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these points, either entirely by measurement with the chain and theodolite, or by partial measurement [principally of the roads], and by sketching the remainder with the assistance of some portable instrument. The degree of accuracy and minuteness to be observed in this detail, will of course determine which of these methods is to be adopted—the latter was practised on the Ordnance Survey of the South of England, which was plotted on the scale of 2 inches to 1 mile, and reduced for publication to that of 1 inch; but on the Survey of Ireland, and that of Scotland and the North of England now in progress, sketching has been entirely superseded by chain measurement, even in the most minute particulars, and the undulations of the surface of the ground are represented with mathematical accuracy by horizontal contour lines traced by actual levelling at equidistant vertical intervals, the whole survey being laid down to the scale of 6 inches to 1 mile. In the survey of only a limited extent of country, there does not exist the same absolute necessity for a triangulation, even though a considerable degree of accuracy should be required; this will appear evident, from the consideration that in every practical operation some amount of error (independent of the errors of observation) is to be expected-sometimes a definite quantity dependent upon the means employed; sometimes a quantity varying in amount with the extent of the operation.

In all angular measurements, the errors to be expected evidently depend upon the quality of the instruments made use of, and are altogether irrespective of the space over which the work extends. In linear measurements, on the contrary, the probable error is some proportional part (dependent upon the circumstances and the means employed) of the distances measured. So long, then, as the extent of the survey, and the scale upon which it is to be laid down, are such that the probable error attendant upon ordinary chain measurement of the largest figures would be imperceptible on the plan, no triangulation is necessary on the score of accuracy alone, though in many cases even of this nature it would be found in the end a saving both of time and expense.

In a new and unsettled country, particularly if flat and thickly wooded, the outlay that would be required, and the time that would be occupied by an accurate triangulation, would probably

prevent its being attempted, at all events in the first instance. If only a general map upon a very small scale is required, the latitude and longitude of a number of the most conspicuous stations can be determined by astronomical observations, and the distances between them calculated, to allow of their positions being laid down as correctly as this method will admit of, within which, as within a triangulation, the interior detail can be filled up. In surveying an extended line of coast, where the interior is not triangulated, no other method presents itself; and a knowledge of practical astronomy therefore becomes indispensable in this, as in all extensive geodesical operations. A topographical survey further requires that some of the party employed upon it should be practically versed in the general outlines of geology, as a correct description of the soil and mineral resources of the different parts of every country forms one of its most important features. The heights of the principal hills, and of marked points along the ridges, plains, valleys, and watercourses above the level of the sea, should also be determined, which, in a survey of no great pretensions to correctness in minute detail, may be ascertained with tolerable accuracy by means of the mountain barometer, or even by observing the temperature at which water boils at different stations.

A sketch of a certain tract of country, on a far larger scale than that of most general maps, is constantly required on service, for the purpose of showing the military features of the ground, the relative positions of towns and villages, and the direction and nature of the roads and rivers comprised within its limits. This species of sketch, termed a "Military Reconnaissance," approaches in accuracy to a regular survey, in proportion to the time and labour that is bestowed upon it. Having thus adverted briefly to the progressive steps in the different species of surveying, they will each be treated of more in detail in their proper order.

The system of forming the "net-work of triangles" alluded to, of as large a size as is consistent with the circumstances under which the survey is undertaken, within and dependent upon which the secondary triangulation and all the interior details are included, is to be considered as the working out of a general principle to be B 2



borne in mind in all topographical and geodesical operations, the spirit of which is as much as possible to work from whole to part, and not from part to whole.

By the former method errors are subdivided, and time and labour economised; by the latter, the errors inseparable from even the most careful observations are constantly accumulating, and the work drags on at a slower rate and an increasing expenditure.



In fixing upon an appropriate site for the measurement of a base line, a level plain should obviously be selected where both ends of the base would be visible from the nearest trigonometrical points. Where extreme accuracy has been required, steel chains, glass, deal, and platinum rods have at different times been used for the purpose of determining its length; but each of these units of measurement, whichever is preferred, must be supported so as to ensure its being laid perfectly level. The whole thus forms a portion of a great circle, which has ultimately to be reduced to its proper measure at the level of the sea at one mean temperature.

In measuring a base for the topographical survey of any small detached portion of ground, it will be sufficient for ordinary purposes to measure its length carefully, two or three times, with a chain which has been compared with a standard *, and if necessary from the irregularity of the ground to take an accurate section along the line (which should be laid out with a theodolite, between marks at each extremity), from which it can be reduced, by calculation, to its true horizontal value. The length of a base, which has subsequently to be determined with the most minute accuracy, by means of glass rods, compensation bars, or other contrivance, is generally first measured two or three times in this manner.

The exact measurement of a base is perhaps the most difficult and the most important part of a trigonometrical survey, as upon its accuracy that of every subsequent proceeding depends. In the account of this operation on the Trigonometrical Survey of England and Wales, published in 1801, will be found detailed accounts of the base measured on Hounslow Heath, in 1784, with

* A spiral spring, something like that used in weighing-machines, is attached to the end of a chain used for purposes requiring much accuracy; this indicates the power of tension exerted, which should always be the same as when compared with the standard. The surveyors under the Tithe Commission Act are furnished with this contrivance.

Ramsden's steel chain, at first intended solely for the purpose of connecting by triangulation the Observatories of Paris and Greenwich, but afterwards made the first step in the trigonometrical survey of England. This base was measured a second time with prepared deal rods *, and again by a combination of these two methods, the mean of the three valuations being 27404.0137 feet at the level of the sea. The details of the base of verification (i. e. the actual measurement of the side of a remote triangle, whose length had been previously obtained by calculation) in Romney Marsh, in 1787, are also given in the same work, as well as the remeasurement of the original base on Hounslow Heath, in 1791, and of another base of verification on Salisbury Plain, in 1794, which is stated to have corresponded exactly with its mean length, as obtained by calculation in three different triangles.

A detailed account has recently† (1847) been drawn up by Captain Yolland, R.E., of the mode adopted by General Colby to obtain the accurate value of the base measured on the Ordnance Survey of Ireland, at Loch Foyle, in the county of Londonderry, in which work will also be found a quantity of scientific information connected with the principal triangulation. The principles of the contrivance, in which it differs from all other methods that have preceded it, consist in always preserving, by a mechanical compensation obtained by the use of two metals having different powers of expansion and contraction, exactly the same distance between two points at the extremities of the compensation bars, instead of allowing, as had been hitherto done, for this expansion or contraction, according to the temperature at which each rod was laid, and in obtaining a visual instead of an actual contact of

* The deal rods were first laid, as it is termed, "in coincidence;" that is, lines drawn across them, near their extremities, were made to coincide most accurately by fine screws,

as in the sketch,

but this method occupying a considerable time,

and the measurement

their spherical ends were afterwards brought in contact was continued in this manner, so that no decision was arrived at as to the comparative accuracy of the two modes; that by coincidence would, however, appear likely to be more minutely correct than the one adopted.

✦ Many years after the 1st edition of this work; the short popular description of the process of using the bars is however retained.

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