1. Never pass an Indian village in the night if you suspect any mischief. They will be sure to find you out, and then, like all bullies, seeing that you are afraid of them, will act upon that knowledge.

2. If you suspect mischief, camp outside at a distance, and pass in daylight; you can then see better what you are about.

3. If you come to a village where you think there is likely to be an attack made on you, go into the chief’s lodge, and, if possible, into one where there are a number of women and children. If their sense of hospitality does not prevent them from molesting you, they know that when white men are attacked bullets fly about, and some may strike the women and children. It is an axiom that no man likes to put his head down a gun-barrel.

4. Trust to an Indian’s honour, and you are tolerably safe—you and your goods; but not to his honesty, for he will steal the ears off your head, unless you are very skilful in making a cache. If in a neighbourhood where there are Indians, you had far better leave your goods in their charge until you come back; you will generally find them safe; but if they find your cache—their honesty being doubted, and having no honourable scruples—they will be sure to clean it out.

5. Never appear to be afraid of them.

6. Never give them one cent less or one cent more than you bargained for—as a right. If you do, they will think it only yielding to them, and then imagine you have cheated them at first. You may give a small present if you like. It is a custom the Hudson’s Bay Company have introduced of giving after a trade has been completed a small “potlatch,” or gift, of their free accord, according to the value of the goods traded. Those Indians who have traded with the Hudson’s Bay Company expect it.

7. In making presents, take into consideration their wants; only make presents where you may expect a return; they do that with you; and goodness of heart is only thrown away. Never calculate on this last weakness.

8. In making presents for conciliatory purposes, always make them to the head people; never mind the smaller tribes’ men. Be sure, however, that it is the chief you are making presents to, and not some forward and impudent fellow, who is usually the first to accost you at the outskirts of a village. The chief generally retires on his dignity, and wants to be sought out. Secure the head man’s regard, and you need not mind the favour of the smaller ones; but even if you had abundance of goods to distribute, you would be sure to create red blood and heart burnings by one man’s present being better than another, or supposed to be, &c.

9. I have generally adopted the practice, when I had not much to give, of giving it to the children. If you win the children, you win the mother, and of course the father. A little present goes a long way with the children. If you give it to the mother, you often excite the father’s jealousy, and frustrate your purpose. Always remember, in addition, that a savage values a man’s generosity, &c., according to the size of his presents, and act accordingly.

10. Never allow the natives to eat with you as your equal. As a rule, play the great man with them.

11. If a savage is travelling with you, give him food whenever he wants it. Food given when he wishes it is of ten times more value than when he gets it when he does not need it, or is not hungry. Consult his wishes in this respect.

12. Never attempt to gain anything by force; always by persuasion, argument, and presents.

13. Notwithstanding all you will be told about the value of a medical knowledge in travelling among savages, I have generally found it of very little benefit, and frequently, when put in practice, of real detriment. An Indian will never come to you unless when at death’s door and he has lost confidence in his own sorcerers. You may give him some medicine, and perhaps in nine cases out of ten the patient dies, as he would have done anyhow. Their professional jealousy is raised, and you are accused by the “medicine men” of killing the person; and the worst of the matter is, it is often believed by the credulous people. If the man recovers, it is rarely that you get the credit of it. It is the medicine men who have done it. With surgery it is somewhat different. If the operation is one not involving any very serious consequences if unsuccessful, by all means perform it. They then see the working of your superior knowledge before their eyes.

14. Be just and firm, patient and equanimous with them. Display no anger or violent and passionate gestures, and never be very prone to notice insults.

15. Never say you will do a thing and not do it. Never threaten to do anything unless you intend to do it.

16. No people notice the weakness and moral shortcomings of a man quicker than savages; therefore beware, especially in re fœminâ.

17. Try by all means to learn the customs and social etiquette of the people; for nothing raises you more in their estimation than this knowledge, or enables you to see when you are slighted.

18. If you are attacked, and at the last extremity have to fire, take to the bush. An Indian does not like to venture in. He knows there is a man there and a gun, and that somebody may be shot, and that somebody may be himself.

19. If you have a watch at night, never stand near the fire; for then you are only giving the man a chance to fire at you.

20. Always, and above everything, remember that the hearts of all mankind are the same, and that all the difference between one and another is merely the overlay caused by etiquette, custom, and education; at heart they are the same.

“There are many arts which might be mentioned as useful in treating with Indians; but, as these depend upon a knowledge of the particular tribal customs, these general rules must suffice.”


CHAPTER XIX.
ON SKETCHING AND PAINTING UNDER THE ORDINARY
DIFFICULTIES OF TRAVEL.

For artists making a tour of the Lake Districts, the Highlands of Scotland, or the mountain districts of Wales, every possible convenience is supplied by the colourmen of London. The explorer-artist must, however, have recourse to many shifts and expedients.

The talented author of “A Painter’s Camp in the Islands” actually fitted out a little studio on wheels, the front of which was a large sheet of clear plate glass, so that, whatever might be the weather, he would be able to paint upon the spot, and with all the truthful reality that working in the presence of nature only can impart. Every effect of storm or sunshine on the hills, catching the passing rain cloud while the shower was still falling, with its misty fragments torn off by the gale, illuminated by the beauteous rainbow, or lighted up by rays of sunshine piercing through the gloom; and when such luxurious appliances can be obtained, and are used, moreover, to so good a purpose, far be it from us to say a word against them. In fact, we would advise every one who determines, as he ought, to make his sketches as perfect and truthful a realisation as possible of the country they illustrate, to provide every convenience he can afford or carry for the successful prosecution of his work; regarding them, however, simply as means towards that end, and casting them aside unhesitatingly when, from the labour of transportation, they become hindrances instead of helps to him.

We will suppose, first, that the intending traveller wishes to take sketches in pencil or in water colours, as occasion may serve, of the objects of interest that he meets with, he should be provided, as we have said, with folding sketch-books of folio and quarto sizes, with drawing paper, white and tinted, cut to their respective sizes. He will be able to form a tolerable estimate of the number of sketches he is likely to make in a day, and had better not encumber his folio with more than a good allowance of paper for the work he expects to do. Suppose he reckons six or eight sketches, and, allowing margin enough, takes a dozen sheets—three white, and two each of the pearl, the warm and cool grey, and the drab paper, putting away at the close of the day his finished sketches in a case specially provided for them, and replenishing his folio from that in which he keeps his store.

The preservation of his folio and its contents from injury by rain, by the dash of sea water, or by other causes, is of the first importance, and for this purpose he should have a haversack of good stout canvas—i.e., sail cloth—for each; this may be slung by a leather strap and buckles, but we prefer that the shoulder strap should be of double canvas 2½in. wide, and that the end, which comes forward over the right shoulder, when the sketch book is carried on the left side should pass through a loop at the corner of the haversack, and doubling back upon itself be provided with points or other means of fastening it at the required length. If buckles, hooks and eyes, or other such expedients are used, let them be not of iron or steel, but of plated or well-tinned material, so that no rust or oxide of metal shall gather on and rot the canvas.

Let the part which would then hang next the body of the wearer be of double canvas so stitched with two vertical seams that it may form three pockets, one large enough for the box of water colours in front, one in the rear for the japanned or plated water bottle, and the central sub-divided, so as to carry a few spare pencils, a memorandum book, to which, if the traveller cares about mapping his route, may be added, a 6in. scale, protractor, and dividers; in which case he will do well to add a sheet or two of the squared mapping paper to the contents of his folio, and two or three sheets of foolscap, with a leaf of semi-carbonic paper and a H H H pencil for his journal. A third thickness of canvas will at once form the pocket for the folio and the front of the haversack; and we would advise that the double strip, already spoken of as forming the sling, should be sufficiently long to form also the sides and bottom of the haversack.

The octavo, 11in. by 7½in. folio, will be found very convenient and handy on boat expeditions, horse or foot journeys, hunting trips, or when the artist has to carry everything himself, and must diminish weight and incumbrance as much as possible. In the Australian exploring trips we were not able to carry any other, and this hangs easily from the quarter of the saddle on the near side. In Kafirland, we slung the sketch-book itself (covered with skin to keep off the occasional rain) by short straps and buckles to our waist belt; and one long strap, passing over the shoulder to the belt in front, remained always fast, so that if a sudden movement, either of our own troops or of the enemy, necessitated it, we could at once throw the sketch-book over our shoulder, and advance or retreat as requisite.

We would advise, however, that the imperial, 15in. by 11in., folio should be carried if possible, as it gives so much more space for detail in landscape or other subjects than can be gained upon the smaller scale. With the large book the twenty-four tube colour box can be carried, with the smaller a twelve tube must be taken; and in either case weight may be economised on short trips by carrying only the lid that forms the palette with the little divisions that should always be found along its edge charged with patches of colour; in this case a slip of tin or copper must be fitted as a temporary cover to the box left at home.

We do not advise the solid sketch-block for hard service; first, because it exposes to risk an unnecessarily large quantity of paper, and next, because, with rough usage, the sheets may become loose, and cease to be a block. The folio with japanned tin frame, for confining the sheet actually in use, is the best. It should be made of strong, light, saddlers’ leather, rather than of the flimsy materials; which serve well enough for lady students a mile or two from home. The millboard surfaces may be varnished with boiled linseed oil, and allowed to dry thoroughly. Do not have them covered with paper pasted on, but with the plain surface of the milled board. We found it very convenient to mark a scale of inches along the sides of our frame, and have a movable slip of thin brass fastened upon it by simply bending the ends round, so as to enable us to draw a truly horizontal line at any height, and this would be especially useful in mapping, or the horizon in sea-views.

If a sketching-stool can be carried, it will be found a great convenience, as, when the artist has to sit upon the ground, to say nothing of possible unpleasantness from storms or dampness, the eye is lowered so much that often the grass in the foreground will hide the greater part of the landscape. The triangular stool, which folds up into a stick but little larger than a policeman’s truncheon, is the most convenient form. One of the legs may be longer, with a couple of cross-bars, on which to rest the sketch-book; or such a convenience may be made with a couple of thumb-screws to slip on when required.

In sketching a landscape it is of great importance to decide, first, what you intend to make the principal object, and how much in the way of accessory you can include beside it. About sixty degrees, or the sixth-part of a circle, is all that can be seen horizontally, without moving the head, and about forty vertically, and this may be roughly estimated by holding up the hands like blinkers on each side of the face, and observing where they shut off the view. Photographers have a little frame made specially for this purpose, and the artist may, by opening the frame of his folio, and holding it nearly at arm’s length, see how much of the landscape it includes. It must also be remembered that no one looking at a landscape can see the spot he stands on; and, therefore, if it is desired that this spot shall be the foreground, he must retire, say ten or fifteen yards, so as to bring it within the limit of his vision. In practice, however—when, for instance, he is looking over the edge of a cliff—this might deprive him of the sight of some of the most beautiful portions of the view, and it might be better to remain on the edge, leaving a sufficient blank at the bottom of the paper, and then retiring to sketch the foreground, choosing such a position as should make its characteristic features enhance the beauty of the view. It conduces very greatly to correctness if the bearings of distant hills are taken by compass and noted in pencil on the upper margin of the sketch, while nearer features are similarly noted at the bottom—if the estimated distance in miles is added, this enhances greatly the value of the sketch, as it becomes then a geographical record, in addition to its merit as a work of art. Holding up the paper steadily at nearly arm’s length, and making on its upper edge the apparent horizontal distances, and on its side the heights, assists the drawing very much; and the pencil may be held up and the distances gauged on it by the thumb-nail, and measured on the paper. Two knots on the ends of a bit of string, one held on the pencil, and the other between the teeth, will ensure the measurements being all taken at the same distance from the eye, which is of great importance. The angle formed by the side of a mountain may be estimated by making the pencil coincide with it, and then bringing it down on the paper. The perspective of receding lines may be found in the same manner; but care must be taken to hold the pencil in the plane of the picture, and not let it point away from the observer; the limits being thus ascertained, the forms may be slightly indicated, and then, after a steady and searching gaze at the object, firmly, but not heavily, drawn. When once the paper is indented by the pressure of the pencil, the line can never be entirely erased; and the surface, once injured, can never be restored. No line should be made at random; be the touches few or many, each should definitely represent some form. The merest outline accurately sketched upon the spot is preferable to any amount of indefinite filling up, which the artist had better leave to his own imagination, assisted by memory and a faithful sketch, when he finishes his picture.

In a pencil sketch, little notes, indicating the nature of the soil, the foliage, the colour or condition of the water or the clouds, may be neatly written in, in such a manner that, unless on close inspection, they blend into the forms of the objects, and rather assist the drawing than detract from its appearance: for instance, the word rocks may run alongside the shadow of a fissure, and their kind or colour—red, grey, basalt, or sandstone, &c.—grass, sandy plain, water, dark clouds, cumuli or light cirri, accidental or cast shadows, or gleams of light, are all worthy of notice; while the direction of a river may be indicated by a small arrow-head. It may also be enough if several objects of a kind are together, as a crowd of men, a herd of animals, or a flotilla of small vessels, to draw one or more carefully and simply indicate the position of the rest. If there is time, a few touches of colour on the principal parts—say the grey of distant hills and the stronger tints of the nearer ones in flat washes. If a sketch is to be finished in colour on the spot, the outlines should be made as before, with the greatest care; but no time should be wasted in attempting to shade or finish with the pencil. If the paper is of a light pearl or a warm grey tint, so that Chinese white will tell upon it, it will be less dazzling to the eye when reflecting the rays of a vertical sun; but it must be remembered that all tinted grounds impart their own character to the work, and, if strict fidelity is sought, nothing but pure white paper, with a sufficient grain or texture to take the colour well, and to give that slight broken uncertainty of touch which is of so much advantage in foliage or rough surfaces, and yet sufficiently fine to admit of the most delicate manipulation where it is required. The right side of the paper is that on which the maker’s name, pressed into its texture, is properly seen; and, if the sheet is cut, each piece that does not include some portion of this should be marked with an “R” on the right side, to prevent mistake. The pencil sketch being completed, wet the paper all over with your largest brush filled with pure water—this somewhat softens, while it fixes the pencil lines, and disposes the paper to receive colour more readily. Take up with the half-dried brush any drops of water that may hang under the edge of your sketching frame, which should, of course, be perfectly clean. Determine now what parts of your picture are to be white, or of pure and unmixed blue, and then, with the large brush, pass a very faint tint of pale orange over all the rest.

The three primitive colours, red, blue, and yellow, in their greatest obtainable purity, should now be placed on the pallette, which ought to be clean, and if possible unencumbered by other colours. Suppose you have Indian yellow, carmine, and cobalt. With a little diluted cobalt wash in the clear blue spaces in the sky, carrying a tint downward on any part of the ground in which grey is to predominate, so as to impart depth of colour as speedily as possible, and reduce the distracting effect of the white paper as seen in opposition to the parts you are painting; if the lights on the clouds are to be pure white, form a grey with a little cobalt and carmine and paint their shadow sides, then with a clean half dry brush soften the harshness of the edges, and reduce them to the form you wish, bearing in mind that the more correctly and evenly you can lay the edge of the original wash, and the less it wants re-touching the better for your picture. If the sky is to be cloudless, turn the picture bottom up, take a very faint wash of cobalt and carmine and lay it along the horizon, letting the lower edge hang full and wet, so as to give you time to work on it before it dries, and yet not so full as to run down in a drip, and so produce unequal lines across the sky; then take up a little pure cobalt and wash in another line of colour a little deeper than the first, the wet edge of which will run imperceptibly into your second line, and thus in succession keep working in lines of deeper blue, until by an imperceptive gradation you reach the zenith. If sunset or sunrise is to be represented, keep a pure white space for the sun, round this lay a wash of Indian yellow, round this another of carmine, and beyond this another of cobalt with a little carmine in it, keeping the picture still reversed, so that in graduating the tints the most brilliant colours may run into those that are less so—as the yellow into the red and the red into the blue, rather than that the colder colours should run into the warm, and thus impair their purity. The sun may then be tinted as required, remembering always that the source of light must be brighter than the atmosphere through which it shines—though, if the sun be setting in a bank of cloud or haze, great effect may be gained by painting it of a deep and lurid red; while its clear and nearly white light shines on the light clouds in the zenith above the influence of the haze.

Calm water will reflect the colour of the sky according to the angle at which it is viewed; if you look down on it, it will reflect the dark blue of the zenith, but at the same time, if it be transparent, it will also transmit the broken colours of the ground beneath, and thus many beautiful effects are produced—the yellow sand of the tropics imparting a brilliant green to the shallow sea, while rocks or sea-weed will give rich tones of brown. If the spectator is low down, the water will reflect the colour of the horizon, and its own local colour will be lost or much diminished; the reflection of objects on its banks will also appear more perfectly in proportion to its stillness; but never fall into the error of making the reflection an inverted facsimile of the real object—it is in reality an image as seen from the level of the water at a point midway between the spectator and the object. Get a good photograph showing a reflection, or lay a looking-glass horizontally and place an object on it, and you will see at once what we mean.

The distant hills may either melt into the soft tints of the sky, partaking of roseate light and faint sky shadow, or may rise cold and dark against a clear horizon, or may be shown in full light against a heavy storm cloud; in any case, the tone of colour proper to their respective distances must be preserved, and in this respect there can be no better rule than to copy those that nature herself presents. Objects in the middle distance will be more strongly coloured; and if any particular object be selected as the subject of the landscape, the attention should be directed to this, and the remainder made subservient to it, by having somewhat less finish bestowed upon them. Fix the eye steadily upon the chosen object, and observe how all detail becomes indistinct towards the limits of the vision, and then in like manner, having worked up the detail around the centre of interest, let the colours become a little fainter, and the work less definite toward the corners of your sketch. In foliage, take the lightest tint, say Indian yellow and French blue, or Prussian blue toward the foreground where intense green is required, and lay in the masses, keeping the forms large and broad, and blending a little more blue with the parts that are to represent the farthest side of the tree; then, when this is dry, take a darker tint and somewhat more minutely represent the forms of those portions that take the middle tint or local colour; and lastly, take a third for the deeper shadow, strengthening this with touches of rich warm brown or cool grey as you wish the masses to advance or to retire. Even pure crimson may be used with advantage as a shadow to cool clear green in the foreground; in like manner the proper shadow for a yellow sandhill on a beach is not a deeper yellow, but a cool purplish grey, composed of the complementary colours blue and red.

To give some idea of the work that may be done with three well-chosen colours, we append the following list, which might be much enlarged:—

Primaries Yellow and red produce orange.
Yellow and blue, green.
Red and blue, purple.
Secondaries Orange and green, citrine.
Orange and purple, russet.
Purple and green, olive.

When the eye is fatigued by looking at one of the brilliant primary colours it seems to relieve itself by seeing the secondary colour which is complementary to it: thus if we have looked at red—say at a red light—for some time, and turn the eye away we shall see a green one of the same size and form, being seen in fact by that portion of the eye only that has been fatigued by the strong impression of the red. If we have looked at a yellow light we shall behold a purple image, because this is composed of the other two colours; blue and red is complementary to yellow. Blue, being a cool colour, does not so much fatigue the eye; hence, though by the foregoing rule we ought to see its image in bright orange, in practice we rarely do so. From these facts we learn that, whenever one of the primary colours is used in a picture, the complementary colour formed of the other two ought to be placed not very far from it, so as agreeably to relieve the eye. In most cases the landscape actually being copied will afford sufficient facility for this; sometimes it will not; but these instances are exceptional, and probably will occur in the snow wastes of the north, on the solitude of the ocean, or in the sandy deserts of the tropics, where drear monotony or wild and terrific grandeur constitute the charm of the picture, and fidelity rather than pleasing composition must be the artist’s aim.

We subjoin also a few combinations of colour which will be found useful in landscape painting: Aerial tints for skies, clouds, and distance: for very delicate preparatory wash, cadmium yellow and rose madder; strong ditto, Indian yellow and carmine; neutral ditto, yellow ochre and brown madder; still darker and less aerial, light red, Venetian red, or Indian red. Cobalt for delicate blue skies; French ultramarine for stronger. Cobalt and rose madder for delicate cloud tints. For golden sunsets: aureolin, gamboge, lemon yellow, cadmium yellow, Indian yellow, yellow ochre—to be used according to the brilliancy or depth of colour required, and to be contrasted by cool greys composed of cobalt and rose madder, or French ultramarine. Crimson sunsets: rose madder, carmine, crimson lake, Indian red, purple madder, contrasted with cool grey; and sometimes greenish tones formed by adding a little yellow to the blue and red.

In dark storm clouds, French blue or indigo, with light red, Venetian red, or Indian red, or purple madder. Indigo and Prussian blue require great caution in their use. With any of the beforementioned yellows, they form rich greens for sea tints or foliage; with raw sienna or burnt sienna, they give very deep greens for stormy seas or heavy forest trees. Light red and Prussian blue give a greenish grey. Light red with cobalt or ultramarine give greys somewhat less aerial for middle distance, mountains, &c. Indian red, with the same blues, gives a more opaque grey. Sepia and French blue make a cool grey; raw and burnt sienna are good colours for autumnal foliage, stems of trees where grey is not required, rocks, Dutch galliots, and many other foreground objects; brown madder and vandyke brown afford great depth for foreground shadows. For native complexions, raw sienna with a little of the burnt will give the colour of a Hottentot. A Kafir requires burnt sienna in the half tints, vandyke brown in the shadows, and a cool grey like the reflection of the sky in the lights—this is best produced by a little Chinese white and cobalt laid on thin over the brown. There may be a little blue put into the black of the hair to contrast the better with the brown skin. For a Negro, crimson lake and blue-black; the lights made with Chinese white and blue as before.


CHAPTER XX.
THE ESTIMATION OF DISTANCES AND HINTS ON FIELD OBSERVING.

On measuring the Distance travelled by Wheeled Carriages.

When no instrument for this purpose is obtainable, the best plan we know of is that adopted by the late Dr. Burchell, the eminent South African traveller, and after him by Captain Cornwallis Harris, the explorer and naturalist, in the more distant parts of the same country; and this is, to measure the large wheel carefully, to mark one of its spokes, and count its revolutions during any given time, say a minute, and then convert the result into miles or parts of a mile per hour. Thus, if a wheel be 5yds. in circumference, and it makes six revolutions in a minute, the distance in that time will be 30yds., or 1800yds., i.e., 40yds. more than a mile per hour; twelve revolutions will of course be 80yds. over two miles; and, during former journeys, when our wheel was making eighteen revolutions, we used to reckon the waggon was going, allowing for occasional unavoidable stoppages, two and a half miles per hour. With a watch having a second hand it is easy to note any fraction of time, but with one not so provided less than a minute cannot easily be estimated. After a little practice we became so accustomed to this that we seldom used a watch; but when sitting on the waggon-box would just look over the side, and estimate the rate at which the wheel was going, just as a sailor would in like manner make a very fair estimate of the speed of his ship.

It will generally be found that an African ox-waggon, not overloaded, and on tolerably fair ground, travels about two and a half miles an hour; and we have also found that with pack horses in Australia, if the same rate is assumed, the resulting measurement of the day’s work will be very nearly correct.

We tried once to make a trocheameter, but at the time had never either seen one or read a description of it, and therefore the principle cost us some thinking out. It was perfectly evident that, for motive power, an axle so weighted that it could not revolve in a revolving box would produce the same effect upon the works as an axle made to revolve, by weights or otherwise, in a fixed box would have on those of a clock. We therefore made a box of such a form as to fit between spokes of the hinder wheels of a waggon, and in it fitted an axle with a heavy plummet, so fixed to it as to prevent its turning when the box revolved; on this axle was one tooth fitting into the cogs of a sixty-toothed wheel, which therefore moved one tooth for every revolution, or once round for every sixty; the axle of this had also one tooth acting on another of sixty teeth, so the two were capable of registering sixty times sixty, or three thousand six hundred revolutions, which, supposing the wheel to be only 5yds. in circumference, would measure ten miles and a quarter, the number of revolutions being indicated by a hand fixed upon the axle of each wheel, each moving on its own dial-plate, like those of a patent log. We found that the machine answered quite well enough to convince us that we were right in principle, and to make us regret that we had not the tools and appliances at hand to fit it so perfectly as to insure smoothness and uniformity of action.

To all, however, who have the means, we would say do not fail to buy a trocheameter: it is a small, compact instrument, fitted in a copper case, capable of being strapped on any convenient part of the wheel; and one of fair quality need not cost above 2l. 10s. or 3l. The instrument is composed of two revolving toothed wheels, the upper wheel having 101 and the lower 100 teeth, suspended from and turned by an endless screw; there are two indices, that on the upper wheel pointing out every single revolution, and that on the lower every hundred. The whole circuit of the instrument is 10,100 revolutions, and the following is an example of its power:

“One complete circuit of 10,100 revolutions, with a carriage-wheel of 12ft. circumference, would indicate 23 miles, minus 80yds. Thus, 55 revolutions give 220yds., or 1 furlong; 110 give 440yds., or a quarter of a mile; 440 give 1760yds., or 1 mile; 7040 give 16 miles; 10,100 equal to 23 miles, minus 80yds.

“To set the instrument unscrew the milled nut from off the steel endless screw, and move the wheels round until both the indices coincide; screw the nut firmly in its place, shut up the instrument, and strap it securely to the off-wheel in the centre of the nave.”

In Africa we cannot literally follow out these instructions, for the nave is not brass capped, as with carriage-wheels at home, but the end of the axle comes through, and the wheel is secured to it by a washer and a linch pin; therefore, we strap the trocheameter between the spokes as near to the nave as possible, and in our journey to the Zambesi Fall we secured a pint pannikin permanently between the spokes as a protection to the trocheameter, which just fitted nicely into it during this journey. We measured a distance of between 2000 and 3000 miles, and do not remember that this instrument failed, except once from being choked with fine dry sand, and once again from equally fine sand and water.

We subjoin a table, by which it will be seen that our waggon-wheel was 5yds. 2½in. in circumference; this fraction gave some little trouble in the preliminary computation, and it looked very absurd to calculate the stages to half an inch, but if we had thrown it out a considerable error would have accumulated, and when the table was once formed the trouble was at an end.

Trocheameter Table.

First Wheel.

No. Fur. Yds. Ft. In. No. Fur. Yds. Ft. In.
1 5 0 52 1 43 1 10   
2 10 0 5    53 1 48 2
3 15 0 54 1 53 2 3   
4 20 0 10    55 1 58 2
5 25 1 56 1 63 2 8   
6 30 1 3    57 1 68 2 10½
7 35 1 58 1 74 0 1   
8 40 1 8    59 1 79 0
9 45 1 10½ 60 1 84 0 6   
10 50 2 1    61 1 89 0
11 55 2 62 1 94 0 11   
12 60 2 6    63 1 99 1
13 65 2 64 1 104 1 4   
14 70 2 11    65 1 109 1
15 76 0 66 1 114 1 9   
16 81 0 4    67 1 119 1 11½
17 86 0 68 1 124 2 2   
18 91 0 9    69 1 129 2
19 96 0 11½ 70 1 134 2 7   
20 101 1 2    71 1 139 2
21 106 1 72 1 145 0 0   
22 111 1 7    73 1 150 0
23 116 1 74 1 155 0 5   
24 121 2 0    75 1 160 0
25 126 2 76 1 165 0 10   
26 131 2 5    77 1 170 1
27 136 2s 78 1 175 1 3   
28 1 141 2 10    79 1 180 1
29 1 147 0 80 1 185 1 8   
30 152 0 3    81 1 190 1 10½
31 157 0 82 1 195 2 1   
32 162 0 8    83 1 200 2
33 167 0 10½ 84 1 205 2 6   
34 172 1 1    85 1 210 2
35 177 1 86 1 215 2 11   
36 182 1 6    87 2 1 0
37 187 1 88 2 6 0 4   
38 192 1 11    89 2 11 0
39 197 2 90 2 16 0 9   
40 202 2 4    91 2 21 0 11½
41 207 2 92 2 26 1 2   
42 212 2 9    93 2 31 1
43 217 2 11½ 94 2 36 1 7   
44 1 3 0 2    95 2 41 1
45 1 8 0 96 2 46 2 0   
46 1 13 0 7    97 2 51 2
47 1 18 0 98 2 56 2 5   
48 1 23 1 0    99 2 61 2
49 1 28 1 100 2 66 2 10   
50 1 33 1 5    101 2 72 0
51 1 38 1  

Second Wheel.

No. Miles. Fur. Yds. Ft. In. No. Miles. Fur. Yds. Ft. In.
1 2 72 0 20 5 6 120 0 10   
2 4 144 0 1    30 8 5 180 1 3   
3 6 216 0 40 11 5 20 1 8   
4 1 1 68 0 2    50 14 4 80 2 1   
5 1 3 14 0 60 17 3 140 2 6   
6 1 5 212 0 3    70 20 2 200 2 11   
7 2 0 64 0 80 23 2 41 0 4   
8 2 2 136 0 4    90 26 1 101 0 9   
9 2 4 208 0 100 29 0 161 1 2   
10 2 7 60 0 5     

We give also an example of the work:—

December 27, 1861.—From Christmas Tree, south-west angle of Lake Ngami, two miles from Bolebeng—trocheameter at zero.

First halt south of the Lake:—

Trocheameter637 
 m.fur.yds.ft.in.
61521203   
37001871
  16179111½

28th.—North of the Vlei Moslenyan:—

Trocheameter2291 
 637 
 1654 
 m.fur.yds.ft.in.
10276005
61521203
54015323
  46105211

29th.—The Big Tree, or Baobab at Mamakahooie:—

Borrow 101 
Trocheameter5073 
 2291 
 2783 
  m. fur. yds. ft. in.
20 5 6 120 0 10   
7 2 0 64 0
83 0 1 200 2
  8 0 165 0 5   

29th, p.m.—A hollow, with water:—

Borrow 101 
Trocheameter7653 
 5073 
 2581 
  m. fur. yds. ft. in.
20 5 6 120 0 10   
5 1 3 14 0
81 0 1 190 1 10½
  7 3 104 0 11   

30th.—A small Vlei:—

Borrow 101 
Trocheameter9344 
 7653 
 1692 
  m. fur. yds. ft. in.
10 2 7 60 0 5   
6 1 5 212 0 3   
92 0 2 26 1 2   
  4 7 78 0 10   

31st.—Outspan in the Bush.

Trocheameter1289 
Add100  
 11289 
 9344 
  m. fur. yds. ft. in.
10 2 7 60 0 5   
9 2 4 208 0
45 0 1 8 0
  5 5 56 1 2   

As a means of measuring a base line for triangulation of a country the trocheameter is invaluable. Suppose the course is north, and that a mountain bears 90°, or east; let the waggon travel till the mountain bears 45° more southerly, or 135°, i.e., south-east; then stop the waggon, read the trocheameter, and the length of road travelled will be equal to the distance of the mountain from the starting place. Even if the course does not form a right angle with the bearing, the same method may be followed, involving only a little more calculation, or the trouble of laying down the angle upon paper. In places where a waggon cannot travel, it would be well to have a large wheel, on the principle of the old perambulator, and fix the trocheameter upon it; only let it be loaded, so as to bear the semblance of usefulness in the eyes of natives, or even of illiterate white men, or they will infallibly carry it over the bad places, as Captain Sturt’s men did, to save themselves trouble. The trocheameter may be fitted to any piece of machinery, as the screw or paddles of a steamer, the sails of a windmill, a waterwheel, or anything capable of turning round.

To ascertain the Variation of the Compass.