then a Colonel of Engineers, took the first real scientific step in the enterprise, by laying down, under command of His Majesty, the famous basis line of triangulation on Hounslow Heath. Little being known of General Roy earlier than what touches the busy middle-age portion of his life, time may not be thought lost in setting down a few words concerning an officer who was at once the foremost surveyor of his day, eminent beyond most in mathematical studies, and, so far as Scotland was concerned, the father of geodetic science. Our West Country has special reason for feeling proud of its connection with a scholar who would have been great had he done nothing more than initiate the Ordnance Survey and write "The Military Antiquities of the Romans in Britain." The son of an intelligent grieve, who combined the duties of factor with that of gardener on the estate of Hamilton of Hallcraig, Carluke parish, William Roy was born at Milton-head, 4th May, 1726. Carluke village at the time was in a state of chronic decay. Small as the place was in the early days of Charles II., a charter was obtained in the second year after the Restoration, erecting it into a burgh of barony under the name of Kirkstyle. Any improving influences that might be supposed likely to spring from such an increase of dignity would appear to have operated for only a short time, as at the birth of Roy the burgh comprised little more than the parish church, the manse, and a very few cottages. The population of the entire parish, ministered to in things spiritual by the Rev. James Dick, was not much, if anything, over 1,460. The latest census return (1881) gives the parish population at 8,552. In Roy's early days the working of iron and coal which has made the district so prosperous, and it may be even said famous, in the annals of industry was on the most limited scale. Even cotton weaving, which first raised the drooping fortunes of the place, was all but unknown. Only a very little is known concerning Roy's early education or pursuits. It may be surmised, however, in a general way that he devoted considerable attention to engineering studies before obtaining a commission in the army as lieutenant in or about 1741. His brother, Dr. Roy, was born in the same parish.

The Rebellion of 1745 first brought Roy into notice as an engineer and surveyor. After the "rising" had been stamped out in blood by Cumberland, at Culloden, in April of the following year, Government became more alive than before as to the necessity of exploring and laying open a country so difficult of access as the Highlands of Scotland. It was determined, therefore, to carry roads through the most remote recesses, and establish efficient military posts along the entire line. In this way it came about that the first methodical operations for a military survey of Great Britain took place at the distant point of Fort Augustus, in 1747. General Watson, Quartermaster-General to Lord Blakeney, was encamped in the fort at the time, and by this officer the Highland survey, afterwards known as "Cumberland's Map," was entrusted to his junior officer, Colonel Roy. Although the original intention would not appear to have embraced more than the Highlands, yet the surveyor gradually found his way into the Lowlands, and even along the more important coast lines. The field work was carried on in summer, and the drawings, on the scale of one inch and three-quarters to a mile, prepared during the winter in Edinburgh Castle. At the end of eight years the undertaking was advancing, but far from finished; and when it was then suspended, Colonel Roy admitted that the survey, having been carried on with inferior instruments, and the sum allowed very inadequate for its proper execution, it ought rather to be looked on as a fair military sketch than an accurate map of the country. The breaking out of the war in 1756—a war waged against France in America, in India, and on the high seas-scattered the surveyors, and called away from Scotland such engineers and foot soldiers as could be spared. The Highlands for the time being crushed into peace, the survey drawings were consigned to the Royal Library, unusually rich in such collections, as any one may see by a glance at the formidable row of cases in the British Museum, and there they lay, almost neglected, while geographers like Ainslie were making private independent surveys, instead of perfecting, as they might have done, the work of Roy. Even in the face of colonial troubles the scheme of a national survey was brought up in Parliament from time to

time; and at length, in 1763, Government undertook to propose a money vote in aid. Yet even preliminaries were not finally settled for twenty years, or in 1783, when Roy was engaged in measuring on his own account a base of 7744°3 feet across the fields between the Jewsharp, Marybone, and Black Lane, near St. Pancras, as a foundation for a series of triangles carried on at the same time, for determining the relative situations of the most remarkable steeples, and other places in and about London, with regard to each other and the Royal Observatory at Greenwich. Some little time before this a correspondence had been going on between the Count d'Adhemar and Mr. Fox as to the advantage which would accrue to astronomical science by carrying a series of triangles from the neighbourhood of London to Dover, there to be connected with the triangulation already executed in France. The King approved of the design, and agreed to share the cost with the Royal Society, that body having taken a lively interest from the first in all the proceedings. Roy was thereupon summoned to Windsor, and instructed by the King to commence the survey. His first step was the measurement of that now historical base-line on Hounslow Heath (5.19 miles) -measurements, it has been found, so careful that no essential error has been discovered by the most rigid scrutiny of modern surveyors. The great threefoot theodolite, constructed for the occasion by the optician Ramsden, after being carried up the highest mountains, placed on the pinnacles of our loftiest churches, and shipped to distant islands, is still in daily use, and as perfect as when it left the hands of its cunning constructor. Ramsden, indeed, made his instrument something more than a theodolite. It is also a quadrant and transit instrument, and capable of measuring horizontal angles to fractions of a second. To the same ingenious optician is also due the invention of the survey measuring chain, superseding at once the varying deal-rod, and rivalling even the glass-rods as a measuring line.

The importance of the base-line in triangulation, for the purpose of calculating unknown distances, is stated with as much simplicity as the subject permits, by the writer of an article on the "Cadastral Survey" in the "Edinburgh Review,"

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 formula 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 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