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sistants, * and in the midst of innumerable interruptions and vexations, completed a survey of 181 triangles, extending along a line more than 600 miles in length, and this, together with the measurement of two bases, and a vast number of observations for determining azimuths, and the latitudes of five dif ferent stations.
The volume before us is far from completing the account of these operations, or at least of the conclusions deduced from them. The part we have already considered, which forms the preliminary discourse, is followed by 510 pages, in which a detailed account is given of the observations made at each station, and of all the circumstances by which their accuracy can be affected. The triangles included in these observations consist of 115 principal, and 66 subsidiary triangles. At the end of the detailed account just mentioned, these triangles are reduced into a table, that exhibits, at one view, every thing concerning their angles, and the necessary reductions. The first column of this table
* Delambre was assisted by Bellet, an astronomical instrument maker of great zeal and intelligence, who adhered to him in all his difficulties, and remained, when the smallness of the allowance from government deprived him of all his other assistants. Francis Lalande also shared with him in the labour of the survey for a considerable time. In the southern survey, Mechain was assisted by M. Tranchot, an engineer of great ability and experience.
contains the angles of every triangle as observed and reduced to the horizon; the numbers here given being the means that were struck by the commissioners in the manner already described. The second column contains the spherical excess for each angle, by comparing which with the sum of the three angles of the triangle, we have a measure of the error committed in the measurement of the three angles, which rarely amounts to 1" or 11". In the third column are given the true spherical angles corrected for the error of observation, according to a principle previously explained. In the fourth column, these are reduced to the rectilineal angles contained by the chords of the arches, or of the sides of the spherical triangles. The last column of all contains the mean angles, as they are here called, that is, the observed angles first corrected for the error of observation, and afterwards diminished each by one third of the spherical excess, so that those of each triangle amount precisely to 180 degrees, and are thus prepared for computation, according to the theorem of Legendre that was mentioned in our account of the trigonometrical survey of England. Delambre has gone through the great labour of calculating the sides of these triangles, and also their reduction to the meridian, by the three different methods that correspond to the nature of the three last columns. These results, however, are not given in the volume before
us. They are reserved for that which is to follow ; and we have no doubt, when they shall appear, will give us new reasons to applaud the skill, the accuracy, and the patience of Delambre and his associates.
Though the formation of the above table, and the arrangement of the whole volume, are the work of Delambre, yet a large part of it, containing the observations of Mechain, is given in the words of that astronomer.
The present volume does not enable us to state any thing with respect to the length of the segments into which the arch of the meridian was divided. Some of these results, however, we have learnt, from the memoirs that have been published on the same subject in the volumes of the National Institute. They appear to be curious; and we take notice of them here, as indicating irregularities very similar to those that Colonel Mudge met with in the meridional arch which he measured between the Isle of Wight and Clifton in Yorkshire.
In the course of their survey, the French astronomers determined the latitudes of five different points of the meridional arch with great exactness, viz. Dunkirk, 51° 2' 10"; Paris, at the Pantheon, 48° 50′ 49"; Steeple of Evaux, 46° 10′ 42′′; Tower of St Vincent at Carcassonne, 43° 12′ 54′′; Tower of Montjouy at Barcelona, 41° 21′ 45′′. The amplitudes of the arches thus found, being
compared with the terrestrial measurements, led to some results that were unexpected, and that are certainly highly deserving of attention. It appears that the length of the degree of the meridian, though it decrease constantly on going from the north to the south, as it ought to do, does in fact decrease very irregularly. Toward the northern extremity of the arch the decrease is slow, and at the rate of not more than four toises in the degrees that lie between Dunkirk and Evaux. From Evaux to Carcassonne the degrees diminish rapidly, at the rate of 30 or 31 toises; and from Carcassonne to Barcelona the diminution becomes again much slower, and is about 14 toises to a degree.
This irregularity in the differences of the degrees does not arise from a cause that is apparent on the surface. It very much resembles that which was experienced by Colonel Mudge as he went northward from the coast of the channel, when he found that the degrees, instead of increasing, came to diminish about the middle of the arch. In both cases, we may suspect the effect to have arisen, partly from the vicinity of the sea, partly, perhaps, from inequalities of density under the surface, or other irregularities in the superficial part of the globe. From whatever causes they arise, the repetition of operations, such as those we are now treating of, is what alone can be ex
pected to throw new light upon the subject. ditional experiments on the attraction of mountains would probably tend to the same object, and might lead to other valuable conclusions.
We cannot finish our account of these scientific operations, without expressing our wishes that the uniformity of measures and of weights were introduced into our own, and into every other civilized country. The difficulty is not so great as we are apt to think, when we consider the matter at a distance; and, to effect it, requires, in reality, nothing but for the legislature to say, it shall be done. As to the standard to be adopted, though we think the pendulum would have afforded the most convenient, yet, when one has been actually fixed on and determined, that circumstance must greatly outweigh every other consideration. The system adopted by the French, if not absolutely the best, is so very near it, that the difference is of no ac
In one point it is very unexceptionable; it involves nothing that savours of the peculiarities of any country; insomuch, as the Commissioners observe, that if all the history which we have been considering were forgotten, and the results of the operations only preserved, it would be impossible to tell with what nation this system had originated. The wisest measure, therefore, for the other nations of Europe, is certainly to adopt the metrical system of the French, with the exception, perhaps, of the