motion, yet pressed forward their operations in spite of obsta cles and dangers of the most sickening kind. After the various triangles, amounting in total to 115, had been observed, they were connected, in the neighbourhood of Paris, with a base of more than seven miles in length, and measuring, at the temperature of 161° on the centigrade scale, or 611° by Fahrenheit, 6075.9 toises from Melun to Lieursaint. A base of verification was likewise traced near the southern extremity of the line of survey, extending 6006.25 toises along the road from Perpignan to Narbonne. This base appeared not to differ one foot from the calculation founded on the other, though separated by a distance of 400 miles,-a convincing proof of the accuracy with which the observations had been made. A specimen of the French triangulation is given in the figure below, where the vertical line represents the meridian of Dunkirk, with the distances expressed by intervals of 10,000 toises. F Montlheri. G Lieursaint. H Melun. I Malvoisine. K Torfou. L Forêt. M Chapelle. N Pithiviers. O Bois Commun. P Chatillon. Q Château-neuf. R Orleans. GH The primary base. Calculation of the sides of the Triangles. ABC 8349.1059 10292.0814 ILM 13438.2345 15756.801370 51 37.77 CDE LMN 9516.5896 L 68 35 59.16 14402.0625 13305.8528 M 51 5 13.26 12036 0949 N 60 18 47.58 Through the whole process of their survey, the French astronomers have certainly displayed superior science. In de ducing the correct results, they seem to exhaust all the refinements of calculation. The angles measured by the repeating circle, it was necessary to reduce, not only to the horizontal plane, but generally besides to the centre of observation. This would have required much nice and tedious computation; the labour of performing such reductions was however greatly simplified and abridged, by help of concise formula, and the application of auxiliary tables. There is even room to suspect that those ingenious philosophers have carried the fondness for numerical operations to an excess, and often pushed the decimal places to a much greater length in their estimates than the nature of the observations themselves could safely warrant. In the spring of 1799, the registers of all these operations were referred to a commission, consisting of the ablest members of the Institute, and some other learned men deputed from the countries then at peace with France. The various calculations were carefully examined and repeated; and a comparison of the celestial arc with that which had been mea 1 sured in Peru having given for the oblateness of the earth, 334 the length of the quadrant of the meridian, or the distance of the pole from the equator, was finally determined at 5130740 toises, the ten millionth part of which, or the space of 443.295936 lines forms the metre. This standard was afterwards definitively decreed by the Legislative Body. Mechain, however, still anxious to realize his early project of extending the meridian as far as the Balearic Isles, again repaired to Spain, and conducted with incredible exertions a chain of triangles over the savage heights from Barcelona to Tortosa, and was about to observe the altitude of the stars, and measure the base of Oropesa, when, worn out by continued fatigue, he caught an epidemic fever, which fatally closed his meritorious labours, at Castellon de la Plana, in the kingdom of Valentia, about the latter part of September 1805.-The prosecution of the plan was subsequently committed to MM. Biot and Arago, who brought it to a fortunate conclusion. In the winter of 1806 and the spring of 1807, these philosophers continued the series of triangles from Barcelona to the kingdom of Valentia, and joined that coast with the Balearic Isles, by an immense triangle, of which one of the sides exceeded an hundred miles in length. At such prodigious distances, the stations, however elevated, and notwithstanding the fineness of the climate, could not be seen during the day; but they were rendered visible at night, by combining Argand lamps with powerful reflectors. These observations give a result which agrees almost exactly with what had been already found by Delambre and Mechain. If the mean were adopted, it would yet scarcely affect the length of the metre by the diminution of a four millionth part, making this to be 443.322 lines of the toise brought by the Academicians from Peru. The meridional arc extending from Dunkirk to Formentera, measures 12° 22′ 13′′.395; and from this ample basis, the circumference of the earth is computed to be 24855.42 English miles, and the ratio of its axes that of 308 to 309. The fourth volume of the Base Metrique, containing the account of the trigonometrical observations made by Biot and Arago in Spain and the Balearic Isles, has been long promised; and I was induced, for a considerable time, to defer the publication of this edition, in the hope of being able to draw some additional information from such a valuable source. In the prosecution, however, of the French measurement, an application from the Institute has been transmitted by Count Laplace to Colonel Mudge, to have Ramsden's Zenith Sector erected near Yarmouth, in order to connect the English arc thence across the sea to near Dunkirk, with the meridional measurement extending through France and Spain to Formentera, which would have the important advantage of being nearly bisected by the parallel of 45°. This proposition, I am happy to learn, will be carried into immediate effect. In England, the prosecution of the trigonometrical survey, without aiming at such splendid views, has, suitably to the genius of the people, been directed to objects of more domestic interest, and perhaps real utility and importance. The perplexing inaccuracy of our best maps and charts had long been the subject of most serious complaint. It was in consequence resolved to extend the series of connected triangles over the 2 E Af whole surface of the Island. But the death of General Roy, happening so early as 1790, threatened to prove fatal to the completion of his favourite scheme, for which the talents and experience he possessed had so eminently fitted him. ter some interruption, however, an opportunity was embraced of resuming that noble plan; and it was, under the direction of the Board of Ordnance, committed to the care of Colonel Mudge, who, with equal ability and undiminished ardour, has, during the space now of upwards of twenty years, been engaged in carrying on the most extensive and varied system of operations ever attempted, and in a style of execution which reflects on him the highest credit. In 1793 and 1794, the chain of primary triangles was continued from Shooter's Hill to Dunnose in the Isle of Wight, including a great part of Surry, Sussex, Hants, Wiltshire and Dorsetshire, and connecting with a new base of verification measured on Salisbury Plain. This base had, after correction, a length of 36574.4 feet, or 6.92697 miles, having lost almost a whole foot in being reduced from an elevation of 588 feet to the level of the sea. It differed scarcely an inch from the computation founded on the base of Hounslow Heath. In 1795, the triangles were carried into Devonshire; and they were continued in 1796 through Cornwall to the Scilly Islands. The West of England became the scene of repeated operations. In 1798, a third base was measured on King's Sedgemoor near Somerton, and found, after various corrections, to be 27680 feet, or 5.242425 miles, differing only about a foot from the result of the calculation dependent on that of Salisbury Plain. The survey now advanced to the centre of England, and was extended in 1803 to Clifton in Yorkshire; another base of verification, 26342.7 feet in length, having been measured at Misterton Carr, on the north of Lincolnshire. The triangles were next carried towards Wales, and made to rest on a base of 24514.26 feet, stretching from the western borders of Flintshire to Llandulas in Denbighshire. From this last base, numerous triangles have been extended in different directions; one series bending through Anglesea and by Cardigan Bay, to the Bristol Channel; another penetrating into the central parts of England; while a third series stretches northwards, through Lancashire, Cum |