northern counties of England and for the southern counties of Scotland. The same scale was employed for platting and engraving in outline the "Ordnance Survey" of Ireland. But a map on a scale of 1 inch to 1 mile (1:63,360) is about to be published, the former scale rendering the maps too unwieldy and cumbrous for consultation. The Ordnance Survey of Scotland was at first platted on a scale of six inches to one mile, (1:10,560). That scale has since been abandoned, and it is now platted on a scale of two inches to 1 mile, (1:31,680), and the general maps are made to only half that scale. The Ordnance Survey scale for the maps of London and other large towns, is 5 feet to 1 mile, (1:1056), or 11 chains to one inch. In the "Surveys under the Public Health act" of England, the scale for the general plan is two feet to one mile, (1:2,640); and for the detailed plan, ten feet per mile, (1:528), or two-thirds of a chain per inch. The Government Survey of France is platted to a scale of 1:20,000. Copies are made to 1:40,000; and the maps are engraved to a scale of 1:80,000, or about 2 inch to 1 mile. Cassini's famous map of France was on a scale of 1:86,400. The French War Department employ the scales of 1:10,000; 1:20,000; 1:40,000; and 1:80,000; for the topography of France. (47) Rail-road Surveys. For these the New-York General Rail-road Law of 1850 directs the scale of maps which are to be filed in the State Engineer's Office, to be five hundred feet to onetenth of a foot, (= 1:5000.) For the New-York Canal Maps a scale of 2 chains to 1 inch (1:1584) is employed. The Parliamentary "standing orders" prescribe the plans of Rail-roads, prepared for Parliamentary purposes, to be made on a scale of not less than 4 inches to the mile, (1:15840): and the enlarged portions (as of gardens, court-yards, &c.) to be on a scale not smaller than 400 feet to the inch, (1:4800.) Accordingly the practice of English Railway Engineers is to draw the whole plan to a scale of 6 chains, or 396 feet to the inch, (1: 4752) as being just within the Parliamentary limits. In France, the Engineers of "Bridges and Roads" (Corps des Ponts et Chaussees) employ for the general plan of a road a scale of 1:5000, and for appropriations 1:500. (48) In the United States Engineer service, the following scales are prescribed: General plans of buildings, 1 inch to 10 feet, (1;120). Maps of ground, with horizontal curves one foot apart, 1 inch to 50 feet, (1:600). Do. comprising three miles square, 1 foot to one mile, (1:5,280). (49) The most convenient scales of equal parts are those of boxwood, or ivory, which have a fiducial or feather edge, along which they are divided, so that distances can be at once marked off from this edge, without requiring to be taken off with the dividers; or the length of a given line can be at once read off. Box-wood is preferable to ivory as much less liable to warp, or to vary in length with changes in the moisture in the air. The student can, however, make for himself platting scales of drawing paper, or Bristol board. Cut a straight strip of this material, about an inch wide. Draw a line through its middle, and set Fig. 17. 3 off on it a number of equal parts, each representing a chain to the desired scale, Sub-divide the left hand division into ten equal parts, each of which will therefore represent ten links to this scale. Through each point of division on the central line, draw (with the T square) perpendiculars extending to the edges, and the scale is made. It explains itself. The above figure is a scale of 2 chains to 1 inch. On it the distance 220 links would extend between the arrow-heads above the line in the figure; 560 links extends between the lower arrow-heads, &c. A paper scale has the great advantage of varying less from a plat which has been made by it, in consequence of changes in the weather, than any other. The mean of many trials showed the difference between such a scale and drawing paper, when exposed alternately to the damp open atmosphere, and to the air of a warm dry room, to be equal to .005, while that between box-wood scales and the paper was .012, or nearly 2 times as much. The difference with ivory would have been even greater. Some of the more usual platting scales are here given in their actual dimensions. In these five figures, different methods of drawing the scales have been given, but each method may be applied to any scale. The first and second, being the most simple, are generally the best. In the third the subdivisions are made by a diagonal line: the distances between the various pairs of arrow heads, beginning with the uppermost, are, respectively, 310, 540, and 270 links. In the fourth figure the distances between the arrow heads are respectively 310, 270, and 540 links. In the fifth figure the scale of 5 chains to 1 inch is subdivided diagonally to only every quarter chain, or 25 links. The distance between the upper pair of arrow-heads on it is 12 between the next pair of arrow-heads, it is 6.50; lower pair, 14.75. Fig. 22. Scale of 5 chains to 1 inch. chains, or 12.25; and between the A diagonal scale for dividing an inch, or a half inch, into 100 equal parts, is found on the "Plain scale" in every case of instru ments. (50) Vernier Scale. This is an ingenious substitute for the diagonal scale. The one given in the following figure divides an inch into 100 equal parts, and if each inch be supposed to represent a chain, it gives single links. Make a scale of an inch divided into tenths, as in the upper scale of the above figure. Take in the dividers eleven of these divisions, and set off this distance from the 0 of the scale to the left of it. Divide the distance thus set off into 10 equal parts. Each of them will be one tenth of eleven tenths of one inch; i. e. eleven hundredths, or a tenth and a hundredth, and the first division on the short, or vernier scale, will overlap, or be longer than the first division on the long scale, by just one hundredth of an inch; the second division will overlap two hundredths, and so on. The principle will be more fully developed in treating of "Verniers," Part IV, Chapter II. Now suppose we wish to take off from this scale 275 hundredths of an inch. To get the last figure, we must take five divisions on the lower scale, which will be 55 hundredths, for the reason just given. 220 will remain which are to be taken from the upper scale, and the entire number will be obtained at once by extending the dividers between the arrow-heads in the figure from 220 on the upper scale (measuring along its lower side) to 55 on the lower scale, 254 would extend from 210 on the upper scale to 44 on the lower. 318 would extend from 230 on the upper scale to 88 on the lower. Always begin then with subtracting 11 times the last figure from the given number; find the remainders on the upper scale, and the number subtracted on the lower scale. (51) A plat is sometimes made by a nominally reduced scale in the following manner. Suppose that the scale of the plat is to be ten chains to one inch, and that a diagonal scale of inches, divided into tenths and hundredths, is the only one at hand. By dividing all the distances by ten, this scale can then be used without any further reduction. But if the content is measured from the plat to the same scale, in the manner explained in the next chapter, the result must be multiplied by 10 times 10. This is called by old Surveyors "Raising the scale," or "Restoring true measure." (52) Sectoral Scales. The Sector, (called by the French "Compass of Proportion"), is an instrument sometimes convenient for obtaining a scale of equal parts. It is in two portions, turning on a hinge, like a carpenter's pocket rule. It contains a great number of scales, but the one intended for this use is lettered at its ends L in English instruments, and consists of two lines running from the centre to the ends of the scale, and each divided into ten equal parts, each of which is again subdivided into 10, so that each leg of the scale contains 100 equal parts. To illustrate its use, suppose that a scale of 7 chains to 1 inch is required. Take 1 inch in the dividers, and open the sector till this distance will just reach from the 7 on one leg to the 7 on the other. The sector is then "set" for this Fig. 24. ONE INCH |