84 LECTURE X. 



is wholly arbitrary. It was resolved, therefore, to employ the second 

 method, which," says Mr. Laplace, " appears to he of very high antiquity ; 

 it is so natural to man to refer measures of distance to the dimensions of 

 the globe which he inhabits, in order that, in transporting himself from 

 place to place, he may know, by the denomination of the space passed 

 through alone, the relation of this space to the entire circumference of the 

 earth. This method has also the advantage of making nautical measures 

 correspond at once with celestial ones. The navigator has often occasion 

 to compare with each other the distance that he has passed over, and the 

 arc of the heavens corresponding to that distance ; it is therefore of conse- 

 quence that these measures should be readily obtained from each other, by 

 altering only the place of the units. But, for this purpose, the funda- 

 mental unit of linear measures must be an aliquot part of the terrestrial 

 meridian, which must correspond to one of the divisions of the circum- 

 ference of a circle. Thus the choice of the metre was reduced to that of 

 the unit of angular measure, and the right angle, as constituting the limit 

 of the inclination of two lines to each other, was considered as entitled to 

 the preference. 



" The arc, which was measured in 1740, from Dunkirk to the Pyren- 

 nees, might have served for finding the magnitude of the quadrant of the 

 meridian ; but a new and more accurate measurement of a larger arc was 

 more likely to excite an interest in favour of the new measures. Delambre 

 and Mechain were therefore intrusted with the direction of the operations 

 for measuring an arc from Dunkirk to Barcelona,* and after making a 

 proper correction for the ellipticity of the earth, according to the measure- 

 ment of the arc in Peru, the quadrant was determined to be equal to 

 5,130,740 of the iron toise used at the equator, its temperature being 61^ of 

 Fahrenheit : the ten-millionth part of this quadrant was taken for the unit 

 or metre. A standard was deposited in the custody of the legislative body, 

 adjusted at the temperature of melting ice. In order to be able always to 

 identify this length, without recurring to an actual measurement of the arc, 

 it was of importance to compare it very accurately with that of the pen- 

 dulum vibrating seconds, and this has been done with great care by 

 Borda, at the observatory of Paris. The unit of measures of land is the 

 are, or 100 square metres : a cubic metre of wood is called a stere, and a 

 cubic decimetre, or a cube of which the side is one tenth of a metre, is a 

 litre, or measure of fluids. 



" Uniformity appeared to require that the day should be divided into ten 

 hours, the hour into a hundred minutes, and the minute into a hundred 

 seconds. This division, useful as it will be to astronomers, is of less 

 advantage in civil life, where arithmetical operations are seldom performed 

 on the parts of time ; and the difficulty of adapting it to clocks and 

 watches, together with our commercial relations with foreign countries, 



* Delambre, Base du Systeme Metrique, 3 vols. 4to, Paris. A fourth volume, the 

 work of MM. Biot and Arago, was added in 1821. They extended the survey tojthe 

 island of Formentera. Consult also Reports to the National Institute. Rozier's 

 Journal, xliii. 169. Jour, de Phys. xliv. (1), 81. Bulletin de la Soc. Phil. n. 28. 

 Nich. Jour. iii. 316. Ph. Mag. i. 269 ; and the article, Figure of the Earth, by 

 Airy, in the Encyclopaedia Metropolitana. 



