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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.")
[Table of Chords to Radius of 1000].
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.
[Contains Table for Rough Triangulation without the usual instruments,
and without Calculation"].
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.
[Small drawing illustrating these directions in above text].
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.
[Fig 1 and Fig 2 appear on p 45].
(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.
[Four diagrams of knots on this page].
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.
[Fig 1 and Fig 2, shapes of axes, are on this page.].
In the first place it is absolutely necessary that one of the cutters
should be made in the form of a pick, as this is by far the best
instrument for hacking into hard ice, and is also extremely convenient
for holding on to a snow-slope, or hooking into crannies, or on to ledges
of rock.
For the other cutter we recommend an adze-shaped blade, and we are
convinced that this is the form which will be found most generally
useful, as being best suited for all the varieties of step-cutting. The
hatchet-shaped blade used by the Chamouni guides is no doubt a better
implement for making a staircase diagonally up a slope, but on the other
hand it is exceedingly difficult to cut steps downwards with a blade set
on in this manner; and as mountaineers rarely come down the way by which
they went up, if they can help it, it is obvious that this objection to
the Chamouni form of axe is conclusive.
We recommend that the edge of the blade should be angular instead of
circular, although the latter shape is more common, because it is clear
that the angular edge cuts into frozen snow more quickly and easily.
The curve, which is the same in all the axes, approaches to coincidence
with the curve described by the axe in making the stroke. A curve is, in
our opinion, desirable, in order to bring the point more nearly opposite
the centre of percussion, and to make the head more useful for holding on
to rocks or a slope.
The axe shown in diagram No. 2, though slightly heavier than No. 1, is
not of sufficient weight or strength for cutting a series of steps in
hard ice. To those gentlemen, therefore, who do not object to carrying
weight, but who desire to have an axe fit for any kind of work, we
recommend No. 3. As this is exactly similar in shape to No. 2, differing
from it only in size, we have not thought it necessary to give a separate
diagram of No. 3.
As to the mode of fastening, which is the same in all three axes, we
should have felt some diffidence in giving an opinion had we not been
fortunate enough to obtain the advice of an experienced metal-worker, by
whom we were strongly recommended to adopt the fastening shown in the
diagrams, as being the method generally considered best in the trade for
attaching the heads of hatchets, or large hammers likely to be subjected
to very violent strains. It will be seen that the axe-head and fastening
are forged in one solid piece, the fastening consisting of two strong
braces or straps of steel, which are pressed into the wood about
one-eighth of an inch, and are secured by two rivets, passed through the
wood and clenched on each side. The braces are put at the side, instead
of in front of and behind the axe, because by this means, the strain
which falls on the axe acts against the whole breadth of the steel
fastenings, and not against their thickness merely.
We believe that this is the firmest method of fastening which can be
adopted, and that so long as the wood is sound, it is scarcely possible
for the head of the axe to get loose or to come off; and it has the
further advantage of strengthening the wood instead of weakening it, and
of distributing the strain produced by step-cutting over a large bearing.
It should be added that these axe-heads and fastenings ought to be made
entirely of steel.
The dimensions of the axe-heads are as follow: --
No. 1. -- Length of blade measured from the wood.. 4 1/2 inches.
Breadth of blade at widest part..........1 1/2 "
Weight, including the braces............13 1/2 oz.
No. 2. -- Length of blade measured from the wood.. 3 1/2 inches.
Length of pick.......................... 4 1/2 "
Breadth of blade at widest part......... 1 3/4 "
Breadth of pick......................... 0 1/2 "
Weight, including the braces............15 1/2 oz.
No. 3. -- Length of blade measured from the wood.. 4 inches.
Length of pick.......................... 5 "
Breadth of blade at widest part......... 2 1/4 "
Breadth of pick......................... 0 5/8 "
Weight, including the brades............21 1/4 oz.
We much desired to recommend to the Club some means by which the axe-head
might be made moveable, so as to be capable of being put on and taken off
the handle quickly and easily. We regret to say, however, that we were
unable to discover any plan by which this can be effectually done. We
examined very carefully the numerous and formidable weapons which have
been sent in by members for exhibition, most of which had elaborate
contrivances for fastening on the axe-head. These were all, however,
liable to very serious objections. Some were evidently insecure; with
others it was necessary that the axe-head should be surmounted by a huge
knob, which would prove a most serious impediment in step-cutting; while
in the best and firmest which we found, the axe-head was attached to the
pole by means of nuts and screws projecting at the side or over the top
of the axe. This latter method of fastening seems to us awkward and
possibly dangerous, as the nuts, from their position, are very likely to
become loose or to get broken off, and cannot, except when dangerously
loose, be fastened or unfastened without a key or wrench--a troublesome
article, certain to be lost on the first expedition.
The Handle of the Axe should, we think, be made of ash. We recommend this
wood in preference to deal, which is lighter and nearly as strong,
because in choosing a piece of ash it is easier to select with certainty
thoroughly sound and well-seasoned wood; and in preference to hickory and
lance-wood, which are stronger, because these woods are extremely heavy.
The handle should, we believe, be of a very slightly oval form, as it is
then more convenient to the grasp than if round. As to the thickness of
the wood, we are satisfied it ought nowhere to be less than 1 3/8 inch,
since a pole of that diameter, made of ordinarily good ash, is the
smallest which cannot be permanently bent by a heavy man's most violent
effort; although we have seen some pieces of unusually strong ash of a
less thickness, which proved inflexible.
We recommend, then, that the oval section of the handle should have a
shorter diameter of 1 3/8 inch, and a longer diameter of 1 1/2 inch, and
that the thickness should be the same from one end to the other. The
length of the handles for Nos. 1 and 2 should be such that they will
reach to just under the arm at the shoulder. The handle for No. 3, which
is intended to be used exclusively as an axe, should be between 3 1/2 and
4 feet long. The lower end of the handle should be strengthened in the
usual way by a ferrule, and armed with a spike.
The spike should be from 3 1/2 to 4 inches long, clear of the end of the
handle, and should be prevented from moving by a slight rivet passed
through it near the upper end after it is fastened in. The exact form of
the spike and ferrule are represented in the diagram.
We have further to recommend for axe-handles an addition which is liable
to suspicion as an entire innovation, but which, we are confident, will
be found valuable at those critical moments when the axe is required to
hold up two or three men. It has happened that when the axe has been
struck into the snow a man has been unable to keep his hold of the
handle, which slips out of his hand, and leaves him perfectly helpless.
To guard against this mischance, we propose to fasten a band of leather
round the handle, at a distance of a foot from the ferrule at the lower
end. This leather should be about an eighth of an inch thick, and will be
quite sufficient to check the hand when it is sliding down the handle. It
should be lashed round the wood and strained tight when wet.
Alpenstocks.--What we have said about the handle of the axe applies in
all respects to the Alpenstock, except that the length of the latter
should be different, and that the leathern ring would of course not be
required. It is generally thought most convenient that the Alpenstock
should be high enough to touch the chin of its owner, as he stands
upright; but this is a matter on which it is scarcely possible, and, were
it possible, scarcely necessary to lay down an absolute rule.
Boots.--Several nails are sure to be knocked out after each hard day's
work, therefore a reserve supply is necessary in lands where none other
are to be found. No makeshift contrivance, so far as I am aware, will
replace the iron last used by shoemakers when they hammer nails into the
boot. There is a well-known contrivance of screws with jagged heads, for
screwing into boots when a little ice has to be crossed. They do
excellently for occasional purposes, but not for regular ice-work, as
they are easily torn out. Crampons are soles of leather with spikes; they
are tied over the shoes, but neither English mountaineers nor modern
guides ever employ them: nailed boots are better.
Snow Spectacles.--The Esquimaux, who have no coloured glass, or any
equivalent for it, cut a piece of soft wood to the curvature of the face;
it is about two inches thick, and extends horizontally quite across both
eyes, resting on the nose, a notch being cut in the wood to answer the
purpose of the bridge of a pair of spectacles. It is tied behind the
ears; and, so far as I have now described it would exclude every ray of
light from the eyes. Next, a long narrow slit, of the thickness of a thin
saw-cut, is made along the middle almost from end to end. Through this
slit the wearer can see very fairly. As it is narrower than the diameter
of the pupil of his eye, the light that reaches his retina is much
diminished in quantity. Crape or gauze is a substitute for coloured
glass.
Mask.--Is merely a pocket-handkerchief, with strings to tie it over the
face; eye-holes are cut in it, also a hole for the nose, over which a
protecting triangular piece of linen is thrown, and another hole opposite
the mouth, to breathe through it is drawn below the chin so as to tie
firmly in place. The mask prevents the face from being cut to pieces by
the cold dry winds, and blistered by the powerful rays of the sun
reverberated from the snow.
CATTLE.
Happy is the traveller who has the opportunity of hiring his cattle with
their attendants: for his delay and cares are then reduced to those of
making a bargain, and of riding what he has hired; and when one set of
animals is tired or worn out, he can leave them behind and ride on with
others. But, for the most part, explorers must drive their own beasts
with them: they must see to their being watered, tended, and run after
when astray; help to pack and harness them; fatigue themselves for their
benefit; and drudge at the work of a cowherd for some hours a day.
In fitting out a caravan, as few different kinds of animals should be
taken as possible, or they will split into separate herds, and require
many men to look after them.
The dispositions of the animals that compose a caravan affect, in no
small degree, the pleasure of travelling with it. Now, it is to be
noticed that men attach themselves to horses and asses, and in a lesser
degree to mules and oxen, but they rarely make friends of camels.
Weights carried by Cattle.--The net weights that these different animals
carry in trying, long-continued journeys--through stages uncertain in
length, sometimes leading to good pasture, sometimes to bad--must not be
reckoned higher than the following; and an animal draws about 2 1/2 times
as much net weight as he carries:--An ass, 65 lbs.; a small mule, 90
lbs.; a horse lbs.; an ox lbs.; a camel lbs. to 200 lbs.;
elephant lbs. In level countries--where there is grain, and where
the road is known and a regularity in the day's work can be ensured--the
weights that may be carried are fully double those of the above list.
Captain Burton's donkeys, in East Africa, carried immense weights. Dogs
will draw a "travail" (which see) of 60 lbs. for a distance of 15 miles a
day, upon hard level country.
Theory of Loads and Distances.--How should we load men or animals of
transport, and how should we urge them, in order to obtain the largest
amount of effective labour? If they carry a mere feather-weight, they may
make long days' journeys; but their value, as animals of transport, is
almost nothing. Again, on the other hand, if we load them with an
excessive weight, they will soon come to a standstill; and in this case,
as in the first, their value as beasts of transport is almost nil. What
then, is that moderate load by which we shall obtain the largest amount
of "useful effect"? this is a problem which many of the ablest engineers
and philosophers have endeavoured to solve; and the formulae--partly
based on theory and partly on experiment--which were used by Euler, are
generally accepted as a fair approximation. They are very simple, and
peculiarly interesting on account of their wide applicability. They are
equally true for men, animals, or machines; and are wholly independent of
the way in which the power is applied: whether, for instance, a man
carries his burden, or draws it, or rows or punts it in a boat, or winds
it up with a crank or tread-mill.
Travellers might well turn the theory to account on their own behalf;
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