FRANCE.
The standard of length of the système ancient was the toise of 6 pieds, divided into 12 pouces of 12 lignes each.
The origin of the toise is not known, but it was probably legally established by Philip Le Bel, about 1300, as he first appears to have taken steps toward a uniform system of measures in France. In the 13th century the toise is mentioned by Ch. Le Rains. In the 14th century Menongier writes that, in marching, the sight should strike the ground 4 toises in front. In the fifteenth century Pereforest brings in the toise, and in the sixteenth century the Contume de Berry says, “We use in this country two toises; one for carpenters of 5 pieds and a half, the other for masons of 6 pieds.”
Picard used the toise in his measurement of an arc of meridian from Malvoisin to London in 1669.
The meridians measured by the Academy in 1735 to settle the question of the figure of the earth were made by means of two standard toises, known as the “Toise du Nord,” and the “Toise du Sud.”
The first, used by Maupertuis, Clairault, and Le Monnier, in Lapland, was destroyed by immersion in sea-water, when their ship was wrecked on the return voyage.
The second, with which La Condamine, Bourgner, and Godin operated in Peru, was the original of the toise Canivet made in 1768, and of the standards used in determining the mètre.
The commencement of the move for a scientific standard of length in France which resulted in the mètre was in 1790, when the revolutionary government proposed to England the formation of a commission of equal numbers from the English Royal Society and the French Academy, for the purpose of fixing the length of the seconds pendulum at latitude 45° as the basis of a new system of measures. This proposal was not favorably received, and the Academy, at the request of government, appointed as a commission Borda, Lagrange, Laplace, Monge, and Condorcet, to decide whether the seconds pendulum, the quarter of the equator, or the quarter of a meridian, should be used as the natural standard for the new system of measures. They settled on the last as best for the purpose, and resolved that the ten millionth of the meridian quadrant, or distance from equator to pole, measured at sea level, be taken for basis of the new system, and be called a mètre.
Delambre and Mechin were at once charged with re-measurement of the meridian surveyed in 1739 by La Caille and Cassini, from Dunkirk to Perpignan, and its extension to Barcelona.
Operations were commenced in 1792, and carried on with great accuracy to completion in 1799; Delambre working between Dunkirk and Paris, and Mechin between Paris and Barcelona.
The distance measured from Dunkirk to Barcelona was 9° 40´ 24·24´´ of arc, or 1,075,059 mètres, as reduced to the new standard.
The “toise de Peru” was the standard used in the work at a temperature of 13° R.
Two base-lines were measured with Borda’s compensating bars of brass and platinum; one at Melun, near Paris, 6076 toises long, and the second at Perpignan, 6028 toises long, and though over 900,000 mètres apart, the calculated length differed by only 10 pouces.
This meridian was afterward, in 1806, extended by Gen. Roy to Greenwich, on the north, and by Biot and Arago to Formentera, on the south. The results, as given by Laplace in centesimal degrees and mètres, are as follows:
| Greenwich | 57·19753° | ·0 | mètres. |
| Pantheon, Paris | 54·27431° | 292,719·3 | “ |
| Formentera | 42·96178° | 1,423,636·1 | “ |
The middle of the arc being 50·079655° Cent., or 45° 4´ 18·0822´´ Sexa., and the middle degree centesimal being very nearly 100,000 mètres.
The determination of the final result of these geodetic measurements was referred to a committee of 20 members; 9 named by the French Government, and the others by the governments of Holland, Savoy, Denmark, Spain, Tuscany, and of the Cisalpine, Ligurian, and Swiss republics, on the invitation of France.
This committee established the meridian quadrant at 5,130,740 toises; making the mètre 0·513074 of the toise, or 36·9413 pouces, or 443·296 lignes, and the toise 1·94903659 mètres.
Iron standard mètre bars, 12 in number were made by Borda, also 2 of platinum and 4 standard toise bars.
The 12 standard iron mètre bars were sent to different countries, after being verified by the French Government, and on the 2d of November, 1801, the mètrical système was legalized by France, and the standard unit of length declared to be the ten millionth part of a meridian quadrant of the earth, as defined by the distance at a temperature of 0° Centigrade (32° F.) between two points on a platinum bar in the keeping of the Academy of Science at Paris. This standard bar is used only once every ten years for exact comparisons, as stated by Dr. F. A. P. Barnard.
About 1837 Bessel, by a combination of 11 measured arcs of meridian, deduced the quadrant of meridian as 5,131,179·81 toises instead of 5,130,740 toises, as fixed by law. This would make to quadrant 10,000,565·278 legal mètres, or would increase the mètre length from 443·296 lignes to 443·334 lignes, agreeing very nearly with result obtained by Airy in 1830, from a combination of 13 measured arcs.
The following are the measured arcs used by Bessel and Airy; the combinations being indicated by initial letters, A and B.
| Measurer. | Mid. Lat. | Arc. | Length. | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| B.— | Svanberg, Sweden | + | 66° | 20´ | 10·0´´ | 1° | 37´ | 19·6´´ | 593,277 | feet |
| A.— | Maupertuis, Sweden | + | 66° | 19´ | 37·0´´ | 0° | 57´ | 30·4´´ | 351,832 | “ |
| A.— | Struve, Russia | + | 58° | 17´ | 37·0´´ | 3° | 35´ | 5·2´´ | 1,309,742 | “ |
| B.— | Struve and Tenner, Russia | + | 56° | 3´ | 55·5´´ | 8° | 2´ | 28·9´´ | 2,937,439 | “ |
| B.— | Bessel and Bayer, Prussia | + | 54° | 58´ | 26·0´´ | 1° | 30´ | 29·0´´ | 551,073 | “ |
| B.— | Schumacher, Denmark | + | 54° | 8´ | 13·7´´ | 1° | 31´ | 53·3´´ | 559,121 | “ |
| A, B.— | Ganss, Hanover | + | 52° | 32´ | 16·6´´ | 2° | 0´ | 57·4´´ | 736,425 | “ |
| A.— | Roy and Kater, England | + | 52° | 35´ | 45·0´´ | 3° | 57´ | 13·1´´ | 1,442,953 | “ |
| B.— | “ “ “ | + | 52° | 2´ | 19·0´´ | 2° | 50´ | 23·5´´ | 1,036,409 | “ |
| A.— | Lacaille and Cassini, France | + | 46° | 52´ | 2·0´´ | 8° | 20´ | 0·3´´ | 3,040,605 | “ |
| A, B.— | Delambre and Mechin, France | + | 44° | 51´ | 2·5´´ | 12° | 22´ | 12·7´´ | 4,509,832 | “ |
| A.— | Boscovich, Rome | + | 42° | 59´ | ·0´´ | 2° | 9´ | 47·0´´ | 787,919 | “ |
| A.— | Mason and Dixon, America | + | 39° | 12´ | ·0´´ | 1° | 28´ | 45·0´´ | 538,100 | “ |
| A, B.— | Lambton, India | + | 16° | 8´ | 21·5´´ | 15° | 57´ | 40·7´´ | 5,794,598 | “ |
| A, B.— | Lambton and Everest, India | + | 12° | 32´ | 20·8´´ | 1° | 34´ | 56·4´´ | 574,318 | “ |
| A, B.— | Lacondamine, Peru | - | 1° | 31´ | 0·4´´ | 3° | 7´ | 3·5´´ | 1,131,050 | “ |
| A.— | Lacaille, Cape Good Hope | - | 33° | 18´ | 30·0´´ | 1° | 13´ | 17·5´´ | 445,506 | “ |
| B.— | Maclear, “ “ | - | 35° | 43´ | 20·0´´ | 3° | 34´ | 34·7´´ | 1,301,993 | “ |
| A.— | Plana and Cartessi, Piedmont | ——————— | 1° | 7´ | 31·1´´ | —————— | ||||
The following different lengths of the mètre have been obtained:
| As adopted by France, 1801 | 443·296 | lignes. |
| According to Delambre | 443·264 | “ |
| “ Bessel | 443·33394 | “ |
| “ Airy | 443·32387 | “ |
| “ Clarke | 443·36146 | “ |
| From Peru Meridian | 443·440 | “ |
The length of a pendulum vibrating 100,000 times in a mean solar day was determined in numerous careful experiments by Biot, Arago, and Mathieu, in mètres of 443·296 lignes, as follows:
| Dunkirk | 56·67 | lat. Cent. | 0 | above sea | 0·7419076 | mètres. |
| Paris | 54·26 | “ | 65 | “ | 0·7418870 | “ |
| “ by Borda | 54·26 | “ | 0 | “ | 0·7416274 | “ |
| Bordeau | 49·82 | “ | 0 | “ | 0·7412615 | “ |
| Formentera | 42·96 | “ | 196 | “ | 0·7412061 | “ |
Borda also determined the length of the seconds pendulum at Paris, in vacuo:
| First result | 440·5595 | lignes | = 0·9938267 | mètre. |
| Second result | “ | “ | = 0·9938460 | “ |
| As given by Ganot | “ | “ | = 0·9935 | “ |
In 1812 the système usuelle was established, of which the unit was one third of the mètre, with the old name of pied, and duodecimally divided into pouces and lignes.
This system continued in use till 1840, when it was abolished by law, and the names of pied, pouce, and ligne forbidden under penalties. So the mètre, decimally divided, remains the only legal measure of length in France.