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Coast Survey of the United States. 237 
of least squares. This is the result accepted by the scientific 
world, and which it is now imperative to employ. Not only are 
new tables to be calculated for future use, but all the old triangles 
are to be recomputed to the original base. The accumulation of 
small errors renders this course obligatory, and indeed indispen- 
sable. But the values in the new tables will be affected not so 
much by the change of ellipticity, as by a proper return to the 
legal ratio of the metre to the toise. The toise was the standard 
of linear measure in France, employed in the measurement of 
the French arc between Dunkirk and Barcelona, and virtually 
also in its continuation by MM. Biot and Arago, by which the 
parallels of Paris and Formentera were connected. Virtually it 
is said, because the legal ratio of the metre was preserved. 'The 
definition of the metre as the millionth part of the quadrant of 
the meridian, having been shown by the laborious computations 
of Colonel Puissant to be imaginary, it only remains to adopt and 
preserve the value given it by the law of 1799, and subsequently 
confirmed by the law of 1837. é 
lt might be argued, if argument were applicable to the case, 
that the attempt to assign to the metre a theoretic value would 
defeat itself,—for neither geodesic-operations, nor the present 
methods of calculation, could settle its value with such certainty 
but that future geometers might find occasion to modify numbers 
which now appear to be the most established. It may be said, 
further, that when the metre was adopted by the commission con- 
sisting of Borda, Lagrange, La Place, &c., it was done with a 
limitation subsequently confirmed ; and this limitation, being a 
very close approximation to the truth, may be regarded as defini- 
tive. Whatever may be the future progress of science, it can 
never be convenient to alter it; but it is only requisite to have a 
distinct idea of what it represents. Upon this subject Mr. Hassler 
assumed a different, and as it has been pronounced by very high 
authority, a novel idea. When the standard metres were distri- 
buted by the committee of weights and measures, Mr. Tralles, 
the deputy from Switzerland, obtained an extra one, perfectly 
authenticated, which he presented to Mr. Hassler. ‘The latter, 
having in his. possession five brass and three iron metres, and 
several standard toises, including those of Canivet and Lenoir, 
instituted a series of comparisons with the comparateur of Trough- 
ton, which can never fail to command the most sincere admira- 
Vol. xxix, No. 2.—July-Sept. 1845. 31 
