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vol. 118. In substance it is this: If the distance between two given points is accurately known, all that is necessary, in order to ascertain the distance of any point that can be seen from both of them, is to observe successively from each end of the known base, the angle subtended by the other end of the base and the point to be determined. The length of the unknown sides may then be calculated by the formulæ of plane trigonometry, and the distances so determined become, in their turn, bases for the determination of fresh unknown distances. By constantly constructing new triangles on the sides successively determined, the whole country is at last covered by stations, the positions of which are known with the nicest accuracy. The whole of the principal triangulation which has consumed so many years of anxious toil, has been simply a series of repetitions of this proceeding. The simplest instruments will suffice to do this work roughly—the levels, the screws, the verniers, the reading microscopes of the theodolite, are only inventions to secure precision otherwise unattainable. To secure approximate accuracy would be easy enough, but to do it in such a way that the whole area of Great Britain—nearly 122,000 square miles—no point fixed by the triangulation shall be more than three, or at most four, inches out of its true position, involved an amount of care and calculation not easy to be imagined. The greatest inaccuracy which can possibly be laid to the charge of one of the modern Ordnance Survey Maps, is far smaller than the breadth of the finest line that the engraver can make upon the copper plate-smaller even than the discrepancy discoverable in two measurements on the same map on two successive days, when some variation of temperature has stretched or contracted the paper on which it is printed.

Working in harmony with the French surveyors, General Roy proceeded at once to carry his series of triangles from Hounslow to the coast of Kent and Sussex, and from thence westward to the Land's End. At his lamented death (to be afterwards referred to) in 1790, the burden of the work fell on Captain Mudge, of the Royal Artillery, and Isaac Dalby. Their “Account" of the Trigonometrical Survey contributed to the “Philosophical Transactions,"

and published separately, 1799, was long the standard work of authority on the interesting project with which they were so thoroughly acquainted. Among their earliest proceedings was to test anew, with most satisfactory results, the original Hounslow measurement, and to lay down a new base line on Salisbury Plain of 36,574 4 feet. This new line, on being triangulated in due course with Hounslow, was found not to vary more than an inch from the actual measurement made on the Plain. A third base was more recently laid down at Lough Foyle, primarily in connection with the Irish Survey, but with the extremely pleasing secondary result that, in tracking across the country for the purpose of determining what ought to be the Salisbury base, the discrepancy with actual measurement was found to be not more than four inches and a-half in a distance of over four hundred miles. It is now possible to measure an arc of parallel extending from Valentia, on the south-west coast of Ireland, to the town of Orsk, on the extreme east of European Russia, the longest ever likely to be measured.

The ingenious contrivances for perfecting the undertaking devised by General Roy are endless, and can only be referred to here by a brief example or two. Mention has already been made of the deal rods, glass tubes, and steel chains used to secure accuracy in measurement. But the expansion and contraction of glass, as well as iron, introduced an element of doubt in the nicer calculations; and, although it was known that the rate of expansion might be ascertained and allowed for, provided the exact temperature of the bar all through was ascertained at the time of observation, yet this could not always be done in out-door work. Availing himself of the ascertained principle that, while metals contract or expand differently at varying temperatures, they always bear to each other the same proportion, Colonel Colby solved the difficulty by clamping together a bar of iron and a bar of brass of the same length at a given temperature, with silver plates let in to transverse bars for the purpose of marking certain immovable points. Again, the heliostat, or revolving mirror, familiar now to newspaper readers from its use by the armies in Afghanistan and Egypt, is in constant use by Ordnance surveyors for flashing from point to point a knowledge of relative positions, even

although the extremities might be one hundred miles apart. Then it is necessary to make the triangulation all over the kingdom consistent with itself-that is say, that the sum of the three angles in every triangle should be 180 degrees, and the sum of all the angles round every station 360 degrees. Three unknown quantities in an equation is generally considered a near enough approximation to the truth. The intrepid calculators of the Ordnance Survey face the solution of equation with thirty-six unknown quantities.

The principal triangulation of the kingdom commenced, as we have seen, by Roy in 1784, was carried on at intervals till 1858, when it may be said to have been practically completed. This survey was extended to Scotland in 1809, and continued with several breaks till 1823, when it was suspended for fifteen years. The survey is now finished, and maps on the 6-inch scale have been published of the whole country, and for the most part also on the 25-inch scale. The useful 1-inch map is far advanced in two styles—contours only, and hills. Nearly all towns and populous places have been issued on the 5-feet or 10-feet scale. Regarding the battle of the “Scales,” fought in the House of Coinmons for over twelve years—1851–63—with a pertinacity hardly surpassed by the battle of the “Guns," it is neither seasonable nor necessary to enlarge on now or here. Nor can further room be occupied by any description of the delicate processes employed before maps can be submitted to the public for acceptance in all their beautiful and accurate details. To the present Director of the survey, Sir Henry James, R.E., belongs the high honour-first, of connecting the triangulation of the United Kingdom with France and Belgium; second, calling in the aid of, and almost inventing, the art, known as Photozincography, by which the maps, with all their delicate outlines, are transferred through a simple method to such a permanent surface as has given us the best copies yet produced of many precious ancient records—Domesday. Book, Saxon Charters, and the most suggestive “National State Papers," illustrating the history of England, Scotland, and Ireland.

Mention has been made of the remarkable care taken to preserve General Roy's wonderful Theodolite. With another of his survey inventions Fortune was less favourable; his Standard Yard, used for measuring the Hounslow base line, and afterwards placed in Exchequer Chambers, Westminster, being burnt in the great fire which in October, 1834, consumed the Houses of Parliament. In this case a Royal Commission on Weights and Measures had luckily provided some years earlier that, if the General's standard measure was lost, it would be lawful to renew it by means of the length of the seconds pendulum. General Roy's death was of startling suddenness. Having prepared for the Royal Society, by command of the King, an elaborate series of papers concerning the exact latitude of Greenwich and Paris Observatories, he was revising the printed sheets at home after a day's work in the office, June 30, 1790, when he was seized with an illness of which he died in two hours. Besides being a Major-General, at this time the great military engineer was Deputy Quartermaster-General, Colonel of the zoth Foot, Surveyor-General of Coasts and Batteries, and a Fellow of the Royal Society, as well as of the Society of Antiquaries. In 1793 the latter learned body issued the General's “Military Antiquities” as a posthumous volume, folio, profusely illustrated with drawings. One year after his measurement of the Hounslow line a paper on the subject, contributed to “Transactions of the Royal Society,” secured to Roy the Copley gold medal. The most eminent mathematicians of his day--Ivory and Leslie among the rest-did not fail to do justice to his great merits, nothing more censorious being written of him than that he had somehow failed to appreciate to its full extent a theorem first propounded by his friend Adrian Legendre, the theorem being to the effect that, if each of the angles of a small spherical triangle be diminished by one-third of the spherical excess, the sines of the angles thus diminished will be very nearly proportional to the length of the sides themselves; so that the computations with respect to such spherical triangles may be made by the rules of plane trigonometry. Aided by this theorem, drawn from the newer mathematics, it was thought that General Roy might have simplified many of his calculations, and in the case of a few-only a very few-been more exact than he arrived at by the old system of calculation. Still, it was universally admitted that General Roy possessed a strong and vigorous understanding; was an excellent draughtsman, and a profound natural philosopher, as was abundantly established in his paper on the measurement of heights by the barometer, printed in the “Philosophical Transactions," 1777. Nor was it judged to be less to the General's credit that he pursued his abstruse studies at a time when the British army afforded few instances of the kind either to encourage him by example or rouse him by emulation, and when the connection between mathematical science and his military art was but imperfectly understood.

BURNS AND HIGHLAND MARY.”

BURNS incense is now offered up with such profusion each January as to make the poet's joke about his own reputation rather a matter of history than prophecy. Writing to his friend, Gavin Hamilton, on the occasion of the first Edinburgh visit, he remarks—“I am in a fair way of becoming as eminent as Thomas à Kempis or John Bunyan, and you may expect henceforth to see my birth-day inserted among the wonderful events in the Poor Robin's and Aberdeen Almanacs along with the Black Monday and the Battle of Bothwell Bridge." Popularity naturally incites inquiry, and many occurrences turn up for discussion which in lesser or more obscure reputations would be allowed to pass unnoticed. One of the unconscious services rendered by the warm admirers of Burns is the inquiry they compel into facts and surmises associated with his life, and so establishing more or less of what is clearly historic. The poet's connection with “Highland Mary” has long had an interest of this kind for plodding inquirers—an interest in no degree lessened, but rather strengthened, by a mystery Burns has himself thrown around the story, quite out of keeping with his usual candour in such affairs. The attachment has been described as the purest and most elevated ever formed by the poet, and the songs in praise

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