SURVEYING INSTRUMENTS.

In previous editions I reprinted here, with a few trifling alterations, part of a paper that I originally communicated to the Royal Geographical Society, and which will be found at the end of their volume for 1854. In addition to it, communications are published there from Lieutenant Raper, Admiral FitzRoy, Admiral Smyth, Admiral Beechey, and Colonel Sykes; the whole of which was collected under the title of 'Hints to Travellers;' they were printed in a separate form and widely circulated. When the edition was exhausted, a fresh Committee was appointed by the Council of the Royal Geographical society, consisting of Admiral sir George Back, Admiral R. Collinson, and myself, to revise the pamphlet thoroughly. This process was again gone through in 1871, and now the pamphlet is so much amended and enlarged that I should do no good by making extracts. It is much better that intending travellers should apply for this third edition of the 'Hints to Travellers' at the society's rooms, 1, Savile Row: for it gives a great deal of information upon instruments that they would find of real value. Its price is 1s.

Porters for delicate Instruments.--Entrust surveying instruments and fragile articles to come respectable old savage, whose infirmities compel him to walk steadily. He will be delighted at the prospect of picking up a living by such easy service.

Measuring low angles by reflexion.--an ordinary artificial horizon is useless for very low angles. They can be measured to within two or three minutes, by means of a vertical point of reference obtained in the following manner:--Tie two pieces of thread, crossing each other at two feet above the ground, put the vessel of mercury underneath it, and look down upon the mercury. When the eye is so placed, that the crossed threads exactly cover their reflexion, the line of sight is truly vertical; and, if the distant object be brought down to them by the sextant, the angle read off will be 90 degrees + altitude. Captain George's arrangement of glass floating on mercury (made by Cary, Fleet Street, London), allows of very low angles being observed, but the use of this instrument requires considerable caution as to the purity of the mercury and the cleanliness of the glass.

Substitute for glass roof to Horizon.--For want of a glass roof to place over the mercury a piece of gauze stretched over the vessel will answer very tolerably for the purpose of keeping off the wind. The diameter of the pupil of the eye is so large, compared to the thickness of the threads of the gauze, that the latter offer little impediment to a clear view of the image.

Silvering Glasses for Sextants.--"Before taking leave of this subject it may not be unimportant to describe the operation of silvering the glasses of sextants, as those employed on surveying duties very frequently have to perform the operation.

"The requisites are clean tinfoil and mercury (a hare's foot is handy)--lay the tinfoil, which should exceed the surface of the glass by a quarter of an inch on each side, on a smooth surface (the back of a book), rub it out smooth with the finger, add a bubble of mercury, about the size of a small shot, which rub gently over the tinfoil until it spreads itself and shows a silvered surface, gently add sufficient mercury to cover the leaf so that its surface is fluid. Prepare a slip of paper the size of the tinfoil. Take the glass in the left hand, previously well cleaned, and the paper in the right. Brush the surface of the mercury gently to free it from dross. Lay the paper on the mercury, and the glass on it. Pressing gently on the glass, withdraw the paper. turn the glass on its face, and leave it on an inclined plane to allow the mercury to flow off, which is accelerated by laying a strip of tinfoil as a conductor to its lower edge. The edges may, after twelve hours' rest, be removed. In twenty-four hours give it a coat of varnish, made from spirits of wine and red sealing-wax. It may be as well to practise on small bits of common glass, which will soon prove the degree of perfection which the operator has attained." (Admiral Sir E. Belcher.)

MEMORANDA AND LOG-BOOKS.

Best form for Memoranda.--I have remarked that almost every traveller who is distinguished for the copiousness and accuracy of his journals, has written them in a remarkably small but distinct handwriting. Hard pencil-marks (HHH pencils) on common paper, or on metallic paper are very durable. Dr. Barth wrote his numerous observations entirely in Indian-ink. He kept a tiny saucer in his pocket, rubbed with the ink; when he wanted to use it, he rubbed it up with his wetted finger-tip, or resupplied it with fresh ink, and filled his pen and wrote. Captain Burton wrote very much in the dark, when lying awake at night; he used a board with prominent lines of wood, such as is adopted by the blind. It is very important that what is written should be intelligible to a stranger after a long lapse of time. A traveller may die, and his uncompleted work perish with him; or he may return, and years will pass by, and suddenly some observations he had made will be called in question.

Professor J. Forbes says:--"The practice which I have long adopted is this:--to carry a memorandum-book with Harwood's prepared paper" (in this point of detail I do not concur; see next paragraph) "and metallic pencil, in which notes and observations and slight sketches of every description, are made on the spot, and in the exact order in which they occur. These notes are almost ineffaceable, and are preserved for reference. They are then extended, as far as possible, every evening with pen and ink, in a suitable book, in the form of a journal; from which, finally, they may be extracted and modified for any ultimate purpose. The speedy extension of memoranda has several great advantages: it secures a deliberate revision of observations, whether of instruments or of nature, whilst further explanation may be sought, and very often whilst ambiguities or contradictions admit of removal by a fresh appeal to facts. By this precaution, too, the risk of losing all the fruits of some weeks of labour, by the loss of a pocket-book, may be avoided."

It has occurred to me, frequently, to be consulted about the best was of keeping MSS. Captain Blakiston, who surveyed the northern part of the Rocky Mountains, and subsequently received the medal of the Royal Geographical Society, for his exploration and admirable map of the Yang-tse-Kiang, in China, paid great attention to the subject: he was fully in possession of all I had to say on the matter; and I gladly quote the method he adopted in North America, with slight modifications, according to the results of his experience, and with a few trivial additions of my own. For the purposes of memoranda and mapping data, he uses three sets of books, which can be ordered at any lithographer's:--

No. 1. pocket Memorandum Book, measuring three inches and a half by five, made of strong paper. (Captain Blakston did not use, and I should not advise travellers to use, "prepared" paper, for it soon becomes rotten, and the leaves fall out; besides that, wet makes the paper soppy.) The books are paged with bold numbers printed in the corners; two faint red lines are ruled down the middle of each page, half an inch apart, to enable the book to be used as a field-surveyor's book when required. In this pocket=book, every single thing that is recorded at all, is originally recorded with a hard HHH pencil. Everything is written consecutively, without confusion or attempt to save space. There may easily be 150 pages in each of these books; and a sufficient number should be procured to admit of having at least one per month. Do not stint yourself in these.

No. 2. Log-Book.--This is an orderly way of collecting such parts of the surveying material as has been scattered over each day in your note-book. It is to be neatly written out, and will become the standard of future reference. By using a printed form, the labour of drawing up the log on the one hand, and that of consulting it on the other, will be vastly diminished. I give Captain Blakiston's form, in pages 28, 29, and I would urge intending travellers not to depart from it without very valid reasons, for it is the result of considerable care and experience. The size in which the form is printed here is not quite accurate, because the pages of this book are not large enough to admit of it, but the proportion is kept. The actual size is intended to be five and a half inches high and nine inches wide, so that it should open freely along one of the narrow sides of the page, in the way that all memoranda books ought to open. Four pages go to a day; of these the pages 1 and 2 are alone represented in this book, pages 3 and 4 being intended to be left blank.

The bold figures 17 and 18 in the right-hand corners of the form I give, show how the pages should be numbered. The lines in p. 18 should be faint blue.

No. 3. Calculation Book.--This should be of the same size and shape as the Log Book, and should contain outline forms for calculations. The labour and confusion saved by using these, and the accuracy of work that they ensure, are truly remarkable. The instruments used, the observations made, and especially the tables employed, are so exceedingly diverse, that I fear it would be to little purpose if I were to give special examples: each traveller must suit himself. I will, therefore, simply make a few general remarks on this subject, in the following paragraph.

Number of Observations requiring record.--A traveller does excellently, who takes latitudes by meridian altitudes, once in the twenty-four hours; a careful series of lunars once a fortnight, on an average; compass variations as often; and an occulation now and then. He will want, occasionally, a time observation by which to set his watch (I am supposing he uses no chronometer). He ought therefore to provide himself with outline forms for calculating these observations, even if he finds himself obliged to have them printed or lithographed on purpose; and in preparing them, he should bear the following well-known maxims in mind:--

Let all careful observations be in doubles. If they be for latitudes, observe a star N. and a star S.; the errors of your instruments will then affect the results in opposite directions, and the mean of the results will destroy the error. So, if for time, observe in doubles, viz., a star E. and a star W. Also, if for lunars, let your sets be in doubles--one set of distances to a star E. of moon, and one to a star W. of moon. Whenever you begin on lunars, give three hours at least to them, and bring away a reliable series; you will be thus possessed of a certainty to work upon, instead of the miserably unsatisfactory results obtained from a single set of lunars taken here and another set there, scattered all over the country, and impossible to correlate. A series should consist of six sets, each set including three simple distances. Three of these sets should be to a star or stars E. of moon, and three to a star or stars W. of moon. Lunars not taken on the E. and W. plan are almost worthless, no matter how numerous they may be, for the sextant, etc., might be inaccurate to any amount, and yet no error be manifest in their results. But the E. and W. plan exposes errors mercilessly, and also eliminates them. One of the best authorities on the requirements of sextant observations in rude land travel, the Astronomer Royal of Cape Town, says to this effect:--"Do not observe the altitude of the star in taking lunars, but compute it. The labour requisite for that observation is better bestowed in taking a large number of distances." So much delicacy of hand and of eyesight is requisite in taking lunars that shall give results reliable to seven or eight miles, and so small an exertion or flurry spoils that delicacy, that economy of labour and fidget is a matter to be carefully studied.

These things being premised, it will be readily understood that outline forms sufficient for an entire series of lunars will extend over many pages--they will, in fact, require eighteen pages. There are four sets of observations for time:--one E. and one W., both at beginning and close of the whole; one for latitudes N. and S.; six for six sets of lunars, as described above; six for the corresponding altitudes of the stars, which have to be computed; and, finally, one page for taking means, and recording the observations for adjustment, etc. Each double observation for latitude would take one page; each single time observation one page; and each single compass variation one page. An occulation would require three pages in all; one of which would be for time. At this rate, and taking the observations mentioned above, a book of 500 pages would last half a year. Of course where the means of transport is limited, travellers must content themselves with less. Thus Captain Speke, who started on his great journey amply equipped with log-books and calculation-books, such as I have described, found them too great an incumbrance, and was compelled to abandon them. The result was, that though he brought back a very large number of laborious observations, there was a want of method in them, which made a considerable part of his work of little or no use, while the rest required very careful treatment, in order to give results commensurate with their high intrinsic value.

MEASUREMENTS.

Distance.--To measure the Length of a Journey by Time.--The pace of a caravan across average country is 2 1/2 statute, or 2 geographical, miles per hour, as measured with compasses from point to point, and not following the sinuosities of each day's course; but in making this estimate, every minute lost in stoppages by the way is supposed to be subtracted from the whole time spent on the road. A careful traveller will be surprised at the accuracy of the geographical results, obtainable by noting the time he has employed in actual travel. Experience shows that 10 English miles per day, measured along the road--or, what is much the same thing, 7 geographical miles, measured with a pair of compasses from point to point--is, taking one day with another, and including all stoppages of every kind, whatever be their cause,--very fast travelling for a caravan. In estimating the probable duration of a journey in an unknown country, or in arranging an outfit for an exploring expedition, not more than half that speed should be reckoned upon. Indeed, it would be creditable to an explorer to have conducted the same caravan for a distance of 1000 geographical miles, across a rude country, in six months. These data have, of course, no reference to a journey which may be accomplished by a single great effort, nor to one where the watering-places and pasturages are well known; but apply to an exploration of considerable length, in which a traveller must feel his way, and where he must use great caution not to exhaust his cattle, lest some unexpected call for exertion should arise, which they might prove unequal to meet. Persons who have never travelled--and very many of those who have, from neglecting to analyse their own performances--entertain very erroneous views on these matters.

Rate of Movement to measure.--a. When the length of pace etc., is known before beginning, to observe.--A man or a horse walking at the rate of one mile per hour, takes 10 paces in some ascertainable number of seconds, dependent upon the length of his step. If the length of his step be 30 inches, he will occupy 17 seconds in making 10 paces. Conversely, if the same person counts his paces for 17 seconds, and finds that he has taken 10 in that time, he will know that he is walking at the rate of exactly 1 mile per hour. If he had taken 40 paces in the same period, he would know that his rate had been 4 miles per hour; if 35 paces, that it had been 3.5, or 3 1/2 miles per hour. Thus it will be easily intelligible, that if a man knows the number of seconds appropriate to the length of his pace, he can learn the rate at which he is walking, by counting his paces during that number of seconds and by dividing the number of his paces so obtained, by 10. In short the number of his paces during the period in question, gives his rate per hour, in miles and decimals of a mile, to one place of decimals. I am indebted to Mr. Archibald Smith for this very ingenious notion, which I have worked into the following Tables. In Table I., I give the appropriate number of seconds corresponding to paces of various lengths. I find, however, that the pace of neither man nor horse is constant in length during all rates of walking; consequently, where precision is sought, it is better to use this Table on a method of approximation. That is to say, the traveller should find his approximate rate by using the number of seconds appropriate to his estimated speed. Then, knowing the length of pace due to that approximate rate, he will proceed afresh by adopting a revised number of seconds, and will obtain a result much nearer to the truth than the first. Table I. could of course be employed for finding the rate of a carriage, when the circumference of one of its wheels was known; but it is troublesome to make such a measurement. I therefore have calculated Table II., in terms of the radius of the wheel. The formulae by which the two Tables have been calculated are, m=l x 0.5682 for Table I., and m=r x 3.570 for Table II., where m is the appropriate number of seconds; l is the length of the pace, or circumference of the wheel; and r is the radius of the wheel.

b. When the length of Pace is unknown till after observation.--In this case, the following plan gives the rate of travel per hour, with the smallest amount of arithmetic.

For statute miles per hour--Observe the number of paces (n) taken in 5.7 seconds: let i be the number of inches (to be subsequently determined at leisure) in a single pace; then ni/100 is the rate per hour.

For geographical miles per hour--The number of seconds to be employed is 5. This formula is therefore very simple, and it is a useful one. (A statute mile is 1760 yards, and a geographical mile is 2025 yards.)

For finding the rate in statute miles per hour in a carriage--Observe the number of revolutions (n) made by the wheel in 18 seconds: let d be the number of inches in the diameter of the wheel; then n d/200 is the rate per hour.

The above method is convenient for measuring the rate at which an animal gallops. After counting its paces it may be through a telescope, during the prescribed number of seconds, you walk to the track, and measure the length of its pace. If you have no measuring tape, stride in yards alongside its track, to find the number of yards that are covered by 36 of its paces. This is, of course, identical with the number of inches in one of its paces.

Convenient Equivalents.--The rate of 1 mile per hour, is the equivalent to each of the rates in the following list:--

Yards. Feet. Inches. 29.333, or 88.000, or 1056.000, in one minute or 0.488, or 1.466, or 17.600, in one second

Measurement of Length.--Actual measurement with the rudest makeshift, is far preferable to an unassisted guess, especially to an unpractised eye.

Natural Units of Length.--A man should ascertain his height; height of his eye above ground; ditto, when kneeling: his fathom; his cubit; his average pace; the span, from ball of thumb to tip of one of his fingers; the length of the foot; the width of two, three, or four fingers; and the distance between his eyes. In all probability, some one of these is an even and a useful number of feet or inches, which he will always be able to recollect, and refer to as a unit of measurement. The distance between the eyes is instantly determined, and, I believe, never varies, while measurements of stature, and certainly those of girth of limb, become very different when a man is exhausted by long travel and bad diet. It is therefore particularly useful for measuring small objects. To find it, hold a stick at arm's-length, at right angles to the line of sight; then, looking past its end to a distant object, shut first one eye and then the other, until you have satisfied yourself of the exact point on the stick that covers the distant object as seen by the one eye, when the end of the stick exactly covers the same object, as seen by the other eye. A stone's throw is a good standard of reference for greater distances. Cricketers estimate distance by the length between wickets. Pacing yards should be practised. It is well to dot or burn with the lens of your opera-glass a scale of inches on the gun-stock and pocket-knife.

Velocity of Sound.--Sound flies at 380 yards or about 1000 feet in a second, speaking in round numbers: it is easy to measure rough distances by the flash of a gun and its report; for even a storm of wind only makes 4 per cent. difference, one way or the other, in the velocity of sound.

Measurement of Angles.--Rude Measurements.--I find that a capital substitute for a very rude sextant is afforded by the outstretched hand and arm. The span between the middle finger and the thumb subtends an angle of about 15 degrees, and that between the forefinger and the thumb an angle of 11 1/4 degrees, or one point of the compass. Just as a person may learn to walk yards accurately, so may he learn to span out these angular distances accurately; and the horizon, however broken it may be, is always before his eyes to check him. Thus, if he begins from a tree, or even from a book on his shelves and spans all round until he comes to the tree or book again, he should make twenty-four of the larger spans and thirty-two of the lesser ones. These two angles of 15 degrees and 11 1/4 degrees are particularly important. The sun travels through 15 degrees in each hour; and therefore, by "spanning" along its course, as estimated, from the place where it would stand at noon (aided in this by the compass), the hour before or after noon, and, similarly after sunrise or before sunset, can be instantly reckoned. Again, the angles 30 degrees, 45 degrees, 60 degrees, and 90 degrees, all of them simple multiples of 15 degrees, are by far the most useful ones in taking rough measurements of heights and distances, because of the simple relations between the sides of right-angled triangles, one of whose other angles are 30 degrees, 45 degrees, or 60 degrees; and also because 60 degrees is the value of an angle of an equilateral triangle. As regards 11 1/4 degrees, or one point of the compass, it is perfectly out of the question to trust to bearings taken by the unaided eye, or to steer a steady course by simply watching a star or landmark, when this happens to be much to the right or the left of it. Now, nothing is easier than to span out the bearing from time to time.

Right-angles to lay out.--A triangle whose sides are as 3, 4, and 5, must be a right-angled one, since 5 x 5 = 3 x 3 + 4 x 4; therefore we can find a right-angle very simply by means of a measuring-tape. We take a length of twelve feet, yards, fathoms, or whatever it may be, and peg its two ends, side by side, to the ground. Peg No. 2 is driven in at the third division, and peg No. 3 is held at the seventh division of the cord, which is stretched out till it becomes taut; then the peg is driven in. These three pegs will form the corners of a right-angled triangle; peg No. 2 being situated at the right-angle.

Proximate Arcs.--

1 degree subtends, at a distance of 1 statute mile, 90 feet.
1' subtends, at a distance of 1 statute mile, 18 inches.
1' subtends at a distance of 100 yards, 1 inch.
1" of latitude on the earth's surface is 100 feet.
30' is subtended by the diameter of either the sun or the moon.

Angles measured by their Chords.--The number of degrees contained by any given angle, may be ascertained without a protractor or other angular instrument, by means of a Table of Chords. So, also, may any required angle be protracted on paper, through the same simple means. In the first instance, draw a circle on paper with its centre at the apex of the angle and with a radius of 1000, next measure the distance between the points where the circle is cut by the two lines that enclose the angle. Lastly look for that distance (which is the chord of the angle) in the annexed table, where the corresponding number of degrees will be found, where the corresponding number of degrees will be found. If it be desired to protract a given angle, the same operation is to be performed in a converse sense. I need hardly mention that the chord of an angle is the same thing as twice the sine of half that angle; but as tables of natural sines are not now-a-days commonly to be met with, I have thought it well worth while to give a Table of Chords. When a traveller, who is unprovided with regular instruments, wishes to triangulate, or when having taken some bearings but having no protractor, he wishes to lay them down upon his map, this little table will prove of very great service to him. (See "Measurement of distances to inaccessible places.")

Triangulation.--Measurement of distance to an inaccessible place.--By similar triangles.--To show how the breadth of a river may be measured without instruments, without any table, and without crossing it, I have taken the following useful problem from the French 'Manuel du Genie.' Those usually given by English writers for the same purpose are, strangely enough, unsatisfactory, for they require the measurement of an angle. This plan requires pacing only. To measure A G, produce it for any distance, as to D; from D, in any convenient direction, take any equal distances, D C, c d; produce B C to b, making c B--C B; join d b, and produce it to a, that is to say, to the point where A C produced intersects it; then the triangles to the left of C, are similar to those on the right of C, and therefore a b is equal to A B. The points D C, etc., may be marked by bushes planted in the ground, or by men standing.

The disadvantages of this plan are its complexity, and the usual difficulty of finding a sufficient space of level ground, for its execution. The method given in the following paragraph is incomparably more facile and generally applicable.

Triangulation by measurement of Chords.--Colonel Everest, the late Surveyor-General of India, pointed out (Journ. Roy. Geograph. Soc. 1860, p. 122) the advantage to travellers, unprovided with angular instruments, of measure the chords of the angles they wish to determine. He showed that a person who desired to make a rude measurement of the angle C A B, in the figure (p. 40), has simply to pace for any convenient length from A towards C, reaching, we will say, the point a' and then to pace an equal distance from A towards B, reaching the point a ae. Then it remains for him to pace the distance a' a" which is the chord of the angle A to the radius A a'. Knowing this, he can ascertain the value of the angle C A B by reference to a proper table. In the same way the angle C B A can be ascertained. Lastly, by pacing the distance A B, to serve as a base, all the necessary data will have been obtained for determining the lines A C and B C. The problem can be worked out, either by calculation or by protraction. I have made numerous measurements in this way, and find the practical error to be within five per cent.

Table for rude triangulation by Chords.--It occurred to me that the plan described in the foregoing paragraph might be exceedingly simplified by a table, such as that which I annex in which different values of a' a" are given for a radius of 10, and in which the calculations are made for a base = 100. The units in which A a', A a", and B b', Bb", are to be measured are intended to be paces, though, of course, any other units would do. The units in which the base is measured may be feet, yards, minutes, or hours' journey, or whatever else is convenient. Any multiple or divisor of 100 may be used for the base, if the tabular number be similarly multiplied. Therefore a traveller may ascertain the breadth of a river, or that of a valley, or the distance of any object on either side of his line of march, by taking not more than some sixty additional paces, and by making a single reference to my table. Particular care must be taken to walk in a straight line from A to B, by sighting some more distant object in a line with B. It will otherwise surprise most people, on looking back at their track, to see how curved it has been and how far their b' B is from being in the right direction.

Measurement of Time.--Sun Dial.--Plant a stake firmly in the ground in a level open space, and get ready a piece of string, a tent-peg, and a bit of stick a foot long. When the stars begin to appear, and before it is dark, go to the stake, lie down on the ground, and plant the stick, so adjusting it that its top and the point where the string is tied to the stake shall be in a line with the Polar Star, or rather with the Pole (see below); then get up, stretch the string so as just to touch the top of the stick, and stake it down with the tent-peg. Kneel down again, to see that all is right, and in the morning draw out the dial-lines; the string being the gnomon. The true North Pole is distant about 1 1/2 degree, or three suns' (or moons') diameters from the Polar Star, and it lies between the Polar Star and the pointers of the Great Bear, or, more truly, between it and [Greek letter] Urs ae Majoris.

The one essential point of dial-making is to set the gnomon truly, because it ensures that the shadows shall fall in the same direction at the same hours all the year round. To ascertain where to mark the hour-lines on the ground, or wall, on which the shadow of the gnomon falls, the simplest plan is to use a watch, or whatever makeshift means of reckoning time be at hand. Calculations are troublesome, unless the plate is quite level, or vertical, and exactly facing south or north, or else in the plane of the Equinox.

The figure represents the well-known equinoctial sun-dial. It can easily be cast in lead. The spike points towards the elevated pole, and the rim of the disc is divided into 24 equal parts for the hours.

Pendulum.--A Traveller, when the last of his watches breaks down, has no need to be disheartened from going on with his longitudinal observations, especially if he observes occulations and eclipses. The object of a watch is to tell the number of seconds that elapse between the instant of occulation, eclipse, etc., and the instant, a minute or two later, when the sextant observation for time is made. All that a watch actually does is to beat seconds, and to record the number of beats. Now, a string and stone, swung as a pendulum, will beat time; and a native who is taught to throw a pebble into a bag at each beat, will record it; and, for operations that do not occupy much time, he will be as good as a watch. The rate of the pendulum may be determined by taking two sets of observations, with three or four minutes' interval between them; and, if the distance from the point of suspension to the centre of the stone be thirty-nine inches, and if the string be thin and the stone very heavy, it will beat seconds very nearly indeed. The observations upon which the longitude of the East African lakes depended, after Captain Speke's first journey to them, were lunars, timed with a string and a stone, in default of a watch.

Hour-glass.--Either dry sand or water may be used in an hour-glass; if water be used, the aperture through which it runs must, of course, be smaller.

CLIMBING AND MOUNTAINEERING.

Climbing.--Climbing trees.--Colonel Jackson, in his book, 'How to Observe,' gives the following directions for climbing palms and other trees that have very rough barks:--"Take a strip of linen, or two towels or strong handkerchiefs tied together, and form a loop at each end, for the feet to pass tightly into without going through; or, for want of such material, make a rope of grass or straw in the same way. The length should embrace a little more than half of the diameter of the trunk to be climbed. Now, being at the foot of the tree, fix the feet well into the loops, and opening the legs a little, embrace the tree as high up as you can. Raise your legs, and pressing the cord against the tree with your feet, stand, as it were, in your stirrups, and raise your body and arms higher; hold fast again by the arms, open the legs, and raise them a stage higher, and so on to the top. The descent is effected in the same way, reversing, of course, the order of the movements. The ruggedness of the bark, and the weight of the body pressing diagonally across the trunk of the tree, prevent the rope from slipping. Anything, provided it be strong enough, is better than a round rope, which does not hold so fast." A loop or hoop embracing the body of the climber and the tree, is a helpful addition. Large nails carried in a bag slung round the waist, to be driven into the bare trunk of the tree, will facilitate its ascent. Gimlets may be used for the same purpose. High walls can be climbed by help of this description; a weight attached to one end of a rope, being first thrown over the wall, and the climber assisting himself by holding on to the other end. Trees of soft wood are climbed by cutting notches two feet apart on alternate sides. Also by driving in bamboo pegs, sloping alternately to left or to right; these pegs correspond to the "rungs" of a ladder.

Ladders.--A notched pole or a knotted rope makes a ladder. We hear of people who have tied sheets together to let themselves down high walls, when making an escape. The best way of making a long rope from sheets, is to cut them into strips of about six inches broad, and with these to twist a two-stranded rope, or else to plait a three-stranded one.

Descending cliffs with ropes is an art which naturalists and others have occasion to practise. It has been reduced to a system by the inhabitants of some rocky coasts in the Northern seas, where innumerable sea-birds go for the breeding season, and whose ledges and crevices are crammed with nests full of large eggs, about the end of May and the beginning of June. They are no despicable prize to a hungry native. I am indebted to a most devoted rock-climber, the late Mr. Woolley, for the following facts. It appears that the whole population are rock-climbers, in the following places:--St. Kilda, in the Hebrides; Foula Island, in Shetland; the Faroe Islands generally; and in the Westmarver Islands off Iceland. Flamborough Head used to be a famous place for this accomplishment, but the birds have become far less numerous; they have been destroyed very wantonly with shot.

In descending a cliff, two ropes are used; one a supply well-made, many-stranded, inch rope (see "Ropes"), to which the climber is attached, and by which he is let down; the other is a much thinner cord, left to dangle over the cliff, and made fast to some stone or stake above. The use of the second rope is for the climber to haul upon, when he wishes to be pulled up. By resting a large part of his weight upon it, he makes the task of pulling him up much more easy. He can also convey signals by jerking it. A usual rock-climbing arrangement is shown in the sketch. One man with a post behind him, as in fig. 1, or two men, as in fig. 2 are entrusted with the letting down of a comrade to the depth of 100 or even 150 feet. They pass the rope either under their thighs or along their sides, as shown in the figures. The climber is attached to the rope, as shown in fig. 2. The band on which he sits is of worsted. A beginner ought to be attached far more securely to the rope.

(I have tried several plans, and find that which is shown in Fig. 1 to be thoroughly comfortable and secure. A stick forms the seat' at either end of it is a short stirrup; garters secure the stirrup leathers to the knees; there is a belt under the arms.)

It is convenient, but not necessary, to have a well-greased leather sheath, a tube of eighteen inches in length, through which the rope runs, as shown in both figures. It lies over the edges of the cliff, and the friction of the rock keeps it steadily in its place.

It is nervous work going over the edge of a cliff for the first time; however, the sensation does not include giddiness. Once in the air, and when confidence is acquired, the occupation is very exhilarating. The power of locomotion is marvellous: a slight push with the foot, or a thrust with a stick, will swing the climber twenty feet to a side. Few rocks are so precipitous but that a climber can generally make some use of his hands and feet; enough to cling to the rock when he wishes, and to clamber about its face. The wind is seldom a gale above, but the air will be comparatively quiet upon the face; and therefore there is no danger of a chance gush dashing the climber against the rocks. A short stick is useful, but not necessary. There are three cautions to be borne in mind. 1. As you go down, test every stone carefully. If the movement of the rope displaces any one of them, after you have been let down below it, it is nearly sure to fall upon your head, because you will be vertically beneath it. Some climbers use a kind of helmet as a shield against these very dangerous accidents. 2. Take care that the rope does not become jammed in a cleft, or you will be helplessly suspended in mid-air. Keep the rope pretty tight when you are clambering about the ledges: else, if you slip, the jerk may break the rope, or cause an overpowering strain upon the men who are holding it above.

Turf and solid rock are much the best substances for the rope to run over. In the Faroes, they tar the ropes excessively; they are absolutely polished with tar. Good ropes are highly valued. In St. Kilda, leather ropes are used: they last a lifetime, and are a dowry for a daughter. A new rope spins terribly.

Leaping Poles.--In France they practise a way of crossing a deep brook by the help of a rope passed round an overhanging branch of a tree growing by its side. They take a run and swing themselves across, pendulum fashion. It is the principle of the leaping-pole, reversed.

The art of climbing difficult places.--Always face difficult places; if you slip, let your first effort be to turn upon your stomach, for in every other position you are helpless. A mountaineer, when he meets with a formidable obstacle, does not hold on the rock by means of his feet and his hands only, but he clings to it like a caterpillar, with every part of his body that can come simultaneously into contact with its roughened surface.

Snow Mountains.--Precautions.--The real dangers of the high Alps may be reduced to three:--1. Yielding of snow-bridges over crevices. 2. Slipping on slopes of ice. 3. The fall of ice, or rocks, from above. Absolute security from the first is obtainable by tying the party together at intervals to a rope. If there be only two in company, they should be tied together at eight or ten paces apart. Against the second danger, the rope is usually effective, though frightful accidents have occurred by the fall of one man, dragging along with him the whole chain of his companions. Against the third danger there is no resource but circumspection. Ice falls chiefly in the heat of the day; it is from limestone cliffs that the falling rocks are nearly always detached. When climbing ice of the most moderate slope, nailed boots are an absolute necessity; and for steep slopes of ice, the ice-axe (described below) is equally essential.

Alpine Outfit consists of ropes, ice-axe or alpenstock (there must be at least one ice-axe in the party), nailed boots, coloured spectacles, veil or else a linen mask, muffettees, and gaiters.

I give the following extracts from the Report of a Committee appointed by the Alpine Club in 1864, on Ropes, Axes, and Alpenstocks:-- Ropes.--We have endeavoured to ascertain what ropes will best stand the sharp jerk which would be caused by a man falling suddenly into a crevasse, or down an ice-slope: and on this subject we lay before the Club the result of nearly a hundred experiments, made with various kinds of rope purchased of the best London makers. We considered that the least weight with which it was practically useful to test ropes, was twelve stone, as representing the average weight of a light man with his whole Alpine equipment. In the preliminary experiments, therefore, all ropes were rejected which did not support the strain produced by twelve stone falling five feet. Under this trial, all those plaited ropes which are generally supposed to be so strong, and many most carefully-made twisted ropes, gave way in such a manner as was very startling to some of our number, who had been in the habit of using these treacherous cords with perfect and most unfounded confidence. Only four ropes passed successfully through this trial; these were all made by Messrs. Buckingham and Sons, of 33, Broad-street, Bloomsbury, and can be procured only of them. We confined our further experiments to these ropes, one of which failed under severer tests, while the remaining three, made respectively of Manilla hemp, Italian hemp, and flax, proved so nearly equal in strength that it may fairly be doubted which is on the whole to be preferred. Each of these three ropes will bear twelve stone falling ten feet, and fourteen stone falling eight feet; and it may be useful to say that the strain upon a rope loaded with a weight of fourteen stone, and suddenly checked after a fall of eight feet, is nearly equal to that which is caused by a dead weight of two tons. None of these ropes, however, will bear a weight of fourteen stone falling ten feet; and the result of our experiments is, that no rope can be made, whether of hemp, flax, or silk, which is strong enough to bear that strain, and yet light enough to be portable. We believe that these ropes, which weigh about three-quarters of an ounce to the foot, are the heaviest which can be conveniently carried about in the Alps. We append a statement of the respective merits of the three kinds, all of which are now made by Messrs. Buckingham, expressly for the Club, and marked by a red worsted thread twisted in the strands:--

No. 1. MANILLA HEMP. Weight of 20 yards, 48 oz. Advantages--Is softer and more pliable than 2. Is more elastic than 2 and 3. When wet, is far more pleasant to handle than 2 and 3. Disadvantages--Has a tendency to wear and fray at a knot.

No. 2. ITALIAN HEMP. Weight of 20 yards, 43 oz. Advantages--Is less bulky than 1 and 3. Is harder, and will probably wear best, being least likely to cut against rocks. Disadvantages--Is much more still and difficult to untie than 1 and 3. When wet, is very disagreeable to handle, and is apt to kink.

No. 3. FLAX. Weight of 20 yards, 44 oz. Advantages--When dry, is softer, more pliable, and easier to handle than 1 and 2, and will probably wear better than 1. Disadvantages--When wet, becomes decidedly somewhat weaker, and is nearly as disagreeable to handle as 2.

Knots.--There can be no doubt that every knot in a rope weakens its power of resisting a sudden jerking strain. How great a loss of strength results from a knot we cannot undertake to estimate, but that the loss is a very serious one the following statement will show: these ropes which we report will resist the strain of fourteen stone falling eight feet, will not resist it if there is a knot in any one of them; or even if the knots used in attaching them to the point of support, or to the weights, be roughly or carelessly made. The rope in these cases breaks at the knot, for two reasons; partly because of the folds, as they cross in the knot, are strained suddenly across each other, and one of them is cut through; and partly because the rope is so sharply bent that the outer side of each fold in the knot is much more stretched than the inner side, so that the strain comes almost entirely upon one side only of each fold. For the first reason, we found it necessary to put a pad of some kind inside the knot--leather, linen, or a little tow or waste rope will do. For the second reason we preferred knots in which the folds are least sharply bent round each other; that is, in which the curves are large. We therefore conclude that--1st. No knot, which is not absolutely necessary, ought to be allowed to remain on the rope: 2nd. The tighter and harder a knot becomes, the worse it is: 3rd. The more loose and open a knot is made, the better it is:--and we append diagrams of those knots which we found by experiment weaken the rope least. For Alpine ropes, only three sorts of knots are ever required, and we suggest one of each kind:--No. 1 is for the purpose of joining two ends. No. 2 is for the purpose of making a loop at one end. No. 3 is for the purpose of making a loop in the middle when the ends are fastened. No. 4 is a knot, of which we give a diagram in order that no one may imitate it. It is one of those which most weaken the rope. The only one which seemed to be equally injurious is the common single knot, of which no diagram is necessary. As the topes which we have recommended are very liable to become untwisted, unless the loose ends are secured, we advise travellers, in order to avoid knots, to have the ends of every piece of rope bound with waxed twine. It should also be known that it is very unsafe to join two pieces of rope by looping one end through the other, so that when the jerk comes, they will be strained across each other as two links of a chain are strained across each other. Unless a pad of some kind divides the loops, one will cut the other through.

Axes.--The axes made in England for the purpose of being taken out to Switzerland, may be divided into two classes, namely: travellers' axes, intended to be used for chipping a few occasional steps, for enlarging and clearing out those imperfectly made, and for holding on to a snow-slope,--and guides' axes, which are the heavier implements required for making long staircases in hard blue ice. We have had three models prepared, of which diagrams are appended; the first two represent the lighter axe, or what we have termed the travellers' axe; and the third, the heavier instrument required for guides' work. Diagram No. 1 represents a light axe or pick, of a kind somewhat similar to that recommended by Mr. Stephen, in a paper published a short time ago in the 'Journal.' It has, in the first place, the great advantage of lightness and handiness, while its single blade, to some extent, combines the step-cutting qualities possessed by the two cutters of the ordinary double-headed axe, though the latter instrument is on the whole decidedly superior. The small hammer-headed axe, though the latter instrument is on the whole decidedly superior. The small hammer-head at the back is added in order to balance the pick, and in some degree to improve the hold when the axe-head comes to be used as a crutch handle. This form, it should be understood, we recommend on account of its lightness and of its convenient shape. Diagram No. 2 represents a travellers' axe, slightly heavier than the first; and as this is the shape which appears to us the best adapted for mountain work of all kinds, we desire shortly to state our reasons for recommending it to members of the Club.