LIBRARY UNIVERSITY OF CALIFORNIA Accession .V<>. .s>}, 08-- HYDROGRAPHICAL SURVEYING. A DESCRIPTION OF THE MEANS AND METHODS EMPLOYED IN CONSTEUCTING MARINE CHARTS. BY CAPTAIN W. J. L. WHARTON, E.N. OP THE UN IYER SIT Y LONDON: JOHN MUEEAY, ALBEMAELE STEEET. 1882. The right of Translation is reserved. LONDON: PRINTED BY WILLIAM CLOWES AND SONS, LIMITED, STAMFORD STliEET AND ClIAlilKG CROSS. PREFACE. I HAVE endeavoured in the following pages to collect together information which has for the most part existed, but in a traditionary form, for many years. Circumstances have led to a partial break in this tradition, and it is no disparagement to the more modern treatises on nautical surveying to say that the young surveyor has no book to which he can refer for information on all details, as they, confessedly, do not enter into them. Belcher's, the former standard work, is out of print, and in many ways out of date, as, though the main principles of chart-making must remain the same, the lapse of time and introduction of steam, &c., have placed many additional means at the disposal of the marine surveyor of to-day. Knowing that there are many older and more experienced hydrographical surveyors than myself, it has been with con- siderable diffidence that I have applied myself during a period of leisure to stop the gap, and I hope my brother surveyors will remember that I write not for them, but for those young officers who wish to become acquainted with the practical portion of our branch of the naval profession. The Appendix, largely composed of reprints of tables either falling out of print, or scattered about in different works, will, it is hoped, be found to save labour and time, and be useful to the Surveying Service at large. W. J. L. WHARTON. H. M. S. SYLVIA, March 29ta, 1882. CONTENTS. PAGE PRELIMINARY .. 1 CHAPTER I. INSTRUMENTS AND FITTINGS ... 4 Sextants and Stands Horizon Theodofite Station Pointer Scales Straight-edges Chains Protractors Pocket , Aneroids Heliostat Ten-foot Pole Drawing-Boards Weights Transfer Paper Paper Books Chronometers Marks Boat's Fittings Lead-lines Beacons. CHAPTER II. A MARINE SURVEY IN GENERAL .. .. .. .. .. 51 CHAPTER III. BASES 57 By Chain By difference of Latitude By Angle subtended by known length By Measured Rope By Sound. CHAPTER IV. * THE MAIN TRIANGULATION .. .. .. ..67 \ CHAPTER V. PLOTTING , 94 vi CONTENTS. CHAPTER VI. PAGE RUNNING SURVEY .. .. 114 CHAPTER VII. COAST-LINING ...... .. 119 CHAPTER VIII. SOUNDING .. 127 Boat Sounding Ship Sounding Searching for Vigias. CHAPTER IX. TIDES .. 143 CHAPTER X. TOPOGRAPHY .. .. .. .. .. .. .. .. 157 CHAPTER XL HEIGHTS .. 162 By Theodolite By Sextant By Depressions to Masthead and Water-line Obtaining Distance from Elevation of a known Height. CHAPTER XII. OBSERVATIONS FOR LATITUDE 179 By Circum-meridian Altitudes of Stars By Circum-meridian Altitudes of Sun. CHAPTER XIII. OBSERVATIONS FOR ERROR OF CHRONOMETER .. .. 198 General remarks on obtaining Longitude Error by Equal Altitudes. CONTENTS. vii CHAPTER XIV. PAGE MERIDIAN DISTANCES .. .. .. .. .. .. .. 218 Telegraphic Chronometric. CHAPTER XV. TRUE BEARING .. .. .. .. .. .. .. .. 241 By Theodolite By Sextant Variation. CHAPTER SEA OBSERVATIONS .. .. .. ,. .. .. .. 254 Double Altitude Sumner's Method Short Equal Altitude Circum-meridian Altitudes of Sun. CHAPTER XVII. THE COMPLETED CHART .. .. .. .. .. .. 263 Fair Chart Reducing Plans Delineation Symbols Colour- ing Graduation. CHAPTER XVIII. DEEP-SEA SOUNDINGS .. .. .. .. .. .. .. 27G CHAPTER XIX. MISCELLANEOUS ................ 288 Distortion of Printed Charts Observations on Under-Currents Exploring a River Swinging Ship. CONTENTS OF APPENDIX. APP PAGE A. To prove that Tan Convergency=Tan Dep. . Tan Mid. Lat. .. 299 B. In Graduating a Chart on the Gnomonic Projection .. .. 300 C. To prove Chord=2rad|vers/90 + |V-l 1 .. .. 302 Cos. I . Cos d Vers h D. To prove Reduction to the Meridian = ^ . g]~ p- 30i3 E. To show that the Distance of Horizon in English Miles = A/- height in feet 304 v 2 F. To obtain distance from an elevation of a known height . . 305 G. Base by Sound ..336 H. To prove Rule for obtaining Height from Angles of Depression of Masthead and Water-line ..307 I. Form for Deck Book .. 308 J. Chronometer Comparison Book . . . . . . . . 310 K. Sounding Book . . L Table of Chords of Arcs ..312 M. Lengths of Degrees, Minutes and Seconds .. .. 324 N. Reduction to the Meridian .. .. .. 338 0. Dip for Calculating Heights .. .. 340 p. n Angles subtended by various lengths at different distances .. .. .. .. 341 Q._ Distance of Visible Horizon .. ..342 R._ Distance of Sea Horizon . . . . 343 S. for Ten-foot pole .. ..344 T. of Time in decimals of a day .. .. .. 345 U. Metrical and English Barometers .. ..346 y. n Corresponding Thermometers . . . . .-. 347 W. Foreign Measures of Depth UNIVERSIT HYDEOGEAPHICAL SUEVEYINGL HYDROGRAPHICAL SURVEYING. ERRATA. Page 60, line 26,/or " Cos." read " Sec." 75, 8, after " BE A " add " -BDA." 242, 14, /or "semi-diameter" read "semi-diameter x Sec. alt. long Clays, onen extenaen into me uignr, wm^suon seem monotonous, and become a bore to one whose heart is not thoroughly in it. Happily, it is a profession of volunteers, and the author's experience is, that in no branch of the public service can the juniors be more anxious to do their duty, not only to the letter, but to the utmost of the spirit, and to such as these no day seems long enough. To them, the interest is constantly kept up. Every day has its incidents. The accuracy of the work of each assistant, when proved, is an infinite gratification B CONTENTS OF APPENDIX. PP A. To prove that Tan Convergency=Tan Dep. . Tan Mid. Lat. .. 299 B. In Graduating a Chart on the Gnomonic Projection .. .. 300 C. To prove Chord=2 rad|vers/9at-V-l I ,. ^_ . . 302 p. M Angles subtended by various lengths at different distances .... ..341 Q._ Distance of Visible Horizon .. ..342 R. n Distance of Sea Horizon . . g.__ for Ten-foot pole T. of Time in decimals of a day U. Metrical and English Barometers .. ..346 y n Corresponding Thermometers . . . . . . 347 W. Foreign Measures of Depth HYDROGKAPHICAL SURVEYING. PRELIMINARY. THERE is nothing mysteriously difficult in the art of Hydro- graphical or Marine Surveying. For the ordinary details, no deep theoretical or mathematical knowledge is needed ; on the contrary, it is an eminently practical branch of the Naval Profession. An aspirant to its acquirement should have a quick eye, should possess the ordinary good common-sense that is .necessary to secure success in all walks of life, but above all he must have a boundless capacity for taking pains in details at all times and seasons. The advice, " Surtout, point de zele," does not apply to surveying. Without zeal, and the utmost keenness for the progress of the work, the attention and interest will soon fail ; and the necessity for constant application throughout long days, often extended into the night, will soon seem monotonous, and become a bore to one whose heart is not thoroughly in it. Happily, it is a profession of volunteers, and the author's experience is, that in no branch of the public service can the juniors be more anxious to do their duty, not only to the letter, but to the utmost of the spirit, and to such as these no day seems long enough. To them, the interest is constantly kept up. Every day has its incidents. The accuracy of the work of each assistant, when proved, is an infinite gratification HYDROGRAPHICAL SURVEYING. to him, and he has also the continual satisfaction of feeling that of all he does a permanent record will remain, in the chart which is to guide hundreds of his fellow-seamen on their way. For any naval officer, then, who is really anxious to learn, the practical part of surveying will soon be mastered. It will quickly become a labour of love, and the con- stant attention and trouble necessary will be merged in the interest taken in the work. Thorough honesty must always guide him, so that nothing may appear that is not known to be correct. Omissions there must always be, but let there be no sins of commission, that pains and care will prevent. It is not of course suggested that all can become thorough good surveyors in all branches. One man will have a par- ticular aptitude for astronomical observing; another will have a natural talent as a draughtsman, that no efforts on the part of another can compete with ; and so on ; but to become a good practical hand is within reach of all who seriously are desirous of being so, and will take the trouble to gain the necessary experience, without which all theory and book-teaching will be useless. Inside of the broad principles of map making, marine surveying is made up of numerous dodges and details, for which there is nothing like practical exposition on the ground, and those who can get others to show them will need but little other help, but as in many cases this instructor will not be at hand, it is hoped that the following pages may sometimes supply the information required. It may seem to many that some points remarked on are too insignificant to be heeded, but those who are acquainted with the work will know how much time is lost by inat- tention to, or ignorance of, these little things, and a young surveyor will be a very few days at work before he finds this out. We assume our readers to have the ordinary knowledge of the sextant that all naval officers are taught, and that he is PRELIMINARY. not entirely ignorant of the first principles of making a plan from a base by means of angles. We write mainly for those who join the Surveying Service, and shall speak throughout as though we had the resources of an ordinarily fitted surveying ship at command. We have endeavoured to take things in the order that they will generally come in the prosecution of a survey. In work of the nature of Hydrographical Surveying, it is impossible to give directions as to how to undertake every detail. Ordinary means fail now and again from exceptional, local, or other circumstances, and ready resource in over- coming difficulties is one of the most important requisites in a nautical surveyor. To invent or improvise a method of doing a particular piece of work is a most satisfactory achievement when successful, but it is scarcely necessary to say that this can only come to the most naturally talented with experience. The following pages will then not be found to provide for every occasion, but will only describe the ordinary and accepted modes, of setting about work. B 2 HYDROGRAPHICAL SURVEYING. CHAP. I. CHAPTER I. Errors of instru- ments to be ascer- tained. No instru- ment perfect. Contents of Chapter. INSTKUMENTS AND FITTINGS. Sextants and Stands Horizon Theodolite Station Pointer Scales Straight-edges Chains Protractors Pocket Aneroids Heliostat Ten-foot Pole Drawing-Boards Weights Transfer Paper Paper Books Chronometers Marks Boat's Fittings Lead-lines Beacons. IN preparing for any surveying work, whether in a regularly- fitted surveying ship or not, the first thing is to test all instru- ments and ascertain their errors. To do the former well, it is necessary to have an intimate knowledge of the points on which each instrument is liable to go wrong, which is only thoroughly to be learnt by experience ; but a few hints will assist the beginner. A thorough acquaintance with the construction of instru- ments will save many an hour, lost by one whose instrument has gone wrong while in the middle of his work, and spent in fruitless efforts to make out where the fault lies. No instrument, not even engine-divided protractors, can be assumed to be without error, and are seldom found so, and though those errors may be small, in some cases they are of importance, and no work can be deemed satisfactory without the knowledge of how much correction should be applied, in such instances as it may be necessary to do so. We shall therefore commence by some observations on instruments, and on all materials and fittings required for conducting a regular marine survey, embodying in these such hints on using each instrument in general, as are likely to be CHAP. i. HADLEY'S SEXTANT. 5 useful, and also some on choosing them that are not mentioned by Heather in his work on Instruments.* This useful work, which should be in the hands of every Heather's surveyor, goes so fully into the construction of instruments, J^gtru n and in most cases into the methods of ascertaining, and, as ments. far as may be, correcting their errors, that we shall refer the reader to it on most points, adding only certain practical suggestions that are not therein mentioned. HADLEY'S SEXTANT. It is not, perhaps, necessary to say much about the sextant, as so many works have already treated the subject ; but there are several practical points not generally mentioned, which may be of value in selecting a sextant with a view to the work of a nautical surveyor. Besides those noted by Heather, then, 1. One of the eye-pieces of the inverting telescope should have a high magnifying power, about 15 diameters, as contacts of the sun's limbs in observations with the artificial horizon are far easier made the larger the suns. 2. Several dark eye-pieces should be provided, with neutral Dark eye- tint glass in them of different intensities. These should pleces * be fitted, not to screw on to the eye-piece, but ground conical, to slip on to a similar conically ground surface on the telescope eye-piece. These will be found very useful on cloudy days, as a little practice will soon enable the observer to substitute one shade for another in a fraction of a second, as clouds sweep on or off the sun, and many sights will thereby be saved. It is very important to have the suns in artificial horizon observations of the same brilliancy, and for this reason the hinged shades on the sextant should never be used for the purpose; as, in the first place, they introduce error, and also, if the * "Mathematical Instruments." J. F. Heather, M.A. Lockwood and Co., London. 6 HYDROGRAPHICAL SURVEYING. CHAP. I. shades have to be altered to suit the varying brightness of the sun during the observation, the suns will be of different brilliancies, as these shades are never of the same tints. By using the dark eye-pieces, the up-and-down piece,* when adjusted to equalise the suns, will bring the axis of the telescope nearly exactly in line with the edge of the silvered surface of the horizon-glass, which is the best position for observing, and from which it must never be moved until the equal altitudes or other observations are complete. No matter what depth of shade is then used by shifting the dark eye-pieces, the two images will be of the same tint. The darker the shade used the better. Beginners are very apt to use too bright suns. If in observing with the sun the observer can accustom himself to use one eye for taking the observation, and the other for reading and setting the vernier, he will find it very convenient, and it will tend to keep both his eyes in good order. Position of 3. It is very convenient for picking up the images in down 1 " tne artificial horizon, if the up-and-down piece is so placed piece. as to enable the observer to look over it into the horizon- In many sextants the up-and-down piece is placed so close to the index glass that this is not possible, and regard should be had to this point. 4. An extended vernier, i.e. a vernier whose divisions are twice the distance apart of those on the arc, will be found convenient for accurate observing. 5. A steel tangent screw will be found to last longer and work more evenly than a brass one. The methods of ascertaining the index and other errors of Hadley's sextant, and correcting them, are so fully entered into by Heather, that they are here omitted, with the exception of the following : * The up-and-down piece of a sextant is the portion that bears the collar for the telescope. CHAP. i. SOUNDING SEXTANT. 7 To find the error caused by the refraction, through non- Errors of parallelism of the sides, of the coloured shades. Measure the diameter of the sun, with different combinations of the shades. Take out the pin which supports one set of the coloured shades, and replace the shades reversed, so that the face before next the index glass is now away from it. Eemeasure the diameter of the sun with same combinations as before, and half the difference of the measurements of each set will be the error due to the shade reversed. These errors can be neglected in sea observations, and if coloured eye-pieces are fitted as recommended above, the shades are not required when the artificial horizon is made use of. SOUNDING SEXTANT. This useful form of sextant is made of various sizes. It chiefly differs from the observing sextant in being generally lighter and handier, in having the arc cut only to minutes, and having a tube of a bell shape so as to include a larger field in the telescope. The graduation of the arc should be plain enough to read without a magnifying glass. The measurable angle should be as large as possible, i.e. about 140. The index glass should be large, so as easily to pick up objects. The telescope should be of a high magnifying power and Good tube clear definition. invaluable. Those supplied by the makers are sometimes very good, but when using a 'sextant for triangulation, as from a ship aloft, a still better glass is a great boon. The writer has found that a tube of an ordinary field binocular (dismembered for the purpose) fitted to a sounding sextant, has been of inestimable service, and enabled many objects to be seen, which, with the ordinary telescope, were quite invisible. All angles in the frame of the instrument should be rounded off, especially that at the zero end of the arc. 8 HYDROGRAPHICAL SURVEYING. CHAP. i. Considerable injuries may result to the face of the observer when using the sextant in a boat in a lively sea, if this is not done. RE-SILVERING MIRRORS. On service, the mirrors of sextants, especially sounding sextants, frequently get dimmed by damp, and the surveyor must be able to resilver them himself. A supply of tinfoil, of good quality, for this purpose, is one of the necessary stores. Mercury is always to be had. The operation Ijas been frequently described, but it is, perhaps, better to repeat it. Take a piece of tinfoil, a little larger than the glass to be silvered, and smooth it out on a perfectly flat surface, as a sheet of plate glass, or a thick smooth book-cover. This smoothing can be well done by a little pad of chamois leather, which can be kept for the purpose, or by the finger. Drop a small bubble of mercury on to the foil, and by gentle rubbing with the pad, spread it over the former so that it shows a bright surface. Pour mercury on until the piece of foil is quite fluid, and brush any large spots of dross lightly off. Lay a piece of clean paper, long enough to handle easily, on the mercury, and the glass, previously well cleaned by means of spirits of wine, on the paper. Pressing on the glass with one hand, withdraw the paper with the other, slowly and steadily, and a pure surface will appear under the glass, the dross all coming away with the paper. Incline the book, or whatever surface we have been work- ing on, so as to let superfluous mercury run off, placing strips of tinfoil at the lower edge to assist in sopping this up. After from twelve to twenty-four hours, the amalgam will be dry, and firmly adhering to the glass. Cut the edges carefully round with a sharp knife, and varnish lightly over, CHAP. i. SEXTANT STAND. either with the clear stuff used by the instrument makers, or with varnish that can be made on board, by dissolving sealing- wax in spirits of wine. The glasses of some sextants seem fitted on purpose to invite the damp to penetrate between glass and silvered surface. These will want protection by sticking thin strips of paper along the edges exposed, and well varnishing. In some cases a stopping of thick amalgam, placed between the glass and the frame at the back, where there is one, will answer well, and prevent any damp getting at the back of the glass at all. The mercury which remains will contain tinfoil in amal- Amalga- gam, and is useless for any other purpose but silvering, but JJJ| d to avoid waste it should be preserved in a bottle by itself, draining off the thick of the amalgam by a sharply twisted paper funnel. It can then be used again for resilvering. Care must be taken not to allow any of this to get into the artificial horizon bottles, as the smallest quantity of it will spoil a whole bottle of pure mercury, and the amalgam can only be removed by evaporation. Notwithstanding, mercury containing tin in amalgam can be used for artificial horizon work, by carefully sweeping the surface after it is poured out, with a piece of paper. Some observers have gone so far as to prefer amalgamated mercury for this purpose, but we do not agree. In resilvering an horizon glass, only the portion required Horizon should be operated on, leaving one half clear. The edge of S lass< the foil must be sharply and smoothly cut before applying the mercury, and not the smallest nick or cut permitted to remain in it. SEXTANT STAND. Though a practised observer will get good observations in an artificial horizon, with a sextant without a stand, he will get them far better with one, and in all work where accuracy is aimed at, a stand should be used. Unsteadiness of hand, which all are so liable to, from 10 HYDROGRAPHICAL SURVEYING. CHAP. i. previous exertion, indisposition, and many other causes, is put out of the question by using a stand. With star observations this is especially the case, as it is extremely difficult to hold the instrument in the hand firmly enough to prevent a little vibration of the images. Sextant stands should be lacquered, not bright, and should have large heads to the foot screws, so as to be grasped easily while observing. The bearing which carries the sextant should be accurately fitted into the socket in the handle, and should be very slightly conical. If too much so, it is liable to jam. The counterbalances are usually too heavy for an ordinary sextant. They should be of such a weight as to balance the sextant without the screws at the ends of the pivot being set up too taut. Sometimes one weight is enough, or as much lead can be taken out of each as is necessary to reduce the weights to balance. stools for Small three-legged stools about 14 inches high, on which to place the sextant stand, should be made, and it will be found convenient to sink hollows in the top to correspond with the three foot screws to prevent slipping. Other little hollows sunk in the top for the spare dark eye- pieces to lie in, will also prevent these falling off, and by placing them in regular order, any one can be at once picked up without delay, when it is requisite to change them. Another similar stool for the observer will make him comfortable, a great point for good observing. ARTIFICIAL HORIZON. The glass in the roof should be of the best quality, and the faces of each pane accurately parallel. A wooden trough to place inside the iron one is a con- venience, as it raises the level of the mercury up to the height of the lower edge of the glasses in the horizon roof, a consideration where low altitudes have to be observed. The reduced area of mercury will not matter when observing CHAP. I. ARTIFICIAL HORIZON THEODOLITE. II the sun. When taking stars, the iron trough only should be used, as stars are more difficult to pick up, and its larger area will facilitate operations. Three short wooden legs or buttons, fitted to the iron trough, will enable it to stand steadier on uneven ground than the four projections usually cast on the under side. In connection with this, an artificial horizon stand is very Horizon useful. This consists of two iron plates ; the lower one standt has three short legs on which it stands firmly; the upper one is pierced by three long large-headed screws, which serve as legs and fit into slight hollows on the lower plate. By adjusting these, the horizon laid on the upper plate can be levelled, when we have uneven ground. Four iron battens, screwed on to the upper plate so as just to permit the horizon roof to fit inside them, will prevent any wind getting to the mercury. The horizon cover should be marked at one end, or side, Mark on and this mark should in most cases be in the same position coyer ' with regard to the observer. Of this more is said under " Observations." THEODOLITE. The less a theodolite is tampered with by unpractised hands the better, but they must be adjusted from time to time, and little things are constantly wanting attention. The adjustments are well described by Heather, but as it is very important to know them, they are here given, in case the former work should not be at hand. The adjustments are 1. Adjustments of the telescope, viz., for parallax and for collimation. 2. Adjustment of horizontal limb, viz., to set the levels on the horizontal limb to indicate the verticality of the azimu- thal axis. 3. Adjustment of the vertical limb, viz., to set the level beneath the telescope to indicate the horizontality of the line of collimation. 12 HYDROGRAPHICAL SURVEYING. CHAP. I. Commence operations by setting up the theodolite as level as you can by eye, by moving the legs. See that the legs are firm, and everything tight. Set all levels as true as you can, by the parallel plate screws and vertical arc tangent screw. Adjust- Parallax is occasioned by the image formed by the object- Paraihu: gl ass n t falling exactly on the cross-wires. First adjust the movable eye-piece until the cross-wires are sharply defined. Then obtain the proper focus for the object by moving the milled head on the telescope. This will throw out the image of the cross-wires, and the eye-piece must be again adjusted, until cross-wires and object are both truly in focus. This has to be done each time the theodolite is set up, and is therefore only a temporary adjustment. The others are more permanent. Adjust- Collimation is effected by directing the telescope on some Cdifma- well-defined point, and bringing it to coincide with the tion. intersection of the wires, with the level downwards. Turn the telescope in the Y's, until the level is uppermost. If the object is still at the intersection of the wires, the collimation in altitude is correct. If not, bring the wires half way towards the object by turning the screws holding the diaphragm. Then re-set the telescope by the tangent screw for the object, and bring the telescope round in the Y's to its former position, when any displacement still existing must be corrected in the same way, half by the diaphragm screws, and half by the tangent screw. After a few trials the error should be corrected. Do the same with the telescope with level right, and level left, at right angles to its former positions in the Y's, for azimuth error. When this is done, the cross-wires, while the telescope is slowly revolved, should remain over the object. Adjust- * The collar being tightened by its clamping screw, unclamp Horizontal ^ e vernier plate, and turn it round till the telescope is over Limb. _ From Heather. CHAP. r. THEODOLITE. 13 two of the parallel plate screws. Bring the bubble of the level beneath the telescope to the centre of its run by turning the tangent screw of the vertical arc. Turn the vernier plate half round, bringing the telescope again over the same pair of the parallel plate screws ; and, if the bubble of the level be not still in the centre of its run, bring it back to the centre, half way, by turning the parallel plate screws over which it is placed, and half-way by turning the tangent screw of the vertical arc. Eepeat this operation till the bubble remains accurately in the centre of its run in both positions of the telescope ; and then turning the vernier plate round till the telescope is over the other pair of parallel plate screws, bring the bubble again to the centre of its run by turning these screws. The bubble will now retain its position, while the vernier plate is turned com- pletely round, showing that the internal azimuthal axis, about which it turns, is truly vertical. The bubbles of the levels on the vernier plate being now, therefore, brought 'to the centre of their tubes, will be adjusted, to show the verticality of the internal azimuthal axis. Now, having clamped the vernier plate, loosen the collar, by turning back the screw, and move the whole in- strument slowly round upon the external azimuthal axis, and, if the bubble of the level beneath the telescope main- tains its position during a complete revolution, the external azimuthal axis is truly parallel with the internal, and both are vertical at the same time ; but, if the bubble does not maintain its position, it shows that the two parts of the axis have been inaccurately ground, and the fault can only be remedied by the instrument maker. To adjust for the vertical limb, the bubble of the level Adjust- being in the centre of its run, reverse the telescope, end for end, in the Y's, and if the bubble does not remain in the same li position, correct for one half the error by the capstan-headed adjusting screw at one end of the level, and for the other half, by the vertical tangent screw. Eepeat the operation till the result is perfectly satisfactory. Next turn the /telescope 14 HYDROGRAPHICAL SURVEYING. CHAP. i. round a little, both to the right and to the left, and if the bubble does not still remain in the centre of its run, the level must be adjusted laterally by means of the screw at its other end. This adjustment will probably disturb the first, and the whole operation must then be carefully repeated. By means of a small screw, fastening the vernier of the vertical limb to the vernier plate over the compass box, the zero of this vernier may now be set to the zero of the limb, and the vertical limb will be adjusted for horizontality. Adjust- The vertical limb should move in a truly vertical plane, vertical ^ n ^ error can on ty ^e adjusted in the larger instruments, plane. but every theodolite must be tested for it, as, if much error exists, the instrument requires alteration by the maker. It will introduce error into all angles to objects much elevated or depressed, and it is especially important for observations for true bearing to know that this adjustment is perfect. To test it, direct the theodolite when horizontal to either the edge of a well-built wall, or still better, a steady plumb- line. The cross-wires, when the instrument is elevated and depressed, should still intersect the line. If they do not, in 6-inch theodolites, the adjustment can generally be made by means of screws on one of the Y frames. In smaller theodolites we must accept the error, and take care not to use them for true bearings. These adjustments completed, the instrument will be ready for work. Points There are, however, a variety of small points on which a derange - tne dolite may go wrong while away in the field, and a know- ment. ledge of the general causes of these temporary derangements is very useful, and may prevent loss of a day's work, and much aggravation to all concerned. The parts of a theodolite, especially in an old instrument, that most frequently get out of order, are the small screws which hold the milled heads of the tangent screws in their places. A young observer is often much bothered* and puzzled by his instrument not coming back to zero, which may result from many things, but most frequently from one CHAP. I. THEODOLITE. of the small screws above mentioned being loose. Screwing it up tight enough to prevent any play when the instrument is clamped, but not so tight as to make the tangent screw work hard, will often remove the difficulty. Other causes of not coming back to zero are : - 1. Looseness of the sockets through which the tangent screws work, and which can be easily tightened by their screws. 2. Looseness of the fittings of the brass stand on the theodolite legs. There are many working parts here, and any of them are liable to get loose. The leverage on the brass plate that fits on each leg head is enormous, if the leg should be allowed to swing out in taking off the rings ; and as the screws that hold them on are small, looseness may easily take place here. 3. In an old instrument, the faces of the clamping plates may screw close together without clamping the instrument tightly. This is from the part that holds the instrument, and which gets all the friction, being much worn. The parts into which the clamping screw fits must be smoothly filed on their inner faces, so as to ensure the other parts coming into contact with the body of the instrument, before the faces of the clamping plates meet. The upper plate will sometimes not revolve freely, but catches every now and then. This is from the piece of metal which clamps the two plates together either not fitting very well, or being dirty inside, or perhaps bent. Placing the finger underneath so as to press it up to the lower plate, whenever the plates are to be revolved, will ensure its work- ing smoothly, and is a better thing for a young hand to do than to attempt to take it off. The same thing will happen to the reading-glass plate ; but here it is often the little screw underneath which is loose, and simply screwing it up will re- lieve it. Lifting it with the finger will always assist it to run round easily. An operation the nautical surveyor has frequently to per- p u tting in form is replacing the wires, or rather cobwebs, of his theodo- ne ^ webs, lite telescope. 16 HYDROGRAPHICAL SURVEYING. CHAP. i. For this purpose catch a garden spider, as a house spider does not spin his rope taut enough. Having cut some holes, say two inches square, in a strip of cardboard about three inches wide, place the spider on it, and shake him off. As he throws out his web in falling, twist it up on the cardboard so as to cross the holes, and lay it on one side. Measuring Having taken the diaphragm from the telescope, and wifhttie scraped off the old balsam, lay it on the table and place the theodolite, smallest drop of Canada balsam on its edges. With the aid of a magnifying glass, place the cardboard across it, in such a manner that the web will lie in the notches cut in the diaphragm, when it will adhere to the balsam. Heather giVes a good description of measuring angles with the theodolite, to which we will add, that, Regard must be had to the purpose for which the angles are to be taken, in settling how many times, and in what manner, the angles shall be repeated. An error of two minutes will make no perceptible difference when plotted, unless the line be very long, say five feet. All objects, therefore, that are simply to be plotted, and do not come into the triangulation, can be taken round once with zero at 360, and a second round taken after with another zero, say 100 for convenience sake, simply for the purpose of making sure that there are no gross errors, as no theodolite in adjustment should give an angle in error as much as two minutes. Bepeating Angles to main stations, however, will be very likely required to enter into the calculation, and the correctness of the plotting will any way depend on them. These must there- fore be repeated, the number of times varying according to the degree of accuracy required. One method of repeating angles is thus given in Heather, somewhat altered. Firs * Having taken the first measurement, loosen the clamp of the lower plate, turn the theodolite bodily round until the telescope is directed upon the zero-object, and again clamping the instrument, perfect the bisection of the zero by the cross- CHAP. i. THEODOLITE. I/ wires by means of the slow-motion screw on the neck of the instrument. The index of the vernier, together with the co- incident division of the limb, will thus have been brought from the position in which it was when the telescope pointed at the object to be measured, round to the previous position of the 360. Now release the upper or vernier plate (looking again at the vernier first to see it has not been moved), turn it until the telescope is again directed towards the object, clamp and perfect the bisection by the tangent screw moving the upper plate. The reading now on the vernier will be twice that formerly read off, or nearly so, and will be entered in the book under the former observation. This process can be repeated as often as required. The mean angle can be obtained by dividing the last reading (increased by as many three hundred and sixty degrees as the plate has revolved) by the number of observations, but it is better for our purposes to put down each individual reading. The difference between every two consecutive readings will give a value for the angle, and we can then see how they agree with one another. An example of this kind of repeating is given on page 72. The above method is perhaps the most accurate ; but, when many angles are to be taken, requires much time, and we shall arrive at a conclusion quite near enough for any hydrographi- Second cal triangulation by taking all the angles in succession with method - the vernier set to 360, and then, changing the degree of the zero to some even number, as 100, 200, take all objects again, repeating thus as often as necessary, which will be found much quicker. The other method can be reserved for taking single angles, as, for example, a flash from a distant station. If both verniers are read, any error arising from bad Beading centering should be eliminated for any given position of the plates ; but this depends on the zeros of the two verniers being precisely in a line, and as a theodolite sees service and gets worn, this adjustment becomes frequently imperfect, and the value of the sum of the readings of the two verniers is considerably diminished. c 18 HYDROGRAPHICAL SURVEYING. CHAP. I. Coloured For practical hydrographical purposes if one vernier is read, with the zero in several positions, it is as a rule sufficient. Different to the sextant, the theodolite has no index error to apply to horizontal angles, but to the vertical arc there is a correction to be found and applied, which will be mentioned in discussing the method of ascertaining heights. A theodolite for hydrographical purposes should be fitted w ^ n c l ure( l shades to the eye-piece of the telescope for observing the sun for true bearing. Theory of Station Pointer. STATION POINTER. This useful instrument is of hourly service in nautical sur- veying. Either in sounding, coast-lining, or topographical plotting, the position of the observer depends mainly on it. The station pointer is used to plot a position on the chart, by means of angles taken at it, to other objects already fixed. Its construction depends upon the fact that the angles sub- tended by the chord of the segment of a circle measured from any point in the circumference, are equal. (Euclid III. 21.) Thus, in the figure, the angles A C B, A D B, A E B are all equal, so that if we have observed the angle subtended by A B, we know at any rate that we are somewhere on the cir- cumference of a circle, the size of which depends on the angle observed. To draw this circle, we take advantage of the fact that the CHAP. I. STA TION POINTER. 1 9 angle at the centre of any segment is double the angle at the circumference. (Euclid III. 20.) We lay off, therefore, from either end of the line whose subtended angle we have observed, the complement of the angle. The point where these lines meet is the centre of the circle, which we describe with the distance from this centre to either end of the line, as a radius. Thus if our observed angle is 64, we lay off A G, B G each making an angle of 26 with A B, and describing the circle with centre G and radius A G or G B, we get the circle we want, for AGB = 180 - (BAG + GB A) = 180 -'52. = 128. AndasAGB = 2 AEB, the angle AEB and all other angles on the circumference will be 64. If the angle observed is more than 90, we describe the circle by laying off the number of degrees over 90, on the opposite side of the line to that on which we know we are, and proceed as before. If we can obtain, besides the angle subtended by A B, the one subtended by B H, another line, one of whose ends is identical with A B, we can draw another circle on whose cir- cumference we must also be, and the intersection of these two circles must be our exact position, as it is the only one from which we could have obtained these two angles at the same time. See Figure 2 (page 20). The station pointer obtains us this position X without the trouble of drawing the circles, as it is manifest that, if we have the angle A X B on one leg of the station pointer and B X H on the other, the only spot at which we can get the three legs to coincide with the points A, B, and H, will beX. We place the station pointer, therefore, on the paper, bring- ing the chamfered edges of the three legs of the instrument to pass over the three points observed, and make a prick with c 2 20 HYDROGRAPHICAL SURVEYING. CHAP. i. a needle in the nick in the centre, which will then mark the spot. A piece of tracing-paper on which the three angles are pro- tracted will answer the same purpose, but, of course, this will entail more time, and in the open air will give trouble, as liable to be blown about by the wind. Nevertheless, this has often to be used, as when points are close together on a small scale, the central part of the station pointer will hide them, and prevent the use of the instrument. Position of A further consideration of the system of two circles will "Points." g k ow ^t the more rectangular the intersection of the circles, the less chance there will be of any error in fixing the posi- FI&2. tion. This depends upon the position of the three points with regard to one another and the observer. Let us take three points placed as A B H in Fig. 3. The angles we have observed give us X as the point of intersection. It is evident that it is difficult to localise this point exactly, as the circles so nearly coincide as make it im- possible to say where the precise point is at which they inter- sect, and, with the station pointer, we should find that we could move the centre of the instrument considerably, without materially affecting the coincidence of the legs with the three points. When H is so placed as to fall on the circle A X E B, there CHAP. i. STA TION POINTER. 2 1 will be no intersection whatever, as the two circles will coin- on the cide ; and we cannot tell where we are on the circumference circle ' of this practically single circle. The nearer, therefore, we are to being on a circle, whose cir- cumference will include all the three points and our own position, the worse will be what is technically called the " fix," and this must always be guarded against in selecting objects to observe. When one object is farther from us than the central one, we shall, as a rule, have a good fix ; but when the central ob- FIG3. ject is the farthest, the two circles will begin to make a bad intersection. Therefore, as a practical rule, never observe objects of General which the central one is most distant, unless it is so much Bules ' farther distant than either of the others, and so placed as to put you well outside the circle, in which case the fix will be just as good as though the central object were the nearest. When moving along, as when sounding, and fixing from time to time ; if both angles change slowly, the fix will be bad, for we must be moving nearly along the circumferences of both circles, and they must therefore nearly coincide. In plotting the angles with the station pointer, the fix will 22 HYDROGRAPHICAL SURVEYING. CHAP. I. be good, if a very slight movement of the centre of the instru- ment throws one or more of the points away from the leg ; but if this can be done without disturbing the coincidence of the legs and all three points appreciably, the fix is bad. Theoretically, the best position is inside the triangle formed by the objects, but in practice it is often impossible to observe the large angles incidental to this position. size of The size of the angles admissible in a good fix depends on ^ e P os iti n f tne tnree objects. If two objects are equi- distant, the angle must not be small, for a slight error in the angle will make a great difference in the position ; but if one object be much farther off than the other, a very small angle between these will suffice, so long as the third object is so placed as to make a fairly large angle. An arrangement of the objects not yet considered, is when two of them are in line from the observer's position. y Points I' This is technically called " transit," and no transit of known marks is allowed to take place without making use of it. One angle to a third object is here enough to fix the posi- tion, which is one advantage, another being that if two angles are taken and placed on the station pointer, the coincidence of the position, as plotted by these two angles with the transit line, gives an excellent check. Here, Fig. 4, A and B are in line or transit (<) ; H is a third object. It will be evident that when the observed angle is on the station pointer, and the latter is placed with one leg coin- ciding with the line A B, that we only have to move it up or down that line, until H coincides with the other leg, which gives us X. Any other position, as X x , would not allow the leg to pass over H. It will also be seen that the farther apart A and B are, the truer will be the direction of the transit line. If one object was at B x , the position pricked through at X might be a little right or left of the true transit line, without the deviation be- ing visible on the leg of the station pointer. Also, it will be seen that the angle to the third object should CHAP. I. STATION POINTER. 2$ be as near 90 as possible, anything under 25 being inad- missible, as the angle of intersection at X would permit of a false position without detection. In choosing a station pointer, of which instrument Heather Choosing a gives but a meagre account, the first important thing to look at is that the smallest angle to be reSd on the leg which will not come to zero, is as small as it should be. A well-planned station pointer should allow this leg to return to 12, or even less, but no instrument which will not read 17 should be bought. It is a great nuisance to find that the only angles you can FIG 4. take, cannot be plotted by means of your station pointer, and the chance of this should therefore be minimised as much as possible. Station pointers are made with brass, and with silver arcs ; the latter are of course more durable, but for many purposes the brass are to be preferred. When sounding, or doing any work in the open, the reflection from a silver arc is often a bother, and hinders speedy setting of the vernier. The use of a reading-glass is almost a necessity with silver arcs for this reason, and also on account of the fineness of the cutting ; whereas, with the brass arcs, a surveyor with good eyes can 24 HYDROGRAPHICAL SURVEYING. CHAP. i. set his instrument quite correctly without one, a great point in a boat. For chart-room use the silver arc is to be preferred. Station pointers are generally made so as to allow the left leg to come back to 0. It does not, of course, matter which leg does this in any Individual instrument, to an officer detached, who will only have one with him ; but in fitting out a ship with several station pointers, some should be chosen with the small angle on the other leg, so as to admit of any pair of angles being plotted in the chart-room con- veniently. The nick in the centre of the instrument should be small, i.e. just deep and wide enough to admit of a needle fairly catching in it. The needle-pricker should always be used for marking the position ; not a pencil-point, which soon wears blunt, and will not mark truly in the centre. The prick also remains, and can be seen under the figure with a reading- glass, when inked in. For ordinary soundings and field work, a station pointer of about 5 inches diameter of arc is most convenient. For ship sounding and chart-room work, larger ones are supplied. Testing a In testing a station pointer, the first thing is to see that the Pointer vernier of the leg which comes back to zero, reads exactly 0, using a magnifying-glass to read off accurately. If it does not, the screws which hold the vernier must be loosened slightly, and the vernier plate moved, until the arrow on the vernier corresponds exactly with of the arc, and the 30' on the vernier with a division of the arc. Testing Take either a large sheet of backed paper, or a white Bristol board, and mark out, by means of chords, lines radiating from a centre, and 10 apart. These lines must be very carefully ruled, and in Indian ink, as this sheet must be kept as the test of all station pointers and protractors, which should be from time to time examined by its means. Screwing on the lengthening legs, and placing the station pointer on this sheet, with the nick in the centre of the arc corresponding exactly with the prick in the centre of your testing circle, and putting CHAP. I. STA TION POINTER. 2 5 weights on the central part of the station pointer, each leg can be in turn moved to correspond with the ruled 10 lines, and the reading of the vernier compared. The error at each 10 should be written on a small piece of paper in the form of a table, and pasted on the inside of the box. If the legs of the instrument are exactly centred, the readings will either be correct, or the same amount in error all round, for each leg ; but as this is a degree of delicacy rarely attained, it will usually be found that the error varies for different positions of the leg. The verniers should be set to minimise the errors between and 90, which is the amount of angle most used in actual work. The chamfered edge of the leg and lengthening piece should correspond exactly with the line in all its length ; if it does not, it is also a result of bad centring or bad fitting on of the lengthening piece, but a good instrument should not have this error in any appreciable extent. It need scarcely be added that if the instrument is found very badly centred, it should be returned to the maker, or not be chosen if buying ; but when an instrument is sent to the other end of the world, you may have to make the best of it, and registering all the errors on the table, be careful to apply them when using the instrument. The necessity for applying a small error depends upon cir- Discretion cumstances, as in some cases, the position of the points used applying will admit of a difference of several minutes in the angle, errors, without any appreciable alteration of the position of the ob- server ; in others, it is necessary to be exact. As the surveyor gains experience, he will learn when to apply the error, and when not. At the commencement, he must always apply the error. It may here be noted, that, if the points used to fix by Caution as are not correctly placed on the chart, the station pointer *J ^f 6 of will not indicate anything wrong, unless a third, or " check " Pointer. angle, be taken and plotted. This must always be remembered in using a station pointer on a published chart, or the adop- tion of this instrument may have a disastrous result. 26 HYDROGRAPHICAL SURVEYING. CHAP. i. In the first place, the chart may be from a rough survey, and there may be absolute errors in the points on it ; and secondly, the distortion caused in printing with damp paper always changes the position of points more or less, and with objects in certain positions, this alone may make an error in a station pointer fix. In navigating, therefore, with a published chart, always use "bearings, as well as the sextant angles plotted by station pointers, or use check angles to each fix. If the result is to show that the points are not correct relatively to one another, use the compass only, as it is less likely to get you into trouble with a defective chart, for the reason that the non- intersection of three bearings will at once indicate something wrong, and the navigator will choose the points of danger in his course ahead to steer by, rejecting the others whose posi- tions with regard to him are of little moment. BRASS SCALES. These must be examined by means of the beam compasses, to see that their divisions are correct, more especially the diagonal portion, as the makers are sometimes not careful enough. If a scale is found to vary, it should be rejected. A brass scale should never be used for ruling, and never taken out of its lox. If it is, some day it will fall from the table, get bent, and its correctness is gone. STEEL STRAIGHT-EDGE. This must be examined to see if its edge is exactly straight, by ruling a very fine line, and reversing the straight-edge, when either ruling another line over the first, or examining the coincidence of the edge with the line already ruled by means of a reading-glass, will prove whether it is perfect. Placing steel straight-edges edge to edge is another method when there are more than one ; but great care must be taken with regard to the light if this is done, as it is difficult CHAP. i. MEASURING CHAINS PROTRACTORS. 2/ to detect a small error if the light falls across. They ought, of course, to touch throughout their whole length. A steel straight-edge must be kept very clean, and care- fully wiped before using, or the paper will soon become very dirty. If kept bright, care must be taken that no emery is allowed to touch the chamfered edge, or it will get so sharp in time as to cut the pencil, and even the fingers of the operator. When once clean, rubbing daily with a warm dry soft cloth will keep it so, with an occasional rub of emery in damp weather. MEASURING- CHAINS. To test measuring chains, which are generally 100 feet long, a hundred feet should be accurately measured along a plank of the upper deck, and marked by nails driven in. Before measuring a base, all the links of the chains should Always to be examined, and bent ones straightened ; the chains are then Jj^ compared with this fixed length and the errors noted. The when used, same reference should be made after measuring, and the mean of these errors applied to the distance measured. It may be as well to note that, when the chain on com- parison proves to be longer than 100 feet, the surplus is to be added to each length measured, and when it is shorter, sub- tracted. The length is to be measured from the outer side of points of one handle, to the inner side of the other. This is to allow for the necessity of having a pin to put in the ground at each length. Each link is a foot long, and every tenth link is marked by a brass label, with as many fingers on it as there are tens of feet from the nearest end. PROTRACTORS. Protractors of all kinds must be tested for correctness of division by the same testing-sheet ruled for the station pointers. 28 HYDROGRAPHICAL SURVEYING. CHAP. I. This is especially necessary in the case of Bullock's protractors, which have extended arms, generally of very light construction, which a slight blow will bend out of the direct line. These sometimes admit of correction by means of screws, which is easily accomplished by placing the protractor on the testing-sheet, with the opposite verniers exactly coin- ciding with the same line, and adjusting the extending points until they also prick precisely on the line. If the divisions of an ordinary protractor are found to be incorrect, there is of course nothing for it but either to return it to the maker to be re-cut, or to mark the errors at each ten degrees, or wherever necessary, on small bits of paper pasted on the protractor. A boxwood or vulcanite protractor is easily kept clean by rubbing it over with a piece of india-rubber, but a brass or electro-plated one is very apt to dirty the^ paper in plotting. It is a good plan to carefully paste a piece of tracing-paper on the under-side of these, when a rub with the india-rubber before use will insure cleanliness. The thinness of the tracing- paper will not interfere with correctness in laying off the Vulcanite protractors are admirable for field work, as they are light, easily read, and, when made thick, do not chip like boxwood ones. POCKET ANEROID BAROMETERS. These are very useful when putting in the topography of a country, as they give sufficiently accurate results for minor heights, with but little loss of time ; but for the more exact measurement of conspicuous hills, &c., they are but of little use, and the theodolite and sextant must be had recourse to. In choosing a pocket barometer for the above-named service, therefore, it is not necessary that it should read very low, as it will be but rarely that nautical surveyors have to deal with the intricacies of land over a few thousand feet high. For this purpose, 25 inches is quite low enough, and o* THRJ CHAP. i. POCKET ANEROID BAROMETER. the five inches of barometric range thus obtained can be so largely marked on the dial, as greatly to facilitate the reading to two places of decimals. An important point for delicate reading is the construction index of the index needle. This should be very thin towards the Nee length when protracted on the paper would be generally so short, that by placing that on the sheet first/ and making it the starting line, errors would be sure to creep in, in increasing the size of the triangles, any little error being multiplied. It therefore is usually necessary to extend the base, as it is termed. 58 HYDROGRAPHICAL SURVEYING. CHAP. HI. This consists simply in calculating a sufficient number of triangles, conveniently arranged, to obtain a side long enough to form a good start, so as to plot inwards as much as pos- sible, when any little errors will be diminished, instead of increased. As a commencement of this process, the base to be measured should, if possible, be placed so that there are two stations, one on each side of it, which can be used for the first triangles and consequent extension of the base. FIG 7. / 5 \ Ease \ Here AB is the measured base, C and D the two first stations. Angles are observed at A, B, C, D. The other two sides in the triangles ABC, A B D being found, C D can be found in both the triangles A C D, BCD, which will check the result, and C D will be the extension of the base for further triangulation. Of course this desired convenience will not always be found, but it is a thing to look out for. It is by no means necessary to measure a long base, pro- vided that convenient triangles can be found for extending the base by calculation. If the angles of these are of the necessary number of degrees, and they are carefully observed CHAP. in. CHAINED BASES. 59 with theodolites, a short base, measured on flat smooth ground, will give a truer result than a longer one measured over inequalities. With a sextant survey it will be well to have as long a base as possible. The ground having been walked over to ascertain it will Planting do, and that the base stations (the ends of the base), are so measuring placed that they see as much as possible on all sides : set b 7- up the theodolite at one end, and at the other a flagstaff or another theodolite, and let a man plant staves (boarding pikes make good ones), exactly in line between the two stations, giving him the position for the first two or three, by looking through the theodolite directed to the other station. After these are in place, he can plant the others in line by guiding himself by them. Having the staves placed and in line, begin to measure from Method of one end. If two persons are to measure, begin from opposite ends. A man is required for each end of the chain. The man at the foremost end of the chain carries ten pins, and the surveyor attends with his book to see the chain fairly placed in line between the staves, and to note down each length of chain measured. Do not let the men stretch the chain too tight, but it must lie straight on the ground between the two ends. The chain being down for the first length, measuring from under the centre of the theodolite, put a pin in the ground, at the foremost end, inside the handle, and touching the flat side. Make a mark in the note book, and walk on together, the man at each end lifting the chain as much as he can, until the hindermost, comes to the pin. He must then place the outside of his handle so as to touch the pin. Another pin is put in at the foremost end inside the handle, the second note made in the book, the first pin taken up by the hindermost man, and on you go. The lengths are best noted by strokes, crossing every fifth over the four, as in ordinary tallying. Check at every ten lengths by the number of pins. When the tenth stroke is made, the foremost man should have no 60 HYDROGRAPHICAL SURVEYING. CHAP. in. pins left in his hand, and the other man should have nine, the tenth having been just put in. The odd feet and inches in the last length are measured by counting the links, which are each a foot long. In walking forward, take care that the hinder man does not overwalk the former, or the chain will have a bight dragging on the ground, links will catch in something and get bent, and the error of the chain will be very different when retested, to what it was before landing. Eepetition The number of times a base must be measured depends on 5ary ' circumstances. If for a harbour plan, only twice, if they agree to a foot or two, will be sufficient. For a survey of greater extent, three or four times will be more satisfactory, unless the two first measurements agree very well. Inequali- Perfectly level ground can seldom be found, and the sur- veyor must make an allowance for inequalities by his judg- ment, which will be of course always subtracted from the measured length. The chain must be tested for length, before and after measuring the base, to ascertain the error. BASE BY DIFFERJENCE OF LATITUDE. When two stations are available from twenty to thirty or forty miles apart, visible from one another, and bearing not more than two points from the meridian, having also a few intermediate points visible from both, a very good base can be got by latitudes, and careful true bearings. The base will then be diff. lat. X os. Mercatorial i Se-c-' bearing. By means of the intermediate points, triangles can be calculated down to a workable length of side for fixing marks. Where no smooth ground for measuring a base can be found, and we want our scale to be near the truth from the first, this method is valuable. CHAP. in. BASE BY ANGLE OF SHORT LENGTH. 6l BASE BY MAST-HEAD ANGLE. This consists in measuring, with a micrometer or sextant, the angle between the mast-head of the ship and the hammock netting, or some other fixed line on the ship's side, not the water-line, as that varies. The vertical circle of a theodolite being only marked to minutes, unless it be a much larger one than is generally available, is not sufficiently accurate for this. It is well to use two sextants to check errors, and read them both on and off the arc. The height of mast-head above the line must be accurately known to give a good result. Working out a right-angled triangle gives the distance required. A table should be formed of the distances corresponding to different angles of the masthead of the ship, as this will be frequently used in sounding banks. BASE BY ANGLE OP SHORT MEASURED LENGTH. Where the ship is not available, a base for a small plan can be obtained by measuring the angle between two well- defined marks placed in the ground at a carefully-measured distance apart, or that subtended by the ends of a long pole. This must also be done with the sextant, or micrometer. If staves in the ground are used, care must be taken that they are at right angles to the required base. Similarly, if a pole is used, care must be taken to hold it at right angles to the observer, which can be ensured, either by having a pointer nailed on to the centre of the pole projecting at right angles, and which must be directed towards the observer by the man holding the pole in both hands horizontal, or by simply waving the pole, held in this position, backwards and forwards gently, when the observer will register the largest angle he observes as the correct one. 62 HYDROGRAPHICAL SURVEYING. CHAP. in. The angle observed should not be smaller than 1, which with a distance of 20. feet, will give a base of over 1100 feet. It would be better, however, if practicable, to get a base by means of a longer distance, and larger angle than this, when a very trustworthy result will be obtained ; or to be content with a shorter base, and extend it by angles, as already described, to a longer working base. Measurements must be made on and off the arc, and it would be well to use more than one sextant. Small lengths of this kind may also be measured by a micro- meter, but a sextant will give just as good results, and is in a ship always handy. No appreciable error will be introduced by taking distance = length of pole X cot. angle. MEASURED BASE BY ROPE. Measuring by a rope is of course not accurate. It is diffi- cult to avoid stretching it more at one time than at another, and if it gets wet, it alters its length considerably. If measuring over ground where it is sure to get wet, it will be better to wet it well beforehand. Test it in that condi- tion, and keep it well wet all the time of measuring. BASE BY SOUND. This consists in counting the interval of time which elapses between the sight of the flash of a gun, and the arrival of the sound of the explosion, the gun being at one end of the required base, and the observer at the other. Final scale Recourse is had to this method of obtaining a base when deend on* no ^ at S 1 " 0111 ^ can be found on which to measure. Its accu- base by racy is not great by any means, but, if the final scale of the chart is to depend on astronomical positions, it is quite near enough for working out details such as heights, small parts measured with ten-foot pole, &c. Its value is much increased by observing from both ends CHAP. in. BASE BY SOUND. 63 which should always be done if possible, and a surveying Useful vessel should have two small brass Cohorn mortars supplied ts * for this purpose, which can be sent away in a boat, and tumbled overboard without damage. The ship is often used at one end of a base by sound, especially in work amongst small islands, and it is also neces- sary sometimes to have a boat at the other, but if at any rate one shore station can be obtained it will be better. If choice of direction can be had, measure with the wind across the base, as, though the error from increase and decrease of velocity is eliminated by measurement from both ends, the sound may be difficult to hear against the breeze, if at all strong. For either end choose positions for the hearers as much out of the wind as possible, as it is the whistling of it in the ears which disturbs the receiver more than anything. A base of three miles is a very good length, but the sur- veyor will generally not have much choice in this matter. Needless to say, on a calm day the sound will be heard farthest and easiest, but the choice of days is seldom possible in practice. If we waited for the best opportunity for every detail of a survey, it would never get on, and the utmost that can be done is, when there is alternative work for which the day or opportunity is more suited, to take that in hand. The guns from the two ends should be fired alternately, at Signal to regular intervals, and at some preconcerted signal, as dipping te made> from the ship a flag visible from both stations, which should be hoisted a minute or half a minute before as warning, or rehoisting a dipped flag steadily, the gun being fired as the flag reaches the masthead. It is distracting to the receiver to be waiting an indefinite period for the flash. A chronometer watch is the best, beating five ticks to the Watch to two seconds. An ordinary watch which beats nine ticks in e the same period, goes at such a pace as to be rather confusing, especially when not in practice, though, if the observer is used to the process, he will measure as accurately with an ordinary watch, and possibly more so. When awaiting the flash, hold the watch to the ear and 64 HYDROGRAPHICAL SURVEYING. CHAP. in. Prepara- count to yourself nought, nought, nought, &c., continually, counting. keeping time with the ticks ; you will then be ready to com- mence one, two, three, &c., as soon as you see the flash or smoke of the gun. If going to use a telescope to watch for the warning signal, tie the watch over the ear with a handkerchief, which will leave both hands free. Count only up to ten or twenty, and mark off each ten or twenty by putting down a finger of the unoccupied hand, or by some such means. Eepeti- If time allows, three or four measurements should be made each way, or more if they do not agree with one another. A signal must be arranged to ask for more than the number previously settled, if it be wanted. Calculat- In meaning the result, the arithmetical mean is not strictly mean! 16 correct, as the acceleration caused by travelling with the wind, is not so great as the retardation caused in the opposite direction, as in the latter case the disturbing cause has clearly acted for a longer period. The formula used is when T is the mean interval required, t the interval observed one way, t l the interval the other way. The mean interval thus found, multiplied into the velocity of sound for the temperature at the time, will give the re- quired distance. Velocity of The velocity of sound varies considerably, and an accurate sound. i aw f or a }i fa causes of variation has not yet been discovered. The main cause is, however, temperature, and for this it can, to a certain extent, be corrected. The most trustworthy experiments made, show'that sound travels about 1090 feet in a second of time, at the temperature of 32 Fahrenheit, and increases at the rate of 1*15 foot for each degree of temperature above the freezing-point, de- * See Appendix G. CHAP. in. BASE BY SOUND. 65 creasing in the same proportion for temperatures lower than 32. This is the only correction that can be made, and a base measured in the manner described, with these data, will give an approximation sufficiently near for all practical purposes. As an example, let us suppose A and B the two ends of Example the base to be measured. Sound, 6 y At A have been observed : 44 beats with watch beating 5 beats to 2 seconds 45 44 Mean 44*33 beats = 18*532 seconds. a, 81 beats with watch beating 9 beats to 2 seconds 82 83 Mean 82 beats = 18*222 seconds Mean at A = 18*376 seconds. At B have been observed : 85 beats with watch beating 9 beats to 2 seconds 87 88 Mean 86*66 beats = 19*258 seconds. 47 beats with watch beating 5 beats to 2 seconds 47 48 Mean 47*33 beats = 18*932 seconds. Mean at B = 19*095 seconds. Then working T = Al*_ t -p t we get T = 18*728 seconds. 66 HYDROGRAPHICAL SURVEYING. CHAP. in. Temperature is 80, at which velocity of sound is 1145*2 feet per second. This multiplied into the interval, gives 21448 feet for the length of our base. The temperature must be taken in the open with the thermometer shaded from the direct rays of the sun, but not in too cool a spot, or it will not give the true temperature of the free air. CHAPTEK IV. THE MAIN TKIANGULATION. THE main triangulation has been already denned as " the Definition, establishment by means of angles of a series of positions, from which and to which angles are afterwards taken, to fix the secondary points of the survey." All positions from which angles are taken, with the inten- Main sta- tion of fixing other objects, are called " stations," the symbol tions - for which is /\. but the ones with which we are immediately concerned, that is, the first and important positions, are dis- tinguished as "main stations," and these collectively form the " main triangulation." The first object of main stations is to see other main sta- tions, and with this in view their positions are chosen accord- ingly; but angles to everything useful, secondary stations, marks, &c., are, of course, taken as well. Secondary stations are those from which angles are taken secondary solely to fix the smaller marks and details, etc., of the survey. statl o ns - They will be nearer together than the main stations, and may often be perforce so placed as to be useless for any other object. All objects fixed and plotted on the skeleton chart are Points, known as "points." A "point" may be a main station, a secondary station, or simply a mark; but when fixed and plotted on the sheet, with the intention of using them in the survey, they are one and all spoken of by the generic term of " points." Main triangulations may be divided into two kinds : " cal- Varieties culated," in which the triangles are all worked out, so that F 2 68 HYDROGRAPHICAL SURVEYING. CHAP. iv. the length of any side, or the distance between any two main stations, can be found ; and " plotted," in which the main stations are simply the first points laid down on the paper. Calculated A calculated triangulation is used in any detailed survey, Triangula- . , f ., . tions. m plans, or whenever from circumstances it is convenient to have different parts of the same survey on separate sheets, which can therefore afterwards be put together in the engraving, without any fear of their not fitting into one another. Bases for plans, on a larger scale than the rest of the chart, can often be taken out of a calculated main triangulation without measuring separate small lengths. Plotted Plotted triangulations may further be subdivided into Tnangula- regu i ar a nd "irregular." A plotted regular triangulation will be when triangles have been obtained which could, if requisite, be calculated tri- gonometrically ; but, as frequently in marine surveys there is nothing to be gained by this, we content ourselves by only placing the triangles on the paper. It is more satisfactory that triangulation should be regular if possible, but it very much depends upon the nature of the coast to be surveyed, in what manner it can be carried out. Irregular In many extended surveys, where, for instance, the land is Triangula- low and densely wooded, or perhaps bordered by reefs to a tions. great distance from the shore, a regular triangulation is hardly possible, or would entail so much loss of time as would not justify its being undertaken. The main points must be plotted in these cases by all sorts of means. The ship enters largely into the scheme, and fre- quently boats also. Stations may have to be fixed solely by angles observed at them. True bearings are freely used in the construction of the chart, and any regular system of triangles disappears. A large proportion of existing charts have been, and many more are now being, constructed, by means of irregular plotting. CHAP. iv. THE MAIN TRIANGULATION. 69 A survey can often be commenced with a regular triangu- lation, when it will be found necessary, after having advanced a certain distance, to have recourse to irregular means to fix main stations. Here it is, when ordinary rules and systems fail, that the skill of the chief of the survey is shown in overcoming these difficulties in the readiest and best method, and these are the circumstances on which we can give the fewest hints. Such as we do mention will be found in the next chapter on Plotting. In the present one we shall confine ourselves to regular triangulations. The angles of the first few triangles in a triangulation, com- Great acou- menced on a measured base, will require to be extra-carefully j^ m observed. For, as we shall be increasing our distances in Triangles, each triangle, until sides long enough to carry on the trian- gulation without further enlargement are arrived at, any little error in an angle will give a larger error in the resulting side. These first triangles will nearly always require to be calcu- lated, as already remarked under the head of Bases, in order to get a side long enough to plot from, whatever it may be the intention to do afterwards. Although we are about to speak of triangulation from Triangula- shore stations, as carried on by means of the theodolite, sextant, as this instrument is always available in a surveying ship, it must be understood that, with care, an excellent triangu- lation may be obtained with that invaluable instrument, the sextant. The point on which care is principally needed, is that the Horizontal angles measured should be horizontal angles. A practised ^fh 68 surveyor will usually be able to note some small natural mark, Bwtant. directly above or below the object whose angle is required, and at his own level, to which to measure his angle, and in most cases of using the sextant this will give a sufficiently near result, but if forced to use the sextant for triangulation, another means may be used. From the end of a longish pole (boat-hook staff will do), 70 HYDROGRAPHICAL SURVEYING. CHAP. iv. planted at a slight angle from perpendicular, let a plumb line fall, and getting the object transit one point in the line, the angle can be taken to any other part of it. The plumb line must not be too close to the observer, or it will be difficult to keep the transit on, and parallax will creep in. It is a question of circumstances as to whether the main triangulation is to be carried on by itself first of all, or in combination with the secondary stations and marks. This in noways affects the principle of the work, but only the detail of what is done when the angles at the main stations are observed. The main triangles should be as large as possible. The fewer triangles there are, the fewer are the chances of errors of observation. MAKING A MAIN STATION. Choice of Observing angles at a station is technically called " making " it. Let us suppose a surveyor making a first station, probably one of the base stations. He has been previously furnished with a list of the main stations visible from him, and has been told how many times his angles to them are to be repeated. He has also received instructions about the secondary stations and minor marks, if any have been selected and marked. Having levelled the theodolite, the first thing is the choice of an object from which to measure all the angles, which is called the zero. A zero should be, if possible, another main station. It must be at some distance, but not so far as to be easily ob- scured on a hazy day ; well defined ; so placed that the rays of the sun, when it moves from the position in which it happens to be when the station is commenced, will not ob- literate it. It should be a fixed object, i.e. not likely to be removed, or to tumble down, and not so high as to be covered with clouds, as a mountain peak. A great deal of trouble is given when a zero has to be CHAP. iv. MAKING A MAIN STATION. 71 changed, or when on a subsequent visit to a station the same zero cannot be had ; so care must be taken on the above-men- tioned points to prevent this happening. The bearing of the zero by the theodolite compass should always be entered in the book. The zero fixed upon, and the theodolite directed upon it, observe observe the main angles, or those to the main stations, first, JJ"| eg repeating them the required number of times, by either of the first, two methods described under " Theodolite." These completed, observe the secondary stations a sufficient number of times, as well as all marks and conspicuous objects. In most instances a sketch will be also necessary, on which the angles to conspicuous objects, tangents, &c., will then be recorded, instead of in the book. All angles should be read twice, in order to prevent mistakes ; ^Repetition but to ensure accuracy when required, the angles must be re- An & leSt peated on different parts of the circular arc, for the following reasons : A theodolite, however well turned out, is seldom exactly centred, hence arises error; as no matter how uniform the graduation of the circular arc may be, a slight deviation of the axis from true centring will give a difference of reading for an angle on different parts of the arc. The sum of the readings of the two verniers is supposed to correct errors of centring, but for remarks on this, see " Theodolite." The reading itself of an angle can never be considered as perfectly correct. Slight parallax frequently exists, especially when an instrument has been some time at work, and is getting worn. In small theodolites the marking of vernier and arc at any given angle will often not coincide exactly, and judgment may assign the wrong reading. By multiplying readings, then, a mean will be obtained which will to a great extent eliminate these errors, and this must always be done in observing main angles. Excepting for main angles, forms ruled in the angle book HYDROGRAPHICAL SURVEYING. CHAP, iv are unnecessary, and in this case the form is simple, consisting of columns to keep the figures separate, as under. I? July 4th, 1881, at Pagoda A, Theod. 77. Compari- son of Methods. A 8 ' L Observed. Difference. Patero A O 1 II 360 00 00 o / // Mango A (flash) 25 14 30 25 14 30 50 29 30 25 15 00 75 44 00 14 30 100 59 00 15 00 Mean 25 14 45 T? July 4th, 1881, at Pagoda A. Patero A, Theod. 77. e Prince A Flag A Snow A o 360 O 1 II 24 18 00 o / n 29 10 30 / // 48 26 00 Z. 0. K. 100 124 19 00 129 11 00 148 27 00 Z. 0. K. 200 20 00 10 30 27 00 Z. 0. K. 300 Means 19 00 11 00 27 00 Z. 0. K. 24 19 00 29 10 45 48 26 45 The first of these forms is adapted for the observation of main angles by repeating round and round singly ; which is done when a solitary angle is required to be observed accu- rately. The second is for ordinary main angles. This method saves much time when there are a number of angles required, and is as correct as is generally necessary. The weak point of the first method is that the zero cannot be referred to, but, as only one angle is taken each time, a theodolite must be very much out of order to introduce error. If the angle to be observed is small, this method will not CHAP. iv. MAKING A MAIN STATION. 73 answer the purpose, as the theodolite will only be rotated through a small part of the circle, unless an inconveniently large number of repetitions be made. The weak point of the second method is that any slight error in setting or reading the zero, affects every station ob- served ; whereas in the other, the vernier being once set at the commencement, is afterwards read only. By either method, the observer will see if his different ob- servations of each angle are agreeing together, and can take more if requisite. In all observations of angles with the theodolite, (except the Verifying case referred to above,) the zero must be looked at from time to time, and invariably at the conclusion of the set of angles, to make certain that the direction of the instrument has not changed by any unnoticed touch or shock. On every occasion of doing this it must be noted in the book, so as to know, in the event of the zero presently being discovered to be wrong, how far back the angles must be recommenced. A common form of notation of this is, Z.O.K., or Z.K., for zero correct. If the zero is found continually getting displaced without Defects of any apparent cause, something is loose, and this must be ment _ " looked to at once, or nothing will be satisfactory. The parts most liable to go wrong have been mentioned under the head of " Theodolite." If using a heliostat, it must be placed in front of the theo- Arrange- dolite, in the direction of the station to which you mean to using flash. When the stations are distant one from the other, it is Heliostat - desirable to arrange who shall flash first ; the receiver of the flash, say at A from B, then takes his angles to it, and does not direct his flash to B until he has got the requisite number of repetitions. When he does flash to B, the latter will know A has done with him, and can direct his flash to some other station, while he observes A. When B in turn has finished with A, he must give the latter another flash to acquaint him with the fact. A's turning off his flash will show B he understands. As already remarked, the amount of time saved when the Heliostat invalu- able. 74 HYDROGRAPHICAL SURVEYING. CHAP. iv. sun is visible, by the use of a heliostat, is incalculable. It is useful for long distances, and short also, and on all sorts of occasions, and is, in fact, one of the surveyor's greatest friends. FALSE STATION. It will often happen that a beacon having been erected, the theodolite cannot be placed exactly on the spot, at any rate without a great deal of trouble ; or if a building or tree has been selected as a station, that the observer finds on going there, that he has to make his station on one side of it in order to see what he wants, or has to make a supplementary station to see a few objects obscured by the building, &c. This is called " False Station," and if the object is already plotted, or it is desirable to plot it instead of the actual theodolite spot, the angles taken there must be corrected for the distance the theodolite was from such object. The correction will vary according to the direction of the objects with regard to the true station, as the figures annexed will show. FIG 8. In Fig. 8 let A be the true station at which angles are required; B the false station; D, E, F, H objects so placed as to illustrate all positions of false and true stations with CHAP. iv. FALSE STATION. 75 regard to them. We have observed at B the angles to D, E, F, H, and A, and measured the distance BA. Firstly. Required the angle E A D. Produce B A towards C and Z. IsrowEAC = andDAC = Subtracting, we have or EAD = EBD+(BEA-BDA). Secondly. Required the angle E A F Here ZAE=ZBE-BEA and ZAF = ZB.F-BFA. Adding, we get ZAE+ZAF=Z BExZBF- (BEA + BFA) or EAF = EBF-(BEA + BFA). Thirdly. Required the angle D A H. Here CAH=CBH+BHA and CAD = CBD + BDA. Adding, we get D AH = DBH + (B H A + BD A). These small angles, B D A, B E A, &c., the angles subtended by the distance between true and false station at each object observed, must be either calculated in each triangle, having two sides and the included angle (for the rough distances B D, BE, &c., will answer the purpose), or else, which is simpler, have a table* made of the angles which are sub- tended by different lengths at different distances, and take the required angles out, thus, Let us suppose the theodolite angle in our book correspond- Calcuia- ing to A is 60, D 160, and E 220. A B is 12 feet. E B is Jjjg \\ miles, and B D 2 miles, measured roughly on the sheet. Table. Required B E A by the table. It will be evident that the angle B E A is that subtended by a chord drawn across to E A from B. This chord we get near enough by considering B N as at right angles to both E B * Appendix, Table P. HYDROGRAPHICAL SURVEYING. CHAP. iv. Arrange- ments for working by the Table. and E A, and looking out in the traverse table with B A, or 12 feet, as a distance, and B A JST or 20 (180 160) as a course, and taking the departure for the length of B N, which in this case is 4 1 feet. We then turn to our table, and see that four feet at 1 J miles subtends 1'31", which is the angle B E A. In a similar manner we can deduce any of the required angles, quite near enough for ordinary purposes. Now this process becomes far simpler, and much time is save( ^> ^> ^ n making a false station, a zero for the theodolite is chosen in a direction exactly opposite to the true station, as, for example, in our figure at Z ; for then each angle taken can easily be corrected separately for the error of the false station, and the true angle entered in the book. Difficulties as to whether the ultimate correction is -f- or will be avoided, as in correcting the angles the error is subtracted from all theodolite angles up to 180, and added to all angles between 180 and 360. Thus, in the case as in the figure above, the angles will stand in the book Object. Observed Angle. Correction. Angle at true /\ Zero, Z o 360 i a 00 o i n 360 00 00 F .. 50 2 08 49 57 52 H .. 130 1 42 129 58 48 D .. 280 3 23 280 03 23 E .. 340 1 31 340 01 31 In using the traverse table, take for the course Up to 90 the observed theodolite angle itself Between 90 and 180 ... 180 the observed angle 180 270 ... observed angle 180 270 360 ... 360 observed angle and the departure is looked out in each instance. The table of angles subtended by different lengths is useful CHAP. iv. FALSE STATION. 77 for other purposes. As when an angle is taken to an object, Table and it is afterwards decided to plot a station made near that object instead of the object itself, the angles to the station can be corrected by it, in precisely the same manner as described above, the distances and direction of the station from the object being known. Distances or lengths, greater than those included in the Extension table, can be got by multiplication or division. Thus, if the angle of 18 feet at 5 miles is required, it is double that of 9 feet. Again, if the angle of 12 feet at 10 miles is wanted, it is half that at 5 miles. SKETCH. A sketch taken from a station is made with the object of more easily identifying details to which it is necessary to take angles. By having a view of hills, islands, houses, trees, &c., from two or three stations, they can, if fairly placed in their proper positions, be easily recognised in the different sketches when plotting. No description in the angle book will do this so well, unless, of course, there is something very remarkable in the object, but even then the position of it as shown in the sketch will assist materially to prevent mis- takes, and a curt description is also written against it on the sketch. Sketching to this extent is within anybody's reach. A fairly correct outline is all that is absolutely necessary, and a very little practice will enable the least likely draughtsman to make a sufficient sketch for practical purposes. It is well for a beginner to commence by taking some checking rough angles to check his scale, or, until he is used to it, he will probably have one part of his view two or three times as big as the other, which is confusing afterwards, although the proper angles will be written against the prominent objects when the sketch is finished. Always put the most distant outline on the paper first, as Preserva- it is far easier to keep the scale uniform if this is done. scale* 78 HYDROGRAPHICAL SURVEYING. CHAP. iv. Begin on the extreme left of your view, or if it is an all round view, choose a point, in the direction least required, to be the left, and always work to the right. Useful If the sketch is too long for one double page of the sketch sketcMn book, when the right-hand end of it is reached, turn over, and turn one or two inches of the last page down, so as to show on the fresh page, this will give a commencement for the part to follow, and the sketch will be continuous. Commence by settling whereabouts on the paper some two well defined points of the distance are to be, and use these after as a scale from which to measure by eye the proper position of everything else. If taking angles to assist correct drawing, as suggested above, a scale for the sketch must be decided on, say about one third of an inch to a degree, but this will vary according to the complication of the sketch. If no divided scale is at hand, mark the edge of a strip of paper by eye, which will answer the purpose perfectly. Take an angle from some definite point of the distance on the extreme left, to some other, say about 20 to its right. Make a dot for the first object, lay the scale or strip of paper on the sketch, and dot again at the proper number of degrees, and, at the proper height, with regard to difference of altitude, for the second object. Other angles can be taken to other objects between these, and the view sketched in between these dots, commencing as already said with the outline most distant, and therefore highest in the sketch. In sketching for this purpose, it is well to rather exaggerate the height of objects, as, where there are hills, range upon range, or many objects, as houses, trees, &c., at different altitudes, they will get so crowded up as to make the sketch difficult to decipher, unless this course is adopted. Important The great thing in a sketch is to place objects fairly cor- observe rec tly with regard to each other horizontally considered ; e.g., if there is a hill, with a point nearly underneath it, take care that the latter is drawn on the correct side of the hill, right or left. Nothing is more calculated to confuse anybody plot- F Rough F I Sketch method of marking LIGHTHOUSE J U L es, elevations, depressions, &c., and also mode of continuous panorama. UNIVERSITY) ^IFC CHAP. IV. PREPARATION FOR TRIANGULATION. ting angles from a sketch, than to find that an object drawn apparently to one side of another object, has an angle which shows it should have been on the other side. Doubt is at once thrown on the angle, when it is probably the drawing of the sketch which is incorrect. When the sketch is finished, resume the theodolite, using Desorip- the same zero, and mark the angles on the sketch itself, o^cta ii noting what the object is, when it may be doubtful, as for Sketch, instance Chimney of red house, Eight of two fir trees, Big white boulder, &c. See example of sketch attached. PREPARATION FOR CALCULATING THE TRIANGULATION. It is well that a true bearing be obtained between two A bearing distant stations, before plotting ; but the method of doing this fa? orien- will be described under observations, and as far as absolute tation of Chart. necessity goes, a good compass bearing from a shore station is quite sufficient to begin on. The bearing is only wanted to plant the meridian fairly square on the paper, and the com- pass bearing will give us this, near enough to be able to lay off any bearings which may be taken in the course of mapping the detail. The compass will never be used in any of the important part of the chart, unless our survey partakes of the nature of a sketch or running survey. If, however, regular triangulation is likely to fail, true bearings in the course of the work may be necessary to carry it on, and in this case we must begin with a careful true bearing. In preparing the triangles for working, they will of course Prepara- never be found exactly correct, i.e. the three observed angles Triangles. will be either more or less than 180. In dealing with this theoretically, the sum of the three Spherical theodolite angles taken at the corners of any triangle will be greater than 180, in consequence of each angle observed being in a different plane. This is known as the spherical excess, and in extended triangulations for topographical pur- 80 HYDROGRAPHICAL SURVEYING. CHAP. iv. poses, as the survey of India, &c., must be taken into account. For practical nautical work we need not regard it, as our instruments are not large enough to measure angles so exactly, nor is our work of sufficient extent. Correcting In dealing with the amount the triangle is in error, for the Triangles three angles of the triangle must be corrected to make the precise 180, before using them for calculation, circumstances must guide its distribution among the angles. An angle observed with a large theodolite should have more value given to it than others. One station may have been more exposed to the wind than others, which would depreciate the value of the angles observed there. Without any indications of this kind to guide, it is as well to divide the error equally among the angles ; but it must be remembered, that an alteration in the small angle will make more difference in the resulting position than in either of the other two, so that if this angle at all approaches the limit which should be used for a receiving angle (30) it is perhaps well to put the smallest amount of change into it, but it is of course impossible to guess where the error is. If the angles have been repeated often enough, the resulting error any way will be very small. Error ad- No ru l e can be laid down with regard to the amount of Triangles, deviation from the 180 that can be admitted, it so much depends on the degree of accuracy required, but in an ordinary theodolite survey the error should not be more than three minutes, and ought to be under two, working with five- inch theodolites, and repeating the angles three times if satis- factory, or more if they vary much. In the first few triangles, the error should not be more than one minute. Calcula- Having corrected the triangles we come to the calculation. The working out of the triangulation is the very simple affair of plane triangles which every naval officer understands. The rule of sines, and the rule to find the third side,* when * The rule where sines only are involved must be used. CHAP. iv. CONVERGENCY OF THE MERIDIANS. 8 1 two sides and the included angle are given, are all that are required. Logarithms of all angles must be taken out to seconds, Loga- so that the possession of tables giving these for every second ^J^ of arc, will save much time and chance of mistake. Into the final calculation of an extended calculated trian- Conver- gulation some other considerations enter. genoy. The actual working of the triangles will be the same ; but here we want the bearing of every side, as well as the distance, and the " convergency of the meridians " must be considered. This convergency will be explained before pro- ceeding further. * CONVERGENCY OF THE MERIDIANS. The true bearing of any two points on the earth, taken one from the other, in both directions, will be found to differ by a quantity which is called the convergency, and varies with the latitude, distance apart, and position of the points 1 in bearing, or in other words, with latitude and departure. Thus, if R and L are two stations lying roughly N.E. and niustra- S.W. of one another, R being nearest the pole, in this case the on North Pole, the true bearing of L from R will be found to be rcy. a greater number of degrees and minutes as measured from the meridian than the reverse bearing of R from L. This results from the form of the earth. The true bearing Expiana- of one position from another, is the angle which the arc of a faon ' great circle drawn between the two positions makes with the meridian of the observing position. As meridians are not parallel, but converge at the poles, the great circle will cut' each meridian it passes at a different angle, the amount of difference, for equal meridians, depending on the latitude. To further the comprehension of this, let us consider the method of projection of the sphere used when graduating a map, made from the original data of angles and measure- ments. It will be evident to any one who considers the subject G 82 HYDROGRAPHICAL SURVEYING. CHAP, iv Projections that as our globe is a sphere, (speaking roughly,) a portion of Sphere. ^ s sur ^ ace cannot "be shown on a flat piece of paper without distortion, more or less, according to the extent so shown. There are a variety of methods used to delineate a portion of the earth's surface on a map, which are called " projec- FIGr 10 tions." Into this variety it is not proposed here to enter, as but one can be used when actually making a survey, which is the " Gnomonic Projection." Gnomonio This projection is the only one on which great circles are s hown as straight lines. As it is on the rejection. CHAP. iv. CONVERGENCY OF THE MERIDIANS. 83 chord of a great circle that we see one object from another, it is evident, that in graduating a map on which we have laid down, or are going to lay down, one position from another by drawing straight lines, we must use this projection. A chart on the Gnomonic Projection is supposed to be drawn on a flat surface laid against the earth, touching it at the central point of the flat surface, and there only. From the centre of the earth lines are supposed to be drawn, passing through the different points to be shown on the map, until they pierce the flat surface. The positions so indicated on the upper side of the flat surface, are those corresponding to the points required. Here, in Fig. 10, P Q S is the globe, and A B C D a flat surface laid against it, touching at the point J, the centre of the flat surface, the under side of which is shown. P is the pole. M F are points taken on the same meridian as J. Imaginary lines drawn from the centre of the earth through these points will touch the flat surface in N" and G, and the line joining them, the central meridian of the chart, will be a straight one. K, another point on the globe east of the central meridian, will be projected at L, by the same method of drawing a line from the centre through K. X is the point in which the axis of the earth, produced, meets the central meridian of the chart also produced. Let us again look at our flat surface, which we may now call the chart, from a different point of view, i.e. from a point in the extension of the line joining the centre of the earth and the central point of the chart. In Fig. 11 (p. 84), A B C D is the chart as before, touching the spherical earth at the central point J. G and K are the positions on the chart of the points on the earth's surface, F and M in the other figure. G J N" is then the central meridian of the chart. X is, as before, the point where the extension of this meridian meets the extended axis of the earth. L is the position on our chart of K (see other figure). K is the position of a similar point, invisible in first figure, being on the other side of the earth. Meridians G 2 8 4 HYDROGRAPHICAL SURVEYING. CHAP. iv. passing through L and E are projected on the chart by the same method as before, i.e. by drawing imaginary lines from the centre of the earth through different points in the re- quired meridian ; they will be found to lie as T L, R 0, and their extensions will also pass through X, making an angle R X L, which is the Convergency of the meridians ; and this FIG II. will be seen at once to be equal to the difference of the reverse bearings of R and L, for, ^ ORL = OXL-f RLX or OXL=ORL-RLX i.e. Convergency = Bearing of L from R - Bearing of R from L. A little consideration of this last figure will show, that, the further towards the pole the central point J is, the greater CHAP. iv. CONVERGENCY OF THE MERIDIANS. 85 will be the convergency of two meridians a fixed number of Conver- degrees apart ; that when the pole P and J coincide, the ff^uaj 1 meridians will radiate over the chart from that centre, and *<> r a*d the convergency will equal the distance between the dtfTiong. meridians ; and that when J is on the equator, the meridians at Poles> will be parallel, and convergency will be nothing. Parallels of latitude will appear on the chart as curves, Parallels, concave towards the poles, and cutting each meridian at right angles. The equator being a great circle will be a straight line, and, generally, the further from the equator, i.e. the higher the latitude, the greater will be the degree of curvature in the parallels. More consideration will show, that, the farther a part of Distortion, the flat surface is from the surface of the earth, the greater will be the distortion of the positions resulting from this method of delineating the globe; or in other words, that the distortion increases from the centre of a gnomonic chart, and will become very considerable towards the edges, if a. large area of the earth is attempted to be shown on a flat surface. But in practice, a marine survey does not extend over a sufficient area to make this distortion in any way apparent. Our diagrams are of course much exaggerated in this respect. It will be understood that the convergency is an actual fact, and does not result merely from the method employed in this projection. We have only considered it in connection with the projection, as it is thought that by so doing the nature of the convergency becomes more plainly apparent. The mean of the two reverse bearings, or either one of Mercato- them, plus or minus half the convergency, will give the Mercatorial Bearing, so called from being the bearing which each station will be from the other in a Mercator's chart, where, the meridians being all parallel, the line joining the stations will cut them at the same angle, this angle being also the one at which the line on our gnomonic chart will cut a meridian midway between the stations. The actual observed bearing of a distant object, if pro- 86 HYDROGRAPHICAL SURVEYING. CHAP. iv. tracted on a Mercator's Chart, will not pass through its position, in consequence of the existence of convergency. Mercator's charts are generally on such a small scale that, for navigating purposes, the error of taking the bearing swallows up the error introduced by not allowing for. convergency. The formula for Convergency is Conver- Tangent Convergency = Tan departure X Tan Mid. lat. (1) fancy omul. Or in anything but high latitude, or when the departure is great, it is correct enough to say Convergency (in mins.) = dep. (in mins) X Tan Mid. lat. (2) which can be converted into Convergency = d. long x Sin Mid. lat (3) = dist. x Sin Merc. Bearing x Tan Mid. lat. (4) any of which can be used as convenient. The proof of the formula is given in the Appendix A. Conver- The convergency can also be found when the latitudes of P noy and difference of longitude between the two stations is Spherical known, by working out the spherical triangle, with the pole, and the two stations, as the three points. Here we have the two colatitudes as the sides, containing the difference of longitude as the polar angle, to find the other two angles, which will be the bearings of each station from the other. The difference of these will be, as before, the convergency.* CALCULATING- THE TRIANGULATION. We now resume our remarks on working out a calculated main triangulation. All sides being calculated by the ordinary method of plane triangles, we now want the bearing, the mercatorial bearing, of each side, or, at any rate, a consider- able number of them, in order that we can take any triangles or sides to work up details on, on a separate sheet, and that such sheet may be complete in itself as to bearing, distance, and position, with regard to other portions of the main triangulation. * See following article for application of Convergency. CHAP. iv. CALCULATING THE TRIANGULATION. 87 We will take as an example the following : FIG 12. Lat. A, 49 30' 24" N. True bearing observed B from A. 1ST. 69 05' 00" W. Angles Observed and as Corrected. Observed. Corrected. A .. 86 06 35 86 06 19 B .. 38 52 02 38 51 47 H .. 55 02 04 55 01 54 180 00 41 180 00 00 B .. 59 33 10 59 33 27 H .. 80 27 51 80 28 09 C .. 39 58 14 39 58 24 179 59 15 180 00 00 C .. 56 58 08 56 58 44 H .. 46 26 22 46 26 58 D .. 76 33 43 76 34 18 179 58 13 180 00 00 C .. 96 50 21 96 50 27 D .. 11 17 06 11 17 13 F .. 71 52 13 71 52 20 179 59 40 180 00 00 B .. 72 40 17 72 40 31 C .. 62 46 39 62 46 53 E .. 44 32 22 44 32 36 179 59 18 180 00 00 88 HYDROGRAPHICAL SURVEYING. CHAP. iv. Example We have in the annexed figure (12) a portion of a triangu- of Calcu- lation, where all the angles have been observed at each station. lated Tri- angula- The latitude of A is known, A B is the original long side obtained by extending the base, and the true bearing of B and A have been taken from one another, from which we have deduced a mean bearing of B from A with which we intend to work. The length of each side has been calculated by ordinary trigonometry. We now want to calculate the bearings of the different sides, so as to be able to break up the triangulation into different sheets. We shall want also the latitude, and difference of longitude from A, of F, which is a station in a plan on a large scale we have made. For the purposes of this plan we have obtained the side F C in the triangulation, which will serve as our base instead of measuring another. We shall commence by calculating the convergency for ten miles of departure at the average latitude of the chart, as we shall want it directly. In this case we find that Convergency for 10' of departure=ll f> 92 Or for each mile of departure = 1 ''2. We then find approximate latitude of B by the formula Diff. lat. = AB x Cos rough mercatorial bearing. We obtain the bearing, near enough for this purpose, by finding the rough convergency and applying half of it to the observed bearing of B from A, thus Take departure from the traverse table, in this instance 9'5. Multiply it by the convergency for a mile, just found to be 1*2, which gives us H''4 as the rough convergency. Adding half of this to the bearing of B from A, we get rough mercatorial bearing K 69 11' W., and working out the difference of latitude, we find it to be 3' 38", which gives for the latitude of B, 49 34' 02", and for middle latitude, 49 32' 13". Then convergency = dist. X Sin mere, bearing X tan mid. lat. Using the rough bearing just found, we get Convergency for A B = 11' 13"-8. CHAP. iv. CALCULATING THE TRIANGULATION. 89 This convergency, and half of it, added respectively to the bearing of B from A, will give the reverse bearing of A from B, and the mercatorial bearing, thus, BfromA = K6905'00"W. A B = S. 69 16 14 E. Mercatorial bearing g* 69 10 37 j,' If this differs much from the rough mercatorial bearing, we must recalculate the latitude of B before proceeding further, but this should not be necessary. Then to calculate bearing of B E, we have the bearing of A from B, just found, to start from. * . Adding the three angles, A B H, H B C, C B E, to it, we shall get the bearing of E from B. The convergency for BE is calculated in the same manner as above, and we shall then have mercatorial bearing of B E. Thus :- A from B .... S. 69 16' 14" E. ABH 38 51 47 HBG 59 33 27 CBE . 72 40 31 EfromB S. 240 21 59 E. Or .... N. 60 21 59 W. J convergency . > . 12 26 Mercatorial bearing N. AA Q/I' o "W. f T> T O "'' "^ "" ~f? Ol X) Jli . . . . b. Jl. In like manner we must calculate the mercatorial bearing Appiica- of all the sides we require* remembering that of the reverse !? on * COHV6T" bearings, the bearing of the station nearest the pole from the gency. one farthest from the pole, is the smallest. In this case then, being in the northern hemisphere, where a bearing is measured from the north point, the convergency is added to obtain the reverse bearing. Having obtained the bearing of each side, we can calculate 90 HYDROGRAPHICAL SURVEYING. CHAP. iv. the relative position of any two stations by working out the traverse between them. Thus to get position of F we have, A B .... K 69 10' 37" W ..... 10-2468 miles. B .... N. 12 20 56 E ..... 191502 C F . . . . N. 1 24 17 W ..... 2-5691 From which we calculate difference of latitude and departure in the ordinary manner. We thus get the mercatorial bearing of AF, 1ST. 12 32' 45" W., and distance 25'5269 miles. Caionia- it will be understood that it is by no means necessary to Triangu- work out all the triangulation as just described when com- menc ^ n g ^ ne plotting. All that is then required is as long a necessary side as we can get on which to begin. The main triangulation survey! 1 can be calculated afterwards, and in many instances must be, as the whole of the angles will not be obtained till later on. In the majority of nautical surveys it will not be necessary to calculate any triangulation at all. Correcting In the example of triangulation we have given we have tioiTfor *" supposed ourselves to be working from a measured base. If error of the survey is extensive, the ultimate scale of the chart will base and depend upon the astronomical positions. It is very unlikely bearing. tnat wnen these are obtained, the distance between the ex- treme points depending upon them will agree exactly with that deduced from the short side, and therefore all the sides will want correction in probably both bearing and distance. The readiest way of doing this is to get a proportion between the two total distances, as found by the triangula- tion and by the astronomical positions respectively, in the shape of a logarithm, and multiply each side found by it ? which will give the true value as dependent on observations. The bearing of every side will have to be corrected by the difference of the bearings of the extreme points. Thus referring again to our example, (which, for the sake of brevity, we have confined to only a few sides,) let us suppose we find by observations that A F is N. 12 36' W. 26'248 miles. CHAP. iv. CALCULATING THE TRIANGULATION. 91 Dividing this distance by the former one, we get a propor- tion whose logarithm is O012097. Adding this to the log of each side required to be corrected will give us the true value. The difference of bearing is 3' 15" more to the westward. The bearing of each side will then have to be corrected by this amount. Thus the bearing of A B will stand K 69 13' 52" W. In a case of this kind the result of both triangulation and astronomical observations would be transmitted home, as their concurrence or otherwise -will form a good test of the value of the work generally. It will be observed that we have a triangle CDF with a Triangles very small angle. This not being a receiving angle does not JJUJjJ" 1 * 11 * matter in the least. We are obtaining the position of F from angles not C and D, which are already fixed, and the angle of intersec- ^condi- tion at F being nearly a right angle, the change of position in tioned, F, resulting from a small error in the angle at either C or D, will be as small as is possible, and much less than if the angle at C being the same, that at D was 60, which would result in the intersection at F being more acute, and any error would consequently change the position of F to a greater degree. If we were obtaining D from C and F, such a small angle would not be admissible for a moment, as it is evident that any small error at C or F would result in a great change of position in D. It would be awkward and inconvenient to have many such triangles in the main framework of the triangulation, as "the small side is of no use in carrying on the chain, and we should be forced to multiply triangles in consequence ; but we are, notwithstanding, sometimes obliged to include some such in our work, from the lie of the land and other causes, and as long as we use them as in the example they will not affect the result, as far as chance of accuracy goes, and should not be under these circumstances considered as " ill-con- ditioned." In working out the diff. lat. and diff. long, of two posi- 92 HYDROGRAPHICAL SURVEYING. CHAP. iv. Correction tions from the triangulation geodetically, we have been Spheroid t rea ti n g t ne earth as a sphere. This is not strictly the case, as the form of our globe is that of an oblate spheroid ; but the error introduced by assuming it to be a sphere is very small, and can generally be disregarded in hydrographical work, as being swallowed up in the larger errors incident on imperfect triangulation. When, however, a triangulation has been carefully done, and we wish to get the difference of longitude as near as we can, either for the scale of the chart, or for purposes of com- parison with that deduced from the astronomical positions, the necessary correction for the spheroid may be applied. This correction is 2 Cos 2 Mid. lat. X compression. The compression of the earth is the proportion that the difference of the equatorial and polar diameters bears to the diameter, and can be taken as -i The formula for correction for a given difference of longitude will then stand, ,__ Cos 2 Mid. lat. Correction = diff. long. 15Q~~ This is subtractive from the calculated difference of longitude by the triangulation. In the latitude of 20, this correction for a difference of longitude of 100', amounts to 35", as will be seen by the following example : Example. In latitude 20 the departure deduced from a triangulation was found to be 94 r required true difference of longitude. Dep 1-973128 Sec. lat. 0-027014 Spherical d. long 2-000142 .. .. 100' -0327 Cos 2 lat. , 9-945972 11-946114 150 2-176091 Keduction 1-770023 -0-5889 True diff. long. 99 -4438' or 1 39' 26" -6 CHAP. iv. CALCULATING THE TRIANGULATION. 93 The true difference of longitude can also be calculated from the tables of lengths of a minute of latitude and longi- tude in the Appendix M as follows : No. of feet in minute of Lat. True dm. long. = dep. T? f f *. 7 T^ No. of feet in minute of Long- Working out the above example this way, we have Dep. . . 6053 . . 5722 . . True d. long .. 1-973128 ,. 3-781971 5-755099 .. 3-757548 .. 1-997551 99' -44 or 1*39' 26" -4 which gives the same result as the other method. 94 HYDROGRAPHICAL SURVEYING. CHAP. v. CHAPTEE V. PLOTTING. Subjects THIS chapter will comprise, besides a description of the in chapter. m ^thod of placing the points on the paper, which is more generally understood by the term " plotting," an account of the different manners in which those points may be obtained, other than by a regular chain of triangles. This is, perhaps, more correctly, a part of triangulation, and for some reasons should be described under that article, but it is thought that it will tend to clearness of comprehension, if it is taken in connection with the mode of laying down the points as obtained, as it is not easy to separate the two steps in many instances. In discussing the general question of Plotting, therefore, we will first take the placing of the points of an ordinary triangulated survey on paper, and then consider some other systems to be adopted when regular triangulation fails us. Great care Plotting the points is a most important operation, and one requisite . . inPiotting, requiring great care. No matter on what scale, or on what system, a survey is being made, equal pains must be bestowed on plotting the points. Indeed, it may almost be said that in proportion as the elements of a survey approach to the least accurate form, viz., a sketch survey, so does the necessity for careful plot- ting increase, as the numerous checks, which in a detailed triangulation will instantly make any error in plotting apparent, will be more or less absent in proportion to the departure from such regular triangulation ; and not only will the minor details of such a chart be inaccurate, which we CHAP. v. PLOTTING. 95 expect, but the main and prominent points may be unneces- sarily out of place unless care is bestowed on the plotting. Before describing in detail the different methods in plot- Plotting ting, it is necessary to understand the system of laying down by ohordSi angles by chords, and why this is done. It will easily be seen that, where lines are to be drawn of considerable length, a protractor whose radius will be much shorter than the desired line, can hardly give the angle exact enough to ensure the extremity of the line being precisely placed ; for the straight-edge, perhaps six feet in length, by which the required line is to be drawn, will only be directed by two pricks in the paper, which, with the largest pro- tractor, will not be more than eighteen inches apart. How- ever exactly the protractor has been placed, and the pricks made, the mere laying of the straight-edge so that the line drawn will pass precisely through the centre of the two FIG 13. pricks near together, is almost an impossibility, and an error, quite imperceptible at the pricks, will be very appreciable at the end of the straight-edge. For this reason, we want our directing prick as far along the straight-edge as we can get it. We accomplish this by using chords. If two radii of a circle of given length of radius, contain- ing between them a given angle 0, be drawn to cut the circumference of the circle, the chord to the arc of the Q circumference thus cut off is 2 radius Sin - * A Thus, by reversing this and describing from the centre A, Fig. 13, an arc of a circle of any radius, drawing the line * Vide proof of this rule in Appendix (X 96 HYDROGRAPHICAL SURVEYING. CHAP. v. A C, and measuring the chord C B (which will be done in practice by describing a short arc of a circle with the required chord as radius, from the centre C), the point B, where the chord cuts the circumference (or the two arcs intersect) joined to A, will give the required angle 0. Table of A table of chords for a radius of 10 inches is given in Ap- Cnords. pendix,* which saves much \irne and chance of errors, as the chord to the angle required can be taken from the table, and multiplied by the radius with which it is meant to lay off the angle, divided by ten ; but in case this is not at hand, we must calculate our own chords. Caiculat- Tables of natural sines are not included in Inman's, the 8t tables generally in use at sea, and logarithms of sines are in that work only given for every fifteen seconds, and we may want to take the angles out exactly. Moreover, by using the logsine, three logarithms will have to be taken out, and the process is somewhat longer. It is simpler, therefore, to use the table of natural versines, which are given in Inman to seconds. 9 B As sin. _ = versine (90 + - ) 1, our required chord 2t 2> will be 2 radius (vers. (90 + - ) - 1.) 2t Versines are given for a radius of 1,000,000, so we have to divide the versine taken out by that number. This reduces the rule in practice to this. Look out the * natural versine of 90 + half the required angle, leaving out the left hand figure 1, and putting a decimal point before the remaining six figures. Multiply this number by twice the radius, and the result will be the chord required. Example. Let us take now an example in practice. At A, Fig. 14, the angle between B and C is 35 14' 30". The line A L from A passing through B is already drawn. We want to lay off this angle, and requiring accuracy, we take a long radius, i.e. 45 in. * Appendix L. CHAP. v. PLOTTING. 97 Forty-five inches must be carefully measured, by the brass diagonal scale, on to a pair of beam compasses, with the two steel points shipped. Flattening the paper down by placing the straight-edge close to the line A B, and putting weights on it, with the centre A describe a short arc of circle D E, scratching lightly the surface of the paper. Then moving the straight-edge into the direction of C (which can be ascer- tained roughly by a protractor), and again weighting it, make another small scratch F G. With the assistance of a reading- glass, and by means of a needle mounted in a handle, and spoken of as the "Pricker," make a fine prick at the in- tersection of the lines A B, D E, i.e. at H. Look out the versine of 10737'15" (90 -f half the required angle) which is 1,302,717. This becomes '302717, which multiplied by 90, gives 27*244 inches as the chord. FIG 14. Measure this distance on the beam compass, and flattening the paper as before, draw, with H as a centre, a short arc K M crossing F G. The point of intersection is to be pricked carefully as before, and the straight-edge can now be laid on A and it, and the line ruled will be at exactly the angle required. This seems a tedious operation, but it is the only way in which points can be got to go down satis- factorily, and in the end much time will be saved. It may be noted here, that it is preferable to make a mark Steel with a steel point instead of a pencil, from the practical difficulty of measuring accurately the required distance on the beam compass when the pencil point is used, as, when the pencil point is cut sharp enough to make a fine line, it is H 9& HYDROGRAPHICAL SURVEYING. CHAP. v. almost impossible to prevent breakage in applying it to the brass scale divisions. It is also cleaner. In marking, the point must be held sloping, so as only to impress, and not actually to scratch the surface of the paper, which it will do if held perfectly upright. Of course, if the paper is stretched on a board instead of being loose on the table, the time and trouble of seeing the paper flat is saved. If the table of chords is available, look out the chord for 37 14' 30" and multiply it by 4*5, as the table is made out for a radius of 10 in. This will give the same quantity of 2 7 '244 inches as found above. C may be of course anywhere on the line A B, and suppos- ing ourselves to be plotting from an original base A B, will probably be much nearer to A than to F G, but by taking such a long radius we get a straight line in the true direction of the angle laid off, and when we want to measure another angle on to another object, perhaps three times the distance of C from A, we have a long line we are certain of, to do it from. Always Here let it be impressed upon the surveyor that all lines drawn f r Pitting the main points, and indeed all points, (except very minor ones, on which the position of nothing else will depend,) must be drawn as long as possible, and with more or less long chords, if we desire correctness. If we have a line drawn between two stations which lie, say six inches apart on the paper, and it only projects a few inches beyond each, and we hereafter require to lay off an angle from one, having the other as zero, to a station which will be, say two feet or more distant, we cannot do it correctly, as this longer line will have to be directed by a prick which cannot be farther off than the length of the zero line ; but by drawing long lines with long chords, we are ready for anything, and it will not matter whether the station we take for zero be near or far, as we use, not it, but the long line ruled through it. length of In no case should a line to a station be laid off with radius. a p ro t rac tor or cn0 rd whose radius is less than the distance CHAP. v. PLOTTING. 99 of the station, excepting in a rough plan which we want to do rapidly, or in most parts of a running survey, where preten- sions to accuracy being thrown to the winds, we get points near enough for our purpose down with a protractor. It is difficult to extend correctly a short line once drawn, lengthen- by simply ruling on with the straight-edge. If a longer line mg a line< is wanted, it is better to lay off the angle to it again from some other long line, with a sufficient radius. To rule a true straight line which will pass exactly over Ruling a the centre of the pricks is by no means an easy thing. The ^ rai & ht ruling pencil, which should be of the hardest lead manu- factured, should be cut to an edge, not a point, and the straight-edge being placed in position, and weighted to keep it in contact with the paper throughout its length, the flat side of the pencil is placed against it, and tried at both points, to see whether the line will pass truly over them. Care must then be taken to hold the pencil in the same position while drawing the whole line. In laying off by chords an angle over 60, or a little under 60, Angles it will be found best to mark off 60 first, and measure the over 60 - remainder of the angle from the 60 prick. This is done by drawing short arcs with the radius used, from the station from which it is desired to lay off the angle, and from the radius prick, (H in last figure) the intersection of these must be pricked off as 60, and another short arc being drawn with the originating station as centre, the chord of the difference of the angle from 60 is measured from the 60 prick to the last short arc, as in Fig. 15 (p. 100). This is done not from any incorrectness of the principle if the angle were laid off at once, but because it is inconvenient to be measuring long distances as chords, as there is a greater chance of some little inequality of the paper causing error, and also, the longer the chord measured, the more acute will be the angle between the two intersecting arcs, and conse- quently the greater the difficulty of pricking in accurately at the intersection. Understanding then how to lay off angles by chords, and H 2 IOCO HYDROGRAPHICAL SURVEYING, CHAP. v. Com- having obtained by calculation as long a side as we can for a ment e o~f plotting base line, so as to plot as much as possible inwards, or Plotting. w fth decreasing distances, and not outwards to stations farther distant than the original two, and having settled whereabouts on the sheet this base line shall be placed, draw a meridian line, parallel with the side of the paper, and passing at one end of where the base is to be. Make a prick on this line for one end of the base, using, as always for pricking, a reading-glass, to ensure getting the prick exactly on the line. Let us call this A. From A, lay off, with as long a chord as can be commanded, FIG 15. the true bearing of the base, and having ruled this line of bearing as long as possible, make another prick on it, at the required distance from A, for the other end of the base. From the two base stations lay off angles to two other main positions, and choose the one of these where the intersection of the lines makes the nearest angle to 90 as the third station to prick in, doing so with great care on the intersection of the two lines. Then from this third station lay off an angle to the fourth, and if this, when ruled, passes exactly over the intersection of the two lines from the base stations, it can be pricked in. All four stations are correct, and the groundwork CHAP. v. . PLOTTING. 10 1 of the chart is laid ; but if there is any little triangle visible with the reading-glass, all must be plotted over again, for unless these first four stations are exactly right, nothing will ever go right afterwards. These four stations settled, proceed in like manner with other main stations ; but now we shall of course have three intersecting lines for each station, and care must be taken that these lines do truly intersect, and no station must be pricked in, that has not got three such converging lines through it. The main stations down, smaller chords may be used for secondary theodolite stations, and the protractors will come in in plotting the marks and other minor points, the necessary angles for which we may suppose some of the party are getting, whilst the first main points are being carefully plotted. The ordinary way of marking the points is to ring a small Marking circle of carmine round them. Larger circles can conveniently " Point8< " be used to distinguish the main stations. It will be found in the course of plotting that the paper stretching will vary so much, expanding at one time and contracting at another, that the arcs of radius once measured and scratched on the paper, cannot be considered as so done once for all. If some hours have elapsed since marking any radius, it must be remeasured, to ascertain if it has altered. In getting angles for plotting stations of all kinds, it must Caloulat- be remembered that two angles of a triangle will always give the third, and that as far as mere plotting goes, it is not necessary to waste unnecessarily time in observing the third angle. If the two observed angles have been got fairly accu- rately, the double error which will be thrown into the third angle deduced from them should not be enough to show in plotting, and if it does, it will soon make itself apparent by not intersecting. An angle from a fourth station will show which of the other three angles is wrong. Thus if we have observed at a station C, which we want to plot, the angle between A and B, and also the angle at A 102 HYDROGRAPHICAL SURVEYING. CHAP. v. between B and C, the angle at B which is wanted to draw a line to C can be calculated without the trouble of visiting B. It is indeed a blessed circumstance for the marine surveyor that the three angles of any triangle equal 180. Plotting Some surveyors have preferred to plot main stations by by dis- distances. In this case the triangulation must necessarily be tances. calculated beforehand. We do not consider that much is gained by this method. Three distances must be measured to obtain an intersection, as three angles must be laid off for the same result. A distance is sometimes useful as a check. IRREGULAR METHODS OP PLOTTING. We have up to the present been considering the plotting of stations for a regularly triangulated survey. Let us now look at some other methods. A Position In plotting the points of a chart which is being constructed n on ^ e P r i nc ipl e f do-with-what-you-can-get, which is very often what has to be done in marine surveys, it is frequently found necessary to plot a position by its own angles, as, for instance, where the ship, anchored or moored oif a low coast, has to be a main station, and only angles from aloft can be obtained to objects inland, such as hills, conspicuous trees, &c., already fixed. Use of A station pointer, generally, has some small errors of paper. centring, &c., that prevents it being used where exactness is required, and, moreover, only two angles can be laid off at a time by this instrument. In this case then it is better to plot all the angles obtainable on to tracing-paper, using chords for the purpose, and being very careful to make a very minute hole at the centre from which they radiate. If the objects are fairly well placed, a very exact position will be obtained, by laying this tracing on the sheet, and pricking through for the position. This will be much assisted if but one line can be got from a fixed station, as the angles can then be plotted on this line, supposing that in this case, back angles cannot be calculated. CHAP. v. IRREGULAR MODES OF PLOTTING. 103 Again, it may sometimes be found necessary to carry on Only two the main stations with a point plotted by. only two angles; but if this happens, efforts must be made to check this, by getting an angle back from stations plotted on by means of this doubtful position, to some old well-fixed station, as a distant mountain ; or if this is not to be had, a regular beginning must be made again by plotting two stations with two angles, pricking one, and then laying the angle from that to the fourth, as practised at the commencement of the chart, which will give a certain amount of check. A well-defined mountain, though miles inland and never Mountains visited by the surveyors, will often prove the very keystone of a chart that cannot be regularly and theoretically triangu- lated. When once well fixed, it will remain to get angles to, long after all the other first points of the survey have sunk below the horizon as the work progresses. True bearings of this will often be useful, and these can be Use of True laid off from the mountain by applying the convergency. Bearings. Let us take an example, which will perhaps explain what is required easier by means of a diagram. FIG 16 We hope that we have made it plain, by what has gone before, that if a distant object bears, say, N. 47 20' W., we do not bear from such object S. 47 20' E., but so much less 104 HYDROGRAPHICAL SURVEYING. CHAP. v. or more by the convergency ; and that in all cases of fixing ourselves by means . of true bearings observed from our own position, the amount of convergency, due to the bearing and distance of the object, must be calculated and applied to our bearing, before we can use it as a bearing from the object. Here, Fig. 16, let B A be the original meridian drawn at the commencement of plotting through any station A. M is the distant mountain. At X our main points are falling short from some reason or another, and we are obliged to have recourse to a true bearing of M, which we accordingly obtain. Kequired to draw this true bearing from the fixed point M. If we have the sheet graduated, it will not much simplify matters, as it is a great chance if a meridian passes close enough to M to use it without further correction ; but let us suppose that we have no other meridian on the chart but A B. We must lay off the true bearing from M, with A as the zero, so we require the angle A M X. If M has been observed from A, whence we had a true bearing by which the meridian A B is directed, we have the bearing or angle BAM. If not, we must measure it from the sheet by reversing the chord method ; drawing a line from A to M, and measuring the chord to the line A B at a given radius with beam compasses, and calculating the angle which corresponds to it, or B A M. Now consider the figure again, M C, X D, being imaginary meridians to assist conception. The bearing of A from M = bearing of M from A + the convergency, as M is nearer the pole than A, or CMA= B A M 4- convergency for difference of de- parture of A and M. In like manner : C M X = M X D (the observed bearing from X) -f con- vergency for difference of departure of M X. Adding, we have CMA + CMX = BAM + MXD + convergency for A X. Or A M X = bearing M from A -f bearing M from X + rorivergency for A X. CHAP. v. IRREGULAR MODES OF PLOTTING. To get convergency in this case, we must assume a position for X, which we can roughly plot for the purpose, and measure the distance A X and bearing B A X. We can then from this calculate the convergency required, knowing roughly the latitude of A, for Convergency = distance X Sin mere, bearing x Tan Mid. lat. If M is likely to be used much in this way, it will be Drawing worth while to lay a meridian off through M, by plotting the bearing AMCorBAM -f the convergency for A M ; from which meridian subsequent bearings can then be laid off, duly corrected for convergency, for the distance between M and the station from which the bearing is observed. Of course it will depend on the latitude how much error Neglect of will be introduced by neglecting the convergency ; but when it is considered that in latitude 45 the convergency is equal to the departure, it will be seen that a large error will result by not applying it ; for in this latitude, supposing A and X are 30 miles apart, an error of half a degree would be made by drawing a meridian parallel to A B, and laying off the bearing observed at X from M. If it is intended to lay off the true bearing of an object from a station plotted on the chart, the convergency must likewise be borne in mind, and the meridian to be ruled through X (in this case considered as fixed) from which to measure the bearing, must be, in transferring it from A B, corrected for the convergency due to the distance A X, by, after ruling a line through X parallel to A B, laying off at X, from the parallel just ruled, towards the pole, and on the side of A, an angle equal to the convergency required, which will give the direction of the true meridian. The system of true bearings may be used in many ways Further whilst carrying on an irregular triangulation. It is impos- sible to give instances of all the difficulties which may be surmounted by this means, but an example, taken from actual practice, will show the style of use to which true bearings may be put. 106 HYDROGRAPHICAL SURVEYING. CHAP. v. Let us suppose ourselves employed in the survey of a piece of coast which offers no facilities for obtaining a base by measurement ; but it is the season for observations, and we have points so placed that we can work directly from the astronomical base, instead of obtaining a base by sound or other doubtful methods, which we should otherwise have to do. In Fig. 17, A and B are two positions invisible from one another near the confines of our chart; C is a distant in- accessible mountain visible from both A and B; D is an elevation visible from B, but not from A, and from which C can also be seen. FIG 17. To utilise this arrangement, we take observations for latitude at A and B, and run the meridian distance ; we also get the true bearing of C from A, B, and D. Calculate the bearing and distance A B astronomically, and place this line on the paper. The lines B C, A C can be now drawn by the difference of the bearings observed and calculated from A and B, which will give us C with two cuts. B D is drawn from B, and the back bearing of D from C (calculated from the observed bearing of C from D, with convergency applied) drawn, by which we shall get D, also with two cuts only. If we can find a point E which can be seen both from B and D, and from which C can be seen, we can lay it down CHAP. v. IRREGULAR MODES OF PLOTTING. IO/ with three cuts, as the angle from C can be calculated in either triangle C E B or C E D, and the intersection of these three will prove the exactness of our work. B E will then be our base for working, as we are supposing B A to be about 60 miles, which, as we have drawn it, will make B E about 15 miles, which is a workable base. In the case which we have put, it is very unlikely that, after all these different bearings, the intersection of the three lines at the point E will be a perfect one. If it is not good, the best way to obtain the base B E may be to calculate it in as many triangles as we can command, and, taking the mean of these results, to commence the actual plotting from this mean base. This would depend, however, upon circum- stances. It is impossible to lay down any hard-and-fast rule with respect to this kind of work, and the case is simply given as an instance of the uses to which true bearings may be put. In some extensive surveys on a small scale, it may be Gradua- necessary to graduate the sheet first, when positions can be JJJJ^* placed on it by their latitudes and longitudes, and the inter- before vening parts plotted or triangulated by means of bases measured at each of these astronomical positions. This will be done when coasts are low and marks scarce. We can scarcely hope that when these different bits meet, they will agree exactly ; but with a small scale, say half an inch to the mile, the discrepancy ought not to be sufficient to introduce much error, if we square in five or six miles of the points worked up from either end, when they meet and disagree. This undoubtedly partakes of the nature of " cooking ; " but when we undertake to map a coast on such a small scale, we cannot pretend to much accuracy in detail, and shall only do this when it has been considered advisable to lay down a large extent of coast in the time available, with the inten- tion of presenting its more salient features as correctly as we can. Work amongst islands (as portions of the Pacific) would be done in this manner. io8 HYDROGRAPHICAL SURVEYING. CHAP. v. Systematic fixing of Marks. Officer marking responsi- ble for sufficiency of Angles. FIXING MARKS. It is not possible to lay down any dogmatic plan for fixing the marks which have to be erected. In many cases it is well to put them all up first, and then get angles to them after- wards ; but if non-surveyors are deputed to make the marks, they will seldom be placed in the right spots. A whitewash, for instance, will be so placed that it cannot be seen in certain directions. A tripod or pole will not be in the most conve- nient position for the officer who afterwards puts in the coast-line, and numerous small errors of this description will be made by one who is not capable of taking in all the little requirements. It is therefore more satisfactory to send a surveyor to do this, and while he is there he may just as well take angles, so that the writer has found it saves time in the end, in general, to have a surveyor at some main or secondary station, whence he can see most of the marks, and let the officer who erects the mark take angles at it to the above station, which we may call the " shooting up " station, and to a sufficient number of other stations which can be seen from the " shooting up " station also, to fix himself. The angles from these other stations can then be calculated. In this way two or three officers can be at work putting up marks, and fixing them at the same time. The officer who erects a mark gives it a name, and notes the time by his watch when he is there. The officer at the shooting up station also takes the time, and notes the position and kind of mark put up, to which he takes his angles, writing the name against it in his book when he returns to the ship and meets the other officers. The officer marking must think for himself whether he has enough angles to fix the point ; and in case any mark cannot be seen from the shooting up station, he must get an angle from some other of his marks, which will be then used to calculate the other angles in the same manner. A heliostat is invaluable here. In hazy weather, and when CHAP. v. FIXING MARKS. 109 the shooting up station is distant especially, a flash will Use of be seen when neither mark, nor boat, nor anything to direct where to look for the mark, will be visible. The officer shooting up should also return the flash, to show he sees the station, as well as give a well-defined object to get the angles to. Of course circumstances may not render this system ad- visable, but it is here suggested as having worked very well in many places. Frequently the minor marks must be fixed by angles from Triangn- the ship, or a boat at anchor, as on a straight coast where ^^ ' and nothing behind can be seen from the marks. When this is Marks by Q* necessary, it will often be also necessary to carry on the main triangulation as well by means of ship and boats, so that a description of one serves for the other. The ship, anchored short, or moored if necessary, should be shot up from one or more shore stations. If the angles taken from the ship are indispensable to fix her own position, try calculating the back angles from other objects first, and lay them off as cuts to the position, as if they agree it will be the most satisfactory manner; but often back angles, calculated from sextant angles, will not be correct enough to give a good intersection, especially if the points are distant. In this case, let all the angles taken at the ship or boat be plotted on tracing-paper as before described, and the position pricked through on the guiding line from the shore station. A signal should be made when the angle to the ship is to be observed, and the angles from the ship taken at the same time. The ship angles should be observed from the fore part of the ship, and frequently the foretop will be found the best place. Whatever spot is used, it must, of course, be arranged beforehand, so that the observer's exact position on board may be taken from the shore station. From the ship, the main angles, that is the angles to the Taking positions already plotted, which are to be taken for the from Ship. purpose of fixing the ship, must be observed first, using some well-defined station as zero, and measuring all the main 110 HYDROGRAPHICAL SURVEYING. CHAP. v. angles from this with the sextant. Some other station must be chosen, as the zero with which to measure the angles to the marks, and the angle to this second zero observed from the main station zero. This second zero is wanted to be in such a position with regard to the marks, that any slight movement in the ship will make the least possible difference in the angles to be observed between it and the marks. It must be, therefore, at about the average distance of the marks. It will not do to choose some object miles away behind the marks, as the least swing of the ship will at once alter the whole of the angles. Generally speaking, the central mark to be fixed will answer the purpose best, but in many cases it will be found necessary to change this zero for some marks, measuring from some other object at an equal distance from the ship. Eepeating When the minor angles have been taken, repeat the main Angles. an gi es to see if the ship has moved, giving another signal to the shore station for another angle from it. All mark angles should then be observed again to check errors. It need scarcely be said that the more rapidly these angles are taken, the less the chance of any error arising from varia- tion of ship's position, by change of direction of current, wind, &c. An experienced hand should therefore be chosen for this work. Telescope A sextant with a telescope of high magnifying power is of Sextant. mog j. use f u L Qn this head see page 7. CALCULATING A POSITION FROM TWO ANGLES TO THREE KNOWN OBJECTS. It may be sometimes required, in the course of a survey not regularly triangulated, to calculate the distance of the observer from an object, from the two angles he has observed between three known " points," one of them being the object whose distance is required. Or he may require the angle, at the object observed, to him, from the same data, This is, perhaps, best accomplished by using the one-circle CHAP. v. CALCULATING A POSITION, ETC. Ill method, so called in contradistinction to the method of pro- traction by two circles already explained under "Station Pointer." The three figures 18-20 give the three possible positions of FIG 18, the objects, viz. : When the observer is inside the triangle formed by the objects ; when he is outside, and the centre object is nearer than one of the others; and when, under similar circumstances, it is the farthest. 112 HYDROGRAPHICAL SURVEYING. CHAP. v. Tf the angles between the three objects are known, which is most probable, the calculation of the second formula will be unnecessary. Let A B C be the objects observed. G the position of observer to be determined. A B = c, B C = a, A C = b, are the sides known, A G B = m and B G C = n t the angles observed. Required G A and the angle BAG. At A, in A C, draw, on the side remote from G, A D, making C A D = n. At C, in A C, draw in like manner C D, making ACD = m. When G is inside the triangle (Fig. 18) CAD, and A CD must be drawn to equal 180 ??, and 180 m re- spectively. Describe a circle to pass through the points A, D, C. Join D B, and produce it until it cuts the circumference of the circle in G. Then G is the position required. For A C D, A G D, being angles in the same segment, are equal, and A C D is drawn = m . ' . AGD = m or A G B = m Similarly BGC = w. Then AD =5 Sin m. Cosec (m + n) ...... (1) BAG /S(S-a) BAD = BACCAD .......... (3) D + ADB) (4) G A = c. Sin A B D . Cosec m ........ (5) G A. Sin m Sin A B G = AB - .......... (6) B A G = 180 - (m + A B G) . . . . . . . . (7) G can now be plotted by the angles from A, B, C, if required. CHAP. v. DRAWING RECTANGULAR LINES. DRAWING RECTANGULAR LINES. The methods of drawing a line perpendicular to another line are well known, but are here repeated. FI&2I. Measure from the point A with the beam compass any Erecting equal distances right and left of A, as A B, A C. dicuS^to From B and C draw, with a radius about half as much again a line from as A B, short arcs intersecting one another. A line drawn jJJJf near through this intersection D, from A, will be at right angles S J^ to AB. FIG 22. tremity. D Take any point B, in a direction about 45 from A, and Erecting a from it as centre, with the radius B A describe a short arc fS^Ja intersecting A D in C, and likewise a short arc E F in the the end of opposite direction. Join C B and produce it to intersect E F in G. A line joining A and G will be at right angles to A B. In all careful work, these operations should be checked by repetition, with different radii. 114 HYDROGRAPHICAL SURVEYING. CHAP. VI. Roughest form of Survey. Modified Banning Survey. Gradua- ting be- forehand. Method of ordinary Running Survey. CHAPTEK VI. RUNNING SURVEY. A RUNNING survey, the least accurate form of "sketch" survey, is one where the best part of the work is done from the ship running along the coast, fixing points, sketching in the coast-line and prominent parts of the land, and sounding, at the same time. It is capable of many modifications, more especially with regard to the fixing of the main points. The rudest form of running survey is where, beginning upon nothing, everything is eventually put on paper by observa- tions, angles, and soundings taken from the ship without anchoring. At the other extreme comes a running survey made upon some main points already fixed by triangulation of some kind, and which has for its object only the sketching of coast-line and detail of an inaccessible coast, which is assisted by occasional anchoring, and where sounding would be carried on in the boats as well as the ship, after enough natural ob- jects have been fixed by the angles from ship stations. In making an extensive running survey of the simplest kind, i.e. where we commence on nothing, and only run past the coast once, it is well to have the paper graduated (see p. 270), as astronomical observations from time to time will fix the scale of the chart, and it is easier to plot these positions when the sheet is graduated. The course and the distance run by the ship between each position where series of angles are taken, as given by patent logs, will form a series of bases, which will have to be, how- CHAP. vi. R UN N ING SURVEY. 115 ever, modified afterwards to agree with the positions astrono- mically fixed, which must be taken as the fundamental points of the chart. A running survey must be roughly plotted, and everything sketched in, as we go on, putting down position after position by course and distance, and cutting in the objects we choose for marks, giving them names by which to recognise them, and to record in the sounding book. Assistants should be told off for separate duties. One to look after the sounding ; an- other to sketch in the coast-line and hills between each object chosen, on another sheet or sheets of paper ; the chief and some assistants getting the angles; one writing down; another plotting the stations and drawing the lines to the points, so as to see what angles are wanted at the next station to objects already chosen, and how far on the next station should be. At each position, as laid down by course and distance, commence plotting by laying down the bearing of the object we have selected for zero for the round of angles. From this, the other angles can then be laid down. It follows that a bearing must be obtained, as a necessity, from each position. This should be taken to the nearest object, which will be of course connected to the others by angles, but this need not, and indeed should not, be the first line drawn. Distant hills are a great help in a running survey, as, when Hills of replotting from the astronomical positions, if these hills can be fixed by bearings (true or compass) from them, the angles taken to the hills, at a position now and then, may possibly be used as fixes, which may be plotted by station pointer, and so get intermediate positions independent of the patent log positions, which are so liable to error by the action of currents. A running survey will nearly always have to be replotted, as the astronomical positions and those by patent log will never agree. Having plotted the positions where astronomical observa- Replotting tions have been taken, if the intermediate stations are to be I 2 Il6 HYDROGRAPHICAL SURVEYING. CHAP. vi. put in by bearing and distance, they must be squared in so as to agree in total distance and bearing with the astronomical positions. Thus, in Fig. 23, let A be the position from which we start ; B, C, &c., to H, are positions of the ship as plotted by course and distance on the rough chart; a, h, are the same positions as A, H, but as given by the astronomical observations. To bring the intermediate positions to agree with a, h, as plotted on the graduated sheet, we join A H and a h. Drop perpendiculars from B, C, &c., to the normal line A H. With the proportional compasses set to correspond to the different lengths a h, A H, measure the corresponding distances along a h for the points where the perpendiculars will cut, and lay off perpendiculars along which the corresponding distances can be measured, and so we obtain &, c, d, &c. If any mountains have been observed both from A and H, their positions should next be put down by these two bearings. The angles taken from the first positions are now laid off, and as objects are fixed, they can be used as checks to the next positions. If we can rely upon the bearings taken to the mountains we shall use them to fix the intermediate positions in preference to course and distance, so that 6, c, &c., may be again shifted, especially if the ship has not been accurately steered on her courses, or we have reason to think currents have varied at different parts of our run. No exact- Nothing will agree exactly in a running survey of this expected kind, but a very fair approximation to the relative positions of conspicuous objects, may be got. Amount of The amount of detail possible will not be very great, but Detail. w i]| vary w ^ n the quickness and accuracy of eye and hand of the officer sketching it in. There is nothing that re- quires the knack which distinguishes a good surveyor so much as this sketching in fairly accurately of a coast-line in a running survey, and good judgment as to depth of bays, and other points that must be mainly put in by eye, is most valuable. It is well to have one officer aloft, who will be able to get CHAP. VI. RUNNING SURVEY. 117 FIG. 23. Il8 HYDROGRAPHICAL SURVEYING. CHAP. vi. a better view of river mouths, &c., and make little sketches of bits not seen frdm deck. He can also take angles to objects that have sunk, or not yet risen above the horizon of the deck. Compass-bearings are of great use, as direction of valleys, &c., may be noted without making a position. The whole course of a running survey will have to be one of compromise between discordant results, and only long practice will enable the surveyor to decide what to throw out, and what to accept. Modified It may often occur in a survey, that a portion of the coast is i naccess ible f r landing by reason of heavy surf; or the shore is so cliffy or densely thick with jungle, that stations cannot be made without loss of more time than they are worth. A running survey of this piece may be as much as is requisite, but the probability is that we shall be able to fix on some main points from the triangulation of the other and more important part of the survey, and these will greatly help us to make the best chart of the portion we can under the cir- cumstances. In such a case, the best course to pursue is to pass along the coast at some distance, stopping at convenient positions, where the ship can get station-pointer fixes by the main points, anchoring, if possible, for this purpose, and cutting in from these positions other secondary points nearer together, and nearer the coast than the first. Then pass along again closer to the land, and fix points on the shore itself, using the secondary points to fix the ship with. Boats may then be sent to sound, if required, or to sketch in more details of little bays, &c., if they can get near enough. Compromise will be required here too, probably, in plotting the points, as, unless the ship is absolutely motionless, it is unlikely the angles will intersect exactly, but it is astonishing what good results can be obtained with a number of officers taking angles at the same time, with the ship's way stopped, each being told off to take two or three angles as quickly as possible. CHAPTEK VII. COAST-LINING. WHEN and how the putting in of the coast-line is done, must depend much upon circumstances. If making a chart with pretensions to accuracy in the in a details, it is better to do it before the soundings are taken, as, for the inshore soundings, the little points and bays, not distinguished by marks, will be very valuable. In this case, too, every yard of the coast that can be walked over should be. If the surveyor pull along the coast in his boat, from one spot to another, he will be liable to miss little details, such as stream entrances, which may be blocked by the sand beach in summer ; lagoons behind the shore, &c. The boat should therefore only be used to pass rocky points and cliffs that cannot be walked along, or to make stations in, at anchor off the coast, if it is necessary to do so, to shoot up the details. The method of putting the coast-line on to the sheet also Plotting varies. The angles can be taken, and the details between sub- J^ 6 Coast ' sidiary fixes on the beach sketched into the angle book, using always a larger scale than that of the chart, and then these fixes and angles plotted on to the chart after return on board ; or the surveyor can take a field board, with the points on it, with him, and plot the coast as he goes along it on to his board. Of these two the writer far prefers the latter method, as a Plotting rule. There is no chance of having necessary angles omitted ^ound if the fixes are plotted at the time, and any little error is easier detected on the spot than when plotting afterwards on board. 120 HYDROGRAPHICAL SURVEYING. CHAP. VH. Of course rainy weather or other circumstances will some- times prevent the work being plotted at the time, but unless some good reason exists, it should be done. Instm- If conveniently situated marks are plentiful, the coast-liner Squired. w ^ on ^ v wan ^ ^ s theodolite or sextant, or both, to take his angles, and a station pointer and tracing-paper for plotting, with protractor, &c. But if the coast has no objects off it to seaward, and landward marks are also short, or invisible from the shore, he will require, very probably, a pole of measured length, whereby to ascertain, by observing the angle subtended by its extremities, the distance of points, &c., from one another. A convenient form of this pole is described under " Ten- foot Pole," page 33. Each assistant should have a copy of the Ten-foot Pole Table,* on a piece of cardboard, always in his angle book, ready for reference in the field. General Let us suppose an officer landed with his board of points S3? Cr to do coast-line. lining. He will start at some point already plotted on the chart, and will take angles from it to all the objects he can dis- tinguish between him and the next fixed point, and beyond, if necessary. He will then walk on to another spot, where he will make a supplementary station, fixing himself by angles to known points, either by theodolite or sextant, according to circumstances. He will then plot this, his No. 2 A, on his board, by station pointer or tracing-paper, taking care to check his position by his line from the 1st A, or by a third or " check " angle from his present position. His No. 2 plotted, he will sketch in on the board, the coast-line between that and the first, having noted any peculiarities as he walked along. The scale of the chart will largely influence the distance between the subsidiary stations to be made by the coast- liner, as will also the character of the shore line, and the intended nature of the chart as to exactitude of detail. Appendix S. CHAP. vii. COAST-LINING. 121 If the work is to be plotted on return on board, the system is precisely the same, only the detail of coast between the stations must be sketched in in the angle-book, instead of directly on to the board. When the coast-liner sees that at the next station he will Using Ten- not be able to fix himself by angles, he must use his ten-foot foot Pole ' pole, sending a man on with it with instructions where to stand, or going on himself, and leaving the pole behind with a man at his present station, with directions, when signalled, to hold the pole horizontal, and at right angles to the observer. To ensure the latter, either a rough pointer of some kind can be attached to the centre of the pole, so as to project at right angles, in which case the holder will be directed to point this to the observer, or, he will be told to sway it gently backwards and forwards, and the observer will read the largest angle he can measure. The angle observed, and the corresponding distance looked out of the table, the latter is measured on the scale of the chart, and applied by a pair of compasses, as a distance from the last station along the line laid off from that last station in the direction of the required station. If necessary, the whole coast can be carried on in this way ; but if the marks are a long way apart, great care must be taken in observing the angles on to the positions to be measured, as there is no check on the work, and each error will be accumulative. In this case the man must be sent on, and must mark the exact place he stood when the angle was observed to him, and the coast-liner must make his next station precisely on that spot. The azimuth compass may sometimes be employed in this work with advantage. Any little elror, when a properly fixed station is reached, can be squared in. It will be understood that this ten-foot pole method is only used for the smaller detail, where sufficient angles to fix cannot be obtained. It is especially useful in delineating the shores of islands, or of small bays which have no fixed point in them. 122 HYDROGRAPHICAL SURVEYING. CHAP. VH. For instance, in Fig. 24, let us suppose the two points, marked Ash and Lime, are fixed, but in between them is the small bay shown. At Ash we obtain the angle between Lime and A, the next point visible, and also the distance by our ten-foot pole. If we can make out that B is a point, and can see any promi- nent spot on it, we shall get an angle to that also. We then go to A, sketching in between on the way. At A we become aware of the little bay, and we send the pole over to C, pointing out to the man with it where to stand, and telling him to put a stick or stone there, when he is signalled to go on to B. At A we get all we can, angles from Lime as zero, to Ash, FIG. 24. 800 Scale of Yard*. B, C, tangent of bay on towards D, and anything prominent, and the distance to C by the pole. Leaving a little mark at our station at A, we go to Lime, and take angles from Ash to A, B, and distance to B by the pole now there. We then go back to B, and send the pole over to D, and again get all angles we 'can, and distance to D. We now sit down and plot our data. We have two angles to A from Ash and Lime, and a distance to A from Ash. These ought to agree, and we prick in A. We have the line to B from Lime, and perhaps from Ash as well, but we will suppose not, and will plot B by the distance from Lime. Then placing our protractor on B, lay off the angle CHAP. VII. COAST-LINING. 12$ observed there to Ash, which ought to go through, and make a check for B. We plot C and D by their distances on their respective lines from A and B. We then walk round the bay, sketching it in, and can get an angle at C, from A to D, as another check, and any other angles to assist in sketching in details. The coast-liner will generally be responsible for all the Coast-liner details of topography close to the coast such as follow, the * r * h topo " scale of the chart being taken into consideration as to with near to what degree of accuracy detail can be laid down. Heights of cliffs must either be measured with a lead-line, or by getting an elevation to some definite point, which must afterwards be fixed, from one of the stations, or may merely be estimated and entered in the angle book. Cliffs have generally to be exaggerated on the chart, to show distinctly. The height in feet should be written against them. The directions of lower parts of streams, or rivers, must either be walked up, and fixed, a certain distance back, or can merely have^ their entrances fixed, and an angle taken up for their general direction. Lower spurs of abrupt hills must be sketched in, assisted by angles to them from different points. Houses standing back from the shore must be put in. These can usually be fixed by angles to them without visiting them, unless it is necessary to get their dimensions, names, &c., or perhaps to ascertain if a good well or spring of water may be near, that would do for watering on an emergency. Swamps near the coast should be sketched in as far as necessary, and a look out kept for evidences of any extension of their area in winter. Information on these points can be picked up from passing inhabitants. Angles should be got also to any conspicuous objects farther inland, as they will be very useful when the topo- graphy is sketched, and the surveyor should always look ahead, and seize any opportunity of the kind for helping on 124 HYDROGRAPHICAL SURVEYING. CHAP. VH. other parts of the work than those he may be immediately engaged in. Eoads near the coast should be walked back to, and fixed here and there, sketching in between. Eocks above water, or breaking, should be fixed. Though these come into the province of the sounding, it is often useful to have them down first ; and in the case of a break only, it may be very much so indeed, as it may be an isolated head, which a boat sounding near high water may miss. Low-water Though it is the high- water line that the coast-liner is more shore line. i mm ediately concerned with, he should mark at low water the position of the dry line, especially where this runs off a long way at points, &c. In a detailed survey on a large scale, it may be necessary to send some one round the water-line at low tide to get it accurately, but this is more usually obtained by the sound- ings, for by reducing these to the low- water level of springs, a series of points will be obtained, where each line of soundings crosses the low-water line, which can then be drawn in as a line passing through these points. Elevations Angles of elevation for heights of the hills should be taken of hills. w h en getting the angles for fixing the points of the chart, from main and secondary stations, or any well-fixed points ; but if the coast-liner gets some more elevations from marks on the water-line, they will never come amiss, as long as the position is well fixed. General The officer coast-lining will make note of anything worth tion for recording in the sailing directions, as little nooks for landing, Directions, convenient places for watering, &c., letting his captain know on return on board, in order that they may be, if necessary, again looked at, or entered in the latter's notes. It may be convenient to keep a book for the purpose, in which any useful information can be entered. Further As an instance of the application of the ten-foot pole of ^Cen^ 11 method, we may mention the following, which is adapted for USe n s ^ ores w ^ f rm gi n g cora l ree f s > or broad sand or mud flats, which dry sufficiently at low water to enable people to CHAP. VII. COAST-LINING. 125 walk on them, and when either the steepness of the hills or the denseness of the vegetation prevent marks being fixed on the coast. Let annexed diagram, Fig. 25, represent an island of this kind. FIG. 25. A long measured lead-line, say of 500 feet, is provided. This is taken by an officer we will call B, who has a pris- matic compass. Another officer, A, is provided with theodolite, or sextant, or micrometer, and prismatic compass, according to circumstances, sextant and compass being quite sufficient. Starting at a, B remains there while A walks to b. B stretches his line out at right angles to a &, and plants a flag at the extremity. A observes angle subtended by flag and A a, with his micrometer or sextant, and both A and B observe the bearing of a I. A waves to B, who goes on to c, when the operation is repeated. A then moves on to d, B pivoting his line round c, so as to be rectangular to c d\ and so on, until /is reached. We will here suppose that, from a to/, we have been able to triangu- late, the reef being broader. We have therefore the correct bearing and distance of a f. 126 HYDROGRAPHICAL SURVEYING. CHAP. vn. To plot this, the mean compass bearings and distances a, I, c, &c., will be put on a separate sheet of paper on a larger scale than the chart, and the positions a f being joined on both, the other stations will be squared in on to the chart. Marks will be left at each station, if required for sounding, or delineating the outer edge of the reef. Subsidiary marks can be made at other points, as x, y, z, and fixed by angles from b, d, &c., with distances measured by the angle of the line. The shore line can either be sketched by A, as he walks from station to station ; or can be put in afterwards, if greater correctness is required, using the ordinary 10-foot pole to fill in between a, I, c, &c. If a theodolite is used, which it is well to do in a case where we have not been able to get any measured base at all, and must consequently work back to a, it must be set up first at a, and the angle to b taken from some fixed object, whose true bearing we should obtain, as we in this case must not be dependent on the compass. B will be at b with his line, and when A has finished, will walk on to c, so that A, when he arrives at &, can take the angle from a as zero, to c. With a theodolite, then, A must visit every station, unless B has one also. At every new position, the last A will be used as zero. The readiest way for B to direct his line so as to be at right angles is to use the so-called " cord triangle," which is simply a triangle formed of a piece of line whose sides are in the proportion of 3, 4, 5, the angles being marked by knots. When stretched on the ground, with the corner between 3 and 4 at the A, and the 4 side coincident with the direction of the other A, the direction of the 3 side is at the right angle required. Any similar contrivance will serve the purpose. NOTE. This method was largely used by Lieutenant W. U. Moore in the survey of the Fiji Islands, and is a good example of the dodges that ha,ve to be improvised to meet circumstances. CHAPTER VIII. SOUNDING. Boat Sounding Ship Sounding Searching for Vigias. IT is difficult to say that any one step in the construction of import- a chart is more important than another, as each is necessary for the completion of the whole, and an error anywhere may cause a disaster ; but if any particular item is to be picked out, perhaps the sounding should rank in the highest place. The operation of sounding is the least pleasant part of a marine surveyor's work, especially when the weather is against him, and the sounding uninteresting, that is, where the depths are regular, and there is no excitement in the way of discovering, and working out, shoals and reefs ; but the notion that it is therefore always to be relegated to the juniors of a survey, is not only hard upon them, but may introduce errors in the very part of the chart which, as we have already said, is the most directly important. As soon as the points are down, i.e. plotted, the sounding can be commenced ; but, as before remarked, on an intricate piece of coast it is better if the coast-line is put in first. The ordinary main plan of sounding is thus. The boat Ordinary proceeds in straight lines in a direction, of a length, and at distances previously decided on, with a man in the bow constantly sounding. Every so many soundings, as the case may be, the officer takes angles with a sextant to fix the position of the boat, always doing this at the beginning and ending of every line. It is evident that this main plan may be largely varied in its details. 128 HYDROGRAPHICAL SURVEYING. CHAP. vm. In the first place rises the question as to whether it is better to plot fixes, and enter soundings on the sheet, regularly, in the boat, or leave them until return on board, merely putting down an occasional fix to see where you are. The writer says, certainly, as a rule, plot them at once. It can be done in ordinary circumstances just as correctly, and gives more information to the officer sounding as to little bits which may want additional casts, and it also gives the men at the oars a little rest from time to time. In very rough water it of course cannot be well done, and must be left till return on board to the comparatively motionless ship ; but when you can, plot at once. In harbour work on large scales, again, it will be better to plot afterwards, as great accuracy will be required. The extent to which the soundings themselves can be entered at the time on the chart, depends of course upon the state of our knowledge of the tide. If the tidal range is small, or the motions of the tide are sufficiently known to form a table of reduction beforehand, the reduced sounding can be written on the board at once. If not, the soundings as taken can be written down, and reduced on inking on return on board, or, only the sounding taken at each fix can be written against the prick of the fix, and intermediate soundings left to be entered on board. The latter will generally be found most convenient. Circum- The pace at which the boat may go, and the necessity, or guide 68 n t> f r stopping at the casts, will depend on the depth of many water and the capacity of the leadsman. Whether it is necessary to stop to get the angles depends upon the convenience and visibility of the marks, and the quickness of the angle-taker. A beginner will of course do everything deliberately, until he feels capable of combining speed with correctness. Whether each fix shall be plotted at once, or whether to wait until two or three have been got, and then lay on oars, or anchor for a few minutes, must also vary with circum- stances. CHAP. vin. SOUNDING. 129 What the distance should be between each fix will depend largely upon the scale of the chart, and the nature of the bottom. On an evenly sloping bottom many soundings can be got without another fix ; but where depths vary or increase rapidly, the fixes must be closer together. The soundings which will be joined together on the finished chart by fathom lines, e.g. the three, five, ten fathoms, &c., should always be fixed, and in doing this it must be remem- bered that it is the outer sounding of any of the same depth that will be on the fathom line, and also the tide reduction must be taken into consideration. This latter will of course be in many cases only approximately known, so that exactly the right sounding may not be fixed. The sounding lines should be in ordinary cases at right Direction angles to the coast, and parallel to one another, as not only lmes ' will a better line be got for tracing the fathom lines, but the boat will easier be kept in her right direction by observing two objects which have been seen to be in transit, in the right direction, at the commencement of the line. In nice work on large scales it may be found to answer to Marks in place two marks in line for this purpose ; but, as a rule, changing them from one line to the other will take far too lines< much time for ordinary work, and marks to answer all practical purposes may usually be found placed by Nature already. In sounding out a small harbour, circumstances must guide the direction of the lines. The depth to which the boat soundings are to be carried Depth to will depend upon circumstances. When soundings of over 20 fathoms are taken from a boat, it gives a great deal of labour, soundings When the boat gets to the end of her line, and turns to pull carried. along to the end of the next one to return, soundings should still be carried on, as before. The method of using the station pointer has been explained under the head of " Station Pointer." It only remains to note that it must be recollected, in getting the fix, that the right or left angle (according to K 130 HYDROGRAPHICAL SURVEYING. CHAP. vm. Construc- tion of Station Pointer to 1)6 remem- bered. Entering soundings in Book, whether a right-handed and left-handed station pointer is in the boat) must be observed of a sufficient number of degrees to be measured on the instrument, if possible. If this cannot be got, recourse must be had to tracing-paper for plotting the position. The sounding book need not be ruled. There are several ways of writing down the objects used for fixing and the angles between them, but the best, if space permits, as it does in the sounding book supplied by the Admiralty, is to put them down as you look at them, the right-hand object to the right, the middle one in the middle of the page, and the left one on the left-hand side. The sounding at the fix goes on the extreme right, and subsequent soundings up to the next fix, in a row underneath, thus X14 Pagoda 28 31' Mat 62 14' Can 7* Ail to be entered. Space for reducing. Check angles. 8 x x s 9 x m 10 x m 23 02' 60 08' Pea 41 17' 11 m The cross ( X ) signifies the same sounding as before ; and it may here be mentioned that all soundings must be put down, even though there may not be room for half of them eventually ; as, the man heaving regularly, if all his casts are not registered, the change of fathom will not come in its true place when interpolating between the fixes. Space must be left under each line for the soundings, as reduced to low water, to be written in in red ink. A check angle should be taken, from time to time, to make certain things are right, as is noted above at the last cast, in the example Can to Pea. This is especially necessary at the commencement of work with new points, as mistakes will occur in plotting points occasionally. A check will show at once if points are true, and if the angles have been taken correctly. The time must be noted every now and then, for the re- duction of the soundings to low water. CHAP. vili. SOUNDING. 131 The nature of the bottom must be taken every few casts, Nature of and recorded, the officer having a look at it from time to time 1)0ttoin< himself, to make certain that the leadsman is calling the stuff he brings up by its right name. For instance, many men will insist on calling " stones," rock, which is of course quite a different thing. The same objects should be taken for the fix as long as same possible. It tends to check errors in reading off, as the angles at each fix will bear a definite proportion to the last set. For instance, if we are pulling off shore with both Mat and Pagoda astern of us, the angle will be less each time, and a reading of say 33 instead of 23 would be at once detected as erroneous, before the disjointing of the line when the fix was plotted showed there was " something wrong somewhere." The variation in the angles will also enable us to see if the "fix" is remaining good. This plan also saves time in setting the station pointer verniers. When assistants are not thoroughly used to the work of Necessity sounding, it will be necessary to have two in each boat, to ensure no mistake ; but when not only officers, but men get used to it, one officer will in most cases be able to carry on the work by himself, with the assistance of a man to write down for him. Now that seamen are all taught to write, there is seldom any difficulty in finding one of the boat's crew, the coxswain if possible, to write down fairly. The same man will steer generally, and so permit the officer to keep his eyes for other matters. In deep water the boat must of course be stopped, and the leadsman will only heave when told. The interval can be timed by watch, or, in very open deep soundings, by the Massey's log towing astern, fitted as described on page 46. The distance between the lines of sounding will depend Distance upon the scale and the character of the survey, also upon {j^^f 1 whether the place is inhabited or not, for where there are Soundings, natives, information can be picked up as to shoals, &c., from the fishermen. The value of this, however, largely depends K 2 for assist- ance. 132 HYDROGRAPHICAL SURVEYING. CHAP. vin. upon the intelligence of the informant, and often cannot be trusted. If the coast or harbour be unknown, and the land of certain geological formations, it takes a great deal of sound- ing to be certain no stray rocks exist undiscovered ; and, as was pointed out in our preliminary remarks, the majority of marine surveys are not on a sufficient scale, nor will time at disposal allow us, to sound as close as to be absolutely cer- tain nothing is missed. The surveyor must make up for this by keeping his eye ever on the look-out for discoloured water, and by examining every suspicious spot. It must always be remembered that in the ordinary scales used for surveying, figures may look close together, and yet be, in nature, quite far enough apart for a rock or bank to exist, without giving any indication in the lines of soundings passing on either side of it. On a scale of 3 inches to the mile, each figure will occupy a space of 50 yards nearly. Suspicions It will depend upon the orders received from the chief of ground. ^ e surve y whether suspicious ground is searched at once, or merely pointed out on return on board for further examina- tion. As a general rule, whenever the soundings, in pulling off shore say, decrease, it is suspicious, and the spot must be examined by intermediate lines, and looking out sharp with the eye as well. Small A small nun buoy, with light chain and a weight to anchor it by, is useful in the sounding boat, to drop over on a shoal spot, so as to guide a boat working round and round while trying for still shoaler water. Doubling In many cases it is convenient to run double the number of .lines in shoal water, (say out to 7 fathoms,) that are required in greater depths. In this case, one set of lines will be run first, and when the boat gets to the end of her allotted space, she will return in the opposite direction, and run inter- mediate lines. See Fig. 26, where we suppose the boat to start at A, work along the long lines to B, and then return to C along the CHAP. VIII. SOUNDING. 133 intermediate lines, crossing the old work at every line, and thereby getting a check on it. In sounding a harbour channel on a large scale, it is often Sounding convenient to stretch a lead-line across from side to side, and 8eotion8 - sound at regular distances apart by this line, shifting it for each section required. Sweeping for a reported pinnacle rock is resorted to when Sweeping, sounding fails to discover it. Two or more boats, pulling , abreast, tow a lead-line between them, well weighted under the stern of each boat. If one weight in the centre is used, the rock may very likely be missed. The size of the boats will govern the length of line between them. It is by no means an easy thing to do efficiently, so that all the ground FIG.26. shall be traversed without unnecessarily going over it again and again. If steam-cutters are used, care must be taken not to go too fast for the weights attached, or the bight of line will be towed nearer the surface than is intended. Shoal banks, out of sight of land, or too far off to use Sounding marks, can be sounded by starring round the ship, at anchor on it, or off its edge. For these, compass-bearings of the ship land, taken from the boat, with distance measured by the mast- head-angle, will probably suffice in accuracy, the boats sound- ing in lines radiating from the ship in all directions. A large canvas ball or cylinder, on a light framework of iron and painted black, will be found very useful at the masthead when taking the angle for this purpose, as it will 134 HYDROGRAPHICAL SURVEYING. CHAP. vin. clearly define the masthead, and also indicates, " Ship in position." Boats or beacons can be moored in convenient positions, and fixed by angles to one another, and to and from the ship, also at anchor, and the base obtained by masthead-angle, if it is necessary to sound a bank a little more accurately. These will then be used as marks, and the soundings fixed by angles in the ordinary way. Measuring In all sounding, the lead-lines should be measured on Une*"" return on board, and a note made in the book, "Lead line correct," or so much out. When the line has not been used for some time, it should be measured before leaving in the morning also ; but if it has been examined the evening before, this will not be necessary. While on this subject, it may be noted that new lead-line should never be used for boats' soundings. At the beginning of the commission it may be necessary to do so, but after- wards make lead-lines out of old well-stretched stuff that has been used for deep lines for ships sounding, and measure and mark them when wet. Necessity The soundings must be put into the book to the exact depth tions. obtained, but it will depend upon the scale, the general accuracy of the chart, and the thickness of the soundings, how far halves and quarters will be placed on the sheet. As a rule, fractions should be retained up to 6 fathoms, and over that depth only the even fathom, taking of course the fathom under the depth. Thus a sounding which, when reduced to low water, is 9|, will appear as 9 fathoms. Reducing The necessity for accuracy in reducing soundings to low *' water will also very much depend on the scale of the chart and the depths. It is evident that with soundings of over 6 fathoms at low water, if we are using a small scale, where the size of the figure placed on the chart will, in reality, cover ground on which we have taken five or six soundings, any nicety of reduction is an absurdity, and labour thrown away; but in shallow water the reduction will be just as necessary in a small scale as a large, as a sounding of 5 CHAP. viii. SOUNDING. 135 fathoms will be a danger or not, according to what amount of reduction we apply. It is usual in surveying vessels to depart from the time- Calling honoured habit of calling soundings, and to call simply " six ^^d^fi and three-quarters," " five and a half," and so on. This is simpler, and saves time. The men should also be trained to call out sharply, and on no account allowed to drawl. There are, however, two exceptions to this. " Seven " and " Eleven " have a great similarity when called from the chains, and to prevent mistakes, "Deep eleven" should be called. Similarly " Mne " and " Five " sound much alike, and " Deep nine" should be given. "Five" and "Seven" are given simply. On all occasions, whether in ship or boats, when the leads- " Shoal man suddenly gets a shoaler cast than expected from his water ' previous soundings, he should call out " Shoal water," without waiting to complete his usually fruitless endeavours to gather in the slack line, and find out the depth. The author has been on shore from the neglect of this, the leadsman being foolish enough to wait until he had repeated his cast, so as to give the correct depth, and gave no warning to the officer on the bridge until too late. Belcher proposes a plan for ascertaining the depth on a bar Belcher's which it is desired to cross, without risking a capsize, which may be quoted, though we have no knowledge of its having been practically tried. He suggests anchoring the boat as close to the bar as is safe, with the tide at flood, and veering away a barricoe with a grapnel hanging at a given length of rope. The barricoe is permitted to drift freely over the bar, when the anchor catching, will give a shock to the barricoe that will be seen by the watcher in the boat, and will indicate that a less depth than the length of the cable allowed to the anchor is on that part of the bar. The line attached to the barricoe, with presumably a tripping connection with the grapnel, will bring the apparatus back to the boat, when she can test another part of the bar in the same manner. 136 HYDROGRAPHICAL SURVEYING. CHAP. vm. Usual plan. Arrange- ment for expe- ditions sounding. SHIP SOUNDING. The soundings over a certain depth, about 20 fathoms, can generally be most advantageously done from the ship. Where a steam winch is fitted, soundings can be got with great rapidity ; and by dropping the lead from forward and heaving it up to a davit fitted on the taffrail, up-and-down casts can be got in 40 fathoms at a speed of about four and a-half knots without stopping, with a 100 Ib. lead. Generally speaking, in making a chart, it is sufficient if the soundings are carried out to a depth of 100 fathoms, but this must vary very much with the nature of the coast. To minimise labour and time, a variety of methods are used to get the lead and line forward after sounding, and to drop it again. The following has been eventually adopted by the writer, and has worked very satisfactorily. An endless rounding line of lead-line was carried from the winch, by leading blocks, to a block on the foreyard-arm, then to a block on the sounding davit aft, and then again to the winch. In this rounding line, at every 5 fathoms, were cut splices, forming loops in the line. On to the lead was lashed a slip, of the form in Figure 27. The block on the foreyard had a square board firmly fixed at its head, projecting about 8 inches beyond it. When the lead was hove up from the bottom to the sound- ing davit aft, the tongue of the slip was passed through a loop on the rounding line. The latter was then brought to the winch, and the lead being lowered into the water, was hove up to the foreyard by the rounding line. When the striker a touched the board on the block, the tongue of the slip was freed, by the striker pushing down the catch c, and the lead fell from the yard-arm. A sounding could be obtained every 2J minutes in this way, when required. By dropping the lead well away from the ship, as was here done, the chances of the lead-line fouling the screw, if the helm was over, were much lessened. CHAP. V11I. SHIP SOUNDING. 137 d a. Iron rod Striker, connected to catch c, by a pin. b. Tongue of Slip. c. Catch, working on hinge. d. Fairlead tor Striker. /. Wooden board. g. Block on foreyard. UNIVERSITY 138 HYDROGRAPHICAL SURVEYING. CHAP. vm. Instm- There are a variety of instruments now invented for giving recording tne accurate depth when the line cannot be got up and down ; depth. some depending on a fan which works a series of cogged wheels, as Massey's ; others, on pressure at different depths. These are all useful, and when their errors have been obtained, may be attached to the lead with frequent advantage. Sir William Thomson's newly invented pressure-gauge has yet to be tried to ascertain whether it stands the test of long and hard work. The first navigational machine by the same inventor is not adapted to surveying as at present fitted, though eminently useful for the purpose for which it was designed. We know nothing personally of Lucas's machine, though informed it is very good. Burt's bag and nipper are useful when the ship drifts away from the vertical position over the lead, and one should always be handy when sounding. Perfect -^ ^ s evident that a perfect machine is more trustworthy machine than the record of an up-and-down cast with the ship in made. motion, as given by a fallible man ; and when such perfect machine is invented, it will be gladly adopted by surveyors ; but, up to the present time, the machines are more liable to error than a trained man, under most circumstances. Long lines In localities where currents are prevalent and vary, when in 8 off d " we are runn ^ n g l n g li nes f soundings in the ship off shore, shore. out of sight of land, it is very important to get, on the re- turn line towards the shore, a fix as soon as possible. The soundings we are obtaining may be hereafter used, especially where fogs are frequent (as, e.g. British Channel, Bay of Fundy), to give vessels a notion of their position, and we must therefore use every dodge to get our true position at the earliest opportunity, so as to depend upon dead reckoning as little as we can. Two theodolite stations, from which a large flag at the mast- head can be observed as soon as it appears above the horizon, is a plan sometimes employed. These need not see one another. As long as their relative positions on the chart are known, CHAP. VIIL SHIP SOUNDING. 139 and the true bearing of the zero employed has been established, the angles to the ship can be plotted. It is scarcely necessary to say that an observer will be on Surveyor the topgallant yard of the ship, as he may, from atmospheric aloftl or local causes, be able to see something on the land before the theodolite observers catch sight of the ship. True bearings come in useful again. The angular distance between the sun and the mountain, or other object, seen from aloft, will be taken by the observer aloft, while the sun's alti- tude is taken from deck for the azimuth. Another method is to have one or two ships anchored as far Tenders, from the land as they can fix, which observe, and are observed from, the sounding ship, as she runs in and out on her lines. A ship can easily, in light winds, anchor in 100 fathoms, and even in deeper water. When land stations are employed, heliostats are useful, as use of informing the running ship that she is seen from the station. heliostat - A flash will tell the officer aloft that a sounding can be taken, with the certainty of an angle being got to the ship, for which, perhaps, she has been waiting. If not able to return and pick up the land before nightfall, Position blue lights and rockets are useful, both from stations and after dark moving ship. A true bearing of a light, or mountain, if visible, as it often Use of is a great distance on moonlight nights, can be obtained in star8 ' the northern hemisphere very conveniently by the angular distance from the Pole star, as described on page 250. This angular distance can again be taken from aloft ; but in the case of Polaris, we require no altitude.. If Polaris is not available, a time azimuth of a star near the prime vertical will give a good result. Should the resulting longitude differ much from the assumed, it may be necessary to re-calculate. Altitude azimuths cannot be much trusted in at night. When objects are visible from deck at night, and we can Compass rely on the compass, very good bearings can be taken with bearm & s - the standard, if a tripod be fitted to carry the lamp and throw 140 HYDROGRAPHICAL SURVEYING. CHAP. vin. the light down on to the card, but yet allow the azimuth arrangements of the compass to be used, as in the daytime. Deck A ruled " Deck Book " is convenient for ship's sounding. In this everything taken from the ship should be recorded, as, rounds of angles when the ship is used as a station in main triangulation ; elevations with sextant, and the corre- sponding fix ; sketches of little bits of coast, &c. SEARCHING FOB VIGIAS. Difficult of In searching for a " vigia," it is difficult to say when its disproof. ex i s tence is to be considered as disproved. Although expe- rience shows that nine out of ten of these bugbears and blots on the oceanic charts have been mistakenly placed there, from reports of floating whales, wrecks, and patches of conferva taken for discoloured water over a bank, &c., still the apparently astounding manner in which coral banks rise from very deep water must always make us careful of assuming from a hasty search, that no shoal water exists near a given locality. Area of The area over which to search must always be large, as search. s hip' s reckonings, especially as regards longitude, are so often considerably in error. In the vicinity of such reefs also, currents are generally accelerated, and altogether we must allow a large margin, in undertaking to search for a danger reported in a particular spot. Small area In clear bright weather, coral banks will show some miles We^Lth* 1 " w ^ ^ e sun * n ^ e r igkt direction ; but under other circum- put much stances it is quite possible for a ship to pass within a mile of indication. a ^^ with as little water as 3 fathoms on it, without its being detected. Assuming that coral reefs are built on submerged mountain- peaks, a little consideration will show that there is nothing extraordinary in a shoal near the surface standing in 2000 fathoms water, on a base of not more than three miles diameter. The annexed sketch, Fig. 28, will show that we are not CHAP. viii. SEARCHING FOR VIGIAS. 14* assuming an improbable steepness of side to the submerged island. This allows us to pass little more than 1J miles from such a shoal, and still get a cast of 2000 fathoms, so that even a positive sounding of great depth will only cover a compara- tively small area, and soundings of a hundred fathoms, no bottom, do not assure us of anything to a certainty, except that the reef does not exist within a few hundred yards of that cast. The difficulty of fixing the position at sea to within three Doubt as miles or so, adds another element of uncertainty to our search, position^ so that it is only by crossing and recrossing the area to be examined that we can at length say, positively, nothing is there. This is especially the case where the reported danger is Credence in reports. FIG. 28. Surface of Sea out of the usual track of ships, as there is nothing improbable then in its having escaped notice up to that time. Where the locality is frequently passed over, there is more prima facie reason for doubting the report, and in many instances, a cross- examination of the person making the report, will show how very slight is the ground for it. An actual cast of the lead seems a fact impossible to make a mistake about, but instances have occurred where this also has proved to be so, even with so-called " bottom " brought up. In cases, however, where a sounding has been obtained, we must conclude the report to be true, and a rigorous search must be made before the vigia can be obliterated. As a general rule, for the first commencement it is best to Prelimi- run lines east and west in or near the latitude reported, as this is more likely to be near the truth than the longitude. 142 HYDROGRAPHICAL SURVEYING. CHAP. vni. When going to make an exhaustive search, the first day is perhaps best spent in doing this without getting more than may be one positive sounding, as we can cover more ground, and, if the danger exists, we have a good chance of finding it by sight, or by the soundings taken when the ship is running, as of course the deep-sea lead will be kept going constantly. Lying-to It is rather unpleasant to be drifting about at night with vigLs at re P rte(i reefs in the vicinity, and by no means a bad precau- night, tion is to to ease a kedge anchor down to 100 fathoms or so, which may bring the ship up, or at any rate show, by drawing ahead, that bottom is reached, before she strikes on the reef. At night the vicinity of a reef in open ocean may be indi- cated by fish, which invariably frequent these isolated spots, and here phosphorescence will help greatly in making their presence very apparent. In daytime, birds, which generally congregate wherever fish are plentiful, may be an indication. Decision In every case, of course, the surveyor transmits home a plan iTdro* 1 * 11 ^ ki g ^ rac k an( ^ soundings, as it is at headquarters only that grapher. a decision on the matter can be arrived at. Under the head of " Sea Observations " will be found hints as to early ascertaining of the ship's position, a most important matter on each morning. (H3 ) CHAPTEE IX. TIDES. ALL soundings in published charts are given for low water at Tidal ordinary spring-tides ; we therefore want all the information jjjjjjj^a. we can get about the tides, and the very first thing to be done menced at on arriving on the surveying ground is to commence observa- OI tions on them. There are very few parts of the world in which we have absolutely no knowledge of the tidal movement, so we have generally something to commence upon. That is, we usually know within an hour or two the time of high water at full and new moon, called H. W. F. and C. on the charts, as, except in estuaries or peculiarly shaped coasts, this will not differ greatly from places near at hand, and the same may be said for the range of the tide. It will altogether depend upon our length of stay in any Different locality, as to what we can hope to find out about the tides, ti^nffor To get full information requires observation during months in different succession, as in many parts the tides vary considerably different times of year. The number of high and low tides in a day, in certain places, departs from the normal phase of from 6 to 7 hours for each rise or fall ; in others, the tide will take longer to rise or fall, than vice versa, &c., &c. A long series of this kind is therefore very valuable, as the tidal theories are at present far from fulfilling all the requirements of observa- tion all over the world, and good data are much wanted, but it is not often we can do this. It will be seen, then, that tidal observations for the practical reduction of soundings for purposes of navigation are one 144 HYDROGRAPHICAL SURVEYING. CHAP. ix. thing, and those for obtaining additional data for scientific investigation are another. We shall mainly concern ourselves with the former, where much rougher observations are usually admissible ; but here, again, it must depend upon the scale and nature of our chart what degree of nicety is requisite. Admiralty The tides are fully discussed in the ' Admiralty Manual of Tides 1 n Scientinc Inquiry/ article " Tides/' to which excellent treatise on the subject we refer the reader for many points of the theory of the tides not touched upon in these pages. The general ' Instructions for Hydrographic Surveyors ' also contain many valuable hints on the tides. Local A regular series of observations, even for our practical work, stances should be taken if possible ; but in many cases the necessity for leaving tide- watchers encamped is inconvenient, and may be unhealthy, and we may have to be satisfied by obtaining what will be sufficient to enable us to construct the chart, which is our immediate business. In other cases we may only be staying a few days at -a place, as when making a plan of a small isolated harbour. Observa- What we absolutely require in making a chart, is to know ti wable S ~ ^ e h^gkt ^ tne water > whilst sounding is going on, above the level of low- water springs, which is called the " datum for reduction." We shall also wish to ascertain, if possible, the " establish- ment," which is the time of high water at full and new moon, called in the charts, " High water at full and change ; " the rise of spring-tides above our datum ; and the range of the tides at neaps, as these will give valuable information to the navigator. We may here give definitions of some of the terms used in speaking of the tides. Defini- " Eise " of a tide is the height of the high-water level above the low spring datum. " Eange " is the difference between the height of high and low- water levels of any one tide, without any reference to the datum. CHAP. IX. TIDES. 145 The " semimensual inequality of heights " is the difference between the heights of spring and neap tides above mean water-level. The "diurnal inequality of heights" is, in irregular tides, the difference between the height of high water of each successive tide. The "age of the tide " is the interval between the time of new or full moon, and the time of the next spring-tide, and varies from 1J to 3 days. The " lunitidal interval " is the time that elapses each day, between the transit of the moon over the meridian, and high water. The " establishment " may be also defined as the lunitidal interval when the time of moon's mer. pass, is O h . O m . or 12 h . 00 m . This is called the " vulgar establishment." The " mean establishment " is the mean of all the lunitidal intervals in a semilunation, and may differ considerably from the vulgar establishment. The latter is the high- water full and change given in the charts. The " semimensual inequality of time " is the difference between the greatest and smallest lunitidal interval. The " diurnal inequality of time " is, in irregular tides, the difference between the lunitidal intervals of each successive tide. The varieties in the motion of the tides is caused, first, by Cause of the relative positions of the sun and moon, and secondly, by local influences, such as the conformation of the land, winds, &c. It is the existence of the latter which causes most irregularity in the tides. Where they are absent, or present in such a form as to exert a continual influence on the movement of the water, the tides will be regular, that is, they will follow a certain rule, which will apparently be dependent solely on the places of the sun and moon. The height of the barometer also affects the tide con- siderably, the higher the barometer the lower is the level of the water. 146 HYDROGRAPHICAL SURVEYING. CHAP. ix. Observa- The time of the moon's transit over the meridian gives us a referred to rou g n measurement -of the relative position of sun and moon Moon's in right ascension, and it is therefore to this meridian passage of the moon that we refer all calculations of the tides. If the tides are regular, we shall find that on days on which the moon passes the meridian at the same time, the times and heights of high and low water will be the same. This knowledge is very valuable in many surveys where from local causes we cannot always have a tide pole going, as from previous observation we can, when the tides have been found to be regular, construct a table founded on moon's meridian passage, from which we can take out a reduction for soundings, when working on a small scale. When we arrive on our surveying ground, then, one of the first things to do will be to set up a tide pole, whatever is going to be the character of our observations. Position For this we want a sheltered spot, if we can find one, and p^J lde also firm ground on which to place it, as nothing is more annoying than to find the pole down, especially when out of sight of the ship, when the tide-watchers, unassisted, generally succeed in putting it up again in a different position. If a pier is available, there is nothing so simple and satis- factory as a plank secured to it, marked in feet and inches, the former being painted red, white, and blue alternately, with bold black figures. Tide poles. If we have no pier, an ordinary spar, shod with an iron spike and painted as above, driven as far into the ground as possible and well stayed to heavy weights, anchors, rocks, or whatever we can get, will stand well, and generally answers our practical purposes. This may sometimes be so placed as to be read from the ship with a glass. If, however, there is no shelter and much wash of the sea, and accurate observations are required, we must use a tube of some kind. A square one of deals can be knocked up on board ; but it must not be too small, as we shall want a slit down one side CHAP. ix. TIDES. 147 through which an indicator fixed to a rod carried by a float inside may work, and the water washing in by this slit will destroy the value of the tube, unless the area of it be large enough to make the water thus admitted too insigni- ficant in quantity to disturb practically the surface of the water inside. Where there is not much range of tide, the slit can be dispensed with, and the rise and fall marked by an indicator protruding from the top of the. tube, (which in this case could be a boiler tube,) and marking on a scale lashed so as to project above the tube. The water would be admitted by holes bored near the bottom of the tube, if it is to be placed on muddy ground. Whenever it can be done, a mark should be made on some Fixed fixed object near the tide pole, corresponding to some mark on the pole, which can then be replaced in the same position if it accidentally gets displaced. The level of the water on the tide-gauge should be noted Time of every hour of, if we are going to make a regular series, both ticna night and day, if simply to get a datum for soundings, only of the day, except at springs, when it is as well to get the high and low water at night also, as night tides in some places and at some seasons are lower or higher than the day ones. It is not amiss in any case, when nothing is known of the tides, to observe for twenty-four hours, at half-hour intervals, as a commencement, as this will tell us whether the tides are regular or not, and we can take observations accordingly. To get the time and height of high and low water accu- High and rately, observe every ten minutes, for half an hour or so, JjJJ^ before and after high and low water, and calculate from these Observa- records the exact time and height required. This is best done by projecting graphically thus : Divide Graphic a line into equal parts to represent hours and minutes, and from this, at the corresponding time, set off at right angles distances, on any chosen scale, to represent the height of tide registered at that time. These spots, joined by a curve, will enable the time and height of high or low water to be arrived at much nearer than by simple observation. L 2 Approxi- mating a Datum. 148 HYDROGRAPHICAL S UR VE YING. CHAP. IX. Thus, suppose we have noted X 00 A M. ft. in. 12 3 10 20 30 40 50 ..XI. 00 .. 12 8 .. 13 .. 13 1 .. 13 1 .. 12 10 .. 12 5 We project these as in accompanying Figure 29, and by FEET 6- 3 13J FIG. 29. 3- 12- !. . \ 40 50 XLl drawing a horizontal line from the X. 10 position to the opposite side of the curve, , bisecting it, and letting fall a perpendicular to the line of time, we find X. 32 as the time of high water. The compasses, measuring the highest point of the curve, gives a little over 13 feet 1 inch as the height marked on the pole. If we are at the place during the spring-tides, we can get a fair low- water datum by observation, and all soundings will be reduced to that, by the height marked on the pole above this datum, at the time the soundings were taken each day, being subtracted from them. But it may happen that we arrive at the place a few days after a spring-tide, and leave again before the next one. The only thing to do is to note the high-water mark on the shore, and ascertain by measure- ment how far it is above the high tide of the day as marked also on the shore, subtract the same quantity from the low- water mark on the pole of that day, and call that the low- water spring datum, subtracting perhaps a foot or two extra, to be on the safe side. CHAP. ix. TIDES. 149 Thus, suppose at high water our pole marks 13 feet 1 inch, and the high-water mark on the beach is 2 feet 6 inches above the level of the sea at that time ; at low water the pole marks 5 feet 8 inches. This will give us 3 feet 2 inches as the probable low-water spring mark. ^ we reduce our soundings 2 feet below this to the 1-foot mark, we shall be pretty certain not to give too much water on shoal spots. An approximation of this kind would be of course noted on the chart when sent home, and also the manner in which the rise of spring-tides, which would be given as 14 feet, has been obtained. In still rougher work, an approximation of the rise of Rougher the tide may be got by having a marked boat-hook held JSSioTo upright at the water-line at time of low water ; the ob- datum, server then places his eye at the high-water mark on the beach, and reads the mark on the boat-hook, where the horizon line cuts the latter, which will be the fall of the tide that day below high-water mark. If it is the high-water mark of the day that is so used^the result is the range of the tide for the day ; and if the distance that the springs' mark is above the day high-tide mark can be measured, we can arrive at the full rise and fall, as in the last article. This may be very useful in making a hurried plan of a bay, and thus the height of the water can be got by the officer putting in the coast-line from time to time during the day, without delaying him much, and to the great advantage of the correctness of the soundings being taken at the time. The "vulgar establishment" is an exceedingly loose term, as Estimation given on the charts. As it is strictly only on days when the moon's mer. pass, is 12 h . or O h ., that it can be directly observed, the surveyor is obliged to approximate to it in most cases. This perhaps matters the less from the fact that the establishment, even when correctly obtained, is seldom in- variable. The best way to approximate is to project the line of semi- mensual inequality as in Fig. 31, and measure the length of ISO HYDROGRAPHICAL SURVEYING. CHAP. ix. the abscissae from XIP. and O h . for the vulgar establishment, meaning them if we. get more than one. Thus, in example of Fig. 31, we should call it 3 h< 55 m . If the tides are regular, especially as regards the semi- mensual inequality, the establishment may be roughly deter- mined by a method given in the ' Admiralty Manual,' from an observation of the tide at any period of the moon's transit, but which we shall not further discuss, as, in a case where it would be required, we should not know whether the tides are regular or not, and any assumption would probably end in very erroneous results. Interpo- In a case where only the high and low waters on any day heMrt f are ^^ a ^ ne( ^> ^ ne height of the tide, at times between, is best Tide. to be got at by drawing a curve in the imagined course of the tide, after the manner of Fig. 30 ; the height on the pole at FIG.30. any time can then be taken from this, and a table of reduc- tion formed for the day. Thus, in Fig. 30, where we have only got the times and heights at high and low water on that day, viz. H. W. at VI. 50, mark on pole 15 feet 7 inches ; L. W. at I. 10, mark on pole 8 feet. CHAP. ix. TIDES. 1 5 1 On a piece of paper, either ruled in squares for the purpose, or on ready-printed squared paper, which is very useful to have by one for these like occasions, we draw a curve after the fashion shown. Then, supposing our datum for reduc- tion to have been settled as 4 feet on the pole, our table of reduction for the day will stand as follows : VI 11 ft. or 2 fms. VII 11J or 2 VIII 11 or 2 IX 91 or If X 8 or 1| XI 6 or 1 Noon 4? or I , I 4 ft. or f fms. II 4 or f III 5 or 1 IV 7 or li V 84 or 1* VI 10| or If VII Hi or 2 This will of course be, as all attempts at arriving at any- thing with insufficient data, only an approximation, but will probably be near enough for the purposes we want. If we intend great accuracy, we shall make arrangements to have the tide carefully observed throughout the day, whenever sounding is going on, and take every precaution not to be reduced to these straits. When tides are found to be regular, a table of reduction Table of may be formed from the observations during one or more ^JJ** complete lunations, by tabulating the tides according to the certain time of moon's upper transit. Such a table may be very stances, useful when the scale of the chart is small ; and sounding can be carried on under these circumstances, viz. regular tides, and scale of chart small, when no direct observations can be got. In many places external circumstances control our wishes. For instance, it was found on the East Coast of Africa that if men were landed to make a regular series of day and night observations on the tides, fever generally ensued, and conse- quently the record was restricted to day tides. Again, the tide pole may have to be so placed on a shelving shore, or among reefs, that a boat would have to be used to go out at high water to read it, and this may not be convenient. Often, for considerable tracts among reefs, observations may be im- 152 HYDROGRAPHICAL SURVEYING. CHAP. ix. possible, and a table deduced, as above suggested, from former observations may be then used. Graphic In forming such a table, it is best to project the tidal f/Tidai 011 curves as snown m Fig. 30, but by the hourly observations. Movement It will then be seen whether the tides are regular, and days of similar time of upper transit of the moon can be compared, to see whether a table will give us the reduction near enough for practical purposes. The movement of the tides, as far as the high and low waters are concerned, can be conveniently projected, as in Fig. 31, which will at once show whether the motion is regular. The example given in the figure shows the tides for a few days only more than a complete lunation, but it will be seen that by continuing it, the regularity or otherwise of the tides will be at once apparent. The diagram (which was made out by observations of day tides only) shows the heights of high and low waters corre- sponding to the time of moon's upper transit, as given on the horizontal scale ; the heights in feet being given on the right- hand vertical line. The scale of lunitidal intervals is given on the left, and the curve of semimensual inequality shows the manner in which the time of high water varies, with regard to the moon's transit at different parts of the lunar month. The time of moon's transit for each day should be roughly corrected for the longitude. The mean between each high and low-water height will give roughly the mean water-level. True Mean To obtain the true mean water-level in a few days, other Level r " observations must be taken, and we subjoin an extract from the " Instructions to H.M.S. Challenger" which contains full directions, only adding that these observations must be made when the tide is moving normally, that is, when there are no strong winds to raise or depress the water-level. " A good determination of the mean level-sea by the simple operation of taking means may be made, in less than two days, with even a moderate number of observations properly distributed so as to subdivide "both solar and lunar days into Intervals Heights above Datum in feet 154 HYDROGRAPHICAL SURVEYING. CHAP. ix. not less than three equal parts. Suppose, for example, we choose 8 -hour intervals, both solar and lunar. Take a lunar day at 24 hours 48 minutes solar time, which is near enough, and is convenient for division ; and choosing any convenient hour for commencement, let the height of the water be ob- served at the following times, reckoned from the commence- ment : h. m. h. m. h. m. 00 80 16 8 16 16 16 24 16 16 32 24 32 32 32 " The observations may be regarded as forming three groups of three each, the member of each group being separated by 8 hours solar or lunar, while one group is separated from the next by 8 hours lunar or solar. In the mean of the 9 results the lunar and solar semidiurnal and diurnal inequalities are all four eliminated. " Nine is the smallest number of observations which can form a complete series. If the solar day be divided into m and the lunar into n equal parts, where m and n must both be greater than 2, there will be mn observations in the series ; and if either m or n be a multiple of 3, or of a larger number, the whole series may be divided into two or more series having no observation in common, and each complete in itself. The accuracy of the method can thus be tested, by comparing the means obtained from the separate sub-series of which the whole is made up. " Should the ship's stay not permit of the employment of the above method, a very fair determination may be made in less than a day, by taking the mean of n observations taken at intervals of the nth part of a lunar day, n being greater than 2. Thus if n = 3, these observations require a total interval of time amounting to only 16 hours 32 minutes. The theoretical error of this method is very small, and the result thus obtained is decidedly to be preferred to the mere mean of the heights at high and low water. " The mean level thus determined is subject to meteorolo- CHAP. ix. TIDES. 155 gical influences, and it would be desirable, should there be an opportunity, to redetermine it at the same place at a different time of year. Should a regular series of observations for a fortnight be instituted, it would be superfluous to make an independent determination of the mean sea-level by either of the above methods at the same time." In some cases the mean level of the water may be made use of as a temporary datum for reducing the soundings. If, for instance, we commence soundings in a place where we do not yet know the spring's range, but intend to get it accurately after some months' observations, we may find it convenient to reduce all soundings to the mean level, as found by meaning each day's high and low water. Then, when we have ascertained the level of low springs below this mean level, one uniform quantity will have to be subtracted from every sounding, which will save a good deal of compli- cation and waiting, as the soundings may all be plotted without fear of mistakes in reducing them afterwards. This mode will be mostly used for shallow channels, where a difference of a foot or two is an important matter, but it is liable to the error caused by variation in the height of the mean tide-level. The direction and rate of the tidal streams and other Tidal 11 i Streams currents must be observed. andSur- This is best done under ordinary circumstances from the faoe Cur rents, ship at anchor by means of a current log, which is simply a Currellt very large log-ship, and is worked in the ordinary manner, log. but with a longer interval of time. The line, which is small, is marked at every 10 feet, and is permitted to run out for an even number of minutes, varying according to the velocity of the current. Then the rate per hour of the current = number of feet run out, divided by one hundred times the number of minutes. Thus, if the log-ship is permitted to run for three minutes, and 220 feet of line pass out, 220 Bate per hour = O = > 73 knots. 156 HYDROGRAPHICAL SURVEYING. CHAP. ix. This current log should be hove at stated times, whenever the ship is on her surveying ground, and at anchor, and an entry made in the current log whether there is anything recorded or not, as negative results are in some ways as valuable as positive ones. Where the tidal range is great, and streams change their direction, these observations will be made at comparatively short intervals, in order to ascertain the movement of the water at different times of the tide. Where streams are strong, and of importance in navigation, assistants will be sent to heave the current log from a boat at anchor in different positions. The current log can be kept by quartermasters, with super- vision. A watch or clock with a seconds-hand is a requisite. In the log will be entered the position, time, direction of drift of the log-ship, number of minutes it was allowed to run out, and number of feet of line run out, wind and force. Blank columns for rate per hour, and time of tide, will be filled up afterwards by the officer discussing the currents. The direction of the tidal stream will frequently change direction' Before ^& n or * ow water > an d when this occurs, we must of Tidal endeavour to find out whether the change of stream occurs at streams. ft jgg-Qigj. ^ me O f ^he t^e, as this is an important point in the navigation of channels. ( 157 ) CHAPTER X. TOPOGKAPHY. THE sketching in of the topography, or detail of the land, is a point on which there is more variation, as to the manner in which it is done, than in any other of the steps of a survey. It is the least necessary part of a chart, which is destined mainly to guide over the water and not on the land ; but as we are guided over the water ly the land, a perfect chart should have the features of the country correctly delineated, so as to assist the mariner in recognising the land by the mutual positions of peaks and other conspicuous objects. Furthermore, with our universal presence and interest all over the globe, it is impossible to say that an expedition may not want to start from some point on our chart, when information for a short distance inland will, in such a case, be most useful. As a general rule, the land should be put in as far back Width of from the shore as it is visible from the sea ; but this is Sophy only a very general guide and must depend upon the distance k 001 Coast of the back ranges, and the size of our sheet of paper. When the most distant mountains are very far back, we cannot spare time to do more than fix their summits by angles, get their heights and the extent of the range, and the country between must be a perfect blank. Often, in savage lands, the country will be too dense with Bough jungle to be able to do much to the topography by walking over it, which is of course the only way to get it correctly mapped, and we must then be content to sketch what we can IS 8 HYDROGRAPHICAL SURVEYING. CHAP. x. see from the sea, and from the coast. By making stations in the ship, drawing a sketch at each, and getting angles to all prominent parts, such as spurs of hills, valleys, ravines, smaller peaks, &c., which will be entered on the sketch, a very fair approximation of the position and shape of the more conspicuous elevations in the land, visible from seaward, will be made. The officer coast-lining will have got the entrances of all little streams fixed, and from the ship off shore we can recognise which ravines, or at any rate which of the larger ones, join on to these entrances. Topography put in in this way will present a somewhat detached appearance, and we can only fill up the hiatus by writing on the chart the general appearance of the land intervening between the hills, as far as we can see it from aloft, as, " rolling grassy plain," " densely wooded and undulating," &c. Sometimes, on a coast of this description, we can get back from time to time to an elevation we see from the ship to be partially clear, and a sketch from a position of that kind will materially improve our knowledge of the topography. By referring to the sketch at page 79 it will be seen how, with similar views from different points, ravines and valleys may be cut in, and roughly drawn on the chart. Regular When, however, we can spare the time to perfect our chart, graphy. an( ^ ^e na ture of the country permits it, we should walk all over it, and sketch the topography on the ground. To do this, we must have as many conspicuous objects as possible fixed beforehand, and pricked on to a board, as for sounding or coast-line. Topography can be plotted afterwards, the same as can be done with coast-line or any other work, but it will be much more satisfactorily done if plotted at the time. We then walk over our country, fixing ourselves with angles on commanding spots, plotting the stations by the station pointer or tracing-paper, and drawing lines from them to all things we want to plot, spurs of hills, houses, valleys, &c., &c., and sketching the details immediately around us. To fix details for this purpose we shall often have to content ourselves with two angles only, and as long we do not CHAP. x. TOPOGRAPHY. 159 use such points to carry on our stations with, this will be sufficient. A good deal of judgment is necessary in selecting spots to make stations, which cannot come without experience. In placing the details on the paper on the rough board, sketch in the line of a valley first by the stream at the bottom, and then the adjacent hills or spurs. These are best shown by contours. We do not of course contour- pretend that our contours are a fixed distance apart, but we "* must endeavour to draw them approximately so, calling each contour line, 25, 50, or 100 feet apart, as the scale may require, and estimating the height of each spur, with the assistance of a pocket barometer, if we have one, which will give us roughly the height of each station above the sea, if we read it when we land, and whenever we have occasion to do so. Each contour must be continued on from one hill to the other, or until it meets itself again round the hill ; and as their number and closeness together will roughly indicate the height of the hill, we must be careful not to get more on one side of a hill than another, or the value of this method will be lost, and the contours will simply show the shape of each spur, without reference to its relation in height, steepness, &c., to the next one, which is what we want to show as well. These contours will perhaps not appear in the finished chart, in which the mountains may be delineated in a different manner, but they will form an excellent guide for the amount of shade to be put on to the different hills and slopes, and it is the readiest and quickest method of showing this at the time. Eed and blue pencils are useful for topography. With the Bed and blue we show streams, and the red is used for marking roads, p 1 ^^ With only a black-lead pencil, the markings of these details are apt to get confused with the contour-lines to express the hills. Much topography can be done with the pocket sextant and Pocket compass only, the latter being only used, however, when l^*** three objects to fix by cannot be got. The magnetic meridian, Compass, or several magnetic meridians, must be ruled on to the rough 160 HYDROGRAPHICAL SURVEYING. CHAP X. board, to permit the use of bearings. When the only objects available are much above us or below us, correct angles cannot be got with the sextant ; and though we allow ourselves a certain amount of latitude in our angles for the purpose of topography, it will often be necessary to take a small theodolite for the purpose. A pocket sextant can be taken as well, and the theodolite, which requires more time to set up and arrange, only be used when the sextant angles will be too erroneous. If we have a theodolite, we must take advantage of good opportunities to get a series of elevations and depressions for heights. Difficulties In taking angles with a sextant to objects on different Sextant l ev els, try to find some natural mark which is exactly above angles. or below, as the case may be, the object the farthest from your level, and nearly on a level with the other object, and take this instead of the object itself. But it must be noted that unless this second object is nearly at the level of the observer, the angle will still be incorrect. Pig. 32 shows a rough field board, before any shading is placed on the sides of the valleys, which will be done with the brush before the work is considered completed. HAP. xi. ROUGH CONTOURING ON FIELD BOARD. 161 162 HYDROGRAPHICAL SURVEYING. CHAP. XL CHAPTER XL HEIGHTS. By Thedodolite By Sextant By Depressions to Masthead and Water- line Obtaining Distance from Elevation of a known Height. Means FOR obtaining heights, we must mainly depend on angles of used ' elevation with sextant from afloat, and of elevation and de- pression with theodolite from shore stations. The pocket aneroid, though useful, as described under " Topography," to get subsidiary heights, and assist in delineation of hills, is not to be depended upon. Stations At all main stations, and, in fact, any station well fixed or obtain- an( j conveniently placed, angles of elevation and depression Heights, to the objects whose heights we want, should be taken throughout the course of the work. These are entered into the " Height Book," and worked out when we can get the dis- tances, and occasion offers, the results being tabulated and meaned. Elevations and depressions can be taken from any station whose height we shall eventually know; but it is evident, that, any slight error in the true height of the observing sta- tion will be carried on into all heights deduced from it, and therefore itis well to get as many observations as we can from stations at the water-level, or so placed that the height above the water-level can be measured with a line. Use of In observing elevations and depressions with a theodolite, Theodo- the instrument must be in fair adjustment, and carefully levelled, and it is further necessary to take into account the errors of level and collimation. CHAP. XL HEIGHTS. 163 There are two ways of doing this. One is to take a series of observations with the telescope in its ordinary position, and then another with the telescope reversed, end for end, in the Y's, when the mean of these two observations for each object will be the correct amount of elevation or depression. This is the best way, and eliminates all error. It may, however, be sometimes convenient to proceed as follows : Ascertain the collimation error by directing the telescope on to an object in elevation, reading the vernier, then turning the telescope round until the level is uppermost, and again adjusting for the object and reading the vernier again. Half the difference between the readings is the collimation error, which, when the reading taken with the level uppermost is greatest, will be added to observations of elevations made with the telescope in : its normal position, and subtracted from depressions. This collimation error is permanent for all positions of the horizontal arc. For level error, at each observation of each separate object, the telescope must be brought horizontal by the level attached to it, and the vernier of the vertical arc read. Whatever it reads will be the level error. The sign of the correction to be applied for this error is, for elevation, +, when the of the arc is above the zero of the vernier when the tube is level, and , when below. For depressions the signs will be reversed. Care must be taken that no mistakes are made as to these signs. For a tyro it is slightly confusing. Both level and collimation error must be applied to each observation. When the ship can be well fixed, sextant angles of elevation Sextant from her with a sea-horizon will be very good, as good, in fact, as elevations with a small theodolite, as they are free from all possible errors of levelling, &c., and a sextant measures angles to 10 seconds, whereas a small theodolite is only cut to minutes. Even when the ship is within the limits of the sea- horizon, the results will be good, providing the distance of the shore line is well known, and is not under half-a-mile. By M 2 1 64 HYDROGRAPHICAL SURVEYING. CHAP. xi. observing from the lowest step of the accommodation-ladder, we can use a shore horizon at even less distances. Sextant elevations, then, are very useful, but we do not generally get so many opportunities of obtaining series of heights by it, and when at any distance from the land, only the skyline of hills will be clearly seen, so that it is principally to the theodolite that we must look to give us a sufficiency of elevations. Result of The angle of elevation measured by a theodolite, or the Formo? * sextant angle when corrected for height of eye above the sea, the Earth, i s the angle between the tangent to the earth's surface at the observer's position, and the line drawn from him to the object. If the surface of the earth was a plane, all that would be necessary to obtain the height would be to work out in a right-angled triangle, Perp. = base X Tan angle of elevation, after the latter had been first corrected for the effects of refraction ; but as the earth is a sphere, the tangent to it> produced, will cut the line representing the height we want, not at the point where it leaves the earth, but somewhere above that, depending upon the distance ; the perpendicular, therefore, as worked out, will only give us a portion of the height required, the other portion being that below the tangent. Expiana- Thus, in Fig. 33, A is the position of the observer, A H the ^Di tangent to the earth's surface at his position, B a mountain peak whose height, B D, we want to obtain. The angle of ele- vation measured by a theodolite is BAH, and it is evident that the height we shall obtain by working out the triangle will be B H, leaving H D to be found independently. It will be seen that we are going to treat the angle B H A as if it was a right angle, when it is evidently more than 90 by the angle D C A at the centre of the earth ; but our figure is much exaggerated to show things clearly, and in practice the distances we use to get elevations are so insignificant, comparatively to the dia- meter of the earth, and consequently the angle D C A so small, that we can neglect this quantity without introducing any error in the result, With a distance of 60 miles, when the CHAP. xi. HEIGHTS. 165 angle is a degree, the discrepancy introduced into a height of 6000 feet is only 2 feet. We require, then, to get H D to add on to B H in order to get the full height B D. This quantity, H D, is called " dip," an awkward nomenclature, as it is the same used at sea to express the angular quantity we apply to elevations taken with a sextant from a height, to reduce them to the tangent to the earth, whereas here it is used to express a linear quantity. ^ FIG 33. Let B H, or difference of level, = h Proof of TT -r^ j . Formulae. H D, or dip - p H A, the distance in sea miles d D C and A C, radii of the earth r Eequired the dip, or p. Now, (p + r) 2 = r* + d* or, p 2 4- r 2 + 2p r = r 2 + d 2 Eliminating r 2 from both sides, we have p 2 is so small in practice, compared to 2pr that we can neglect it. 166 HYDROGRAPHICAL SURVEYING. CHAP. xi. .-. '2pr = d 2 d 2 or, p~- This will give us p in miles. To bring out p in feet, we must multiply by the number of feet in a nautical mile, using an average latitude, 30. 72 6060 ..; F *- 5T But, 2 r = circumference, 7T 360 X 60 7T 21600 7T 6060 - ' ' 21600 Which worked out gives Dip, or p = d z X 0-8815. We can by this formula calculate a table of dip for different distances, by looking at which we can at once take out the dip required. See Appendix, Table O. Eefrac- The dip we can therefore correct for pretty accurately ; but there is another thing to be taken into consideration, viz. the refraction, which, being variable, we cannot allow for so cer- tainly. The apparent position of one object from another, as seen through our atmosphere, appears higher, whether we look up or down. The amount varies with the difference of densities of the various strata of the air, which are constantly changing. All we can do is to take the mean refraction, and it has been found by experiment, that by taking ^ of the distance, re- garded as minutes and seconds of arc, and applying this to the observed angle of elevation, it will give us a fair mean result for the true angle of elevation, when this is small, as in all practical cases it is. It follows from this unknown amount CHAP. XI. . HEIGHTS. 167 of error in the coefficient of refraction that, when possible, objects should not be observed for elevation or depression at more than a few miles distance. We cannot always command the maintenance of this limit, any more than we can many other theoretical points in practical hydrographical work, but when circumstances are favourable, they must be regarded. Looking upwards, or from a denser into a rarer medium, the effect of refraction is to increase the apparent elevation This correction is therefore to be subtracted from elevations As the effect, when looking downwards, is also to raise the object, or, in other words, to decrease the angle of depression* the correction for refraction must be added to angles of de- pression. An excellent ruled form is supplied by the Hydrographic Height Office, which much facilitates the calculation of heights. This Jo^ int form, bound into a book, constitutes the Height Book. A Book, specimen is given on next page, which nearly speaks for itself. The angle observed to the object is entered under the head Entering of either elevations or depressions, as the case may be ; as ** t i n calcu observed, in the case of theodolite ; minus the correction for Eleva- height of eye, if with the sextant; and the distance in miles tl0n< and decimals is entered under its head. To get this distance, if we happen to have it worked out in the triangulation, we shall of course use the calculated distance; but if not, which will be the case generally, we must measure it on our sheet, and enter the corresponding distance according to the scale. To get the refraction, multiply the distance by 5, which will give it us at once in seconds, aff dlstance x 6Q/ ' = dis- tance x 5. This is entered in its proper column, and the angle, cor- rected by -f or this refraction, according as it is an angle of depression or elevation, is entered under Corrected Angle. We then work out the difference of level with these data on the opposite side of the page, the constant log being the log of feet in a mile, by which the distance must be multiplied to bring 00 oo 8 o 10 o O "^ t>* OO (N co oq o rH !> 1C CO * CO CO CO rH rH rH *O O o rH rH O rH - O O O O : : : o o o ca co I o O rH O O -3 s I a o s -a I 1 cS PH w O <^J fi <] _M O, 'S .S 1 44 o .-3 o O 02 02 10 OOS oo * tO-^t- 00 r-l O> oo co to *-oo oo 05 000 00 Ti< O *- co o "S ^P . eo III S II I/O HYDROGRAPHICAL SURVEYING. CHAP. xi. result out in feet. The log given is that for 6075 feet, the number of feet in a mile in Lat. 44. Theoretically we should have a different log. for different latitudes, but, as the utmost extent of error by neglect of this is 22 feet in a height of 6000 feet, we need not regard it. This difference of level is entered in its proper column. Take out the dip corresponding to the distance from the table,* which should be pasted into the commencement of the book, and enter that in the proper column. The column for height of theodolite is a little confusing, as sometimes it will be merely the height of the theodolite- telescope above the ground, and sometimes the height of it above the sea-level, which we shall enter, according as we want the height of observer's position, or of object observed as will be presently explained. We have now all the data necessary to obtain heights. When we have accumulated enough observations, we set about getting out results. Height There are four problems for obtaining heights, and the data Problems. we h a y e f or g^^ observation will be combined according to what we want to arrive at. These four problems are as follows : 1st. To find height of object observed, when height of observer is known, and the angle is one of elevation. 2nd. Ditto, when angle is one of depression. 3rd. To find height of observer, when height of object ob- served is known, and the angle is one of elevation. 4th. Ditto, when angle is one of depression. To understand the mode of combining the data, let us con- sider the Figs. 34 and 35. In Fig. 34, which is the case where the angle observed is of elevation, and comprises Problems 1 and 3, we may have either X or Y known, and wish to obtain the other. Height Suppose X to be known (Problem 1), to find Y, we have Formula 1. * Appendix Table 0. CHAP. XI. HEIGHTS. I/I If Y is known (Problem 3), to find X, 3. In Fig. 35, the case where the observed angle is one of de- pression, and comprises Problems 2 and 4, Suppose X known (Problem 2), to find Y, Y = X + (* + d) -f ....... 2. Suppose Y known (Problem 4), to find X, X = -(* + <*)+/ ....... 4. These four formulae, which it is also convenient to have FIG 35. X = Height of Observer's position. Y= Observed d = Dip. / = Difference of level. t = Height of theodolite above ground. written for reference in the Height Book, will enable us to solve any of the problems. When we are getting the height of the Object observed, we Column shall enter in the column of " Height of theodolite," X + t, ** f or the height of theodolite above the sea ; but when the ob- HYDROGRAPHICAL SURVEYING. CHAP. XL Elevations level first Meaned. Sextant tions*" Aneroids. servation is used to obtain the height of Observer, only t, the height of the theodolite above the ground, will be inserted. We must commence by collecting results of elevations fr m stations at the sea-level, or from stations whose height above the sea-level has been measured, which will give us the heights of objects observed ; and also with depressions from stations to the sea-level, or to stations whose height above sea-level has been measured ; which will give us the height of the observing-stations. Heights so obtained are termed " absolute," as being calcu- lated directly from the sea-level. All such heights must be obtained first, then, meaning the heights of one station which has the most observations, or of which the results agree best, we can work out all other observations from that station to other objects. We then mean another, and so on, using our observations either to obtain height of observer or of observed object, as is most convenient, as we proceed. TheSG hei S nts wil1 be " dependent," as resting on the as- certained height of other stations. No height can be considered as exact, that is not the result of both elevations and depressions, as no matter how nicely a set, of depressions say, comes out, they will all include the refraction error, for the refraction correction is only approximate. This is with reference to detailed surveys only. Sextant angles of elevation must be corrected for the height f eve before being entered in the Height Book as angle ob- served. They are then treated in precisely the same manner as the theodolite elevations. The pocket aneroids should be tested up a known height, to get the value of each tenth, which will be from 92 to 100 feet for a tenth, each instrument varying slightly. As before mentioned, they are useless in getting accurate heights, but will give very good approximations up to about 4000 feet, if in good order and constantly worked ; but their delicate CHAP. XL HEIGHTS. 173 chain-work is so liable to rust slightly at sea, that the links will frequently stick if the instrument is not carried up heights continually to work it. Placing under an air-pump will serve the same purpose. See Barometer, page 30. It is useless to enter into intricate calculations of data ob- Only for tained by so small a scaled instrument as a pocket aneroid ; J^ * 1 " the impossibility of reading it exactly precludes any but Heights. approximate results, and a simple multiplication of the deci- mals of inches by the value of a tenth, as obtained above, is quite sufficient for the purposes for which we use the in- strument. There is a method of obtaining the height of an observer Height above the sea, from depressions taken to the masthead and J^J^ water-line (or hammock-netting) of the ship, by a theodolite, of Mast- which sometimes is very useful, as when, for instance, a rough plan of a small harbour is being made. The result depends line< entirely on the height of the masthead, distance not entering into the calculation. The angles of depression must be ob- served as carefully as possible, but in no case can the method be considered as exact. The formula is : Height above masthead = height of masthead X sin depression of masthead X cos depression of water-line X cosec difference of the two depressions. When the observer's position is such that the angle to fj|jjf *Ele- the masthead is one of elevation, the formula is as vation of ,, Masthead follows : an a Depression Height below masthead = height of masthead X sin ele- of Water- vation of masthead x cos depression of waterline line ' X cosec sum of angles of elevation and depression. (See Appendix H.) If the hammock-netting, or other fixed line, is observed in- stead of the water-line, the height of it above the water must be added. The height of theodolite-telescope above the ground must be subtracted. 174 HYDROGRAPHICAL SURVEYING. CHAP. XL EXAMPLE. From a hill, observed angles of depression to masthead and hammock-netting (13 feet above water-line) as follows. Height from hammock-netting to masthead being 98 feet. O I II Dep. of masthead 13 56 20 ham. netting .. .. 15 41 30 Difference 1 45 10 98 1-991226 Sindep. M. H. .. .. .. 9-381813 Cosdep. H. N 9*983505 Cosecdiff. .. . 11-514464 2-871008 = 743 Height above masthead .. .. 743 of do. above water .. .. Ill observer's eye .. .. 854 theodolite .. .. .. 5 Height of Hill = 849 feet. Obtaining To obtain distance from an angle of elevation of a known fronTel*. height is like using a lever with the ends reversed, and is vationof seldom had recourse to in surveying, as not being correct known , height. enough. As it may be, however, sometimes useful, we give two formulae. The proof of the first, which is fairly accurate, is given in Appendix F. First Distance in Method. nautical miles 6060 Where h is the height of mountain in feet, r is radius of earth in sea miles = 3438, and E is observed elevation reduced to water-level, and corrected for -^ the estimated distance, for re- fraction. CHAP. XI. HEIGHTS. 175 If the estimated distance should differ much from that given by the calculation, it should be recalculated with the correct allowance for refraction. An example is appended. Given height of mountain observed = 2384 feet. Elevation .. .. 36' 26" Height of eye .. .. 16ft. Estimated distance 30 miles. h = 3-377306 6060 = 3-782473 h in miles 1-594833 2r 3-837303 2rh .. 3-432136 2rh 2705 (rTanE) 2 899 '7 3604-7 Obs. elevation Height of eye Refraction E .. 36' 26' 3 56 2 30 = 30 00 r = 3-536179 TanE = 7*940860 1-477039 2 2-954078 30' = r Tan E 7 = (r Tan E) 2 2) 3-556905 1-778452 = 60-04 30-00 Distance = 30' 04 The second method is more approximate, and is in con- Second nection with the Table E in Appendix. It is a handy Metllod> method, and as correct as is required for navigational purposes. Distance = \/ depr. 2 + alt in mins. 2 alt in mins. The depression squared is taken out of the table direct, and the square of the altitude can also be looked out to save the trouble of multiplying. The altitude is corrected for refraction as in the other case. 176 HYDROGRAPHICAL SURVEYING. CHAP. XL Working out the same example, we have Dep. 2 for 2384 2704 Elevation 2 900 3604 V 60 Elevation .. .. 30 Distance 30' LEVELLING. Simple Levelling with a staff is not much required in marine Levelling, surv eying. Ascertaining the heights of the bases of light- houses above the sea is perhaps the purpose for which it is most used. This is called simple levelling, and gives us the height between the two required points only, without any regard to distance. A levelling staff and level is usually supplied to surveying ships ; but a theodolite and marked boat-hook or pole will answer the purpose, if we have not got the regular apparatus. Holding the staff at high-water mark, we place the instru- ment (level or theodolite) so far up the slope that we shall, when it is carefully levelled by the level attached to the telescope, read off near the top of the staff. The reading of this, called the lack station, being taken, the staff is taken above us, and planted so that we can read just above zero of the staff, which is now at the fore station. The theodolite is now moved up the hill until we shall again, when levelled, read near the top of the staff; this will be another observation of lack station, and so on until the levelled telescope reads the staff on the spot whose height we want. There is no necessity to keep in one line directly for the spot whose height we wish to measure ; we shall do so if we can, as it is the shortest way, but in practice we are generally forced to zigzag. The difference of the sums of the readings of back and fore stations will be the height required. Where former are the CHAP. XI. LEVELLING. 177 greatest, we are going up hill, and it is called rise ; vice versa is called &fall. FOR HEIGHT OF LIGHT-HOUSE. Back ^ Fore ^ Reading of Staff. Reading of Staff. Water-level 12 '64 (1) .. .. 13-42 (2) .. .. 13-81 (3) .. .. 12-50 (1) .. (2) .. (3) (4) 0-63 1-22 1-52 0-32 (4) 13-06 (5) :: 0-87 (5) 12-18 Base of L. H. *. 3-45 77-61 8-01 8-01 69-60 Height of base of Light-house above High-water level . . 69 6ft. For our purposes, when the distance of the staff from the Correc- theodolite is not great, or when the distance of fore and back ^^j station from the theodolite are nearly the same, it will be necessary. sufficient to observe readings with the telescope in one position only; but when the rise of the hill is slight and distances increase, especially when the difference of distance between fore and back station is great, and we require accuracy, the telescope should be reversed in the Y's, and being again brought level by the bubble, readings should be taken a second time. The mean will be the true reading. If the axis of the telescope and the attached level are per- fectly parallel, and therefore in adjustment, it will be shown by the readings agreeing when reversed at the first station, and we shall know that we need not take this trouble ; but it is necessary to ascertain this, as theodolites continually under- going carriage by boat are liable to many accidents. This method enables us, if necessary, to calculate the height of any of the stations where the pole is erected, but gives us no information as to the height of the spots where the theodo- N 178 HYDROGRAPHICAL SURVEYING. CHAP. xi. lite stands. This can be obtained, if wished, by measuring the height of the axis of the telescope above the ground, when, Height of theodolite position = height of back station -f present reading of said back station height of eye (back station being below us). Distances measured will enable us to make a section of the ground traversed, but, as already remarked, this is not often required from the marine surveyor, and will not be enlarged upon here. (179) CHAPTER XII. OBSERVATIONS FOE LATITUDE. By Circum-meridian Altitudes of Stars By Circum-meridian Altitudes of Sun. ASTRONOMICAL observations are largely used in all descrip- General tions of marine surveying. In all but small plans the even- Kemarks - tual scale of the chart is decided by the latitude and longitude as obtained by observations of sun or stars, and we have seen that true bearings often enter largely into the construction of charts. In running surveys, or in searching for, or sounding over shoals, in mid-ocean, everything depends on the positions astronomically found, and every method of correctly finding the latitude and longitude is in requisition. In considering this subject, we will take first shore observations with artifi- cial horizons, where we require results as accurate as we can obtain with the sextant, to which instrument remarks will b"e confined, excepting so far as the theodolite is used for true bearings ; and afterwards, sea observations. In all observations of the heavenly bodies, instrumental Eiimina- errors, atmospheric effects, and personal differences, largely influence the results. No matter how correctly we may take the actual observations, unless we can eliminate these variable quantities, the positions obtained will be in error. On every occasion, therefore, where accuracy is aimed at, the mode in which this elimination can be best carried out must be considered. The general principle used in doing this is to get two sets of observations for one result, in such a manner that the errors of all kinds will act in opposite N 2 i So HYDROGRAPHICAL SURVEYING. CHAP. xii. directions in each set, and therefore disappear when the mean is taken. The precise way in which this is done will be described under each different observation. Latitude by Obser- vations " Abso- lute." But more difficult. Elimina- tion of Errors in observa- tions for Latitude. LATITUDE BY CIRCUM-MERIDIAN ALTITUDES OF STARS. Determinations of latitude are more simple in one respect than those for longitude, as they are " absolute," that is to say, they depend solely upon themselves ; whereas longitude has to be obtained by the difference of two sets of observa- tions at two different places, and is further complicated by the eccentricities of the chronometers upon which, when there is no telegraph, we have to rely. But, on the other hand, the observations required for correct latitude are more difficult to take, as, to arrive at anything like an exact result, we must use stars, and each step of the observation of these in an artificial horizon is rendered less easy by the fact of their being made at night. It is much easier to become a good day observer than a good night one. The errors to be eliminated as far as possible in observing for latitude are, firstly, errors of observation ; secondly, instrumental errors, as index error of sextant, error caused by refraction in the rays passing through the glasses of the roof of the horizon, &c. ; thirdly, atmospheric refraction, which varies much, and for which no known rule of correction thoroughly suffices ; fourthly, personal errors, caused by each individual's mode of observing the contacts. Errors of observation are eliminated by taking as many observations of altitude as we can, and we must therefore observe off the meridian, or what are known as circum- meridian altitudes; which consist in observing from a short time before the meridian passage to a short time after it, and adding a certain correction to each altitude to make it equal to the meridian altitude, and thus get a mean meridian altitude, which, if we can calculate the correction exactly, will CHAP. xii. LATITUDE BY ALTITUDES OF STARS. l8l be of much more value than actual observation on the meridian only. There remain the other errors, some of which may be directly allowed for, but only approximately ; others cannot be corrected at all, and the latitude resulting from observations of a single body, as e.g. the sun, will be therefore always more or less in error. The only way satisfactorily to clear these errors is to ob- Pairs of serve stars, in pairs, of as equal altitude as can be found, one north, and one south, of the zenith. These errors will then act in opposite directions, as everything tending to increase or diminish the altitude on one side of the zenith, will act simi- larly on the other; but, in working out the latitude, the resulting error will increase the latitude in one case, and decrease it "in the other, so that the mean of the latitudes obtained by each star of such a pair will approximate very closely to the correct one. To eliminate the artificial horizon roof error when observing pairs of stars, the roof must always be in the same position with respect to the observer, and therefore must be reversed when changing from face north to face south, and vice versa. If observing a single object, as the sun, the roof must be reversed when halfway through the observation. The use of a sextant stand, when once the observer has got Sextant thoroughly accustomed to it, is an immense assistance to good an ' observations, as the images of the stars, instead of quavering and shaking with every slight motion of the hand of the observer, remain perfectly still, and can be made to pass over one another with great accuracy. Certain preparations are necessary for good star observa- Prepara- tions, for all scurry that can be avoided, should be. In the first place stars must be selected and arranged for observations according to their pairs. If stars given in the ' Nautical Almanac ' only, are used, the chances are very much against a sufficient number of pairs being obtainable, as only a small proportion of observable stars are there included, especially with regard to south stars, of which there is great lack. 182 HYDROGRAPHICAL SURVEYING. CHAP. xii. Star Cata- A surveying vessel will have the Greenwich and Cape logues. Observatory Catalogues of Stars, and out of these enough pairs can nearly always be picked to enable us to get a satisfactory latitude in one night, including stars down to the fourth magnitude, which can be easily observed on an average night by a practised observer with good instruments. Choosing The approximate altitude of each star must be calculated Stars. an( j i n g er ted in a list in the angle book, together with the time of its meridian passage, its magnitude, the time that will be shown by the pocket chronometer that is to be used for taking time, whether it is N. or S. of the zenith ; and each pair must be numbered. The nearer together in point of time the two stars of a pair can be placed, the greater will be the chances of the elimination of the refraction errors, as in a few hours temperature often varies much, dews form, and many differences may arise in the atmospherical conditions. Stars over 60 of altitude are not usually good to observe ; as, though a sextant will measure over 120, the image of the star will not be sharp when reflected from the index glass at such a large angle, unless the glass be unusually good. Altitudes of stars selected for pairs should not differ more than four degrees if possible. Generally j^iirs within this limit can be found. If one star of a pair be lost, it is useless taking the other, unless a substitute for the one lost can be had. It is well, therefore, to be provided with spare stars for pairs, as this may often happen from clouds intervening, &c. Care must be taken, in choosing pairs, to leave sufficient time between each meridian passage for the due observation of each star before and after culmination. This will vary with the latitude and declination, as a star should not be observed so far from the meridian as to bring the mean of the altitudes observed less than a minute or so under the meridian altitude. Fifteen minutes, elapsing between each passage, will give plenty of time under most circumstances. Time must also be allowed for changing the position from north to south, and vice versa; but all this will vary with the OP 1 THE 'UN I V B R SIT CHAP. xii. LATITUDE BY ALTITUDES OF STARS. quickness and experience of the observer. Beginners must be satisfied with a few stars, and must allow more time. In preparing the ground we must look out for a spot Preparing whence we can see clear in the line of the meridian north and south, and one far enough from the beach to be beyond the distance where surf will shake our quicksilver. The latter point is sometimes, as for instance where jungle comes down to the very beach, difficult to find, but it is well worth looking for, and going inland a bit to get it; as otherwise good observations may be rendered impossible from the vibration set up. The more solid the ground the better, as it is astonishing what slight causes will suffice to set the surface of the mercury in motion. t Wind is a frequent source of quaking mercury, and care should be taken to have the horizon trough firmly placed, and the roof so fitted that the wind cannot get under its lower edge.* A screen of canvas to windward is sometimes a good thing, but on some ground this causes such vibration of the earth as to be worse than the free blast of the wind. If more than one officer is to observe, a screen of some kind should be put up north and south between the observers to keep the lights out of one another's eyes. In the tropics, and some other localities, mosquitoes must not be forgotten. In places where these plagues abound, it is preferable to court the wind instead of shutting it out, in order to free ourselves if possible of them. Sandflies are perhaps worse, as nothing will get rid of them, and many an otherwise favourable opportunity of getting stars has been spoilt by these wretched little insects. The spot for the artificial horizon being settled on, and the direction of the meridian taken with a compass, it is a good plan to dig holes, if the nature of the soil permits, in which to place the lantern used for reading off when not required, so as to avoid unnecessary glare. The best place Vide Artificial Horizon, page 11. 184 HYDROGRAPHICAL SURVEYING. CHAP. XH. for these will be on the left side of, and a little behind the observer's seat, and two will be wanted for each observer, one for the north stars' position, the other when facing south. If the ground will not admit of digging holes, buckets will answer the same purpose well enough, but not so well. If special lanterns can be got, these precautions will not be necessary ; but we are assuming observations with ordinary ships' lanterns. All these kinds of preparations should be made before sunset, if possible ; confusion will be sure to occur if things are delayed till after dark. For observations with a sextant stand, a small stool is wanted, as described under " Sextant Stand," and another for the observer's seat. It much facilitates good observations for the observer to be comfortable, especially when he is about to observe for several hours consecutively, star Map. A good star map is very useful to assist in recognising the objects chosen. Error of It will have been necessary to obtain the error of the nwter " chronometer on the day of our star observations, unless we required, have recently obtained error at the same place, and have confidence that the chronometers are going sufficiently well to give us the true time of place to, say, two seconds. Having thus made all preparations, and compared the pocket watches with the standard chronometer, and another as a check, we land to observe. We may here remark that we must again compare on returning on board. Observing Placing the artificial horizon north and south, we put on stars. ^ roo w tih the mark on it in the settled direction, according as our first star is north or south of the zenith. We then place the sextant on its stand, having first screwed in the inverting tube with the weakest-powered eye- piece. This should be adjusted to focus, as near as possible, before screwing into the collar. Place the sextant and stand on the stool, so that one of the three legs which support the stand is at right angles to the meridian, and on the right of the observer. CHAP. XII. LATITUDE BY ALTITUDES OF STARS. 185 Set the vernier to a few minutes less than the estimated double altitude of the star. Move the stool with the instrument on it, so that, looking over the tube, we can see the reflection of our star in the artificial horizon. Point the telescope at this, and set taut the screw that fixes the handle of the sextant on to the bearing of the stand, then working the sextant right and left in the stand pivots, the other image of the star will soon dash across the field. Unless the star is moving rapidly in altitude there will be no further need to move the sextant on its bearing, and care should be taken that the screw is tight enough to prevent its moving while turning the sextant up to read, or the telescope will not point to the star, when directed to the horizon again, which it should do at once, and so save time in redirecting. Beginners often neglect this, failing to see the necessity for it ; and, losing time in looking again for the star after each reading, miss one of the great advantages of a stand, viz. that once fixed, the stars will always be in the field without any bother. With faint stars, when there are several of nearly the same brightness close together, it is sometimes rather con- fusing, and a beginner will find it very difficult to be sure of his star ; but comparison with the star atlas, and consideration of how the star wanted lies with regard to the others, will, after a little experience, clear up the difficulty. If the star be a faint one, it is difficult to bring it down to meet its image in the horizon by taking the sextant off its stand ; and if it is a bright one, there is no need to do so, as it cannot be mistaken if the estimated altitude is anywhere near the truth. There is then, in regularly pre-arranged observations, no necessity for doing this, and we shall trust entirely to the vernier being set to the calculated altitude for finding the star. Having brought the two images into proximity by hand, place the right hand on the- screw at the end of the stand-leg that has been arranged at right angles, and the left hand on 186 HYDROGRAPHICAL SURVEYING. CHAP. xn. the tangent screw of the sextant, when, by working these two screws, the images of the stars can be made to pass over one another exactly, and the word " stop " given. At this signal, the attendant bluejacket will hold the lantern up for reading off. The light should be thrown on to the arc from a direction as nearly at right angles to the plane of the sextant as possible, to avoid parallax. Besetting In taking the next observation, turn the tangent screw on observa 1 - or back, before commencing to bring the images together tion again, so as to be entirely free from bias as to whether the star is rising or falling. Time from The amount of time to observe before and after culmination en an ' varies with the position of the star and the latitude of the place as before mentioned ; but, as a rule, commencing six minutes before the calculated time of meridian passage, and continuing for a like time afterwards, will be ample, as we do not wish the correction eventually to be applied to the mean of the observed altitudes to bring it up to the meridian altitude to be more than one minute, if we can manage it. Decimals Observing as close to the meridian as is recommended above, the decimal parts of seconds need not be recorded in taking the time. Reduction The observed altitude of a heavenly body can be corrected to the meridian when the hour angle and the latitude are known ; but if the hour angle is large, the calculation of the quantity to be added to the altitude is a complicated process, and it is only when the hour angle is small, and very little in error, that the formula assumes a simple and practical form. The error introduced by working with an assumed latitude also increases rapidly with the hour angle, so that we are confined in using this method to about twenty minutes of the time of meridian passage in ordinary latitudes ; but in obser- vations such as we are discussing now, which have for their object as correct a determination of the latitude as we can obtain, we must not observe more than about ten minutes from the meridian, and perhaps less. CHAP. xii. LATITUDE BY ALTITUDES OF STARS. 187 The best method to use in reducing observations to the meridian is that known as Eaper's, in which the principle is to add on to the observed altitude the amount necessary to make it equal to the meridian altitude, and then to calculate the latitude as in a meridian observation. This amount is known as the " Eeduction to the Meridian," and is so called because it is subtractive from the observed zenith distance. The formula used by Eaper is* Eeduction ) n -, , n , , f a u Vers hour angle i = Oos dec. X Oos lat. x oecalt. x ^ ^_ insecs.ofarc) Sin 1 Vers H A Eaper gives a table of ^ *-,, for every minute and oin 1 second of hour angle up to thirty minutes from the meridian, which is very convenient, and is given in Appendix N. It saves a considerable amount of figures in the calculation, and thereby diminishes the chances of clerical errors ; but the formula, as given above, can be worked out, if Eaper's table is not at hand. The hour angle as marked by a watch beating mean time, sidereal or nearly mean time, will not be strictly correct either for a star or the sun; as, for the former, it should be taken by a watch beating sidereal time, which gets over its 24 hours while a mean solar watch has only advanced 23 h- 56 m< 04 s - nearly ; and apparent solar time varies from day to day as the speed of the earth in her orbit varies ; but, within the limits we observe, the difference in ordinary latitudes is scarcely perceptible, and if we observe the stars of a pair about the same distance from the meridian, any little discrepancy will disappear in the mean. If it be desired to correct for the difference when observing stars, a constant log of 0*002000 added to the other parts of the equation will give a close approximation to the exact reduction. * For proof, see Appendix D. 188 HYDROGRAPHICAL SURVEYING. CHAP. xn. Calcula- In working out the circum-meridian observations of a star, Deduction, it is not necessary to~ calculate the reduction for each individual Vers TT A observation. As - - lT is the only variable quantity in bin 1 the equation, and as it varies with the hour angle, by taking this out for each observation and meaning these quantities, we Vers H A obtain a mean value of -- - which we insert in the Sin 1 equation, and add the mean reduction so found, to the mean of the altitudes. If working with Raper's tables, we take out Vers HA the whole quantity ; if without them, we look out Sin I the Vers. H A only, and introduce the log Sin 1" into the calculation with the other logarithms. Knowing then the error of the watch used on mean time of place, and the approximate latitude and longitude, the rule for working out circum-meridian observations of stars will stand thus: Rule for 1. Calculate Greenwich date. Smof" ^' C rrect r ig nt ascension of mean sun (sidereal time of Reduction. Nautical Almanac) for this Greenwich date, and subtract it from the right ascension of the star, which will give the mean time of star's meridian passage. 3. Apply to this the error of the watch, which will give the time shown by the watch at the star's meridian passage. 4. Mean the observed altitudes, correct this mean for index error, and divide it by two. To this apply refraction (corrected for thermometer and barometer) which will give true altitude. 5. Write down the times of each observation in a column, and taking the difference between each, and the time shown by the watch at meridian passage, we get the hour angle at each observation, which place in another parallel column. 6. Take out for each of these hour angles the quantity from Raper's Reduction Table, or, if we have not got that, the natural versine. CHAP. xii. LATITUDE BY ALTITUDES OF STARS. 189 7. Add these quantities together, and divide the sum by the number of observations, to get a mean. 8. Add together log cosine declination, log cosine estimated latitude, log secant true altitude, and the logarithm of the result of No. 7. If we are using versines, a constant log 9-316400 is also to be added. (This is log cosec 1" -f 4 + 0-002000): 9. Look out the sum of these logs as a natural number, which will be the number of seconds of reduction required. 10. Add this to the mean observed true altitude, which will give the calculated meridian altitude, from which the latitude is obtained in the usual manner. The following is given as an example. On July llth, 1879. At Buyuk Chekmejeh A the following observations were taken. Index error of sextant 35" Latitude (approx.) 40 57' 45" K Longitude 28 30' E. Mean Time of Transit of star calculated, Xh. 12m. Time by watch (Breguet 2086). Altitude a Ophiuchi. h. m. s. o / 10 09 36 123 22 00 10 11 22 40 10 42 22 50 11 14 23 15 11 43 23 25 12 09 23 35 12 50 23 50 13 14 23 50 13 38 23 55 14 06 24 00 14 33 24 00 14 55 23 50 15 16 23 50 15 37 23 45 16 04 23 30 16 24 23 15 * 16 50 23 00 17 20 22 40 17 46 22 30 18 15 21 55 Mean .. .. 123 23 16-7 HYDROGRAPHICAL SURVEYING. CHAP. xn. The calculation will appear as follows : Watch Times. Hour Angle. Vers H. A. Sin. 1" h. m. 8. m. s. 10 09 36 4 27 38-9 10 11 3 52 29-4 10 42 3 21 22-0 11 14 2 49 15-6 11 43 2 20 10-7 12 09 1 54 7-1 12 50 1 13 2-9 13 14 49 1-3 13 38 25 0-3 14 06 03 o-o 14 b3 30 0-5 14 55 42 1-0 15 16 1 13 2-9 15 37 1 34 4-8 16 04 2 01 8-0 16 24 2 21 10-8 16 50 2 47 15-2 17 20 3 17 21-2 17 46 3 43 27-1 18 15 4 12 34-6 20)254-3 Mean .. .. 12-71 Mn. Time of Transit Long, in time G.M.T. .. K. A. Mean .. Corr. for8h. 18m. .. E. A. * .. .. M. T. Transit .. Watch fast Time by watch at Transit . Mean obs. alt. I.E App. alt. .. Refraction .. Tr. alt. 7 17 10 h. m. 10 12 1 54 8 18 16 1 05-9 18-9 3-0 17 27-8 29 22-6 11 2 54-8 08-1 10 14 02-9 O t // .. 123 23 16-7 .. -35-0 2)123 22 41-7 .. 61 41 20-8 .. -29-4 61 40 51-4 Cos dec. Cos lat. Sec alt , 12-71 Reduction Tr. alt. .. Red .. Z. D. .. Dec. Latitude 9-989329 9-878027 323871 1-105510 61 40 51-4 + 19-8 61 41 11-2 28 18 48-8 N. 12 38 57 -ON. 40 57 45-8 N. CHAP. xii. LATITUDE BY ALTITUDES OF STARS. IQI When the pole star is observed, it must be worked out by Pole Star, the rule given in the Nautical Almanac, care being taken to take out all the quantities from the tables exactly by inter- polation. The moon is but of little use for observations of any kind. Moon not Its rapid motion necessitates very careful corrections, which ni e nt." take more time than they are worth, and besides we have nothing to put against it to eliminate errors. The separate stars being worked out, we mean the result of Results of each pair, and the mean of these again will give us the mean latitude. Although from circumstances many more observations may be got of one star of a pair than of the other, no value can be assigned to one over the other, and the direct mean must be taken ; but in meaning up the results of pairs, less value would be given to a pair in which the observations of one star are few in number, than to a pair where a proper number of observations of each star has been obtained. The necessity for assigning this value is increased where the observations are not only few but indifferent ; but it would be a question whether it would not be better to omit such a pair from the final result altogether, and certainly it would be best to do so, if there are several other good pairs. An example of the method of tabulating the different obser- vations and pairs is given on next page. The sets of stars given as an example were taken under favourable circumstances of sky and weather, and are not meant as a standard which we must expect always to get. Here no value is given, as each pair were nearly equally good, and the observations were nearly the same as to number. Only the direct mean is taken. If, however, the observations had been less uniform, and there Valuing were not sufficient pairs manifestly better than others, by Eesults ' which we could elect to stand, value would be assigned by some such system as the following. Assume a number as perfection, say 10, and give to each pair its value in that scale. Then the sum of the products of II s 1 | o ts^ I :3 -S d -^ Jo ^o s rt - rH CO Th . j " (M 05 00 rH CO rH -f ^ -^ iO >o iO 2 ^ t 10 s rS 1 *s O IO T^ T^ TH CO 1 " o g ^1 <>4 CM (M rH (M (M H fi * 1 jj M O "*^ O ^ \J)6Q *O V G ^> 1 00 IO rH OO rH ^ a '5b J i rS & M O E-t e * CO J o * 13 ' ^-^ 00 S 02 * cq 10 O r -" ri r ^-^ CO III CD CO t> CD C || 00 " ^ i rH 00 ^ lO t- ^ 5^ <^ ^ aiiRA. '. ^ rH rH 00 CO lO O co CO o Ill *% 3 i 8 c O J3 i |l J? " rH o 10 1 H rH O t*" >O 1 OQ 1 t co 02 10 cq a H o 10 : H H < oQ jz; d o^ o^ co (M rH rH .^ S M fc I 1 . 1 1 P i * I3| E a 8 - C 1 4 n 00 rH rH rH CO 10 10 CD O CD CD lO O K* 5 CO t~ !> CO CO CO CO CO | i ^ CO P H rH B o 10 o 03 M ^tl JO CO rJH ft i o O ^ rH O CHAP. XII. LATITUDE BY ALTITUDES OF STARS. 195 Observer. Latitude. Virtue of each result. Product of Value and Sees of Lat. / // A 5 14 16-3 3 48-9 r, 08-8 5 44-0 Mean Latitude by 4 c 03-0 5 15-0 observers : D 12-0 6 72-0 5 14' 09"'4S. 19 179-9 _ f\a A 19 In using stars from the Greenwich or Cape Catalogues, it is necessary to calculate the apparent place of the star for the day. Three methods of doing this are given in the Nautical Almanac, in the explanation under the head of "Stars," where examples of each are shown worked out. Method No. II. is perhaps the simplest for Greenwich Catalogue Stars ; but when calculating a star from the Cape Catalogue, No. III. must be used, as there are no constants given in that catalogue. Care must be taken, with this last method, to give the proper signs -f or to each logarithm. Next to the observation of stars in pairs, the circum- meridian observation of the sun in the artificial horizon is the most correct and simple method we have of obtaining latitude ; but it is evident that we cannot use it when the altitude exceeds 65, as a sextant will not measure the double angle. We must, in the case of the sun, be doubly careful in correcting the refraction, if we wish to get as near the truth as possible. There is nothing to be gained by observing both limbs of the sun, as the motion in altitude will be so small that it will not matter whether the images are opening or closing. The roof of the horizon should be reversed at about noon and the sights worked out as two sets, roof one way and roof the other. , o 2 Calculat- ing appa- rent places of Stars from Cata- logues. Latitude by Circum- meridian Altitudes of Sun. 196 HYDROGRAPHICAL SURVEYING. CHAP. xn. However careful we may be, we shall not expect our latitude by the sun. only to be exact, and in most cases where we are going to be satisfied with this observation, it will not matter if the latitude be a quarter of a mile or so in error, and the reversal of the roof may often be dispensed with. Sun and An observation of the sun cannot be meaned with an not r be Can " observation of a star the other side of the zenith, as all paired. refraction errors, as well as errors introduced into the instru- ment by the heat of the sun, will be entirely different. Caioula- Circum-meridian observations of the sun are worked out in Sitn Obser- precisely the same manner as those of a star, the only vations. difference being in the ordinary corrections to declination, &c. We want the error of the watch on apparent time to calculate what it shows at apparent noon, the time the sun will be on the meridian. An example is given opposite. On November 15th, 1876, circum-meridian altitudes of the were observed with artificial horizon at Maghabiyeh I d . Approx. lat. 18 15' K, long. 40 44' E. Bar. 30'00 ins. Ther. 80. Mean of observed altitudes Sun's Upper Limb, 106 47' 09"1. LATITUDE BY ALTITUDE OF SUN. Time by Watch. Hour Angle. Vers. H. A. Sin. 1" h. m. 8. m. s. 5 36 39 6 09 74-3 37 06 5 42 63-8 37 46 5 02 49-7 38 07 4 41 43-1 38 28 4 20 36-9 38 53 3 55 30-1 39 21 3 27 23-4 41 32 1 16 03*1 41 54 54 01-6 42 16 32 0-6 42 37 11 o-i 42 57 09 o-o 43 21 33 0-6 43 43 55 01-6 44 44 u 56 07-3 45 24 2 36 13-3 45 40 2 52 16-1 46 04 3 16 20-9 46 29 3 41 26-6 47 12 4 24 38-0 47 32 4 44 44-0 48 18 5 30 59-4 48 51 6 03 71-9 23)626-4 Mean .. .. 27'23 App. noon . . . . h. m. s. ..12 App. noon . h. m. s. ..000 Watch slow .. 6 17 12 Long .. 2 43 Watch at Transit 5 42 48 Obs. alt. ^ t II 106 47 09-1 Dec. ap. noon Gr. 18 39 47'8 1 42-4 I.E -40*0 Dec. at Transit. . 18 38 05-4 S. 2) 106 46 29-1 Var n S. D 53 23 14-5 -16 13 2-71 Refraction . 53 07 01.5 -35-0 2646 756 True alt. . 53 06 26-5 Corr . . . . ., 102'43 Cos dec. Cos lat. . Sec alt. 27-23 9-976613 9-977586 0-221713 1-435048 1*610960 Tr. alt Red Mer. alt o / // 53 06 26-5 + 40-8 53 07 07-3 Z D 36 52 52-7 Reduction 40"'8 Dec Latitude 18 38 05-4 18 14 47-3 N. I9 8 HYDROGRAPHFCAL SURVEYING. ' CHAP. xin. CHAPTEE XIII. OBSERVATIONS FOR ERROR OF CHRONOMETER. General remarks on obtaining Longitude Error by Equal Altitudes. Shadwell's THE whole question of obtaining longitude by means of Chrono- On chronometers is so ably and exhaustively treated by Captain meters." Shadwell on his " Notes on the Management of Chrono- meters," both as regards the treatment of the watches, the method of observation, and the various systems of obtaining meridian distances, that we refer the reader to that work for full information on the subject. Here we do not pretend to give more than the broader principles of the general question, but a work of this kind, intended for the perusal of young surveyors, would be incomplete without some reference to it. Absolute The methods of obtaining longitude, called "absolute tud~ methods," which give the longitude of the place as measured from the first meridian, directly and independently, such as observations of occupations of the stars by the moon, moon culminating stars, eclipses of Jupiter satellites, &c., are now rarely employed in nautical surveying, and may be said to be decidedly inferior in value to the results of good chfono- metric runs. Similarly, altazimuths, portable transits, and other like astronomical instruments, are now seldom or never supplied to a surveying vessel. The sextant in a practised hand will give results equal to those obtainable by fixed instruments Remarks ^ sma ^ s ^ ze > an ^ nas ^ ne g rea -t advantage of being more confined to portable, and always ready. rential ^o the sextant, telegraph, and chronometers, therefore, our Longitude remarks will be confined, and Sex- tant. CHAI\ xiii. ' OBTAINING LONGITUDE. IQ9 By the use of the two latter we obtain only the " difference of longitude," or "meridian distance," between two places, neither of which may have its meridian distance from the primary meridian of Greenwich determined; but by the accumulation of such observations, the absolute longitudes of certain places are from time to time decided. These, then, become secondary meridians, on which the Secondary longitude of places in their vicinity depend. Meridians. When therefore a secondary meridian is changed in its value as regards its distance from the first meridian, all places whose longitude have been measured from it are changed also. This is the work of the Hydrographic Office, which receives and collates all information. The nautical surveyor simply finds the difference of longitude, and transmits that informa- tion only. A list of secondary meridians is given in the Instructions for Hydrographic Surveyors. For our purposes we may look upon difference of longitude Cases as divided into two main cases. The first, where the scale of defined - a chart we are making depends on the astronomical observa- tions for latitude and longitude at either extremity of our piece of coast. The second, when we wish to determine the relative positions of places more or less far apart, which are mainly required for the purposes of navigation. In the first, we can nearly always use the system, hereafter described, of "travelling rates," which much adds to the accuracy of the result. In the second, time, distance, and general circumstances often prevent our obtaining these, and compel us to use what we can get. In obtaining the meridian distance between two places, Principle either by means of a telegraph, or by carrying chronometers rentiS 3 " between them, the principle is the same, and is this, viz. Longitude that the difference of mean time of place at any moment at the two places is their difference of longitude in time. If, therefore, we can find out that at the time that at a position A it is 9 o'clock, it is 8 o'clock at B, we know that 200 HYDROGRAPHICAL SURVEYING. CHAP. xm. the difference of longitude is equal to one hour of time, and that A is east of B. . The telegraph enables us to do this in its simplest form, as, ascertaining the exact time at each end by astronomical observations, we can find out by an exchange of signals what is the difference of time. Chrono- In chronometric difference of longitude we have literally to Difference Carr ^ ^ 6 ^ me ^ r0m One P* aCC t0 ^ 16 ot ^ er - ^ e ascerta i n tne of Longi- time at one place on a certain day, or, what is the same thing, we find out the Error of our chronometer on local time. Supposing for the moment that our chronometer is keeping exact mean time, by carrying it to the other place and finding out its Error on local time there, we can deduce the difference of longitude by the difference of the two Errors. Thus, if our chronometer is four hours slow on mean time at A, and we find when we get to B that it is three hours slow, we know the difference of longitude is one hour, and that A is east of B. Unfortunately, chronometers do not keep mean time, and the problem is complicated by having to ascertain what time they do keep, or, in other words, what they gain or lose in each day, which is called the rate. If we can find this, we shall be able to get the difference of longitude just as accu- rately as if the chronometer was keeping mean time, as we can correct for this rate ; but here, again, chronometers are not, and probably never will be, perfect instruments, and are liable to change of rate, and it by no means stands to reason that because a chronometer gains five seconds a day one week, it will do so the next, especially when the ship has been at anchor during one period, and under weigh for the other, and the temperature has not been invariable. Chronometric runs are therefore liable to the errors arising from change of rate. To overcome this as far as possible, a number of chronometers are carried instead of one, and, if possible, what is called the travelling rate is obtained. Travelling If the rate of chronometers is obtained at a station A, and Bate. we ^ en g t another station, B, and obtain rate again there, and apply the mean of these rates as the assumed rate of the chronometers while being carried from A to B, we have no CHAP. xill. OBTAINING LONGITUDE. 2OI guarantee whatever that this assumption is correct, as the time employed in carrying the chronometers does not enter into the calculation at all, and they may have been going quite differently when the ship was at sea, with the vibration of the engines, motion of the ship, &c., to influence them, to what they were when the ship was at anchor, besides the important factor of change of temperature. If, however, we can return at once to A, and obtain the Error again, we can positively say that the chronometers have gained or lost so much between the first and second observations at A. Assuming this loss or gain to have been uniformly carried on throughout the interval, we shall have a travelling rate which will give a far nearer result than by using rates obtained at either end of our required base. By this means we only obtain one meridian distance for our double run for- wards and backwards, but it will be of more value than two separate meridian distances obtained by fixed rates. Even if we have to stop at B a few days, by observing Modifica- on arrival, and immediately before departure, we can eliminate Travelling the gain or loss of the chronometers during the stay there, by Kate, subtracting it from the total gain or loss during the time of our absence from A, and dividing the remainder by the number of days actually travelling. We shall thus still get a fair travelling rate, if the chronometers are at all trustworthy as timekeepers. This, then, is the system of travelling rates, which can be generally, and always should be, if possible, used in determin- ing difference of longitude for the scale of a chart. Whatever be the system of rates employed, good observa- tions must of course be regarded as the foundation of all of them. We cannot control the irregularities of our chrono- meters, but we can, to a certain extent, make sure of getting fairly correct time by using the proper means. To ascertain the Error of the chronometer as exactly as we Eiimina- can with sextant and artificial horizon, we must endeavour to errors^ get rid of the atmospheric and other errors, as we do in obser- Equal AI- vations of stars for latitude, which in this case is attained by 202 HYDROGRAPHICAL SURVEYING. CHAP. xin. observing at equal altitudes east and west of the meridian. It will be evident that, -whatever be the instrumental and other errors, (excepting those of observation,) supposing them to remain unaltered, the middle time between the observations will be the same, as whatever tends to make the observed altitude more or less in the forenoon, will act in the same manner in the afternoon, and as we do not want to know at all what that altitude is, but merely to ensure that it is equal, A.M. and P.M., the amount of the errors is immaterial. The method of equal altitudes, therefore, must be used whenever we wish to get Error exactly. The Error of watch obtained by single altitudes, called " absolute observations," will depend for its accuracy upon the corrections for each source of error, which, as we have before stated, can only be considered as approximate. Superior Equal altitudes can be taken either in the forenoon and ferior 11 " afternoon of the same day, so as to find the Error at noon, Transit, called Error at superior transit ; or in the afternoon of one day and the forenoon of the next, by which means we obtain the Error at midnight, or at inferior transit. Theoretically, these are equally correct, but in practice it is better to get Error at noon, if we can, as the elapsed time being less, gives less lati- tude to the chronometers or hack watches for eccentricity. The alternative is, however, very valuable, and saves many a day, as when, for instance, we arrive at the place we wish to observe at, an hour or two too late for forenoon sights. We can then begin our set in the afternoon, and get away, if we wish to do so, the next morning after forenoon sights, and thus save several hours, a considerable consideration in running meridian distances. Principle The principle of finding the Error of a timekeeper by obser- va ti n of equal altitudes is, that the earth revolving at a uniform rate, equal altitudes of a body, on either side of the meridian, will be found at equal intervals from the time of transit of that body over the meridian, and that therefore the mean of the times of such equal altitudes will give the time at transit. CHAP. XIIL OBSERVATIONS FOR ERROR. 203 In the case of a body whose declination is practically invariable, as a star, this is strictly true, and the calculation of the Error of the watch is confined to taking the difference of the time shown by the watch, and the true calculated time of transit. In the case of the sun, however, the declination is constantly Equation changing ; the altitudes are thereby affected, and an altitude ^titudes equal to that observed before transit will be reached after transit, sooner or later, according to the direction of change in the decimation. It is therefore necessary to make a calculation of the correc- tion, resulting from this change of declination, to be applied to the middle time, to reduce it to^apparent noon, which cor- rection is termed the " equation of equal altitudes." The observation of stars at equal altitudes will therefore be, stars and theoretically, the best to use, as being the simplest, and they p^ed will indeed give as good results as those of the sun ; but practically, the latter is generally observed in marine sur- veying for the purpose of obtaining time. In many cases .the inconvenience of landing, and carrying watches backwards and forwards for comparison, &c., by night, besides the in- creased difficulties of observing, and reading instruments by lamp-light, lead to the choice of day observations ; but in places where clouds persistently veil the sun in forenoon or afternoon, the nights are often clear, and equal altitudes of stars become most valuable. In taking the observations of equal altitudes in the artificial Limita- horizon, we are limited, as always, to altitudes between 20 Qbserva- and 60, as the horizon will not permit us to observe a lower tions. altitude than 20, and the sextant will not measure much more than 120. These restrictions will, however, only be inconveniences, as regards the sun, in extreme latitudes, as we must choose, as our time of observation, so as to minimise the effects of errors of observation, the period at which its motion in altitude is the greatest, i.e. when it is near the prime vertical, at which time, in all but high latitudes, the altitude will come between our limits. When the place of observation 204 HYDROGRAPH1CAL SURVEYING. CHAP. xm. is near the equator, and the latitude and declination are nearly the same, we could observe up to a very short time of noon, the sun's motion in altitude being nearly uniform throughout the day ; but we are in this case limited by the range of the sextant. It is difficult to lay down any rule as to what is the smallest rate of motion in altitude we should observe at, as the greatest motion in altitude during the day varies so much with the latitude and declination. We can only say that we should, when we have any choice, not observe beyond an hour when the time of changing 10 f of double altitude exceeds 30 seconds. Sets of Opinions have much differed on the number of consecutive Observa- observations that it is best to take to comprise in a set. The only theoretical limit is that the equation of equal altitudes should be practically the same throughout the set, as the variation in the time required by the sun to traverse the number of minutes of altitude between observations at the beginning and end of the set will not matter, as we do not care whether the mean of the times agrees exactly with the mean of the altitudes. It seems well, therefore, to observe tolerably long sets, as errors of -observation are thereby eliminated. The same result in the end will be attained by a larger number of shorter sets ; but the value of each set is much enhanced if composed of a considerable number of observations, and it saves time and trouble in the calculations. Too long sets are to be deprecated as wearying to the eye and hand, and the observations will therefore suffer from that cause, especially in hot countries, where the necessity for observing in the full glare of the sun makes it a trying operation. We prefer to take eleven observations in a set. This allows the observer to commence his second set, of lower limbs, (A.M. observations) at exactly one degree more altitude than his first one, of upper limbs. It does not much matter; as each one has his own plans for these details, and soon falls CHAP. xni. OBSERVATIONS FOR ERROR. 205 into a regular method, which is the great thing to prevent mistakes. The only point in fact of importance is, always to observe Observa- in the same way. Not only does it save time and errors, but ^in^ar! it is necessary in combining observations, whether for rate or meridian distance, that they be as similar in all respects as we can get them. The whole system is a system of differences, and it is manifest that the result is the better the more like the observations are. It follows from this that the observers employed in any string of meridian distances should be the same, the instruments and watches the same, the temperature and time of observing the same, as far as possible. Also, supposing temperature to be the same, that a rate will be probably more correct if obtained by combining single altitudes of different days, than by taking equal altitudes one day and single altitudes the other. If clouds prevent observation at precisely the same altitude, after transit, the mean of Error obtained by absolute sights, A.M. and P.M., at nearly the same altitudes, will be almost as good as equal altitude sights. When the observers are good, the greatest error is frequently Comparing introduced in comparing the hack watches to be used for taking time with the chronometers, and great pains should therefore be taken with this operation. The watches used for taking time must be compared before, and after, both forenoon and afternoon sights, with the standard and another chronometer ; and at noon, all the chronometers should be compared with the standard, and the hack watches with the same two chronometers. Before saying more about comparing, we must remark that Defects in the seconds-hands of pocket chronometers are rarely placed symmetrically in the centre of the dial on which the seconds meters. are marked. These watches beat five times in two seconds, commencing with the even minute. The beat of the watch should therefore coincide exactly with every even second ; the first beat from the minute being O4 sec., the second 0'8, the third 1*2, the 206 HYDROGRAPHICAL SURVEYING. CHAP. xm. fourth 1'6, the fifth at 2'0, and so on throughout the whole 60 seconds. But it will be found, in nearly every watch, that the hand does not fall over the even second on some parts of the dial, although it may on others, and each watch must be examined by counting the beats from the even minute, to ascertain how the hand falls in different parts of the dial, or the time-taker will be at a loss to know what is the exact decimal which his watch is beating. For instance, supposing that at the 40 seconds' mark on the dial, the hand falls a little short of the mark one beat, and a little in advance at the next ; unless he knows which of those beats is meant for the 40 seconds, he may be giving the time four-tenths of a second wrong. This, of course, refers both to comparing and taking time for the observations. Method of In comparing, which is perhaps best done by two persons, the " Stop " is given on an exact second of the box-chrono- meter (which beats half seconds), and the time by the pocket- watch noted. A check is then taken, by comparing the reverse way, calling the " stop " at an exact second by the pocket-watch, and noting the seconds and parts of seconds of the box-chronometer. As parts of seconds have to be estimated on both watches, these two comparisons will fre- quently differ two-tenths of a second. This is as near as we shall probably be able to arrive at the truth ; but if the dif- ference exceeds this, more checks should be taken, until we are satisfied which was wrong. In the same manner checks should be taken when com- paring one box-chronometer with another. If two pocket- watches are available, it will not be amiss to use both, even when there is only one observer, as it helps to eliminate errors of comparison. In this case half the sets will be taken with one watch, and the other half with the other. Preparation of the ground is not necessary, as in the case of observing stars, excepting so far as selecting the spot, to ensure being able to see in both the A.M. and P.M. directions. Having compared the watches, we land to observe. CHAP. xiii. OBSERVATIONS FOR ERROR. 2O/ The watches to be used on the ground should always be Care in carried in their boxes, and great care must be taken not to hacif jerk them, and above all to avoid any circular motion. watches. The method of observation for time differs from that Method of already described of stars for latitude, inasmuch as we ob- ticT^ serve at stated altitudes, generally at every 10', setting the sextant for the purpose, and noting when the contact takes place. In observing with the stand, therefore, we only need to work the screw of the stand leg, to get the suns vertically under one another. It is well to observe both upper and lower limbs, as though Observing it will make no difference to the result, it is good to have constant practice at both opening and closing suns, and not have all one way in the forenoon and the other in the after- noon. If we begin by a set of upper limbs, and immediately after take a set of lower, as an invariable practice, there will be no confusion, and we shall soon naturally fall into the system. It may be here noted that with the inverting tube, the movable sun (the sun reflected from index and horizon- glass) is above the other, when we are observing upper limb, and below when lower limb. Also that upper limbs in the forenoon are closing suns, and in the afternoon opening suns. It is necessarily vice versa for lower limb. Always use the dark eye-pieces, of which there should be Dark eye- several of different degrees of shade, as, if the brilliancy of the sun varies by passing clouds, no inherent error is intro- duced by changing these, which is the case with the hinged shades on the sextant. Moreover, the suns having been once equalised as to brilliancy with one eye-piece, by moving the up-and-down piece screw, they will remain equal, no matter what shade of eye-piece we use ; but with the hinged shades, the position of up-and-down piece which equalises the suns as seen through one set of them, will be different to that required for others, besides the possibility of error thus introduced. The suns should be as dark as possible. If too light 208 HYDROGRAPHICAL SURVEYING. CHAP, xm- Suns shades are used, the irradiation spoils the sharpness of the should not limb. bright. Use the eye-piece with the greatest magnifying power, as Should be it much facilitates correct contacts. possibfe aS Great care must be taken in setting the vernier, and we Settingthe must see that the tangent screw at the commencement of each vernier. se ^ j s run b ac k to its full extent, so as to avoid risk of being " two blocks " in the middle of the set, and so probably lose an observation. After bringing the zero of the vernier into what we believe to be coincidence with the minute of arc required, glance right and left to see that the marks on vernier and arc are displaced in a symmetrical manner on either side. The eye will easier catch any inaccuracy in the setting by this means. Warning Some observers, after giving a preliminary " Eeady " at the calls. commencement of each set, give no warning after, and simply " Stop " at each observation. With very careful time-takers this is sufficient, but experience of human nature leads us to say that it is better to call " Eeady " about three seconds or so before each " Stop," and thereby avoid all chance of the time- taker having his eye and ear off the watch. Allowance We should take more observations in our first half of equal lfter 10UdS altitudes than will be absolutely needed, so as to allow of Transit, some losses in the observations after transit, from obscurations of the sun. index At the conclusion of observations it is always well to take w \ the index error. It tells us whether our sextant is keeping a steady error, and also, by calculation of semi-diameter there- from, whether the instrument is in adjustment in collimation, and also, if we lose the other half of equal altitudes, and decide to work single altitudes instead, we shall have the index error observed at the time. Caiculat- After sights before transit, we must calculate the time the fof obBer- observations after transit will commence. By far the simplest vations plan, when engaged in observations, is to have an ordinary Transit, watch set to apparent time, which time the ship herself will in many cases be keeping, when by noting the time by this CHAP. xili. OBSERVATIONS FOR ERROR, ETC. 209 watch at the last observation, the time of commencement of the first observation after transit will be found by taking the time noted from twelve hours. If we do not do this, and the ship be keeping mean time, we must find the mean time of the last observation by apply- ing the approximate Error of the watch. Subtract this from twelve hours, and apply twice the equation of time, subtract- ing if apparent noon is before mean noon, and adding if vice versa. This will give mean time of the first observation after transit, which can be re-transferred to the watch by the application of the Error. We want the time by the ship's clock, to ensure leaving her at the right time, and the time by our watch, to avoid the chance of being too late on one hand, and scurry after reaching the observation spot, on the other. Algebraically we can express this, T= 12- (t + e)2q where T is mean time of first observation required. t is time by watch of last observation. e is Error of watch slow of mean time. q is equation of time. The book in which the observations are registered should Form in be ruled as in annexed specimen. ggf t The first column is for the intervals between each observa- Book - tion of the first set of sights. The second, the time taken at those sights. The third, the double altitude. The fourth, the sum of the seconds of the two times. The fifth, the time at second set of sights ; and the sixth for the intervals between the latter. On page 210 is an example of a set of sights as written in the angle book. When the time-taker is practised, it is well for him to Noting note down the interval between the sights as he notes down J^^ 8 the time, as it enables the observer at once to know, when the sights, set is over, whether he has been getting good observations or not, as the intervals should theoretically be precisely the same. 2IO HYDROGRAPHICAL SURVEYING. CHAP. xm. T? April 3rd, 1880, at Nagara Light-house A. Time by Breguet (2086). Method of Meaning. Interval in seconds. Time by watch. S Sum of sees. Time by watch. Interval in seconds. h. m. s. / 8 h. m. s. 8 03 10-8 57 20 14-8 3 40 04-0 27-6 28-0 38-8 30 15-2 36-4 28-2 27-6 04 06-4 40 14-6 39 08-2 27-2 27-2 33-6 50 14-6 41-0 27-8 28-0 05 01-6 58 00 14-8 38 13-2 28-0 27-2 28-8 10 14-0 45-2 27-6 27-4 56-2 20 13-8 37 17-6 28-0 28-2 06 24-4 30 14-0 49-6 27-4 27-2 51-6 40 13-8 36 22-2 27-2 28-0 07 19-6 50 14-6 55-0 27-8 28-0 47-6 59-00 14-8 35 27-2 11 ) 5-0 14-45 h. m. s. Times at middle sight | J ^ |8 18 2)23 43 14-0 Mean mid. time by watch 11 51 37 '22 N.B. The seconds of the result are obtained by halving the mean of Column 4. We do not usually attempt to estimate time with a pocket- watch to less than two-tenths of a second, so we shall not find the intervals agreeing exactly, even supposing no errors of observation to exist. Taking everything together, if the difference in these intervals does not exceed one second and a half, we may consider that we have obtained very good observations. Another reason for noting these intervals is that we shall see if the sun's motion is becoming too slow. In working out sights for equal altitudes, it is merely the mean of the middle times of each set that we wish to get, so that we need not mean up each column of times, but merely the sum of the seconds of each corresponding times which we have in the fourth column of our sight book. Then taking CHAP. xiii. OBSERVATIONS FOR ERROR, ETC. 21 1 the times of the middle observation, meaning those, and sub- stituting, for the seconds of this mean, the mean of the seconds just found from the fourth column, we shall have the true mean middle time of our observations. Thus, in our example the mean of the fourth column is 14 8> 5. We sub- stitute this for the 14 8< obtained by adding the two times at the middle observation, and dividing by two, we get the mean middle time by the set as llh. 51m. 37'22s. In cases where the equation of equal altitudes is varying rapidly, we shall not find the middle times of two successive sets agreeing exactly, as they should differ by the amount of the variation of the equation of equal altitudes in the time. Theoretically, this is an objection to long sets of observation, but practically, the errors of observation will exceed any little discrepancy introduced by assuming the equation to be uni- formly variable during a set of 11 to 15. If a contact is missed in either half set, it is no use to inter- Sights polate a time. The sight must be missed out of the double nusse B ( do. ) = -U| Tan dec x Cot elapsed time. J.O A 2> where - is half the change of declination in the elapsed time, a or, as we use it in the computation, the change of declination in half the elapsed time. The rules for noting the algebraic signs of A and B will be given hereafter. In making the observations it is most convenient to ascer- tain the Error of the hack watch, and thence, by using the comparisons, to arrive at the Error of the standard. In the case where the watch has a large rate, as shown by the com- parisons before and after sights, the elapsed time must be corrected for the amount gained or lost by the watch in the interval on mean time, which can be roughly calculated from the known rate of the standard. Having meaned the sights, and obtained the mean middle time for each set, and knowing the estimated latitude and longitude, the rule for working a set of equal altitudes at superior transit will stand thus : 1. Ascertain elapsed time by subtracting the central time of observation before transit from the central time after transit, increased, if necessary, by 12 hours. Halve this. Error obtained of hack watch. Practical Eule for Calcula- tion of Equation. CHAP. xill. OBSERVATIONS FOR ERROR, ETC. 213 2. To hours apply longitude to find Greenwich date of apparent noon at place ; this is first Greenwich date. 3. Find second Greenwich date, by subtracting the half elapsed time from the first Greenwich date. 4. Correct declination at apparent noon in Nautical Alma- nac for the second Greenwich date. 5. Correct equation of time at apparent noon for first Greenwich date. 6. Multiply the variation in declination for one hour, by ' , /> the half elapsed time, to get - 2i. KB. The variation we want is that at Greenwich time of local noon, we must therefore correct the variation given in the Nautical Almanac for the longitude. /i 7. For A, add together the logarithms of -o, the tangent of the latitude, and cosecant of half elapsed time ; and for B the logarithms of ~ } the tangent of the declination, and the co- 2 tangent of half elapsed time. Either subtract the log. of 15 from each of these sums, to reduce the results to time at once, or take out the natural numbers of the sums as they stand, and when A and B have been added or subtracted, divide the result by 15, to reduce it to time. N.B. Tables are given in various works on nautical astro- nomy to facilitate the calculation of A and B ; but as these are only made out for every so many minutes of elapsed time, interpolation is necessary when working with any pre- tence to accuracy, and very little is gained by their use in their present form. 8. To the mean middle time of the set, apply the equation of equal altitudes with its proper sign (rule given below), which will give the time shown by the watch at apparent noon. N.B. When working several sets, calculate them simultaneously as far as this, and mean the results, thus getting the mean time shown by the watch at apparent noon. 214 HYDROGRAPHICAL SURVEYING. CHAP. xm. All watches to be either slow or fast of Mean Time. Signs of Equation. 9. Find the mean time of apparent noon, by applying the equation of time with its proper sign to or 24 hours, and take the difference between this and mean time shown by the watch, for the Error of the latter, subtracting one from the other, according as it is intended to show the watch as fast or slow on mean time. An universal system must be adopted of showing all chronometers and hack watches as fast or slow of the standard and on mean time, not some one way and some another, which leads to confusion. It does not much matter which is taken. The writer has always shown them as slow on mean time. Thus all chronometers are shown slow of the standard, and the standard and all others slow on mean time of place, or of Greenwich, as the case may be. The rule for giving A and B their proper algebraic signs is as follows: Change of declina- tion in Inferior Transit. At Superior Transit. A is B is + if declination is decreasing and of same name. + if declination is increasing and of diffe- rent name. if otherwise. + if declination is \ increasing [When elapsed time is if declination isj less than 12 hours. decreasing J Reversed when elapsed time is greater than 12 hours. At Inferior Transit. A is reversed from what it would be at superior transit. B is the same as at superior transit. In working with inferior transit, whereby we find the Error at midnight, there is no difference in the rule, except that in calculating the change during the half-elapsed time, we use the variation of declination found by interpolation for the Greenwich time of local midnight. The next step is to calculate, from the comparisons taken with the standard before and after sights, a mean comparison CHAP. xiii. OBSERVATIONS FOR ERROR, ETC. 215 to apply to the Error of watch found above, to arrive at the Error of the standard. To do this, we take any sight, and by interpolation calcu- late the comparison at the A.M., and also the P.M. time corresponding. The mean of these two will give the com- parison at noon. This should, if the watch has been going well, correspond very closely with the comparison actually taken at noon, and it will be satisfactory if it does so. If it does not, we cannot help it; but we shall know that the Error of the standard will be slightly incorrect from a jump in the watch, and shall be prepared to give the result a smaller value in consequence, in event of discrepancies with others. The mean comparison, as found above, must always be used, not the comparison taken at noon, which is done solely to ascertain how the watch has been going. An example of the calculation follows. Calcu- lating a Mean Compa- rison for Hack Watch. Noon Com- parison not to be used. AT MESALE I d A AUG. 31st, 1878. SIGHTS OBTAINED FOE ERROR BY EQUAL ALTITUDES. LONG 39 40' E. LAT. 5 14' S. P.M. Time by watch A.M. El. time El. time Dec. .. 8 36 30 Correction 5 14 h. in. s. 10 16 22-4 3 55 50-6 h. m. s. Long .. -2 38 44 El. T. 3 10 16 6 20 31-8 3 10 15-9 2ndG. date.. -5 49 31st. Var. Dec. 8 41 44 Var E.T. , 54-18 3-17 37926 5418 16248 c -= 171 -6906 54-18 5-8 43344 27090 314-244 Eq.T. m. s. 12-09 2-03 3072 4608 1536 2-02752 2l6 HYDROGRAPHICAL SURVEYING. CHAP. xin. Tan lat E.T. Cosec -g c I 15 .. A 8-961866 131907 2-234770 Tan dec c 2 15 B = 9-184541 9-961038 2-234770 1-328543 1-176091 1-380349 1-176091 0-152452 = - 1-421 0-204258 - 1-600 A - 1-421 Equation of equal alt. 3 '021 sees. h. m. s. .. 7 06 06-51 Eq. of Eq. alts .. .. -03'02 h. m. s. Mean mid. time .. .. 7 06 06*51 Time by watch at App. Noon 7 06 03-49 h. m. s. Time by watch by 11 observations. 75 7 06 03-41 ) h. m. s. ~ ft o., VMeanoftwosets 7 06 03-45 11 ill 03 4 j 11 ~7^ 03-30 1 \ , 03-44 11 Q. 33-59 Mean Time by watch .. 7 06 03-45 Mean time of App. Noon 12 00 14-12 Watch (Breguet) slow .. 4 54 10-67 To calculate the comparison between standard (A) and watch at noon, we have the following comparisons ob- served : Before A.M. Sights. Check. After A.M. Sights. Check. h. m. s. sees. h. m. 8. M :s. A. 4 16 55 o 02-6 .. 5 37 10 19 2 Breguet . . 3 30 02 4 10-0 .. 4 50 17 26 o 46 52-6 52-6 . . 46 53'0 53'2 Mean 52 s -6 Mean 53 s '1 Noon. Check. Before P.M . Sights. Checks. h. m. 8. sees. h. m. 8. sc< ;s. sees. A 7 50 50 06-2 .. 9 47 25 o 38 8 50-0 Breguet . . 7 03 55-8 12-0 .. 8 50 30 6 44 o 55-4 46 54-2 54-2 . . 46 54-4 54-8 54'6 Mean 54 s -2 Mean 54 s -6 After P.M. Sights. Check. h. m. s. sees. A .. .. 11 26 10-0 21-0 Breguet .. .. 10 39 14 -8 25 '8 46 55-2 55-2 Mean 55 s '2 CHAP. xiii. OBSERVATIONS FOR ERROR, ETC. 21? Taking any sight, say the middle times at the set we have shown worked out, we find by interpolation that in. s. At 3 * 56 by watch, comparison is 46 52 74 At 10 -16 46 55-07 and as these are equal times from noon, the noon-comparison will be the mean of these, or 46 m 53 8 '90. This differs 8 '3 from the observed noon-comparison, which, supposing the comparisons to have been carefully observed, means that there has been a slight irregularity in. the motion of the watch, which must be remembered in comparing any meridian distance founded on these sights with others ; but in this case it is so small as scarcely to be takeji into consideration. We now apply this mean comparison to Error of watch : h. m. s. Breguet slow 4 54 10'67 Comparison 46 53 '90 Standard A slow on M. T. place .. 4 07 14-77 We next take the comparisons observed at noon between A and all the other chronometers ; and applying then to A's Error, we get the Error of each. 2l8 HYDROGRAPHICAL SURVEYING. CHAP. xiv. CHAPTEE XIV. MERIDIAN DISTANCES. Telegraphic Chronometric. UNDER this head we shall consider all the methods, avail- able for our purposes, of obtaining difference of longitude. TELEGRAPHIC MERIDIAN DISTANCE. Where a telegraph can be used, it is of course the best, and at the same time the simplest, means of obtaining difference of longitude. This method consists in sending a current through the wire at a known local time from one place, the local time of arrival at the other place being noted. The difference of these is the difference of longitude. Eetarda- I n theory, the passage of the current through the wire is tion. instantaneous ; but in practice it takes an appreciable time, when the distance is considerable, and the electrical condition of the wire is not first-rate ; and to eliminate this, and also to decrease errors of sending and receiving, we must send several sets of signals in both directions equally, the mean of which will give the true time. A little consideration will show that if a signal is sent from A to B, a place to the westward, and it takes two seconds to traverse the wire, the time at B will have had those two seconds in which to catch up the A time, which is so much ahead ; or, in other words, the difference of the two times as shown will be two seconds too little. Whereas, if the signal is sent from B to A, the watch at A, already ahead, will ad- vance another two seconds before the signal arrives, and the CHAP. xiv. TELEGRAPH MERIDIAN DISTANCE. 219 difference of the two times will be two seconds too much. The mean of the two will therefore be correct, and half the difference of the two will give the " retardation of the wire," a matter, however, purely of curiosity as far as our results are concerned. In this case a number of chronometers is not necessary. All only one that is wanted is one good time-keeper. If, however, two watches are at hand, it is not amiss to ascertain the Errors of each separately, and use them both in transmitting the signals. A box-chronometer is the best for sending and receiving signals by, and if practicable, it may be a good plan to land one, and let it stand in the telegraph office for a few days before- hand to settle down, comparing the watch actually used at sights with it, before and after observations. Sights must be obtained on the day of sending the signals, Time to and the latter should be transmitted at or about noon. Where the places are far apart in longitude, it can only be near noon at one place, and Error must be obtained at the other, either on the day before or after, as well, so as to be able to correct the Error to the time of interchange of signals. If the observation spot can be at, or close to, the telegraph Observa- office, it is convenient, as the watch will not have to be carried tio11 Spott about ; but in many instances the local arrangements will not admit of this. Telegraphic instruments differ very much ; but it does not Galvano- much matter which are used, as long as they are similar at meter * both ends. The deflection of an ordinary galvanometer-needle of Wheatstone's instrument, or of the Morse recorder, or of the more delicate mirror of long submarine cables, will all serve our purpose. Preference is given to one or the other by different observers. The writer prefers an instrument giving a sound, to the silent movement of the suspended mirror. Each signal will consist of one deflection, and the key should be kept pressed down for about a second. In sending the signals, it must be clearly arranged before- Pre- hand what is going to be done. method of A good plan is as follows : sending In commencing, give a warning, say of three rapid signals, n ' 220 HYDROGRAPHICAL SURVEYING. CHAP. xiv. at ten seconds before an even minute by the sender's watch. The first signal will .then go at the even minute, and at every ten seconds another, missing the fifty seconds, to mark the even minute, for three minutes, ending with another even minute. After an interval of three or four minutes, a similar set will be sent in the reverse direction. If at the receiving ends the signals agree, this will be quite sufficient, unless we intend to use another watch. An example of a telegraphic meridian distance is appended. It will be seen that the resistance of the wire and instru- mental retardation was less on' one day than on the other, amounting at one time to nearly a tenth of a second, and at the other to only twenty-five thousandths. CHRONOMETRIC MERIDIAN DISTANCES. When we have no telegraph we must have recourse to chronometers for conveying the time. Having obtained sights at the two places whose meridian distance we require, we come to the consideration of the rate to be used. If we have been able to run backwards and forwards, as recommended on page 201, we shall use a travelling rate. Formula The algebraic formula for finding the meridian distance by Travelling travelling rate, when we return at once to the original station, Kate. is as follows : * /- M.=fl-a-n where M = meridian distance a = error at place A, before starting, a' = , on returning, ft = B, n = No. of days between first observations at A and those at B, m = No. of days between observations at B and those at A, on returning. Then 2^2- = travellin rate. CHAP. xiv. CHRONOMETRIC MERIDIAN DISTANCES. 221 MERIDIAN DISTANCE BY TELEGRAPH SIGNALS EXCHANGED BETWEEN CONSTANTINOPLE AND DARDANELLES. April 3rd and 18th, 1880. Observation spot at Constantinople was at Leander's Tower, observers having to go 1 miles to Telegraph Office by caique. Observation spot at Dardanelles at Nagara Light-house, observers having to go three miles to Telegraph Station by steam pinnace. 1 Watch Time. Local Times. Meridian Remarks. 1 Sending. Receiving. Sending. Receiving. Distance. h. m. s. h. m. s. 11 31 00 Missed. h. m. s. 11 42 48-2 Missed. h. m. s. h. m. s. Sent by Breguet 10 11 44 15-2 58-2 11 53 22-1 10 23-9 2084. 20 25-3 43 08-2 32-2 24-0 Keceived by Dent 30 35-2 18-2 42-1 23-9 6119. PU o 40 45.3 28-2 52-2 24-0 a ' d 32 00 45 05-3 43 48-2 54 12-2 24-0 I 10 15-2 58'2 22-1 23-9 B 1 20 25-2 44 08-2 32-1 23-9 a 30 35-2 18-2 42-1 23-9 s 40 45-3 28-2 52-2 24-0 VI 1 33 00 46 05-2 48-2 55 12-1 23-9 o> 10 15-2 58-2 22-1 23-9 20 25-2 45 08-2 32-1 23-9 i 30 35.2 18-2 42-1 23-9 p 40 45-2 28-2 52-1 23-9 34 00 47 05-2 48-2 56 12-1 23-9 Mean . . 10 23-93 11 49 00 11 35 55-2 11 58 06-9 11 47 43-4 10 23-5 Sent by Dent 6119. 10 05-0 16-9 53-2 *7 Received by Bre- 20 15-0 26-9 48-03-2 7 guet 2084. 30 25-0 36-9 13-2 7 40 35-0 46-9 23-2 '7 50 00 54-9 59 06-9 43-1 8 o 10 37 04-8 16-9 53-0 9 ^ d 20 14-8 26-9 49 03-0 9 c3 30 24-9 36-9 13-1 8 P 40 35-0 46-9 23-2 7 3 51 00 54-8 12 00 06-9 43-0 9 r% 10 04-9 16-9 53-1 8 PM o 20 14-9 26-9 50 03-1 8 .3 30 Missed. __ -i 40 34-9 46-9 23-1 8 1 52-00 55-0 01 06-9 43-1 .7 O C. to D. Mean 10 23-76 D. to C. 23-93 April 3rd Mean Mer. Dist. .. 10 23-84 222 HYDROGRAPHICAL SURVEYING. CHAP. XIV. April 18th, 1880. Watch Times. "Local Times. 1 Meridian Distance. Remarks. Sending. Receiving. Sending. Receiving. h. m. B. h. m. s. h. m. s. h. m. s. h. m. s. 11 41 00 11 51 50-8 11 50 06-4 12 00 30-1 10 23-7 Sent by Breguet 10 52 00-8 16-4 40-1 7 2084. 20 10-8 26-4 50-1 7 Received by Dent 30 20-8 36-4 01 00-1 7 6119. ,3 40 30-8 46-4 10-1 '7 1 42 00 50-8 51 06-4 30-1 7 -g 10 53 00-8 16-4 40-1 7 s 20 10'8 26-4 50-1 7 3 30 20-8 36-4 02 00-1 7 5 40 30-8 46-4 10-1 7 -2 43 00 50-8 52 06-4 30-1 7 S 10 54 00-8 16-4 40-1 7 a 20 10-8 26-4 50-1 7 -I 30 20-8 36-4 03 00-1 7 1 40 30-7 46-4 10-0 6 44 00 50-8 53 06-4 30-1 '7 10 23-7 11 57 00 11 46 09-2 12 05 39-3 11 55 15-6 10 23-7 Sent by Dent 6119. 10 Missed. Received by Bre- * 20 29-2 59-3 35-6 7 guet 2084. * 30 39-2 06 09-3 45-6 7 pi 40 49-2 19-3 55-6 7 1 58 00 47 09-2 39-3 56 15-6 7 10 19-2 49'3 25-6 7 HH 20 29-2 59 3 35-6 7 r 30 39-3 07 09-3 45-7 6 "ft 40 49-2 19-3 55-6 '7 O .9 59 00 48 09-3 39-3 57 15-7 6 "1 10 19-3 49-3 25-7 6 g 20 29-3 59-3 35-7 6 PI o 30 39-4 08 09-3 45-8 5 O 40 49-2 19-3 55-6 7 12 00 00 49 09-3 39-3 58 15-7 6 C. to D. Mean 01023-65 D. toC. 23-70 April 18th, Mean Mer. Dist. .. 10 23 -67 3rd, .. 10 23-84 Final Mean Mer. Dist. .. 01023-75 CHAP. xiv. CHRONOMETRIC MERIDIAN DISTANCES. 223 This can be put another way, by example, as follows : Let us suppose we have obtained Error at Maziwi at noon, Example August 27th ; we have been to Mesale, and there obtained Error at noon on the 31st ; and then, returning to Maziwi, have obtained another Error there at midnight of September lst-2nd. To find rate in this case, we simply divide the difference of the Errors ascertained on the 27th and 1st by 5 J (the interval between them). This rate, multiplied by 4 (the interval between sights at Maziwi on 27th and Mesale on 31st), will give the quantity to be applied to the error of the chronometer in question at Maziwi on the 27th, to give the error on the 31st on mean time of Maziwi. The difference of this and the error of the same chronometer on mean time of Mesale, as ascer- tained on that day, will be the meridian distance by that chronometer. In working out a meridian distance with several chrono- Form for meters, it is convenient to use a form, as shown in the example Diatimce 1 of the above-cited instance (Page 224). Here so many of the chronometers agree closely, that Rejection the result by D seems doubtful, and, looking at the compari- of result8< sons taken every day with the standard, we see it has been going very irregularly ; we therefore reject it. This should not be done without some independent evidence of this kind ; and in a meridian distance, where the interval of time is great, or where all the chronometers have been going but fairly, as shown by the daily comparisons, it is very unsafe to reject chronometers solely because they vary from a small majority of the others. Supposing that we had had to stay at Mesale for a few Another days before returning to Maziwi, we can still find a fair travelling travelling rate. Bates, The formula for this is as follows : where, the other letters representing the same values, /3 1 is the error at place B before leaving. CO 10 ^ CO t~- iO CO I 1 b- iO 00 O iO * w S 8 CO i I 8 8 3 8 S'S 3 rH CO rH rH CM .dso - CO CO CO J-O (M rH iO CO t- O5 t- o CO 10 O L- CO "^ 8 05 T\ CO 4n O5 co rH IO O 8 Bus 10 1 cq 10 iO 10 ex, JUD IO iO CO 10 05 10 tr- io 1 iO CO CQ C^ C^ "^ C5 CO co 8 rH -* iO CO O rH CO CO r-i - : rH co -^ tKf\ -4^ ^P ^ 22 o -2 -5 ^3 . co 1 2 1 i CO '> 03 " I*" c? ^> ^2 ' N R rtf "5 r ^ o J^ IO p "* J S ' i e ^ J t If "8 j. CHAP. xiv. CHRONOMETRIC MERIDIAN DISTANCES. 22$ Here the travelling rate is, m-f- n This can be exemplified thus. We obtain sights at Maziwi on 27th and 31st as before. Then sights again at Mesale on the 4th noon, and again at Maziwi on the 6th noon. From the difference of the "errors on the 27th and 6th we should deduct the difference of the errors on the 31st and 4th, and divide the remainder by 6, the sum of the intervals from the 27th to the 31st, and of the 4th to the 6th, or, in other words, the number of days actually travelling, which will give us the rate. We then proceed as before. The travelling rate obtained in this instance will not be as good as in the former case, as the chronometers will have had two disturbances instead of one, and the rate they may settle into on starting the second time, after four days' quiet at anchor, may not be the same as before ; but it will still be better than obtainable by any other method, and, if circumstances of weather, sea, and temperature are nearly alike on both journeys, and the intervals are not long, we shall probably get a very good result. Travelling rates, obtained thus, should always, as already remarked, be used when the scale of the chart depends on the observations. The method is very simple, and, used for this purpose, none of the considerations of temperature, &c., hereafter mentioned need be thought of, as the time is short. We now come to the consideration of the rates to be used other on other occasions, especially when voyages are long, and B>ates< circumstances change much during them. This is a very wide subject, and besides the fact that it has already been fully discussed by Captain Shadwell, in his masterly treatise before referred to, neither space nor the intention of these pages permit our going very far into it, and we shall content ourselves with giving general descriptions of cases, together with formulae for them, with just sufficient reasons to allow of their being understood. Q 226 HYDROGRAPHICAL SURVEYING. CHAP. xiv. The whole question rests on, What makes chronometers vary ? Why The labours of many observers show us that the answer Watches . change their 1. Imperfection in the workmanship of the watch, rates, 2. Changes of temperature. 3. The quality of the oil in the pivots, and its age (i.e. the time elapsed since the watch was last cleaned). 4. Accidental shocks or vibrations imparted to the watch. A supplementary question may be asked Which of these is the most important ? To which the general answer is that, according to circumstances, any one may be. First. Imperfection of workmanship. Imperfec- For this manifestly there is nothing to be done. A badly made chronometer will go so erratically that we shall soon lose confidence in it, and reject it from all results, returning it as soon as we can. There are, however, but few chronometers that pass through the hands of the Eoyal Observatory which will come under this head, and doubtless many a chronometer has been classed in this category from ignorance of the circumstances of its compensation, and its resulting variation under change of temperature. If on a voyage, during which temperature is uniform, a chronometer placed with others, under the same conditions of protection from injury, &c., goes erratically, while the others maintain their rates pretty steadily, we may fairly conclude it to be inferior. The uniformity of rate of a chronometer while on shore, or when the ship is at rest, cannot be taken as a conclusive test. Secondly. Change of temperature. Change of A chronometer is supposed to be compensated in such a manner that at two temperatures, a varying number of degrees apart, the rates will be equal. At all other temperatures the rates will vary, reaching a maximum at about the mean tempe- rature between the other two. Let us, for brevity, call this temperature of maximum rate T. CHAP. xiv. CHRONOMETRIC MERIDIAN DISTANCES. 227 If we then examine the rates of a chronometer we should Tempera- find a steady change of rate in one direction (nearly always Maximum in the direction of acceleration of gaining) from low tempera- Eate ' tures to high, until we reach T, when the change of rate should vary in the opposite direction. For every chronometer we shall have a different quantity for T, and different coefficients of change. Many chrono- meters are supposed to be compensated for T = 60, the mean temperature generally experienced over the globe; but it would seem that makers cannot command the point T; anyway many have T over 90, so that for such a watch, in practice, the direction of change is invariable, which will result in a great accumulation of difference of rate when passing through hot and cold climates, and where the coeffi- cient is large, in great absolute change of rate. Different observers on the performances of chronometers Different have come to different conclusions on the subject of the law c . onclu " sions. of change for a degree on all parts of the scale, which can only be accounted for by supposing that they have experi- mented on different classes of time-keepers. Some have stated that they vary regularly, so as to have the same rate at an equal number of degrees above or below T, and have established the proportion of variation at . the square of the difference of T, and the temperature required. Other experiments have shown that the manner in which watches vary is not quite so regular as this, and that the coefficient of change is generally less at temperatures higher than T, than at those below. The fact is, that there is no invariable law on the subject, a No strict watch being too complicated a machine to admit of any prac- tical conclusion, unbased on actual experiment with each individual watch. Experiment, however, does give results that can be prac- Practical tically used, and tables of rates can be formed from observa- me nts. tion of the watch at different fixed temperatures, which, with some watches, will undoubtedly give better results than by using invariable rates. Q 2 228 HYDROGRAPHICAL SURVEYING. CHAP. xiv. Liverpool Observa- tory. Chro- nometers inH.M. Ships. Quality of oil. Tables of this kind are now furnished to ships sailing from Liverpool, whose chronometers are rated at the Bidston Obser- vatory, the director of which, Mr. Hartnup, has studied the question for many years. The rate of the watch to be used for determining the position at sea is then taken day by day from the table, according to the temperature experienced, and added to the accumulated rate since departure, obtained in a similar manner. It seems pretty well established that the coefficient of change for a degree remains the same, or nearly the same, for each individual watch, although the absolute rates of the watch (which depend upon many things) may vary. The chronometers issued to H.M. ships have no such information sent with them, for this reason. The timekeepers are carefully chosen from many sent to the Eoyal Observatory by different makers for trial, and only those whose compensation is such that they show very little change of rate at a great variation of temperature, or, in other words, whose compensation is as perfect as may be, are taken, the limit allowed being one and a .quarter second of change of daily rate for forty-five degrees of temperature. This reduces the variation of rate, arising from change of temperature probable in a voyage, to very small quantities, which would be lost in the variation arising from other causes, and it is not considered necessary under these circumstances to give data for allowing it. For ordinary purposes of navigation, then, H.M. ships may safely neglect any allowance for change of temperature ; but for ascertaining difference of longitude for hydrographical purposes, when the voyage is long and changes of temperature considerable, it may be as well to endeavour to make this correction. Thirdly. The oil in the pivots. With good oil the ine- quality arising from age shows itself in the shape of a gradual and tolerably uniform acceleration of rate, generally in the direction of gaining, with a new chronometer, and when the instrument is older and all parts somewhat worn, in the CHAP. XIV. CHRONOMETRIC MERIDIAN DISTANCES. 229 contrary direction. It should be excessively small, and our opinion is that in the practical question of meridian distances, the labour of ascertaining it is not repaid by the result. It is difficult to separate the error due to this from that originating in defective mechanism, and though formulae have been ela- borated for its detection, we do not propose to give them here. Fourthly. Vibration and shocks. However well chrono- Vibrations meters may be stowed, the jars from seas striking the ship, andshooks - and other like accidents, must be communicated more or less to the chronometers. The vibration of the screw is in some vessels sufficient to pass through all the soft cushions in which they may lie, and must have its effect, more especially from the fact that the watches themselves are hanging in the metal gimbols, in which there must be play sufficient to allow them to swing easily, and therefore enough to set up small shocks on any violent movements of the ship.* * In connection with the obser- vations of the Transit of Venus of 1874, Lord Lindsay conveyed nearly sixty chronometers to Mauritius. These were kindly permitted by him to be used in assisting to determine the meridian distance between Mauritius and Rodriguez, when they were shipped on board H.M.S. " Shearwater? under the author's command. As the results by these watches, both of the distance be- tween Mauritius and Eodriguez, and Mauritius and Aden, (between which latter places they were conveyed in the mail steamer,) were remarkably good, and as the results by the " Shearwater's " chronometers which were admitted into the distance Mauritius to Rodriguez were not so satisfactory, a description of the manner in which Lord Lindsay's watches were stowed may not be out of place. We may add that the " Shearwater " had to beat up. for eight days against a strong trade- wind on one occasion, and was a very lively ship. The watches were taken out of their gimbols and placed in square boxes, which held nine of them each. The partitions of these boxes were thickly stuffed with very soft material (cotton wool) covered with satin, so that each watch lay in a bed of down which was made exactly to fit it. Each box was fitted with a metal framework after the fashion of gimbols, the outer pivots of which fitted into carefully turned sockets, in two upright columns of wood, which were firmly screwed to the deck. Each pair of uprights carried three boxes of watches. The effect of this was that any 2 3 HYDROGRAPHICAL SURVEYING. CHAP. xiv. In our opinion the variation of rate arising from these causes is, with the generality of Admiralty watches, the larger proportion of the total change. The only notice that can be taken of variation of rate due to this, is to consider it as detracting from the general value of the meridian distance; and the nature of the passage, whether rough or smooth, should therefore be noted in the returns. Magnetism is another disturbing cause, to which irregu- larities of chronometers have been referred. As no trust- worthy conclusion as to this has been arrived at, we do no more than mention it. It follows as a matter of course, from the preceding obser- vations, that not only will the rate of a chronometer as ascer- tained before leaving a port be different to that found on arrival at another port, but that the sea rate for the interval will probably be different from either of them. We have now to consider the means at our disposal for approximating to the true rate under different circumstances. The most satisfactory circumstances under which we can slight shocks to the boxes caused by seas striking the ship, or by longitudinal slipping of the pivots, were entirely deadened before reach- ing the watches themselves. This mode of stowing necessitated taking the watch up bodily in the hand to wind, which at first sight seems dangerous, and undoubtedly does present more opportunity for accident than the ordinary method ; but, as far as the author is aware, none took place during the five or six months the watches were thus treated, and the admirable agree- ment of the results seems to show that this system was unusually successful. Whether it could be adopted on board men-of-war, especially small ones, which are usually employed in surveying duties, is another matter, as it certainly demands more space, both for the swinging of the box and to allow of free access for handling the watches. It was very convenient for com- paring, as one watch could be held to the ear while the eye took the time by the standard. It seems probable, also, that the temperature would be more con- stant, from the fact of the watch being imbedded in thick soft ma- terial. The lid of each box was also stuffed softly, and, when in place, pressed on the glass of each watch, excluding all air. CHAP. xiv. CHRONOMETRIC MERIDIAN DISTANCES. 231 determine meridian distance (after those already described) Interpola- is when, having left a port A, called at B (the position we between want), where we have only stayed long enough to get Error, and eventually arrived at K without further stoppage, the longitude longitudes of A and K are sufficiently well known to take them ^bu as secondary meridians. In this case, by applying the known difference of longitude between A and K to the observations at A, we find the Error on mean time at K at the epoch of starting from A. The difference between this and the Error ascertained on arrival at K, divided by the duration of the voyage, will give us a fair sea rate, which we shall assume to be uniform and invariable during the voyage. A simple application, then, of accumulated rate up to the time of observations at B, will give us the meridian distance from A to B, dependent upon A and K being in certain longitudes. We can use the same means if we call at more places than one on the way between A and K, but each stoppage will probably detract from the value of the sea rate. We are here using the sea rate only, and therefore shall take the date of the last observations at departure, and first on arrival, as the epochs for calculation. If we have obtained rate on departure and arrival, we shall gain valuable informa- tion about our chronometers, as we shall be able to see how far they have obeyed any theory as to gradual or uniform change of rate, according to the ordinary assumption that the sea rate is the mean of the two harbour rates. The value of a meridian distance by this method will, as always, be influenced by the conditions of temperature, fair passage, &c., which must therefore be taken into consideration and recorded. It will be remarked that by this method, a large amount of time is saved, and opportunities otherwise wasted are utilised to their full extent. Instead of the necessity of waiting, certainly at A and K, and perhaps at B as well, for from five to eight days, a simple call of a few hours at each is sufficient to obtain an excellent result. Moreover, instead of involving 232 HYDROGRAPHICAL SURVEYING. CHAP. xiv. Shadwell's Treat- ment. Formula for Inter- polation. the eccentricities of chronometers during the time in harbour at each end, we only include in the calculation the actual time while travelling at sea, and thereby save the irregu- larities of a good many extra days. Captain Shadwell, in treating of this case, does not use an invariable sea rate pure and simple, but supposes that the rate of departure has gradually and uniformly changed into the sea rate, which he considers as the rate on the middle day of the passage only. He therefore applies for his determination of B from A an intermediate rate between the sea rate and rate of departure; but our experience does not lead us to think that this is an advantage, although by doing the same to the sea rate and rate of arrival, he gets a second meridian distance from B to K, and takes the mean of the two as his result. Our opinion is that, temperature being left out of the question, a better result is likely by using a uniform sea rate. The algebraic formula for meridian distance by above method of uniform sea rate, is, = Xi-X-h T X 2 -X-M t Where M is meridian distance between the terminal points A and K of the voyage. Mj is meridian distance between port of departure, and a port B touched at on the voyage. X is error at A on leaving. Xj B on touching. X 2 K on arriving. t is interval between observations at A and K. T A and B. In any case of a ship's calling at a place as an inter- mediate port on her voyage between two other places, it may be well to send home, beside the meridian distance obtained in the ordinary manner, the information which would enable the office, if or when it possesses the true difference of longitude between the terminal ports, to calcu- late the difference of longitude of the intermediate place by the last formula. e CHAP. xiv. CHRONOMETRIC MERIDIAN DISTANC. This necessary information will be X, X b X 2 , t, and T. In transmitting this information we could, for the facilita- Meaning tion of computation afterwards, give only the mean of the Errors of all the chronometers, instead of the individual error of each, or in other words, assume an imaginary watch, the result of which will give the same meridian distance, as the mean of the meridian distances by each chronometer ; but the adoption of this method will of course preclude any estima- tion of the value of the distance by the concurrence of individual results, and should be therefore only adopted when we have reason to believe from inter-comparisons during the voyage that the watches have" been going well together.* There is another adaptation of the method of sea rates as obtained by Error at two places whose longitude is known, which is often useful. If we obtain Error before leaving A, and after some days Adapta- call at B, whose difference of longitude from A is known, and there obtain Error again, we get a very good sea rate for the subsequent part of our voyage, which we can utilise to determine the position of C, any third place at which we may hereafter soon call, with a probable better result than by means of harbour rates. This method is especially useful for navigational purposes. Suppose a ship to leave Portsmouth and to call at Gibraltar for a few hours only. Error can be obtained, and by means of the known difference of longitude a sea rate deduced, which will give a better landfall for Malta, than the harbour rates at Portsmouth. When our voyage is simply from one port to another, and Mean we wish to find the meridian distance between them, we must depend mainly upon the harbour rates ascertained before departure and on arrival. * This method of Interpolation is not recognised as being as valu- able as I believe it to be, and the remarks on it must be taken as my private opinion only. W.J. L.W. 234 HYDROGRAPHICAL SURVEYING. CHAP. xiv. The ordinary and rougher method is to assume that the rate has changed uniformly from the rate of departure to that of arrival, and that therefore the mean of the two rates will represent the mean rate during the passage. "We believe that (owing to the many causes of variation impossible to formulate) in most cases, and especially where temperature has been, in the chronometer room, fairly uniform, this method will give as good a result as any other ; but where temperature has changed much, the result of long meridian distances with such rates will have but very little value, and that a correction for temperature will much improve the result, if we can apply it. French naval officers have done much in working out this question, and Captain Shadwell gives their separate theories and formula. To our mind the method of M. Mouchez is the most practical ; and not undertaking to enter into the question of acceleration, nor depending on observations on the watches while in the Observatory, it is more adapted to actual work. Mouchez's Mouchez proceeds on the assumption, which is near enough Bule< to truth for the method, that the rate varies uniformly with the temperature ; but in working on this hypothesis, we must not forget that for each chronometer there is a point of temperature at which the rate is at a maximum, and that the sign of the variation will change as we pass it. He ascertains by observations for rate at different tempera- tures, undertaken by the officers when the chronometers are embarked, the coefficient for temperature by simply dividing the difference of rate by the difference of mean temperatures during the intervals of rating. This coefficient of change will remain constant for some period, though the actual rates themselves will alter from other causes ; nevertheless, the more these observations are multiplied the better, and the latest determinations will be used in practice. In determining the sea rate for a meridian distance, he applies to the rate of departure the change of rate due CHAP. xiv. CHRONOMETRIC MERIDIAN DISTANCES. 235 to the difference between the mean temperature during rating, and the mean temperature during the passage, which gives one value for the sea rate. Doing the same for the rates of arrival, he gets another value for sea rate. The mean of these two he takes as the final mean sea rate to be used. One weak point here is that the mean temperature, T, of the compensation will not be indicated, unless many observations at different temperatures are made. It will therefore add considerably to the value of this method if we can find T. It will be more satisfactory if we can get this from the Lieussou's Observatory ; but a formula for ascertaining it is given by ? ormula <; ' ~- J for ascer- Capt. Shadwell, from M. Lieussou, which we here append, taining T. but we apprehend that in practice not many opportunities will present themselves for making use of it. It depends on the results of four observations for rates, at equal intervals of time, and at different temperatures, a difficult condition to satisfy except with artificial aid for the temperature. M. Lieussou remarks, "that four rates and four tempera- tures, observed at intervals of ten days, determine the constants for each chronometer with a precision sufficiently remarkable." With the other constants we do not propose to deal, but solely to give his formula for ascertaining T, which is T = } . Q.-2m 2 +m j ) Q:-2r+* 4 2 ) - ( TOg - 2i 3 + mj (?-*? + ^) 0i-2m $ +,) ( 2 -2^ 4 )-(m 2 -2m 3 +m 4 ) (^-2^+fj Here T = mean temperature of compensation required. ?% m 2 m 3 m 4 are the four observed rates corresponding to t\ t 2 t 3 4 the four temperatures. The intervals between the sets of observations for rates should be between 10 and 30 days. Mr. Hartnup's formulae are somewhat different, and do not Hartnup's give exactly the same results with the same data. He observes the rate at three different temperatures not less than 15 apart, but there must be an equal number of degrees between them. The same remark already made as to M. Lieussou's method 236 HYDROGRAPHICAL SURVEYING. CHAP. xiv. will apply here, viz. that in service afloat it will be difficult to fulfil the conditions of observation. His formulae are as follows : 2(d-d,) K = r l -(T-t i : d 2p Where C is the coefficient of change of rate, T is temperature of maximum rate, K is rate at that temperature. #! is the middle temperature, r l is observed rate at temperature t l5 d is difference of rate between that at lowest tempera- ture and t lt d^ is difference of rate between t l and that at highest temperature, p is difference between highest and lowest tempera- tures observed at. Then to find the rate in any required temperature. If N = any number of degrees from T. Rate at T N = R + C N 2 . Epochs of In using the rates of departure and arrival in calculating a Caicula- meridian distance, the Errors at the last observation at de- parture and first at arrival should not be "taken for the epochs of calculation, but the mean of the two should be used for the purpose, for it is at the mean date between the two observa- tions for each rate at which the latter is actually fixed. Thus, if we observe at a place A on the 2nd and 8th, and again on arrival at B on the 20th and 27th, we should take the mean of the two Errors on 2nd and 8th, and call it the Error at A on the 5th, and similarly at B on the 23 rd *5, and use the interval between these two epochs for the multiplication of the mean rate. CHAP. xiv. CHRONOMETRIC MERIDIAN DISTANCES. 237 The formula given by Tiarks, and generally adopted, for Tiarks' calculating the meridian distance between two places by Formu a> rates at departure and arrival, without any consideration of temperature is M = X'- j\ + <( + !)} Where M is meridian distance required, X the Error at mean epoch of departure, X I arrival, t the interval between the two epochs, a the rate at departure, b the difference between rate at departure and arrival. In calculating t, the difference t)f time, due to difference of Calculat- longitude between the two places, must not be forgotten ; but ? jf erva i being reduced to the decimal of a day, must be added or subtracted to the interval between the epochs, according as we have moved westward or eastward. Thus, if our mean epoch at A is at noon on the 20th, and at another place, B, 30 degrees to the westward, at noon on the 30th, the interval of time for accumulated rate will not be ten days, but ten plus the difference of longitude of the two places, or 10 d< 08 ; for the sun, having completed the ten days by returning to the meridian of A, will take yet another '08 of a day to be on the meridian of B. Similarly, in calculating sea rate from observations at different places where longitude is known, we must allow for this difference of time. Thus, having taken sights at A at noon on the 2nd, and at B, 20 degrees eastward, on the llth at noon, the interval with which to divide the difference of Error at A (corrected for difference of longitude) and Error at B, to ascertain the daily rate, will be 8 d> 94, as the sun will be on the meridian at B 06 of a day earlier than at A. The same formula, when intending to correct for tempera- Tiarks' ture, will stand thus : iSi I/ 7>\ /fl_i_/}i \1 perature x + t(a + 238 HYDROGRAPHICAL SURVEYING. CHAP. xiv. Where, the other letters signifying as before, is mean temperature during rating at departure, 1 arrival. e. during the passage. y is the coefficient for temperature found from previous observations. Algebraic In all cases of correction for temperature the algebraic sign Signs. Q ^ must be remembered, that is, it must be applied accord- ing to the observed effect in altering the rate. The same remark applies to the algebraic signs of all quan- tities in the formulae. Thus in the formula : M =\ l - The signs which are here given, as throughout, for chrono- meters slow of mean time and losing rates, will only be true under those circumstances with increasing losing rates and when moving eastward. A consideration of the facts, and obvious effects of the corrections, is perhaps the best course to take to determine these signs. A meridian distance, founded only upon rates obtained at one end, without any further correction, cannot be considered as of any value whatever, unless the voyage be very short. Tiarks' When using the combination of harbour rates at each end for^te"- f a v y a o e > A to K, to determine the position of some inter- polation mediate place, B, we must, to be consistent, remember that we are assuming that the rate has gradually and uniformly changed from that of departure to that of arrival, and that the rate to be used for a portion of the voyage will not therefore be the same as that for the whole of it. Tiarks, interpreted by Capt. Shadwell, gives us the follow- ing formula. with harbour Bates. Where M! is meridian distance A to P>. A, Error at B. X ,, Error at mean epoch at A. CHAP. xiv. CHRONOMETRIC MERIDIAN DISTANCES. 239 Where M is meridian distance A to B. a rate of departure. 1) difference of rates of departure and arrival. t interval between mean epochs of rating at A and K. T interval between mean epoch at A and observa- tions at B. It is to this case that our observations on page 232 refer, to the effect that the data for calculating the position of B, as interpolated between A and K, may be also transmitted home. A very good way of measuring meridian distance for the Use of ' "R.n*Vpt 18th Zanzibar Feb. 1st Qth 5> )> ) VVU )) j) Duration of passage, Jan. 18th, 6 P.M. to Jan. 30th, 4 P.M. Epochs for calculating accumulated rate, Jan. 15, Feb. 5th = 20 545 days. 1 By Observer 1. Date. Mean Temp. Date. Mean Temp. Remark Rate of Departure. Rate of Arrival. Meridian Distance. Jan. o o A -1-280 -l'-544 i. m. s. 1 05 04-54 13 14 80 81 29 30 80 81 Sea smooth ing passa B -1-158 -1-211 05-40 15 82 31 79 Steaming 7 C -1-888 -2-849 04 59-48 16 17 80 79 Feb. 1 80 Sailing 5 d Head ger D + 2-212 + 2-026 05 05-03 18 81 2 78 West. E -2-068 -2-361 04-96 19 20 78 77 3 4 80 81 C. H. & F. irregular F -4-908 -5-267 02-80 21 78 5 80 intercom G + 4-832 + 4-864 03-40 22 23 76 77 6 7 79 81 sons. H -2-668 -5-261 None calculated. 24 78 8 80 25 75 9 81 J 26 77 K 27 79 28 80 Chronometers rejected C. F. & H. Number used, 5. h. m. s. Mean Meridian Distance by Observer 1 .. 1 05 04-59 2 05 '43 h. m. s. Final Mean Meridian distance by arithmetical mean 1 05 05 -0 , values assigned CHAPTEK XV. TRUE BEARING. By Theodolite By Sextant Variation. IN nearly all descriptions of surveys true bearings will be used. The most correct method, from a shore station, is to use the By theo- theodolite, which will alone give a very good result for sextant. azimuth; but it is better to get the altitudes with a sextant and artificial horizon, when two observers are available. The theodolite in this case is only used for taking the horizontal angle between the sun and the zero. There are two principal methods in "use for obtaining the TWO azimuth. By observations at equal altitude A.M. and P.M., or metnods< by single observations. The former is theoretically the more correct, as many errors single are eliminated ; but our experience is that with single observa- tions taken with the sun near the prime vertical, with instru- sufficient. ments in good order, the result is quite as near the truth as is generally requisite in marine surveys. When an extensive piece of coast is being surveyed, we shall, as before stated, depend upon the astronomical positions for the scale and bearing of the chart, and extreme accuracy in obtaining the original bearing for working is therefore unnecessary. In the former case, the sun will be observed at an even stated altitude, and the sextant will be set beforehand, the observer using it giving the " stop " to the theodolite observer. In the latter, the theodolite observer generally calls the " stop," and the sextant observer takes whatever altitude it happens to be. R 242 HYDROGRAPHICAL SURVEYING. CHAP. xv. Changing To arrive at a satisfactory result in either case, it is neces- 66 sar y t take sever al se ^s, with a different degree of the arc pointed at the zero in each, so as to eliminate the errors of the horizontal arc of the instrument. Correcting As it is the bearing of the sun's centre which we obtain centre! 8 ^7 working out the azimuth, the aim of the theodolite observations is to get the horizontal angle between that centre and our zero ; but it is manifest that we cannot trust our eye to place the cross-wires of the telescope exactly on the centre of the sun, nor can we place the wires truly vertical and horizontal. If we could do the latter, we could arrive at the angles to the centre by merely observing the sun in one quadrant, and applying the semi-diameter^ but we must not trust this, if we want fair accuracy. Method in In equal altitude observations, the method is to fix on an equa^ y altitude for both sextant and theodolite, and set the vertical altitudes. arc o f latter at it. In the forenoon, bring the sun so that it is in the lower half of the field, and approaching the vertical wire. The theodolite observer then keeps the limb of the sun in contact with the vertical wire, and below the hori- zontal one. If the theodolite is truly levelled, he will not need to touch his vertical tangent screw, but if necessary he must do so, to keep the upper limb of the sun as nearly touching the horizontal wire as he can. When the upper limbs of the sun in the artificial horizon are in contact, the observer calls " stop," and the motion of both tangent screws of the theodolite cease. The horizontal arc is then read. Then, without moving the theodolite in altitude, the other limb of the sun is brought on the other side of the vertical wire, and the reading made when the artificial horizon observer gives " stop," on the lower limbs of the sun coming in contact. The sun will thus have passed between opposite quadrants of the cross- wires, as in the diagram Fig. 36. Similar observations are made at the same altitude in the afternoon, the lower limb coming first. Each set will thus consist of two observations A.M. and two P.M. In this CHAP. XV. TRUE BEARING. 243 method the time must be taken exactly, which is a drawback, as it either requires three persons, or that one should take time as well as his observation. There is, however, no necessity to know the local time very exactly, all we want is the true elapsed time. To work out the equal altitude observation, the means of Caicu- the times, and of the horizontal angles of A.M. and P.M. respec- Bearing tively, are taken. FIG 36. by Equal Altitudes. If the sun had no motion in 'declination, the mean of A.M. and P.M. horizontal angle would be the angle on the horizontal arc corresponding to the true meridian, or, in other words, the bearing of the zero ; but as this is not so, we must work a correction similar to the Equation of equal altitudes when obtaining time, to be applied to this mean of the angles. The formula for this is Correction = - Cosec time ela P sed Sec lat., 2i 2t where - is half the change of declination in elapsed time. 2 This correction is additive to the angle when the sun is moving from the nearest pole, and subtractive when moving towards it. Let us take the following example AT NUT ^. PAGODA ^ 360. Alt. Times. Hor. Angle. 39 h. m. 8. A.M. 8 20 14 8 23 22 P.M. 4 02 13 4 05 20 o / n 15 05 30 15 09 15 193 24 30 193 28 45 Z. K. ?> Z. K. K 2 244 HYDROGRAPHICAL SUR VE YING. CHAP. xv. Lat. 30 K Declination corrected to Greenwich time of A.M. observation 18 14' N. Sun moving north. h. m. s. O t 1 Mean A.M. Times .. 8 21 48 A.M. angle .. 15 07 22 P.M 16 03 46 P.M. .. 193 26 37 Elapsed Time 7 41 58 Mean 208 33 57 angle .. 104 16 58 Elapsed Time 3 50 59 _______ Var. of dec. in 1 hour 37" -44 3-85 c 2" 2-15866 Cosec ^- -' -07279 18720 2 , 29952 Seclat.. 06249 11232 2-29394 .. 196" -7 c __ 2 ~ 144-144 Cor = 3' 17" Mean angle Angle of South Point Or. bearing of Pagoda .. 104 16 58 - 3 17 .. 104 13 41 ..S.104 13 41 E. A number of similar sets, taken with different degrees as zero, will give a very correct result, and though all instru- mental errors will not be eliminated, the majority of them will disappear. Method by In " single " observations, each set will consist of four Altitudes, contacts, in each of which the sun will be tangential to the vertical wire in a different quadrant of the field. The mean of these will then be the angle to the sun's centre, corresponding to the mean of the four altitudes. When the altitude is being taken by a sextant, it will only be necessary for the theodolite observer to be very exact with the contact of the side-limb of the sun ; but his upper or lower limb, as the case may be, should be as nearly touching the horizontal wire as possible, to insure the elimination of the wire error. It is quite immaterial in which quadrant the observer commences ; but whatever plan he adopts, he should always observe in the same manner, as it prevents confusion and CHAP. XV. TRUE BEARING. 245 mistakes. The sun will appear as in the diagrams in Fig. 37. When taking the observation with the theodolite alone, it will of course be necessary to see that both the horizontal and vertical wires are truly tangential to the sun's limbs. Six sets should give a very good bearing ; but if the theo- dolite is a very small one, or is known to be badly graduated, more may be necessary. Half the altitudes in the artificial horizon may be taken with upper limb and half with the lower; but this is not FIG 37. important, as if the observation be made when the sun is near the prime vertical, a small error in the altitude will but slightly affect the azimuth. The azimuth of the sun having been obtained by the ordinary rule of nautical astronomy, the true bearing of the object is found by applying the mean of the theodolite angles of that set. Care should be taken that the vertical circle of the theodolite is truly in adjustment in the vertical plane, as neither " single " nor " double " observations will eliminate any error of this kind. 246 HYDROGRAPHICAL SURVEYING. CHAP. xv. Method by In finding a true bearing with sextant only, it will save Sextant, trouble if two observers are employed one to take the alti- tude, the other to measure the angular distance at the same instant. If only one observer is available, he must take altitude and angular distance alternately, taking care to end with the same observation as that with which he begins, so that the mean of each kind will correspond as nearly as may be in time. Thus, if he begins with altitude, he must also end with altitude. Caicuia- In this instance we have to calculate the horizontal angle, turaof -which ^h the theodolite we obtained directly. Horizontal J Angle. The object should be so chosen that the line joining it with the sun should not make a larger angle with the horizon than 20, and the less the better, as any inaccuracies of observation will not then be much increased when the horizontal angle is deduced. If we take an object 90 or more from the sun, these conditions will be fulfilled, the sun being of course com- paratively low, and near the prime vertical. Two Cases. There are two separate cases : First, when the object whose bearing is desired is on the horizon ; and secondly, when it has a sensible altitude, as a mountain top. Object on In the first we have to solve a quadrantal triangle as shown horizoiL in Fig. 38. FIG 38. O Here, Fig. 38, Z is zenith, S is sun, and the object on the horizon. We have Z = 90. Z S the apparent zenith distance, CHAP. XV. TRUE BEARING. 247 and OS the observed angular distance, to find OZS, the horizontal angle required, or Cos horiz. angle = Cos ang. dist. x Sec. app. alt. Example. (Object on horizon, two observers with sextants and artificial horizon.) On June 1st, 1881, at Cob A 7 h 24 m A.M. mean time of place, observed altitude of Q 60 18' 35", mean angular distance of Gl to Pine A on horizon 84 26" 20', object right of 0. Lat. 40 26' 15" 1ST. Long. 28 00' E. Index Errors - 35" and 0". M. Time pi. .. 7*5 Long, in time .. 1'52 O 1 II 'a. dec. 1st .. 22 6 59-6 N. 2 08 Gr. Date 31st .. 17 '32 Corrected dec. .. 22 04 51*6 1st ..-6-28 Pol. dist. ..67 55 08 O 1 It Obd. alt. .. 60 18 35 Index error.. -35 n Var. .. 20-0 6-4 2)60 18 00 800 1200 128" -00 O 1 II Obs. Ang. dist. .. 84 26 20 S. D 15 48 30 09 00 S. D. .. +15 48 App. alt. .. 30 24 48 Ref. .. - 1 31 T. alt. 30 23 1 7 True Ang. dist. .. 84 42 08 Lat. Alt. P.D. .. 40 26 15 .. 30 23 17 Sec. Sec. 118550 064181 10 02 58 67 55 08 77 58 06 Hav. 57 52 10 Hav. Azimuth of sun 4-798724 , 4-684677 9-666132 N. 85 49' 25'' E. 248 HYDROGRAPHICAL SURVEYING. CHAP. xv. Cos. true Ang. dist. . . 8 965353 Sec. app. alt. .. -064294 Cos. Hor. ang. .. 9-029647 .. 83 51 14 Hor. ang. O I II Azimuth N, 85 49 25 E. Hor. angle 83 51 14 N. 169 40 39 E. True bearing Pine A S. 10 19 21 E. Ob j eot In the second case, we have a spherical triangle with three elevated sides known, as in Figure 39. FIG 39, Here, Fig. 39, we have Z 0, the zenith distance of the object, Z S, and O S, as before, the apparent zenith distance of sun, and angular distance ; to find Z S, the horizontal angle re- quired, which can be done by any of the applications of the formula Cos Z S - Cos S "" Cos Z S ' Cos Z SinZS . SinZO Example. (One observer with sextant, sea horizon, alternate observations, object elevated.) At St. Ann's A, October 5th, 1881, Lat. 5 10' S. Long. 57 14' E., the following observations were taken for true CHAP. XV. TRUE BEARING. 249 bearing of Snow Peak. Height of eye 10 feet, object right of 0. M.T. place 8.00 A.M. I.E. - 50". Alt. Q Ang. Distance of Snow Peak Q Elevation of Snow Peak. O 1 30 06 13 20 28 36 42 10 00 15 00 10 50 o i n 94 14 40 16 10 18 30 20 00 21 20 On arc .. 1 Off ., 1 26 10 24 30 1 25 20 4thM.T.pl... Long. h. m. 20 00 3 49 dec. O t .. 4 53 * 7 44 S. Var 30 M .. 57-7 7-8 Gr. date 4th 5th - 16 11 7 49 Corr. dec. P D .. 4 46 85 13 14 46 4616 4039 mmmmmmmmm,^ 6)450-06 Mean. obs. alt I. E H. E .. Q. .. O / // 30 24 24 -50 30 23 34 -3 07 Mean c I. E. S. D. ibs. ang. dist. 7' -30" / //. .. 94 18 08 - 50 94 17 18 .. +16 02 S.D App. alt. Kef. .. " 30 20 27 + 16 02 30 36 29 -1 30 Corr. ar ig. dist. .. 94 33 20 Tr. alt. 30 34 59 Lat. Alt. o / // .. 5 10 00 .. 30 34 59 Sec. Sec. .. '001768 .. -065052 P.D. 25 24 59 .. 85 13 46 I Hav. .. 4-915068 110 38 45 j 59 48 47 j i Hav. .. 4-697741 9-679629 S. 87 30' .11" E. Azimuth 250 HYDROGRAPHICAL SURVEYING. CHAP. xv. App. alt. Alt. snow peak-.. Ang. dist Horizontal ar Azimuth o 30 1 36 25 n 29 20 Sec. Sec. Hav. *Hav. o / 96 08 87 30 .. -065163 .. '000134 .. 4-945413 .. 4-732408 29 94 11 33 09 20 123 44 29 65 22 11 igle .. .*; s. 9-743118 33 HE. True bearing snow peak .. S. 8 38 22 W. Use of The Pole star may be used in the northern hemisphere to Polaris, obtain true bearings at night. Circumstances under which this is useful are related at page 139, which see. The Greenwich time must be known, and the angle between the Pole star and object whose bearing is required, must be large. Measure the angle and take the time. Ascertaining the sidereal time of observation as in ordinary Pole star calculation, add six hours to it for a second sidereal time. Out of Table I. in Nautical Almanac, take the correc- tion with first sidereal time, which, applied with the reverse sign to the latitude, will give the altitude at the time. Take out a second correction with second sidereal time, which will be the rectangular deviation of Polaris from the meridian. To calculate the horizontal angle answering to this, the formula is Sin horizontal angle = Sin correction x Sec. alt. which will give the true bearing of Polaris, east of meridian when first sidereal time is between 13 h. 20 m. and 1 h. 20 m., west when otherwise. CHAP. XV. VARIATION. 251 Example. August 10th, 1881, Lat. 43 30' K, Long. 66 30' W., at 13.34 G.M.T. Observed angle from Polaris to Seal I d . Light, 80 10', right of Polaris. G. M. T. .. Long M. T. ship .. Sid T. noon .. Acceler. h. m. 13 34 4 26 9 08 9 16 2 1st S. T. Obs. 18 26 + 6 2nd .. 026 Corr. for 2nd S. T .. Cos ang. dist. Sec. alt. Cos. hor. ang. Hor. ang. Polaris Seal I". L*. Cor. for 1st Sid. T. Latitude Altitude Polaris .. Sin. Corr. for 2nd S. T. Sec. alt. Sine'True B 1 17' Polaris - 17 43 30 43 13 8-35018 13741 8-48759 .. N. 1 45' E. 9-2324 0-1374 . 9-3698 . 76 27' N. 1 45 E. N.78 12 E. VARIATION. Accurate variations are very useful in all parts of the world, as from them the lines of equal variation shown on charts are drawn ; but to enable them to be so used, they must be trustworthy. Variations can be taken either at sea, or on shore. In the first instance, we cannot expect great accuracy from any one set of observations, but they are very useful in assist- ing the determination of the lines of equal variation, and by meaning the results of many ships a good value is obtained. The local deviation of the compass must be accurately known, and as this varies in different latitudes it must be ascertained from time to time.* * See page 294. 252 HYDROGRAPHICAL SURVEYING. CHAP. xv. Shore variations are of most value, when we, are sure of no local attraction. Shore The requirements for a good shore variation, that the Hydro- tionir*" graph* Office can put confidence in, are as follows : for Varia- 1. The true bearing of different points (about six) as equally tion * distributed as possible round the circle whose centre is the observation spot, must be well and accurately observed with a theodolite. 2. Bearings of all these points must be taken by the com- pass from the observation spot. 3. More than one compass must be used, and their errors must be known at the office. 4. Different sets of observations must be made with different pivots and with different cards. 5. The ground on which the observation is made should be free from every suspicion of containing any iron, and the nature of the rock, or whatever the formation may be in the vicinity of the observation spot, should be mentioned in the return transmitted home. Points 1 and 2 are necessary precautions against the errors of the card caused either by bad graduation of its arc, or from accidental bending of the edge. In ascertaining the true bearings, it will only be necessary to observe one object, when theodolite angles to the others will give their difference of bearing. As regards No. 3, all compass cards have an error caused by inaccurate affixing of the magnetic needles, which requires to be applied to the results. No. 4 is necessary to multiply observations, and make certain the card is working properly. Shore observations should be obtained at stations where the variation is already well known, when opportunity offers, as these will enable the Office to calculate the errors of the compass. Variation An example of observation for variation is appended. Office Ced at Although the variation is here deduced to show the method, this would not be done in forwarding these observations to the Admiralty, as there are certain card-errors to be applied first. 81O CO U3 CO lO O CO CO rH CO O 10 00 latitude. In this case we should assume the latitude we believe ourselves to be in, and taking from the tables the corresponding bearing, lay the Sumner line off at right angles to it, through the single position obtained. Where we know our latitude to a few miles, as is frequently the case, this method saves a good deal of calculation without introducing any error. s 2 260 HYDROGRAPHICAL SURVEYING. CHAP. xvi. Thomson's Table. Sir William Thomson has published some tables for facili- tating the calculation of Sumner lines, which, with practice, saves a little time and chances of clerical errors. Bearing of The true bearing of a distant mountain whose position is land and Sumner known, will also give a position by combination with a Sumner Line. FIG 40. OE Bun 20 10 20 10 44 50 line, if its direction is such as to make a good cut with the latter. Example Iu Fig, 40, let us suppose A and B to be the positions found of Sumner. ^y assum ing two latitudes and working out the altitude of a CHAP. xvi. SHORT EQUAL ALTITUDE. 261 star obtained at daybreak. Joining A and B, we get our first Sumner line, and we know we are somewhere on it. Having run W. \ N. 7'5 miles, we get an altitude of the sun ; and assuming in this case the same latitudes, we get two more positions, C, D, and the line joining them is another Sumner line. To project the run, we draw a line in the required direction, and for the distance run, from any part of the line A B, and draw another line parallel to A B through the end of the run line. The position S, where this last intersects C D, is the position of ship at second observation. Eunning on in the same direction for 11 miles, we get another altitude of the sun, and another resulting Sumner line E F. Transferring the two fi^st lines by the run as before, we now have three lines intersecting, or nearly so, at T, and by their coincidence or not we can measure the accuracy of our former positions to a certain extent, that is, for it must be remembered that as the intersection of our lines is governed by the run allowed, a current, or constant error . in calculating the run, might give an apparently good position which may really be considerably in error, even when the third inter- section is obtained, with certain arrangements of the lines and the run. SHORT EQUAL ALTITUDE. In low latitudes, where the motion of the sun in altitude is rapid nearly to the time of transit, a very good longitude may be obtained at noon, by a short equal altitude, taking obser- vations about 20 minutes before and after noon. The change of declination in this short interval will not affect the time, so that the middle time between the observations as shown by the watch, can be taken for the time by the watch at apparent noon. All we have to do, therefore, is to take the difference between mean time of apparent noon and the Greenwich time, as shown by our chronometer, which gives us longitude directly. 262 HYDROGRAPHICAL SURVEYING. CHAP. xvi. CIRCUM-MERIDIAN ALTITUDES OP SUN. These are of great value, as, when the observations are within the limits of time from noon, the resulting latitude is as correct as from a meridian observation, which may be lost from clouds. They should be worked in precisely the same manner as the shore observations of the same description, and should be obtained as near noon as possible. If more than four or five minutes have to be added to the observed altitude, they will not be of much value. If Eaper's most valuable book is at hand, a short and cor- rect rule, in connection with two of his tables, will be found at page 232 of the thirteenth edition, which will give the re- duction as nearly as requisite for sea work. CHAPTER XVII. THE COMPLETED CHART. Fair Chart Reducing Plans Delineation Symbols Colouring Graduation. THE work is sent home to be .published in several ways, Trans- according to circumstances. Home. n When the detail, as it proceeds, is inked on the original sheet itself, it may be necessary to transmit a portion home before the survey is all complete, and a tracing is often used for this purpose, as the original sheet, with the " points " still accumulating, must be retained on board ; but, if possible, it is better to send work home on drawing-paper, which is not liable to so many accidents from tearing, &c., can be more fully worked up as regards detail, and can be better kept as a record, though the originals will in the end be transmitted to the Admiralty in any case. When the detail is placed directly on the original sheet, it Original is very difficult to keep it clean enough for everything to be Cnart< clear and distinct, as straight-edges, protractors, &c., will be constantly placed on the chart over the completed part, and lines must be often drawn over it. It can be kept clean enough for transmission home as the finished chart, and by doing so, all errors arising from imperfect transferring will be avoided ; but the surface of the paper must get so rubbed by constant cleanings, that, if a large sheet, it is seldom satis- factory. Several hands may have been employed in it, and the chart will then bear a piecemeal look. If this original sheet is not sent home, a copy has to be made on another sheet of paper, which will be the fair chart. 264 HYDROGRAPHICAL SURVEYING. CHAP. XVH. Fair The usual mode of making this is to place the new sheet under the old one, and prick the " points " through the latter, on to the former. A careful tracing having been made of the working sheet, it is placed on to the fair sheet, so that the points all correspond, and by means of transfer paper is traced on to the fair sheet, and inked in. Great care is requisite, in transferring in this manner, that the tracing does not move from its proper position, and heavy weights must be used to prevent it from so doing. Errors have often crept in from careless transferring, and want of proper examination and comparison afterwards. In working with the method recommended by the writer, viz. each assistant's work plotted and inked on to his own separate board, and all then placed on one tracing, the final sheet can either be the original on which all the points have been plotted, if that has been kept clean enough ; or a sheet may be pricked through, as mentioned above, for the purpose ; but in either case only one complete chart will be made, the general tracing sufficing to show whether the work of different assistants has met, and what is wanted to complete. This, or these (as in a large sheet there will be several tracings for different parts), will be the tracing used for making the final chart in this case. This chart will also be the work of one hand, who will, after transferring outline, soundings, &c., from the general tracings, have the original little bits before him while inking in ; these little bits having been taken off their boards, and so reduced, by having superfluous paper cut off, as to be handy to lay on the sheet. Original By washing off the field boards, the paper will have become Sheets. distorted and contracted, but not to a sufficient degree to inter- fere with the small detail of sinuosity of the coast, which is what we mainly want them for. Everything will have been traced on the general tracing before the paper has been re- moved, and care must be taken that this is so, as it cannot be done afterwards. In whatever manner the final chart is sent in to the office, all " points " must be distinctly marked on it, especially main CHAP. xvn. REDUCING PLANS. 265 points. These latter are often distinguished by the triangle " Points " which means theodolite station, and in surveys where the B h wn. sextant has also been employed in triangulation, should cer- tainly be so. The " points " are necessary to join one chart to another, and also, in case of future revision of the chart, they afford means to the reviser of measuring the accuracy of his predecessor's groundwork. Plans sent home by officers in general service ships often lose much of their value from neglect of this. The existence of the " points," and their proper position, will at once give a confidence in the detail of the plan, that it is impossible to accord to the work of an officer, however zealous, of whom nothing is known as to his hydjrographical capability, and who fails to give any indication in his chart of how it has been constructed. REDUCING- PLANS. In a survey of an extensive nature, bays, harbours, &c., will often be done on a larger scale than the rest of the sheet. These must be either left blank on the coast sheet, or else re- duced from the large scale plans. It may sometimes happen that a portion of an anchorage is surveyed on the small scale before it is decided to make a large plan of it, on discovering it to be worth while to do so. This must not appear, however, on the completed chart, it must be all reduced from the larger scale. Instruments for reducing, e.g. eidographs, are not supplied, Reduction and the reduction is accomplished by " squaring." \L^**~ This consists of ruling similar lines on both sheets, forming squares and diagonals all over the part to be reduced. The two stations farthest apart on the plan, which must also be plotted on the small scale chart, are joined by a line on both sheets, the " directing line." Then, taking the smaller first, divide this line into as many equal parts as is thought necessary. These parts will be from a quarter to an eighth of an inch long. Set off lines at right angles to the directing line from each point measured, and then lines parallel to the directing line, at the same distances apart as the pthers. The 266 HYDROGRAPHICAL SURVEYING. CHAP. xvn. portion of the sheet required is now covered with squares. Kule also the diagonals. These will check the correctness of the squares, as they should, of course, pass exactly through each corner. Now do the same for the large scale, making an equal number of squares. It will be seen that nothing is measured, everything being done by subdivision of the directing line. Great care is necessary to rule all these lines truly rect- angular and equidistant. Number the lines on each plan, to prevent mistakes, giving the same number to similar lines. Letters may be put to one set of lines, and numbers to those at right angles. Then, taking proportional compasses, set to the difference of the scale as ascertained by measuring the distances apart of similar lines, the distance of each little detail of the plan from the nearest lines, can be put down by the same distance from the similar lines on the small scale. Eeducing is an operation demanding even more patience and trouble than usual, and it is better to leave the space blank than to reduce it carelessly. DELINEATION, SYMBOLS, AND COLOURING. The annexed specimen chart, taken from the 'Admiralty Manual/ shows the method of delineation employed in fair chart work. The following symbols are in use in surveying, in field books, and rough charts. Signs for The days of the week are thus symbolised by the astrono- Da y 6 s mical signs of the planets. Sunday .. .. Sun's Day .. .. Sun .. Monday .. .. Moon's Day .. .. Moon .. ]) Tuesday .. .. Teut's Day .. .. Mars .. $ Wednesday .. Woden's Day .. Mercury Thursday.. .. Thor's Day .. .. Jupiter It Friday .. .. Friga's Day .. .. Venus.. $ Saturday.. .. Saturn's Day .. Saturn J? CHAP. xvil. SIGNS AND COLOURING. 267 The following signs are useful in the field books. other Symbols. Objects in line, called transit .. .. .. Station, where angles are taken .. .. .. A. Zero, from which angles are measured .. .. Single altitude Sun's lower limb .. .. 0. ii upper .. ..S3 Double lower limb in artificial horizon Q upper Sun's right limb .. .. .. .. .. (3 left .... |3 Sun's centre .. .. .. .. .. ..0 Right extreme, or tangent, as of an island .. .. ^ Left ., .. .. ^ Zero correct .. .. Z. K. Windmill .. > Water-level .. .. .. .. ,, .. w. 1. Whitewash .. .. .. .. .. .. w. w. Some charts are worked up by indian-ink alone in all parts ; in others, colour is used to assist the delineation of the different parts, indian-ink being always used over the colour, in exactly the same manner as if there was no groundwork. A wash of some colour on the land helps to throw it up Colouring, very much ; but care is very necessary in giving this edging that it be not too deep, and that too much water is not used, or the paper will distort, and the tracing will not fit. Also in drying, that it does so gradually and generally, not allowing a streak of sunlight, for example, to fall across one part of the sheet. If using colour, the following tints should be used for the different parts. Sand .. .. .. .. Gamboge, dots black. Low- water sand edge . . . . Do. dots carmine. Mud, dry low- water .. .. Neutral tint, edge of fine black dots. Coral, dry low-water, or any rocky Burnt sienna and carmine, mixed, ground covering and uncovering for wash; same darker, for edging. Cliff .. .. .. .. Dark neutral tint. Roads Burnt sienna. 268 HYDROGRAPHICAL SURVEYING. CHAP. xvn. Fathom lines up to five fathoms . . Either a faint wash of cobalt all over the area included within the fathom line, or a narrow edg- ing of the same colour inside the dots of the fathom line. N.B. To make indian-ink perfectly black, mix a little indigo with it. When the country is mountainous, no general wash, but only a local green in the valleys, and on flat ground, has a good effect. Hills. 'Hills are done in various ways. Hachures of indian-ink done with a pen in the same fashion as they will be eventually engraved, takes most time and is most difficult to do, but when well done looks best. Shading of indian-ink, put on with a brush, is done much quicker, and shows up very well. Simple contour lines will enable the chart to be engraved almost as well as the other modes, but does not look so well. In charts issued by the British Admiralty, the shading is put on hills as though it were a raised map, with the light coming from the north-west. Names. In inserting the names, care should be taken that no letters are upside down. Thus, it is often necessary to write a name in nearly a meridional direction, and it will depend upon whether the trend of the name is east or west of the meridian, whether it written from south to north or north to south. FIG 41. Thus in the two instances given here, if the names had been written in the opposite direction, part of them would have been upside down. All names should be readable by turning the head, without the necessity of moving the chart.* * Vide " Instructions for Hydrographic Surveyors " for useful hints. CHAP. xvii. DELINEATION, ETC. 269 All names of capes, &c., should be as much on the land as possible. The soundings being the most important part of a chart, they should be kept as clear and distinct as practicable. Different characters should be used for the names of different classes of objects. Thus, one style for bays, another for points, another for shoals, and so on. The scale of the chart is got from the longest calculated Side for distance on it. This will, in cases of plans, generally be the sc same as that we originally plotted from, in which case we already know our scale. But if we were obliged to plot from a short side, and have since obtained data which will enable us to calculate a longer distance, we must measure the dis- tance between the two points on our chart, and dividing this number of inches and decimals by "the distance as calculated, we shall get the true scale. It is well to indicate the two stations from which the scale is derived, by drawing a red line between them, and writing, either against it, or elsewhere on the chart, the calculated dis- tance and bearing. If a long distance, this last should be the Mercatorial bearing. In the case of extended surveys, or when there is no regular triangulation, the scale will depend upon the distance obtained between two stations by astronomical observations. This distance being calculated, the scale will be obtained as before. The soundings in the chart sent home should be as thick as Soundings possible, without sacrificing legibility. There is always a thlok ' great temptation to thin them out, so. as to look better ; but that is the work of the Office, and will probably have to be done again there in any case, as the scale on which the chart is published is usually smaller than that on which it is con structed, and if so, will not permit all soundings in the original to appear. The natural scale, or the proportion which our chart lineally Natural bears to the actual size of the portion of the globe it repre- 8oa ^ e< sents, is obtained by dividing the number of inches corre- sponding to one mile on our chart, obtained as above, by the 2/0 HYDROGRAPHICAL SURVEYING. CHAP. XVH. number of inches in the nautical mile at the latitude. It is given in the form of a fraction, whose numerator is one. Thus, supposing our scale is found to be 1*8 inches to a mile, in latitude 3, we divide 72552 (the number of inches in a mile) by 1*8. This gives as the natural scale. This natural scale should be noted on all sheets that are not graduated. When the chart includes a considerable extent of coast-line that is intended to form part of a navigational sheet, it will have eventually to be redrawn on Mercator's projection, as it is on that projection all charts are published. To do this, the sheet must be graduated, i.e. have the meridians and parallels placed upon it, as it is by means of them that a chart on one projection is redrawn on another. GRADUATION OP THE SHEET. Gnomonic We have before said that a chart constructed by drawing rejection, ^g^ ^ nes f rom one object to another, when graduated, has to be considered as being on the Gnomonic projection, and the general features of this projection have been explained.* It now remains to consider how to graduate such a chart. A sheet may be graduated either before or after the chart is drawn on it. The methods are substantially the same, and will differ only in some preparatory work necessary in the latter case. We will first consider the case of graduation after the chart is complete, and to do this we must suppose our observations to be obtained, and that we know the latitudes and longitudes of two stations on our chart as far apart as possible, in oppo- site corners of the chart. We require, first of all, the reciprocal bearings of each from the other, and the distance between them. * Page 82. CHAP. xvii. GRADUATION OF THE SHEET. 271 In Fig. 42 let A and B be two stations whose latitudes and longitudes we have obtained ; P is the pole. Calculate by spherical trigonometry the bearing of each from the other. FIG42. We have P B, P A the co-latitudes, and B P A the diff. longitude. P B A and BAP are the angles required. The latter subtracted from 180 will give us B A Q, and the differ- ence between P B A and B A Q is the convergency. Find also the distance A B, to get the scale. I FIG 43. Now in Fig. 43 let A B be these same stations plotted on our chart. Eequired to graduate it. 2/2 HYDROGRAPHICAL SURVEYING. CHAP. xvn. Join A B, and from A and B lay off (by chords) the reci- procal bearings of one another, ascertained as above, as A N, B M, which will be meridians passing through those points. From A and B measure, on the meridians, AH, BE, the distance, according to scale, to the nearest even minute of latitude (as 1', 5', 10', &c., as convenient). At H and E lay off short perpendiculars to the meridians, and on these measure the distances H C, E D, the lengths of departure, according to scale, to the nearest even minutes of longitude that may be convenient. In high latitudes and large scales, if the even meridian required is many miles distant, error will be introduced by this latter operation. It will only be correct for short dis- tances, as the curve of the parallel, on which we ought to measure this departure, will not coincide with the perpen- dicular to the meridian for more than a mile or two in such a case. We have now C and D, two stations on even meridians and even parallels, which we shall take as our points for gradua- tion. This is exactly the case when we wish to graduate the sheet first, so that henceforward the methods are identical. In the case of after-graduation, when these even points have been obtained, we can rub out on our chart all lines already ruled, to prevent confusion, and we will take a new figure for the similar purpose of facilitating comprehension. In Fig. 44, let C and D be the positions for graduation, Calculate spherically, as before, the bearings of C and D from one another, and lay off the meridians C N, D M. From C and D lay off the perpendiculars C H, D F, and from these perpendiculars lay off, on the side of the pole, half the convergency calculated for the difference of longitude in the latitude of C and D respectively, as C 11, D 5, cutting the opposite meridians respectively in J and G. Then J will be on the same parallel as C, and G as D, and J D, C G, should be equal.* * See Appendix B. CHAP. xvii. GRADUATION OF THE SHEET. 273 To get the central meridian of the chart, bisect JC and D G in A and B, and join them. Then J G joined should intersect C D in the central meri- dian. This is a capital check for our correctness so far. FIG.44. N To get other meridians, divide J C and D G as many times as there are meridians required, and join them, as S, P T, QV, &c. , T 2/4 HYDROGRAPHICAJL SURVEYING. CHAP. xvn. To get the parallels, which it will be remembered are curves, divide the half convergency chord, already measured, into as many parts as we have meridians. In our figure we want five meridians from D to G, therefore we divide the chord into five parts, as 1, 2, 3, 4. Draw a small portion of D 4, cutting E W in Z. Z will then be the position on E W of the parallel of D G. By similarly drawing D 3 to cut Q V in E, D 2 to cut P T in H, and D 1 to cut S in F, we obtain a series of points on the meridians, which, con- nected together, will form the curve of the parallel D G required. In high latitudes we want more meridians, to draw the curve exactly, than in low, and we must therefore be guided by circumstances as to the number of them. Similarly, we obtain the curve of the parallel J C. To draw more parallels, divide each meridian between the parallels obtained into as many parts required, and join them. This process demands considerable care and accuracy in drawing every line, and should be checked wherever prac- ticable. The margin of the chart is marked by subdividing the distance between each parallel or degree to the unit required. There are other ways of drawing this graduation, all founded on the same principle. As this is, in the writer's opinion, the best of them, it is here given. Memoir of Finally, every original chart must have a memoir written tion 8 . r ' on it> giving a brief description of how the chart has been constructed, the base used, observations for latitude and lon- gitude, &c. &c., enabling the authorities at home to put the proper value on the work. Transfer- It is scarcely necessary to describe the construction of a Mercator's Mercator's Chart, as every naval officer learns it as part of Projection. hi s education. To redraw a survey on Mercator's projection, similar meri- dians and parallels must be drawn on both charts, and enough of them to make the parallelograms formed by them small CHAP. xvii. GRADUATION OF THE SHEET. 275 enough to reduce the discrepancy between the shape of any parallelograms on either chart to as little as possible. The soundings, coast-line, &c., in each parallelogram of the gno- monic chart are then transferred to the same parallelogram of the Mercator, by the latitude and longitude of each detail. T 2 276 HYDROGRAPHICAL SURVEYING. CHAP. xvm. CHAPTER XVIII. DEEP-SEA SOUNDINGS. Treatises THIS subject has been well and fully treated by Staff-Com- j ec t. mander Davis, and Capt. Shortland. A variety of papers have also been 'written on the subject, notably one by Mr. Buchanan in February 1881, who writes with the unparalleled advantage of having been in the ' Challenger ' Expedition.* We could not therefore, even if it were desired, add any- thing to the experience of the above-mentioned officers, and what we shall give will be merely the gist of their more exhaustive experiments, and will be confined to a description of the practical operation of " taking a sounding " with a hempen line, without minutely discussing the different instru- ments which can be made use of, or touching on the question of dredging or temperatures. Wire. Wire is now being supplied to surveying vessels in the shape of the Lucas machine ; but as we personally know nothing of this, we cannot say anything about it. As all wire requires special fittings, it is not probable that the hempen line will be entirely superseded. Diffioul- In deep-sea sounding there are, or we may say were, two main difficulties to overcome. To tell when the lead got to the bottom, and to devise some means by which the scend of the ship would not carry away the line, on heaving up. Both of these difficulties are now of the past, but the * Notes on Deep Sea Sounding: Staff Comr. Davis, K.N. Sounding Voyage of H.M.S. * Hydra :' Capt. Shortland, K.N. Paper in Journal of Society of Arts, March 1881. CHAP. xvni. DEEP-SEA -SOUNDINGS. 277 operation of deep-sea sounding is, and always must be, one demanding great care and attention. A general description of a deep-sea cast is perhaps the best General Descrip- way to explain the system. ti on of a The line is led from the reel (placed in a convenient position Deep-Sea at one end of the ship) through leading blocks, to a block on the main or foreyard. This block is suspended by means of a number of strips of india-rubber, called " Accumulators." The sinker used is in the form of separate iron weights, built up round a rod, which detach on reaching the bottom, leaving only the rod for the line to bring up. The time occupied by each 100 fathoms in running out, as the lead descends, is taken, "\yhen, as frequently happens, the actual striking of the lead is not indicated by any well- marked check in the line, the intervals will enable us to know when it has occurred. For, as long as the lead is falling, the time occupied by each successive 100 fathoms will gradually Increase, by reason of the friction constantly becoming greater as the line out becomes longer ; but when the lead reaches the bottom, the rate of running out of the line will be found to be suddenly slower and then remain uniform, being due to the drift of the ship and the weight of the line only. In heaving up, as the ship scends, the india-rubber accumulators will, by stretching, prevent any jerking or sudden straining of the line. Let us consider these points in detail. The line, of the best Italian hemp, has been supplied of Sounding two sizes, No. 1 and Medium ; but the issue of the latter is e * now rare, and the larger one-inch line is usually employed. The line is supplied on reels holding 1000 fathoms each. The reels are fitted with steel axles, and by erecting uprights with proper bearings on them, can be used without shifting the lines. This entails bends at every 1000 fathoms, but in an ordinary cruise it is the best method. If fitting for a regular sounding expedition, it will be better to have a large deck reel which will hold 3000 fathoms ; but this is an awkward object to stow away in a small ship. 278 HYDROGRAPHICAL SURVEYING. CHAP. xvm. Aocumula- The accumulators are solid cylindrical strips of vulcanised india-rubber, with an. eye formed at either end, are of J-in- diameter and 3 feet in length, capable of being stretched to about six times their length, and of bearing a weight of about 65 Ibs. In practice, we should not use more than 5-feet stretch and 40 or 50 Ibs. strain. This is accomplished by combining a number of accumu- lators. About thirty of these, their ends lashed together, and prevented from fouling or twisting by being passed through holes in two circular boards, are used to suspend the block at the yard-arm. The breaking strain of the sounding line will then be reached before the accumulators have got to the limit of their elasticity. A rope must also be made fast to the sounding block, and led through a leading block on the yard, so that the weight of the block can be taken on this, and the accumulators thrown out of gear, so to speak, when necessary. Sinkers. The sinkers are cylindrical iron drums of 50 Ibs. each. These have a hole in the centre, and are fitted with two depressions on one flat surface, and two corresponding knobs on the other, so that a number of them can be built up, one on the other, to the required aggregate weight, the knobs on one fitting into the depressions on the other, and so preventing slipping. Bods. The rods in use are Brooke's, the Hydra, and Baillie's. They differ in size, and in the mode of detaching the weights. Brooke's rod, the first sounding machine, is the lightest and simplest, detaching by means of a tumbler. It has fallen into disrepute from the fact of its disengaging at once on striking, and bringing up a very small specimen of the bottom. It has the advantage, however, of being very easily made on board, in case of loss of other machines. The " Hydra," invented by the blacksmith of that ship, is more complicated, and disengages by means of a spring. Butterfly valves are fitted at the bottom of the lower section, with the intention of retaining the specimen of the bottom which has entered by the penetration of the rod on striking. CHAP, xviii. DEEP-SEA SOUNDINGS. 279 It is better, however, to remove these valves, as they do more harm by preventing the free admission of the mud, than good in retaining it. The diameter of the tube being small, the mud has ordinarily sufficient cohesion to remain in of itself. The Baillie tube used in the 'Challenger' expedition is much larger, and disengages by a movable shoulder. Here valves are necessary, on account of the increased diameter. Whatever rod is used, the slinging of the weights is accom- plished in the same manner. Under the bottom sinker is placed a flat iron ring, into holes Slinging weights, on either side of which the ends of a piece of stout wire are twisted. This wire carries the weights, and is of such a length that when held up, the bight will be sufficiently above the . upper sinker to permit the proper length of rod to project below the lower sinker. The rod is passed through the holes in the sinkers, and the bight of the wire is hooked to the detaching apparatus on the upper part of the rod. When the weights are lifted by touching the bottom, the bight of the wire is thrown off, and the rod is then clear to return, leaving the weights at the bottom. In the " Hydra " and " Baillie " the rod is forced into the bottom, until the lowest weight touches it. Care has therefore to be taken in adjusting the length of the wire, that the lower part of the rod does not project too far through the weights, or when the bottom is stiff, or the weight is descending very slowly, the rod may not penetrate sufficiently to lift the weights, and they may not in such a case detach. Sounding is carried on either from the fore or main yards. The fore yard has the advantage of being at the extremity Use of Fore of the ship, and it is perhaps easier to keep the latter in the y r ard ain right position with regard to the line, when sounding from forward. If the main yard is used, the officer superintending is close to the engine telegraph, and the spot is clear of the men con- gregated in the fore part of the ship. Our opinion is that, 280 HYDROGRAPHICAL SURVEYING. CHAP. xvm. with a small ship, it is better to sound from forward, but that in a larger one, the main yard will be found most convenient. In a regularly fitted surveying vessel, a platform vail be built, projecting from the ship's side under the yard to be used, on which the machine is prepared for launching, and from which the officer can closely watch his line. Letting go. Lowering the apparatus into the water, and letting go, are ticklish operations, and have to be performed tenderly. The weights detach so easily with any jerk, that every care has to be taken. The rope fast to the sounding block must be hauled taut, as if we lower with the accumulators in action, their elasticity will very soon jerk the weights free. Before lifting the machine, stop the spring, if it is a Hydra, or the tumbler, if Brooke's, and then heave up on the line, get the machine over the side ready for lowering, and cut the stops. There are two methods of lowering ; either by means of the steam winch, or by a number of men walking back with the line. If the winch will work smoothly, and there is no surging on the barrel, it is simplest to use it, easing down to 100 fathoms or so, and then throwing the line off. Otherwise walking back is very good. When 100 fathoms or more are under water, let the men increase their pace, and after due warning, let go. The line cannot be eased round a cleat. It is sure to jerk the weights off. After letting go, ease up the rope holding the block, and let the accumulators come into action. Taking The time of running out is carefully taken by a watch ; the minute and seconds of each 100-fathom mark touching the water, or passing some definite mark, is noted in the ruled form supplied for the purpose.* When there is no current, a smooth sea, and the ship has been kept well over the line, the check when the weight Appendix, Form K. CHAP, xviii. DEEP-SEA SOUNDINGS. 281 readies the bottom at 2000, or even a greater number of fathoms' depth, will be clearly seen by eye, but under less favourable circumstances this will be impossible. Failure to keep the ship in her right position, steaming up to the line, lurching and scending, will prevent any steady running out of the line, and it will be only by the diminution of the rate, as shown by the interval elapsed between the 100- fatliom marks passing out, that we can be sure the weights are down. Thus we may be forced to allow many more fathoms of line to run out than would be otherwise necessary, before we can ascertain this, and it is well worth making sure of, as, if we heave up with the weights still on, k the chances are greatly in favour of the line carrying away. , Heaving in requires a careful man, and should be done Heaving very quietly and slowly at first. The accumulators will m ' stretch as soon as the line is held, and in a few seconds such a strain will be apparent, even if the weights are detached, as will demand very careful handling, the weight of the line itself, and the friction set up in hauling it through the water, being almost as much as the strength of the line will bear. During sounding, the ship will be kept so that the line is Position as nearly up and down as may be, slightly drawing to wind- p ward if anything. The wind must be kept a trifle on the weather bow, so as to prevent the chance of the ship drifting down on the line, when the latter, chafing against the bottom, will very probably be cut by barnacles, or the edge of a sheet of copper. It will be evident that the greatest care will be necessary on this point, and the ship will require to be very sharply watched, and all movement in the wrong direction counteracted by a turn of the screw, aided by the helm, and possibly now and then the spanker. In a very strong current, with the wind in the opposite direction, the ship will be very often difficult to manage. In a current, under any circumstances, the ship will be, at Surface the end of the sounding, far from being vertically over the Current< 282 HYDROGRAPHICAL SURVEYING. CHAP. xvm. lead. The latter, when first let go, will, as long as it is in the influence of the current, descend perpendicularly under the ship, being carried horizontally in the same direction as she is ; but as soon as it passes into still water, it will go on falling in a true vertical line, while the ship will still be drifted away. The upper portion of the line, being acted on also by the current and therefore drifting with the ship, will not permit the latter to steam up so as to remain vertically over the lead, or the line would be fouled ; nor indeed is there any- thing to indicate that there is a current while the line is running out. When, however, the line is held to haul in, the current will soon be apparent. The line will at once draw away from the ship, and the first thing to look out for is to see that it does not do so under the bottom. As generally in a strong current, in open ocean, the wind blows in the same direction as the former runs, this is happily not often the case, and it more usually stretches ahead, or on the weather bow. As the amount of the current is an important factor in reducing the depth attained, as will presently be seen, it is very desirable to use all endeavours to ascertain its rate. Ascertain This is very difficult in the open sea, other than by the rent * 1 *" difference of the astronomical observations and dead reckon- ing. If a boat can be lowered and moored to the line, it can be ascertained by a large log-ship ; but this requires a smooth sea, or the line may very likely be carried away, or the boat swamped. For the latter reason the boat must be large. An approximation may be made when heaving in, by steaming slowly up in the direction of the line, keeping this at the same angle with regard to the surface of the sea, and heaving the log. Effect of Let us now consider the effect of a surface current upon the Surface , ,, ,, -,. Current, depth of a sounding. The sounding selected as an illustration is an actual cast taken in the Gulf Stream. CHAP. XVIII. DEEP-SEA SOUNDINGS. 283 SOUNDING BY H.M.S. "GANNET," JULY 4ra, 1868. Machine .. Brooke's Eod. Bottom .. Soft ooze. Line .. .. Medium. Current . . 1 5 knts. Weight .. 224 Ibs. Lat. 42 22' N Wind .. Light W.S.W. Long. 57 16' W. Sea .. .. Quiet Fms. Time. Interval. 2nd Diff. Remarks. 100 h. m. s. 4 57 11 m. 8. sees. Let go at 100 fathoms. 200 58 00 49 300 58 53 53 -1- 4 400 59 50 57 4 500 5 00 56 1 06 9 600 2 03 07 1 t 700 3 15 12 5 800 4 35 20 8 900 5 52 17 - 3 1000 7 18 26 + 9 1100 8 45 27 1 1200 10 18 31 4 1300 11 55 37 6 1400 13 31 36 - 1 1500 15 18 47 + 11 1600 17 02 44 - 3 1700 18 47 45 + 1 1800 20 34 47 2 1900 22 09 35 -12 Steaming. 2000 23 52 43 + 8 2100 25 41 49 6 2200 27 36 55 6 2300 29 33 57 2 2400 31 31 58 1 Steaming. 2500 33 38 2 07 9 2600 35 30 1 52 -15 2700 37 36 2 06 + 14 2800 40 07 27 21 Steaming. 2900 42 17 14 -13 3000 44 23 06 8 3100 46 30 07 + 1 3200 48 55 25 18 3300 52 01 3 06 41 3400 54 49 2 48 -18 3480 58 40 3 51 Odd number of fathoms 3580 6 02 53 4 13 + 85 caused by bending new 3680 07 28 35 22 and incomplete line here. 3780 11 40 12 -23 Bottom Rom e where here. 3880 15 59 19 + 07 Checked the line. 284 HYDROGRAPHICAL SURVEYING. CHAP. xvm. The current, by astronomical observations, was found to be 1*7 knots. By the log, when heaving up, it was 1*3 knots. The mean of these was therefore assumed, which gave a drift in the minute of 25 fathoms. As the line was eased down to 100 fathoms before letting go, we have the first interval at 200 fathoms. The lead will be pretty well out of the influence of the current before letting go, and will go on descending vertically while the ship drifts away. At the end of ten minutes, when 1000 fathoms of line were out, the ship had drifted 250 fathoms. If we protract this, as in the Figure 45, we shall find that the lead was only at 930 fathoms depth. When the 2000-fathom mark passed out, 16J minutes had elapsed, and the ship had drifted 660 fathoms. The lead was only at 1700 fathoms. At 3000 fathoms the ship was 1200 fathoms from her "Let go " position, and the lead was 2300 fathoms down. At 3480 fathoms, where the intervals suddenly increase, the ship had reached 1540 fathoms, and the lead was 2600 fathoms from the surface, presumably the bottom. We, however, still let the line run out, and at 3880 held it, by which time the ship had got 2000 fathoms from her original position. This also gave us the same depth of 2600. This result was of course very satisfactory, as it proved that we had arrived at the right amount of drift. This is a very good instance of the amount of error which crept in before allowances of the kind were made, and fully accounts for the stupendous depths reported in the early days of deep-sea sounding. Curve em- The curve of the line is purely arbitrary, but is founded on construe* the consideration of facts observed under similar circumstances, tion. an( j cann ot be far from the truth. Any slight deviation will not have a great effect on the result. The error, owing to the drift of surface current, will increase in a much larger proportion than the variation in the rate of the current. CHAP. XVIII. DEEP-SEA SOUNDINGS. Thus, taking our example, and supposing the current to have been one-third, or half an knot an hour, when 2000 fathoms of line were out, the lead would have been at 1950 FIG.45. 2600H Bottom fathoms, only 50 fathoms less than the full length. At 3000 fathoms it would be only 130 fathoms short. It results, then, that in the majority of deep-sea soundings 286 HYDROGRAPHICAL SURVEYING. CHAP. xvm. Effect of Under- current. the correction owing to current will be small, as it is only in certain localities where ocean water is in motion at a speed over half a knot. The error due to under-currents will be almost nil. The lead, on entering the under-current, will be carried away by it, as long as it is passing through it. It will then resume its vertical direction, and a small " sagg " in the line will be the only record of the motion, for, the line being as it were held at both ends by the tension, the bight will never become large. This is of course on the supposition that the under-current is only of a certain depth, and does not extend to the bottom. FIG. 46. 400 J 800- 1200- 1600 2000- 2400 Sea Surface Fig. 46 shows this case. Even supposing that it does assume this unlikely form, and should be moving at the almost impossible speed of one knot, the error will be but small. CHAP, xviii. DEEP-SEA SOUNDINGS. 287 Assuming that below 1000 fathoms depth the water is all moving at the rate of a knot, when 3000 fathoms are out the lead will be more than 2900 fathoms from the surface, which we cannot consider a great error, as all soundings at these depths made with line must only be accepted as approximate. After every sounding, the line must be carefully dried, Care of before reeling up. Neglect of this will certainly end in rotting at some point, and it must be remembered that the line is no stronger than its weakest point. 288 HYDROGRAPHICAL SURVEYING. CHAP. xix. CHAPTEE XIX. MISCELLANEOUS. Distortion of Printed Charts Observations on Under-Currents Exploring a Kiver Swinging Ship. Distortion IN printing charts from an engraved plate, the paper has to ChariT ^ e damped. This results in distortion on the sheet drying, and angles laid off on a published sheet will never be found to agree exactly, especially if the sheet is large. This must always be borne in mind, in trying angles on a published chart. For this reason, when a published plan is to be examined, a " dry proof " is supplied to the surveyor from the Admiralty. This is an impression " pulled," as it is termed, on to a dry sheet. It is much fainter than a damp-pulled copy, and would not do for ordinary use ; but being an exact facsimile of the copper plate, all angles, bearings, &c., should agree pre- cisely, if the original survey is correct. This fact of the distortion of published charts is not gene- rally known, and many reports of so-called inaccuracies have been made in ignorance of it. The amount of it varies with the goodness of the paper, and the trouble bestowed by the printer in damping his paper uniformly. It is a fact much to be deplored, and the man who invents a means of obviating it, will bestow a great boon on cartography. OBSERVATIONS ON UNDER-CURRENTS. Though not in the ordinary run of surveying operations, a slight description of the method of discovering the direction and approximate rate of under-currents may be useful. CHAP. xix. OBSERVATIONS ON UNDER-CURRENTS. 289 To ascertain these satisfactorily, special gear is necessary. The general principle is to expose a large surface to the General action of the under-current, and to support this in the water rmcip e< by a floating buoy which will present as small a surface as possible to the action of the surface stream. The experiments must be carried on from boats, and there- fore the gear must be as light as possible, for easy handling. A series of observations on the under-currents in the Bos- porus and Dardanelles resulted in the author's adopting the following :* A light, flat wooden board, 6 feet square, with a wing Apparatut 2 feet in length, at right angles to the rest of the frame, was u * used as the submerged drag. (See Sketch, Fig. 47.) To the extremities of the wing the sling a a, was made fast, and to this sling the supporting line to the buoy was bent, at such a point as kept the surface of the drag vertical when the strain came on. It weighed 70 Ibs. in air, and took 120 Ibs. of lead to sink it satisfactorily. These leads were made fast with a little drift, and another line, c, was bent, both to them and to the lifting sling, b b, so that the weight of the leads could be taken off the drag, when pulled up to the surface, before finally hoisting it in to the boat. An iron buoy, 1 foot in diameter and 5 feet long, supported this structure well when the surface current was not very strong, and only presented an area of less than one square foot to pull through the water. When the surface current was swift, other buoys had to be added, attached in line to the upper end of the first, for under these circumstances the single buoy was dragged under water, and its motion could not be followed. Several disappeared in this way, some to reappear when the apparatus got into slacker water, some for good and all. To ascertain the movement of the floating buoy, and there- fore the direction in which the drag was carried by the under- * Observation of Currents in Dardanelles and Bosporus. U 290 HYDROGRAPHICAL SURVEYING. CHAP. xix. FIG. 47. CHAP. xix. OBSERVATIONS ON UNDER-CURRENTS. 29! current, a " fix " was taken to shore objects, and plotted on a Method of large scale sheet of points, when the drag was let go free from f^^ate " the boat. Subsequent fixes and times taken enabled the and Direc- course and distance of the buoy in the intervals to be re- ^"^ corded on this sheet. A small buoy, weighted so as to float awash, put into the Surface water at the same spot and time, and followed by another Current - boat, afforded means of ascertaining, the surface current. This arrangement worked very satisfactorily altogether, but Defects. there are several defects in it. The depth of the submerged drag will not be the length of the line allowed, but some unknown quantity less, as will be seen by accompanying sketch. te FIG. 48. This must be estimated. The force expended in dragging the buoy through the 2 9 2 HYDROGRAPHICAL SURVEYING. CHAP. Xix. Bate less than true Bate. Current Meter. Tempera- ture and Density. Running Survey. surface water, and overcoming the friction of the suspending line, is also an unknown quantity, but will always have the effect of retarding the motion of the submerged drag. The rate therefore recorded, by the movement of the surface buoy, will always be less than the true rate of the under-current. Several instrument makers now turn out " Current Meters " of various forms. Doubtless these could be, with a little ingenuity, adapted to sea work, at least to show the true rate of an under-current. We do not imagine that the apparatus described above may not be much improved upon, but we give it as a starting- point for any officer employed in future investigations of a similar character. The observations are made more complete by ascertaining the temperature and density of the water, at the depths ex- perimented on. EXPLORING A RIVER. Narrow rivers, navigable for boats, will generally be suffi- ciently laid down on a marine chart by a sketch survey, made from the boat (a steam pinnace, if possible), while passing up and down. Patent log and compass will be the instruments mainly used for putting down the direction and length of each reach ; though if we have objects that we can use for a sextant fix, we shall of course use them in preference, at any rate from time to time. We must endeavour in every case to get a good fix at our furthest point, and the course of the river, as mapped by patent log and compass, will then be squared in on that, and the fixed points at the entrance and any other fixes we may have got. Any elevated points near, which we can ascend and fix, and from them get angles to bends and reaches of the river, will much assist us, especially when, which is so often the case, the river is thickly lined with trees and jungle. The patent log will be fitted, as already described, with the dial on the gunwale and the fan towing astern. Theodolite legs standing in the stern-sheets make an excellent stand for CHAP. xix. EXPLORING A RIVER. 293 a prismatic compass, and enable us to get a better bearing than by holding it in the hand. It is in rounding the bends that the greatest error in- map- ping a river is introduced, as the distance run over while gradually altering course must be estimated by eye, which requires considerable experience at judging distances. Current must be taken into consideration, and may be Current, obtained, if time allows, by anchoring the boat for half an hour, and reading the patent log. In a river where the tide extends some distance up, and where the land is low and jungly, as in so many mangrove rivers, our difficulties are much increased, as the velocity of the current will be constantly varying, and we cannot hope to obtain any sextant fixes to check our position. In cases of this kind, if it is desired to have any degree of accuracy in the sketch, the only way is to run over the work again, making an independent map, and squaring in afterwards a mean of the two. It is best always to plot as we go. Mistakes are thus ren- Plotting dered less likely, and the vexed question of the bends can best in Boat< be solved by placing their shape on the paper at once. We can also look at our work on the way down again, and correct little inaccuracies more readily. If it is desired to make a large scale plan of a river of Survey on greater width, the best method is to employ several boats at S cl?e * once, four if possible, which will triangulate their way up, two on either side. Starting from two fixed points at the mouth of the river, two boats will remain there while the other two go up to convenient positions, whence they can see the boats remaining at the first points. Angles will then be taken from all, to everything conspicuous, and to one another, and the lower boats will, leaving marks at their old stations, move up to two new positions above the other boats, when the angles will be repeated, and so on, the lower boats moving on each time. The shore line can either be sketched by the boats as they go up, or done afterwards more correctly when the marks are 294 HYDROGRAPHICAL SURVEYING. CHAP. xix. all up and fixed. Soundings, in the same way, can either be taken from the boats as they move from station to station, in which case they would cross over each time so as to get a diagonal line across the channel, or can be more regularly taken afterwards, as the circumstances of the case may require. Everything must be plotted afterwards, and communication between the boats as they pass one another, when names can be given and objects pointed out for mutual observation, will greatly facilitate the comprehension of one another's angles, when putting down the points. SWINGING SHIP. Though the compass is but little employed in surveying, it is occasionally unavoidably brought into use. Correct results for variations obtained by observations at sea, can only be deduced from accurate tables of deviation. As deviation varies, with time and latitude, it must be con- stantly ascertained by swinging ship. The methods in use in swinging ship are well known, but perhaps a repetition may not be thrown away. They are two in number. One, by observing the compass-bearing of a distant object whose true magnetic bearing is known. The other, by reciprocal bearings of the compass on board, and another on shore. By distant The first is the best and simplest when the magnetic bearing Object. O f ne ^^ant object can be well determined. The object should be, at the least, six miles distant, and the more the better. Its bearing can be obtained from observations on shore, from a spot in line with the ship, with the same card as is to be used in swinging, or by true bearing with known variation applied. Objects for this purpose are sometimes indicated on the charts or in the sailing directions, and the bearings given. The deviation, for each position of ship's head, is then the CHAP. xix. . SWINGING SHIP. 295 difference between this fixed magnetic bearing, and the ob- served bearing by compass. The ship can either be hauled round with hawsers, at anchor, or, if the object be far enough off, can be steamed round a circle small enough to make no difference in the bearing. If steamed round, it is well to repeat the operation, turning in the opposite direction, as the compass may partake of the swing of the ship, which will introduce error. The mean of the two will then be the bearing to use. The second method is perhaps the one generally employed, Byrecipro- and is very convenient with a theodolite at hand. An officer is landed with azimuth compass and theodolite. He obtains the bearing with the compass of some well- defined object, and setting up his theodolite, takes it for his zero. In arranging the theodolite on zero, it saves calculation to point the degree and minute of the magnetic bearing to the zero instead of 360. Thus, if the zero bears by compass S. 44 20' E., and the ship is going to steam round to the westward of the station, set the vernier to 315 40'. The angles read to the ship will then be the angle west of the magnetic south. A flag on a long staff is held behind the theodolite, when all is ready. The ship, under steam, and with a flag placed exactly over the standard compass, steams slowly round, hoisting a large flag close up to the mast-head just before the ship's head comes to each point, which is dipped at the moment of observation, when the bearing of the shore station is taken. The flag on shore is dipped, to show that the angle of the flag over the compass has been obtained by the theodolite, and is again shown as a response, when the flag is mast-headed for the next observation. The time of each observation is taken by previously com- pared watches. In this case, too, the ship should be swung in the opposite direction, if it is deemed necessary. 296 HYDROGRAPHICAL SURVEYING. CHAP. XIX. 3.30 3.45 NorUi East S.E JW 3.30 CHAP. xix. SWINGING SHIP. 297 The difference of the reciprocal bearings is the deviation at each observation. If more than one observation at any or all points has been obtained, the results are meaned for the accepted deviation. It is usual to observe at every point of the compass, for the ship's head, but in some vessels it may be necessary to sub- divide this. Valuable results for Variation may be deduced from the Variation ordinary swinging of a ship, if carefully carried out, by noting swinging, on the Deviation form the True Bearing used if swinging by distant object; the Variation allowed if taking the Sun as the object, as is done at sea ; and True Bearing of Zero and Variation allowed if using reciprocal bearings. The Hydrographic Officers are very glad of any information of this kind. The readiest way of examining the results of our observa- tions is by use of the Graphic method. (Fig. 49.) Drawing a long line, measure off equal parts along it, for the points of ship's head, and at each point on this normal lay off, at right angles, a line equal to the degrees and minutes of the deviation, on any scale we choose easterly deviation to the right, westerly to the left of the normal. Lines drawn through the extremities of these abscissae will denote the curve of deviation observed. By the irregularities of this curve, we can judge of the correctness of the observations very fairly ; and for our final table of deviation, we can draw a mean curve, if there are many irregularities, and measure to that for the amount of deviation for each point. UNIVERSITY APPENDIX. A. To prove that Tan Convergence/ = Tan Dep. . Tan Mid. Lat. FIG 55. Here C is the centre of the earth, P is the pole, E P, Q P, two meridians a known distance apart. B L, EL, are two tangents to the meridians, at the middle latitude known, in the same plane as the meridian, and meeting one another and the axis of the earth C P, produced, in L. Then BLD is the Convergency required, and DLC is the middle latitude, and BCD the departure. D C is a radius of the earth = r. Now as B D is small, it can be taken as a straight line without sensible error. We can also assume BLD and B C D to be right-angled triangles. Then B D = D L x Tan B L D. Similarly B D = r x Tan BCD. Equating, we have D L x Tan B L D = r x Tan B C D. But D L = r x Cot D L C ; .-. r x Cot D L C x Tan B L D = r x Tan B C D, or Tan BLD = Tan BC D x Tan DLC, or Tan. Convergency = Tan dep. x Tan Mid. Lat., and when Convergency is very small, we can say Convergency = Dep x Tan Mid Lat. Y 300 HYDROGRAPHICAL SURVEYING. APP. B. B. In Graduating a Chart on the Gnomonic Projection. To show that the angle of half convergency laid off from the rectangle intersects the opposite meridian on the parallel, and also that the further subdivisions of the convergency intersect their respective meridians on the same parallel. FIG 50. R From K and H, the graduating positions, draw the true bearings, lines KP, PG, which are meridians and will meet at P, the pole of the projection, making the angle K P C, or the Convergency. Make H C = difference of latitude of H and K. Then P C will equal P K. Join K C, bisect it in D, and join P D, the central meridian. Lay off K G- perpendicular to K P. Then Z. C K G is the half convergency ; For in APDK . . . DKP = 90-DPK, and as F K P is drawn = 90 ; ...... DKP = 90 - DKF; /. DPK = DKF. But D P K = | K P C the convergency ; .*. DKForCKG = i convergency. Q. E. D. APP. B. APPENDIX. 301 Bisect C K Gr in K N, making GKNorXKZ = convergency, Then E where K N intersects P F is on the parallel K C, or P E = P K. Bisect KPE in PX. Now MKZ = KZP + KPZ, but M K Z = 90 + \ Convergency (by construction) and K P Z = i Convergency ; /. 90 + i Conv. = K Z P + i Conv. ; /. KZP = 90 = PZE, and asKPZ = ZPE and P Z is common, the As K Z P & P Z E are equal and similar ; .-. PE = PK. Q. E. D. Y 2 302 HYDROGRAPHICAL SURVEYING. APP. c. C. To prove Chord = 2 rad j Vers. A)0 + - j - 1 1. FIG 52. Let C A B = 0, the angle whose chord is required. At any radius A C = r, describe arc C B. Join C B, then C B is Chord required. Bisect B C in I) and join A IX Then I) A B = |. Now DB = AB, Sin DAB = r . Sin f , 2 hutBC = 2 DB; .-. BC=2r.Sin- ........ (.). But A^ersine - = 1 -Cos^; .-. Yersine Ao + ^ = 1 - Cos ^ 90 + = 1 + Sin Substituting this in (a) we get APP. D. APPENDIX. 303 D. To prove deduction to the Meridian = FIG 51. Cos I . Cos d Vers Sin. z Sin. 1" Let X be a heavenly body near the Meridian, P the pole, Z the Zenith. Let Hour Angle Z P X = h, Latitude = 90 - P Z = I, Zenith distance X Z = z, Declination = 90 - P X = d.^ CosZX - CosPX.CosPZ Then Cos ZPX = or Cos h = SinPX.SinPZ Cos 2 - Sin I . Sin d Cos I. Cos d .'. Cos z - Sin I . Sin d = Cos Z . Cos d . Cos A = Cos I . Cos d.(l- Vers A) = Cos I . Cos e Cos I . Cos d . Vers h ; .*. Cos z + Cos Z . Cos d . Vers h = Cos Z . Cos d + Sin Z . Sin d = Cos(Zc^d) = 1 - Vers (I ^ d); Vers (I ^ d) = 1 - Cos z - Cos I . Cos d . Vers h = Vers z Cos I . Cos. d . Vers /^. Working with Declination = 90 4- PX, we shall get Vers (I + d) = Vers z - Cos I . Cos d . Vers h. But Z t"> c or I + cZ is the Meridian Zenith Distance = Z. Then Vers Z = Vers z - Cos Z . Cos d . Vers h -Cos 1. Cos d Vers h = Vers Z - Ver z = 1 - Cos Z - 1 + Cos z = Cosz - Cos Z but z and Z are nearly alike, so z + Z may be taken = Z, and z Z is very small /. 2 Sin may be taken = (z Z) Sin 1"; .-. Cos I . Cos d . Vers h = Sin z . (z Z) Sin 1", Cos I . Cos d Vers h or z - Z = Cos = , Sin z Sin 1 but z Z is the Reduction to the Meridian ; Cos I . Cos d Vers h Sin z Sin 1"' .*. Reduction to Mer. = 304 HYDROGRAPHICAL SURVEYING. APP. E. E. To show that the Distance of Horizon in English Miles -V height in feet. 2 Let r be radius of earth. h height of observer In feet. d distance of horizon. 2 + r z = (h + r) 2 h 2 being small may be omitted. d* = 2 hr; but h in Eng. miles is - oZoO and2r is 7910; 72 791 ''* = = - h very nearly ; .'.d = This is the distance disregarding refraction, which has the effect of increasing the distance of the visible horizon. If having found d as above, we subtract of itself from it, the remainder will be the true 18 distance in sea miles very nearly, with the effects of refraction taken into consideration. APP. F. APPENDIX. 305 F. To obtain distance from an elevation of a known height. FIG 56. h = height in miles. I = diff of level, a = dip. d = distance. E= angle of elevation. Now h = I + a ; .-. l = h-a, but I = d. Tan E ; .*. h a = d . Tan E, and h d . Tan E + , d 2 buta = - ; .-. A = Second. Degree. Minute. """V Second. 5 o' 362783-6 6046-39 100-77 5 o' 363853-2 6064*22 101-070 10 362785-5 6046-42 100-77 10 3 6 3759-7 6062*66 101-044 2O 362787-5 6046-46 100*77 20 363663*2 6061*05 IOI-OI8 30 362789-5 6046*49 100-77 30 363563-5 6059-39 100-990 40 362791-6 6046-53 100*78 40 363460-9 6057*68 100.961 5 362793-7 6046-56 100.78 50 363355.1 6055-92 100*932 6 o' 362795-9 6046-60 100- 78 6 o' 363246-3 6054*11 100-902 10 362798-2 6046-64 100*78 IO 363I34'5 605 2 * 24 100-871 20 362800*5 6046-68 100*78 20 363019*6 6050*33 100-839 30 362802-9 6046-72 TOO- 78 30 362901-7 6048*36 I00*8o6 40 362805-4 6046*76 100*78 to 40 362780-7 6046*35 100*772 50 362807-9 6046-80 100*78 50 362656-6 6044-28 100*738 7 o' 362810-4 6046*84 100*78 7 o' 362529-5 6042*16 100*703 10 362813-1 6046-89 100*78 IO 362399-4 6039*99 100*667 20 362815-2 6046*93 100*78 20 362266*2 6037*77 100-630 30 362818-5 6046*98 IOO*78 30 362130*0 6035*50 100-592 40 362821-3 6047*02 100* 78 40 361990*7 6033*18 100-553 5 362824-2 6047*07 100*78 5 361848-4 6030-81 100-513 8 o' 362827-1 6047*12 100* 79 8 o' 361703*0 6028*38 100-473 IO 362830-1 6047-17 100*79 10 361554*6 6025*91 100-432 20 362833-2 6047*22 100-79 20 361403-2 6023*39 100-390 30 362836-3 6047*27 100*79 3 361248*7 6o20*8l 100-347 40 362839-4 6047-32 200- 79 40 361091*2 6018*19 100-303 50 362842-7 6047*38 100*79 50 360930*6 6015-51 100-258 9 o' 362846-0 6047-43 100-79 9 o 360767*0 6012-78 100-213 10 362849*3 6047-49 100*79 IO 360600-4 6010*01 100-167 20 362852-7 6047-55 100-79 20 360430*7 6007-18 IOO-I2O 30 362856-2 6047*60 100*79 30 360258*0 6004-30 IOO-072 40 362859-7 6047-66 100* 79 40 360082-3 6001-37 IOO*O23 50 362863-3 6047*72 100-80 50 359903'5 5998-39 99-973 10 o' 362866-9 6047*78 100*80 10 o' 359721-7 5995*36 99-923 10 362870-7 6047*85 100-80 IO 359536-7 5992-28 99*871 20 362874-4 6047*91 100*80 20 359349*1 5989*15 99-819 30 362878*2 6047*97 100-80 3 359158*3 5985-97 99-766 40 362882-1 6048*04 100-80 40 358964*4 5982-74 99-7I2 5 362886*1 6048-10 100-80 50 358767*5 5979-46 99-658 326 HYDROGRAPHICAL SURVEYING. APP. M. LATITUDE. LONGITUDE. Latitude. Length in Feet of a Latitude. Length in Feet of a X' Degree. Minute. Second. /""" Degree. Minute. ^v Second. 11 o' 362890'! 6048 ' 1 7 100*80 11 o' 358567-6 5976-13 99-602 10 362894'! 6048-23 100-80 10 358364-7 5972*75 99*546 20 362898-2 6048*30 100-80 2O 358158-7 5969*3I 99-489 30 362902-4 6048*37 IOO-8I 30 357949*8 5965-83 99*431 40 362906*6 6048-44 I00'8l 4 357737*8 5962-30 99*372 50 362910*9 6048*52 IOO-8I 50 357522-8 5958-71 99*312 12 o' 362915-2 6048.59 100-81 12 o' 357304*8 5955*08 99-251 10 362919 6 6048-66 100-81 10 357083-9 5951-40 99*190 20 362924-1 6048 * 74 100-81 20 356859-9 5947*67 99*128 30 362928-6 6048-81 100-81 30 356632-9 5943*88 99*065 40 362933-2 6048-89 100-81 40 356402-9 5940*05 99*001 50 362937*8 6048-96 100-82 50 356169*9 5936-17 98-936 13 o' 362942-5 6049-04 100-82 13 o' 355933*9 5932-23 98-871 10 362947*2 6049-12 100-82 IO 355694-9 5928-25 98-804 20 362952*0 6049-20 100*82 20 35545 2 *9 5924-22 98*737 3 362956-9 6049*28 100-82 30 355207-9 5920*13 98-669 40 362961-8 6049-36 100*82 40 354959*9 5916-00 98-600 50 362966-8 6049-45 100*82 50 354709-0 5911-82 98*530 14 o' 362971*8 6049-53 100-83 14 o' 354455*1 5907*59 98-460 IO 362976-9 6049-62 100-83 10 354198-1 5903*3o 98-388 20 362982-0 6049 70 100-83 20 353938-2 5898-97 98-316 30 362987-2 6049-79 100-83 30 353675*3 5894*59 98-243 40 362992-4 6049-87 100*83 40 353409*4 5890-16 98-169 5 362997-7 6049-96 100-83 50 353140*6 5885-68 98-095 15 o' 363003-1 6050-05 100-83 15 o' 352868-8 5881-15 98*019 IO 363008-5 6050-14 100-84 IO 352594*1 5876*57 97*943 20 363013-9 6050-23 100*84 20 352316-3 5871-94 97*866 30 363019-4 6050-32 100-84 30 352035-6 5867-26 97-788 40 363025-0 6050-42 100-84 40 351751-9 5862-53 97-709 50 363030-6 6050-51 100-84 50 35i465'3 5857-76 97-629 16 o' 363036-3 6050-61 100-84 16 o' 35"75'7 5852-93 97*549 10 363042*0 6050-70 100-84 IO 350883-1 5848-05 97-468 20 363047-8 6050-80 100-85 20 350587-6 5843*13 97.386 3 363053-6 6050-89 100-85 30 350289*1 5838-15 97-303 4o 363059-3 6050-99 100-85 40 349987'7 5833-I3 97-219 5 363065-4 6051*09 100-85 50 349683-4 5828-06 97-134 APP. M. APPENDIX. 327 LATITUDE. LONGITUDE. Latitude Length in Feet of a Latitude. Length in Feet of a Degree. Minute. Second.; Degree. Minute. X Second. ir o ; 363071*4 6051-19 100-85 17 o' 349376-0 5822-93 97-049 IO 363077-4 6051-29 100-85 10 349065-8 5817-76 96-963 20 363083-5 6051-39 100-86 20 348752-6 5812-54 96-876 30 363089-7 6051*50 100-86 30 348436-5 5807-28 96-788 40 363095-9 6051-60 100-86 40 348117-4 5801*96 96-699 5 363102-1 605 1 70 100-86 5 347795*4 5796-59 96-610 18 o' 363108-4 6051*81 100-86 18 o' 347470-5 5791-18 96-520 10 363114-8 6051-91 100-87 IO 347142-6 5785-71 96-429 20 363121-2 6052-02 100-87 20 346811-8 5780-20 96-337 30 363127-6 6052-13 100-87 , 3 346478-1 5774*64 96*244 40 363134*1 6052-24 100-87 40 346141-5 5769-03 96*150 50 363140-7 6052-35 100-87 50 345801-9 5763*37 96-056 19 o' 363147-3 6052-46 100-87 19 o' 345459'5 5757*66 95*96i IO 363153-9 6052-57 100-88 IO 345114-1 5751-90 95-865 20 363160-6 6052-68 100-88 20 344765'8 5746-10 95*768 30 363167-4 6052-79 100-88 30 344414-6 5740-24 95*671 40 363174-2 6052-90 100-88 40 344060-6 5734*34 95*572 5 363181-0 6053-02 100-88 50 343703-6 5728-39 95*473 20 o' 363187-9 6053-13 100-89 20 o' 343343 * 7 5722*40 95*373 IO 363194-8 6053-25 100-89 10 342980-9 5716-35 95-171 20 363201-8 6053-36 100-89 20 342615-2 5710-25 95-272 30 363208-8 6053.48 100-89 30 342246-7 57o4-ii 95-069 4 363215-9 6053-60 100-89 40 341875-2 5697-92 94-965 5 363223-1 6053-72 100-90 50 341500-9 5691-68 94-861 21 o' 363230-2 6053-84 100-90 21 o' 341123-7 5685-40 94*756 IO 363237-5 6053-96 100-00 IO 340743-6 5679-06 94-651 20 363244-7 6054-08 100-90 20 340360-6 5672-68 94*545 30 363252-1 6054-20 100-90 30 339974-8 5666-25 94-438 40 363259-4 6054-32 100*91 40 339586-1 5659-77 94-330 1. 5 363266-8 6054-45 100-91 5 339i94*5 5653'24 94*221 22 o' 363274-3 6054-57 100-91 22 o' 338800-1 5646-67 94'ni IO 363281-8 6054*70 100*91 IO 338402-8 5640-05 94-001 20 363289-3 6054-82 100-91 20 338002-7 5633*38 93.890 30 363296-9 6054-95 100-92 30 337599*7 5626-66 93*778 40 363304-6 6055-08 100-92 40 337!93'9 5619-90 93*665 50 363312-2 6055-20 100-92 50 336785-2 5613-09 93*551 328 HYDROGRAPHICAL SURVEYING. APP. M. LATITUDE. LONGITUDE. Latitude. Length in Feet of a Latitude. Length in Feet of a f Degree. Minute. Second. x"~ Degree. Minute. ^^v, Second. 23 o' 363320-0 6055-33 100-92 23 o' 336373-6 5606*23 93*437 IO 363327-7 6055-46 100-92 10 335959-3 5599-32 93*322 20 363335'5 6055-59 100-93 20 335542-1 5592'37 93-206 3 363343*4 6055-72 100*93 30 335122-0 5585-37 93-089 40 36335 T '3 605 5 '86 100-93 40 334699-2 5578-32 92*972 50 363359-2 6055-99 100-93 50 334273-5 557J-23 92*854 24 o' 363367-2 6056-12 100-94 24 o' 333845-0 5564-08 92-735 IO 363375-2 6056-25 100-94 IO 3334I3-7 5556'89 92-615 20 363383-3 6056-39 100*94 20 332979-5 5549*66 92-494 30 363391-4 6056-52 100-94 30 332542-6 5542-38 92-373 40 363399-6 6056-66 loo- 94 40 332102-8 5535*05 92-251 50 363407*8 6056-80 100-95 40 331660-3 5527-67 92-128 25 o' 363416-0 6056*93 100-95 25 o' 331214-9 5520-25 92-004 10 363424*3 6057-07 100-95 10 330766-7 5512-78 91-879 20 363432-6 6057-21 100-95 20 330315-8 5505-26 9I-754 30 363440-9 6057-35 100-96 3 329862-0 5497'70 91-628 40 363449-3 6057-49 100-96 40 329405-5 5490-09 91*502 50 363457-7 6057-63 100-96 50 328946-2 5482-44 91-374 26 o' 363466*2 6057-77 100-96 26 o' 328484-1 5474*74 91-245 IO 363474-7 6057-91 100-97 IO 328019-2 5466-99 91-116 20 363483-3 6058-06 100-97 20 327551*6 5459.19 90*987 30 363491-9 6058*20 100-97 30 327081*2 5451-35 90-856 40 363500-5 6058-34 100*97 40 326608-0 5443*47 90*724 50 363509-2 6058-49 100-97 50 326132-1 5435*54 90*592 27 o' 363517-9 6058-63 100-98 27 o' 325653-4 5427*56 90*459 IO 363526*6 6058-78 100-98 IO 325171-9 5419*53 90-326 20 363535'4 6058-92 100-98 20 324687-7 5411*46 90-191 30 363544-2 6059-07 100-98 30 324200-8 5403*35 90-056 40 363553-0 6059-22 100-99 40 323711-2 5395*19 89-920 50 363561-9 6059-37 100-99 50 323218-8 5386-98 89-783 28 o' 363570-8 6059-51 100*99 28 o' 322723.6 53/8*73 89-645 IO 363579-8 6059-66 100-99 IO 322225.7 5370*43 89-507 20 363588-8 6059-81 101*00 20 321725-1 5362-09 89-368 30 363597-8 6059-96 lOl'OO 30 321221-8 5353*7 89-228 40 363606-8 6060 -ii 101-00 40 320 7I5 *8 5345-26 89.088 50 363615-9 6060-27 101-00 5 320207-1 5336-78 88-946 APP. M. APPENDIX. 329 LATITUDE. LONGI TUDE. Latitude. Length in Feet of a Latitude. Length in Feet of a Degree. Minute. ~~N Second. Degree. Minute. ~~"\ Second. 29 o' 363625*0 6060*42 roi-oi 29 o' 319695*6 5328-26 88-804 10 363634-2 6060*57 IOI-OI IO 319181-5 5319-69 88-661 20 363643*4 6060-72 loi-or 20 318664-6 53II*08 88-518 30 363652*6 6060-88 101-01 30 3I8I45' 1 5302*42 88-374 40 363661*9 6061-03 101*02 4 317622-8 5293-71 88-229 50 363671*2 6061-19 IOI-O2 5 317097-9 5284*97 88-083 30 o' 363680*5 6061-34 101-02 30 o' 3i65 7' 3 5276-17 87-936 IO 363689*9 6061-50 101-03 IO 316040*0 5267-33 87-789 20 363699*3 6061-66 101-03 20 3151507-0 5258*45 87-641 30 363708*7 6061 -81 101.03 30 314971*4 5249-52 87-492 40 363718-1 6061-97 101*03 40 3i4433*i 5240*55 87-343 5 363727*6 6062-13 101-04 50 313892*1 5 2 3l-54 87*192 31 o' 363737*1 6062*29 101*04 31 o' 3I3348-5 5222-48 87*041 10 363746*7 6062-45 101-04 IO 312802-2 5 2I 3'57 86*889 20 363756-2 6062*60 101-04 20 3i2253'3 5204-22 86-737 30 363765*8 6062*76 101-05 30 3ii7 OI *7 5195-03 86-584 40 3 6 3775-4 6062-92 101-05 40 3iii47-5 5185*79 86*430 5 363785-1 6063*09 101-05 50 310590-7 5176-51 86-275 32 o' 363794*8 6063-25 101-05 32 o 310031* 2 5167*19 86-119 10 363804-5 6063-41 101-06 10 309469' I 5157-82 85-963 20 363814*2 6063-57 101-06 20 308904*4 5148-41 85-807 30 363824*0 6063*73 101-06 30 308337-I 5138-95 85-649 40 363833-8 6063*90 101-07 40 307767-2 5129*45 85-491 50 363843-6 6064-06 101-07 50 307194*6 5119*91 85-332 33 o' 363853*5 6064*23 101-07 33 o' 306619-5 5110*33 85-172 10 363863*4 6064*39 101*07 10 306041-7 5100-70 85-011 20 363873-3 6064-56 101-08 20 305461-4 5091-02 84-850 30 363883-2 6064-72 101-08 30 304878-5 5081-31 84*688 40 363893*1 6064-89 101-08 40 304293-0 507I-55 84*526 50 363903-1 6065 05 101*08 50 303704-9 5061-75 84-362 34 o' 363913-1 6065*22 101-09 34 o' 303II4'2 5051*90 84-198 IO 363923*1 6065 '39 101-09 IO 3O252I-O 5042*02 84-034 20 363933-2 6065*55 101-09 20 30I925-2 5032*09 83*868 30 363943-2 6065*72 IOI-IO 30 301326*8 5022-11 83-702 40 363953'3 6065-89 101*10 40 300725-9 5012-10 83-535 5 363963-4 6066-06 101*10 50 300122*4 5002-04 83*367 330 HYDROGRAPHICAL SURVEYING. APP. M. LATITUDE. LONGITUDE. Latitude. Length in Feet of a Latitude. Length in Feet of a Degree. Minute. ^^\ Second. X"~ "" Degree. Minute. ^S Second. 35 o' 363973-6 6066-23 101-10 35 o' 299516-4 4991-94 83-199 IO 363983-7 6066*40 IOI-II IO 298907-8 4981-80 83*030 20 363993'9 6066-57 IOI-II 20 298296-8 4971-61 82-860 30 364004*1 6066-74 lOI'II 30 297683-1 4961*38 82-690 40 364014-3 6066-91 101*12 40 297067-0 4951*12 82-519 50 364024*6 6067-08 101-12 50 296448*4 4940-8I 82-347 36 ' 364034-9 6067-25 101-12 36 o' 295827-2 4930-45 82-174 IO 364045-1 6067-42 101-12 IO 295203-5 4920-06 82-001 20 364055-4 6067-59 IOI-I3 20 294577*3 4909-62 81-827 30 364065-8 6067- 76 IOIT3 30 293948-7 4899*15 81-652 40 364076*1 6067-94 101-13 40 293317-5 4888-63 81-477 50 364086-4 6068-11 IOI-I4 5 292683-8 4878-06 81-301 37 o' 364096-8 6068-28 IOI-I4 37 o' 292047-7 4867.46 81-124 10 364107-2 6068-45 IOI-I4 IO 291409-0 4856-82 80-947 20 364117*6 6068-63 IOI-I4 20 290767-9 4846-13 80-769 30 364128-1 6068-80 101-15 30 290124-4 4835-41 80*590 40. 364138-5 6068*98 101-15 40 289418-3 4824-64 80-411 50 3 64149 * 6069-15 IOI-I5 50 288829-8 4813-83 80-231 38 o 364159-5 6069-33 101-16 38 o' 288178-9 4802-98 80-050 10 364170-0 6069-50 101-16 10 287525-5 4792-09 79-868 20 364180-5 6069-68 101-16 20 286869-7 4781*16 79-686 30 364191-0 6069-85 101*16 30 286211-4 4770-19 79*503 40 364201-5 6070-03 101-17 40 285550-7 4759.18 79-320 5 364212*1 6070-20 101-17 50 284887-0 4748-13 79-136 39 o' 364222-6 6070*38 101-17 39 o' 284222-0 4737*03 78-951 10 364233-2 6070-55 101-18 10 283554-0 4725-90 78-765 20 364243-8 6070-73 101-18 20 242883-7 47I4'73 78-579 30 364254-4 6070-91 101-18 30 282210*9 4703-52 78-392 40 364265-1 6071-09 101-18 40 281535-8 4692-26 78 204 50 364275*7 6071-27 101-19 5 280858-2 4680-97 78-016 40 o' 364286-3 6071-44 101*19 40 o' 280178-2 4669-64 77*827 IO 364297-0 6071-62 101*19 10 279495-9 4658-27 77-638 20 364307-7 6071-80 101*20 20 278811-2 4646-85 77*448 30 364318-3 6071-97 IOI-2O 30 278124-1 4635-40 77* 2 57 40 364329-0 6072*15 IOI*2O 40 277434-7 4623-9! 77-065 50 364339*7 6072-33 IOI*2I 50 276742-9 4612-38 76.873 APP. M. APPENDIX. 331 LATITUDE. LONGITUDE. Length in Feet of a Length in Feet of a Latitude. _ Latitude X"~~ Degree. Minut'\ Second . Degree. Minute. '^v. Second. 41 o' 364350-4 6072-5 r ior- 2r 41 o' 276048-7 4600-81 76-680 10 364361* I 6072-69 101-21 IO 275352-2 4589-20 76-480 20 364371-9 6072-87 lOI* 21 20 274653-4 4577'56 76-293 30 364382-6 6073-04 IQI'22 30 273952-2 4565-87 76-098 4 364393-4 6073-22 101-22 40 273248-7 4554-75 75-902 50 364404-1 6073-40 IOI-22 50 272542-9 4542-38 75-706 42 o' 364414-9 6073-58 101 -23 42 o 271834-7 4530-58 75'509 10 364425-6 6073-76 101-23 10 271124-3 4518-74 75-312 20 364456-4 6073-94 IOT-23 20 270411-5 4506-86 75-114 3 364447-2 6074-12 IOI-24 -30 269696-4 4494- 94 74-916 40 364458-0 6074-30 TCI' 24 40 268979-1 4482-99 74-7I7 5 364468-8 6074-48 IOI-24 50 268259-5 4470-99 74"5 r 7 43 o' 364479-6 6074-66 IOI-24 43 o 267537-5 4458-96 74-316 10 364490-4 6074-84 IOI-2!? IO 266813-3 4446-89 74-115 20 36450I-2 6075-02 IOI-25 20 266086-8 4434-78 73'9i3 30 364512-0 6075 * 20 JOI-25 30 265358-1 4422*64 73-711 40 364522-8 6075-38 IOI-26 40 264627-1 4410-45 73-508 50 364533-6 6075-56 IOI-26 50 263893-8 4398-23 73-304 44 o 364544-4 6075-74 101-26 44 o 263158-3 4385-97 73-100 IO 364555*2 6075-92 101-27 10 262420-5 4373-68 72-895 20 364566-1 6076-10 101- 27 20 261680-6 436i-34 72-689 30 364576-9 6076-28 IOI-27 30 260938-4 4348-97 72-483 40 364587-7 6076-46 IOT-27 40 260193-9 4336-57 72-276 5 364598-5 6076-64 101-28 50 259447*3 4324-12 72-069 45 o 364609-4 6076-82 101-28 45 o 258698-4 4311-64 71-861 IO 364620-2 6077-00 IOI*28 10 257947-3 4299-12 71-652 20 364631-0 6077-18 IOI29 20 257194-1 4286-57 71-443 30 364641-9 6077-37 IOI-29 30 256438-6 4273-98 71-233 40 364652-7 6077-55 IOI29 40 255681-0 4261-35 71-022 50 364663-5 6077-73 IOI-3O 50 254921-2 4248-69 70-811 46 o' 364674-4 6077-91 IOI-30 46 o 254159-2 4235-99 70-600 IO 364685-2 6078-09 IOI-30 10 253395-0 4223-25 70-388 20 364696-0 6078-27 101*30 20 252628-7 4210-48 70-175 30 364706-8 6078-45 IOI-3I 30 251860*2 4197-67 69-961 40 364717-7 6078-63 IOI-3I 40 251089-6 4184-83 69-747 50 364728-5 6078-81 IOI-3I 5 2503 16-8 4171-95 69-532 2 A 332 HYDROGRAPHICAL SURVEYING. APP. M. LATITUDE. LONGITUDE. Latitude. Length in Feet of a Latitude. Length in Feet of a Degree. Minute. > Second. Degree. Minute. N Second. 47 o' 364739'3 6078-99 101-32 47 o' 249541-9 4159-03 69-317 IO 364750-1 6079-17 101-32 10 248764-9 4146-08 69-101 20 364760-9 6079-35 101-32 20 247985-8 4I33-IO 68-885 30 364771-7 6079-53 101-33 30 247204-5 4120-08 68-668 40 364782-5 6079-71 101-33 40 246421-2 4107-02 68-450 50 364793*3 6079-89 101-33 5 245635-8 4093-93 68-232 48 o' 364804-1 6080*07 101-33 48 o' 244848*2 4080-80 68-013 IO 364814-9 6080- 25 101-34 IO 244058-5 4067-64 67-794 20 364825-6 6080-43 101-34 20 243266-8 4054-45 67-574 30 364836-4 6080-61 101-34 30 242473-0 4041-22 67-353 4 364847' I 6080-79 id-35 40 241677-1 4027-95 67-132 5 364857-9 6080*97 101-35 50 240879-2 4014-65 66-911 49 o' 364868-6 6081*14 101-35 49 o' 240079-2 4001-32 66-689 10 364879-4 6081-32 101*36 10 239277-1 3987-95 66-466 20 364890-1 6081-50 101*36 20 238473-1 3974*55 66-242 30 364900-8 6081-68 101-36 3 237667-0 3961-12 66-018 4 364911-5 6081-86 101-36 40 236858-9 .3947-65 65 ' 794 5 364922-2 6082-04 101-37 50 236048-7 3934-15 65-569 50 o' 364932-9 6082-22 101-37 50 o' 235236-5 3920-61 65-343 IO 364943-6 6082-39 101-37 10 234422-3 3907-04 65-117 20 364954-2 6082-57 101-38 20 233606-1 3893-44 64-890 30 364964-9 6082-75 101-38 30 232787-9 3879-80 64-663 40 364975'5 6082-93 101-38 40 231967-8 3866-13 64-435 5 364986-2 6083*10 101-38 50 231145-7 3852-43 64-207 51 o' 364996-8 6083*28 101-39 51 o' 230321-4 5838-69 63-978 10 365007-4 6083-46 101-39 IO 229495-3 3824-92 63-749 20 365018-0 6083-63 101-39 20 228667-2 38II-I2 63-519 30 365028-6 6083-81 101-40 30 227837-2 3797-29 63-288 40 365039-1 6083-99 101-40 40 227005-3 3783-42 63-057 50 365049-7 6084-16 101-40 50 226171-4 3769-52 62-825 52 o 365060-2 6084-34 101-41 52 o' 225335-5 3755*59 62-593 10 365070-7 6084-51 101-41 IO 224497-7 3741-63 62-360 20 365081-2 6084-69 101*41 20 223658-1 3727-64 62-127 30 365091-7 6084-86 101-41 30 222816-5 37I3-6I 61-893 40 365102-2 6085 04 101-42 40 221973-0 3699-55 61-659 50 3651:2-7 6085-21 101-42 50 221127-6 3685-46 61-424 APP. M. APPENDIX. 333 LATITUDE. LONGITUDE. Latitude. Length in Feet of a Latitude. Length in Feet of a Degree. Minute. Second. Degree. Minute. ^"X Second. 53 o' 365123-1 6085-39 101-42 53 o' 220280-3 3671-34 61-189 IO 365133-6 6085-56 10! -43 IO 219431-1 3657-19 60-953 2O 365144-0 6085-73 101-43 2. 218580-0 3643-00 60.717 30 365154-4 6085-91 101-43 30 217727-1 3628-79 60-480 40 365164-7 6086-08 101-43 40 216872-3 3614-54 60-242 50 365175-1 6086-25 101-44 50 216015-7 3600-26 60 004 54 o' 365185-4 6086-42 101-44 54 o' 2 I5 I5 7 -2 3585-95 59-766 10 365195-7 6086 '60 101*44 IO 214296-9 3571-62 59-527 20 365206-1 6086-77 101-45 20 213434-7 3557^5 59-287 30 365216-3 6086-94 101-45 * 30 212570-7 3542-85 59*047 40 365226-6 6087-11 101-45 40 211704-9 3528-42 58-807 5 365236-8 6087-28 101-45 50 210837-3 3513*96 58-566 55 o' 365247-0 6087-45 . 101-46 55 o' 209968-0 3 499 '47 58-324 10 365257-2 6087-62 101-46 IO 209096-8 3484-95 58-082 20 365267-4 6087-79 101-46 20 208223-8 3470-40 57-840 30 365277-6 6088-96 101-47 30 207349-0 3455-82 5 7 '.5 97 40 365287-7 6088-13 101-47 40 206472-5 3441-21 57*353 5 365297-8 6088-30 101-47 50 205594-2 3426-57 57-109 56 o' 365307-9 6088-47 101-47 56 o' 204714-0 3411-9 56-865 IO 365218-0 6088-63 101-48 10 203832-2 3397*20 56-620 20 3653 2 8-0 6088-80 101-48 20 202948-6 5382-48 56-375 30 365338-0 6088-97 101-48 30 202063-3 3367-72 56-129 40 365348-0 6089-13 101-49 40 2oir 76-2 3352-94 55-882 5 365358'0 6089-30 101-49 50 200287-4 3338-12 55-635 57 o' 565367-9 6089-47 101-49 57 o' 199396-9 3323-28 55-388 IO 365377-8 6089-63 101-49 10 198504-7 3308-41 55-140 20 365387-7 6089-80 101-50 20 197610-8 3293-5I 54-892 30 365397-6 6089-96 101-50 30 196715-2 3278-59 54-643 40 365407-4 6090- 12 101*50 40 195817-9 3263-63 54-394 50 365417-2 6090- 29 101-50 5 194919-0 3248-65 54-I44 58 o' 365427-0 6090-45 101-51 58 o' 194018-3 3233-64 53-643 TO 365436-8 6090-61 101-51 IO 193116-0 3218-60 53^43 20 365446-5 6090-78 101-51 20 192212-1 3203-54 53-392 30 365456-2 6090-94 101*52 30 191306-5 3188-44 53-i4i '40 365465-9 609I-II 101-52 40 190399-3 3i73'32 52-889 50 365475-5 6091-26 101-52 5 189490-4 3158-17 52-636 \ A 2 334 HYDROGRAPHICAL SURVEYING. APP. M. LATITUDE. LONGITUDE. Latitude. Length in Feet of a Latitude. Length in Feet of a /*"" "" Degree. Minute. ^s Second. Degree. Minute. Second. 59 o' 365485-1 6091-42 101-52 59 o' 188579-9 3143-00 52-383 IO 365494'7 6091-58 101-53 IO 187667-8 3127-80 52'130 20 365504-3 6091-74 101-53 20 186754-1 3112-57 51-876 30 365513-8 6091-90 101-53 30 185838-8 3097-31 51-622 40 3655 2 3'3 6092-06 101-53 40 184921-9 4082-03 5I-367 5 365532-8 6092-21 101-54 50 184003-4 3066-72 51-112 60 o' 365542-2 6092-37 101-54 60 o' 183083-3 3051-59 50-856 10 365551-6 6092-53 101-54 10 182161-6 3036-03 50-600 20 365561*0 6092-68 101-54 20 181238-4 3020-64 50-344 30 365570-3 6092-84 101-55 30 180313.7 3005-23 50-087 40 365579-6 6092-99 101-55 40 179387-4 2989-79 49-830 50 365588-9 6093-15 101-55 50 178459*5 2 974-33 49-572 61 o' 365598-1 6093-30 101*56 61 o' I77530-I 2958-84 49-3I4 10 365607-3 6093-46 101*56 IO 176599-2 2943-32 49-055 20 365616-5 6093-61 101-56 20 175666-8 2927-78 48-796 30 365625-7 6093* 76 101-56 30 I74732-8 2912*21 48-537 40 365634-8 6093-91 101-57 40 173797*4 2896-62 48-277 50 365643-9 6094-07 101-57 50 172860-5 288I-OI 48-017 62 o' 365652-9 6094-22 101-57 62 o' 171922-1 2865-37 47-750 IO 365661-9 6094-37 101-57 IO 170982*2 2849-70 47*495 20 365670-9 6094-52 101-58 20 170040*9 2834*02 47-234 30 365679-8 6094*66 101-58 30 169098*1 2818-30 46-972 40 365688-7 6094-81 101-58 40 168153-8 2802-56 46-709 5 365697-6 6094-96 101-58 50 167208-1 2786-80 46-447 63 o 365706-4 6095* II 101-59 63 o' 166261-0 2771-01 45-I84 10 365715-2 6095-25 101-59 IO 165312-4 2755-21 45'920 20 365723-9 6095-40 101-59 20 164362-5 2739-38 45*656 30 365732-6 6095-54 101-59 30 163411-1 2723-52 45-392 40 365741-3 6095-69 101-59 40 162458-4 2707-64 45-I27 50 365749-9 6095-83 101-60 50 161504-2 2691-74 44*862 64 o 365758-5 6095-98 101-60 64 o' 160548-6 2675-81 44-587 10 365767-1 6096-12 101-60 10 159591-6 2659-86 44-331 20 365775-6 6096-26 101*60 20 158633-2 2643-89 44-065 30 365784-1 6096-40 101-61 30 157673-5 2627-90 43-798 40 365792-6 6096-54 101*61 40 156712-5 2611-88 43-53I 50 365801-0 6096-68 101-61 50 155750-1 2595-84 43 ' 264 A PP. M. APPENDIX. 335 LATITUDE. . LONGITUDE. Latitude. Length in Feet of a Latitude. Length in Feet of a /** Degree.- Minute. Second. Degree. Minute. ^^s, Second. 65 o' 365809-3 6096-82 101-61 65 o' 154786-3 2579-77 42-996 10 365817-6 6096-96 fOI*62 10 153821-2 2563*69 42*728 20 365825-9 6097- 10 101-62 20 152854*8 2547*58 42-460 30 365834-2 6097-24 101-62 30 151887*2 253!*45 42-191 40 365842-4 6097-37 101-62 40 150918*2 2515*30 41-922 50 365850-5 6097-51 101-63 50 149947*9 2499*13 41-652 66 o' 365858-6 6097-64 101-63 66 o 148976-3 2482-94 41*382 IO 365866-7 6097-78 101-63 10 148003-4 2466*72 41*112 20 365874-7 6097*91 101-63 20 147029-3 2450-49 40-841 30 365882-7 6098-05 101-63 30 146053-9 2434-23 40*570 40 365890-7 6098-18 101-64 40 I45977-3 2417-96 40*299 5 365898-6 6098-31 101*64 50 144099-3 2401-66 40-028 67 o' 365906-4 6098-44 101-64 67 o 143120-2 2385-34 39*756 10 3659I4'3 6098-57 101*64 IO 142139-8 2369*00 39*483 20 365922*0 6098*70 101-65 20 141158*2 2352-64 39-211 30 365929-8 6098-83 101-65 30 140175-4 2336-26 38-938 40 36593y4 6098-96 101-65 40 139191-4 2319-86 38-664 50 365945-1 6099*09 101-65 50 138206-1 2303-44 38-390 68 o' 365952-7 6099-21 101-65 68 o' 137219-7 2287-00 38*116 IO 365960-2 6099-34 101*66 10 136232-1 2270-54 37-842 20 365967-7 6099-46 101*66 20 i35 2 43-3 2254*06 37-568 30 365975-2 6099*59 101*66 30 134253-4 2237-56 37' 2 93 40 365982-6 6099-71 101*66 40 133262-3 2221*04 37-017 5 365989-9 6099-83 ioi 8 66 50 132270-1 2204-50 36-742 69 o' 365997^ 6099*96 101*67 69 o' 131276-7 2187-95 36-466 10 366004-5 6100-08 101*67 IO 130282-2 2171-37 36*190 20 366011-7 6100- 20 101*67 20 129286-6 2154*78 35'9i3 30 366018-9 6100-32 101*67 30 128289-9 2138-17 35-636 40 366026-1 6100-44 101*67 40 127292-1 2121-54 35-359 50 366033-1 6100-55 101-68 5 126293*2 2104-89 35-082 70 o' 366040-2 6100-67 101-68 70 o' 125293-2 2088-22 34-804 10 366047-2 6100- 79 101-68 IO 124292-1 2071-54 34-526 20 366054-1 6100-90 101-68 20 123289-9 2054-83 34-247 50 366061-0 6101-02 101-68 30 122286-7 2038-11 33-968 40 366067-8 6101- 13 101-69 40 121282-4 2021-37 33-690 50 366074-6 6101-24 101*69 5 120277-1 2004-62 33*410 336 HYDROGRAPHICAL SURVEYING. APP. M. LATITUDE. LONGITUDE. Latitude. Length in Feet of a Latitude . Length in Feet of a Degree. Minute. Second. /"""" Degree. Minute. Second. 71 o' 366081-3 6101*36 101*69 71 o' 119270*7 1987-85 33'I3I ro 366088*0 6101*47 101*69 10 118263*3 1971-06 32-851 20 366094*6 6101*58 101-69 20 117254-9 1954-25 32*571 30 366101-2 6101-69 101-69 30 116245*6 1937-43 32-290 40 366107-8 6101-80 101*70 40 115235-2 1920-59 32-009 50 366114-3 6101-91 101*70 5 114223-8 1903-73 31-729 72 o' 366120-7 6102*01 101*70 72 o' 112311-4 1886-86 31-448 IO 366127-1 6lO2- 12 101*70 IO 112198-0 1869-97 31*166 20 366133-4 6IO2-22 101-70 20 111183*7 1853-06 30-884 30 366139-7 6102-33 101*71 30 110168-4 1836*14 30-602 40 366145-9 6102-43 101-71 40 109132-2 1819*20 30-320 5 366153*1 6102*54 101*71 50 108135-0 1802*25 30*038 73 o' 366158-2 6102-64 101-71 73 o' 107116-9 1785*28 29'755 10 366164-3 6102- 74 ioi7i 10 106098*0 1768-30 29-472 20 366170-3 6102-84 101-71 20 105077-9 1751-30 29-189 30 366176*3 6102-94 101-72 30 104057-0 I734-28 28*905 40 366182-2 6103*04 101-72 40 103035-3 1717-26 28-621 50 366188-1 6103-14 101-72 50 IO2OI2-8 1700-21 28-337 74 o 366193*9 6103-23 101-73 74 o' 100989*1 1683-15 28-053 10 366199-6 6103*33 101.73 IO 99964'7 1666-08 2 7 - 7 68 20 366205-3 6103-42 101-73 20 98939-5 1648-99 27-483 30 366211-0 6103-52 101-73 30 979I3H 1631-89 27-198 40 366216-6 6103-61 101-73 40 96886-5 1614-78 26-913 50 366222*1 6103- 7 101-73 5 95858*7 1597-65 26-627 75 o' 366227-6 6103-79 101-73 75 o' 94830-1 1580-50 26-342 10 366233-0 6103-88 101-73 IO 93800-6 I563-34 26-056 20 366238-4 6103-97 101-73 20 92730-4 1546-17 25-770 30 366243-7 6104-06 101-73 30 91739-4 1528-99 25-483 40 366249-0 6104-15 101-74 40 90707-6 1511-79 25*196 50 366254-2 6104-24 101-74 5 89675-0 1494-58 24-901 76 o' 366259-6 6104-32 101-74 76 o 88641-6 I477-36 24-623 IO 366264*4 6104-41 101-74 10 87607-4 1460-12 24-335 20 366269*5 6104*49 101*74 20 86572-5 1442-88 24-048 30 366274-5 6104-58 101-74 30 85536-9 1425-62 23-760 40 366279-4 6104-66 101-74 40 84500-5 1408*34 23-472 50 366284-3 6104-74 101-75 50 83463*4 1391-06 23-184 APP. M. APPENDIX, 337 LATITUDE. LONGITUDE. Latitude. Length in Feet of a ^^^^ Latitude. Length in Feet of a X" Degree. Minute. A Second. Degree. Minute. ~"~*^ Second. 77 o' 366289'! 6104-82 101-75 77 o' 82425*6 1373-76 22-896 10 366293-8 6104-90 101-75 10 81387-0 I356-45 22-108 20 366298-5 6104-98 101-75 20 80347-8 I339'I3 23-319 P 366303*1 6105 -05 101-75 30 79307-9 1321-80 22-030 40 366307-7 6105 -13 101-75 1 ! 40 78267-3 1304-46 21-741 5> 366312-3 6105 -21 loi -75 50 77226-0 1287-10 21-452 78 o' 366316-7 6105-28 101-75 78 o' 76184-0 1269-73 21-162 79 o' 366342-3 6105-71 TOI ' 76 79 o' 69918-8 1165-31 19-422 80 o' 366365-8 6106-10 IQI'77 80 o' 63631-8 1060*53 17-676 81 f o' 366387-1 6106-45 101-77 81 o' 57325'2 955*42 15-924 82 o' 366406-3 6106-77 101*78 82* o' 51000-6 850-01 14*167 S3 o' 366423-2 6107-05 101- 78 83 o' 44660-3 744-34 12-406 84 o' 366438-0 6107-30 101-79 84 o' 38306" I 638-44 10-641 85 o' 366450-5 6107-51 101-79 85 o' 31939-9 532-33 8-872 86 o' 366460-7 6107-68 101-79 86 o' 25563-9 426-07 7-101 87 o' 366468-7 6107-81 101-80 87 o' 19179-8 319-66 5-328 88 o' 366474-4 6107-91 ioi'8o 88 o' 12789-9 213-17 3'553 89 o' 366477'9 6107-97 101*80 89 o' 6395-9 106-60 1-777 90 o' 366479-0 6107-98 101*80 90 o' o-o O'O o-o O C^ OO t^* O *^N ^t" fv ^ *^ M ^.^^ ^^^^-- 1 ffaSS'SkSSS.q.S: ^^^.o,---^^e; S ; OO PAOO PAOO PAOO PAOO ^A OOPAON^ON,,- 0^0 ^ rf rf r rr rr 1 OOOOOOOOOO OOOOOOOOOO OOOOOOOOOO 1 aV^ s rAsO O -^-OO >-( kj^ ON PAvO ^oo r o -4-oo r* so ^oo r< so ^-oo r so I I oooooooooooooooooooo t^-OO OOOOOOOOOOOO ONON OO3O3OOOOOOOOOOOOOOO c o o o 1 r}-sO t^OO O 1-1 Tf WTN.SO ONONQOOOOOOO t-.r^oooooooooooooooo OO CO OO OO OO OOOC OO OO OO 1 k^sO OO ON O -i (S T^- u-\sO r^ oo O ' ' <** PA TJ- so t'^ oo o^ O f ^ ^t" VA^D oo o c s ^^SssSSsS SS-iSS-i.^t Ib vus2sr2 PA ^J- u^sO t^OO ON O M r* pA^-Uo ^i b r, ^ 1 rH SNk^S'vS-sS-NSN.SxSNSAkj-x lASAk^kAk^k^krNLAUT>>^ krNkrNk^k^v^kAVJ^^NkrN^ 1 so so so sO so k^k^k^k^kr\ .nk^k^^vAkj^kj-Nirvk^iTN k^^k^kj^kj-v^krskru-skrx h 5J5I^5*H 1 h -HSHHH SHIHBH OOOOOOOO'- 11 - o rH PA PA PA PA P-"> P^> PA PA PA PA **3;|SJ?-|S5 * S ^ X^ ^ ^ $ ^ CD ^. t^ tt s. fi fi ?c ic rc ?: rj- r^ H-I <^~ OO -( kj^QO M kr\ OO C* wr\ O^ r*\\O O ^ t^. O 10 Cr, IX kt 3s t^ ^ u^\O vO vO r^ t-^oO OO CO CN & PA PA fv% PA P*N PA P^ PA PA ^N 1, tiii^i^ii^ ONONON.ONaNONbbbb s rH S - --------- ^mmm O M CJ r^ -rf u^^D t^-OO O^ OOOOOOOOOO ed O ONOO t^vO VA *^~ rA C* M ONOO r-so "* r< ON Tl- r~- r--oo oo oo oo oo oo ON ON g^a^^ss ^?r & CO rAOO <$ ON VA O O >-i ^-(H OOrAONrt-OvA0 Tt~ tj- VAVC r^OO OO ON O M " <*> s 00 rf^ ^"S'S^'S^^^ rsr^r.r.r.^r.^^r* r.r.^rAMr.r.r.r.r, r. |t|fm|s"a sHsssssss O M >-J fS * h ^" -^f- rj- \r\\O vD t^ s O5 r OO rt- O ^ rA ONVO r OO T*-- 1^-T^-OvO rAONvAIN OO u^MOO -^M l>*-^t-O t^r^ r^ r-oo ON ON O O M ^> M i^ rs. i^. r^ r^oo oo oo oo oo oooooooooooooooooooo O\O *- w r*r^r^'rh^ tryvD i M rs rA rA "^* ^J* VA VAVO vO w^5&|3.5 5 *^ rA Ti~ ^* vr\sO vD f^- r^-OO O^ r\ r\ fcj^ ^r\ *~r\ wn ^r\ r\ \j~\ \s\ \^\ s II s O -4- x> r< I-.P-I VAO ^oo t^. M so O *-r\ o^* ^" OO f*\ f^> cs . r^ t^oo oo oo s rA rt" NO OO ON ~ rA Kj~vO OO UUiioii^kk^ k -i^i^s-^ VA VA VA VA VAVO VO \O VO vO ONONQOMMMMrArA 1 ^ ^ VA VANO vO r^oO OO ON O s 00 s as Jt|S5m O M (^ rA TJ- VAVO t^OO ON O 340 HYDROGRAPHICAL SURVEYING. APP. O. TABLE 0. Dip Table for calculation of Heights to 30 miles. Dip in feet = 0-8815 d? (in miles). Dist. Dip in feet. Dist. Dip in feet. Dist. Dip in feet. Dist. Dip in feet. Dist. Dip in feet. I 0-9 1C* 97 It* 240 2IJ 398 26 596 If 2'O II 107 I*| 247 21* 407 26| 607 2 3'5 "i 117 17 255 2I| 417 26| 619 *i 5'5 12 127 i.Tt 262 22 427 26f 6 3 I 3 7*9 "i 138 i?i 270 221 436 27 643 3* 10-8 13 149 i7l 278 22* 446 27i 655 4 14-1 i3i 155 18 286 22| 456 27* 667 4* 17-8 iji 161 1 8J 294 23 466 27f 679 5 22*0 i3i 167 iH 302 '23i 476 28 691 5* 26*6 Z 4 173 i8| 310 23* 486 281 703 6 31*7 I4i 179 19 318 231 497 28* 716 6* 37*2 i4i 185 i9i 327 24 507 28f 729 7 43'i Hi 192 i9i 335 Mi 518 29 741 7i 49-6 15 198 i9f 344 24* 529 9i 754 8 56-4 i5i 205 20 353 24f 540 9i 767 8* 63-7 15* 212 20J 36i 25 551 29f 780 9 7i i5l 219 20^ 370 25i 562 30 793 9 79 16 226 20| 379 25* 573 10 88 r6J 233 21 388 5l 584 pp. p. APPENDIX. 341 ^" OO M t~*- M SO O ^" OO M SO M ir\ O^ Tf~ 00000000000000" = ^0 ^ VA n-ONrhON^-OsrA0 rA OOOOOOOOOOOOtHMM : ^ Z ^ X <8 ^^-^^^S.'S 5-^M~ OOOOOOOOOOMMMMM H| U HOJ = 00 ^M 0M M M rAsO r-I-OO fc BB rA - b b b 6 b M M M 1 M M M M M M 1 HO) "^^^^gs^as^^^^M^ OOOOMMMHMMMMMrArA 8 = r^^^OO^MONsOrA^sOrAOr-^ 1 M - b b b M H M M M M M ^ ^ ^ ^ V P . CO* M hOM CAU^M rAVAH rA^AMrA^ HM = M^.^^^^^8M-^^^^^^ OOM MMMMrArArATj-rj-^-^VA 4* -000 OoOsO O M O ^t-M Oooso^r-- " .OO^-r^M^^^^^^^soso _^OOMSO rt-r-MsOOrAr-M ^C3N M . b M M M M 'CA -CA ^ U ^ SO SO ^ ^ _T}-MSOMSO MsOrl-OOOOM-^-OOOOM "" . MM ^OOsO ThM OOO T^-ri-MOOsO T}-M O OO ^ + MMMMM MM __ SO M OO ^J" O sO OO OO ^ O M OO *3~ O SO H* _M TJ-sO OSM rAvr\OO O M ^t^OSM rA ^A t I > MMCA^^SO^OOOSOMM^^.^ 1 I 342 HYDROGRAPHICAL SURVEYING. APP. O. TABLE Q. Table of Distances at which Objects can be Seen at Sea, according to their respective Elevations and the Elevation of the Eye of the Observer. Height in Feet. Distance in English or Statute Miles. Distance in Geographical or Nautical Miles. Height in Feet. Distance in English or Statute Miles. Distance in Geographical or Nautical Miles. 5 2-958 2-565 IOO 13-228 11-47 10 4-184 3-628 110 13*874 12-03 IS 5-123 4*443 120 14-490 12-56 20 5-916 5-130 130 15-083 13-08 25 6-614 5-736 140 15-652 13*57 30 7-245 6-283 150 16-201 14-22 35 7*826 6-787 '200 18-708 16-22 40 8-366 7-255 2 5 20-916 I8-I4 45 8-874 7-696 300 22-912 19-87 50 9'354 8-112 35 24-748 21-46 55 9-811 8-509 4OO 26-457 22-94 60 10-246 8-886 450 28-062 24*33 65 1.0-665 9-249 500 29-580 25-65 70 11-067 9-598 55 36-024 26-90 75 11-456 9*935 600 32-403 28-10 80 11-832 10-26 650 33-726 29-25 85 12-196 10-57 700 35-000 30-28 90 12-549 10-88 800 37-416 32-45 95 12-893 11-18 9OO 39-836 34*54 IOOO 41-833 36-28 Example. A tower 150 feet high will be visible to an observer whose eye is elevated 15 feet above the water 19 nautical miles; thus, from the Table : 15 feet elevation distance visible 4-44 nautical miles. 14-22 18-66 From Admiralty Tables. APP. R. APPENDIX. 343 TABLE E. True Depression or Distance of the Sea Horizon. Height. Dep. Square. Height. Dep. Square. Height. Dep. Square. Dep. Square. ft. / ft. ft. , / I'l I I 3293 61 3 7 2I 12966 121 14641 181 32761 3*5 2 4 3403 62 3844 13183 122 14884 182 33124 8.0 3 9 3513 63 3969 !3?97 123 15129 183 33489 14-2 4 16 3924 64 4096 13615 I2 4 J 5376 184 33856 22*1 5 25 374 65 4225 13836 I2 5 15625 185 34225 31*9 6 36 3855 66 4356 14061 126 15876 186 34596 43*3 7 49 3974 67 4489 14282 127 16129 187 34969 56-6 8 64 4093 68 4624 14502 128 16384 188 35344 71-7 9 81 4213 69 4761 14737 I2 9 16641 189 35721 88-5 10 100 4337 70 4900 14970 130 16900 190 36100 107 ii 121 4461 7i 5041 15197 I 3 I 17161 I 9 ! 36481 127 12 144 4587 72 5184 15429 132 17424 192 36864 149 13 169 47r6 73 5329 15664 J 33 17689 *93 37249 J 74 i4 I 9 6 4846 74 5476 15901 134 17956 194 37636 199 15 225 49/6 75 5625 16139 J 35 18225 !95 38025 226 16 2 5 6 5112 76 577 6 16380 136 18496 196 38416 256 17 289 5249 77 5929 16622 137 18769 197 38809 287 18 324 5385 78 6084 16866 138 19044 198 39204 319 19 36l 5524 79 6241 17111 J 39 19321 199 39601 354 20 4OO 5665 80 6400 17362 140 19600 200 40000 390 21 441 5808 81 6561 17608 141 16881 201 40401 428 22 484 5952 82 6724 17860 142 20164 202 40804 468 23 529 6098 83 6889 18111 143 20449 203 41209 510 24 57 6 6246 84 7056 18366 144 20736 204 41616 55 25 62 5 6394 85 7225 18622 J 45 21025 20 5 42025 598 26 676 6547 86 7396 18878 146 21316 206 42436 645 27 739 6700 87 7569 19140 *47 21609 207 42849 694 28 784 6855 88 7744 19401 148 21904 208 43264 744 29 841 7012 89 7921 19664 149 22201 209 43681 797 30 900 7172 90 8100 19930 150 22500 2TO 44IOO 850 31 961 7332 9i 8281 20197 151 22801 211 44521 906 32 1024 7942 92 8464 20465 152 23104 212 44944 964 33 1089 7656 93 8649 20736 153 23409 213 45369 1023 34 1156 7824 94 8836 21008 T 54 23716 214 45796 1084 35 1225 7987 95 9025 21282 *55 24025 215 46225 1147 36 1296 8158 96 9216 21558 156 24336 216 46656 I2II 37 1369 8330 97 9409 21836 157 24649 2I 7 47089 1278 38 1444 8504 98 9604 22115 158 24964 218 47524 1346 39 1521 8678 99 9801 22397 159 25281 219 4796i 1416 40 1600 8852 100 IOOOO 22680 1 60 25600 22O 48400 1487 4i 1681 9032 IOI I020I 22964 161 25921 221 48841 1561 42 1764 9210 102 10404 23251 162 26244 222 49284 1636 43 1849 9393 103 10609 23540 163 26569 223 49729 1713 44 1936 9577 IO4 I08l6 23830 164 26896 224 50176 I 79 2 45 2025 9760 105 II025 24121 165 27225 225 50625 1872 46 2116 995 1 106 II236 24415 166 27556 226 51076 *954 47 2209 10135 107 II449 24711 167 2 7 889 227 51529 2039 48 2304 10325 108 11664 25008 168 28224 228 51984 2124 49 2401 10518 109 Il88l 25307 169 28561 22 9 52441 2212 5 2500 20712 no I2IOO 25608 170 28900 230 52900 2301 5 1 2601 10908 in I232I 25911 171 29241 231 5336i 2393 52 2704 11105 112 12544 26215 172 29584 232 53824 2485 53 2809 11304 II 3 12769 26521 173 29929 233 54289 2581 54 2916 11506 114 12996 26829 174 30276 234 54756 2677 55 3025 11700 H5 13225 27139 175 30625 2 35 55225 2 775 56 3136 11913 116 13465 27451 176 30976 2 3 6 55696 2875 57 3246 I2I20 117 13689 27764 177 31329 237 56169 2977 58 33^4 12328 118 13924 28079 178 31684 238 56644 3081 59 348i 12538 119 I4l6l 28396 179 32041 239 57121 3186 60 3600 12749 I2O 14400 28715 180 32400 240 57600 From Eaper. 344 HYDROGRAPHICAL SURVEYING. APP. S. TABLE S. Angles subtended at different distances by a pole ten feet length. Yds. Angle. Yds. Angle. Yds. Angle. Yds. Angle. 17 II 25 20 92 2 05 OO 167 08 46 242 o 47 26 18 10 23 20 93 2 02 50 168 08 oo 243 o 47 08 20 9 oo oo 95 2 00 40 170 7 24 245 o 46 48 22 8 47 48 97 58 30 172 06 44 247 o 46 28 23 8 10 18 98 56 30 06 04 248 o 46 08 25 7 37 54 IOI 54 3 175 05 30 250 o 45 48 27 7 09 10 102 52 40 177 04 40 252 o 45 50 28 6 45 48 I0 3 50 54 178 04 16 253 o 45 12 30 6 21 36 105 49 oo 180 03 40 2 55 o 44 .54 32 6 01 32 I0 7 47 20 182 03 04 257 o 44 38 33 4 43 28 108 45 44 183 02 30 258 o 44 20 35 5 27 10 no 44 10 185 oi 56 260 o 44 02 37 5 12 20 112 42 20 187 OI 22 262 o 43 50 38 4 58 44 113 41 oo 188 oo 50 263 o 43 36 40 4 46 16 115 39 40 190 oo 18 265 o 43 14 42 4 34 5 117 38 14 92 o 59 46 267 o 43 oo 43 4 24 20 118 36 50 193 o 59 16 268 o 42 42 45 4 14 oo 120 i 35 30 195 o 58 46 270 o 42 26 47 4 05 30 122 T 34 10 197 o 58 16 272 o 42 n 48 3 57 oo 123 i 32 50 198 o 57 48 273 o 41 55 5 3 49 06 125 31 40 200 o 57 18 275 o 41 40 52 3 4i 42 127 30 30 202 o 56 48 277 o 41 25 53 3 34 5 128 29 16 203 056 20 278 o 41 10 55 3 28 20 130 28 10 205 o 55 54 280 o 40 55 57 5 22 10 132 27 oo 207 o 55 26 382 o 40 41 58 3 16 24 133 26 oo 208 o 55 oo 283 o 40 26 60 3 10 5 135 24 50 210 o 54 34 285 O 40 12 62 3 05 40 T 37 23 5 212 o 54 16 287 o 39 58 63 3 01 oo 138 22 50 213 o 54 oo 288 o 39 44 65 2 56 14 140 21 50 2I 5 o 53 26 290 o 39 30 67 2 51 40 142 2O 50 217 o 52 54 292 o 39 17 68 2 47 40 143 20 OO 218 o 52 28 293 o 39 04 70 2 43 40 145 19 oo 22O 052 04 295 o 38 50 72 2 40 00 147 18 08 222 o 51 42 297 o 38 37 73 2 36 14 148 17 16 223 051 20 298 o 38 24 75 2 32 44 150 l6 22 22 5 o 50 56 300 o 38 n 77 2 2 9 30 152 15 30 22 7 o 50 34 302 37 59 78 2 26 20 153 14 44 228 O 50 12 303 o 37 47 80 2 23 14 155 14 oo 230 o 49 50 305 37 34 82 2 20 l6 157 13 08 2 3 2 o 49 28 307 o 37 22 83 2 17 30 158 12 20 233 o 49 06 308 o 37 10 85 2 14. 50 160 II 40 235 o 48 44 310 o 36 58 87 2 12 10 162 II 00 237 o 48 22 312 o 36 46 88 2 09 44 163 10 10 2 3 8 o 48 02 o 3 6 34 90 2 07 20 165 09 30 240 o 47 44 315 o 36 23 APP. T. APPENDIX. 345 TABLE T. For converting Intervals of Time or Longitude into Decimals of a Day. Long. Time. Decimals of a Day. Long. Time. Decimals of a Day. Long. Time. Decimals of a Day. o h O ' o / 15 I 0417 o 15 I 0007 7 45 31 0215 30 2 0833 o 30 2 0014 8 o 32 0222 45 3 1250 o 45 3 OO2I 8 15 33 O229 60 4 1667 I O 4 0028 8 30 34 0236 75 5 2083 1 15 5 0035 8 45 35 0243 90 6 2500 i 30 6 0042 9 o 36 0250 105 7 2917 i 45 7 0049 9 15 37 0257 120 8 '3333 2 O 8 0056 9 3o 38 0264 *35 9 3750 2 15 9 ^0062 9 45 39 0271 150 10 4167 2 3 10 0069 10 40 0278 165 ii 4583 2 45 ii 00076 10 15 4i 0285 180 12 5000 3 o 12 0083 10 30 42 O292 195 13 5417 3 15 13 0090 10 45 43 0299 210 14 5833 3 30 14 0097 II 44 0306 225 15 6250 3 45 15 0104 ii 15 45 0312 240 16 6667 4 o 16 OIII ii 30 46 0319 2 55 17 -7083 4 15 17 0118 ii 45 47 0326 270 18 7500 4 30 z8 0125 12 48 0333 285 19 7917 4 45 19 0132 12 15 49 0340 300 20 8333 5 o 20 0139 12 30 50 0347 315 21 8750 5 J 5 21 0146 12 45 5 1 0354 33 22 9167 5 30 22 0153 13 o 52 0361 345 23 9583 5 45 23 0160 13 15 53 0368 360 24 I'OOOO 6 o 24 0167 13 30 54 0375 6 15 25 0174 13 45 55 0382 6 30 26 0181 14 o 56 0389 6 45 27 018' 14 15 57 0396 7 o 28 0194 14 30 58 0403 7 15 29 O2OI 14 45 59 O4IO 7 30 30 0208 5 o 60 0417 From Shadwell's " Chronometers." 34^ PIYDROGRAPHICAL SURVEYING. APP. U. TABLE U. Metrical and English Barometers. Barometer Scales. Barometer Scales. Barometer Scales. FT. Mill. Eng. In. Fr. Mill. Eng. Jn. Fr. Mill. Eng. In. 640 25-2 691 27-2 742 29-2 643 25-3 693 27-3 744 29*3 645 25-4 696 27-4 747 29-4 648 25*5 698 27'5 749 29-5 650 25-6 701 2 7 -6 752 29-6 653 25-7 704 27'7 754 29-7 655 25-8 706 27-8 757 29-8 658 25-9 709 27-9 759 . 29-9 660 26-0 711 28-0 762 30-0 663 26-1 7M 28-1 765 30-1 665 26-2 716 28-2 767 30-2 668 26-3 719 28-3 770 30-3 670 26-4 721 28-4 772 30-4 673 26-5 724 28-5 775 30-5 676 26-6 726 28-6 111 30*6 678 26-7 729 28-7 780 30-7 681 26-8 732 28-8 782 30-8 683 26*9 734 28-9 785 30-9 686 27-0 737 29-0 787 31-0 688 27-1 739 29-1 APP. V. APPENDIX. 347 TABLE V. Corresponding Thermometers, Fahrenheit, Centigrade, Reaumur. F. C. R. F. C. . R. F. C. R. o o o o o O -17-8 - I4'2 41 5-0 4-0 81 27'2 2T'8 J -17.2 -13-8 42 5'6 4'4 82 2 7 '8 22'2 2 -16-7 -13-3 43 6-1 4'9 83 28-3 22'7 3 -16-1 -12-9 44 6-7 5'3 84 28-9 23-1 4 -15-6 - 12-4 45 7*2 5'8 85 29-4 23-6 5 -15-0 - I2'0 46 7'8 6-2 86 30*0 24*O 6 -i4'4 -ii-6 47 8'3 6-7 87 30-6 24*4 7 -13-9 - 11*1 48 8-9 7-1 88 31-1 24'9 8 -13-3 -io'7 49 9*4 " 7*5 89 31-7 25-3 9 - I2'8 - 10*2 5 IO'O 8-0 90 32-2 2 5 -8 10 - I2'2 - 9'8 5* 10*6 8'4 9 1 32-8 26-2 ii -11-7 - 9*3 52 ii'i 8'9 92 33'3 26-7 12 -ii-i - 8-9 53 11*7 9*3 93 33'9 27-1 13 - 10*6 - 8-4 54 I2'2 9'8 94 34'4 27-6 14 - IO'O - 8-0 55 I2'8 10*2 95 35-0 28-0 15 - 9'4 - 7'5 56 13*3 I0'7 96 35-6 28*4 16 - 8-9 - 7'i 57 13*9 II'I 97 36-1 28-9 17 - 8-3 - 6-7 58 14*4 ii'6 98 36'7 29-3 18 - 7'8 - 6-2 59 15-0 I2'0 99 37-2 29-8 J 9 - 7'2 - 5'8 60 15-6 12-4 IOO 37-8 30-2 20 - 6-7 - 5*3 60 15-6 12-4 IOI 38-3 to- 7 21 - 6-1 - 4*9 61 16-1 12-9 102 38-9 31-1 22 - 5*6 - 4'4 62 16-7 13-3 103 39*4 31-6 23 - 5-0 - 4-0 63 17-2 13-8 104 40*0 32-0 24 - 4'4 - 3'6 64 17-8 14-2 105 40*6 32*4 25 - 3'9 - 3'i 65 18-3 14- 7 106 41-1 32-9 26 - 3*3 - 2-7 66 18*9 15-1 107 41-7 33'3 27 - 2-8 - 2*2 67 19-4 15-6 108 42-2 33*8 28 - 2'2 - 1-8 68 20*0 16-0 109 42-8 34-2 29 - i-7 - i'3 69 20*6 16-4 no 43 '3 34*7 30 - I'l - 0-9 70 2I'I i6'9 III 43'9 35' 1 31 - 0-6 - 0-4 7i 21'7 17-3 112 44.4 35*5 32 o o 72 22'2 17-8 113 45 'o 36*0 3J 0-6 0-4 73 22-8 18-2 114 45*6 36-4 34 i'i 0-9 74 23-3 18-7 U5 46*1 36-9 35 1-7 i*3 75 23-9 19-1 116 46-7 37'3 36 2'2 1-8 76 24-4 19*6 117 47'2 37'8 37 2-8 2'2 77 25-0 2O'O 118 47-8 38-2 38 3'3 2-7 78 25-6 20'5 119 48-3 38-7 39 3'9 3'i 79 26-1 20 '9 1 20 48'9 39-1 40 4*4 3-6 80 26-7 21-3 2 B 348 HYDROGRAPHICAL SURVEYING. APP. U. TABLE W. Measures used to express depths in Foreign CJiarts. National Measure. Eng. Feet. Eng. Fathoms. French Metre 3*281 0-5468 Brasse 5*329 0-8881 Spanish Braza 5-492 0'9I53 Swedish Fomn 5 '843 0-974 Danish Favn 6-175 1-0292 Norwegian i 6-175 1*0292 German Faden 5-906 0-984 Dutch Vaden 5'575 0-929 Russian Marine Sashine 6*OOO I'OOO Portuguese Braca 6-004 i-ooo ( 349 ) INDEX. A. PAGE Accuracy, remarks on .. .. .. .. . .. 54 Accumulators .. .. .. .. 4 . .. ..- .. 278 Adjusting theodolite .. .. .. .. .. .. .. 11 Age of tide .. .. .. .. .. ; .. .. 145 Altitude, double .. 256 Altitudes, Circum-meridian 180, 262 equal 201 short 261 Aneroids .. ,, .. .. .. .. .. .. 28 limitations to use of 172 Angle, calculating third .. .. .. .. .. .. 101 Angles from ship .. .. ,. .. .* .. .. 109 observing main .. ,. .. .. .. .. 71 plotting .. .. .. . .. .. .. 95 repeating theodolite .. .. .. .. .. ..16,71 sextant 160 subtended by different lengths .. .. .. App. P. Artificial horizon 10,181,184 Astronomical observations for scale .. .. .. .. 179,269 when taken .. .. .. .. 56 positions, correcting triangulation to .. .. 90 B. Banks, indications of .... . . 142 , y sounding .. .. <. .. .. 133 searching for .. .. .. .. .. .. .. 140 Bar, sounding a .... .. 135 Barometer, aneroid ...... 28 metrical and English compared .. App. U. Bases .. 57 2 c 350 INDEX. PAGE Bases chained .. .. .. .. .. .. .. .. 57 by angle of short measured length . . . . . . . . 61 by difference of latitude . . . . . . . . . . 60 by masthead angle .. .. .. .. .. .. 61 by sound .. .. .. .. .. .. .. 62 Beacons, floating ., .. .. .. .. .. .. 50 use of .. .. .. 134 Bearing, mercatorial .. .. .. .. .. .. ..85,89 true (see True bearing) Board, drawing mounting field .. .. .. .. .. .. 39 field 161,264 Boats' fittings 44 stores 47 Book, deck 140 sight 209 Books, ruled .. 40 Buoy, beacon .. .. .. .. .. .. .. .. 50 small, for boats .. .. .. .. .. .. 132 C. Calculated triangulations .. .. .. ..67 Calculating heights 167 position from two angles 110 third angle 101 time of P. M. observations .. .. .. .. 208 triangulation .. .. .. .. .. .. 86 Calling soundings .. .. .. .. .. .. .. 135 Catalogues, methods of obtaining apparent place from .. .. 195 of stars .. ... .. 182 Chains, measuring .. .. .. .. .. .. .. 27 Chart, completed 263 distortion in printed 288 fair .. .. .. .. 264 sending home .. .. .. .. .. .. .. 263 Choosing stars .. .. .. .. .. .. .. 182 Chords, calculating .... .... 96 plotting by .... 95 table of .. .. .. .. App. L. Chronometer, error of .. .. .. .. .. .. .. 201 Chronometers .. .. .. .. .. .. .. 40 comparing .. .. .. .. .. .. 205 defects in pocket .. .. 205 effect of temperature on . . . . . . . . 262 INDEX. 351 PAGE Chronometers, Hartnup's method for rates of . . . . . . 227 rejecting results by .. .. .. .. .. 223 stowage of 40,229 variations in rate of .. .. .. .. .. 226 Circle, on the .. .. .. .. .. .. .. .. 21 one method .. .. .. .. ..- .. .. HO testing 24 two method .. .. .. .. .. .. .. 19 Circum-meridian altitudes of stars 180 sun .. .. .. . .. 195 Coast-lining .. .. .. .. .. .. .. .. 119 Coast-line plotting .. .. .. .. .. .. .. 120 Collimation, adjustment for, in theodolite .. .. .. .. 12 error of theodolite .. .. .. .. .. 163 Colouring .. .. .. .. .. .. .. .. 267 Comparing watches .. .. .. .. .. . .. 205 Comparison book .. .. .. .. .. .. App. J. calculating mean, for hack watch .. .. 215,217 Compass, not used .. .. .. .. .. .. .. 79 deviation of .. .. .. .. .. .. .. 294 variation of 251 Compensation, temperature of mean .. 226,235 Contouring .. .. .. .. .. .. .. ,. 159 Convergency of meridians .. .. .. .. .. ..81,88 by spherical triangle .. .. 86,271 formulae for .. .. .. .. 86 neglect of .. .. .. .. 105 Correcting triangles .. .. .. .. . .. .. 80 Correction to spheroid .. .. .. .. .. .. 92 Current, ascertaining rate of 155,282 drag .. .. 289 effect of on sounding . . . . . . . . . . 282 log .. .. .. 155 under, in deep-sea sounding . . . . . . . . 286 observations on 288 D. Dark eyepieces 5,207 Datum for reduction .. .. . .. .. .. .. 144 approximating a . . . . * . . . 148 mean level as . . . . . . * . . . 155 Decimals of day, time in < . . . . . . . App. T. Deck book .. 140, App. I. Deep sea sounding . . . . . . . < . . . . . . 276 2 o 2 35 2 INDEX. Definition of triangulation .. ~7. .. .. .. ..55,67 Definitions, tidal .. .. .. .. .. .. .. 144 Degree, lengths of .. .. .. .. .. .. App. M. Delineation .. .. .. .. .. .. .. .. 266 Depressions for heights .. .. .. .. .. .. 162 table of true .. .. ... .. .. App. R. Dip for heights .. 164, App. 0. Distance from elevation of height .. .. .. .. .. 174 of sea horizon .. .. .. .. .. App. E. visible horizon .. .. .. .. .. App. Q. Distances, meridian (see Meridian distances). plotting by .. .. .. ... .. .. 102 Distortion of printed charts .. .. .. 26,288 Diurnal Inequality .. .. ... .. .. .. .. 145 Double Altitude 256 Drawing boards . . . . . . . . . . . . . . 34 lines at right angles *. .. .. .. 113 Dry proof .. 288 E. Elevations 124 Eliminating errors of observation .. .. .. .. .. 179 for latitude 180 for Error 201 Epochs for calculating rate .. .. .. .. .. .. 236 Equal altitudes, elimination of errors by ., .. .. .. 201 equation of 203,212,214 meaning 210 of stars 203 of sun 202 principle of .. .. 202 short at sea .. .. .. .. .. 261 working 212 at inferior transit .. .. 202,204 Equation of equal altitudes 203,212,214 Error, collimation, of theodolite .. .. .. .. .. 163 index, of sextant 208 level, of theodolite 163 observations for .. .. .. .. .. .. 198 of hinged shades of sextant .. .. .. .. .. 7 Errors of observation, eliminating .. .. .. .. .. 179 personal .. .. .. .. .. .. .. 211 Establishment 144, 145 estimation of . . . . . . . 149 INDEX. 353 PAGE Excess spherical ,. .. .. .. ..79 Exploring a river .. .. .. .. .. .. .. 292 Eyepieces, dark 5,207 of sextant .. .. .. .. ... .. 5 F. Fair chart 264 False station .. 74 Feet, number of in degrees and minutes . . . . . . App. M. Field boards .. 161 Fittings for boats 44 Fix 21 Fixing, care in choosing objects for . . 20 marks .. .. .. 108 from ship .. .. .. .. .. .. 109 soundings . . . . . . . . . . . . 127, 130 Foreign measures of depth . . . . . . . . . . App. W. Form for comparison book .. .. .. .. .. App. J. deck book .. .. .. .. .. .. App. I. height book.. .... ..168 deep-sea soundings . . . . . . . . . . App. K. G. General description of marine survey . . . . . . . . 51 Gnomonic projection .. graduating on .. .. .. .. .. 270 Graduating beforehand .. 107,272 Graduation, method of . . . . . . . . 270 Graphic projection of tides . . . . . . . . . . . . 152 H. Hack watches, calculating comparison for .. .. .. 215,217 care of .. .. .. .. 207 Hadley's sextant .. .. .. .. .. .. 5 Hartnup's formulas .. .. .. .. .. 235 Height book, form for .. ..167 of tide, interpolating . . . . . . . . . . . . 150 problems ...... .. 170 Heights, allowance for refraction in obtaining .. 166 calculating .. .. .. .. .. .. .. 167 dip for .. 164, App. 0. obtaining .. .. .. .. 162 354 INDEX. PAGE Heights, obtaining by depression of masthead . . . . . . 173 sextant elevations .. .. .. .. 163 Heliostat , 30 use of 139 using 32,73 High water, time of 147 Hills, delineation of 268 Horizon, artificial . . . . . , , . . . . . . . 10 distance of true .. .. .. .. .. App. R. visible App. E., App. Q: stand 11 Ill-conditioned triangles ., .. .. .. .. .. 91 Inferior transit, equal altitudes at 202,214 Inequality, diurnal .. .. .. .. .. .. .. 145 semi-mensual .. .. .. .. .. .. 145 Interpolation, meridian distance by .. .. ., .. .. 231 with harbour rates .. .. 238 Interval, calculating, for meridian distance .. .. ,, .. 237 Intervals of time in decimals of day .. .. ,. App. T. Irregular methods of plotting 102 L. Latitude by circum-meridian altitude of sun .. .. .. 195 pole star.. .. .. .. .. .. .. 191 example of, by star .. .. .. ., .. 189 observations for .. .. .. .. .. .. 179 Lead-lines ,. .. 48 measuring .. .. .. .. .. .. .. 134 Levelling 176 Lieussou's M. formulae .. 235 Log, current .. .. .. .. .. .. .. .. 155 Massey's 46 Longitude : difference of 198 obtaining of 199 Low water line .. .. .. .. .. ., .. 124 Lunitidal interval ., .. .. .. .. .. .. 145 M. Machines, sounding .. .. .. .. .. .. .. 138 Main stations .. .. .. .. .. .. .. .. 67 making .. .. .. .. 70 INDEX. 355 PAGE Main triangulation .. .. .. .. .. .. .. 67 Marks 42 fixing 108 Massey's log .. .. .. .. .. .. .. .. 46 Meaning equal altitudes .. .. .. .. .. .. 210 Mean level as datum .. .. .. .. .. .. .. 155 Measures, foreign of depth .. .. .. .. ., App. W. Measuring a base .. .. .. .. .. .. .. 59 lead-lines .. .. .. .. .. .. .. 134 Mercatorial bearing .. .. .. .. .. .. .. 85, 89 Meridian distances 199,218 by harbour rates 233,237 by interpolation . . . . . . . . . . 231 with harbour rates . . . . 238 by travelling rates 220,223 chronometric .. ,. .. .. .. .. 220 form for .. .. .. .. .. .. 224 interval for 237 return of .. .. .. .. .. .. 240 telegraphic 218 Meridian, reduction to .. .. .. .. ;. .. 186 Meridians, secondary .. .. .. .. .. .. .. 199 Moon : not adapted for observation .. .. .. .. .. 191 Moon's transit .. .. .. .. .. .. .. .. 146 Mirrors, resilvering .. .. .. .. .. .. .. 8 Mounting field boards .. .. .. .. .. .. 39 paper 35 Mouchez's correction for temperature .. .. .. .. 234 N. Natural scale . 0. Observations, astronomical when to be taken . . . . . . 56 at sea : 254 for Error of chronometer . . . . . . . . 201 for latitude 179 for true bearing . f .. .. .. .. 241 general remarks on .. .. .. .. .. 179 Observing stars, method of . . . . . . . . . . . . 184 tides 147 Obtaining heights . . . . . . . . . . . . . . 162 longitude .. .. .. .. .. .. .. 199 356 INDEX. p. PAGB Pairs of stars 181 Paper mounting .. .. ,. .. ,. . .. 35 sizes of .. .. .. .. .. .. .. .. 39 Parallax, adjustment for in theodolite ,. .. .. .. 12 in reading sextant .. .. ... .. .. .. 186 Patent log, Massey's ., ... .. .. .. .. 46 Personal errors .. .. ., .. .. .. .. 211 Plans, amateur .. ... ., .. ... .. .. 265 scale in .. ,. .. .. ,, .. .. 269 reducing ... ... .. .. .. .. .. 265 Plotting 94 by chords 95 by distances .. ., .. .. .. .. .. 102 with tracing paper .. .. .. .. .. .. 102 Points 67,265 in transit .. ... 22 Polaris (see Pole star). Pole star, bearing by 139,250 latitude by 191 Pole, ten foot .. 33 extension of method of . . . . . . . . 124 using 121 Problems for obtaining heights .. .. .. .. .. 170 Proofs of rules .. .. .. ... ... .. App. A. to H. Protractors 27 B. Range of tide 144 Rate, causes of variation of .. .. .. .. .. .. 226 epochs for accumulation of .. .. .. .. .. 236 harbour 233 Tiark's formula with .. : 237 sea .. .. ; 231 travelling 200,220 Rectangles, drawing lines at .. .. .. .. .. .. 113 Reducing plans .. .. .. .. .. .. 265 soundings .. .. .. .. .. .. .. 134 Reduction, datum for of soundings . . . . . . . . 144 table of of soundings .. .. .. .. .. 151 to meridian .. .. .. .. .. 186, App. N. Refraction, allowance for in obtaining heights 166 elimination of in astronomical observations . . 180, 201 Rejection of results 223 INDEX. 357 PAGB Repeating angles with theodolite .. .. .. .. ..16,71 Resilvering mirrors . . . . . . , . . . . . . . 8 Rise of tide ; .. .. 144 River, running survey of .. .. .. .. .. .. 292 triangulating with boats .. ,. .. .. .. 293 Roads, marking .. .. .. .. .. .. .. 159 Rock, sweeping for .. .. .. .. .. .. .. 133 Rockets, use of 139,239 Ruling a straight line .. .. .. .. .. .. 99 Running survey .. .. .. .. .. .. .. 114 of river 292 S. Scales, brass .. .. .. .. .. .. .. .. 26 Scale, natural .. fc v 269 of chart.. .. .. " 56,179,269 Sea observations . . . . . . . . . . . . . . 254 Searching for vigias .. .. .. - .. ... .. 140 Secondary meridians .. .. .. .. .. .. .. 199 Sextant angles 160 from ship .. .. .. 108 Hadley's .. 5 heights from-^-elevations .. .. .. .. .. 163 sounding .. .. .. .. .. .. .. 7 stand .. .. .. .. .. .. .. .. 9 use of . . . . . . . . . . . . . . 181 triangulation by .. .. .. .. .. .. 69 Shades, error of hinged sextant . . . . . . . . . . 7 Ship, angles from .. .. .. .. .. .. .. 109 sounding .. .. .. .. .. .. .. 186 use of in triangulation .. .. .. ,. .. 109 Sight book 209 Silvering mirrors .. .. .. .. .. .. .. 8 Sizes of paper .. .. .. .. .. .. .. .. 39 Sketch 77 Sound, base by . . , . . . . . . . . . . . 62 velocity of .. .. .. .. .. .. .. 64 Sounding 127 a bar 135 banks 133 book .. .. .. .. .. .. App. K. direction of lines of . . . . . . . . . . 129 effect of current on deep sea . . . . . . . . 282 importance of . . . . . . . . . . . . 127 35$ INDEX. PAGE Sounding lines doubling .. .. .. .. .. .. 132 rods .. .. 278 sextant .. .. .. .. .. .. .. 7 ship 136 off shore 138 fitting for 136 machines for .. .. .. .. .. .. 138 Soundings, calling .. .. .. .. .. .. .. 135 deep sea 276 fixing 127, 130 recording .. .. .. .. .. .. .. 130 reducing .. .. .. .. .. .. .. 134 to be thick in original 269 Spherical excess .. .. .. .. .. .. .. 79 Spheroid, correction for .. .. .. .. .. .. 93 Squaring in .. .. .. .. .. .. .. 115,265 Stand, artificial horizon .. .. .. .. .. 11 sextant .. .. .. ' .. .. .. .. 9 Star atlas 184 catalogues .. .. .. .. .. .. .. 182 example of latitude by circum-meridian .. .. .. 189 observation of a at daybreak .. .. .. .. .. 258 Stars, choosing pairs of .. .. .. .. .. .. 182 circum-meridian altitudes of .. .. .. .. ,. 180 method of observing .. .. .. .. .. .. 184 preparing ground for observations of .. .. .. .. 183 pairs of .. .. .. .. .. .. .. .. 181 Station, false .... .... 74 main .. .. .. .. .. .. .. .. 67 pointer .. .. .. .. .. ,. .. 18 caution as to use of .. .. .. .. 25 testing a .. 24 secondary .. .. .. .. .. .. .. 67 Stores for boats 47 Stowage of chronometers .. .. .. .. .. 40,229 Straight-edge 36 line, ruling a .. .. .. .. .. .. 99 Streams, observing tidal . . . . . . . . . . . . 155 Sumner's method .. .. .. .. .. .. ,. 256 Sun, equal altitudes of .. .. .. .. .. .. 207 latitude by circum-meridian altitudes of .. .. .. 195 Survey, general description of .. .. .. .. .. 51 general plan of . . . . . . . . . . . . 55 running .. ,. .. .. .. .. .. 114 replotting running ,. .. .. .. .. .. 115 INDEX. 359 PAGE Surveys, detailed . . . . . . . . . . . . . . 52 . ordinary .. .. .. .. .. .. .. 52 sketch 51 Suspicious ground . . . . . . . . . . . . . . 132 Sweeping for a rock .. .. .. .. .. .. .. 133 Swinging ship .. .. 294 Symbols 266 T. Table of reduction 150 Telegraphic meridian distance .. .. .. .. .. 218 example of 221 Temperature effect of change of on chronometers .. .. 226 Mouchez's correction for .. :. .. .. 234 of mean compensation .. ^ .. .. .. 226,235 ascertaining .. .. 235, 236 Hartnup's correction for .. .. .. 228, 235 Ten-foot pole 33 use of 121 extension of method of .. .. .. .. 125 Testing circle 24 station pointers .. .. .. .. .. .. 24 Theodolite, adjusting .. .. ,. .. .. ., .. 11 collimation error of .. .. .. .. .. 163 obtaining level error of .. .. .. .. .. 163 Thermometers, corresponding ... .. .. .. App. V. Tidal definitions 144 streams, observing .. .. .. .. .. .. 155 Tide, age of '.. .. .. .. 145 interpolating height of . . . . . . . . . . 150 pole .. 146 range of .. .. .. .. .. .. .. .. 144 rise of .. .. .. .. .. .. .. .. 144 Tides 143 graphic projection of . . . . . . . . . . . . 152 observing .. .. .. .. .. .. .. 147 Topography .. .. .. .. .. .. 157 Tracing paper in plotting .. .. .. .. .. .. 102 Travelling rate 200,220,223 Transfer paper, making .. .. .. .. .. .. 35 Transit of moon .. .. 146 points in .. .. .. .. .. .. .. 22 Triangles, correcting . . . . . . . . . . . . ... 80 Triangles, preparing for calculation . . . . . . . . . . 79 360 INDEX. PAGE Triangulation .. .. .. .. .. .. .. .. 53 by sextant .. .. .. .. .. .. 69 calculating .. .. .. ., .. .. 86 correcting to astronomical positions . . . . 90 definition of .. . .. .. .. .. 55,67 . kinds of ., ., . .. .. .. 67 main .. .. .. .. .. .. .. 67 Triangulations, calculated .. .. .. .. .. .. 67 example of . . . . . . . . 88 True bearing .. .. .. .. .. .. .. .. 241 by equal altitudes . . . . . . . . . . 242 by Pole star .. .. 139,250 by sextant 246 single altitude 242 for orientation . . . . . . . . . . . . 79 use of in plotting . . . . . . 103, 106 U. Undercurrents in deep sea sounding .. .. ., .. 286 observations on .. .. .. .. .. 288 Use of beacons .. ,. .. ., .. ,, .. 134 V. Valuing results of observations, method of .. .. .. .. 191 Variation 251 by swinging ship .. .. .. .. .. .. 297 shore observations for .. .. .. .. .. 252 Vernier, setting in equal altitudes .. .. .. .. 208 plate, setting of station pointers .. .. .. .. 24 Vigias, searching for .* .. .. .. .. .. .. 140 W. Water level, finding true mean .. .. .. .. .. 152 Water line, low 124 Whitewash - .. .. 42 Z. Zero, choosing a .. .. .. .. .. .. .. 70 verifying 73 LONDON: PRINTED BY WILLIAM CLOWKS AND SONS, LIMITED, UNIVERSITY 50 ALBEMARLE STREET, LONDON, January 1882. MR. MURRAY'S LIST OF WORKS IN GENERAL LITERATURE, CONTAINING THE SPEAKER'S COMMENTARY ON THE BIBLE. HISTORY, ANCIENT & MODERN. EDUCATIONAL WORKS. BIOGRAPHY, MEMOIRS, &c. GEOGRAPHY, VOYAGES, AND TRAVELS. HANDBOOKS FOR TRAVELLERS. THEOLOGY, RELIGION, &c. SCIENCE, NATURAL HISTORY, GEOLOGY, &c. ART, ARCHITECTURE, AND AN- POETRY, THE DRAMA, &C. NAVAL AND MILITARY WORKS. PHILOSOPHY, LAW, AND POLI- TICS. RURAL & DOMESTIC ECONOMY. 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MELVILLE'S Marquesas 75. 14. ABBOT'S Missionary in Canada. 2s. 15. Letters from Madras. 2s. 16. ST. JOHN'S Highland Sports. 35. 6d. 17. The Pampas. Sir F. HEAD. 2s. 1 8. FORD'S Spanish Gatherings. 33. 6d. 19. EDWARDS' River Amazon. 2s. 20. ACLAND'S India. 2s. 21. RUXTON'S RockyMountains. 3s6d 22. CARNARVON'S Portugal. 35. 6d. 23. HAYGARTH'S Bush Life. 2s. 24. ST. JOHN'S Libyan Desert. 2s. 25. Letters from Sierra Leone. 35. 6d DR. WM. SMITH'S ANCIENT ATLAS. AN ATLAS OF ANCIENT GEOGRAPHY, BIBLICAL AND CLASSICAL. Intended to illustrate the ' Dictionary of the Bible,' and the ' Dictionaries of Classical Antiquity.' Compiled under the superintendence of WM. SMITH, D.C.L., and GEORGE GROVE, LL.D. Folio, half-bound, 6: 6s. 1. Geographical Systems of the Ancients. 2. The World as known to the Ancients. 3. Empires of the Babylonians, Lydians, Medes, and Persians. 4. Empire of Alexander the Great. 5. 6. Kingdoms of the Successors of Alex- ander the Great. 7. The Roman Empire in its greatest extent. 8. The Roman Empire after its division into the Eastern and Western Empires. 9. Greek and Phoenician Colonies. 10. Britannia. 11. Hispania. 12. Gallia. 13. Germania, Rhaetia, Noricum. 14. Pseonia, Thracia, Moesia, Illyria, Dacia. 15. Italy, Sardinia, and Corsica. 16. Italia Superior. 17. Italia Inferior. 1 8. Plan of Rome. 19. Environs of Rome. 20. Greece after the Doric Migration. 21. Greece during the Persian Wars. 22. Greece during the Peloponnesian War. 23. Greece during the Achaean League. 24. Northern Greece. 25. Central Greece Athens. 26. Peloponnesus. With Plan of Sparta. 27. Shores and Islands of the /Egean Sea. 28. Historical Maps of Asia Minor. 29. Asia Minor. 30. Arabia. 31. India. 32. Northern Part of Africa. 33. ^Egypt and ^Ethiopia. 34. Historical Maps of the Holy Land. 35. 36. The Holy Land. North and South. 37. Jerusalem, Ancient and Modern. 38. Environs of Jerusalem. 39. Sinai. 40. Asia, to illustrate the Old Testament. 41. Map, to illustrate the New Testament. 42. 43. Plans of Babylon, Nineveh, Troy, Alexandria, and Byzantium. Index. INDEX. ABERCROMBIE'S Works - 20 Churton's Poetical Works 23 Giffard's Naval Deeds - 24 Acland's India I Classic Preachers 15 Gill's Ascension - 9, 16 Admiralty Manual - 16 ./Esop's Fables - 22 Clode's Military Forces 24 Martial Law 20 River of Golden Sand 8 Gladstone's Rome. 16 Agricultural Journal - 25 Coleridge's Table-Talk - 22 - Essays - - 20, 22 Albert (The) Memorial - 18 Speeches 21 Cookery 25 Cooke's Sketches - - 19 Gleig s Waterloo 5 Washington 5 Army Lists 24 Cook's Sermons - - 16 Glynne's Churches - 19 Austin's Jurisprudence - 20 Crabbe's Life and Works 23 Goldsmith's Works - 23 BARBAULD'S Hymns - 29 Crawford's Argo 23 Cripps on Plate 18 Gomm's Life 7 Grey's Wm. IVth - - 6 Barclay's Talmud - - 14 Barkley's Turkey - - 10 Croker's Geography - 29 Crowe's Flemish Painters 19 Grote's Histories 3 Works - - 20, 21 My Boyhood - - 25 Barrow's Autobiography 7 Painting in Italy - 19 Titian - - - 7, 19 Life - - - 7 Mrs. 7 Barry's (Sir C.) Life - 7, 20 (Canon), Witness for Christ - - - - 15 (E.) Architecture - 19 Bates' River Amazon - 1 1 Bax's Eastern Seas - 8 Cumming's South Africa 9, 25 Currie, Divinity of Christ 15 Curzon's Monasteries - 10 Curtius' Works - - 22 Gust's Annals of the Wars 24 HALLAM'S England - 4 Middle Ages - - 4 Literary History - 22 (Arthur), Remains - 23 Hall's English Grammar 28 Beckett's (Sir E.) Revised N. T. - - - - 15 Bees and Flowers - - 25 DARWIN'S Works 17 (Erasmus), Life - 8 Davy's Consolations 21 First Latin Book - 29 Hamilton's Rheinsberg - 6 Handbooks for Travellers 12,14 Bell's (Sir Charles) Letters 6 Bell's Tower of London 5 Salmonia 25 De Cosson's Blue Nile - 9 Hatch's Aristotle - - 21 Hatherley on Scripture - 15 Bertram's Harvest of the Dennfs' Etruria 19 Hayward's Statesmen - 6 Sea - - - - 17 Dent's Sudeley - - 5 Head's Engineer 24 Bible Commentary - 2 Bigg Wither's Brazil - 1 1 Bird's Sandwich Islands 10 Derby's Homer 23 Derry's Bampton 15 Deutsch's Talmud - 21 Burgoyne 7 Bubbles from Nassau n Stokers and Pokers 22 Japan - - - 9 Rocky Mountains - 10 Bisset's Sport in Africa 9, 25 Blackstone's Comments - 20 Blunt's Works - - 15 (Lady A.), Bedouins, &c. - - - - 10 Borrow's Works - n, 22 Dilke's Papers of a Critic 22 Douglas's Gunnery and Bridges 24 Horse-Shoeing - 25 Ducange's Dictionary - 21 Du Chaillu's Africa - 9 Midnight Sun - n Dufferin's High Latitudes n Heber's Poetical Works 15, 23 Herries' Life - - 6 Herschel's Memoir - 8 Hollway's Norway - n Home and Colonial Library 30 Homer's Iliad, Odyssey 23 Hook's Church Dictionary 14 Hook's (Theodore) Life 6 Boswell's Johnson - 7 Brewer's Studies 4, 5, 22, 27 British Association - 16 Speeches, &c. 20, 22 Duncan's Artillery - 5, 24 English in Spain - 5, 24 Hope's (B.) Worship - 16 Houghton's Monographs 6 Poetical Works - 23 Brugsch's Egypt 3 Bunbury's Geography - n Burbidge's Borneo 10, 17 Diirer, Albert - - 7, 19 EASTLAKE'S Essays - 7 Eldon's Life - - 8 Houstoun's Wild West - n Hutchinson's Dog-Breaking 25 Hutton's Principia Graeca 29 Burckhardt's Cicerone 12, 19 JAMESON'S Ital. Painters 7, 19 Burn's Nav. & Mil. Terms 24 Burrows' Constitution - 20 Ellis's Madagascar - 9 Jennings' Field Paths and Rambles - - u, 22 Buttmann's Works - 29 Buxton's Memoirs, &c. - 6 Buxton's Political Handbk. 20 Byles on Religion - - 15 Byron's Life 7 Poetical Works - 23 CAMPBELL'S Chancellors and Chief-Justices - 8 Ellis's Catullus - 23 Elphinstone's India - 5 Elphinstone's Turning - 17 Elton's Eastern Africa 9 Elze's Byron 7 English in Spain - - 5, 24 Essays on Cathedrals - 15 FERGUSSON'S Architec- Jervis's Gallican Church 4, 15 Jesse's Gleanings - - 17 Jex-Blake's Sermons - 16 Johnson's (Dr.) Life 7 Julian's Dictionary of Hymnology - - 14 Junius' Handwriting - 22 KERR'S Country House '20, 25 King Edward Vlth's Campbell's Napoleon - 7 Carnarvon's Athens - TO Agamemnon - - 23 Cartwright's Jesuits 4, 16 Cathedral (The) - - 15 Cathedrals of England i, 4, 19 Cesnola's Cyprus - TO, 18 tural Works - - 19 Forbes' Burma 8 Forsyth's Hortensius - 20 Novels and Novelists 21 Foss' Biographia Juridica 8 Frere's India and Africa 21 Deccan Days 22 Grammars 29 Kirk's Charles the Bold 4 Kirkes' Physiology - 17 Kugler's Italian Schools 19 German Schools - 19 LANE'S Modern Egyptians, 4, 9 Chaplin's Benedicite - 16 GALTON'S Art of Travel n Lawrence's Reminiscences 7 Chisholm's Polar Seas - n Choice of a Dwelling 20, 25 Geographical Journal - n George's Mosel & Loire n Layard's Nineveh 9 Leathes' Heb. Grammar 29 Church and the Age - 15 Gibbon's Roman Empire 3, 27 Leslie's Hbk. for Painters 19 Index. Levi's British Commerce 21 Lex Salica 21 OWEN'S Modern Artillery 24 Oxenham's Latin Elegiacs 29 Somerville's Physical Sciences, &c. - - - !6, 18 Liddell's Rome - - 3, 27 Lispings from Low Lati- tudes 22 Little Arthur's England 27 Livingstone's Travels - 9 T T FACET'S Crimea - - 24 Palgrave's Taxation - 21 Palliser's Monuments - 22 Parkyns' Abyssinia - 9 South 's Household Sur- gery - - - !7 ; 2 J Stael, Madame de - - 6 Stanhope's Histories - 5 Pitt ... 6 Life 6 Livingstonia o Loch's China 5 Percy's Metallurgy - 16 Perry's St. Hugh - - 6 Miscellanies - - 22 Retreat from Mos- Lockhart's Spanish Ballads 23 Loudon's Gardening - 25 Lyell's Works - - 18 Life ... 8 Lyell's Handbook of Ferns 17 Lytton's Julian Fane - 6 M'CLINTOCK'S Arctic Seas n Phillip's Literary Essays 22 Philosophy in Sport - 16 Pollock's Family Prayers 14 Pope's Works 23 Porter's Damascus - 10 Prayer-Book - - - 14 Privy Council Judgments 21 Puss in Boots 29 cow - - - 5, 22 Stanley's Sinai - - 10 Bible in Holy Land 10 Eastern, Jewish, and Scottish Church - - 4, 16 Canterbury - - 4 Westminster Abbey 5 Sermons in East - 16 Macdougall's Warfare - 24 Macgregor's Rob Roy - 10 QUARTERLY Review - 21 the Beatitudes - 16 Madras, Letters from - 8 Mahon's Belisarius - 7 RAE'S Barbary 9 White Sea - - n Arnold 6 Corinthians - - 16 Maine's (Sir H. S.) Works 21 Malcolm's Persia - - 10 Mansel's Lectures 21 Bampton Lectures - 15 Letters, Reviews, &c. 21 Marco Polo's Travels - 8 Markham's Histories - 27 (C. R.), Cinchona - 25 Marryat's Pottery - - 18 Masters in Theology - 15 Matthiae's Greek Gram. 29 Mayo's Sport in Abyssinia 9, 25 Meade's New Zealand - 10 Rassam's Abyssinia - 9 Rawlinson's Herodotus 3 Ancient Monarchies 3 Russia in the East 10, 20 Redcliffe (Lord S. de), East- ern Question - - 20 Reed's Shipbuilding, &c. 16 - Japan - - 9 Rejected Addresses - 23 Reynold's Life 7 Ricardo's Works - - 21 Robertson's Church His- tory - 4 15 Christian Institutions 15 Stevens's Madame de Stael 6 Stephens's Chrysostom - 6 Stories for Children - 29 Street's Architectural Works 19 Stuart's Nile - 3, 9, 18 Student's Manuals ; i 14, 26, 28 Sumner's Life 6 Swainson's Creeds - 15 Swift's Life 7 Sybel's French Revolution 5 Symonds' Records of the Rocks 18 Melville's Typee and Omoo 10 Meredith's New So. Wales 10 Michel Angelo - - 7, 19 Middleton's Rembrandt 19 Millington's Land of Ham 14 Milman's Histories - 4, 16 Robson's School Archi- tecture 20 Robinson's Palestine 10, 15 Physical Geography 18 (W.), Alpine Flowers 25 Sub-Tropical Garden 25 TEMPLE'S India - - 8, 21 Thibaut's Musical Art 19 Thielmann's Caucasus - 10 Thomson's Sermons 15, 16 Titian's Life and Times 7, 19 Tocqueville's France - 5 St. Paul's - - s, 14 Wild Garden - - 25 Christianity - - 4, 16 Latin Christianity - 4, 14 Fall of Jerusalem - 23 Rochester's (Bp.) Charge, 1881 - - - - 15 Rowland's Constitution 20 Tozer's Turkey & Greece 10 Tristram's Land of Moab 10 Great Sahara Q Horace - - - 7, 23 (Bishop), Life of - 6 Mivart's Essays - - 17 The Cat - - 17 Moore's Life of Byron - 7 Moresby's New Guinea 10 Mossman's Japan - - 8 Motley's Histories - 4 Barneveld - - 4, 6 Mounsey's Satsuma Rebel- Laws of Nature - 20 ST. JAMES' Lectures - 15 St. John's Wild Sports - 25 Libyan Desert - 9 Saldanha's Memoirs - 7 Sale's Brigade in Affghan- istan - - - - 5 Scepticism in Geology - 18 Schliemann's Troy and Truro (Bp. of), The Cathe- dral, &c. - - 15 Turkey, Lady's Life in - 10 Tylor's Primitive Culture 21 Tylor's Hist, of Mankind 21 VAN LENNEP'S Asia Minor 9 Bible Lands 15 Vatican Council - - 16 Virchow's Freedom of Mycenai - - 9, 18 Mozley's Predestination 15 Muirhead's Vaux-de-Vire 23 Murchison's Siluria - 18 Schomberg's Odyssey - 23 School and Prize Books - 29 Scott's Architecture - 19 Science 17 WAGE'S Gospel and its Witnesses - - - 14 Memoirs - - 8 Music and Dress - - 2^ Seebohm's Siberia - n, 17 Selborne on the Liturgy 4, 15 Weigall's Princess Char- lotte 6 Musters' Patagonians - n NAPIER'S English Battles 5 Nautical Almanack - 24 Shadows of Sick Room - 15 Simmons' Court-Martial 20 Smiles' Popular Biographies and Works Wellington's Despatches 5, 24 White's Naval Architecture 24 Whymper's Matterhorn - n Wilberforce's Life - - 6 Navy List - - - 24 New Testament - - 14 Newth's Works on Science 16 Nicholls, Sir G., Poor Laws 21 Nicolas' Historic Peerage 5 Nile Gleanings (Stuart) 3, 9, 18 5, 6, 8, 18, 22, 25, 29 Smith (Dr. G.), Geography of India 8 Smith (P.) Ancient History 3,4 Smith's (Dr. Wm.) Diction- aries ^ 3, 4, 6, 7, n, 14, 26 Wilkinson's Egyptians - 3 Wilson's Life and Diary 7 ^ (Dr. John), Life of 6 Wilson's Michel Angelo - 7, 19 Wood's Oxus - - 8 Words of Human Wisdom 22 Nimrod - - - - 25 Ancient Atlas 11,30 Nordhoff's Communistic Educational Course 3, 28 YOUNG'S Nyassa 9 Societies - - n, 20 Smaller Histories 16, 26 Yule's Marco Polo - - 8 Northcotes's Note-Book 5 Somerville's Life 8 (A. F.), Crete - - 21 RETURN TO: CIRCULATION DEPARTMENT 198 Main Stacks LOAN PERIOD 1 Home Use 2 3 4 5 6 ALL BOOKS MAY BE RECALLED AFTER 7 DAYS. - Renewals and Recharges may be made 4 days prior to the due date. Books may be renewed by calling 642-3405. DUE AS STAMPED BELOW. IG 2 2003 MUM 2 2004 f JUlV w . . 1, '*>* :"* ' ' \ V - ; ^ " ' . ; FORM NO. DD6 UNIVERSITY OF CALIFORNIA, BERKELEY 50M 5-02 Berkeley, California 94720-6000