The Adventures of Three Englishmen and Three Russians in Southern Africa/Chapter IV
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 metre, 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 1/334, 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.
1^ `whole line' is an invention by the translator. Verne states qui se trouve être de 0.513074; which works out to be 0.513074 (toises).
2^ By using English units, the translator has messed up the preciseness of Verne's work. Verne wrote trois pieds onze lignes deux cent quatre-vingt-seize millièmes de ligne; three feet and 11.296 lines (i.e. 443.296 lines, the line being 1/12 of a French inch). This was the definition of the metre adopted by the French law of 1799. The toise is six French feet, or 864 lines, and the metre 443.296/864=0.513074074... toises.
Note that in imperial units, the inch is defined as 0.0254 metres, so the metre is 1/0.0254=39.37007874 inches.
3^ Verne states deux dix millièmes de ligne; about 0.00045 millimetres, or 4 metres over the entire quadrant. This is inconsitent with the difference of 856 metres stated previously.
The polar circumference of the Earth is currently measured at 40,007.86 km, meaning that the error is slightly less than 2 kilometres per quadrant, or 0.2 millimetres per metre.