lating the distances of the stations from the meridian, or the perpendicular to it, where the hypothenuse of a right-angled triangle is given, and one of the oblique angles. In such cases, an attention to the above theorem will enable the calculator to bring out a far more accurate conclusion than he can 'otherwise obtain. It must be confessed, that the General has not calculated on this principle, and that he has not taken as a substitute for it, the reduction of the observed angles to the angles contained by the chords of the arches, (the method that Major Mudge has adopted in the further pro-secution of the trigonometrical survey ;) and that therefore his calculations are deficient in accuracy, at least in that extreme accuracy, which the correctness of the observations themselves entitles us to expect. His method is sufficiently correct for any of the older measurements,-for those in Peru, Lapland, France formerly, and indeed for all that were made any where, till the great theodolite of Ramsden, or the repeating circle of Borda, were introduced. It in effect supposes the series of triangles to be laid out or extended on a plane surface, and to this plane every thing is understood to be reduced. This supposition is no doubt inaccurate; yet the inaccuracy is not considerable, and of no account at all, when the angles of a triangle have not been observed within twenty or thirty seconds of the truth. But when the error of observation is re

duced to less than a tenth part of that quantity, a more exact method of calculating must necessarily be pursued; as the calculus should ever be so instituted as to preserve to the conclusions all the accuracy possessed by the data themselves. No portion of this, however small, should be suffered to escape; and since it is a quantity which the calculator cannot increase, he should be careful not to diminish it.

The slight degree of incorrectness, therefore, which we have remarked in General Roy's computations, would not deserve to be mentioned, if it were not for the excellence of his observations. It is, besides, an imperfection which it is easy to remove the part of the work which no one could amend, fortunately stands in need of no emendation.

It is not wonderful if these slight inaccuracies escaped General Roy. The only principle on which they can be completely avoided, without a mode of calculating extremely long and laborious, is the theorem already mentioned; a proposition by no means obvious, and drawn by the excellent mathematician who discovered it, from the recesses of the new geometry. The General, possessing from his youth a decided turn for the mathematics, had bent the whole force of a very strong and vigorous understanding chiefly to the practical parts of that science, and those most immediately con

nected with his profession; but probably was not much conversant with the branches which are more theoretical and abstract. A life spent in continual activity, and of which a large proportion had been passed in the camp or the field, afforded no leisure for such acquirements, and held out, even to the mathematician, more interesting objects of pursuit. The duties of the field-engineer and the quarter-master-general had particularly engaged his attention; and in every thing connected with them he was profoundly versed. He drew excellently, and thoroughly understood the art of representing the inequalities of ground with admirable distinctness, and great beauty of effect. How perfectly he was skilled in surveying, in the highest sense of the word,-how conversant in the use of mathematical instruments, and in astronomical observation, -it is unnecessary to state, after what has been already said. He was, besides, a most expert and indefatigable calculator; his acquaintance with natural philosophy, too, was extensive and accurate; and his paper on the measurement of heights by the barometer, is a proof of his skill in conducting experimental inquiries, even when very remote from the line of his ordinary pursuits. General Roy, it should be observed, had pursued this track' while the British army afforded few instances of the same kind, either to encourage him by example, or rouse him by emulation, and when the con

nection between the mathematical sciences and the military art was not so well perceived as it haps begins to be at the present moment.

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The death of this excellent and accomplished officer, which took place soon after the period we now speak of, seemed for a long time to have put a stop to any design that might have been formed of extending the operations, already so happily begun, to the survey of the whole island; and here we must be permitted to remark, that the account given of the resuming of the survey is unsatisfactory and imperfect. After acknowledging the liberal assistance which the Duke of Richmond, as Mastergeneral of the Ordnance, had given to every part of the preceding operations, (an acknowledgment which we believe to be most justly due,) it is said that a considerable time had elapsed without any apparent intention of renewing the survey, "when a casual opportunity presented itself (to the Duke of Richmond) of purchasing a very fine instrument, the workmanship of Ramsden, of a construction similar to that which was used by General Roy, but with some improvements; as also two steel chains, of one hundred feet each, made by the same incomparable artist."

Are we then to suppose that a great and national object was in danger of being dropt, or indefinitely delayed, but for a fortunate and unforeseen accident? Did not the instrument which General

Roy had used still remain in the possession of the Royal Society? and if the work was now to be prosecuted, not under the immediate direction of that society, but of the Board of Ordnance, can we suppose that, on that account, the use of it would have 'been withheld? This is the less probable, that it has since been actually put into the hands of Major Mudge, and is at present employed by him in the survey. But be this as it may, the purchase of the new theodolite by the Duke of Richmond was indeed purely accidental; for it had been made, if we are not misinformed, by order of the East India Company, for the purpose of surveying their possessions in the East; and Ramsden, in the construction of it, had exerted that increased ingenuity and attention with which the presence of a great and new object used always to inspire him. In the end, some misunderstanding arose; and a fit of ill-humour, or of ill-timed economy, induced the sovereigns of India to refuse an instrument which could do nothing to enlarge their dominions, though in skilful hands it might have done much to render them more secure. The Duke of Richmond was a better judge of its value; and has rendered it no less useful to the public, than if it had followed its original destination.

In 1791, Captain Mudge of the Royal Artillery, and Mr Dalby, who has been already mentioned, both well qualified for the work they were to under