# Marks and Beacons

MARKS AND BEACONS Every survey must have fixed objects which are first plotted on the sheets, technically known as "points." Natural marks of all kinds are utilized, but these must be supplemented by white wash marks, cairns, flags, etc. On low coasts and islets flag staffs upwards of ioo ft. high made of several spars lashed together must sometimes be erected in order to get the necessary range of vision. A fixed beacon can be erected in shallow water by constructing a tripod of spars about 45 ft. long. The heads of two of them are lashed together and the heels kept open at a fixed distance by a plank nailed at about 5 ft. above the heels of the spars. These are taken out by three boats and the third tripod leg lashed in position on the boats, the heel in the opposite direction to the other two. The first two legs, weighted, are let go together; using the third leg as a prop, the tripod is hauled into position and secured by guys and by additional weights. A vertical pole with bamboo and flag, the heel being weighted, is lashed to the fork.

## Floating Beacons.

These as a rule are specially constructed to carry a flag 12 to 16 ft. square on a bamboo from 3o to 35 ft. long. The beacon is secured to an anchor by means of chain or wire moorings and is visible under good conditions for a distance of about 5 o miles. A beacon has been moored by sounding wire in depths of 3,00o fathoms with a weight of ioo lb.

## Fixing.

In nautical surveying a thorough knowledge of the principles involved in a station-pointer fix is essential. The method of fixing by two angles between three fixed points is generally known as the "two-circle method," but there are really three circles involved. The "station-pointer" is the instrument used for plotting fixes. Its construction depends upon the fact that angles subtended by the chord of a segment of a circle measured from any point in its circumference are equal. The lines joining three fixed points form the chords of segments of three circles, each of which passes through the observer's position and two of the fixed points. The more rectangular the angle at which the circles inter sect each other, and the more sensitive they are, the better will be the fix; one condition is useless without the other. A circle is "sensitive" when the angle be tween the two objects responds readily to any small movement of the observer towards or away from the centre of the circle passing through the observer's position and the objects. This is most markedly the case when one object is very close to the observer and the other very dis tant, but not so when both ob jects are distant. In the accom panying diagrams A, B, C are the objects, and X the observer. Fig. i shows the circle passing through C, B and X, cutting the circle ABX at a good angle, and therefore fixing X independently of the circle CAX, which is less sensitive, but being nearly tangential they give no cut with each other. The third cuts both at right angles; it is, however, far less sensitive, and for that reason if the right and left hand objects are both distant the fix must be bad. In such a case as this, because the angles CBX, BXA are both so sensitive, and the accuracy of the fix depends on the precision with which the angle CXA is measured, that angle should be observed direct, together with one of the other angles composing it. Fig. 3 rep resents a case where the points are badly disposed, approaching the condition known as "on the circle," passing through the three points. All three circles cut one another at such a fine angle as to give a very poor fix. The centre of the station-pointer could be moved considerably without materially affecting the coincidence of the legs with the three points. To avoid a bad fix the following rules are safe..

Choose objects disposed as follows: (a) One outside object dis tant and the other two near, the angle between the two near ob jects being not less than 3o° or more than 140°. The amount of the angle between the middle and distant object is immaterial. (b) The three objects nearly in a straight line, the angle between any two being not less than 3o°. (c) The observer's position being inside the triangle formed by the objects.

A fix on the line of two points in transit, with an angle to a third point, becomes more sensitive as the distance between the transit points increases relatively to the distance between the front transit point and the observer ; the more nearly the angle to the third point approaches a right angle, and the nearer it is situated to the observer, the better the fix. If the third point is at a long distance, small errors either of observation or plotting will affect the result considerably.

Tracing-paper answers exactly the same purpose as the station pointer. The angles are laid off from a centre representing the position, and the lines brought to pass through the points as before. This has often to be used, as when points are close together on a small scale the central part of the station-pointer will often hide them and prevent the use of the instrument. The use of tracing paper permits any number of angles to different points to be laid down on it, which under certain conditions of fixing is sometimes an advantage.

## Bases.

Marine surveys are founded upon triangulation and measured bases of some description, yet when plotted irregularly the system of triangles is not always apparent. The triangulation ranges from the rough triangle of a running survey to the carefully formed triangles of detailed surveys. The measured base for an extended survey is provisional only, the scale resting ultimately mainly upon the astronomical position observed as its extremes. In the case of a plan the base is absolute. The main triangulation establishes a series of points known as main stations, from which and to which angles are taken to fix other stations. A sufficiency of secondary stations enables the detail of the chart to be filled in between them. The points embracing the area to be worked on, having been plotted, are transferred to field boards, upon which the detail of the work in the field is plotted ; when complete the work is traced and re-transferred to the plotting sheet, which is then inked in as the finished chart, and is graduated on the gno monic projection on the astronomical positions of two points situated near opposite corners of the chart.

The kind of base ordinarily used is one measured by a steel tape of i oo or Soo ft. length on flat ground of convenient length, between two points visible from one another and so situated that a triangulation can be extended from them to embrace other points in the survey. The error of the steel tape is noted before leaving the ship, and again on returning, by comparing its length with a standard. The correction so found, also corrections for tempera ture, sag, etc., are applied to obtain the final result. A masthead angle base is at times useful for small plans, etc., when circum stances do not permit of a base being measured on shore. The height of the masthead to the water line being known the simple calculation necessary to obtain the distance is easily computed.

## Astronomical Base.

The difference of latitude between two stations visible from each other and nearly in the same meridian, combined with their true bearings, gives an excellent base for an extended triangulation; the only drawback to it is the effect of local attraction of masses of land in the vicinity on the pendulum, or, in other words, on the mercury in the artificial horizon. The base stations should be as far apart as possible, in order to mini mize the effect of any error in the astronomical observations. The observation spots would not necessarily be actually at the base stations, which would probably be situated on summits at some little distance in order to command distant views. In such cases each observation spot would be connected with its corresponding base station by a subsidiary triangulation, a short base being meas ured for the purpose. If possible, the observation spots should be east or west of the mountain station from which the true bearings are observed.

If the base stations A and B are so situated that by reason of distance or of high land intervening they are invisible from one another, but both visible from some main station C between them, when the main triangulation is completed, the ratio of the sides AC, BC can be determined. From this ratio and the observed angle ACB, the angles ABC, BAC can be found. The true bearing of the lines AC or BC being known, the true bearing of the base stations A and B can be deduced.

## Extension of Base.

A base of any description is seldom long enough to plot from directly, and in order to diminish errors of plotting it is necessary to begin on the longest side possible so as to work inwards. A short base measured on flat ground will give a better result than a longer one measured over inequalities, pro vided that the triangulation is carefully extended by means of judiciously selected triangles, great care being taken to plumb the centre of each station. To facilitate the extension of the base in as few triangles as possible, the base should be placed so that there are two stations, one on each side of it, subtending angles at them of from 3o° to 4o°, the distances between which, on being cal culated in the triangles of the quadrilateral so formed, will consti tute the first extension of the base. Similarly, two other stations placed one on each side of the last two will form another quad rilateral, giving a yet longer side, and so on.

## Main Triangulation.

The angles to be used in the main triangulation scheme must be very carefully observed and the theodolite placed exactly over the centre of the station. Main angles are usually repeated several times by resetting the vernier at intervals equidistant along the arc, in order to eliminate instru mental errors as well as errors of observation. The selection of an object suitable for a zero is important. It should, if possible, be another main station at some distance, but not so far or so high as to be easily obscured, well defined, and likely to be permanent. Angles to secondary stations should be repeated. Rough sketches from all stations with angles are of great assistance in identifying objects from different points of view.

## False Station.

When the theodolite cannot for any reason be placed over the centre of a station, if the distance be measured and the theodolite reading of it be noted, the observed angles may be reduced to what they would be at the centre of the station. False stations have frequently to be made in practice; a simple rule to meet all cases is of great assistance to avoid the possibility of error in applying the correction with its proper sign It may very easily be found as follows.

Rule.—Put down the theodolite reading which it is required to correct (increased if necessary by 36o°), and from it subtract the theodolite reading of the centre of the station. Call this remainder 0. With 0 as a "course" and the number of feet from the theodolite to the station as a "distance," en ter the traverse table and take out the greater increment if 0 lies between 45° and 135°, or be tween 225° and 315°, and the lesser increment for other angles.

The accompanying diagram (fig.

4) will assist the memory. Refer this increment to the "table of subtended angles by various lengths at different distances" (using the distance of the object observed) and find the corre sponding correction in arc, which mark + or — according as 0 is under or over 180°. Apply this correction to the observed theodo lite angle. A "table of subtended angles" is unnecessary if the formula The difference of the reciprocal true bearings between two stations is called the "convergency." The formula for calculating it is : Cony. in minutes = dist. in sea miles X sin. Merc. bearing X tan. mid. lat. Whenever true bearings are used in triangulation, the effect of convergency must be considered and applied. In north latitudes the southerly bearing is the greater of the two, and in south latitudes the northerly bearing. The Mercatorial bearing between two stations is the mean of their reciprocal true bearings.

## Triangulated Coast Survey.

After a preliminary run over the ground to note suitable positions for stations on prominent headlands, islands and summits not too far back from the coast, and, if no former survey exists, to make at the same time a rough plot of them by compass and patent log, a scheme must be formed for the main triangulation with the object of enclosing the whole survey in as few triangles as possible, regard being paid to the limit of vision of each station due to its height, to the existing meteorological conditions, to the limitations imposed by higher land intervening, and to its accessibility. The triangles decided upon should be well-conditioned, taking care not to introduce an angle of less than 3o° to 35°, which is only permissible when the two longer sides of such a triangle are of nearly equal length, and when the determination of this length does not depend on the short side. In open country the selection of stations is a com paratively easy matter, but in country densely wooded the time occupied by a triangulation is largely governed by the judicious selection of stations quickly reached, sufficiently elevated to command distant views, and situated on summits capable of being readily cleared of trees in the required directions, an all-round view being, of course, desirable though not always attainable. The positions of secondary stations will also generally be decided upon during the preliminary reconnaissance. The object of these sta tions is to break up the large primary triangles into triangles of smaller size, dividing up the distances between the primary sta tions into suitable lengths; they are selected with a view to greater accessibility than the latter, and should therefore usually be near the coast and at no great elevation. Upon angles from these will depend the position of the coastline marks, to be erected and fixed as the detailed survey of each section of the coast is taken in hand. The nature of the base to be used, and its position in order to fulfil the conditions specified under the head of Bases must be considered, the base when extended forming a side of one of the main triangles. It is immaterial at what part of the survey the base is situated, but if it is near one end, a satisfactory check on the accuracy of the triangulation is obtained by comparing the length of a side at the other extreme of the survey, derived by calculation through the whole system of triangles with its length deduced from a check base measured in its vicinity. It is generally a saving of time to measure the base at some anchorage or harbour that requires a large scale plan. The triangulation involved in ex tending the base to connect it with the main triangulation scheme can thus be utilized for both purposes, and while it is being cal culated and plotted the survey of the plan can be proceeded with. The bearings are observed at both ends of the survey and at other selected stations and the results subsequently compared. Astro nomical observations for latitude and longitude are obtained at observation spots near the extremes of the survey and are con nected with the primary triangulation; they are usually disposed at intervals of from 1 oo to i so m., and thus errors due to a tri angulation carried out with theodolites of moderate diameter do not accumulate to any serious extent.

## Calculating the Triangulation.

The triangles as observed being tabulated the angles of each triangle are corrected to bring their sum to exactly 180°. We must expect to find errors in the triangles, but under favourable conditions they will only amount to a few seconds. In distributing the errors we must consider the conditions under which the angles were observed; failing any particular reason to assign a larger error to one angle than to an other, the error must be divided equally. The various quadri laterals and polygons are then adjusted to make the whole trian gulation as rigid as possible and bring the whole network into agreement. The length of base being determined, the sides of all the triangles involved are calculated by the ordinary rules of trigonometry. Starting from the true bearing observed at one end of the survey, the bearing of the side of each triangle that forms the immediate line of junction from one to the other is found by applying the angles necessary for the purpose in the respective triangles, not forgetting to apply the convergency be tween each pair of stations when reversing the bearings. The bear ing of the final side is then compared with the bearing obtained by direct observation at that end of the survey. The difference is principally due to accumulated errors in the triangulation; half of the difference is then applied to the bearing of each side. Convert these true bearings into Mercatorial bearings by applying half the convergency between each pair of stations. With the lengths of the connecting sides found from the measured base and their Mercatorial bearing, the Mercatorial bearing of one observation spot from the other is found by middle latitude sailing. Taking the observed astronomical positions of the observation spots and first reducing their true difference longitude to departure, as measured on a spheriod from the formula then with the d. lat. and dep. the Mercatorial true bearing and distance between the observation spots is calculated by middle latitude sailing, and compared with that by triangulation and measured base. To adjust any discrepancy, it is necessary to con sider the probable error of the observation for latitude and merid ian distance ; within those limits the astronomical positions may safely be altered in order to harmonize the results; it is more im portant to bring the bearings into close agreement than the distance. From the amended astronomical position the Mercatorial true bearings and distance between them are re-calculated. The difference between this Mercatorial bearing and that found from the triangulation and measured base must be applied to the bearing of each side to get the final corrected bearings, and to the loga rithm of each side of the triangulation as originally calculated must be added or subtracted the difference between the logarithms of the distance of the amended positions of the observation spots and the same distance by triangulation.

Calculating Intermediate Astronomical Positions.—The latitude and longitude of any intermediate main station may now be calculated from the finally corrected Mercatorial true bearings and lengths of sides. The difference longitude so found is what it would be if measured on a true sphere, whereas we require it as measured on a spheroid, which is slightly less. The correction No. ft. in I m. of lat.

From the foregoing it is seen that ft. in i m. of long. • in a triangulation for hydrographical purposes both the bearings of the sides and their lengths ultimately depend almost entirely upon the astronomical observations at the extremes of the survey; the observed true bearings and measured base are consequently more in the nature of checks than anything else. It is obvious, therefore, that the nearer together the observation spots, the greater effect will a given error in the astronomical positions have upon the length and direction of the sides of the triangula tion, and in such cases the bearings as actually observed must not be altered to any large extent when a trifling change in the astro nomical positions might perhaps effect the required harmony. For the reasons given under Astronomical Base, high land near observation spots may cause very false results, which may of ten account for discrepancies when situated on opposite sides of a mountainous country.

## Plotting.

Great care is requisite in projecting on paper the points of a survey. The paper should be allowed to stretch and shrink as it pleases until it comes to a stand, being exposed to the air for four or five hours daily, and finally well flattened out by being placed on a table with drawing boards placed over it heavily weighted. If the triangulation and co-ordinates have been calcu lated beforehand throughout, it is more advantageous to plot by co-ordinates or distances rather than by chords. The main sta tions are thus got down in less time and with less trouble, but these are only a small proportion of the points to be plotted, and if chords or distances are used long lines must be ruled between the stations as zeros for plotting ,other points by chords. In ruling these lines care must be taken to draw them exactly through the centre of the pricks denoting the stations, but, however, carefully drawn, there is liability to slight error in any line projected to a point lying beyond the distance of the stations between which the zero line is drawn. In plotting by distances, therefore, all points that will subsequently have to be plotted by chords should lie well within the area covered by the main triangulation. Three distances must be Measured to obtain an intersection of the arcs cutting each other at a sufficiently broad angle; the plotting of the main stations once begun must be completed before distortion of the paper can occur from change in the humidity of the atmos phere. Plotting, whether by distance or by chords, must be begun on as long a side as possible, so as to plot inwards, or with de creasing distances. In plotting by chords it is important to remember in the selection of lines of reference (or zero lines), that that should be preferred which makes the smallest angle with the line to be projected from it, and of the angular points those nearest to the object to be projected from them.

## Irregular Methods of Plotting.

In surveys for the ordinary purposes of navigation, it may happen that a regular system of triangulation cannot be carried out ; the judicious use of the ship in such cases is often essential, and with proper care excellent results may be obtained. A few examples will best illustrate some of the methods used, but circumstances vary in every survey. Fixing a position by means of the "back-angle" is one of the most ordinary expedients. Angles having been observed at A, to the station B, and certain other fixed points of the survey, C and D for instance ; if A is shot up from B, at which station angles to the same fixed points have been observed, then it is not necessary to visit those points to fix A. For instance, in the triangle ABC, two of the angles have been observed, and therefore the third angle at C is known (the three angles of a triangle being equal to 18o° ), and it is called the "calculated or back-angle from C." A necessary condition is that the receiving angle at A, between any two lines (direct or calculated), must give a good cut; also the points from which the "back-angles" are calculated should not be situated at too great distances from A, relatively to the distance between A and B. A station may be plotted by laying down the line to it from one station, and then placing on tracing-paper a number of the angles taken at it, including the angle to the station from which it has been observed. If the points to which angles are taken are well situated, a good position is then obtained. Sometimes the main stations must be carried on with a point plotted by only two angles. An effort must be made to check this subsequently by getting an "angle back" from stations dependent upon it to some old well-fixed point ; failing this, two stations being plotted with two angles, pricking one and laying down the line to the other will afford a check. A well-defined mountain peak, far inland and never visited, when once it is well fixed is of ten invaluable in carrying on an irregular triangulation, as it may remain visible when all other original points of the survey have disappeared, and "back-angles" from it may be continually obtained, or it may be used for plotting on true bearing lines of it. In plotting the true bearing of such a peak, the convergency must be found and applied to get the reversed bearing, which is then laid down from a meridian drawn through it ; of the reversed bearing of any other line already drawn through the peak being known, it may simply be laid down with that as a zero. A rough position of the spot from which the true bearing was taken must be assumed in order to calculate the convergency. Fig. 5 will illustrate the foregoing marks. A and B are astronomical observation spots at the extremes of a survey, from both of which the high inaccessible peak C is visible. D, E, F are intermediate stations; A and D, D and E, E and F, F and B being tively visible from each other. G is visible from A and D, and C is visible from all stations. The latitudes of A and B and meridian distance between them being determined, and the true bearing of C being observed from both observation spots, angles are observed at all the stations. ing the spheroidal correction from the formula, correction = d.

d. long. between A and B to obtain the spherical d. long. ; with this spherical d. long. and the d. lat., the Mercatorial true bear ing and distance is found by middle latitude sailing (which is an equally correct but shorter method than by spherical trigonometry, and may be safely used when dealing with the distances usual between observation spots in nautical surveys). The convergency is also calculated, and the true bearing of A from B and B from A are thus determined. In the plane triangle ABC the angle A is the difference between the calculated bearing of B and the observed bearing of C from A. The distance AB having been calculated, the side AC is found. Laying down AC on the paper on the required scale, D is plotted on its direct shot from A, and on the angle back from C,• calculated in the triangle ACD. G is plotted on the direct shots from A and D, and on the angle back from C, calculated either in the triangle ACG or GCD.

The perfect intersection of the three lines at G assures these f our points being correct. E. F and B are plotted in a similar manner. The points depend on calculated angles, and except for the first four points we have no check, either on the accuracy of the angles observed in the field or on the plotting. Another well-defined ob ject in such a position, for instance as Z, visible from three or more stations, would afford the necessary check, if lines laid off to it from as many stations as possible gave a good intersection. If no such point, however, exists a certain degree of check on the angles observed is derived by applying the sum of all the calculated angles at C to the true bearing of A from C (found by reversing observed bearing of C from A with convergency applied), which will give the bearing of B from C. Reverse this bearing with con vergency applied, and compare it with the observed bearing of C from B. If the discrepancy is but small, it will be a strong pre sumption in favour of the substantial accuracy of the work. If the calculated true bearing of B from A be now laid down, it is very unlikely that the line will pass through B, but this is due to the discrepancy which must always be expected between astro nomical positions and triangulation. If some of the stations be tween A and B require to be placed somewhat closely to one an other, it may be desirable to obtain fresh true bearings of C instead of carrying on the original bearing by means of the calculated angle. In all cases of irregular plotting the ship is very useful, especially if she is moored taut without the swivel, and angles are observed from the bow. Floating beacons also assist an irregular triangulation.

## Sketch Surveys.

Surveys of various degrees of accuracy are included among sketch surveys. The roughest description is the running survey, when the work is done by the ship steaming along the coast, fixing points, and sketching in the coast-line by bearings and angles, relying for her position upon her courses and distances as registered by patent log, necessarily regardless of the effect of wind and current and errors of steering. At the other extreme comes the modified running survey, which in point of practical accuracy falls little short of that attained by irregular triangula tion. Some of these modifications will be briefly noticed. A running survey of a coast-line between two harbours, that have been surveyed independently and astronomically fixed, may often be carried out by fixing the ship on the points already laid down on the harbour surveys and shooting up prominent intermediate natural objects, assisted by theodolite angles. Theodolite lines to the ship and floating beacons suitably placed, materially increase the value of any such work. A sketch survey of a coast upon which it is impossible to land may be carried out by dropping beacons at intervals of about 8 m., well out from the land and placed abreast prominent natural objects called the "breastmarks," which must be capable of recognition from the beacons anchored off the next "breastmark" on either side. The distance between the bea cons is found by running a patent log both ways, noting the time occupied by each run; if the current has remained constant, a tolerably good result can be obtained. At the first beacon, angles are observed between the second beacon and the two "breast marks," and "intermediate" mark, and any other natural object which will serve as "points." At the second beacon, angles are observed between the first beacon and the same objects as before. Plotting on the line of the two beacons as a base, all the points observed can be pricked in on two shots. At a position about mid way between the beacons, simultaneous angles are observed to all the points and laid off on tracing-paper, which will afford the necessary check, and the foundation is thus laid for filling in the detail of coast-line, topography, and soundings off this particular stretch of coast. Each section of coast is complete in itself on its own base; the weak point lies in the junction of the different sec tions, as the patent log bases will not agree precisely, and the scales of adjacent sections are liable to be slightly different. This is obviated, as far as possible, by fixing on the points of one section and shooting up those of another, which will check any great irregularity of scale creeping in. The bearing is preserved by getting occasional true bearing lines at the beacons of the most distant point visible. In all cases of using angles from the ship under weigh, several assistants are necessary, so that the principal angles may be taken simultaneously, the remainder being con nected immediately afterwards with zeros involving the smallest possible error due to the ship not being absolutely stationary, these zeros being included amongst the primary angles. When close to a beacon, if its bearing is noted and the distance in feet obtained from its elevation, the angles are readily reduced to the beacon itself. Astronomical positions by twilight stars keep a check upon the work.

Sketch Surveys by Compass Bearings and Vertical Angles.—In the case of an island culminating in a high, well defined summit visible from all directions, a useful and accurate method is to steam round it at a sufficient distance to obtain a true horizon, stopping to make as many stations as may be desirable, and fixing by compass bearing of the summit and its vertical angle. The height is roughly obtained by shooting in the summit, from two positions on a patent log whilst approaching it. With this approximate height and Lecky's vertical danger angle tables, each station may be plotted on its bearing of the summit. From these stations the island is shot in by angles between its tangents and the summit, and angles to any other natural features, plotting the work as we go on any convenient scale which must be con sidered only as provisional. On completing the circuit of the island, the true scale is found by measuring the total distance in inches on the plotting sheet from the first to the last station, and dividing it by the distance in miles between them as shown by patent log. The final height of the summit bears to the rough height used in plotting the direct proportion of the provisional scale to the true scale. This method may be utilized for the sketch survey of a coast where there are well-defined peaks of sufficient height at convenient intervals, and would be superior to an ordinary running survey. From positions of the ship fixed by bearings and eleva tion of one peak, another farther along the coast is shot in and its height determined; this second peak is then used in its turn to fix a third, and so. on. Lecky's tables will show what effect an error of say I' in altitude will produce for any given height and distance, and the limits of distance must depend upon this consideration.

## Surveys of Banks out of Sight of Land.

On striking shoal soundings unexpectedly, the ship may either be anchored at once and the shoal sounded by boats starring round her, using compass and masthead angle ; or if the shoal is of large extent and may be prudently crossed in the ship, it is a good plan to get two beacons laid down on a bearing from one another and patent log distance of 4 or 5 m. With another beacon (or mark-boat, carrying a large black flag on a bamboo 3o ft. high) fixed on this base, forming an equilateral triangle, and the ship anchored as a fourth point, sound ings may be carried out by the boats fixing by station-pointer. The ship's position is determined by observations of twilight stars.

## Coastlining.

In a detailed survey the coast is sketched in by walking along it, fixing and plotting at intervals. Fixed marks along the shore afford a check on the minor coast-line fixes. When impracticable to fix in the ordinary way subtense methods are used. Greater accuracy is obtained if the work is plotted on the field board at once; this is not always possible but the angles being registered and sketches made of the intervening coast the work may be plotted afterwards. It is with the high water line that the coast-liner is chiefly concerned, delineating its character according to the accepted symbols. The sounder is responsible for the position of the dry line at low water. Heights of cliffs, rocks, islets, etc., must be inserted either from measurement or from the formula, and details of topography near the coast, including roads, houses and enclosures must be shown. Rocks above water or on which the sea breaks should be fixed. Coast-line may be sketched from a boat off shore by fixing and shooting up natural objects from selected positions.

## Soundings.

The most important feature of a chart is the sounding, and the more complete this is the better is the survey.

Small scale surveys are apt to be misleading ; such a survey may appear closely sounded but in reality it sometimes fails to dis close indications of shoal water. Sounding may be commenced as soon as sufficient points are plotted ; but off an intricate coast it is better to get the coast-line in first. Lines of soundings are run by the boats perpendicular to the coast, at a distance apart governed by the scale ; five lines to the inch is about as close as can be run without overcrowding. The distance apart will vary with the depth of water and the nature of the coast; for instance a rocky coast with shallow water off it will need closer examination than a steep coast. The prolongation of a point under water will require special care to ensure the fathom lines being correct. When soundings begin to decrease to seaward intermediate lines or lines crossing those previously run should be obtained. If pos sible lines of soundings should be run on transits ; these may generally be picked up by fixing when on the required line, noting the angle on the protractor between the line and some fixed mark on the field board, then placing the angle on the sextant and noting what objects intersect at that angle. On large scale sur veys it may be necessary to place transit marks in the required positions. The boat is fixed by two angles, with an occasional third angle as a check; the distance between the fixes is dependent upon the scale of the chart and the rapidity with which the depth alters; the 3, 6 and 1 o fathom lines should always be fixed, allow ing roughly for the tidal reduction. The nature of the bottom must be taken every few casts and recorded. It is best to plot each fix on the sounding board at once, joining the fixes by straight lines and numbering them for identification. The tidal reduction being obtained, the reduced soundings corrected for any lead line error are written in the field-book in red underneath each sounding as originally noted ; they are then placed in their proper position on the board between the fixes. Suspicious ground should be closely examined; a small buoy anchored on the shoal is useful to guide the boat while trying for the least depth. Sweeping for a reported pinnacle rock should be resorted to when sounding fails to discover it. Local information from fishermen and others is often of value. Up to depths of about 15 fathoms the hand lead-line is used from the boats, but beyond that depth the Lucas machine for wire effects a great saving of time and labour. The deeper soundings of a survey are usually obtained from the ship, but steamboats with wire sounding machines often assist very materially. By the aid of a steam winch, a i oo-lb. lead is hove forward to the end of the lower boom rigged out, from which it is dropped by reversing the winch, soundings of 5o fathoms may be picked up from the sounding platform aft, whilst going at a speed of 5 to 6 knots. In deeper water it is quicker to stop the ship and sound from aft with the wire sounding machine. In running lines of soundings on and off shore, it is essential to be able to fix as far from the land as possible. Angles will be taken from aloft for this purpose, and floating beacons dropped in selected positions will be of assistance. A single fixed point on the land used in conjunction with two beacons suitably placed will give an admirable fix.

## Echo Sounding.

This method of obtaining the depth is likely to prove of increasing value as time goes on and its efficiency be comes known. Tie principle is that an electric impulse is trans mitted from the bottom of a ship, strikes the bed of the ocean and is reflected as an' echo which is received by a hydrophone. The sound waves are sent out at fixed intervals and the echo is heard in telephone receivers connected with the hydrophone. The velocity of sound in water being known the depth can be alcu lated provided the time interval is accurately measured. A hand wheel, working a depth scale and connected with the telephonic gear is manipulated until echoes are heard in the receiver; the depth can then be read off the circular scale.

The Admiralty echo sounding apparatus shallow water type is designed to register depths of from 3 to 120 fathoms; for greater depths a modified form of echo gear is utilized. The saving of time is particularly noticeable where great depths are being obtained, the echo gear giving a result in a few seconds, whereas with a wire sounding machine the operation is a lengthy proceed ing of ten occupying more than an hour. The disadvantage of echo sounding is that it is impossible to determine the nature of the bottom by this means and where a survey is in progress this must be obtained with the lead.

## Vigias..

A certain percentage of vigias which are reported and placed on the charts eventually turn out to have no existence, but before it is possible to expunge them the area has to be examined. Submarine banks rising from great depths necessarily stand on bases many square miles in area. Of recent years our knowledge of the angle of slope that may be expected to occur at different depths has been much extended. From depths up wards of 2,000 fathoms the slope is so gradual that a bank could hardly approach the surface in less than 7 m. from such a sound ing; therefore anywhere within an area of at least 15o sq.m. all round a bank rising from these depths, a sounding must show some decided indications of a rise in the bottom. Under such cir cumstances, soundings at intervals of 7 m., and run in parallel lines 7 m. apart, enclosing areas of only 5o sq.m. between any four adjacent soundings, should clear up the ground and lead to the discovery of any shoal. As the depth decreases the angle of slope rapidly increases, and a shoal might occur within three quarters of a mile or even half a mile of such a sounding as 500 fathoms. An appreciation of these facts will indicate the distance apart at which it is proper to obtain soundings. Contour lines will show in which direction to prosecute the search. When once a decided indication is found, it is not difficult to follow it up by paying attention to the contour lines as developed by successive soundings. Discoloured water, ripplings, fish jumping or birds hovering about may assist in locating a shoal, but the submarine sentry towed at a depth of 4o fathoms is here most valuable, and may save hours of hunting. Reports being more liable to errors of longitude than of latitude, a greater margin is necessary in that direction. Long parallel lines east and west are preferable, but the necessity of turning the ship more or less head to wind at every sounding makes it desirable to run the lines with the wind abeam, which tends to disturb the dead reckoning least. The current should be allowed for in shaping the course to preserve the parallelism of the lines, but the less frequently the course is altered the better. A good position should be obtained at morning and evening twilight by pairs of stars on opposite bearings, the lines of position of one pair cutting those of another pair nearly at right angles. The dead reckoning should be checked by lines of position from observations of the sun about every two hours throughout the day, preferably whilst a sounding is being obtained and the ship stationary.

## Tides.

The datum for reduction of soundings is mean low water springs, the level of which is referred to a permanent bench mark in order that future surveys may be reduced to the same datum level. Whilst sounding is going on the height of the water above this level is observed by a tide gauge. The time of high water at full and change, called the "establishment," and the heights to which spring and neap tides respectively rise above the datum are also required. It is seldom that a sufficiently long series of observations can be obtained for their discussion by harmonic analysis, and therefore the graphical method is preferred. A good portable automatic tide gauge suitable for all requirements is much to be desired.

Tidal streams and surface currents are observed from the ship or boats at anchor by means of a current log. An alternative method is to follow a drifting buoy fixing the position at intervals. Tidal streams often run for some hours after high or low water by the shore ; it is important to determine whether the change of stream occurs at a regular time of the tide.

Undercurrents are also of importance. A deep-sea current meter devised (1876) by Lieutenant Pillsbury, U.S.N., has been used with success on many occasions, notably in the investigation of the Gulf Stream. More recent developments of deep-sea current meters are the Ekman, Jacobsen, Sverdrup, Woolaston and Car ruthers instruments. The instrument is lowered to the required depth and brought into action by a messenger, travelling down the supporting line and operating a lever which sets the instrument 'Spanish word meaning "look-out," used of marks on the chart signifying obstruction to navigation.

free, or some similar contrivance. On the completion of the necessary interval the meter is locked whilst still below the sur face, hauled up and examined. The time during which the instru ment has been working at the required depth is known and the direction and strength of the current can be determined from the mechanical arrangements.

## Topography.

Generally speaking the topographical features should be delineated as far back as the skyline viewed from sea ward, in order to assist the navigator to recognize the land. Sum mits of hills, conspicuous spurs, cliffs, etc., are fixed and their heights determined by theodolite elevations or depressions to and from positions where the height above the water is known. The shape is delineated by contour lines sketched by eye, assisted by an aneroid barometer. In wooded country much of the topography may have to be determined from the ship ; sketches from different positions at anchor with the necessary angles to fix the features give a fair idea of the general lie of the country.

## Latitudes.

Circum-meridian altitudes of stars observed by sextant in the artificial horizon is one of the methods adopted for observations for latitudes. Arranged in pairs of nearly the same altitude north and south of zenith, the mean of each pair give a result from which instrumental and personal errors and errors due to atmospheric conditions are eliminated. The mean of several such pairs should have a probable error of not more than ±I". The observations of each star should be confined to within 5 or 6 minutes on either side of the meridian. Two stars selected to "pair" should pass the meridian within an hour of each other, and should not differ in altitude more than 2° or 3°. Artificial horizon roof error is eliminated by always keeping the same end of the roof towards the observer; when observing a single object, as the sun, the roof must be reversed when half way through the obser vations. The observations are reduced to the meridian by Raper's method. When pairs of stars are not observed, circum-meridian altitudes of the sun may be resorted to, but being observed on one side of the zenith only, none of the errors to which all observa tions are liable can be eliminated.

## Chronometer Errors.

Equal altitudes of sun or stars by sex tant and artificial horizon are employed to obtain chronometer errors. Six sets of eleven observations, A.M. and P.M., observing both limbs of the sun, should give a result which, under favourable conditions of latitude and declination, may be expected to vary less than two-tenths of a second from the normal personal equation of the observer. Stars give equally good results. In high latitudes sextant observations diminish in value owing to the slower move ment in altitude. In the case of the sun all the chronometers are compared with the "standard" at apparent noon ; the comparisons with the chronometer used for the observations on each occasion of landing and returning to the ship are worked up to noon. In the case of stars, the chronometer comparisons on leaving and again on returning are worked up to an intermediate time. A con venient system, which retains the advantage of the equal altitude method, whilst avoiding the necessity of waiting some hours for the P.M. observation, is to observe two stars at equal altitudes on opposite sides of the meridian, and, combining the observations, treat them as relating to an imaginary star having the mean right ascension and mean declination of the two stars selected, which should have nearly the same declination and should differ from 4h to 8h in R.A.

## Meridian Distances.

The error of chronometer on mean time of place being obtained, the local time is transferred from one observation spot to another by the ship carrying usually eight box chronometers. The best results are found by using travelling rates, which are deduced from the difference of the errors found on leaving an observation spot and returning to it ; from this dif ference is eliminated that portion which may have accumulated during an interval between two determinations of error at the other, or any intermediate, observation spot. A travelling rate may also be obtained from observations at two places, the meridian distance between which is known ; this rate may then be used for the meridian distance between places observed during the passage. Failing travelling rates, the mean of the harbour rates at either end must be used. The same observer. usine the same instrument.

must be employed throughout the observations of a meridian distance.

If the telegraph is available, it should be used. The error on local time at each end of the wire is obtained, and a number of telegraphic signals are exchanged between the observers, an equal number being transmitted and received at either end. The local time of sending a signal from one place being known and the local time of its reception being noted, the difference is the meridian distance. The retardation due to the time occupied by the current in travelling along the wire is eliminated by sending signals in both directions. The relative personal equation of the observers at either end, both in their observations for time, and also in receiv ing and transmitting signals, is eliminated by changing ends and repeating the operations. If this is impracticable, the personal equations should be determined and applied to the results. Chro nometers keeping solar time at one end of the wire, and sidereal time at the other end, materially increase the accuracy with which signals can be exchanged, for the same reason that comparisons between sidereal clocks at an observatory are made through the medium of a solar clock. Time by means of the sextant can be so readily obtained, and within such small limits of error, by skilled observers, that in hydrographic surveys it is often em ployed ; but if transit instruments are available, and sufficient time can be devoted to erecting them properly, the value of the work is greatly enhanced.

## True Bearings

are obtained on shore by observing with theod olite the horizontal angle between the object selected as the zero and the sun, taking the latter in each quadrant as defined by the cross-wires of the telescope. The altitude may be read on the vertical arc of the theodolite ; except in high latitudes, where a second observer with sextant and artificial horizon are necessary, unless the precise errors of the chronometers are known, when the time can be obtained by carrying a pocket chronometer to the station. The sun should be near the prime vertical and at a low altitude ; the theodolite must be very carefully levelled, especially in the position with the telescope pointing towards the sun. To eliminate instrumental errors the observations should be repeated with vernier set at intervals equidistant along the arc, and A.M. and P.M. observations should be taken at about equal altitudes.

At sea true bearings are obtained by measuring with a sextant the angle between the sun and some distant well-defined object making an angle of from 100° to 12o° and observing the altitude of the sun at the same time, together with that of the terrestrial object. The sun's altitude should be low to get the best results, and both limbs should be observed. The sun's true bearing is calculated from its altitude, the latitude and its declination ; the horizontal angle is applied to obtain the true bearing of the zero. On shore the theodolite gives the horizontal angle direct, but with sextant observations it must be deduced from the angular dis tance and the elevation.

See Wharton and Field, Hydrographical Surveying (192o) ; C. F. Close, Textbook of Hydrographical Surveying (1925) ; John Ball and H. Knox Shaw, The Handbook of the Prismatic Astrolabe, Egyptian Government, Cairo Government Press (1919) ; Echo Sound ing, H. M. Stationery Office (1926) ; R. M. Abraham, Surveying Instruments, London. (J. A. ED.)