing, will be found to result from register- ing all the observations in a tabular form. The following is an example of the observations made in ascertaining lie IIYDROMETRICAL OBSERVATIONS. the discliarge of tlie River Conon in Rossliire on the 29th Au^ist 1827. Phite XIII., fig. 3, is a sketch of the cross section made iu the field book. The numbers marked horizon- tally on the level line are the distances ; and those marked diagonally above it are the depths. The whole distance was divided into eleven compartments. The velocity of each was tried three times with the tachometer, their mean be- ing taken as the correct velocity, and the following table contains the results of the calculations : — No. of Section. Surface Velocity per second iu inches as observed. Tabular Mean Velocity in inches. Area of Section in square feet. IJischarge in cubic feet per second. 1 34 28.669 124.791 298.136 2 60 52.754 149.375 656.678 3 65 57.437 149.503 715.966 4 60 52.754 150.416 661.254 5 45 38.791 139.291 450 270 6 42 36.019 116.458 349.549 7 38 32.335 87.291 235.213 8 30 25.022 63.333 132.060 9 19 15.141 49.916 62.981 10 9 6.500 26.041 14.105 11 4 2.500 18.333 3.819 3580.031 (J-^1. The velocity of currents in the open sea or in estuaries may be determined from a boat at anchor, by allowing a float to run out during a given interval of time, and observing the quantity of graduated line which has been let out. lIYimOMETllICAL OBSERVATUNS 117 Massey's log is also very suitable for such experiments ; but it is not found to be well adapted for registering velocities mucli below 2 miles an hour. It has occasionally been found interesting, if not abso- lutely indispensable, in certain inquiries which come before the civil engineer, to ascertain to what depth the currents penetrate, and whether under-currents exhibit the same phenomena in regard to direction and velocity as those of the surface. The tachometer of Woltmann, which has been already described, is the most convenient and accurate in- strument that can be employed for depths of from 15 to 20 feet. I understand from Professor Gordon, that it is often employed in Germany for measuring velocities at much greater depths by the use of an apparatus erected on a plat- form supported on two boats.* But as its application under such circumstances may be regarded rather as a purely scientific than as an engineering experiment, it is not necessary to describe it in this place. The direction of the under current, which it is sometimes interesting to know, cannot, however, be obtained by means of the tachometer, and I shall describe a plan for obtaining an approxi- mation to both the velocity and direction of under currents, which is of easy application, and may be useful to those em- ployed in engineering investigations. The plan to which I allude was devised and used at the Cromarty Frith in 1837, by INIr Alan Stevenson, who discovered, by means of the in- strument he employed, the interesting fact, that, at the depth * Raucourt measured the velocity of the Xeva at St Petersburgli with the tachometer at depths of 60 feet ; Defontaine tlie Rhine at upwards of 40 feet; and Funk many rivers at depths of from 40 to 60 feet. 118 IIYDROMETRICAL OBSERVATIONS. of 50 feet, tb<3 velocity of the current, at both flood and ebb, is in certain places of the Frith nearly double that at the surface. This instrument, which of course merely gave an approximate result, consisted (as shewn in the accom- panying cut, fig. 8, at letter a) of a flat plate of sheet iron. Fig. 8. measuring 12 by 18 inches, having a vane made of the same material, and measuring 4 feet in length, fixed at right angles to the centre of it. The lower edges of the plate and vane were loaded with bars of iron, for the purpose of causing the instrument to sink to the requisite depth ; and it was so slung as to preserve the surface of the plate in a vertical plane. This apparatus was secured by a cord of sufficient length to sink it to the required depth, and the whole was attached to a tin buoy, letter &, which floated on the surface, its form being such as to produce little resist- ance to its passage through the water. The buoy served not only to preserve the vane plate at the same depth, but also indicated its progress through the water in a very satis- factory and often interesting manner. The plate, sunk at the depth of 50 feet, when acted upon by the force of a strong under current, was hurried along, HYDROMETRICAL OBSERVATIONS. 119 carrying the buoy, which Hoated on the surface, along with it, a circumstance which was ascertained by tlie buoy pass- ing the floats thrown out on the water as gauges of the ve- locity and direction of the upper current, one of which is shewn at c. The only precaution to be observed in making such observations, is to exclude that part of the commence- ment of the buoy's course, which is more rapid than it ought to be, owing to the effort made by it to overtake the plate, wdiich, being sunk first, has been influenced by the velocity of the under current before the buoy has been launched. It is evident that, by means of this simple apparatus, we can approximate to the direction as well as to the velocity of under currents ; but it must be kept in view that, in either case, there are several deranging influences in operation, which tend to render the results obtained merely rude ap- proximations to the truth. The direction of surface currents may be easily observed by means of a string of cork floats. Any change in the di- rection of the line traced by the floats is noted by observa- tions made wdtli the surveying compass or the sextant, by an observer stationed in a boat, which is row^ed alongside of the line marked out. The last hydrometrical topic which shall engage our at- tention, is the method of obtaining specimens of water at diff'erent depths, with a view to ascertain its qualities in re- gard to the proportion of sea salt which it contains, or the quantity of sand or mud held in mechanical suspension. The first observations made on this subject, so far as I am aware, were those instituted by my father on the River Dee in Aberdeenshire, in the summer of the year 120 IIYDIIOMETRICAL OBSERVATIONS. 1812, when engaged in surveying that river in reference to a sahiion fishing case.* " He observed in the course of his survey that the current of the river continued to flow to- wards the sea with as much apparent velocity during flood as during ebb tide, while the surface of the river rose and fell in a reuular manner with the waters of the ocean. He was led from these observations to enquire more particu- larly into this phenomenon, and he accordingly had an ap- paratus prepared, under his directions, at Aberdeen, which, in the most satisfactory manner, shewed the existence of two distinct layers or strata of water ; the lower stratum consisting of salt or sea water, and the upper one of the fresh water of the river, which, from its specific gravity being less, floated on the top during the whole of flood as well as ebb tide. The apparatus consisted of a bottle or glass jar, the mouth of which measured about 2^ inches in diameter, and was carefully stopped with a wooden plug, and luted with wax ; a hole, about half an inch in diameter, was then bored in the plug, and to this an iron peg was fitted. To prevent accident in the fevent of the jar touching the bottom, it was coated with flannel. The jar so prepared was fixed to a spar of timber about 20 feet in length, which was graduated to feet and inches, for the conveniency of readily ascertain- ing the depths to which the instrument was plunged, and from which the water was brought up. A small cord was attached to the iron pin for the purpose of drawing it at pleasure for the admission of the water. When an experi- * Report to the Earl of Aberdeen and the other proprietors of the " Raik" and '• Stell" fishings of the river Dee, at Aberdeen, by Rol^ert Stevenson, Civil Engineer. Edinburgh, Feb. 1813. HYDROMETRICAL OBSERVATIONS. 121 ment was made, the bottle was plunged into the water ; by drawing the cord at any depth within the range of the rod to which it was attached, the iron peg was hlted or drawn, and the bottle was by this means filled with water. The peg was again dropped into its place, and the apparatus raised to the surface, containing a specimen of water, of the quality at the depth to which it was plunged. In this man- ner, the reporter ascertained that the salt, or tidal water of the ocean flowed up the channel of the River Dee, and also up Footdee and Torryburn, in a distinct stratum next the bot- tom and under the fresh water of the river, which, owing to the specific gravity being less, floated upon it, continuing perfectly fresh and flowing in its usual course towards the sea, the only change discoverable being in its level, which was raised by the salt water forcing its way under it. The tidal water so forced up continued salt, and when the speci- fic gravities of specimens from the bottom, obtained in the manner described, were tried, and compared with those taken at the surface, by means of the common hydrometer of the brewer (the only instrument to which the reporter had access at the time), the lower stratum when compared with that at the surface was always found to possess the greater degree of specific gravity due to salt over fresh water." The appearance of the fresh water floating on the surface of the sea, is no doubt familiar to most persons. It occurs at the mouths of many of our rivers, and is most apparent when they are in flood, from the brown tinge given to the water, which is easily discoverable for many miles at sea. The great American rivers furnish many remarkable instances of this, particularly the Amazons and La Plata. On this 122 IlVDROMETllICAL OBSERVATIONS. subject, the following |)ii,^sage i'rom the work* of Father IManucl Rodriguez, a Spanish Jesuit, is interesting, and its correctness as regards the extent to which the influence of these rivers is felt, has since been corroborated by the investi- gations of Colonel Sabine. f " This river," says Rodriguez, in speaking of the Amazons, " is like a tree, its roots enter as far into the sea as into the land. It communicates to it a flavour ; so that at 80 leagues within the sea, its wa- ters are seen and taste sweet, and in a semicircle of 100 leagues in circumference, they form a gulph not in the least degree brackish, so that the sailors call it the fresh sea." The instruments now used for obtaining water from dif- ferent depths, are more perfect in their construction than that already alluded to as having been used at the Dee, which, as has been seen, was made for a temporary purpose. Instruments of various constructions have of late been tried for experimenting on this subject by Scoresby, Sabine, and others ; and as I am not aware that any work on ma- rine surveying, or on surveying instruments, contains a de- scription of such an apparatus (to w^hich I have applied the name of the ki/drop/iorel), the following account of two modifications of it, both of wdiicli I have been in the habit of using, may perhaps be instructive. Fig. 9. represents a hydrophore used for procuring spe- cimens of water from moderate depths, drawn on a scale of one tenth of the full size. It consists of a tight tin cylinder, letter a, having a conical valve in its top &, which * El Maranam y Amazonas. ^ladrid, 1684, p. 18, t An Account of Experiments to determine the figure of the Earth, as well as on various other subjects of philosophical inquiry, by Edward Sabine. London, 1825, j). 445. X u8aig and ^o^scj. HYDROMETRICAL OBSERVATIONS. 12.3 is represented in the diagram as being raised for the adi sion of water. The valve is fixed dead^ ^'s- ^• or immovable, on a rod working in guides, the one resting between two uprights of brass above the cylinder, and the other in its interior, as shewn in faintly dotted lines. The valve-rod is by this means caused to move in a truly vertical line, and the valve attached to it consequently fills or closes the hole in the top of the cylinder with greater accuracy than if its motion was undirected. A graduated pole or rod of iron c, which, in the dia- gram is shewn broken off, is attached to the instrument, its end being inserted into the small tin cylinder at the side of the large valve or water cylinder, and there fixed by the clamp screws shewn in the diagram ; the bottom of the water cylinder may be loaded with lead to any extent re- quired, for the purpose of causing the apparatus to sink ; but this, when an iron rod is used for lowering it, is hardly ne- cessary. The spindle carrying the valve has an eye in its upper extremity, to which a cord is attached for the purpose of opening the valve when the water is to be admitted, and on releasing the cord, it again closes by its own weight. When the hydrophore is to be used, it is lowered to the required depth by the pole which is fixed to its side, or if the depth be greater than the range of the pole, it is loaded with weights and let down by means of a rope so attached as to keep it in a vertical position. Care must be taken while lowering or raising it, that the small cord by which the valve is opeued be allowed to hang perfectly free and slack. When the appa- 1-24: IIYUKOMETIIICAL OBSERVATIONS. nitus has been lowered as far as is required, the small cord is pulled, aud the vessel is immediately filled with the water which is to be fouud at that depth. The cord being then thrown slack, tlie valve descends and closes the opening, and the instrument is slowly raised to the surface by means of the rod or rope, as the case may be, care being taken to preserve it in a vertical position. This apparatus is only applicable to limited depths, but will generally be found to answer all the purposes of the civil engineer. Fig. 10. Yhe form of hydrophore represented in fig. 10 is used in deep water, to which the small one just described is inapplicable. It consists of an egg shaped vessel, letter a, made of thick lead, to give the apparatus weight, having two valves h and c, one in the top and another in the bottom, both opening upwards ; these valves (which are repre- sented as open in the diagram) are, to ensure more perfect fitting, fixed on separate spindles, which work in guides, in the same manner as in the in- strument shewn in fig. 9. The valves, however, in the instrument I am now describing, are not opened by means of a cord, but by the impact of the pro- jecting part d, of the lower spindle on the bottom, wdien the hydrophore is sunk to that depth. By this means the lower valve is forced upwards, and the upper spindle (the lower extremity of which is made nearly to touch the upper extremity of the lower one, when the valves are shut) is at the same time forced up, carrying along with it the upper valve which allows the air to escape, and the water rushing in fills the vessel. On raising the instrument from the bottom, iIYDRvOMETRICAL OBSERVATIONS. 125 botli valves aguiii slmt by their own weight and that of tlie mass of lead d, which forms part of the lower s[)indIo. The mode of using this hydrophore is sufficiently obvious ; it is lowered by means of a rope, made fast to a ring at the top, as shewn in fig. 10, until it strikes on the bottom, wdien the valves are opened in the manner described, and the vessel is filled ; on raising it the valves close, and the vessel can be drawn to the surfiice without its contents being mixed with the superincumbent water through which it has to pass. This instrument weighs about half a hundred weight, and has been easily used in from 30 to 40 fathoms v.ater in making engineering surveys, and could no doubt be employed for much greater depths if necessary. It is re- presented in the cut on a scale of one-twentieth of the full size- In all these experiments, the water being emptied into bottles, is corked up, sealed, and labelled with certain num- bers, which should be entered in a book containing remarks as to the place of observation, time of tide, and such other particulars as, from the nature of the inquiry, seem to deserve notice, and the water thus preserved may be sub- jected to analysis, produced in evidence, or employed in any other way required by the circumstances of the case. The marine productions of an estuary, such as the fish, shells, and plants which occur in it, occasionally aftect ques- tions regarding which an engineer may be consulted ; but as it is not my present intention, as stated at the beginning of this Chapter, to enter into the nature of the questions in which such investigations are required, or the manner in which they bear upon them, it is not considered necessary, in mentioning these productions, to do more than simply di- rect attention to the subject. ( 12t) ) CHAPTER IX. PROTRACTION OF THE TRIANGULATION, BASE LINE AND TRAVERSE SURVEY. Metliods of protracting- triangulation — By tlie calculated sides of the triangles — By the bearings — Principle on which protraction bj' the bearings is based — Protractors used — Drawing protractor on the paper — Method of dividing it — Method of transferring bearings to different parts of the pa- per — Protraction of base line, first. When it lies between two triangu- latlon stations ; second, When it does not extend between triangulatlon stations, but is nevertheless connected with the triangulatlon by bearings ; third, When the base is not connected with the triangulatlon — Tri- gonometrical calculation for solving third case — Method of protracting triangulatlon before laying down base line — Objections to this mode — Correction of the measured length of the base necessary — Protra(?tion of the survey of the high water margin when the system of chain or traverse surveying Is employed — Checking accuracy of the measurement of the survey lines. Protraction may be defined as that process whereby the data obtained during a survey are transferred to paper and recorded for the use of the engineer. Being conducted entirely in the office, it is termed " house" or " office work," to distinguish it from the operations treated of in the fore- going chapters, all of which are performed in the field. It has been already shewn, that these field operations are the groundwork of the opinions, designs, and estimates, of PROTRACTION. 127 engineers ; and as it is only when represented on a })lan that they can he advantageously applied to such practical purposes, the most accurate means of protracting them is obviously a subject of no less importance than that of con- ducting the survey itself, and to its consideration, therefore, the remaining chapters will be devoted. In treating of the field work, it was thought advisable, in order to simplify the subject, to devote separate chapters to the consideration of the triangulation, the selection and measurement of the base line, and the survey of the high water margin of the river ; but in describing the protrac- tion of these difi^erent departments, it will be more conve- nient to include the whole of them in the same chapter. The method of protracting the triangulation by calculat- ing the distances between the different stations and laying- down their positions by measurement,is perhaps betteradapted than any other process to extensive surveys in which great ac- curacy is required. In almost all engineering surveys, how- ever, the positions of the triangulation stations may be de- termined with sufficient accuracy by the intersections of the bearings taken in the field, when laid down in the manner hereafter described, and this system should be adopted in pre- ference to the other in all cases where it is practicable to do so, laborious trigonometrical calculations being thereby avoided, and greater convenience aff'orded for laying down the traverse survey. To it, therefore, I shall confine my remarks. It may be stated in the outset, that, in the mode of pro- tracting about to be described, the principle on which the bearinofs are laid down is the same as that on which the 128 PROTRACTION OF THE TRIANGULATION, field work of the survey is conducted, and is based on the parallelism of the same bearings at all the different stations, ■which has already been fully explained in Chapter I., and is illustrated in Plate II. Tlic accuracy of the plan or chart to be constructed may be said to depend, in a great measure, on the correctness of the triangulation, and the whole of this important depart- ment should, if possible, be protracted before the comple- tion of the survey, or, at all events, before the surveyors leave the neighbourhood, so that if any error has been com- mitted, an opportunity may be afforded of rectifying it by revising the field work. It is therefore of much conse- quence to be possessed of some simple, and at the same time efficient means, for accomplishing this desirable object. Many protractors of different forms and materials have been constructed, most of which are useful for the peculiar pur- poses for which they were more especially intended ; but I have never met with any portable protracting instrument which seemed at all well adapted for laying down the bearings of a trigonometrical survey of even moderate extent. The method which I have invariably found to be most convenient, and at the same time best fitted for effecting this operation, is to draw the protractor on the sheet of paper on which the survey is to be laid down ; or, in other words, to describe on it a circle of 12 or 14 inches in dia- meter, and to divide it into 360 equal parts. The graduation requires to be done with great care, and a little time is oc- cupied in executing it ; but if an accurately divided circle, or even a semicircle of brass or card, be employed for the BASE LINE AND TRAVERSE SURVEY. 129 purpose, the process is greatly simplified, and much time and trouble saved. The graduated circle is placed on the spot to be occupied by the protractor, and the degrees care- fully pricked off on the sheet of paper, an operation which may be performed in a very few minutes. In most cases, it is necessary, as will be shewn more particularly hereaf- ter, to draw several of these protractors on the paper, their number varying according to the size of the plan to be made ; and it therefore becomes an object of importance, when much surveying of this kind is to be done, to have a graduated in- strument constructed for laying down the circles in the man- ner described. Sheets of paper having protractors engraved on them are also used for extensive surveys ; but an objection has been raised to this method, as the process of printing the impression of the plate is said to injure the paper for drawing. I am not aware, however, whether this objection be founded on good grounds, as I have never employed protractors of this descrip- tion. I believe that, in the practice of most engineers, the method of pricking off the circle on the sheet will be found fully to answer every purpose. If a graduated circle be not used for laying down the pro- tractor, the following neat method of performing the divi- sion, which is recommended by ^Ir Simms, may be adopted.* " The great difficulty," says Mr Simms, " of dividing a circle accurately, is well known, but if the arcs are laid off by means of their chords, the division may be performed * A Treatise on tlie Principal Mathematical Instruments employed in Sur- veying, Levelling, and Astronomy, by Frederick M. Simms, p. fl3. liondon^ 1834. 130 PROTRACTION OF THE TRIANGULATION, with siifiicieiit exactness for tlie purpose in hand. The lengths of the chords should be taken from an accurately di- vided beam compass, which, to ensure success, should be set with the utmost possible exactness. " With a radius of 5 inches describe a circle, and imme- diately, without altering the compasses, step round the circle, making a fine but distinct mark at each step ; this will divide the circle into six parts of 60° each. " Next set the compasses to the natural sine of 15°, which to radius five will be equal to the chord of 30°" (the ra- dius of the tables of natural sines being 10), " and this dis- tance will bisect each 60°, and divide the circle into arcs of 30° each. A proof may be obtained of the accuracy of the work as it proceeds, by setting the succeeding chords off each way from those points which they are intended to bi- sect ; for if any inaccuracy exists, the bisection will not be perfect, and if the error proves inconsiderable, the middle point may be assumed as correct. " Each sixty degrees may next be trisected by setting off the natural sine of 10° (equal to the chord of 20° to our ra- dius), which w^ill divide the circle to every ten degrees. " Next the natural sine of 7° 30' (equal to the chord of 15°) stepped from the points already determined, will divide the circle to every fifth degree. " The natural sine of 3° (equal to the chord of 6°) being laid off, divides 30° into five parts, and, set off from the other divisions, divides the circle to single degrees. " Fifteen degrees bisected or the natural sine of 3° 45' (equal to the chord of 7° 30') set off from the other divisions, divides the circle into half degrees. BASE LINE AND TRAVERSE SURVEY. 131 " The natural sine of 3° 20' (equal to the chord of 0" 40') divides 20° into three parts, and, set off from the rest of the divisions, divides the whole circle to every ten minutes, which is as minute a subdivision as such a circle will possibly admit of; smaller quantities must therefore be es- timated by the eye." This method of dividing refers to a circle of 10 inches in diameter, which, in some cases, will be found to be rather too small, but if one of 20 inches be adopted, which for large surveys is a very convenient size, the same steps may be taken for graduating it, the natural sines of the whole, in- stead of half the angles, being laid off. In Plate I., which represents part of the river Tay drawn on a scale of about one fifth of that on which the work was originally protracted, two of the plotting circles are shewn. In laying down these circles, care should be taken that the bearing coinciding with the direction of the greatest ex- tent of the survey (which, in most cases, can be approxi- mately ascertained with ease) be placed so as to coincide with the gi'eatest axis of the sheet of paper. Thus, in the case of a survey, where the river lies due north and south, the bearing of 360° should be placed in the direction of the greatest axis of the paper ; or if the river lies east and west, the bearing, 90°, should be made to coincide with it. If this precaution as to the coincidence of the greatest limits of the survey with those of the sheet on which it is to be pro- tracted be not attended to, the work may, as the protrac- tion proceeds, run off the paper long before it has been filled, a circumstance which is attended with great inconvenience. In treating of the measurement of the base line, it will 132 PROTRACTION OF THE TRIANGULATION, be remembered tliat three cases were alluded to, in all of which the observations for fixing its extremities were con- ducted on somewhat different principles ; and as the methods by which they are protracted also differ, each case mnst be explained separately. In proceeding to shew in what way the triangulation of the survey is to be laid down, I shall, in the first instance, advert to those cases in which the base line has been measured between two of the triangulation stations, the method which was recommended to be adopted wherever it is at all practicable. Before laying off any of the bearings, the scale (in the proportion of a certain number of inches to the mile) on which the plan is to be made, ought to be determined and laid down on the paper. The size of what is called the rough plan should, for facilitating the protraction, be as large as is consistent with convenience, especially as it may be afterwards accurately and easily reduced, by means of the eidograph, to any scale that may be required. When the scale has been drawn in, the bearing of the two base line stations must be ascertained by referring to the field book, and the corresponding bearing on the pro- tracting circle having been transferred to the part of the paper on which the base line is to be placed, a pencil line should be drawn to represent its direction. On the principle of the parallelism of the same bearings at all the stations, it is necessary to be able to transfer them from the circle to any part of the paper without altering their relative directions in reference to the divisions of the circle itself. This may be done either by means of a pair of large parallel rulers, or by a T square moved along a BASE LINE AND TRAVERSE SURVEY. 133 Straight edge. In either case, the straight line formed by one of the edges of the apparatus employed for the purpose is made to coincide on the circle, with the bearing which is to be laid down. The square or the rulers, as the case may be, are then moved to the part of the paper on which the bearing is to be drawn, care being taken not to disturb the parallelism of the straight edge to the line of bearing to which it had previously been adjusted. When this bearing has been protracted, the leng-th of the base, as measured on the ground, must be carefully taken from the scale of distances attached to the plan, and pricked off on the line of bearing which has been drawn on the paper. It is evident that the positions of two of the tri- angulation stations, in reference to both the scale and the protracting circle, have been fixed on the plan by this pro- cess. These stations, for the sake of rendering further ex- planation more clear, we shall call A and B. The angles taken from A to the several stations C, D, E, &c., are next to be laid down, the whole of them being carefully trans- ferred from the circle to the point A, from which they were observed, and drawn in on the plan in pencil lines. The same operation is to be gone through at station B. Now, if the work is accurate, the points at which the bearings laid off from A and B to the different stations intersect each other, will be the positions of these stations on the plan. Their positions cannot, however, be finally deter- mined without a third bearing, as a check on the intersec- tion of the other two ; and for this purpose some one of the stations, which we may suppose to be C (whose position has, if we may use the expression, been temporarily fixed 134 PROTRACTION OF THE TRI ANGULATION, by the intersection of tlie two bearings laid off from A and B), must be assumed as correct. It must be remembered, however, in making choice of the third station C, that, in all cases where the angle made by the two bearings at the point of their intersection is either very acute or very ob- tuse, the accuracy of the position of the station so fixed is not to be relied on, and one should therefore be selected at which the bearings for its determination include as nearly as possible 90 degrees, the angle which forms the most favourable intersection. As a further precaution in assum- ing the point C, it is proper, by reference to the field book, to ascertain whether the observed angles included in the triangle A B C, formed by the three stations, be equal, or very nearly equal, to 180°. If this proves to be the case, it may be inferred that the angles ABC, B A C, and A C B have been accurately observed and noted in the field book ; and the point C may, if the intersection be good, be safely adopted as the third station. "When the third station C has been assumed, the bearings taken from it should be laid off, and drawn in pencil lines ; and if the work be correct, these lines will exactly intersect the points of intersection of the several bearings from A and B before protracted, thus proving the accuracy of points whose posi- tions have been determined by them. Any of the points whose positions have been thus fixed by the coincidence of three bearings may now be chosen from which to protract the angles, and in this way the whole triangulatio)i is laid down, the positions of many of the stations being fixed by the intersection of eight or ten bearings from different points, a result which is always satisfactory. BASE LINE AND TRAVERSE SURVEY. 135 It is necessary to remark, that, whenever the distance ho- tween the protracting circle and the stations to be laid down becomes so great as to occasion inconvenience and loss of time, and create the chance of committing errors in trans- ferring the bearings, another circle, as represented in Plate I., should be drawn on the plan, from which the bearings can be transferred in the manner already described. It is indispensable, however, that the bearings of the second cir- cle be made parallel to the corresponding bearings of the original one ; and if this be strictly adhered to in every case, any number of circles may be employed in the pro- traction, according to the size of the plan. Plate I. illustrates the process which I have attempted to explain. The lines joining the different stations repre- sent the bearings taken in the field, and correspond with those of the same name on the circles. Thus, in the ex- ample of the field book given at page 15, the bearing from Balmerino to Invergowrie station is noted as being 189° 34' on vernier A, and 9° 34' on vernier B ; and the line on the plate joining these two stations will be found to corre- spond in parallelism with that which passes through the di- visions, 189° 34' and 9° 34' on each of the two protracting circles shewn ; and so with all the other lines drawn on the plan. The bearings laid down, in the manner described, being the same as those taken in the field, and the length of the protracted base being made to agree (with reference to the scale which has been determined on) with the distance mea- sured on the ground ; it is obvious, on the principles on which trio-onometrical calculation is founded, that the distances be- 136 PHOTR ACTION OF THE TRI ANGULATION, tween tlie difFerent stations, when measnred by the same scale, will agree with those distances when measured on the ground, or, in other words, that the plan constructed will (if the w^ork has been accurately executed) exhibit a correct representation of the relative positions of the several sta- tions on the banks of the river. The accuracy of the pro- traction may be tested by means of a base of verification, which is obtained by calculating from the data procured in the field, the length of the line joining any two stations of the survey between which the distance is considerable ; and if this calculated length be found nearly to agree with the distance on the plan measured by the scale, the survey may be considered as having been accurately protracted. I use the expression nearly to agree^ because (as must have been all along perceived) I am treating of a mode of working adapted to the ordinary practice of civil engineering. It must be recollected that, in the system I have described, the angles are read off only to minutes. The refinement of cal- culating the sides of the triangles and protracting by mea- surement from a scale, as well as that of making an allow- ance for the unequal expansion and contraction of the draw- ing paper produced by changes in the hygrometric state of the air, although indispensable for some purposes, are not in the present case taken into account. The nearness of the agreement between the calculated and measured dis- tances ought therefore to be estimated by the degree of re- finement that has been gone into in surveying and protract- ing the work, and is a point which must be left to the judg- ment of the engineer, whose knowledge of the object of the BASE LINE AND TRAVERSE SURVEY. 137 survey and the whole bearings of the case, will enable him to decide. I must now proceed to explain the method of connecting the measured base with the triangulation in cases where the line does not extend between two of the triangulation sta- tions. When the line is measured on a marsh or a sand bank, in the manner explained in Chapter II., and the bearings taken at its extremities are referred, by means of a back sight, to the triangulation of the survey, the method of procedure is sufficiently obvious and simple, for the bearing of the base line being known, its site may be laid down from the pro- tracting circle. Its length, as measured on the ground, is then pricked off on the bearing which has been drawn on the paper, and the extremities of the line become the starting stations of the triangulation, the angles taken from them being protracted in the manner already de- scribed. The process of protracting the third case, however, is not so simple as either of the two I have explained. In that case, it was supposed that the base line was measured on a sand bank, and that angles were taken from its extremities to the surrounding stations of the triangulation, in order to fix its position ; but it was further supposed, that, owing to certain circumstances, it was impossible to make an obser- vation from any of the stations in the triangulation to either of the extremities of the base line. In order to protract the work, it is necessary, from the data obtained by measuring the base, and observing at its extremities the angles sub- tended by the sui-r^unding stations, to calculate the distance 138 PKOTIIACTION OF THE TRI ANGULATION between any two of them, and assume that distance as the first hne of the protraction. The case may assume either of the two forms represented in figs. 11 and 12, in which A B represents the base line, and D and C two of the triangulation stations, the distance between which is required. In fig. 11, the angles, from the extremities of the base line, are supposed to be taken to two stations which are on the same side of the river ; and in fig. 12, the angles are taken to stations on opposite sides of the river. The same trigonometrical calculation, however, ap- plies to both, and is as follows :— Fiii. 11. Fia. 12. / " v.. , Jj ;/..... (Ac^ \ """"' D Let A B in either of the figures be the measured base line. From the point A observe the angles DAB, BAG, CAD, and from the point B observe the angles ABC, A B D, D B C* Then in the triangle A C B AT- ^ B X sin A B C sin A C B ' '^ It is proper, in practice, to observe the sum of the two angles, as a check on their accuracy. BASE LINE AND TRAVERSE SURVEY. 139 and in the triangle A D B A D = A B ^ sin D B A sin A D B Now, in the triangle A D C, we know D A and A C, and the included angle D A C, and consequently the sum of the angles A D C and A C D, which is supplementary to D A C. But tani(ADC-ACD)=^^"^(^P^ + ^^P):;(^^-DA) ^ (D A + A C) ' and therefore the neater anole ADC= i(ADC- ACD) + ^(ADC + ACD), and the less angle ACD = i(ADC + ACD)-i(ADC-ACD), sin D A C X A C and C D = or CD = sin A D C sinDAC X AD sin A C D The bearing of the line C D is then to be laid down, and its calculated length being pricked off, the points C and D become the starting points from which the observed angles are to be protracted in the manner already described. Before leaving the subject, it is necessary to remark, that the whole of the triangulation may be protracted before the base line is laid down, the distance between the two start- ing stations being assumed without reference to any scale. In proceeding in this way (which is not by any means ge- nerally recommended, though it may be occasionally useful and convenient), the site of the base line is fixed on the plan after the whole or a part of the triangulation is laid down, and the distance determined by the protraction of the angles fix- 140 PKOTRACTION OF TJIE TRIANGULATION ing its extremities is assumed as the scale to tlie plan. Thus, if the length of the hase measured were 8000 feet, the protracted line would represent that distance on the plan, and be divided accordingly for a scale. Hence the neces- sity, if this mode of protracting be adopted, of making the length of the base line an easily divisible quantity, as noticed at page 27 ; for if, instead of 8000, the distance were 8007 feet, it would be difficult to divide the line accurately in terms of the latter quantity. The greatest disadvantage which attends the practice of laying down the triangulation before the base line, consists in the difficulty, if not the impossibi- lity, of constructing the plan so protracted according to any definite scale, as eight, ten, or twelve inches to the mile, which it is in all cases advisable to do. It will readily be perceived in what way this difficulty arises. In the one case, the scale of the plan is, in the first instance, adopted at the rate of any number of inches to the mile, and from this scale the length of the base line is laid down ; but, in the other case, the plan may be said to be constructed before the scale is formed, the length of the base line being deter- mined by the protraction of the bearings which fix its ex- tremities, and hence there is only a chance, and that a very remote one indeed, that its protracted, will bear to its mea- sured length the exact ratio of any number of inches to one mile. If a land surveyor has been employed to survey the mar- gin of the river, he ought to be furnished with a skeleton plan shewing the positions of all the triangulation stations, on which to protract the several compartments of the sur- vey extending between them. The fixed points on this BASE LINE AND TRAVERSE SURVEY. 141 skeleton plan serve as checks on the correctness of the work, and as guides for the directions of the measured lines ; while the division of the siu'vey into compartments, as al- ready noticed, prevents the accumulation of error. As the engineer, however, may in some cases be obliged to execute this part of the work by traverse surveying, in the manner described in Chapter VI., I shall explain the method of protracting the survey when made in this manner. The bearings of the different station lines, as already noticed in explaining the system of traverse surveying, are connected with those of the triangulation by starting from one of the triangulation stations, and taking back bearings throughout the whole of the survey. It is evident, there- fore, that the method of protraction used for the trian- gulation will answer equally well for laying down the lines of the traverse survey. The bearing of the tirst line of the survey ought to be laid off, by means of the protract- ing circle, from the triangulation station at which the sur- vey was commenced. The measured distance of the sur- vey line must then be taken from the scale, and pricked off on the bearing laid down, the extremity of the line thus fixed, being the point from which the bearing of the se- cond line is to be laid off. The bearings and lengths of all the lines are successively protracted in this manner, un- til the last line of the compartment is reached ; and if the work be right, the extremity of this line should, of course, coincide with the position of the station, as fixed on the plan at which the compartment was made to terminate. This process will be clearly understood by the example given in Plate I., on which, in order to illustrate the subject, the survev lines between Flisk and Birkhill stations have been 142 PROTRACTION OF THE TRIANGULATION, &c. laid down. The small circles along tlie shore represent the stations at the extremities of the different lines. If the extremity of the last survey line do not coincide with the triangulation station, some error has been com- mitted, either in the field work or in the protraction. If the work on revisal is found to have been correctly protracted, the accuracy of the positions of the different survey stations at the extremities of the lines should be tested, by laying off at each of them, the bearings taken during the survey to the different triangulation stations. By this means it will generally be discovered that the position of some one of the survey stations is erroneous ; and in most cases it happens that the amount of error is exactly 100 feet, prov- ing a faulty measurement, owing to some error in chang- ing or counting the number of the marking pins. On exa- mining the field book, the part of the line at which the er- ror occurred can generally be detected. After correcting this error, and reprotracting the lines, the extremity of the survey will be found exactly to coincide with the station, if no other error exists in the work. The benefits arising from dividing the survey into compartments, and taking bearings at each of the survey stations to all the triangulation sta- tions within view, as explained in Chap. VI., is thus very apparent. When the whole of the lines have been laid down and verified in the manner described, the measurements of the lengths and oflPsets are then to be protracted,* and the out- line of the ground, as represented in the field book, care- fully traced in. * A plotting offset scale, as recommended by Mr Simms, will be found ver}' convenient for this pxirpose. ( 113 ) CHAPTER X. PROTRACTION OF LOW WATER SURVEY AND SOUNDINGS. Protracting sextant observations for fixing- positions of points — The station pointer — Protracting them by construction — Ordinary rule for this — Im- proved method — Solution of the problem on which the method is based — Practical application of the principle — Objections to protracting by con- struction — Protracting the outlines of low water channel and sand banks — Protraction of soundings — High water soundings — Low water sound- ings — Formulae for ascertaining the rise of tide and the heights of the sand banks above low water — Method of protracting a longitudinal sec- tion. Before entering particularly on certain details whicli have still to be noticed with reference to laying down the sound- ings and sand banks, it seems necessary to offer a few re- marks regarding the protraction of the sextant observations, made in the manner described in Chap. V, for the pur- pose of determining their positions. The most convenient methodof doing this, isbyusing the instrument called the Sta- 144 PROTRACTION OF LOW WATER tioii Pointer. The construction and the mode of applying that instrument, are fully described in Mr Simms' treatise, to which I have had occasion already to refer, and it is there- fore unnecessary to enter on the subject here. As it may occasionally happen, however, that access can- not be had to a station pointer, or that the points to be laid down are so near the stations observed, or the scale of the plan is so small as altogether to preclude the use of the m- strument, the surveyor should not be unprovided with the means of protracting his work without its aid. The rule generally given for protracting the work in such cases, is as follows : — Subtract double the observed angle from 180% and from the two stations observed^ draiv straight lines making angles with the line joining them^ each equal to half the remaining angle. The point at tvhich the lines so laid off intersect each other, will be the centre of a circle pass- ing through the observed stations^ and the point from which the observations was made. But as this is a tedious opera- tion, and the rule does not apply to every case, I shall take the liberty of describing a simple and efficient method of protraction, of which, when necessary, I invariably avail myself. I have never met with a description of this me- thod in any work on the subject, and first saw it employed by the late Mr James Ritson of Edinburgh. In order, however, that the system of protracting about to be described may be easily understood, it is necessary that the reader should know the principles on which it is based, and these will probably be best explained by giving the solution of the following problem. Given the positions of three objects, and also the angles SURVEY AND SOUNDINGS. 145 which they subtend at a station in their plane, to find the position of the station. 13. 14. Let A, B, C, (figs. 13 and 14) be three objects whose posi- tions are known, and which subtend at D, the point of ob- servation, two known angles A D B, B D C ; it is required to determine the position of the point D. Through C draw C E perpendicular to C B, and make the angle EOF equal to the observed angle B D C. Bisect B C in G, and draw G F perpendicular to B C and meeting C F in F. From the point F with the radius F C, describe the circle B C D ; the point D will be found in its circumference. By a similar construction in reference to the angle B D A subtendino- the line B A, a circle A B D maybe described, passing through the point D, and the point at which the circles C D B and A D B intersect each other, is the point of observation required. For, join F B, D C, and D B, and draw C H porponrllcu- lar to F C. 146 PROTRACTION OF LOW WATER Now, since E C G = F C H, each being a right angle, and F C G being common to both, E C F = G C H. But F B = F C (EucHd B. I, p. 4) ; and the point B is in the clrcnmference of the circle B D C (Euc. I Def. 15) ; and the line C B cuts it (Euc. III. 2) ; and since C B cuts the circle C B D, and C H touches it (Euc. III. 18), then (Euc. III. 33) G C H = C D B, the angle in the alternate segment. But G C H = E C F, and E C F by construction = the observed angle .*. C D B in the segment of the circle C D B = the observed angle. In the same way, it may be shewn that the angle A D B in the segment of the circle A D B = the observed angle, and (Euc. III. 21) the point D must be that from which the observations were made. It will be observed that the foregoing proof refers to the two cases where the observed angle is either above or below Fig. 15. 90°. When the observed angle C D B, as in fig. 15, is a right angle, the line C F will evidently coincide with C B, and the point F, with the point G ; and F, being the centre of the circle B D C and F C the radius, the line C B will be the diameter, and (Euc. III., 31) C D B will be equal to 90° the angle observed. SURVEY AND SOUNDINGS. 147 Now, 111 order to apply the principles demonstrated to practice, a little construction only is required ; and I have in the following diagram (fig. 16) shewn how this may be done. Fig. 16. Let A and B be two stations to which we shall suppose many observations for laying down the positions of the banks and soundings have been taken. Join A B, bisect the line in G, and through G draw H F perpendicular to A B in red, or any coloured ink. At either of the points B or A, draw as at A the line A D perpendicular to A B. From A as a centre, describe in red ink an arc D K, of 3 or 4 inches radius, according to the radius of the protractor to be used in dividing it. Divide the arc by plotting off the degrees from the protractor into 120°, the zero being made to coincide with the line A D, and 90° with the line A B. Now, if it be wished to protract a point which we may call Z from which the angle subtended by the stations A and 148 PROTRA(^TION OF LOW WATER B was observed to be 45', it is only necessary to apply a ruler to the point A passing through the division 45° on the di- vided arc, and cutting the line G F in F. Then F will be the centre of a circle, from which, with the radius FA or FB, de- scribe the arc op in which the point Z must be. If the same operation be performed with an adjacent station line B C, to which an angle has been taken from Z, the same re- sult will be obtained, namely, an arc r s, in which the point must be found intersecting the arc op in Z, the point re- quired. If the observed angle be 90°, then the point G will be the centre of the circle in the circumference of which (with G A as radius) the point is to be found. If it exceed 90°, and be, for example, 110°, then a ruler applied at A, and passing through the division 110° on the arc, will cut the perpendicular F G in H, and H will be the centre of the circle in the circumference of which (with the radius HA) the point required must lie. The only objection which can be urged against the adop- tion of this mode of protracting extensive surveys, in which many observations have been made, consists in the wearing and cutting up of the paper on which the plan is plotted, by drawing on it the numerous graduated protractors and straight lines required in the process, and by sweeping the arcs of the circles, the intersections of which are to deter- mine the positions of the points of observation. When the protractors have been drawn on the paper^, the work may be laid down much more quickly in the manner de- scribed than by using the station pointer, the difficulty of obtaining a nice coincidence of the arms of that instrument with the points observed being a constant source of deten- SURVEY AND SOUNDINGS. 149 tion, even although a needle be fixed at one of the stations to facilitate that part of the operation. Under all circum- stances, however, the employment of the station pointer is recommended as that which is, generally speaking, found to be the most convenient method of protracting sextant observations ; and in cases where it cannot be apphed on account of the smallness of the scale, or the proximity of the points to be protracted to the observed stations, the me- thod which I have just described may be beneficially em- ployed ; — an ivory or a brass protractor being used in such cases to lay off the observed angles, the graduation of the arc of a circle for that purpose being necessary only when the number of angles to be laid down is great. Having described generally the method of protracting sextant observations, I shall now make a few brief remarks regarding the protraction of the sand banks and sound- ings. The method of laying down the outlines of the low water channel and sand banks, a part of the work which ought to be completed before the protraction of the soundings is commenced, is so simple and obvious as to require almost no explanation. The different prominent points in the outlines, which have been fixed in the manner shewn in Plate X. and explained at page 75, are to be laid down in either of the ways just described, and the intervening lines carefully traced in from the field book ; as exact a repre- sentation of the outhne being made as the memory of the surveyor, aided by his field sketches, will admit of. The manner in which sand banks are represented on the finished plan will be seen on referring either to the chart of the 150 PROTRACTION OF LOW WATER Lunc or to Plate I., on both of which several of them are shewn. It will be recollected that, in treating of the mode of sounding, two sorts of soundings were alluded to, the first being those which are taken throughout the area of the estuary during flood or ebb tide, and the second those taken in the navigable channel at low water. The sound- ings belonging to the first class are to be reduced to the high water of ordinary spring tides by the formula given at page 58 ; those of the second, or low water series, require no reduction. After the sand banks and low water chan- nel have been protracted, the whole of these depths are to be laid down, their positions being determined by protract- ing the angles taken for that purpose. When this has been done, we shall have the high water soundings distributed over the several sand banks throughout the area of the esituary, and also a line of low water soundings in the centre of the navigable channel ; but it is still necessary to ascer- tain the heights of the sand banks above low water. For this purpose, the rise of the tide at diff'erent parts of the river must be ascertained ; which, together with the deter- mination of the height of the sand banks above the low water mark, is done in the following manner. From the system followed in taking the soundings which is described in Chapter IV., it is evident that a high and a low water sounding nearly corresponding in position, can generally be obtained at all the places where lines of soundings cross the low water channel, as will be easily un- derstood by referring to the chart of the Lune, on which a few of the soundings have been laid down, although, from SURVEY AND SOUNDINGS. 151 tlie smallness of the scale, the exact lines in which thoy were taken, are not very definitely exhibited. Let «, therefore (without reference to the plate), represent a high water sounding (corrected by the formula given at page 58) whose position is in the navigable channel, and let /3 be the low water sounding which most nearly coincides with the posi- tion of a. Then a — /S will be the vertical rise of tide (which we shall call 7) at that point. The values of 7 being thus found at as many points as possible in the channel of the river, the number of which points will be limited by the num- ber of the lines of high water soundings that cross the low water channel, they should be marked on the plan in large figures, as shewn in the chart of the Lune already referred to. Now, the values of the soundings a a a, &c. distributed through- out the estuary, will either be equal to, greater, or less, than those of 7 7 7, &c., which we may suppose to represent the vertical rise of tide at the points nearest which the soundings occur, and the three results maybe expressed as follows, when 7 - a = n, the sounding has occurred in the navigable channel or some deep pool in the sand banks, and n = the depth at low water; when 7 = a, the sounding has been made exactly at the edge of low water, or perhaps of a pool on a level with low water, as the case may be ; or, in other words, at the point where the level of low water cuts the sand bank ; and when a _ 7 = - n, the soundinof has occurred on a sand bank or other raised obstruction, and - n = the height of the bank above low 152 PROTRACTION OF LOW WATER water. In marking tliese soundings on the plan, it is neces- sary to shew the depths both at high and at low water, and the most convenient way of doing this is, to put them in a frac- tional form, the depths at high water being placed as the numerator, and those at low water as the denominator, dis- tinguishing the heights of the sand banks above low water, by prefixing the negative sign. According to this notation, the three results alluded to would be stated thus on the plan : — a. 9 ) APPENDIX. Abstract of the Standing Orders of tlie Honses of Lords and Commons with reference to giving Notices, and Con^ structing and Lodging Plans, in making application to Parliament for Bills for making, maintaining, varpng, extending, or enlarging any Bridge, Turnpike Road, Cut, Canal, Reservoir, Aqueduct, Waterwork, Navigation, Tunnel, Archway, Pier, Port, Harbour, Ferry, or Dock. 1842. 1. Notices of Application. — That notices shall be given in all cases where application is intended to be made for leave to bring in a bill included under any of the heads above mentioned, 2. Notices to be publishecl. — That such Notices shall be published in three successive weeks in the months of October QXi(\. November, or either of them, immediately preceding the Session of Parlia- ment in which Application for the Bill shall be made, in the Lon- don, Edinburgh or Dublin Gazette^ as the case may be, and in some one and the same Newspaper of every County in which the City, Town or Lands to which such Bill relates shall be situate ; or if there is no Newspaper published therein, then in the Newspaper of some County adjoining or near thereto, or if such Bill does not relate to any particular City, Town or Lands, in the London, Edinburgh or Dublin Gazette only, as the case may be ; and that all Notices re- quired to be inserted in the London, Edinburgh or Dublin Gazette 160 APPENDIX. sliall be delivered at the Office of the Gazette in which the inser- tion is required to be made, during the usual office hours, at least Two clear Days previous to the publication of the Gazette, and that the receipt of the Printer for such Notice shall be proof of its due delivery. 3. Intention to levy or alter Tolls to be stated. — That if it be the intention of the Parties applying for leave to bring in a Bill, to levy any Tolls, Rates or Duties, or to alter any existing Tolls, Rates or Duties, or to vary any other rights or privileges, the Notices shall specify such intention. 4. Notice to be affixed on Doors of Sessions House at the Session preceding the Meeting of Parliament. In Scotland, on Doors of Parish Churches in October and November. — That all Notices shaU also be given at the General Quarter Session of the Peace which shall have been holden for every and each County, Riding, or Di- vision, in or through which the work shall be made, maintained, varied, extended or enlarged, at Michaelmas or Epiphany preced- ing the Session of Parliament in which such application is in- tended to be made, by affixing such Notice on the Door of the Ses- sion House of each and every such County, Riding, or Division, where such General Quarter Session shall be holden ; save and ex- cept as to any Bill for such purposes in Scotland ; in which case, instead of affixing such Notices on the door of the Session House, such Notices shall be written or printed on paper, and affixed to the Church door of the Parish or Parishes in or through which such work is intended to be made, maintained, varied, extended, or enlarged, for two Sundays in each of the months of October and November immediately preceding the introduction into Parliament of the Bill for which such application is intended to be made. 5. Notices to contain Names of Parishes, 8fc. — That all Notices shall contain the Names of the Parishes, Townships and extra- parochial places from, in, through, or into which the Work is in- tended to be made, maintained, varied, extended, or enlarged, and shall state the time and place of deposit of the Plans, Sections, and Books of Reference, respectively, with the Clerks of the Peace, APPENDIX. 161 Parish Clerks, Schoolmasters, Town Clerks, and Postmasters, as the case may be. 6. Plans, S^c. with Clerk of the Peace. — That a Plan, and also a duplicate of such plan, on a scale of not less than Four Inches to a Mile, exhibiting thereon the height of the several embankments and the depth of the several Cuttings on a scale specified thereon, with a Section and Duplicate thereof as hereinafter described, be deposited for public inspection at the office of the Clerk of the Peace for every County, Riding, or Division in England or Ire- land, or in the Office of the principal Sheriff Clerk of every County in Scotland, in or through which the work is proposed to be made, varied, extended, or enlarged, on or before the 30th day of November immediately preceding the Session of Parliament in which application for the Bill shall be made ; which Plans shall describe the line or situation of the whole of the Work, and the Lands in or through which it is to be made, maintained, varied, extended, or enlarged, or through which every communication to or from the Work shall be made, together with a Book of Refe- rence containing the Names of the Owners, or reputed Owners, Lessees or reputed Lessees, and Occupiers of such Lands respec- tively. 7. Lands within Deviation to be on Plan. Buildings, ^r. on enlarged Scale. — That where it is the intention of the parties to apply for powers to make any lateral deviation from the line of the proposed Work, the limits of such deviation shall be defined upon the Plan, and all Lands included within such limits shall be mark- ed thereon, and that in all cases, an additional Plan of any Build- ing, Yard, Court- Yard, or Land within the curtilage of any Build- ing, or of any Ground cultivated as a Garden, either on the origi- nal line or included within the limits of the said deviation, shall be laid down on the said Plan or on the additional Plan deposited therewith, upon a scale of not less than a quarter of an inch to every 100 feet. 8. Section.— "Vh-At the Section shall be drawn to the same hori- 1C2 APPENDIX. zontal scale as the Plan, and to a vertical scale of not less than one inch to every 100 feet, and shall shew the surface of the ground marked on the Plan, and the intended level of the proposed Work, and a datum horizontal line, which shall be the same throughout the whole length of the Avork, or any Branch thereof respectively, and shall be referred to some fixed point stated in writing on the Section near either of the Termini. 9. Clerks of Peace to indorse a Memorial on Plans ^ ^c. — That the Clerks of the Peace or Sheriif-Clerks, or their respective De- puties, do make a Memorial in writing iipon the Plans, Sections, and Books of Reference so deposited with them, denoting the time at which the same were lodged in their respective offices, and do at all seasonable hours of the day permit any person to view and examine one of the same, and to make copies or extracts therefrom ; and that one of the two plans and Sections so deposited, be sealed up and retained in the possession of the Clerk of the Peace or She- riff-Clerk until called for by order of one of the two Houses of Par- liament. 10. Playi and Section with Parish-Clerk, ^~c. — That on or before the 31st day of December, a copy of so much of the said Plans and Sections as relates to each Parish in or through which the Work is intended to be made, maintained, varied, extended, or enlarged, together with a book of Reference thereto, shall be deposited with the parish Clerk of each such parish in England, the Schoolmaster of each such parish in Scotland (or in Royal Burghs with the Town Clerk,) and the Postmaster of the Post-town in or nearest to such Parish in Ireland. 11. Time for Deposit in Private Bill Office. — That on or before the 31st day of December, a copy of the said Plans, Sections, and Books of Reference, shall be deposited in the Private Bill Office for the Commons, and in the Office of the Clerk of the Parliaments for the Lords. 12. Estimate and Subscription Contract. — That an Estimate of the Expense be made and signed by the person making the same, APPENDIX. 163 and that a Subscription be entered into under a Contract, to three- fourths the amount of the Estimate. 13. Cases wherein Declaration may he substituted for Subscrip- tion Contract. — That in cases where the Work is to be made by means of Funds, or out of Money to be raised upon the credit of present Surplus Revenue, under the control of Directors, Trustees, or Commissioners, as the case may be, of any existing Public Work, a Declaration stating those facts, and setting forth the Particulars of such control, and the Nature and Amount of such Funds or Surplus Revenue, and given under the common seal of the Com- pany, or under the hand of some authorized Ofhcer of such Direc- tors, Trustees, or Commissioners, maybe substituted in lieu of the Subscription Contract, and in addition to the estimate of the ex- pense. 14. Cases wherein Declaration and Estimate of amount of Bates may he substituted for Subscription Contract. — That in cases where the Work is to be made out of Money to be raised upon the Se- curity of the Rates and Duties to be created by any Bill, under which no private or personal pecuniary profit or advantage is to be derived, a Declaration stating those facts, and setting forth the means by which Funds are to be obtained for executing the Work, and signed by the Party or Agent soliciting the Bill, together with an Estimate of the probable Amount of such Rates and Duties, signed by the Person making the same, may be substituted in lieu of the Subscription Contract, and in addition to the estimate of the expense. 15. Contract to contain Christian and Surnames of Parties. — That all Subscription Contracts shall contain the Christian and Surnames, Description and Place of Abode, of every Subscriber ; his Signature to the amoimt of his Subscription, with the amount which he has paid up ; and the Name of the Party witnessing such Signature, and the date of the same respectively ; and that it be proved to the satisfaction of the Committee on Petitions that a sum equal to one-tenth part of the amount subscribed has been deposited 164 APPENDIX. with the Court of Exchequer in England, if the work is intended to be done in England, or with the Court of Exchequer either in England or Scotland, if such work is intended to be done in Scot- land, and with the Court of Chancery in Ireland, if such work is intended to be done in Ireland ; and that not less than three-fourths in number of the Subscribers shall have paid up their Shares of such Deposit. 16. Kot valid unless entered into subsequent to close of previous Session. — That no Subscription Contract shall be valid unless it be entered into subsequent to the close of the Session of Parliament ' previous to that in which application is made for leave to bring in the Bill to which it relates, and unless the Parties subscribing to it bind themselves, their Heirs, Executors, and Administrators, for the Payment of the Money so subscribed. 17. To be printed at expense of promoters of Bill. — That pre- vious to the presentation of a Petition for the Bill in the Com- mons, and the second reading in the Lords, copies of the Sub- scription Contract, with the Names of the Subscribers arranged in alphabetical order, and the amou.nt of the Deposit respectively paid up by each such Subscriber, or wliere a Declaration and Es- timate of the probable amount of Rates and Duties are substituted in lieu of a Subscription Contract, Copies of such Declaration, or of such Declaration and Estimate, be printed at the expense of the Promoters of the Bill, and be delivered at the Vote Office of the clerk of the Parliament, for the use of the Members of the respec- tive Houses. 18. Application to be made to Owners, List of Assents, ^c. — That on or before the 31st day of December immediately preceding the Application for a Bill by Avhich any Lands or Houses are in- tended to be taken, or an extension of the time granted by any for- mer act for that purpose is sought for. Application in writing be made to the Owners or reputed Owners, Lessees or reputed Les- sees, and Occupiers, either by delivering the same personally, or by leaving the same at their usual place of abode, or, in their ab- sence from the United Kingdom, Avith their Agents respectively, APPENDIX. 165 of which Application having been duly made, the production of a written acknowledgment by the party applied to of the receipt of such Application, shall be sufficient evidence, in the absence of other proof, of the same having been duly delivered or left as afore- said ; and that separate lists be made of the Names of such Own- ers, Lessees, and Occupiers, distinguishing which of them have as- sented, dissented, or are neuter in respect thereto. 19. Application to he made to Owners^ ^c.^ when the Bill is to abridge the extent of any Public TFork. — That before any Ap- plication is made to the House for a Bill whereby any part of a Work authorized by any former Act is intended to be relinquished. Notice in writing of such Bill be given to the Owners or reputed Owners and Occupiers of the lands in which the part of the said Work intended to be thereby relinquished is situate. 20. Wlien it is intended to divert TFater from an existing Cut, ^c, into an intended Cut, ^c, the name of the existing Cut, ^c, to be mentioned. — That in all cases where it is proposed to divert in- to any intended Cut, Canal, Reservoir, Aqueduct, or Navigation, or into any intended variation, extension, or enlargement thereof respectively, any water from any existing Cut, Canal, Reservoir, Aqueduct, or Navigation, whether directly or derivatively, and whether under any agreement with the Proprietors thereof, or otherwise, the notices shall contain the name of every such exist- ing Cut, Canal, Reservoir, Aqueduct, or Navigation, the waters supplying which by virtue of any Act of Parliament, will either directly or derivatively, flow or proceed into any such intended Cut, Canal, Reservoir, Aqueduct, or Navigation, or into any in- tended variation, extension or enlargement thereof. 21. Plan to describe Brooks, ^c., to be diverted. — That in all cases where it is proposed to make, vary, extend, or enlai-ge any Cut, Canal, Reservoir, Aqueduct, or Navigation, the Plan shall de- scribe the Brooks and Streams to be directly diverted into such intended Cut, Canal, Reservoir, Aqueduct, or Navigation, or into any variation, extension, or enlargement thereof respectively, for supplying the same with Water ; it shall also exhibit the height U\{] APPENDIX. of the several embankments, and the depth of the several Cuttings respectively, on a scale specified thereon ; and in cases of Bills for improving the navigation of any River, there shall be a Section which shall specify the Levels of both Banks of such River, and where any alteration is intended to be made therein shall describe the same by feet and inches. 22. Plans, S^r. to he lodged. — That all Plans, Sections, Books of Reference, Lists of O^vners and Occupiers, Estimates and Copies of the Subscription Contracts, required by the Standing Orders of the House, be lodged in the Private Bill Office ; and that the re- ceipt thereof be acknowledged accordingly, by one of the Clerks of the said Office, upon the said Documents, and upon the Petition, before it is presented. ( 167 ) INDEX. Amazons, River, fresh water of, visible 100 leagues at sea, 121. Agents which produce disturbance in the tidal lines of rivers, 38. Angles, mode of observing and registering in triangulation, 14. — Sextant, for determining positions of soundings, 65 ; and for fixing points in low water line, 74. Bearings, mode of observing and registering, 14 — parallelism of, 18. — Reverse, Rule for correcting, 19. Base Line^ most desirable length for, 22, — Process of measuring, 23. — Method of determining extremities of, 26. — Verification of chain to be used in measurement of, 25. — Correction to make the measured length an easily divisible quantity, 27. — Protraction of, 132. — Calculation for protraction of, when the extremities are unconnected with triangulation^ 139, Beaches, Sea, low water surveys of, 73. Banks, Sand, low water surveys of^ 73. Borings, where required, 93. — Reference of, to datum line, 94. — Most favourable times for making, 95. — Directions for making, 95. — Form of field book for, 101.— Use of, in making designs, 102.— Case of the Ribble in Lancashire, 102.— Fossdyke in Lincolnshire, 104.— Protraction of, 100, Boring Rods, 98, Chain, verification of length of, 25. Chain Surveying, 84. ConoUj River, discharge of, 116. 168 INDEX. Currents in the open sea, or estuaries determining velocity of, 119. Currents, Under, float for determining, 117. Cromarty Firth, under currents at, 117. Compass, local variation of, 9. — Construction of a, for plan, 10. Camera Lucida, use of, in low water surveys, 73. Capacity, tidal of a river or estuary, means of determining, 63. Cord for cross sections, borings, &c., 95, 107. Circles, protracting, division of, 129. Chart of the Lune, 154. Commons, House of, extract from standing orders of, 1 59. Clerks of Peace, depositing plans with, 161. Dee, Eivor, in Cheshire, tidal lines of, 47. — Anomalous flow of tide at, 78. Datum Lines for surveys, 55. — Half tide level, 55. — H. W. of ordinary spring tides, 56. — For soundings, 55. — For borings and cross sections, 94. — For longitudinal section, 153. — Parliamentary, 161. Designs, use of cross sections and borings in making, 102. Discharge of rivers, ascertaining, 107. — Of the Conon, 116. Dee, River, in Aberdeenshire, tides at, 119. Dornoch Firth, half tide level at, 56. Division of protracting circles, 129. Diversion of streams or brooks. Parliamentary orders relative to, 165. Estimate of works, data required for, 93. Estimate, Parliamentary, 162. Flags, Station, 6. Field Books for triangulation, 15. — Tidal observations, 42. — Soundings, 69, 70. — Low water survey, 75. — High water survey, 86. — Cross sections and borings, 101. — Hydrometrical observations, 116. Forth, Eiver, Stirlingshire, tidal lines of, 54. Forth, Frith of, half tide level at, 56. Fossdyke, in Lincolnshire, section of, 104. Fords in rivers, making sections and borings of, 93. Fisheries, Salmon, questions relative to, 106. Float under cun-ent, 118. Formulae for correcting reverse readings, 19. — Reducing soundings to high wa- INDEX. 169 tcr, 58. — For ascertaining rise of lide at different points, 151. — For ascer- taining heights of sand banks above low water, 151. — For calculating base line in protraction, 139. Gauge, Tide, 39. — Levelling for, 44. — Method of fixing, 40. — Selecting sites for, 37. Glass Tubes for tide gauges, 44. H Half tide level, 56. Harbour Surveys, tide gauges for, 44. — Datum line for, 55. — Low water survey of, 73. High water margin, survey of, 83. — Objects of, 83. — Survey of, by chain and traverse surveying, 84. — Form of field book for, 86. — Checks on accuracy of field work, 88. — Survey of outlines of marshes in, 90. — Protraction of, 141. Hydrometrical observations, application of, to engineering questions, 105. — As- certaining discharge of rivers, 107. — Making section and determining ve- locity, 107. — Instruments for measuring velocity — floats, 108. — Description of Woltmann's tachometer, 110. — Method of using, HI. — Ascertaining scale for, 112. — Formula for reducing surface to mean velocity, 113. — > Table of mean velocities, 114. — Form of field book, 116. — ^Discharge of Eiver Conon, 116. — Determining velocity of currents in open sea, 118. — Determining the velocity of under cun-ents, 117. — Under current float, 118. — Application of it at Cromarty Frith, 117. — Tides of the Dee, inAberdeen- sliire, 119. — Fresh water of the Amazons discovered at sea, 121. — The Hydrophore, 122. — Marine productions, 125. Hydrophore, the, 122. I Isle of Man, half tide level at, 56. Lengths for base Hues, 22. — Correction for, to produce an easily divisible quan- tity, 27. Levelling for tide gauges, 44. Levelling instruments, 45. Lune, Eiver, in Lancashire, tidal lines of, 50. — Note relative to chart of, 154. L 170 INDEX. Levelling for cross sections and borings, 94. Local variation of the needle, 9. Low water survey, objects of, 72. — Difficulties in making, 73. — Surveys of beaclies, banks, androcks, in harbour surveys, 73.— Use made of triangulation stations, 74. — Sextant observations for fixing positions of points in survey, 74. — Form of field book. 75. — Method of executing it, 77. — Dangers to be avoided in consequence of anomalous flow of tide, 78. — Example of this on the Dee, 79. — Cause of phenomenon, 81. — Protraction of, 149. Liverpool, half tide level at, 56. Line, datum for survey, 5G. — Half tide level, 56. — High water of ordinary spring tides, 57. Longitudinal section of river, 67. — Protraction of, 153. Low water soundings, 68. — Protraction of, 152. Lords, House of, extract from standing orders of, 159. M Magnetic, north, determination of, 10. — Selection of stations from which to determine, 11. Measurement of base line, 23. Margin, high water, survey of, 83. Marshes, survey of, 90. Mean velocity, formula for reducing, from surface velocity, 113. — Table of mean velocities, 114. Marine productions, 125. N Needle, variation of, 9. — Use of, as a check in traverse surveying, 90. North magnetic, determination of, 10. Nonparallelism of tidal lines explained, 32, 47. — Errors in reducing soundings arising from, 59. — Means of obviating, 60. Navigation of rivers, sections and borings required as data for improvement of the, 92. Notices for Bills, giving of, 159. Ordinary spring tide, high water of, used as datum line for surveys, 56. Observations, sextant, for fixing soundings, 65. — For fixing points in low wa- ter survey, 74. Orders, standing, extracts from, 159. INDEX. 171 Poles, station, 5, Potainometer, 110. Parallelism of triangulation bearings, 18. Protraction, 126.— Of triangulation, 131.— Of base line, 133. —Calculation for protracting base line when unconnected by bearings with the triangula- tion, 139. — Of traverse survey, 141. — Of sextant observations by the sta- tion pointer, 144. — By construction, 145. — Protracting out lines of low water channel and sand banks, 149. — High water soundings, 58, 150. Low water soundings, 151. — Method of ascertaining rise of tide, 151. Heights of banks above low water, 151. — Protracting of longitudinal sec- tion, 153. Protractors, 128. Parliamentary orders, 1 59. Plans for Parliament, construction of, 155, 161. — Depositing, 161. Private bill office, depositing plans in, 162, 166. R Reverse readings, formula for correcting, 19. Rivers, tides of, 31. — Discharge of, 107. — Velocity of, 107. Robison's, Professor, remarks on tides, 32. Rocks, low water surveys of, 73. Ribble, River, cross sections and borings of, 102. Rods, boring, 98. Rods, sounding, 66. Rivers. Dee in Cheshire, 47, 75, 78.— Tay, 15, 86.— Ribble, 102.— Lune, 50, 154. — Dee in Aberdeenshire, 119. — Forth, 54, 56. — Conon, 116.— Foss- dyke, 104. Rules for guidance in fixing triangulation stations, 2. — For guidance in making soundings, 61. Reference, book of, for Parliament, 161. Stations, triangulation, selection of, 2. — Distinctions for, 6. Soundings, 46. — Example of the variation in the tidal lines on the Dee in Cheshire, 47. — The Lune in Lancashire, 50. — The Forth in Stirlingshire, 54. — Reference of soundings to one datum line, 55. — Half tide level, 56. — High water datum, 56. — Use of tide gauges in reducing soundings, 57. — Formulae for reduction of soundings, 58. — Errors from non-parallelism of tidal lines, 59. — General rules of direction for taking of soundings, 61. — Sextant observations for fixing their positions, 65. — Theodolite obser- 172 INDEX. vations for determining their positions, G6. — Sounding rod, 66. — Form of field book, 69, 70. — Soundings to be taken on the sites of new channels, or river walls, 67. — Low water soundings, 68. — Protraction of, 150. Scale for plan, 140, 155. — Parliamentary, 161. Sextant observations for fixing soundings, 65. — For fixing points in low wa- ter survey, 74. — Protraction of, by the station pointer, 144. — By construc- tion, 145. Sections, Cross, where required, 93. — Eeference of, to datum line, 94. — Di- rections for making, 95. — Form of field book for, 101. — Use of, in making designs, 102. — Of the Eibble in Lancashire, 102. — The Fossdyke in Lin- colnshire, 104. — Protraction of, 100. Section, longitudinal, 67. — Protraction of, 153. — Of the Lune, 157. Sections, Parliamentary, construction of, 161. Surface velocity of rivers, means of ascertaining, 108. Sea beach, low water survey of, 73. Sand banks, low water survey of, 73. — Protraction of, 149. — Method of ascer- taining heights of, above low water, 151. Stream gauge, 110. Skerryvore rocks, half tide level at, 56. Spring tide ordinary, high water of, used as datum for surveys, 56. Salmon fisheries, questions relative to, 106. Standing orders, extracts from, 159. Subscription contract, parliamentary, 162. Triangulation, conditions required to constitute a good, 2, — Poles for, 5. — Flags, 6. — Distinctions of stations, 6. — Local variation of needle, 9. — Determination of magnetic north, 10. — Adjustment of theodolite for ob- servation, 13. — Mode of observing, 14. — Field book, 15. — Eulefor adjust- ing instrument at succeeding stations, 17. — Parallelism of the bearings, 18. — Reverse readings, 19. — Eule for correcting them, 19. — Use made of, in low water survey, 74. — Protraction of, 128. Theodolite, adjustment of, for observation in triangulation, 13, 17. — For fixing position of soundings, 66. — In traverse surveying, 88. Tides of rivers, remarks on, 30. — Anomalous flow of, at the Dee, 78. — "Varia- tions in tidal lines, 32, 47. — Professor Robison's remarks as to river tides, 32. — Explanation of nature of investigations on the tides, 35. — Selection of stations for tide observations, 37. — Agents which produce disturbance in tidal lines, 38. — Method of fixing them, 40. — Keeping time, 41. — Form of field book, 42. — Ascertaining relative levels of gauges, 44. — Method of ascertaining rises of, at different parts of a river, l5l. INDEX. 173 Tide book, form of, 42. Tide gauges, 39. — Use of, in reducing soundings, 57. — Ascertaining levels of, 44. — Method of fixing, 40, — Selecting sites for, 38. Traverse surveying 84. — Protraction of 141. — ^Field book of, 86. Tidal lines, variations in parallelism of, 32, 47. — Errors arising from, 59. — Means of obviating, 60. Tachometer, Woltmann's, description of, 110. — Method of using, 111. — Ascer- taining scale for, 112. Time keeping, for tide observations, 41. Tubes, glass, for tide gauges, 44. Tidal capacity of a river or estuary, means of determining, 63. U Under currents, 1X7. Under current float, 118. Variation of needle, 9. Velocity of rivers, instruments for ascertaining, 108. — Floats, 108. — The Ta- chometer, 110. — Formula for reducing surface to mean velocity, 113. — Table of mean velocities, 114, W Woltmann's Tachometer, 110. Water, apparatus for obtaining specimens of, from different depths, 119. THE END. KDINBUROII : PUIXTKD BY NKILL & COMPANY, OLD FI.SHMARKET. -h A an the last date st^P^ only- sfs^.'s;ss»- ,P-Sfet«ti.» UDivetsuy Berkeley ^0 0060, o UNIVERSITY OF CALIFORNIA LIBRARY iSlffiilfflWS; mm iiiiiii II