CHAPTER VII.THE BASE OF THE TRIANGLE.[edit]
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 metres 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 table-land
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.”
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.
The base measured exactly 8037.75 toises, and upon this
they were now to place their series of triangles.