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of surveying, compared with that which places the instrument immediately in the plane of the horizon, and so gives the result directly, and without any reduction whatsoever.
Besides a reduction to the plane of the horizon, another reduction is necessary to bring the observed angles to the true angles, at the centres of the signals. For this reduction, as well as for the preceding, Delambre has given rules and formulæ, by which they may be calculated with great accuracy, and with all the expedition that the nature of the thing will admit.-It were, nevertheless, very desirable, that these reductions, as well as the former, should be avoided, by placing the instrument with which the angles are taken, exactly at the angular point. This method has been generally followed in the trigonometrical survey of England, where no pains have been spared to place the theodolite in the same spot that was occupied by the centre of the signal and from thence results great additional accuracy, as well as additional simplicity, in conducting the calculations. It is the same with respect to the reduction to the horizontal plane. The great theodolite, first employed by General Roy, and now in the hands of Colonel Mudge, is always placed horizontally; and hence a great deal of labour in calculation is saved, and many sources of inaccuracy are entirely avoided. In no other survey, we believe, has the work in the field been
conducted so much with a view to save that in the closet, and at the same time to avoid all those causes of error, however minute, that are not essentially involved in the nature of the problem. The French mathematicians trust to the correction of those errors; the English endeavour to cut them off entirely; and it can hardly be doubted that the latter, though perhaps the slowest and most expensive, is by far the safest proceeding.
The principal defect of the reflecting circle, we believe to consist in the small power of the telescope which it bears; an imperfection inseparable from an instrument of such a size as can be held in the hand. The accuracy of the observations is necessarily limited, by the imperfections of the telescope, to whatever degree of minuteness the divisions on the limb of the instrument may be carried. If an object that subtends an angle of 3 or 4 seconds is the least that is distinctly visible through the telescope, an angle can never be measured nearer than 3 or 4 seconds, even if you can read off to a single second. The want of sufficient light, also, in the field of vision, seems to have occasioned considerable difficulty, and may have produced some inaccuracy in the observations. The signals, when the distance was considerable, were not always distinctly seen; and the construction of them became, on that account, an object of very great attention. Delambre made his signals in the form of a pyra-.
mid, truncated at the top, of the height of nearly
5 of the distance; so that they subtended an angle of about 30". They were built of wood, and the base was a third part of the height. The powerful telescopes used by General Roy and Colonel Mudge in the trigonometrical survey of England, relieved them from all difficulties of this kind; as a simple mast, or staff, as it is called, with the ordinary illumination of a clear day, can be seen distinctly through the telescope of the great theodolite at the distance of 15 or 16 miles. The advantage of these large glasses was experienced by the French Academicians, when they met with the committee of the Royal Society of London, in order to unite the surveys made in France and in England, for the purpose of ascertaining the relative position of the observatories of Greenwich and Paris, as we had occasion to remark in our review of the trigonometrical survey.
It probably arose from the same cause, in some measure, that the signals made by lamps in the night were not found to answer with the French astronomers. The difficulty of illuminating the hairs in the focus of the telescope, is the impediment chiefly complained of. Such signals, however, were sometimes employed; and Delambre mentions a curious phenomenon which he observed, more than once, to accompany them. This was a kind of undulation, which made the apparent place
of the light oscillate very sensibly about the true, as was particularly remarked at Mont-Martre, on the 15th of August 1792. Something similar to this, he says, he had met with in the case of the ordinary signals viewed during the day.
"These oscillations," says he, "I have sometimes thought would remain suspended for a few minutes, when the apparent object was at its greatest distance from the real. I will not, however, answer for this fact, which I have not been able to investigate sufficiently. I have also been disposed to think that there existed a lateral refraction. The only way to guard against the effects of such illusions, is to wait the arrival of fine weather, and to repeat the observations in circumstances as unlike as possible."
The confidence which the French astronomers place in the repeating circle, is such, that they have not, in the course of this work, had recourse to a zenith sector, or any of the more delicate instruments of astronomy, for the purpose of determining the differences of latitude, or the amplitudes of the celestial arches, corresponding to the lines measured on the surface of the earth. This, we confess, appears to us not a little extraordinary, though we must, at the same time, remark, that this reliance on the repeating circle is confirmed by the opinion of the Swedish astronomers, who have lately mea
sured the degree in Lapland anew. They used no other instrument but the repeating circle; and Lalande says, in his sketch of the history of astronomy for 1805, that they thought that instrument less liable to error than a zenith sector of nine feet radius, such as was used by Maupertuis and his colleagues.
On the whole, when we compare the methods and instruments used in the French and in the British survey, though we see many circumstances that would induce us to give a preference to the latter; yet, when we consider the results of each, they seem, in exactness and consistency, to approach very near to an equality. We are not sure to what this should be ascribed; nor can we form a decided opinion till the reductions of the distances to the meridian are given. It may be, that the great expedition with which the repeating circle is used, and the vast number of observations which it admits of being made in a short space of time, may balance the greater size and more exquisite division of the theodolite and the sector employed by our observers; instruments which, in themselves, are perhaps the most perfect that have ever been constructed. Indeed, the expedition with which the repeating circle can be used, is one of its greatest advantages. It is such, that, in the space of five years, two observers, with very few as