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: