Chapter II

The Ordnance Survey of Great Britain as it exists to-day is a remarkable Publishing Bureau, from whose presses are given the most elaborate and accurate series of maps which any country possesses.

Maps not alone confined to the representation of the physical features of the country, but containing every detail of interest or value for civil or military purposes.

It has justly gained the commendation of the French that it is "a work without precedent, and should be taken as a model by all civilized nations."

The principal scales of publication adopted by the Ordnance Survey are: (1) A general map on the scale of one mile to one inch. (2) County plans on the scale of six inches to one mile. (3) Cadastral or Parish plans for the whole country on the scale of 1/2500 or about 25-1/3 inches to one mile, on which one square inch on the plan represents an area of one acre. (4) For towns of over 4000 inhabitants a scale of 1/500 of actual length on the ground or 10-56/100 feet to one mile.

On the latter scale the city of London with its environs could not be well shown on a sheet of paper less than 300 feet long by 200 wide.

When the facts are taken into consideration, that the Ordnance Survey is a cadastral one, in other words, that one of its many objects is the measurement and definition of all existing boundaries, political, municipal, parochial or private, and a survey and valuation of property for assessments, that its maps are accepted in courts of law as authoritative on such questions, then the problem of the scales of publication is the most important one to be considered.

As an illustration of the relation of the scale of a map to the amount of detail, which can well be represented on it without confusion, assume for a moment that an observer is stationed in a balloon, which can be raised or lowered or placed at any desired height above the ground, and in addition that he is provided with a horizontal screen on which he is able to trace the details of the landscape below. The eye of the observer well represents the lens of a camera, and the screen the focussing plate. Therefore to produce a perfect image or map of the ground below it will be necessary to assume that all parts are stationary, balloon, plate and eye. For convenience assume that the eye remains over the centre of the screen at a distance of two feet. At a height of four miles above the ground the scale of the image on the screen would be exactly six inches to one mile, or a reproduction of the popular county map, on which every detail of importance such as houses, roads, paths, and fences is shown, and the smallest scale on which any attempt is made to preserve the relative proportions of such details.

On such a scale the 1/100th part of an inch represents a distance of very nearly nine feet on the ground and consequently however accurate the map might be in its projection, as an image showing the relative positions of all objects of importance on the ground, the scale is clearly too small for the measurement of areas for valuation purposes, and it is but a reproduction of the larger cadastral map.

Again assume that the balloon is stationed at a height of twenty-four miles above the ground, and that the observer places his eye at the same distance of two feet above the screen and attempts to construct a map from the image on the screen, which is now reproduced at a scale of one mile to one inch, or the exact scale of the general map. It needs but little imagination to foretell that houses would be mere specks, roads, faint lines, and forests, masses of color, in other words, that it would be more instructive to consult the general map, on which all details are magnified to be clearly visible and topographic features brought out with great distinctness than to attempt to trace with unaided eye, from the image of objects at a distance of twenty-four miles, the course of streams or roads through forest or moor, or to judge of the relative elevations or modeling of the ground from the values of light and shade. Without an intimate local knowledge of the county there would be nothing to indicate the name or boundaries of villages, or estates or the political and other subdivisions of the land, which are most clearly indicated on the map, in unmistakable styles of lettering.

Another and more serious problem which would be lessened as the balloon receded from the earth would be the distortion in perspective produced by the irregularities of the surface. The higher points being nearer the balloon would appear in the image on larger scale than the lower, and only in the case of a perfectly level country, would it be possible to produce a map without distortion by the method proposed, and then only for a limited area.

As the balloon receded, the relative differences of elevation would bear a smaller and smaller proportion or ratio to the distance, in other words, the distortion would grow less until at an infinite distance it might be neglected.

We might conceive that the observer was stationed at an infinitely great distance, and provided with a series of magnifying lenses of suitable powers to produce maps of any desired scale, yet, beyond a limited area, he would still be confronted with the problem of eliminating the distortion produced by the curvature of the earth.

Such is the conception of an accurate map which is an attempt to produce on a plain surface or sheet of paper, a horizontal projection of objects on the ground, which will show the relative positions of every detail on any desired scale with as little distortion as possible, and on which distances may be measured in any direction, and areas computed with a degree of accuracy only limited by the scale.

When a survey of a small area is made, such as an estate or parish, which bears but a small proportion in area to the surface of the earth, curvature is neglected, distortion due to this cause being imperceptible, but in the survey of a large country it is of primary importance.

Returning to the conception of an observer stationed at an infinite distance his position with reference to the new general one-inch map of England and Wales would be in the plane of a meridian passing through Delamere in Cheshire, and the published quarter sheets would be a series of rectangles each 18 miles by 12 miles, containing an area of 216 square miles whose edges were parallel to, and at right angles to the central meridian.

Those of Scotland and Ireland have for each country a central meridian and projection.

In viewing the county maps of six inches to one mile and larger scales, it would be necessary to assume that the observer was stationed over the center of each county except that, where two or three counties lie so well north and south of one another, the same meridian serves for more than one.

In the reproduction by photography of the maps on the scale of one mile to one inch from those of larger scale, these facts, that different planes of projection are used for the latter, have to be taken into consideration.

In countries of larger areas than England it is more customary to assume a central meridian for each sheet, in other words, the observer would be stationed in the zenith of the center of each sheet and would sketch but a limited area. The successive planes of projection, represented by the maps, would resemble the facets of a diamond, and it would be impossible to combine with any degree of precision a large number together in one plane surface. On the other hand, the whole of the one-inch series of England and Wales of Scotland or Ireland register perfectly, and the distortion due to curvature cannot be great, as the combined area of the three countries bears but a small ratio to the whole surface of the globe.

Attention has been called to the fact that viewed from a balloon in ordinary sunlight the minor features of topography become flattened and indistinct.

If, therefore, we regard a sheet of the one-inch map held at a distance of two feet from the eye as the picture of a country seen at the distance of twenty-four miles, we see that details, that would be invisible from above, are brought out with great distinctness on the map and every detail of topography is shown in bold relief. In other words the map is a diagram rather than a picture.

In the representation of relief on the one inch series, two systems are common, contours and hachures. Contours represent the successive shore lines which water at rest would form in following the modelling of the ground at successive stages or elevations. If now we assume that the water, having reached the highest point, is allowed to retreat steadily to sea level the paths which the particles of water would take from all points of the surface are those which the engraver would endeavor to reproduce in the shade lines of a hachured map. In addition he would adopt an arbitrary scale of shade increasing with the steepness of the slopes, from white on a horizontal surface to dead black on slopes of forty-five degrees, or greater, to produce the effect of a model of the surface illuminated from above.

In the Irish maps this effect is bolder and more artistic, an illumination from the northeast quarter having been carried out. The shade lines still preserve the paths of particles of water in motion on the surface, the color values being deeper on the eastern and southern slopes, shadows have even been projected across valleys and horizontal surfaces are in half tone, producing much the same effect as the illumination of the country at sunset in midsummer.

The Irish maps exhibited are considered the finest specimens of careful hill shading and will bear critical examination. For comparison with these, other topographic maps are exhibited of many scales and countries.

So far attention has simply been drawn to a few of the problems of map-making, which are, briefly:

1st. The reproduction on a finite scale on a plain surface, of the natural features of the terrain, with all the artificial boundaries and objects added by man, so far as the scale permits.

2d. The extension of such a series of maps to cover a large area of country still carried out with as little distortion as possible.

3d. The reproduction of such maps on suitable scales to meet all demands.

If the conception is still carried out that the map, at a distance of two feet, is but the image of the ground viewed from above, then the cadastral map of England, from which areas of fields and estates are measured for valuation purposes, would represent a view of the country from above at a range of 5,000 feet or nearly one mile, and a town plan, an image at 1,000 feet or a possible view from a series of Eiffel towers.

This suggestion of an observer stationed in a balloon will not have been valueless if it draws attention to the fact that vastly more information is given on the map than it would be possible for any single observer to discover from an elevated station with an unobstructed view, the map being the compilation of the results of hundreds of observations by many workers, and that its scale and the amount and character of the detail shown have been specially designed to meet definite ends.

It is beyond the limits of the paper to enter into the theory or practice of surveying, or to say more than a few words of the delicate and refined operations necessary in carrying out the geodetic or trigonometrical work of a national survey which binds together the many parts to make a complete whole.

The principal triangulation of the British Isles was begun in 1784 and finished in 1852. Two magnificent 3-feet theodolites made by Ramsden, one for the Royal Society, the other for the Master General of the Ordnance, an 18-inch theodolite also by Ramsden, and 2-feet theodolite by Troughton and Simms were used in these observations.

In the principal triangulation of Great Britain and Ireland there are 218 stations, at 16 of which there are no observations, the number of observed bearings is 1554--and the number of equations of condition, 920.

In order to avoid the solution of this enormous number of equations, containing 920 unknown quantities, the network covering the kingdom was divided into a number of blocks, each presenting a not unmanageable number of equations of condition. These calculations, all in duplicate, were completed in two years and a half, an average of eight computers being employed. Many of the sides of the principal or primary triangulation are of great length, 66 of them exceeding 80 miles, while 11 measure more than 100 miles, the longest being 111 miles, that from Sea Fell to Sheir Donard. So great, however, had been the accuracy of the observers' work, that the average amount of correction of the observed angles was no more than 0".6, and the measured length of the Salisbury base differed from its length as computed from the Irish Base, 350 miles distant, by a difference of only five inches.

The secondary triangulation interpolates points at shorter distances apart ranging down to five miles, the observations being made with theodolites of 12-inch circle. These triangles again are broken up into smaller ones of sides from one to two miles in length, for the use of the surveyor who is to follow and measure between the stations with the chain; and a further subdivision of the trigonal spaces is made in towns to points about 10 chains apart, where the survey is to be made on the very large special scale. In the two last cases, 7 inch instruments suffice for the measurement of the angles.

LEVELLING.

From 1839 to 1855, lines of initial levelling extending all over England, Scotland and Ireland were run, and the observed altitudes of the bench marks were reduced by the method of least squares.

In England and Scotland, these levels are based on the Ordnance Datum at Liverpool, which is approximately the mean tide level of that place; in Ireland, they are based on the low water level at Dublin, which is about 8 feet below the mean level round the coast of Ireland.

The detail levelling is carried out contemporaneously with the progress of the cadastral survey. Starting from the marks on the initial series, lines are run along nearly all the turnpikes and parish roads, and bench marks cut at intervals of about a quarter of a mile.

The whole of the bench marks of the initial levelling are shown in position on the 25-inch manuscript plans, and their heights given to the nearest tenth of a foot. Surface heights, to the nearest foot are also marked on the plans, at frequent intervals between the bench marks.

CONTOURING.

Contrary to the custom in other countries, the contours of the English survey have all been surveyed and levelled on the ground, checked by the numerous bench marks, the standard of accuracy demanded in levelling being two-tenths of a foot.

Owing to the expense of the process, about $1.25 per lineal mile, only the 100 foot contours have been surveyed, except where greater detail is required for military purposes, which information is not furnished to the public.

HILL SHADING.

The hill features for the one inch maps are first sketched in the field by the military method of slopes and sketch contours or proof impressions of the contoured sheet.

Finished drawings from the field sketches are then made on cardboard impressions from the one inch outline plates, and finished as guides for the engraver to work by.

Beautiful and delicate in finish as is all the work of the copperplate engravers on the Ordnance Survey, there is perhaps no branch in which they so peculiarly excel as in their delineation of hills on the one inch maps.