The rule for ascertaining this by the bearing of the rising or setting sun is given in all epitomes of navigation, and need not be repeated here; but this is only practicable in a level country, where the sun can be seen within at most a few minutes of the proper times, and cannot be carried out among mountains or thick forests. In such case we were in the habit of setting up two sticks (A A), stretching a thread (B) across them, and from the middle of this letting fall a plumb line (C); then, taking a flat board, with a sheet of paper (D) stretched on it and projecting a little over the edge, make a hole in the projecting part to let the plumb line hang through, taking care not to vitiate its correctness; then select an object (E), the small upright stem of a tree, or set up a stick at a good distance, 100yds. or 200yds., or more, as nearly compass north of the plumb line as possible—if it is not exactly so, note its deviation on either side with the utmost correctness, and draw on the paper the line F D, which, if prolonged, would reach the tree at E. Then, between ten and eleven in the forenoon, set out the artificial horizon, and take an altitude of the sun; call “stop” sharply at the moment of observation, and let an assistant, with a straight-edged rule and pencil, draw the line of shadow cast by the plumb line at that moment; read off, and let your assistant record your observed altitude beside the line he has drawn; rest a minute or two at least; then take another observation, and so on, till three or five, or any odd number of lines have been drawn, forming a pencil of rays from the plumb line. Leave the sextant clamped at the last observation, and in the afternoon, before the sun comes down at that altitude, be ready with the horizon, and call “stop” at the moment, or even just before, the sun comes into contact, your assistant being ready, as before, to draw the shadow of the plumb line. You will now find that the short interval of rest taken between the morning observation will give you time to set your sextant to the next altitude, and to wait quietly till the sun comes down to it; do the same with the rest; and, when all are drawn, take the mean of each pencil of lines, and between them draw an exact central line, radiating like the rest from the plumb line; it will be evident that this must represent the shadow when the sun’s centre was exactly on the meridian, and therefore it must be due north and south. Measure the angle between this and the magnetic north line already drawn, and the result in degrees and minutes will be the variation of your compass; or, take the bearing of the line by compass, and the result in points or in degrees will be the variation, which call east or west, as the compass north is to the east or west of the true meridian. Take the bearing again of the tree or mark set up in the morning to ascertain that your paper has not been shifted during the observations. If your magnetic line has not been drawn exactly north and south it is not of great importance; but remember that the exact error must be ascertained and allowed for by addition or subtraction in calculating the angle between it and the true north. An unknown error, however small, renders an observation useless; but a known error, however great, involves only the trouble of correction.

To obtain Levels or low Altitudes.

In mapping a country, it is desirable to give as nearly as possible the comparative heights of the hills; or it may be necessary to take the altitude of a low star, or the height of a tree or other object. For this purpose take a wide-mouthed jar or glass bottle, such as is used for the collection of specimens; round the neck of it splice or tie a cord or thong of leather to carry it by; then tie or fix by sealing-wax, gum, or resin, two hairs or threads crossing each other at right angles; and then, standing over the jar with the face towards the object to be measured, take a pocket, or full-sized sextant, and bring the top of the object to the spot where the threads cross each other, taking care to keep the eye so perpendicularly above their junction that the crossed lines and their reflected image may appear in one; then read off the observed angle—for instance 110° 42′ 30″. Apply the index error, which suppose to be 30″ subtracted, and subtract 90° from the corrected altitude, the remainder will be the true altitude; thus:

It will conduce very greatly to steadiness if a rest is used; the stand of a theodolite, with the instrument removed, or of a photographic camera, or three forked sticks set up so that the sight could be directed downwards through a central aperture, would answer the purpose. If the sextant is set to 90°, allowing for index error, and the horizon is swept round with it, the eye being kept steadily perpendicular to the cross lines, it will at once show what objects are above or below the level of the observer’s eye. A looking-glass may be used in the same manner, but it must be very carefully tested in every direction with a spirit level and even then it is but an inefficient substitute for the mercury, which levels itself, and which cannot possibly give a false result, because nothing but agitation can destroy the perfect level of its surface, and unless it is at rest it cannot reflect an unbroken image, and no observation can be made.

A looking-glass may also be suspended vertically, its surface being tested by two plumb lines, one on each side its centre. A horizontal line may be stretched at a foot or two from its front; then, if the observer, retiring a few paces, raises or lowers himself till the line and its reflection appear in one—his eye and the line must be in the same horizontal plane—and he may observe the altitude of the sun, or other celestial body, when in the zenith or too high to be observed in the mercurial artificial horizon; this plan, however, is only an approximation to correctness, and should only be used when the mercurial horizon is not available.

The Plane Table, and its Use.

In making a plane table, discard all the complicated arrangements of sights, protractors, fixed compasses, spirit levels, and levelling screws, each of which has an individual error, which must be found and allowed for before correctness can be attained; while the approximation to perfection gained by their most careful use is almost certain to be vitiated by the contraction of the paper when removed from the table on which it has been stretched.

Take any flat board—Fig. 1 (an artist’s drawing-board) is as good as any—and stretch on it a sheet of drawing or stout cartridge paper: the best levelling apparatus is a wooden hemisphere (Fig. 2), screwed temporarily on to its back, and working in a circular aperture (Fig. 3) in the top of such a stand as is used for the photographic camera or theodolite; there is no necessity that the surface should be truly horizontal; indeed, it is much better that it should be capable of alterations of position, so that objects above or below its horizon may be sighted and mapped at pleasure. Set up a needle (a) in the centre of the drawing-paper, and lay against it a straight-edged ruler (b) with two other needles (c c), set perfectly upright in each end as near as possible to the fiducial edge, as sights; then, choosing some principal object—say a well-marked conical peak, the bluff edge of a precipice, or a deep and narrow cleft in distant mountains—and keeping your ruler pressed against the central needle, bring the others, which serve as sights, in careful alignment with the object, and draw a pencil line along the fiducial edge right across the paper; then, with your prismatic compass (resting on the table for greater steadiness, if there is no iron in it to affect the magnet), take very carefully the bearing of the object, and note it in degrees from north, or zero, say 40°, on the line you have drawn; then lightly sketch the object on the line, estimating its distance from the centre, according to the scale on which you are working, say one or more inches to a mile. Direct the sights to any number of well-marked and recognisable objects, draw lines, and sketch them lightly at their estimated distances. Then have a mark set up as far off as possible, say a mile, or any carefully-measured distance, direct the sights, and draw a line towards it; mark its distance accurately on the paper, and insert the pivot needle there; remove the table to the marked spot, and, with your prismatic compass, set the first line again to 40°; then bring your sights to bear upon the object, draw another line along your straight edge, and the point at which this cuts the first will be the true position of your object; correct your first sketch still lightly, but do not efface anything; sight all the other objects, and sketch them where the second set of lines cut the first. Then choose another station, forming, if possible, an equilateral triangle with the other two; mark its position on the map, remove the proof needle there, carry the table to the spot, set the first line again to 40°, and sight the same objects a third time all round, and the third set of lines crossing the other two will give their true distances from the centre with sufficient accuracy for all ordinary purposes.

A ball and socket joint for adjusting the table to the necessary alterations of level may be made by nailing on beneath it a hemisphere of wood (Fig. 2), working in a circular hole (Fig. 3) in the top of the stand.

Extemporised Sight Vane for Levelling Staff.

Fig. 5. Suppose your staff 1½in. thick: take a piece of tin about 7in. wide, and of any convenient length, say nearly square; line it off as in Fig. 4, so that there shall be three divisions parallel to each other, as wide as the staff is thick, and on one side of them leave another division, about ¾in. wide, and on the other mark and cut out two projections ¾in. square, and a semicircular eyepiece, somewhat larger, with a quadrant-like aperture, as in the illustration; bend the tin at the divisional lines, so as to clasp the staff loosely, with the sight vane projecting from it; let a cord be attached to the top of the tin, and pass through a hole in the top of the staff to draw it up by, and attach another cord to the bottom to draw it down again if required. Upon the edge of the narrowest divisions draw the subdivisions of the measures already marked upon your staff, letting them commence from the level of the bottom of the aperture in the sight vane, and read downwards; then, directing the telescope of your levelling instrument towards the staff, let an assistant lower or raise the sight vane according to your signals, and then read off the number of subdivisions on the vernier until you come down to a line, marking a division on the staff; read off this, and add the fractional parts, and the excess or deficiency over or below the height of the eye will be the difference of level in feet, inches, or whatever measurement may be used.

Movable stands for instruments must be light for the sake of portability, but steadiness cannot be obtained without weight; and for this purpose a bucket of water, a bamboo filled with water or sand, a bag of stones or sand, a large stone, or lashing to a tent peg driven into the ground, may be employed, as in our illustration.

Makeshift Clinometer.

Captain Lendy recommends a simple form of clinometer, which is constructed as follows: The clinometer consists of a quadrant of pasteboard or of brass, having a plummet, A H, suspended at its centre, and graduated, as in the diagram, on both sides. When we require an angle of elevation, we look along the edge, A C, till B is in sight, when the plummet indicates the angle. For an angle of depression reverse the instrument. This instrument is an excellent substitute for the ordinary form of sextant in case of accident or breakage.

The same officer describes an ingenious substitute for an ordinary water level, which can always be replaced by a little ruler, A B, suspended by strings, C A, C B, having a little weight under it to prevent the wind from shaking it. When held by the string the line A B will give a horizontal direction. To make use of it for levelling along A B, start from A, hold the ruler up to the eye, and, aiming along its edge, notice to what point (B) of the ground the visual ray corresponds. Repair there, we shall have ascended a distance—the height of the eye above the ground. Start afresh from B, and in this manner the number of stations made between A and B, multiplied by the height of the eye above ground, will give the difference of level required.

The same author gives the following useful hints on the estimation of distance: “Pacing is generally resorted to while filling in the details of a survey. The trotting of a horse might also be made available. Distances can also be measured by time when we have previously ascertained over how many yards we walk or ride in a given time. This is not a rare occurrence in the field. When distances are measured by pacing or riding a correction is necessary, owing to the lengthening caused by acclivities and the turnings of roads. On slightly uneven ground we subtract 1-7th of the distance paced, and 1-5th when the inductions are more important.”

When the atmosphere is even sound travels at the rate of 1118ft. per second; therefore a musket fired may serve to measure a distance. A watch gives the number of seconds elapsed between the instant the light is seen and that when the report is heard; that number, multiplied by 1118ft., gives very approximately the distance. If no watch is to be had the time is obtained by counting the pulsations of an artery. A sound pulse averages from 75 to 80 in a minute. Distances may even be guessed by observing that in clear weather the windows of a house can be counted at 4000yds. Horses and men appear as dots at 2200yds. A horse is clearly seen at 1200yds. The movements of men are perceived at 800yds.; and the head is distinctly visible at 400yds.

For the measurement of time, as we have said before, a thoroughly well-made English lever watch is preferable to a chronometer, as it will withstand the rough jolts and vibrations caused by being carried on horseback, or in a waggon, far better. Sun-dials, properly so called, are rarely of much use to the traveller; still the pocket compass may be made to do duty as an indicator of time. There is a small and very portable little instrument to be obtained of most opticians, in the formation of which a silk cord is so attached to the border of the compass case that on adjusting the compass, so that the needle shall point to a black stud inserted for the purpose, a shadow is cast by the silk on the figure indicating the hour of the day. A small equation table is attached to the inside of the cover.

When no watch is at hand seconds can be indicated closely enough for practical purposes by suspending a small bag of shot or bullets from the end of a piece of fine fishing line or copper wire. Attach the upper end to a cross bar, laid in the crutches of two forked sticks, let the bag hang, and regulate the length of the string until you find that it describes the proper arc in swinging; your own pulse, the number of which has been already given, or that of a horse, which may be roughly set down as thirty-six beats per minute, will be a sufficient guide. If great accuracy is sought, recourse may be had to repeated astronomical observations.

An excellent makeshift hour-glass can be made from two empty soda-water bottles, and a little fine dry sand. A wooden plug of 3in. long should be so cut as to fit the necks of the bottles tightly. Through the centre of the plug, from end to end, burn with a red-hot wire a fine even hole, then with your pocket-knife make a funnel-shaped or flared-out mouth to each hole, cutting away until the extreme edge of the plug is reached. See that your sand is free from small stones or lumps, pour it into one of the bottles, insert the plug half-way, and test the quantity by letting it run out at the hole. When you have the proper charge to run for fifteen or thirty minutes, place the bottles mouth to mouth in such a way that one-half the plug shall be in the neck of each bottle. A bit of raw hide sewn round the union of the bottle mouths makes all secure. The joined bottles can then be mounted in a wooden frame for use. Two bits of flat square board, with holes in the centre for the bottoms of the bottles to come partly through, pinned at the corners by four bars of wood, is as good a form of frame as any.

The Malays make use of a very convenient and simple form of time indicator or water clock, which is made as follows:—A large-sized cocoa-nut shell is obtained; this is first scraped perfectly smooth, and then at the bottom a very minute hole is bored. The nutshell is then set floating in a pail of sea water. As the shell fills it gradually settles deeper and deeper, and at last sinks to the bottom with a gurgle and a thud. The rapidity of filling, and consequent duration of time, is regulated by increasing or diminishing the size of the orifice. Thus a man may be set to keep a two-shell watch or a four-shell watch, and so on. The instant the shell sinks to the bottom of the pail it attracts attention by the disturbance made. It is then immediately taken up, the water is poured out, and it is set afloat again. Excellent time can be kept by this primitive arrangement.

For ascertaining the altitude of high lands, ranges of hills or mountains, a thoroughly good “compensated” aneroid barometer should be taken. This will not only be valuable for measurements, but will be of considerable service in the observation of weather signs. We have one now in use made expressly for us by Mr. Cary, of 181, Strand. It is protected by a smooth wooden cover or case, enveloped in tightly-stretched leather. A sling is fitted to it by a swivel loop, which admits of its being carried over the shoulder or in the jacket pocket. The Table of Altitudes, given on the next page, will prove a useful guide when conducting observations with it.

Table of Altitudes.

This Table is intended more particularly for the graduation of aneroids with a circle of measures in feet concentric with the ordinary circle of barometric height measured in inches. The circle of feet is to be read off, at the upper and lower stations, by the index; and the rule for measuring the height will be: Subtract the reading at the lower station from the reading at the upper station; the difference is the height in feet.

Example.

In using the instrument here described in the measurement of altitudes, the movable needle point which is turned by the mill-edged rim is set opposite the index hand. This is to be done at the foot of the mountain or hill. Then the difference between the index hand and the movable needle point will be the number of feet ascended (vide Table appended, and “Example”). Suppose the index hand stand when at the foot of the hill at 30in. ¹⁰⁄₁₀₀, and when you again look at the instrument you find the index hand has gone back, or has fallen to 29in. ¹²⁄₁₀₀, then you would have ascended 900ft.

At page 26 of this work we referred to the hypsometrical or boiling-point apparatus used in taking altitudes. Since the remark there made was penned we have endeavoured, and we hope successfully, to so guard the improved form of aneroid barometer, referred to at p. 741, from the chance of accident, that it can be safely carried by the explorer of even the most rugged and inhospitable regions.

On the Use of the Sextant and Artificial Horizon.

We do not propose in this work to trespass on the province of books on nautical astronomy. We take it for granted that every traveller using a sextant will also provide himself with an Epitome—Norie’s, Rapers, or Kerigan’s (of course the latest possible edition of either), and with the “Nautical Almanac,” which may be had for three years in advance, by persons contemplating a long journey.

The most important instrument is the sextant itself, and in the selection of this the greatest care should be used. Ebony or other wood may do for the frames of such as are to be used at sea in temperate climates, but for tropical use, even for sea service, we recommend a brass or gun-metal frame, and for observing on land no other should be used.

The quadrant, which is quite equal to the observation of altitude at sea, will take an angle of 90°, but should read up to 10° or 20° more; but the sextant, or sixth of a circle, is made to take in an angle of twice 60°, or 120°, and should also read 10° or 20° higher. When we were at the Zambesi mouth, in 1858, Dr. Livingstone’s sextant reached only 127°, while our own would read to 137° or 140°, which, when the altitude of the sun was increasing daily, gave us the advantage of observing a week or ten days longer than he could. We left the instrument in the care of the Portuguese Commandant of Tette, but have no hope of ever seeing it again, the town having been burnt and the inhabitants massacred by Landeens, Banzai, or other ferocious savages.

The sextant we generally use—and which we have tested by many years’ constant use—is brass framed, reads to 126° 56´, is of 8 inches radius, and has its arc and vernier on which the figures are engraved of gold, which has a soft lustre, exceedingly agreeable to the eye under a tropical sun, and is equally pleasant to read by lamp light; a screen of ground glass is placed before it to soften the light still more, and prevent annoying glitter and reflection; the degrees are divided into sixths of ten minutes each, and the minutes likewise into ten seconds; the microscope travels on a fixed frame, and a small milled-headed screw brings it to the figures to be read. A small lamp fixed on the axis of the index arm, with a reflector to shed the light upon the arc and vernier, is sometimes made use of.

For nearly all angular measurements that an explorer is likely to require, a really good sextant will be found sufficient, but some, for the sake of still greater power and accuracy, provide themselves with a repeating circle; but although this possesses many advantages, we doubt whether the expense of such an instrument will not place it beyond the reach of the generality of travellers, while the extra care required will constitute too great a claim upon the time of any who cannot devote themselves entirely to astronomical observations, but must, perhaps, give the greater part of their time to other avocations. The double sextant invented by Captain George, R.N., of the astronomical department of the Royal Geographical Society, described at page 27 of this work, will be found a portable and most convenient instrument for the use of explorers.

The theodolite has also many advantages, especially in taking a round of angles; but from what we have seen of it in practice we should be inclined to think that an explorer, with his sextant and compass, is more independent, and can do more than he could possibly effect with the theodolite.

The artificial horizon is, as its name imports, intended to obviate the difficulties caused by the fact that the real, or sea horizon, may be at times invisible, obscured by fog or clouds, or that the observer may be absent from it, and often far inland, where the unevenness of the earth’s surface prevents anything like a reliable real horizon being found. Of the artificial horizons used at sea we have not much to say, the unsteadiness of the vessel forbidding the use of any instrument that can be disturbed by motion. The best we have seen is Captain Becher’s pendulum horizon, a little frame swinging near the object-glass of the sextant, and carrying a couple of horizontal wires, so arranged that when they appear in one to the eye of the observer they ought to be on a level with the horizon and parallel with it; a small lamp is so fitted to the sextant as to render these wires visible at night if the altitude of the moon or a star is required; but we do not think the latitude deduced from such an observation can be more than approximately true.

It is on shore, and most of all in the far interior of the great continents of the world, that the artificial horizon is most needed, and that it renders the truest service to the explorer; and therefore it is of the greatest importance that the instrument should be at once simple in construction, easy of management, not easily put out of order, and, above all, perfectly reliable in the result obtained from it. The first requisite is a perfectly flat and horizontal reflecting surface, in which, when the observer looks down upon it, the image of the sun or star may be distinctly seen. Now, it is easy to find flatness: a disc of silvered glass, or polished metal, or even a bit of crown glass, painted black on the under side, or a common round shaving-glass would do if this only were required; but this flat surface must also be perfectly horizontal, and to attain this various arrangements of tangent screws and spirit levels have been invented, all of which require great care in levelling, and have the defect that the slightest accidental touch while they are in use may alter the level, and so vitiate the observation. By common consent, therefore, observers almost universally trust to fluid mirrors, which must be perfectly level if they are sufficiently quiescent to reflect a perfect image. Water, darkened with any colouring matter—ink; water with a little treacle, to render it less liable to be agitated by the wind, or thin tar will do; but all these have disadvantages which render them only fit to be looked upon as substitutes when mercury cannot be obtained; in fact, long ago we were told by the late Captain Washington, Hydrographer to the Admiralty, to use nothing but mercury.

The horizon trough, as it is called, is simply a block of wood of oblong form, about 6in. long, 4in. wide, and 1in. thick; this is hollowed to the depth of about ⅜in. or ½in., leaving a sufficient rim to retain the mercury which is poured into it. Sometimes a hole is pierced in the rim, and is continued in the solid wood under the hollow, so that the mercury, being poured into a small funnel fitted in the rim, runs underneath and rises like a fountain in the centre of the trough. The various arrangements of this kind and others more complicated are called fountain horizons, but they are not really necessary, their principal object being to insure the perfect purity of the mercurial surface by forcing it to flow downward first through the funnel, and so to leave the scum behind; but this object may be just as well attained by inverting the bottle, so that all the impurities may float upon the surface, and allowing the pure mercury to run through the perforated stopper into the trough. The bottle is generally of iron, and has the perforated stopper already mentioned, which, when the mercury has to be returned to it, serves also as a funnel. Wooden bottles are also made, but no traveller ought to depend upon them, as in hot climates they shrink and split; and we have found in Namaqualand all our mercury adrift in a tinned box, forming an amalgam which did not at all improve it. We have therefore, for many years, kept it in a common stoneware ink bottle, with a bit of washleather tied over the cork, and have found this to answer admirably; in pouring out the mercury, having removed the cork, we stop the mouth of the bottle with the forefinger, completely invert it, and then, slightly moving the finger, leave an opening sufficient for a stream of pure mercury to flow into the horizon. Our trough is round, and about 4in. across, which is quite large enough. In perfectly calm weather we prefer to observe on the plain surface of the uncovered mercury; but if wind comes on, as it often does in Africa and Australia about noon, we cover it with a roof of the usual form, i.e., two small panes of glass fixed in a frame so as to form an angle of 45° each with the horizon, or 90° with each other, and, standing like a roof over the mercury, allow the rays from the heavenly body to pass down to it, and be reflected to the eye of the observer. Various methods of rendering this roof as portable as possible have been tried; our own is figured in the first chapter of this work.

Captain George’s new artificial horizon, however, bids fair to supersede all the old forms of arrangement, as its portability, strength, and simplicity of adjustment stand unrivalled. Captain George’s horizon may be made sufficiently large to equal the surface of the one now used; but the portable or pocket form here alluded to is of the following dimensions:—

The improvements herein specified are not only its reduced size and weight, but its mechanical arrangements, form, and moderate price.

It consists of two circular disc-like reservoirs, about 2½in. in diameter, and ¾in. in depth, made of iron, at the same casting: one contains the mercury, and the other is the trough, fitted with glass cover for observing.

The discs are connected at their circumference by a narrow neck, and in it is drilled a hole, through which the mercury passes from one reservoir to the other; and this communication is opened or shut off by a stop-cock, on the cone principle, such as is used for water or gas, so that the mercury can be passed from one disc to the other without removing the glass cover, or the risk of losing any mercury.

The mercurial disc, A, is fitted with a cylinder-stopper, D, acting on a spiral spring, by which air can be admitted or allowed to escape.

The trough disc, B, is fitted with two glasses, G and E, which are ground mathematically parallel: one of the glasses is fitted to a frame, and screws on the disc, and is used while passing the mercury in or out of the trough; after which operation it is removed and replaced by the other glass, the edge of which next the stop-cock should be supported by the blade of a pocket-knife and then lowered on the mercury at the opposite side, and by a gentle pressure, force out the intervening air, leaving the glass to float on the surface of the mercury. Without this care, some of the mercury might be pressed over the edge of the disc.

The glass then presents a clear reflecting surface, which is not only protected from the effects of the wind, &c., but also maintains so great a steadiness as to mark a decided improvement over the old triangular glass roof which is placed over the mercury, instead of, as in this case, being on it.

It may be used afloat under favourable circumstances (the observer and artificial horizon being placed on a pendulum table). Another great advantage to this improved artificial horizon is the facility with which altitudes can be observed at 2° elevation, and consequently its adaptation for the measurement of very low stars, as well as the peaks of mountain ranges.

To return the mercury to its reservoir, remove the glass G that floats on the mercury, by lifting it up with the point of a knife, and then screw on the other glass cover, E. It is now only necessary to hold the instrument vertically, the trough end being uppermost (Fig. 4), turn the stop-cock, and press gently downward on the cylindrical stopper, and the mercury will rapidly return to its reservoir.

The following diagrams (half the actual size of the instrument), show the various parts of the instrument, and the method of filling and emptying the reservoir.