OPTICAL ILLUSIONS IN SKETCHING TOPOGRAPHY. 45

than a nearer divide or pass to which it is referred in one sweep of the vision, whereas it may be higher (Fig. 7).

A

FIG. 7.-OPTICAL ILLUSION AS TO RELATIVE HEIGHTS of Divides. A is nearer and lower than B.

6. The eye invariably exaggerates the steepness of the slopes of mountains, these appearing to have inclinations of from 60 degrees to almost vertical, whereas in fact the steepest slopes are rarely as great as 45 degrees.

7. The eye trained to estimate slopes and distances in regions of large topographic features-that is, regions of extreme relief or differences of elevation-will be at a disadvantage in making similar estimates in a country in which the differences of elevation are small. The tendency of one accustomed to estimating the topographic forms in the Rocky Mountains, where differences of elevation and distances visible to one sweep of the eye are great, will be to overestimate heights and distances in the less rugged country of the Eastern States, where great detail in topography exists, and thus deceives the eye into an exaggerated notion of the amount of the relief.

8. In viewing the terrane with an idea of estimating its roughness as affording a possible route for railways, canals, or similar works, a rugged mountain gorge with occasional precipitous narrows, separated by river flats, may appear much more difficult and much rougher than it is in fact. This is especially so as compared with a gently undulating or rolling

country, which, when viewed from a distance, appears to be comparatively level, while a nearer view will show it to be full of elevations or depressions which will render construction most expensive, because of the rapid and numerous succession of large cuts and fills.

The effect on the eye and the mind is to exaggerate the ruggedness of a country which is difficult to travel because of such impediments as broken stone, fallen timber, creeks, and swamps, whereas a region where travel is easy and free, as in open rolling plains country or where good roads abound, is often estimated to be much simpler and more level topographically than is the other region.

CHAPTER III.

SURVEYING FOR DETAILED OR SPECIAL MAPS.

21. Topography for Railway Location.-Some of the worst errors in engineering location originate in reconnaissance, for the reason that the average reconnaissance surveys are not of areas, but of routes or lines, and there is great danger of serious error in the selection of the line to be surveyed. It may, accordingly, be stated that a railway reconnaissance should not be of a line, but of an area sufficiently wide on each side of an air line between the fixed termini to include the most circuitous routes connecting these. The results of such a survey should be embodied in a topographic map of greater or less detail, according to the nature and extent of the country. If the reconnaissance be of a great railroad, such as some of the Pacific roads, built through hundreds of miles of unknown country the resulting map should be on a small scale, perhaps 2 to 4 miles to the inch, and with contour intervals varying from 20 to 100 or 200 feet, according to the differences of elevation encountered and the probable positions of several locations. With such a map

the number of possible routes may be reduced to two or three, and a more detailed topographic survey should then be made of these on which to plan the final location.

As ordinarily practiced, topographic surveys for railways are made by the older methods, with transit and chain or stadia and with spirit-level; notes of the surveys are kept with accompanying sketches in note-books, and these are reduced to map form in the office. The same results can be much

more satisfactorily and more rapidly procured by using the plane-table in place of the transit, and the resulting map, being plotted in the field, is a more accurate and available. representation of the terrane than can possibly be made from plotting notes in an office.

The Germans, who are very thorough in taking topography for railroads, divide the work into three separate surveys of different degrees of accuracy: first, recourse is had to the government topographic maps on a scale of approximately 1:100,000, and on this a preliminary route or routes are laid down: second, a more detailed topographic survey is made in the field on a scale of 1:2500 as a maximum or 1: 10,000 as a minimum, with contour lines of 15 feet interval. This map is limited in area from a few yards to a few hundred yards in width, according to the nature of the country. Where no previous small-scale topographic survey exists, the base of this more detailed or second survey is a transit (Art. 87) or plane-table (Art. 83) and level (Art. 129) traverse, following as nearly as possible the approximate route of the proposed railway. Bench-marks (Art. 135) are established along this at distances of from 500 to 1000 feet, by which the aneroid may be checked. With this transit line completed on the proper scale, the topographer goes over the ground and, by means of distances from pacing (Art. 95) or odometer (Art. 98), and elevations by aneroid (Art. 176), constructs a hasty contour map on which are indicated all roads, watercourses, structures, high-water marks of bridges, width and height of existing bridges and culverts; and all other necessary topographic details as to the position of rock masses, strike and dip of strata, swamps, springs, quarries, etc.

On such a map as this, hastily and cheaply made, it is possible to plan the detailed topographic map, limited from a few yards to 100 or 200 yards in width and covering what will practically be the final route of the located line as obtained from the second survey. This final detailed survey,

DETAILED TOPOGRAPHIC SURVEYS.

49

from which the paper location is to be taken, should be on a scale of from 1:500 up to 1:1000 and with contours of about 5 feet interval, more or less, according to the nature of the land. There is plotted on the plane-table sheet the transit and level base line previously run for the second survey, and the instruments now used by the topographer are of a more accurate nature, consisting of a plane-table (Arts. 58 and 83) for direction and mapping, two or more stadia rodmen for distances (Art. 102), while elevations are had by vertical angles with the alidade (Art. 59). On this final map are shown much the same topographic details as on the second, but all are more accurately located and the elevations are of a more refined nature. The data furnished by this final map will serve all the purposes of making a last paper location of the line, from which the engineer will in the field possibly deviate according to the appearance of the route traveled as presented to his eye when the location is laid down.

Mr. Wellington's location of the Jalapa branch of the Mexican Central Railway (Fig. 8) is an excellent example of a detailed contour topographic map for railway location. This was platted in the field on the scale of 1: 1000, or about 83 feet to 1 inch. The contour interval was 2 meters, or 6.56 feet.

22. Detailed Topographic Surveys for Railway Location. Prior to making the location, which may be made in part from the notes of preliminary surveys, a narrow belt of topography should be mapped in detail, its width being restricted as far as possible, providing the preliminaries have been skillfully conducted or have been preceded by a smallscale topographic map executed with especial care along the possible routes of the location (Art. 21). On the detailed topographic map a paper location may be made, from which full notes of the alignment can be derived, the points of curve and tangent taken off, and a profile of the paper location pre