tangents, etc., will find that the natural cotangent of 1° is 57.3; we therefore infer that an angle of 1° gives a slope of 1 in 537. For practical purposes Therefore 1-30 would be a 2° slope, and 1-20 a 3° one, we call this 1-60. and so on. Thus, given our contour = = Fig. 7 As the vertical interval is 50′ and a 1° slope a gradient of 1 in 57.3 (if we are making these for permanent use, we had better say 573 instead of 60, and so secure accuracy once and for all), we shall, to rise 50' on a 1 slope, want 50 x 573 2865 ft. horizontal; on a slope of 2°, 1432.5 ft., etc.; and by similar reasoning we obtain our scale of slopes. shows the same, constructed to scale for the 6-inch maps. By selecting two points on any two contours and fitting between them the nearest distance on the scale of slopes we can read off the gradient at a glance. Now, in reference to fig. 3, and in order to choose the best route for a road between A and B, the ruling gradient being taken at 1 in 30, by use of the scale of slopes we find that the dot-and-dash line satisfies all requirements; or if we have not enough data to satisfy us making such a scale, take as before a gradient of 1-30- =a 2° slope. Now 28.6 is the natural cotangent of 2°, .. 50 × 28.6 = 1430-0 say 1430 ft. Take 1430 ft. horizontal on the dividers and step from contour to contour. By these means we obtain a line similar to the = dot-and-dash line in question, which appears to answer our purpose well. But we see by again inspecting the map that the dash line runs practically along the line of the contour (400). Therefore this line is practically level, but it was avoided, owing to the very stiff gradient on the road running northward from A. By the examples given, it will be seen that for those who have to prepare road schemes, and who do not want the trouble of an expensive and tedious preliminary survey, the above principle is very expeditious. It applies not only to roads, but to railways, to the laying of pipe lines, drains, and sewers. The vertical interval of contours on maps will of course vary with the scale of the map. In the old 5-foot maps, they were 5 ft. apart, but on the 6-inch they are usually 50 ft. on fairly stiff ground, but less in very flat districts. In concluding these few remarks on maps I need scarcely add that accuracy is the main thing, and neatness and conformity in printing and colouring second only to it. A question which frequently confronts the young engineer is, why have the buildings and other parts of the map thick and thin lines? The explanation is this. The map maker considered Shade Lines FIG. 8. the light as coming from the top left-hand corner of the map. He therefore assumed that the righthand side and bottom side of any building were more or less dark or in the shade. He therefore put thick lines here, showing a projection. If, however, the reverse should occur, that is, lines facing the imaginary ray of light be thick lines, then there is a depression here, such as a well, cellar, or watercourse. A little study of a map will soon show the Representing Depression reader that this is so. Shade Lines They are what are called shade lines, and, when one is accustomed to using them, make the map very clear (fig. 8). One can, if in doubt, distinguish between a road and a watercourse by means of these lines. In the same way, on all good engineering drawings shade lines occur, with the object of defining projections and depressions. A special index is issued by the Ordnance Survey, for use with the 25-inch Ordnance map. It gives much useful information. The maps show the position of practically every farm in a parish, and the boundaries and names of every parish represented in the index. Every parcel of land is numbered and its area computed, the area being given beneath the number on the map. A catalogue of maps is issued by the Director of the Ordnance Survey, and the maps themselves may be obtained through the local post office, and many of them are, indeed, kept in stock at the head offices of many of the larger towns. CHAPTER II. ON SURVEYING WITH THE CHAIN. SURVEYING is the term given to the art of measuring up and representing truly to scale on paper the actual configuration of a particular portion of the earth's surface considered as a plane. The art has been practised since very ancient times. Owing, however, to the excellent edition of the Ordnance maps of the United Kingdom, the practice of extensive surveys has now been largely abandoned. Such work is rarely, if ever, now carried out in this country except by Ordnance men, whereas persons who have similar work to do abroad, and particularly in new countries, are usually specialists. in their work and do little else. Surveys nowadays are usually of a more restricted nature, conducted generally with the aid of good maps, and for the purpose of waterworks, sewage works, railways, roads, and drainage. schemes, and the sale and conveyance of landed property. Surveys abroad in undeveloped and unmapped country are carried out on such entirely different lines to those at home that it would be foreign to the scope of the present work to treat of these here. Small surveys in the country are often conducted by means of the chain only. This statement, however, only applies to the survey of very open country. When at all complicated, a theodolite has to be used if anything like accuracy is desired and time is a secondary consideration. As a preliminary to survey proper, a rough sketch should be made in the "field book" showing the nature of the ground. This will serve to show where best to run chain line. Having then carefully reconnoitred the ground we can start chaining. All surveys are made on the principle of "triangulation," that is, of setting out the ground in triangles. These triangles should be as nearly equilateral as possible. Before going any further, however, it 9 is desirable fully to describe the surveyor's implements, such as the chain, arrows, etc. The 66-foot chain, commonly known as Gunter's chain, was invented by Edmund Gunter in 1620. It is divided into 100 links. Each link measures 7.92 inches. The reason for using a 66-foot chain is because it is an exact decimal part of an acre and a mile, that is, 80 chains = 1 mile, and 10 square chains = 1 acre. This latter must not be confused, however, with 10 chains square, that is, 10 x 10 = 100 square chains = 10 acres. The 66foot chain is chiefly confined to estate work and railways. 18" Red webbing 10 L For general surveys, town surveying, and county engineers' work a 100foot chain of 100 links is much more useful and a less likely source of error. Upon examining a chain we find two brass swivel handles, one at each end, as shown in fig. 9, and brass tablets at equal intervals of 10 links, those at 10 and 90 being similar, and likewise those at 20 and 80, 30 and 70, 40 and 60. At 50 links a circular tablet is inserted. This may puzzle the beginner at first, and until he gets quite conversant with the chain he should be very careful to make sure his reading is correct, and to think twice as to which end he is reading the distance from. It is with the object of being able to read from both ends of the chain that the brass tablets, or "Tellers," as they are called, are arranged so. When purchased, all chains should read within in. of exact measurement, and where constantly used they must be frequently tested either by means of a steel tape kept for the purpose or on known public testing-places. These occur in most large town or public buildings, such as those at the Guild Hall and on the north side of Trafalgar Square in London, and the City Hall in Dublin. Alternatively, a surveyor may make permanent marks once and for all on the plinth of a public building, or on a footpath or other suitable spot. FIG. 10.-Arrow. Shoe Ranging Pole. chain Line FIG. 12. Chains are of two qualities, "strong" and "light." The former are made of 8 BWG and the latter of 12 BWG steel wire. Arrows are made from the same gauges of wire as the chain (fig. 10). They are made in sets of 10; and 10, and 10 only, must be used on any survey. They are about 18 in. long, and usually have a strip of red webbing tied to them to make them easily visible. Surveyors' Rods.-These are shown in fig. 11, and have an iron ferrule at one end, and are painted alternate black and white in lengths of a link. They are used to put the chain men in line for taking sights by means of a theodolite or other instruments, and for measuring offsets. The foregoing appliances, together with a 100-foot tape line, which is best made of Scotch linen, form the necessary equipment for a chain survey. To set about a survey, two men should always be employed-where possible a |