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 2_l._ 10_s._ or 3_l._ 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. 2-1/2in. 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.
--------+--------+--------+--------+---------
| | | |
1 | - | 5 | 0 | 2-1/2
2 | - | 10 | 0 | 5
3 | - | 15 | 0 | 7-1/2
4 | - | 20 | 0 | 10
5 | - | 25 | 1 | 0-1/2
6 | - | 30 | 1 | 3
7 | - | 35 | 1 | 5-1/2
8 | - | 40 | 1 | 8
9 | - | 45 | 1 | 10-1/2
10 | - | 50 | 2 | 1
11 | - | 55 | 2 | 3-1/2
12 | - | 60 | 2 | 6
13 | - | 65 | 2 | 8-1/2
14 | - | 70 | 2 | 11
15 | - | 76 | 0 | 1-1/2
16 | - | 81 | 0 | 4
17 | - | 86 | 0 | 6-1/2
18 | - | 91 | 0 | 9
19 | - | 96 | 0 | 11-1/2
20 | - | 101 | 1 | 2
21 | - | 106 | 1 | 4-1/2
22 | - | 111 | 1 | 7
23 | - | 116 | 1 | 9-1/2
24 | - | 121 | 2 | 0
25 | - | 126 | 2 | 2-1/2
26 | - | 131 | 2 | 5
27 | - | 136 | 2 | 7-1/2
28 | - | 141 | 2 | 10
29 | - | 147 | 0 | 0-1/2
30 | - | 152 | 0 | 3
31 | - | 157 | 0 | 5-1/2
32 | - | 162 | 0 | 8
33 | - | 167 | 0 | 10-1/2
34 | - | 172 | 1 | 1
35 | - | 177 | 1 | 3-1/2
36 | - | 182 | 1 | 6
37 | - | 187 | 1 | 8-1/2
38 | - | 192 | 1 | 11
39 | - | 197 | 2 | 1-1/2
40 | - | 202 | 2 | 4
41 | - | 207 | 2 | 6-1/2
42 | - | 212 | 2 | 9
43 | - | 217 | 2 | 11-1/2
44 | 1 | 3 | 0 | 2
45 | 1 | 8 | 0 | 4-1/2
46 | 1 | 13 | 0 | 7
47 | 1 | 18 | 0 | 9-1/2
48 | 1 | 23 | 1 | 0
49 | 1 | 28 | 1 | 2-1/2
50 | 1 | 33 | 1 | 5
51 | 1 | 38 | 1 | 7-1/2
52 | 1 | 43 | 1 | 10
53 | 1 | 48 | 2 | 0-1/2
54 | 1 | 53 | 2 | 3
55 | 1 | 58 | 2 | 5-1/2
56 | 1 | 63 | 2 | 8
57 | 1 | 68 | 2 | 10-1/2
58 | 1 | 74 | 0 | 1
59 | 1 | 79 | 0 | 3-1/2
60 | 1 | 84 | 0 | 6
61 | 1 | 89 | 0 | 8-1/2
62 | 1 | 94 | 0 | 11
63 | 1 | 99 | 1 | 1-1/2
64 | 1 | 104 | 1 | 4
65 | 1 | 109 | 1 | 6-1/2
66 | 1 | 114 | 1 | 9
67 | 1 | 119 | 1 | 11-1/2
68 | 1 | 124 | 2 | 2
69 | 1 | 129 | 2 | 4-1/2
70 | 1 | 134 | 2 | 7
71 | 1 | 139 | 2 | 9-1/2
72 | 1 | 145 | 0 | 0
73 | 1 | 150 | 0 | 2-1/2
74 | 1 | 155 | 0 | 5
75 | 1 | 160 | 0 | 7-1/2
76 | 1 | 165 | 0 | 10
77 | 1 | 170 | 1 | 0-1/2
78 | 1 | 175 | 1 | 3
79 | 1 | 180 | 1 | 5-1/2
80 | 1 | 185 | 1 | 8
81 | 1 | 190 | 1 | 10-1/2
82 | 1 | 195 | 2 | 1
83 | 1 | 200 | 2 | 3-1/2
84 | 1 | 205 | 2 | 6
85 | 1 | 210 | 2 | 8-1/2
86 | 1 | 215 | 2 | 11
87 | 2 | 1 | 0 | 1-1/2
88 | 2 | 6 | 0 | 4
89 | 2 | 11 | 0 | 6-1/2
90 | 2 | 16 | 0 | 9
91 | 2 | 21 | 0 | 11-1/2
92 | 2 | 26 | 1 | 2
93 | 2 | 31 | 1 | 4-1/2
94 | 2 | 36 | 1 | 7
95 | 2 | 41 | 1 | 9-1/2
96 | 2 | 46 | 2 | 0
97 | 2 | 51 | 2 | 2-1/2
98 | 2 | 56 | 2 | 5
99 | 2 | 61 | 2 | 7-1/2
100 | 2 | 66 | 2 | 10
101 | 2 | 72 | 0 | 0-1/2
--------+--------+--------+--------+---------
_Second Wheel._
-----+--------+------+------+-----+-------
No. | Miles. | Fur. | Yds. | Ft. | In.
-----+--------+------+------+-----+-------
1 | -- | 2 | 72 | 0 | 0-1/2
2 | -- | 4 | 144 | 0 | 1
3 | -- | 6 | 216 | 0 | 1-1/2
4 | 1 | 1 | 68 | 0 | 2
5 | 1 | 3 | 14 | 0 | 2-1/2
6 | 1 | 5 | 212 | 0 | 3
7 | 2 | 0 | 64 | 0 | 3-1/2
8 | 2 | 2 | 136 | 0 | 4
9 | 2 | 4 | 208 | 0 | 4-1/2
10 | 2 | 7 | 60 | 0 | 5
20 | 5 | 6 | 120 | 0 | 10
30 | 8 | 5 | 180 | 1 | 3
40 | 11 | 5 | 20 | 1 | 8
50 | 14 | 4 | 80 | 2 | 1
60 | 17 | 3 | 140 | 2 | 6
70 | 20 | 2 | 200 | 2 | 11
80 | 23 | 2 | 41 | 0 | 4
90 | 26 | 1 | 101 | 0 | 9
100 | 29 | 0 | 161 | 1 | 2
-----+--------+------+------+-----+-------
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:--
Trocheameter 6 37
m. fur. yds. ft. in.
6 1 5 212 0 3
37 0 0 187 1 8-1/2
---------------------------
1 6 179 1 11-1/2
28th.--North of the Vlei Moslenyan:--
Trocheameter 22 91
6 37
------
16 54
m. fur. yds. ft. in.
10 2 7 60 0 5
6 1 5 212 0 3
54 0 1 53 2 3
-----------------------
4 6 105 2 11
-----------------------
29th.--The Big Tree, or Baobab at Mamakahooie:--
Borrow 101
Trocheameter 50 73
22 91
------
27 83
m. fur. yds. ft. in.
20 5 6 120 0 10
7 2 0 64 0 3-1/2
83 0 1 200 2 3-1/2
-----------------------
8 0 165 0 5
-----------------------
29th, p.m.--A hollow, with water:--
Borrow 101
Trocheameter 76 53
50 73
------
25 81
m. fur. yds. ft. in.
20 5 6 120 0 10
5 1 3 14 0 2-1/2
81 0 1 190 1 10-1/2
-----------------------
7 3 104 2 11
-----------------------
30th.--A small Vlei:--
Borrow 101
Trocheameter 93 44
76 53
------
16 92
m. fur. yds. ft. in.
10 2 7 60 0 5
6 1 5 212 0 2
92 0 2 26 1 10-1/2
------------------------
4 7 78 1 10
------------------------
31st.--Outspan in the Bush.
Trocheameter 12 89
Add 100
------
112 89
93 44
------
19 45
m. fur. yds. ft. in.
10 2 7 60 0 5
9 2 4 208 0 4-1/2
45 0 1 8 0 4-1/2
------------------------
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.
[Illustration]
The rule for ascertaining this by the bearing of the rising or setting
sun is given in all epitomes of navigation, and need not be repeated
here; but this is only practicable in a level country, where the sun
can be seen within at most a few minutes of the proper times, and
cannot be carried out among mountains or thick forests. In such case
we were in the habit of setting up two sticks (A A), stretching a
thread (B) across them, and from the middle of this letting fall a
plumb line (C); then, taking a flat board, with a sheet of paper (D)
stretched on it and projecting a little over the edge, make a hole in
the projecting part to let the plumb line hang through, taking care
not to vitiate its correctness; then select an object (E), the small
upright stem of a tree, or set up a stick at a good distance, 100yds.
or 200yds., or more, as nearly compass north of the plumb line as
possible--if it is not exactly so, note its deviation on either side
with the utmost correctness, and draw on the paper the line F D, which,
if prolonged, would reach the tree at E. Then, between ten and eleven
in the forenoon, set out the artificial horizon, and take an altitude
of the sun; call "stop" sharply at the moment of observation, and let
an assistant, with a straight-edged rule and pencil, draw the line of
shadow cast by the plumb line at that moment; read off, and let your
assistant record your observed altitude beside the line he has drawn;
rest a minute or two at least; then take another observation, and so
on, till three or five, or any odd number of lines have been drawn,
forming a pencil of rays from the plumb line. Leave the sextant clamped
at the last observation, and in the afternoon, before the sun comes
down at that altitude, be ready with the horizon, and call "stop" at
the moment, or even just before, the sun comes into contact, your
assistant being ready, as before, to draw the shadow of the plumb
line. You will now find that the short interval of rest taken between
the morning observation will give you time to set your sextant to the
next altitude, and to wait quietly till the sun comes down to it; do
the same with the rest; and, when all are drawn, take the mean of each
pencil of lines, and between them draw an exact central line, radiating
like the rest from the plumb line; it will be evident that this must
represent the shadow when the sun's centre was exactly on the meridian,
and therefore it must be due north and south. Measure the angle between
this and the magnetic north line already drawn, and the result in
degrees and minutes will be the variation of your compass; or, take the
bearing of the line by compass, and the result in points or in degrees
will be the variation, which call east or west, as the compass north
is to the east or west of the true meridian. Take the bearing again of
the tree or mark set up in the morning to ascertain that your paper has
not been shifted during the observations. If your magnetic line has
not been drawn exactly north and south it is not of great importance;
but remember that the exact error must be ascertained and allowed for
by addition or subtraction in calculating the angle between it and the
true north. An unknown error, however small, renders an observation
useless; but a known error, however great, involves only the trouble of
correction.
TO OBTAIN LEVELS OR LOW ALTITUDES.
[Illustration]
In mapping a country, it is desirable to give as nearly as possible
the comparative heights of the hills; or it may be necessary to take
the altitude of a low star, or the height of a tree or other object.
For this purpose take a wide-mouthed jar or glass bottle, such as is
used for the collection of specimens; round the neck of it splice or
tie a cord or thong of leather to carry it by; then tie or fix by
sealing-wax, gum, or resin, two hairs or threads crossing each other at
right angles; and then, standing over the jar with the face towards the
object to be measured, take a pocket, or full-sized sextant, and bring
the top of the object to the spot where the threads cross each other,
taking care to keep the eye so perpendicularly above their junction
that the crossed lines and their reflected image may appear in one;
then read off the observed angle--for instance 110° 42´ 30´´. Apply the
index error, which suppose to be 30´´ subtracted, and subtract 90° from
the corrected altitude, the remainder will be the true altitude; thus:
° ´ ´´
Observed [delta] 110 42 30
Index error 0 0 30
-----------
110 42 0
90 0 0
-----------
Altitude required 20 42 0
-----------
It will conduce very greatly to steadiness if a rest is used; the stand
of a theodolite, with the instrument removed, or of a photographic
camera, or three forked sticks set up so that the sight could be
directed downwards through a central aperture, would answer the
purpose. If the sextant is set to 90°, allowing for index error, and
the horizon is swept round with it, the eye being kept steadily
perpendicular to the cross lines, it will at once show what objects are
above or below the level of the observer's eye. A looking-glass may be
used in the same manner, but it must be very carefully tested in every
direction with a spirit level and even then it is but an inefficient
substitute for the mercury, which levels itself, and which _cannot_
possibly give a false result, because nothing but agitation can destroy
the perfect level of its surface, and unless it is at rest it cannot
reflect an unbroken image, and no observation can be made.
[Illustration]
A looking-glass may also be suspended vertically, its surface being
tested by two plumb lines, one on each side its centre. A horizontal
line may be stretched at a foot or two from its front; then, if the
observer, retiring a few paces, raises or lowers himself till the
line and its reflection appear in one--his eye and the line must be
in the same horizontal plane--and he may observe the altitude of the
sun, or other celestial body, when in the zenith or too high to be
observed in the mercurial artificial horizon; this plan, however, is
only an approximation to correctness, and should only be used when the
mercurial horizon is not available.
THE PLANE TABLE, AND ITS USE.
In making a plane table, discard all the complicated arrangements of
sights, protractors, fixed compasses, spirit levels, and levelling
screws, each of which has an individual error, which must be found and
allowed for before correctness can be attained; while the approximation
to perfection gained by their most careful use is almost certain to be
vitiated by the contraction of the paper when removed from the table on
which it has been stretched.
[Illustration: 1-5]
Take any flat board--Fig. 1 (an artist's drawing-board) is as good as
any--and stretch on it a sheet of drawing or stout cartridge paper:
the best levelling apparatus is a wooden hemisphere (Fig. 2), screwed
temporarily on to its back, and working in a circular aperture (Fig.
3) in the top of such a stand as is used for the photographic camera
or theodolite; there is no necessity that the surface should be truly
horizontal; indeed, it is much better that it should be capable of
alterations of position, so that objects above or below its horizon
may be sighted and mapped at pleasure. Set up a needle (_a_) in the
centre of the drawing-paper, and lay against it a straight-edged
ruler (_b_) with two other needles (_c c_), set perfectly upright in
each end as near as possible to the fiducial edge, as sights; then,
choosing some principal object--say a well-marked conical peak, the
bluff edge of a precipice, or a deep and narrow cleft in distant
mountains--and keeping your ruler pressed against the central needle,
bring the others, which serve as sights, in careful alignment with the
object, and draw a pencil line along the fiducial edge right across
the paper; then, with your prismatic compass (resting on the table for
greater steadiness, if there is no iron in it to affect the magnet),
take very carefully the bearing of the object, and note it in degrees
from north, or zero, say 40°, on the line you have drawn; then lightly
sketch the object on the line, estimating its distance from the centre,
according to the scale on which you are working, say one or more
inches to a mile. Direct the sights to any number of well-marked and
recognisable objects, draw lines, and sketch them lightly at their
estimated distances. Then have a mark set up as far off as possible,
say a mile, or any carefully-measured distance, direct the sights, and
draw a line towards it; mark its distance accurately on the paper, and
insert the pivot needle there; remove the table to the marked spot,
and, with your prismatic compass, set the first line again to 40°; then
bring your sights to bear upon the object, draw another line along
your straight edge, and the point at which this cuts the first will
be the true position of your object; correct your first sketch still
lightly, but do not efface anything; sight all the other objects, and
sketch them where the second set of lines cut the first. Then choose
another station, forming, if possible, an equilateral triangle with the
other two; mark its position on the map, remove the proof needle there,
carry the table to the spot, set the first line again to 40°, and sight
the same objects a third time all round, and the third set of lines
crossing the other two will give their true distances from the centre
with sufficient accuracy for all ordinary purposes.
A ball and socket joint for adjusting the table to the necessary
alterations of level may be made by nailing on beneath it a hemisphere
of wood (Fig. 2), working in a circular hole (Fig. 3) in the top of the
stand.
EXTEMPORISED SIGHT VANE FOR LEVELLING STAFF.
Fig. 5. Suppose your staff 1-1/2in. thick: take a piece of tin about
7in. wide, and of any convenient length, say nearly square; line it off
as in Fig. 4, so that there shall be three divisions parallel to each
other, as wide as the staff is thick, and on one side of them leave
another division, about 3/4in. wide, and on the other mark and cut out
two projections 3/4in. square, and a semicircular eyepiece, somewhat
larger, with a quadrant-like aperture, as in the illustration; bend
the tin at the divisional lines, so as to clasp the staff loosely,
with the sight vane projecting from it; let a cord be attached to the
top of the tin, and pass through a hole in the top of the staff to
draw it up by, and attach another cord to the bottom to draw it down
again if required. Upon the edge of the narrowest divisions draw the
subdivisions of the measures already marked upon your staff, letting
them commence from the level of the bottom of the aperture in the
sight vane, and read downwards; then, directing the telescope of your
levelling instrument towards the staff, let an assistant lower or raise
the sight vane according to your signals, and then read off the number
of subdivisions on the vernier until you come down to a line, marking
a division on the staff; read off this, and add the fractional parts,
and the excess or deficiency over or below the height of the eye will
be the difference of level in feet, inches, or whatever measurement may
be used.
[Illustration]
Movable stands for instruments must be light for the sake of
portability, but steadiness cannot be obtained without weight; and for
this purpose a bucket of water, a bamboo filled with water or sand, a
bag of stones or sand, a large stone, or lashing to a tent peg driven
into the ground, may be employed, as in our illustration.
MAKESHIFT CLINOMETER.
[Illustration]
Captain Lendy recommends a simple form of clinometer, which is
constructed as follows: The clinometer consists of a quadrant of
pasteboard or of brass, having a plummet, A H, suspended at its centre,
and graduated, as in the diagram, on both sides. When we require an
angle of elevation, we look along the edge, A C, till B is in sight,
when the plummet indicates the angle. For an angle of depression
reverse the instrument. This instrument is an excellent substitute for
the ordinary form of sextant in case of accident or breakage.
The same officer describes an ingenious substitute for an ordinary
water level, which can always be replaced by a little ruler, A B,
suspended by strings, C A, C B, having a little weight under it to
prevent the wind from shaking it. When held by the string the line A
B will give a horizontal direction. To make use of it for levelling
along A B, start from A, hold the ruler up to the eye, and, aiming
along its edge, notice to what point (B) of the ground the visual ray
corresponds. Repair there, we shall have ascended a distance--the
height of the eye above the ground. Start afresh from B, and in this
manner the number of stations made between A and B, multiplied by the
height of the eye above ground, will give the difference of level
required.
[Illustration]
The same author gives the following useful hints on the estimation of
distance: "Pacing is generally resorted to while filling in the details
of a survey. The trotting of a horse might also be made available.
Distances can also be measured by time when we have previously
ascertained over how many yards we walk or ride in a given time. This
is not a rare occurrence in the field. When distances are measured by
pacing or riding a correction is necessary, owing to the lengthening
caused by acclivities and the turnings of roads. On slightly uneven
ground we subtract 1-7th of the distance paced, and 1-5th when the
inductions are more important."
When the atmosphere is even sound travels at the rate of 1118ft. per
second; therefore a musket fired may serve to measure a distance. A
watch gives the number of seconds elapsed between the instant the light
is seen and that when the report is heard; that number, multiplied by
1118ft., gives very approximately the distance. If no watch is to be
had the time is obtained by counting the pulsations of an artery. A
sound pulse averages from 75 to 80 in a minute. Distances may even be
guessed by observing that in clear weather the windows of a house can
be counted at 4000yds. Horses and men appear as dots at 2200yds. A
horse is clearly seen at 1200yds. The movements of men are perceived at
800yds.; and the head is distinctly visible at 400yds.
For the measurement of time, as we have said before, a thoroughly
well-made English lever watch is preferable to a chronometer, as it
will withstand the rough jolts and vibrations caused by being carried
on horseback, or in a waggon, far better. Sun-dials, properly so
called, are rarely of much use to the traveller; still the pocket
compass may be made to do duty as an indicator of time. There is a
small and very portable little instrument to be obtained of most
opticians, in the formation of which a silk cord is so attached to the
border of the compass case that on adjusting the compass, so that the
needle shall point to a black stud inserted for the purpose, a shadow
is cast by the silk on the figure indicating the hour of the day. A
small equation table is attached to the inside of the cover.
When no watch is at hand seconds can be indicated closely enough for
practical purposes by suspending a small bag of shot or bullets from
the end of a piece of fine fishing line or copper wire. Attach the
upper end to a cross bar, laid in the crutches of two forked sticks,
let the bag hang, and regulate the length of the string until you
find that it describes the proper arc in swinging; your own pulse,
the number of which has been already given, or that of a horse, which
may be roughly set down as thirty-six beats per minute, will be a
sufficient guide. If great accuracy is sought, recourse may be had to
repeated astronomical observations.
An excellent makeshift hour-glass can be made from two empty soda-water
bottles, and a little fine dry sand. A wooden plug of 3in. long
should be so cut as to fit the necks of the bottles tightly. Through
the centre of the plug, from end to end, burn with a red-hot wire a
fine even hole, then with your pocket-knife make a funnel-shaped or
flared-out mouth to each hole, cutting away until the extreme edge of
the plug is reached. See that your sand is free from small stones or
lumps, pour it into one of the bottles, insert the plug half-way, and
test the quantity by letting it run out at the hole. When you have the
proper charge to run for fifteen or thirty minutes, place the bottles
mouth to mouth in such a way that one-half the plug shall be in the
neck of each bottle. A bit of raw hide sewn round the union of the
bottle mouths makes all secure. The joined bottles can then be mounted
in a wooden frame for use. Two bits of flat square board, with holes
in the centre for the bottoms of the bottles to come partly through,
pinned at the corners by four bars of wood, is as good a form of frame
as any.
The Malays make use of a very convenient and simple form of time
indicator or water clock, which is made as follows:--A large-sized
cocoa-nut shell is obtained; this is first scraped perfectly smooth,
and then at the bottom a very minute hole is bored. The nutshell
is then set floating in a pail of sea water. As the shell fills it
gradually settles deeper and deeper, and at last sinks to the bottom
with a gurgle and a thud. The rapidity of filling, and consequent
duration of time, is regulated by increasing or diminishing the size
of the orifice. Thus a man may be set to keep a two-shell watch or a
four-shell watch, and so on. The instant the shell sinks to the bottom
of the pail it attracts attention by the disturbance made. It is then
immediately taken up, the water is poured out, and it is set afloat
again. Excellent time can be kept by this primitive arrangement.
For ascertaining the altitude of high lands, ranges of hills or
mountains, a thoroughly good "compensated" aneroid barometer should
be taken. This will not only be valuable for measurements, but will
be of considerable service in the observation of weather signs.
We have one now in use made expressly for us by Mr. Cary, of 181,
Strand. It is protected by a smooth wooden cover or case, enveloped in
tightly-stretched leather. A sling is fitted to it by a swivel loop,
which admits of its being carried over the shoulder or in the jacket
pocket. The Table of Altitudes, given on the next page, will prove a
useful guide when conducting observations with it.
TABLE OF ALTITUDES.
+----------+--------++----------+--------++----------+--------+
|Aneroid or| Height ||Aneroid or| Height ||Aneroid or| Height |
|Corrected |in Feet.||Corrected |in Feet.||Corrected |in Feet.|
|Barometer.| ||Barometer.| ||Barometer.| |
+----------+--------++----------+--------++----------+--------+
| in. | ft. || in. | ft. || in. | ft. |
| 31·00 | 0 || 26·76 | 4000 || 23·11 | 8000 |
| 30·94 | 50 || 26·72 | 4050 || 23·07 | 8050 |
| 30·88 | 100 || 26·67 | 4100 || 23·03 | 8100 |
| 30·83 | 150 || 26·62 | 4150 || 22·98 | 8150 |
| 30·77 | 200 || 26·57 | 4200 || 22·94 | 8200 |
| 30·71 | 250 || 26·52 | 4250 || 22·90 | 8250 |
| 30·66 | 300 || 26·47 | 4300 || 22·86 | 8300 |
| 30·60 | 350 || 26·42 | 4350 || 22·82 | 8350 |
| 30·54 | 400 || 26·37 | 4400 || 22·77 | 8400 |
| 30·49 | 450 || 26·33 | 4450 || 22·73 | 8450 |
| 30·43 | 500 || 26·28 | 4500 || 22·69 | 8500 |
| 30·38 | 550 || 26·23 | 4550 || 22·65 | 8550 |
| 30·32 | 600 || 26·18 | 4600 || 22·61 | 8600 |
| 30·26 | 650 || 26·13 | 4650 || 22·57 | 8650 |
| 30·21 | 700 || 26·09 | 4700 || 22·52 | 8700 |
| 30·15 | 750 || 26·04 | 4750 || 22·48 | 8750 |
| 30·10 | 800 || 25·99 | 4800 || 22·44 | 8800 |
| 30·04 | 850 || 25·94 | 4850 || 22·40 | 8850 |
| 29·99 | 900 || 25·89 | 4900 || 22·36 | 8900 |
| 29·93 | 950 || 25·85 | 4950 || 22·32 | 8950 |
| 29·88 | 1000 || 25·80 | 5000 || 22·28 | 9000 |
| 29·82 | 1050 || 25·75 | 5050 || 22·24 | 9050 |
| 29·77 | 1100 || 25·71 | 5100 || 22·20 | 9100 |
| 29·71 | 1150 || 25·66 | 5150 || 22·16 | 9150 |
| 29·66 | 1200 || 25·61 | 5200 || 22·11 | 9200 |
| 29·61 | 1250 || 25·56 | 5250 || 22·07 | 9250 |
| 29·55 | 1300 || 25·52 | 5300 || 22·03 | 9300 |
| 29·50 | 1350 || 25·47 | 5350 || 21·99 | 9350 |
| 29·44 | 1400 || 25·42 | 5400 || 21·95 | 9400 |
| 29·39 | 1450 || 25·38 | 5450 || 21·91 | 9450 |
| 29·34 | 1500 || 25·33 | 5500 || 21·87 | 9500 |
| 29·28 | 1550 || 25·28 | 5550 || 21·83 | 9550 |
| 29·23 | 1600 || 25·24 | 5600 || 21·79 | 9600 |
| 29·17 | 1650 || 25·19 | 5650 || 21·75 | 9650 |
| 29·12 | 1700 || 25·15 | 5700 || 21·71 | 9700 |
| 29·07 | 1750 || 25·10 | 5750 || 21·67 | 9750 |
| 29·01 | 1800 || 25·05 | 5800 || 21·63 | 9800 |
| 28·96 | 1850 || 25·01 | 5850 || 21·59 | 9850 |
| 28·91 | 1900 || 24·96 | 5900 || 21·55 | 9900 |
| 28·86 | 1950 || 24·92 | 5950 || 21·51 | 9950 |
| 28·80 | 2000 || 24·87 | 6000 || 21·47 | 10000 |
| 28·75 | 2050 || 24·82 | 6050 || 21·44 | 10050 |
| 28·70 | 2100 || 24·78 | 6100 || 21·40 | 10100 |
| 28·64 | 2150 || 24·73 | 6150 || 21·36 | 10150 |
| 28·59 | 2200 || 24·69 | 6200 || 21·32 | 10200 |
| 28·54 | 2250 || 24·64 | 6250 || 21·28 | 10250 |
| 28·49 | 2300 || 24·60 | 6300 || 21·24 | 10300 |
| 28·43 | 2350 || 24·55 | 6350 || 21·20 | 10350 |
| 28·38 | 2400 || 24·51 | 6400 || 21·16 | 10400 |
| 28·33 | 2450 || 24·46 | 6450 || 21·12 | 10450 |
| 28·28 | 2500 || 24·42 | 6500 || 21·08 | 10500 |
| 28·23 | 2550 || 24·37 | 6550 || 21·05 | 10550 |
| 28·18 | 2600 || 24·33 | 6600 || 21·01 | 10600 |
| 28·12 | 2650 || 24·28 | 6650 || 20·97 | 10650 |
| 28·07 | 2700 || 24·24 | 6700 || 20·93 | 10700 |
| 28·02 | 2750 || 24·20 | 6750 || 20·89 | 10750 |
| 27·97 | 2800 || 24·15 | 6800 || 20·85 | 10800 |
| 27·92 | 2850 || 24·11 | 6850 || 20·82 | 10850 |
| 27·87 | 2900 || 24·06 | 6900 || 20·78 | 10900 |
| 27·82 | 2950 || 24·02 | 6950 || 20·74 | 10950 |
| 27·76 | 3000 || 23·97 | 7000 || 20·70 | 11000 |
| 27·71 | 3050 || 23·93 | 7050 || 20·66 | 11050 |
| 27·66 | 3100 || 23·89 | 7100 || 20·63 | 11100 |
| 27·61 | 3150 || 23·84 | 7150 || 20·59 | 11150 |
| 27·56 | 3200 || 23·80 | 7200 || 20·55 | 11200 |
| 27·51 | 3250 || 23·76 | 7250 || 20·51 | 11250 |
| 27·46 | 3300 || 23·71 | 7300 || 20·47 | 11300 |
| 27·41 | 3350 || 23·67 | 7350 || 20·44 | 11350 |
| 27·36 | 3400 || 23·62 | 7400 || 20·40 | 11400 |
| 27·31 | 3450 || 23·58 | 7450 || 20·36 | 11450 |
| 27·26 | 3500 || 23·54 | 7500 || 20·32 | 11500 |
| 27·21 | 3550 || 23·50 | 7550 || 20·29 | 11550 |
| 27·16 | 3600 || 23·45 | 7600 || 20·25 | 11600 |
| 27·11 | 3650 || 23·41 | 7650 || 20·21 | 11650 |
| 27·06 | 3700 || 23·37 | 7700 || 20·18 | 11700 |
| 27·01 | 3750 || 23·32 | 7750 || 20·14 | 11750 |
| 26·96 | 3800 || 23·28 | 7800 || 20·10 | 11800 |
| 26·91 | 3850 || 23·24 | 7850 || 20·07 | 11850 |
| 26·86 | 3900 || 23·20 | 7900 || 20·03 | 11900 |
| 26·81 | 3950 || 23·15 | 7950 || 19·99 | 11950 |
| 26·76 | 4000 || 23·11 | 8000 || 19·95 | 12000 |
+----------+--------++----------+--------++----------+--------+
This Table is intended more particularly for the graduation of aneroids
with a circle of measures in feet concentric with the ordinary circle
of barometric height measured in inches. The circle of feet is to be
read off, at the upper and lower stations, by the index; and the rule
for measuring the height will be: Subtract the reading at the lower
station from the reading at the upper station; the difference is the
height in feet.
EXAMPLE.
In. Ft.
Barometer at Upper Station, 23·50 7550
" Lower " 24·20 6750
----
Actual height 800
There is no correction for temperature required with aneroids which
are "compensated."
In using the instrument here described in the measurement of altitudes,
the movable needle point which is turned by the mill-edged rim is
set opposite the index hand. This is to be done at the foot of the
mountain or hill. Then the difference between the index hand and the
movable needle point will be the number of feet ascended (_vide_ Table
appended, and "Example"). Suppose the index hand stand when at the foot
of the hill at 30in. 10/100, and when you again look at the instrument
you find the index hand has gone back, or has fallen to 29in. 12/100,
then you would have ascended 900ft.
At page 26 of this work we referred to the hypsometrical or
boiling-point apparatus used in taking altitudes. Since the remark
there made was penned we have endeavoured, and we hope successfully,
to so guard the improved form of aneroid barometer, referred to at p.
741, from the chance of accident, that it can be safely carried by the
explorer of even the most rugged and inhospitable regions.
ON THE USE OF THE SEXTANT AND ARTIFICIAL HORIZON.
We do not propose in this work to trespass on the province of books on
nautical astronomy. We take it for granted that every traveller using a
sextant will also provide himself with an Epitome--Norie's, Rapers, or
Kerigan's (of course the latest possible edition of either), and with
the "Nautical Almanac," which may be had for three years in advance, by
persons contemplating a long journey.
The most important instrument is the sextant itself, and in the
selection of this the greatest care should be used. Ebony or other wood
may do for the frames of such as are to be used at sea in temperate
climates, but for tropical use, even for sea service, we recommend a
brass or gun-metal frame, and for observing on land no other should be
used.
The quadrant, which is quite equal to the observation of altitude at
sea, will take an angle of 90°, but should read up to 10° or 20° more;
but the sextant, or sixth of a circle, is made to take in an angle of
twice 60°, or 120°, and should also read 10° or 20° higher. When we
were at the Zambesi mouth, in 1858, Dr. Livingstone's sextant reached
only 127°, while our own would read to 137° or 140°, which, when
the altitude of the sun was increasing daily, gave us the advantage
of observing a week or ten days longer than he could. We left the
instrument in the care of the Portuguese Commandant of Tette, but have
no hope of ever seeing it again, the town having been burnt and the
inhabitants massacred by Landeens, Banzai, or other ferocious savages.
The sextant we generally use--and which we have tested by many years'
constant use--is brass framed, reads to 126° 56´, is of 8 inches
radius, and has its arc and vernier on which the figures are engraved
of gold, which has a soft lustre, exceedingly agreeable to the eye
under a tropical sun, and is equally pleasant to read by lamp light; a
screen of ground glass is placed before it to soften the light still
more, and prevent annoying glitter and reflection; the degrees are
divided into sixths of ten minutes each, and the minutes likewise into
ten seconds; the microscope travels on a fixed frame, and a small
milled-headed screw brings it to the figures to be read. A small lamp
fixed on the axis of the index arm, with a reflector to shed the light
upon the arc and vernier, is sometimes made use of.
For nearly all angular measurements that an explorer is likely to
require, a really good sextant will be found sufficient, but some, for
the sake of still greater power and accuracy, provide themselves with a
repeating circle; but although this possesses many advantages, we doubt
whether the expense of such an instrument will not place it beyond the
reach of the generality of travellers, while the extra care required
will constitute too great a claim upon the time of any who cannot
devote themselves entirely to astronomical observations, but must,
perhaps, give the greater part of their time to other avocations. The
double sextant invented by Captain George, R.N., of the astronomical
department of the Royal Geographical Society, described at page 27 of
this work, will be found a portable and most convenient instrument for
the use of explorers.
The theodolite has also many advantages, especially in taking a round
of angles; but from what we have seen of it in practice we should be
inclined to think that an explorer, with his sextant and compass, is
more independent, and can do more than he could possibly effect with
the theodolite.
The artificial horizon is, as its name imports, intended to obviate
the difficulties caused by the fact that the real, or sea horizon, may
be at times invisible, obscured by fog or clouds, or that the observer
may be absent from it, and often far inland, where the unevenness of
the earth's surface prevents anything like a reliable real horizon
being found. Of the artificial horizons used at sea we have not much
to say, the unsteadiness of the vessel forbidding the use of any
instrument that can be disturbed by motion. The best we have seen is
Captain Becher's pendulum horizon, a little frame swinging near the
object-glass of the sextant, and carrying a couple of horizontal wires,
so arranged that when they appear in one to the eye of the observer
they ought to be on a level with the horizon and parallel with it; a
small lamp is so fitted to the sextant as to render these wires visible
at night if the altitude of the moon or a star is required; but we do
not think the latitude deduced from such an observation can be more
than approximately true.
It is on shore, and most of all in the far interior of the great
continents of the world, that the artificial horizon is most needed,
and that it renders the truest service to the explorer; and therefore
it is of the greatest importance that the instrument should be at
once simple in construction, easy of management, not easily put out
of order, and, above all, perfectly reliable in the result obtained
from it. The first requisite is a perfectly flat and horizontal
reflecting surface, in which, when the observer looks down upon it,
the image of the sun or star may be distinctly seen. Now, it is easy
to find flatness: a disc of silvered glass, or polished metal, or even
a bit of crown glass, painted black on the under side, or a common
round shaving-glass would do if this only were required; but this
flat surface must also be perfectly horizontal, and to attain this
various arrangements of tangent screws and spirit levels have been
invented, all of which require great care in levelling, and have the
defect that the slightest accidental touch while they are in use may
alter the level, and so vitiate the observation. By common consent,
therefore, observers almost universally trust to fluid mirrors, which
must be perfectly level if they are sufficiently quiescent to reflect
a perfect image. Water, darkened with any colouring matter--ink; water
with a little treacle, to render it less liable to be agitated by the
wind, or thin tar will do; but all these have disadvantages which
render them only fit to be looked upon as substitutes when mercury
cannot be obtained; in fact, long ago we were told by the late Captain
Washington, Hydrographer to the Admiralty, to use nothing but mercury.
The horizon trough, as it is called, is simply a block of wood of
oblong form, about 6in. long, 4in. wide, and 1in. thick; this is
hollowed to the depth of about 3/8in. or 1/2in., leaving a sufficient
rim to retain the mercury which is poured into it. Sometimes a hole
is pierced in the rim, and is continued in the solid wood under the
hollow, so that the mercury, being poured into a small funnel fitted
in the rim, runs underneath and rises like a fountain in the centre
of the trough. The various arrangements of this kind and others more
complicated are called fountain horizons, but they are not really
necessary, their principal object being to insure the perfect purity of
the mercurial surface by forcing it to flow downward first through the
funnel, and so to leave the scum behind; but this object may be just as
well attained by inverting the bottle, so that all the impurities may
float upon the surface, and allowing the pure mercury to run through
the perforated stopper into the trough. The bottle is generally of
iron, and has the perforated stopper already mentioned, which, when
the mercury has to be returned to it, serves also as a funnel. Wooden
bottles are also made, but no traveller ought to depend upon them, as
in hot climates they shrink and split; and we have found in Namaqualand
all our mercury adrift in a tinned box, forming an amalgam which did
not at all improve it. We have therefore, for many years, kept it in
a common stoneware ink bottle, with a bit of washleather tied over
the cork, and have found this to answer admirably; in pouring out
the mercury, having removed the cork, we stop the mouth of the bottle
with the forefinger, completely invert it, and then, slightly moving
the finger, leave an opening sufficient for a stream of pure mercury
to flow into the horizon. Our trough is round, and about 4in. across,
which is quite large enough. In perfectly calm weather we prefer to
observe on the plain surface of the uncovered mercury; but if wind
comes on, as it often does in Africa and Australia about noon, we cover
it with a roof of the usual form, _i.e._, two small panes of glass
fixed in a frame so as to form an angle of 45° each with the horizon,
or 90° with each other, and, standing like a roof over the mercury,
allow the rays from the heavenly body to pass down to it, and be
reflected to the eye of the observer. Various methods of rendering this
roof as portable as possible have been tried; our own is figured in the
first chapter of this work.
Captain George's new artificial horizon, however, bids fair to
supersede all the old forms of arrangement, as its portability,
strength, and simplicity of adjustment stand unrivalled. Captain
George's horizon may be made sufficiently large to equal the surface of
the one now used; but the portable or pocket form here alluded to is of
the following dimensions:--
Self-replenishing, 6in. long, 2-1/2in. broad, 3/4in. thick, weighs
1-1/4lb., cubic measure 11-1/4in.
The wooden one of olden date, 9-1/2in. long, 5-1/2in. broad, 5-1/2in.
thick, weighs 5-1/3lb., cubic measure 287-1/3in.
Improved folding roof, &c., all iron, 8in. long, 4-1/2in. broad,
2-1/2in. thick, weighs 6-3/4lb., cubic measure 90in.
The improvements herein specified are not only its reduced size and
weight, but its mechanical arrangements, form, and moderate price.
It consists of two circular disc-like reservoirs, about 2-1/2in. in
diameter, and 3/4in. in depth, made of iron, at the same casting: one
contains the mercury, and the other is the trough, fitted with glass
cover for observing.
The discs are connected at their circumference by a narrow neck, and
in it is drilled a hole, through which the mercury passes from one
reservoir to the other; and this communication is opened or shut
off by a stop-cock, on the cone principle, such as is used for water
or gas, so that the mercury can be passed from one disc to the other
without removing the glass cover, or the risk of losing any mercury.
The mercurial disc, A, is fitted with a cylinder-stopper, D, acting on
a spiral spring, by which air can be admitted or allowed to escape.
The trough disc, B, is fitted with two glasses, G and E, which are
ground mathematically parallel: one of the glasses is fitted to a
frame, and screws on the disc, and is used while passing the mercury
in or out of the trough; after which operation it is removed and
replaced by the other glass, the edge of which next the stop-cock
should be supported by the blade of a pocket-knife and then lowered on
the mercury at the opposite side, and by a gentle pressure, force out
the intervening air, leaving the glass to float on the surface of the
mercury. Without this care, some of the mercury might be pressed over
the edge of the disc.
The glass then presents a clear reflecting surface, which is not
only protected from the effects of the wind, &c., but also maintains
so great a steadiness as to mark a decided improvement over the old
triangular glass roof which is placed over the mercury, instead of, as
in this case, being on it.
It may be used afloat under favourable circumstances (the observer and
artificial horizon being placed on a pendulum table). Another great
advantage to this improved artificial horizon is the facility with
which altitudes can be observed at 2° elevation, and consequently its
adaptation for the measurement of very low stars, as well as the peaks
of mountain ranges.
To return the mercury to its reservoir, remove the glass G that floats
on the mercury, by lifting it up with the point of a knife, and then
screw on the other glass cover, E. It is now only necessary to hold the
instrument vertically, the trough end being uppermost (Fig. 4), turn
the stop-cock, and press gently downward on the cylindrical stopper,
and the mercury will rapidly return to its reservoir.
The following diagrams (half the actual size of the instrument), show
the various parts of the instrument, and the method of filling and
emptying the reservoir.
[Illustration: _Fig 1-4._]
Fig. 1 is the instrument complete. A, the mercurial reservoir; B, the
observing trough; C, the stop-cock; D, the cylindrical stop.
Fig. 2 is the instrument with the parts of the observing trough
removed, which are shown above it. E, rim with glass shade; F, rim
without glass shade; G, the glass that floats on the surface of the
mercury.
Fig. 3. Position of the instrument while filling the observing trough.
Fig. 4. Position of the instrument while returning the mercury into its
reservoir.
In moderate weather the glass G will be quite sufficient protection
against the wind, but in gusty weather screw on the rim F, but it must
not touch the glass G.
The glass E will protect it from any weather, taking care to level the
ground on which the horizon stands.
In filling the observing trough, be careful that the glass cover, E,
is screwed on tight; by pressing on the cylindrical stop D (Fig. 1)
the mercury flows quickly: the trough half filled, as shown in Fig. 3,
is sufficient for ordinary observations; but for very low altitudes
the trough must be three-quarters filled or more as found necessary to
raise glass G (Fig. 1).
[Illustration: FIG. 1-2. ]
Before returning the mercury into the reservoir, unscrew the short
tube near the stop-cock, tapping it smartly at the same time, to shake
down the globules of mercury that may remain in the tube; there is a
small hole in the screw, which must be brought in sight, then turn
the stop-cock, and the mercury will run rapidly into the reservoir.
When about to use a sextant and artificial horizon of the common
form of construction, our first care is to select a tolerably level,
and, if there be wind, a sheltered spot of ground, with a clear view
to the north or south, or, if the stars admit of a north and south
observation, to see that the view is clear both ways. On this we place
our artificial horizon, sometimes on our sextant case, sometimes on
a stand (wash leather), but seldom, if we can avoid it, on the bare
ground, because then the mercury, if spilled, would be difficult to
gather up. The horizon roof we keep near to cover the mercury, in case
wind should arise, but we never use it unless in case of necessity;
then, sitting either north or south of the horizon, according to the
position of the celestial object, we look with the naked eye for its
reflected image in the mercury, and so seat ourselves that we can
conveniently keep it steadily in view. We set the sextant nearly to
zero, and look up without the telescope to the sun or star, and then,
gradually moving the index forward, we bring its image down to meet
the reflection in the quicksilver; then, screwing on the inverting
telescope, which is the simplest and best for observation, we move
the index by hand, till the contact is nearly perfect; then fasten the
index by the clamping screw, and with the tangent screw complete the
contact; and so long as the object is rising, by gradually turning the
tangent screw we keep the images together; when they separate more
slowly, and at length remain in contact for nearly half a minute, we
know that the meridian altitude has been observed; we wait another
minute to see them separate in the opposite direction as the body
begins to descend, and then read off the observed altitude. Our
illustration will sufficiently explain that the sextant is held in the
left hand and the tangent screw worked with the thumb and forefinger
of the right. Fig. 2 is the method recommended by Captain George: the
arc is steadied by the forefinger, and the tangent screw turned by the
middle finger and the thumb; a police or bull's-eye lantern is good to
read off by, and the light, of whatever nature, should be placed behind
the observer, so that it may not interfere with his work, and yet may
be ready for him to use when he wishes to read his altitude.
PROJECTION OF ROUTES.
The following directions for the projections of routes by Captain
George, R.N., are so thoroughly plain and practical that it will
be well for the travelling observer to have recourse to them:--For
out-door or field work the easiest method is by the plane projection,
the data thus obtained being transferred to a Mercator's projection
at the first halt or stopping station. In the plane projection one
equal length is assigned to all the degrees of latitude and longitude.
It was first adopted on the erroneous supposition that the earth's
surface is a plane; it is still the best for the traveller to use in
his early attempts to project his journey while the objects are still
in sight. This projection is available as far as 20° on either side of
the Equator; beyond the parallel of 20° and as far as 60° Mercator's
projection is preferable. Between 60° and the pole the distortion of
both the plane and Mercator's projection is so apparent, that a polar
or circular projection must be adopted. Sheets of paper, ruled into
squares by strong lines, and subdivided by finer ones, afford great
assistance in map work. For out-door work the scale of 1in. to one
mile is amply large enough to register every particular of one day's
journey on a sheet of 12in. square. The in-door, or table plan, may be
reduced ten miles to the inch, and plans for transmission home maybe
again reduced to 1in. to 1° when larger plans cannot be sent. The chief
point aimed at in the following directions is to draw more attention
than has hitherto been given to the true bearing of objects, for the
following reasons: First. Any object whose true bearing is east or west
must be in the same latitude as the place of the observer. Secondly.
Any object whose true bearing is north or south must be in the same
longitude as the place of the observer.
[Illustration]
While travelling in a northerly or southerly direction, from a station
whose latitude is known, and carefully noting the distance and
direction travelled, it is only necessary to watch when objects come to
the true east or west, and their latitude is obtained. When travelling
in an easterly or westerly direction from a fixed station, noting
distance and direction, it is only necessary to watch when objects
come to the true north or south, and their difference of longitude can
be obtained by using Table B, from the station left. Thus, suppose a
traveller passes from A, whose latitude is known, towards some distant
hill (B), his route making an angle of 25° with the meridian. He sets
his sextant to 65° (65° + 25° = 90°), or to 115° (180° - 65°); then as
the objects 1, 2, 3, and 4 successively come into contact with B or
A, as the case may be, he ascertains with precision the moment when
they are truly east or west of him, and so, knowing the distance he has
travelled from A, he can readily calculate or project their latitude.
When the traveller, as will frequently be the case, has to deviate from
the line of route, his position can be determined by compass, or true
bearing of any object, and an angle of a second object; or he may have
recourse to transit observations; that is to say, wherever two fixed
objects come in line, an angle to a third object will determine the
position with great accuracy.
[Illustration]
Observe that in travelling along X Y Z the hills A B C can be mapped
for at X, or thereabouts; the bearing of B from C can be determined
at Y; that of A from B; and at Z that of A from C, and so on, for any
number of hills. And it is very important to recollect that it is
not necessary to catch these lines of sight precisely, for by taking
bearings twice, and the intermediate course approximately, there are
sufficient data for protracting out upon paper the required bearing.
Thus, as soon as the peak of a distant hill is about to be occulted
by the shoulder of a nearer one, a bearing should be taken, and again
another as soon as it has reappeared on the other side, and the
intermediate course noted.
The advantage of this method of filling up a field sketch will become
more apparent as experience is gained. A third and accurate method
of fixing the position is in general use among marine surveyors, but
has hitherto been but little resorted to by land travellers, viz.,
by the angles subtended between three known objects. The instrument
called the station-pointer is generally used for this purpose, but the
position may also be found with a pair of compasses and a protractor,
or more simply as follows by means of a protractor and a sheet of
tracing paper. Draw a line through the centre of the paper, place the
protractor on it, near to the bottom of the sheet, lay off the right
hand angle to the right, and the left hand angle to the left of the
centre line; rule pencil lines, radiating from the point over which
the centre of the protractor had been placed, to the points that had
been laid off, then place the paper on the plan or map, and move it
about until the three lines coincide with the objects taken, prick
through the points that lay beneath the centre of the protractor, and
the observer's position is transferred to the plan. When possible the
centre object should be the nearest.
TO CONSTRUCT A MAP ON MERCATOR'S PROJECTION.
On a sheet of cartridge paper, 38in. by 20in., it is proposed to
construct a map on Mercator's projection, on a scale of ten miles to an
inch equatorial, _i.e._ 6in. to a degree of longitude.
Lat. 31° to 33° N.
Long. 34° to 36° E.
Draw a base line, find its centre, and erect a perpendicular to the top
of the paper; the extremes of longitude 34° and 36°, added together and
divided by 2°, give 35°, the central meridian, and which is represented
by the perpendicular. On each side of it lay off 6in., and erect
perpendiculars for the meridians 34° and 36°; divide the base line into
ten mile divisions, and the part from 35° 50´ to 36° into miles for the
latitude scale. From Table A take the following quantities:--
° ° ° ´ ° °
Lat. 31 to 32 = 1 10·4 = the distance between parallels 31 and 32
Lat. 32 to 33 = 1 11·1 " " 32 and 33
-------
2 21·5 " " 31 to 33
Having thus obtained the distance between the required parallels,
divide the map into squares of ten miles each way, and the map is ready
for the projection of the route.
A.--TABLE TO CONSTRUCT MAPS ON MERCATOR'S PROJECTION.
--+------+------+------+------+------+--------+-------+-------+-------+-------
| 0° | 1° | 2° | 3° | 4° | 5° | 6° | 7° | 8° | 9°
--+------+------+------+------+------+--------+-------+-------+-------+-------
|° ´ |° ´ |° ´ |° ´ |° ´ | ° ´ | ° ´ | ° ´ | ° ´ | ° ´
0| |1 00 |1 00·1|1 00·1|1 00·1| 1 00·2 | 1 00·3| 1 00·4| 1 00·5| 1 00·6
10|1 00·9|1 01 |1 01·2|1 01·5|1 00·7| 1 02 | 1 02·2| 1 02·6| 1 02·9| 1 03·3
20|1 03·6|1 04·1|1 04·5|1 04·9|1 05·5| 1 05·9 | 1 06·5| 1 07 | 1 07·7| 1 08·2
30|1 09 |1 09·6|1 10·4|1 11·1|1 12 | 1 12·8 | 1 13·7| 1 14·6| 1 15·7| 1 16·7
40|1 17·6|1 19 |1 20·1|1 21·4|1 22·7| 1 24·2 | 1 25·6| 1 27·1| 1 28·8| 1 30·6
50|1 32·4|1 34·3|1 36·4|1 38·6|1 40·8| 1 43·4 | 1 45·9| 1 49 | 1 51·4| 1 54·8
60|1 58·3|2 01·8|2 05·8|2 09·9|2 14·5| 2 19·14| 2 24·7| 2 30·5| 2 36·8| 2 43·8
70|2 51·3|2 59·8|3 09·1|3 19·6|3 31·3| 3 44·6 | 3 59·8| 4 17·1| 4 37·4| 5 01·1
80|5 29·5|6 03 |6 46·4|7 40·3|8 51·1|10 27·7 |12 47·9|16 29·6|23 14·3|39 42·2
--+------+------+------+------+------+--------+-------+-------+-------+-------
_Use of the table._--Find the required parallel; the tens at the side,
and the units at the top. At their intersection will be found in
degrees and minutes the distance of the required parallel from the next
less degree, to be measured from the scale of longitude on the map in
progress.
Given the parallel of 30°, required that of 31°. 30 at the side and 1
at the top intersects at 1° 09·6´, the required distance of the two
parallels.
Given the parallel of 31°, required that of 33°:
° ° ´
32 = 1 10·4
33 = 1 11·1
------
2 21·5 the distance between the 31° and 33° parallels.
B.--GIVEN THE DEPARTURE TO FIND DIFFERENCE OF LONGITUDE.
--+------+------+------+------+------+-------+-------+-------+-------+-------
| 0° | 1° | 2° | 3° | 4° | 5° | 6° | 7° | 8° | 9°
--+------+------+------+------+------+-------+-------+-------+-------+-------
0| |1·0001|1·0006|1·0013|1·0026| 1·0038| 1·0055| 1·0075| 1·0098| 1·0125
10|1·0154|1·0187|1·0224|1·0261|1·0306| 1·0353| 1·0403| 1·0457| 1·0514| 1·0578
20|1·0642|1·0711|1·0785|1·0864|1·0946| 1·1034| 1·1126| 1·1224| 1·1326| 1·1434
30|1·1547|1·1666|1·1792|1·1924|1·2062| 1·2208| 1·2361| 1·2521| 1·2690| 1·2868
40|1·3054|1·3250|1·3456|1·3673|1·3902| 1·4142| 1·4395| 1·4663| 1·4945| 1·5242
50|1·5557|1·5890|1·6242|1·6616|1·7013| 1·7435| 1·7883| 1·8361| 1·8871| 1·9416
60|2·0000|2·0626|2·1301|2·2027|2·2812| 2·3662| 2·4586| 2·5593| 2·6695| 2·7904
70|2·9238|3·0716|3·2361|3·4204|3·6280| 3·8637| 4·1337| 4·4454| 4·8097| 5·2406
80|5·7587|6·3925|7·1856|8·2057|9·5664|11·475 |14·334 |19·108 |28·653 |57·307
--+------+------+------+------+------+-------+-------+-------+-------+-------
_Use of the table._--Find the required parallel, the tens at the
side and the units at the top, at their intersection will be found a
quantity, which, multiplied by the departure, gives the difference of
longitude.
The departure from the meridian on the parallel of 34° was 25 miles,
required the difference of longitude:
25´ × 1·20 = 30·00´ the difference of longitude.
In the parallel of 60° the departure was 30 miles:
30´ × 2 = 60 miles, or 1 degree.
In the parallel of 35° N. the route was N. 40° W. 37 miles distance.
By traverse table, 40° course, dist. 37° = dep. 23·8´ × 1·22 = 29·03
miles difference of longitude.
The following example will serve to show how the traveller's record
of progress may be conveniently kept. It was framed by S. W. Norie
expressly for the use of navigators; but explorers and travellers will
find it a simple and useful form for recording the day's work:
------------------+-----------+-------------------------+-------------
Corrected | | Difference of Latitude. | Departure.
Courses. | Distance. +------------+------------+------+------
| | N. | S. | E. | W.
------------------+-----------+------------+------------+------+------
N.E. | 36 | 25·5 | | 25·5 |
N. by W. | 14 | 13·7 | | | 2·7
N.E. by E. 1/2 E. | 58 | 27·3 | | 51·2 |
N. by E. | 42 | 41·2 | | 8·2 |
E.N.E. | 29 | 11·1 | | 26·8 |
| +------------+ +------+------
| Difference| 118·8 | |111·7 | 2·7
| of Lat. | | | 2·7 |
| | | | -- |
| | | Dep. |109·0 |
------------------+-----------+------------+------------+------+------
The difference of latitude 118·8 and departure 109·0 give the course
N. 42° 32´ E., and distance 161·2.
° ´ ° ´
Latitude left 52 36 N. Merc. prjctns. 3724 Longitude left 21 45 W.
Diff. lat. 1 59 N. Diff. lon. 184 or 3 4 E.
-- -- -----
Latitude in 54 35 N. Merc. prjctns. 3925 Longitude in 18 41 W.
------ ----
Sum of lats. 2)107 11 Merc. diff. lat. 201
Mid lat. 53 35
TO MEASURE THE NUMBER OF CUBIC FEET OF WATER CONVEYED BY A RIVER IN
EACH SECOND.
In traversing regions watered by rivers and running streams, it not
unfrequently becomes important to ascertain the speed at which they
flow in their downward course towards the sea, and the following
directions given by Captain George, R.N., are so perfectly clear and
practical that both time and trouble will be saved by the traveller who
follows them out in conducting his investigations. The data required
are--the area of the river, section, and the average velocity of the
whole current. All that a traveller is likely to obtain without special
equipment is the area of the river, section, and the average velocity
of the "surface" of the current which differs from that of its entire
body, owing to fractional retardation at the bottom.
To make the necessary measurements, choose a piece where the river
runs steadily in a straight and deep channel and where a boat can be
had. Prepare half a dozen floats of dry bushes, with paper flags,
and be assured they will act. Post an assistant on the river bank at
a measured distance (of about 100 yards), down stream, in face of a
well-marked object; row across stream, in a straight line, keeping two
objects on a line in order to maintain your course. Sound at regular
intervals from shore to shore, fixing your position on each occasion
by a sextant angle between your starting place and your assistant's
station, and throw the floats overboard, signalling to your assistant
when you do so, that he may note the interval that elapses before they
severally arrive opposite him. Take an angle from the opposite shore to
give the breadth of the river. To make the calculation approximately,
protract the section of the river on a paper, ruled to scale in square
feet, and count the number of squares in the area of the section.
Multiply this by the number of feet between you and the assistant, and
divide by the number of seconds that the floats occupied on an average
in reaching him.
Important rivers should always be measured above and below their
confluence, for it settles the question of their relative sizes, and
throws great light on the rainfall over their respective basins. The
sectional area at the time of the highest water, as shown by marks on
the banks and the slope of the bed, ought also to be ascertained.
ON OBTAINING GEOGRAPHICAL INFORMATION FROM NATIVES OR FRONTIER
COLONISTS.
Many highly-accomplished travellers fail to obtain much reliable
information beyond the actual limit of their own observation, because
they do not sufficiently allow for the great difference in the manner
of expressing a geographical idea between an educated European observer
and an untutored savage; and yet it would not be too much to say that
the latter has often enough a thoroughly practical idea of the district
he actually knows.
The man who wants information must not talk latitude and longitude to a
native or to an uneducated European, nor must he expect them to shape
their answers to the form in which he expects to receive them; for if
he does he may be told that "rivers run from the sea to the mountains,"
and other absurdities, which are related as proofs of native stupidity,
when they are in reality no more than discrepancies between the form of
question and that of the answer. At the same time he must estimate the
mental calibre of his informant, and avoid wearying him too much; for
sometimes the native mind, over burdened with a succession of ideas,
becomes confused, and not unfrequently suspicious, and in this last
case actual falsehoods will be told, in order to gain time to find out
the intention of the questioner, before the truth is revealed.
In all dealings with natives the European must remember that they have
no idea of the value we place upon time; there is no use in saying,
"Let us come to the point at once." It is far better, indeed it is
absolutely necessary, to delay judiciously, as there is always an
implied contest between visitors; and the man who is in a hurry to
speak loses dignity. Do not disturb your informant's train of thought,
but try to accommodate your own to it. Let him tell as minutely and
tediously as he pleases how he has travelled; how long he walked with
the rising sun on his right or left; how much he turned either way;
where he halted for rest or refreshment; whether he crossed rivers
on foot or in canoes; induce him, if possible, to trace a map upon
the ground, in doing which he will most probably begin by making the
direction of all his lines coincide with the actual bearing of the
country; for natives, though they may be brought to comprehend a map
when its north point coincides with the real north, cannot believe
that it is also right when it is placed in any other position. We have
frequently tested Hottentots with regard to the direction of places a
thousand miles distant, and have found them point as correctly as we
could take the bearing with a pocket compass.
Sometimes it will be found that the same individual will give a river
a dozen different names; and this is often because, in speaking of the
different parts of it, he gives to each the name of the chief who has
his village there, and who "drinks water" at the place which is called
after him; therefore, endeavour to ascertain whether the river has a
real name, and do not apply to it the first and, perhaps, the most
inappropriate name that is given.
Europeans who have settled in the colonies, and have become traders or
hunters, frequently push very far into the interior, and such men have
generally very clear ideas of direction and locality, but are often
very modest and diffident when asked to furnish information to be laid
down on paper. In 1849, while staying at the Vaal River, we persuaded
our friend Macabe, with some difficulty, to give us the length in
"hours" and the direction of the various stages of his journey on the
river Limpopo. These, with the rivers, mountains, villages, and other
features of the country, we laid down, on a scale of one inch to a
mile, on several sheets of cartridge paper, and tested the correctness
of our work by laying it on the floor, with its north coinciding with
the real north, and requesting our Dutch visitors to stand as if they
were about commencing the same journey, and indicate how much they
turned to the right or left as they proceeded.
The following facts relating to time should be impressed on the memory
of every traveller:--The earth is divided in its circumference into
360°; the day is divided into twenty-four hours. It therefore follows
that 15° of longitude will represent one hour of time; consequently, as
you travel towards the east, when you have journeyed over 15°, you will
have gained one hour on the sun, which will rise just one hour earlier
than it did at the starting point.
If natives accompany you on a journey, ask them to point in the
direction of places at different times, and particularly to tell you
when you are exactly abreast of them, as well as before, and after you
have passed, and thus, by a kind of rough triangulation, you will gain
their approximate position.
If cattle stray to great distances, ask the men who go after them
the reason of their having taken any particular direction, and you
will probably gain some information respecting the form of valleys or
mountains, and perhaps of watering places.
In North Australia we were led by the tracks of horses, which had been
lost about a fortnight, to a considerable stream.