A FEW WORDS ABOUT THE "MÈTRE."
The idea of an invariable and constant system of measurement, of
which nature herself should furnish the exact value, may be said to
have existed in the mind of man from the earliest ages. It was of the
highest importance, however, that this measurement should be accurately
determined, whatever had been the cataclysms of which our earth had
been the scene, and it is certain that the ancients felt the same,
though they failed in methods and appliances for carrying out the
work with sufficient accuracy. The best way of obtaining a constant
measurement was to connect it with the terrestrial sphere, whose
circumference must be considered as invariable, and then to measure
the whole or part of that circumference mathematically. The ancients
had tried to do this, and Aristotle, according to some contemporary
philosophers, reckoned that the stadium, or Egyptian cubit, formed
the hundred-thousandth part of the distance between the pole and the
equator, and Eratosthenes, in the time of the Ptolemies, calculated
the value of a degree along the Nile, between Syene and Alexandria,
pretty correctly; but Posidonius and Ptolemy were not sufficiently
accurate in the same kind of geodetic operations that they undertook;
neither were their successors.
Picard, for the first time in France, began to regulate the methods
that were used for measuring a degree, and in 1669, by measuring the
celestial and terrestrial arcs between Paris and Amiens, found that
a degree was equal to 57,060 toises, equivalent to 364,876 English
feet, or about 69.1 miles. Picard's measurement was continued either
way across the French territory as far as Dunkirk and Collioure by
Dominic Cassini and Lahire (1683-1718), and it was verified in 1739,
from Dunkirk to Perpignan, by Francis Cassini and Lacaille; and at
length Méchain carried it as far as Barcelona in Spain; but after
his death (for he succumbed to the fatigue attending his operations)
the measurement of the meridian in France was interrupted until it
was subsequently taken up by Arago and Biot in 1807. These two men
prolonged it as far as the Balearic Isles, so that the arc now extended
from Dunkirk to Formentera, being equally divided by the parallel of
lat. 45° N., half way between the pole and the equator; and under
these conditions it was not necessary to take the depression of the
earth into account in order to find the value of the quadrant of the
meridian. This measurement gave 57,025 toises as the mean value of an
arc of a degree in France.
It can be seen that up to that time Frenchmen especially had undertaken
to determine that delicate point, and it was likewise the French
Convention that, according to Talleyrand's proposition, passed a
resolution in 1790, charging the Academy of Sciences to invent an
invariable system of weights and measures. Just at that time the
statement signed by the illustrious names of Borda, Lagrange, Laplace,
Monge, and Condorcet, proposed that the unit of measure should be the
_mètre_, the ten-millionth part of the quadrant of the meridian; and
that the unit of weight should be the _gramme_, a cubic centimètre
of distilled water at the freezing-point; and that the multiples and
subdivisions of every measure should be formed decimally.
Later, the determinations of the value of a terrestrial degree were
carried on in different parts of the world, for the earth being not
spherical, but elliptic, it required much calculation to find the
depression at the poles.
In 1736, Maupertuis, Clairaut, Camus, Lemonnier, Outhier, and the
Swedish Celsius measured a northern arc in Lapland, and found the
length of an arc of a degree to be 57,419 toises. In 1745, La
Condamine, Bouguer, and Godin, set sail for Peru, where they were
joined by the Spanish officers Juan and Antonio Ulloa, and they then
found that the Peruvian arc contained 56,737 toises.
In 1752, Lacaille reported 57,037 toises as the length of the arc he
had measured at the Cape of Good Hope.
In 1754, Father Boscowitch and Father le Maire began a survey of the
Papal States, and in the course of their operations found the arc
between Rome and Rimini to be 56,973 toises.
In 1762 and 1763, Beccaria reckoned the degree in Piedmont at 57,468
toises, and in 1768, the astronomers Mason and Dixon, in North America,
on the confines of Maryland and Pennsylvania, found that the value of
the degree in America was 56,888 toises.
Since the beginning of the 19th century numbers of other arcs have been
measured, in Bengal, the East Indies, Piedmont, Finland, Courland,
East Prussia, Denmark, &c., but the English and Russians were less
active than other nations in trying to decide this delicate point,
their principal geodetic operation being that undertaken by General Roy
in 1784, for the purpose of determining the difference of longitude
between Paris and Greenwich.
It may be concluded from all the above-mentioned measurements that the
mean value of a degree is 57,000 toises, or 25 ancient French leagues,
and by multiplying this mean value by the 360 degrees contained in the
circumference, it is found that the earth measures 9000 leagues round.
But, as may be seen from the figures above, the measurements of the
different arcs in different parts of the world do not quite agree.
Nevertheless, by taking this average of 57,000 toises for the value of
a degree, the value of the mètre, that is to say, the ten-millionth
part of the quadrant of the meridian, may be deduced, and is found to
be 0.513074 of the whole line, or 39.37079 English inches. In reality,
this value is rather too small, for later calculations (taking into
account the depression of the earth at the poles, which is 1/(299.15)
and not 1/134, as was thought at first) now give nearly 10,000,856
mètres instead of 10,000,000 for the length of the quadrant of the
meridian. The difference of 856 mètres is hardly noticeable in such a
long distance; but nevertheless, mathematically speaking, it cannot be
said that the mètre, as it is now used, represents the ten-millionth
part of the quadrant of the terrestrial meridian exactly; there is an
error of about 1/5000 of a line, i.e. 1/5000 of the twelfth part of an
inch.
The mètre, thus determined, was still not adopted by all the civilized
nations. Belgium, Spain, Piedmont, Greece, Holland, the old Spanish
colonies, the republics of the Equator, New Granada, and Costa Rica,
took a fancy to it immediately; but notwithstanding the evident
superiority of this metrical system to every other, England had refused
to use it. Perhaps if it had not been for the political disturbances
which arose at the close of the 18th century, the inhabitants of
the United Kingdom would have accepted the system, for when the
Constituent Assembly issued its decree on the 8th of May, 1790, the
members of the Royal Society in England were invited to co-operate
with the French Academicians. They had to decide whether the measure
of the mètre should be founded on the length of the pendulum that
beats the sexagesimal second, or whether they should take a fraction
of one of the great circles of the earth for a unit of length; but
events prevented the proposed conference, and so it was not until
the year 1854 that England, having long seen the advantage of the
metrical system, and that scientific and commercial societies were
being founded to spread the reform, resolved to adopt it. But still
the English Government wished to keep their resolution a secret until
the new geodetic operations that they had commenced should enable them
to assign a more correct value to the terrestrial degree, and they
thought they had better act in concert with the Russian Government,
who were also hesitating about adopting the system. A Commission of
three Englishmen and three Russians was therefore chosen from among
the most eminent members of the scientific societies, and we have seen
that they were Colonel Everest, Sir John Murray, and William Emery,
for England; and Matthew Strux, Nicholas Palander, and Michael Zorn,
for Russia. The international Commission having met in London, decided
first of all that the measure of an arc of meridian should be taken in
the Southern hemisphere, and that another arc should subsequently be
measured in the Northern hemisphere, so that from the two operations
they might hope to deduce an exact value which should satisfy all the
conditions of the programme. It now remained to choose between the
different English possessions in the Southern hemisphere, Cape Colony,
Australia, and New Zealand. The two last, lying quite at the antipodes
of Europe, would involve the Commission in a long voyage, and, besides,
the Maoris and Australians, who were often at war with their invaders,
might render the proposed operation difficult; while Cape Colony, on
the contrary, offered real advantages. In the first place, it was under
the same meridian as parts of European Russia, so that after measuring
an arc of meridian in South Africa, they could measure a second one
in the empire of the Czar, and still keep their operations a secret;
secondly, the voyage from England to South Africa was comparatively
short; and thirdly, these English and Russian philosophers would find
an excellent opportunity there of analyzing the labours of the French
astronomer Lacaille, who had worked in the same place, and of proving
whether he was correct in giving 57,037 toises as the measurement of a
degree of meridian at the Cape of Good Hope. It was therefore decided
that the geodetic operation should be commenced at the Cape, and as the
two Governments approved of the decision, large credits were opened,
and two sets of all the instruments required in a triangulation
were manufactured. The astronomer William Emery was asked to make
preparations for an exploration in the interior of South Africa, and
the frigate "Augusta," of the royal navy, received orders to convey the
members of the Commission and their suite to the mouth of the Orange
River.
It should here be added, that besides the scientific question,
there was also a question of national vainglory that excited these
philosophers to join in a common labour; for, in reality, they were
anxious to out-do France in her numerical calculations, and to surpass
in precision the labours of her most illustrious astronomers, and that
in the heart of a savage and almost unknown land. Thus the members of
the Anglo-Russian Commission had resolved to sacrifice every thing,
even their lives, in order to obtain a result that should be favourable
to science, and at the same time glorious for their country. And this
is how it came to pass that the astronomer William Emery found himself
at the Morgheda Falls, on the banks of the Orange River, at the end of
January, 1854.