THE BASE OF THE TRIANGLE.
The work undertaken by the Commission was a triangulation for the
purpose of measuring an arc of meridian. Now the direct measurement
of one or more degrees by means of metal rods would be impracticable.
In no part of the world is there a region so vast and unbroken as to
admit of so delicate an operation. Happily, there is an easier way of
proceeding by dividing the region through which the meridian passes
into a number of imaginary triangles, whose solution is comparatively
easy.
These triangles are obtained by observing signals, either natural or
artificial, such as church-towers, posts, or reverberatory lamps, by
means of the theodolite or repeating-circle. Every signal is the vertex
of a triangle, whose angles are exactly determined by the instruments,
so that a good observer with a proper telescope can take the bearings
of any object whatever, a tower by day, or a lamp by night. Sometimes
the sides of the triangles are many miles in length, and when Arago
connected the coast of Valencia in Spain with the Balearic Islands,
one of the sides measured 422,555 toises. When one side and two angles
of any triangle are known, the other sides and angle maybe found; by
taking, therefore, a side of one of the known triangles for a new base,
and by measuring the angles adjacent to the base, new triangles can be
successively formed along the whole length of the arc; and since every
straight line in the network of triangles is known, the length of the
arc can be easily determined. The values of the sides and angles may be
obtained by the theodolite and repeating circle, but the _first_ side,
the base of the whole system, must be actually measured on the ground,
and this operation requires the utmost care.
When Delambre and Méchain measured the meridian of France from Dunkirk
to Barcelona, they took for their base a straight line, 12,150 mètres
in length, in the road from Melun to Lieusaint, and they were no
less than 42 days in measuring it. Colonel Everest and Matthew Strux
designed proceeding in the same way, and it will be seen how much
precision was necessary.
The work was begun on the 5th of March, much to the astonishment of
the Bochjesmen, who could not at all understand it. Mokoum thought it
strange for these learned men to measure the earth with rods six feet
long; but any way, he had done his duty; they had asked him for a level
plain, and he had found it for them.
The place was certainly well chosen. Covered with dry, short grass,
the plain was perfectly level as far as the horizon. Behind lay a line
of hills forming the southern boundary of the Kalahari desert; towards
the north the plain seemed boundless. To the east, the sides of the
tableland of Lattakoo disappeared in gentle slopes; and in the west,
where the ground was lower, the soil became marshy, as it imbibed the
stagnant water which fed the affluents of the Kuruman.
"I think, Colonel Everest," said Strux, after he had surveyed the
grassy level, "that when our base is established, we shall be able here
also to fix the extremity of our meridian."
"Likely enough," replied the Colonel. "We must find out too, whether
the arc meets with any obstacles that may impede the survey. Let us
measure the base, and we will decide afterwards whether it will be
better to join it by a series of auxiliary triangles to those which the
arc must cross."
[Illustration: Commencement of the Geodesic Operations.]
They thus resolved to proceed to the measurement of the base. It would
be a long operation, for they wanted to obtain even more correct
results than those obtained by the French philosophers at Melun.
This would be a matter of some difficulty: since when a new base was
measured afterwards near Perpignan to verify the calculations, there
was only an error of 11 inches in a distance of 330,000 toises.
Orders were given for encamping, and a Bochjesman village, a kind of
kraal, was formed on the plain. The waggons were arranged in a circle
like the houses, the English and Russian flags floating over their
respective quarters. The centre was common ground. The horses and
buffaloes, which by day grazed outside, were driven in by night to the
interior, to save them from attacks of the wild beasts around.
Mokoum took upon himself to arrange the hunting expedition for
revictualling; and Sir John Murray, whose presence was not
indispensable in the measurement of the base, looked after the
provisions, and served out the rations of preserved meat and fresh
venison. Thanks to the skill and experience of Mokoum and his
companions, game was never wanting. They scoured the district for miles
round, and the report of their guns resounded at all hours.
The survey began on the next day, Zorn and Emery being charged with the
preliminaries.
"Come along," said Zorn, "and good luck be with us."
The primary operation consisted in tracing a line on the ground where
it was especially level. This chanced to be from S.E. to N.W., and
pickets being placed at short intervals to mark the direction, Zorn
carefully verified the correctness of their position by means of the
thread-wires of his telescope. For more than eight miles (the proposed
length of the base) was the measurement continued, and the young men
performed their work with scrupulous fidelity.
The next step was to adjust the rods for the actual measurement,
apparently a very simple operation, but which, in fact, demands the
most continuous caution, as the success of a triangulation in a great
measure is contingent on its preciseness.
On the morning of the 10th, twelve wooden pedestals were planted along
the line, securely fastened in their position, and prepared to support
the rods. Colonel Everest and Matthew Strux, assisted by their young
coadjutors, placed the rods in position, and Nicholas Palander stood
ready, pencil in hand, to write down in a double register the figures
transmitted to him.
The rods employed were six in number, and exactly two toises in length.
They were made of platinum, as being (under ordinary circumstances)
unaffected by any condition of the atmosphere. In order, however, to
provide against any change of temperature, each was covered with a rod
of copper somewhat shorter than itself, and a microscopic vernier was
attached, to indicate any contraction or expansion that might occur.
The rods were next placed lengthwise, with a small interval between
each, in order to avoid the slight shock which might result from
immediate contact. Colonel Everest and Matthew Strux with their own
hands placed the first rod. About a hundred toises farther on, they
had marked a point of sight, and as the rods were each provided with
iron projections, it was not difficult to place them exactly in the
proper direction. Emery and Zorn, lying on the ground, saw that the
projections stood exactly in the middle of the sight.
"Now," said Colonel Everest, "we must define our exact starting-point.
We will drop a line from the end of our first rod, and that will
definitely mark the extremity of our base."
"Yes," answered Strux, "but we must take into account the radius of the
line.
"Of course," said the Colonel.
The starting-point determined, the work went on. The next proceeding
was to determine the inclination of the base with the horizon.
"We do not, I believe, pretend," said Colonel Everest, "to place the
rod in a position which is perfectly horizontal."
"No," answered Strux, "it is enough to find the angle which each rod
makes with the horizon, and we can then deduce the true inclination."
Thus agreed, they proceeded with their observations, employing their
spirit-level, and testing every result by the vernier. As Palander was
about to inscribe the record, Strux requested that the level should
be reversed, in order that by the division of the two registers a
closer approximation to truth might be attained. This mode of double
observation was continued throughout the operations.
Two important points were now obtained: the direction of the rod with
regard to the base, and the angle which it made with the horizon. The
results were inscribed in two registers, and signed by the members of
the Commission.
There were still two further observations, no less important, to be
made: the variation of the rod caused by differences of temperature,
and the exact distance measured by it. The former was easily determined
by comparing the difference in length between the platinum and copper
rods. The microscope gave the variation of the platinum, and this
was entered in the double register, to be afterwards reduced to 16°
Centigrade.
They had now to observe the distance actually measured. To obtain
this result, it was necessary to place the second rod at the end of
the first, leaving a small space between them. When the second rod
was adjusted with the same care as the former, it only remained to
measure the interval between the two. A small tongue of platinum,
known as a slider, was attached to the end of the platinum bar that
was not covered by the copper, and this Colonel Everest slipped gently
along until it touched the next rod. The slider was marked off into
10,000ths of a toise, and as a vernier with its microscope gave the
100,000ths, the space could be very accurately determined. The result
was immediately registered.
Michael Zorn, considering that the covered platinum might be sooner
affected by heat than the uncovered copper, suggested another
precaution: accordingly they erected a small awning to protect the rod
from the sun's rays.
For more than a month were these minutiæ patiently carried on. As soon
as four bars were adjusted, and the requisite observations complete,
the last of the rods was carried to the front. It was impossible to
measure more than 220 to 230 toises a day, and sometimes, when the wind
was violent, operations were altogether suspended.
Every evening, about three quarters of an hour before it became too
dark to read the verniers, they left off work, after taking various
anxious precautions. They brought forward temporarily the rod "No.
1," and marked the point of its termination. Here they made a hole,
and drove in a stake with a leaden plate attached. They then replaced
"No. 1" in its original position, after observing the inclination, the
thermometric variation, and the direction. They noted the prolongation
measured by rod "No. 4," and then with a plumb-line touching the
foremost end of rod "No. 1," they made a mark on the leaden plate.
They carefully traced through this point two lines at right angles,
one signifying the base, the other the perpendicular. The plate was
then covered with a wooden lid, the hole filled in, and the stake left
buried till the morning. Thus, if any accident had happened to their
apparatus during the night they would not be obliged to begin afresh.
The next day, the plate was uncovered, and rod "No. 1" replaced in the
same position as on the evening before, by means of the plumb-line,
whose point ought to fall exactly on the point intersected by the two
straight lines.
These operations were carried on for thirty-eight days along the plain,
and every figure was registered doubly, and verified, compared, and
approved, by each member of the Commission.
Few discussions arose between Colonel Everest and his Russian
colleague; and if sometimes the smallest fraction of a toise gave
occasion for some polite cavillings, they always yielded to the opinion
of the majority. One question alone called for the intervention of Sir
John Murray. This was about the length of the base. It was certain
that the longer the base, the easier would be the measurement of the
opposite angle. Colonel Everest proposed 6000 toises, nearly the same
as the base measured at Melun; but Matthew Strux wished that it should
be 10,000 toises, since the ground permitted. Colonel Everest, however,
remained firm, and Strux seemed equally determined not to yield. After
a few plausible arguments, personalities began: they were no longer two
astronomers, but an Englishman and a Russian. Happily the debate was
interrupted by some days of bad weather, which allowed their tempers
to cool. It was subsequently decided by the majority that they should
"split the difference," and assign 8000 toises as the measurement of
the base. The work was at length completed. Any error which occurred,
in spite of their extreme precision, might be afterwards corrected by
measuring a new base from the northern extremity of the meridian.
[Illustration: Taking the Measurements.]
The base measured exactly 8037.75 toises, and upon this they were now
to place their series of triangles.