In this register, each angle in the successive triangles is, for the sake of conciseness, marked by the single letter affixed to it, and the computed length of its opposite side in feet ranges in the same line. The addition of an asterisk denotes that an angle was not actually observed, but only deduced from cal. culation. The oblique triangles ABC and ABE have their sides BC and BE derived from other larger triangles, which were nearly equiangular. The triangles ELN and ENP had their angles discovered from conjoined observations. In ge neral, the several angles, as affected by the spherical excess, were corrected for computation by a sort of tentative process. It results from a train of calculations, that Dover Castle lies south 67° 44′ 34′′ east, and at the distance of 328231 feet or 62.165 miles, from Greenwich Observatory. On their part, the French astronomers, under the direction of Cassini, carried forward the trigonometrical operations from Dunkirk to Paris; employing Borda's repeating circle, an instrument much smaller and less perfect than Ramsden's theodolite, but formed on a principle which always procures the observer a near compensation of errors. From a comparison of the whole, it follows, that the meridian of the Observatory of Paris lies 2o 19′ 51" east from that of Greenwich, differing only nine seconds in defect from what the late Dr Maskelyne had previously determined from combined astronomical observations, The success with which that great survey was attended, gave occasion both in France and England to still more extensive projects. The National Assembly, amidst other essential improvements which it meditated, having resolved to adopt a general and consistent system of measures, the length of a degree of the meridian at the middle point between the pole and the equator was proposed as a permanent basis. But to secure greater accuracy in determining the standard, it had been decided to prolong the observations on both sides of the mean latitude, and trace a chain of triangles over the whole extent from Dunkirk to Barcelona. This bold plan was exe cuted in the course of the years 1792, 1793, 1794 and 1795, with equal sagacity and resolution, by MM. Delambre and Mechain, who, during all the horrors of revolutionary commotion, yet pressed forward their operations in spite of obstacles 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. The 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. A 76° 2' 30.66" 17310.3013 C 37 1 40.59 9516.5896. 13305.8528 BCD CEF B 59 52 2.20 15756.8013 C 61 13 47.94 13101.0845 C 48 17 34.50 D 71 50 23.30 13601.3539 E 55 51 48.75 12370.8194 F 62 54 23.31 I, 74 8 41.99 E 40° 32′ 37.60" 8852.8293L 68 35 59.16 14402.0625 12374.2130 M 51 5 13.26 12036.0949 N 60 18 47.58 Through the whole progress of their survey, the French astronomers have certainly displayed superior science. In deducing 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 |