Lay a piece of paper with a straight edge, in any position cutting the lines A B in B', A C in C', A S in S' in A D in D' and mark these cutting points on the paper.
Now lay the paper strip on the map and fit it upon the lines a b, a c, and a d, so that B', C' and D' lie upon these lines.
Mark on the map the position of a point s' opposite the mark S' on the paper strip. Join a s'. Then s, the position of point S, upon the map, lies upon the line a s'.
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FIG. 4.
Repeat this proceeding from B, C, or D, and another line b s', c s', or d s', will be secured, the intersection of which with a s' will define the position of S.
The camera lucida (see 5.104) has been used extensively for plot- ting. The upright carrying the prism is mounted on a stand upon which are also mounted two boards roughly at right angles to each other called respectively the map and photograph boards. Move- ments are added to allow of rotating the photograph in its own plane, of tilting the map (or tracing of control points) around an axis parallel to a marked horizontal line on the photograph board, and of increasing or decreasing the distance between the prism and the photo board (fig. 5).
Mill-headed Screur actuating pinion for raising, and lowering Photo-carrier
Slide and Rack tarrying the Prill
Mill-headed Screui actuating and oinion for rotating Photo- carrier
Hilt. headed Screat actuating Slide carrying Pritm
The movement! peculiar to thlt Instrument
are indicated oy dotted lines and arrwt
FIG. 5.
^Graphic and optical methods are tedious and lengthy compared with a photographic rectification. The ordinary enlarging camera can be made to answer the purpose with little modification. It must provide, in addition to its focussing movements, as follows:
1. The negative must be capable of rotation in its own plane around its centre.
2. The copying board and negative carrier must be capable of rotation around parallel axes which are at right angles to the optical axis of the lens.
3. The copying board and negative carrier must be capable of movement along the line axis of the lens.
> 4. The negative carrier must be capable of a movement bodily at right angles to its axis of rotation.
By means of these movements a coincidence can be obtained between the four control points on the map and on the photograph, and a " rectified " print may be obtained.
Little contouring has as yet been based on air-photographs. It must be recognized at the outset that it is impossible to calculate relative heights from measurements taken from a single photograph ; for the accurate determination of relative heights we must have at least two photographs taken from different places. An outline of photogrammetry from the air has already been given and mention has been made of interpolation in space, and of the survey of new points by intersecting rays. A short additional step the measure- ment of vertical angles on the plate makes it possible to calculate the height of these new points.
Stereo-photogrammetry from the air may develop in the future, but has not been made use of hitherto. On the other hand much use has been made of the stereoscopic effect visible on two photographs of the same area taken from different positions. Such information is not of an exact nature but gives a valuable indication of ground forms and brings out the system of drainage.
Until 1920 mapping from air-photographs had been confined almost entirely to war time, and to areas already covered by a trigonomet- rical control, hence there had been little opportunity of comparing the cost of this method with that of any other, or of laying down definitely its possibilities and limitations. Clearly its greatest value lies in the mapping of inaccessible country.
So far as can be judged, the chief fields of usefulness open to air- photo-topography are, the surveying of native towns on scales of about 1/10,000, or 6 in. to I m. ; the surveying of deltas and intricate water channels; and the surveying of ancient sites, on which the indications of a former civilization become far more evident in the air than on the ground. Topography on ordinary small scales, and accurate large scale cadastral mapping are, so far, ruled out. But it appears that developments may very well be looked for in each of these directions.
Photographic Surveying
The idea of applying photography to surveying was originally due to Col. Laussedat (1819-1907), who made some experiments in the matter in 1859, and continued during his long life to expound and develop the method. Although the system origi- nated in France not much was done in that country in the way of its practical application, and, if we except some minor work by MM. J. and H. Vallot in the Mont Blanc regionin 1892 and some similar mapping by M. Flusin in 1905, it is to Canada that we must go for its first use on any considerable scale.
In 1895 Mr. E. Deville, surveyor-general of Dominion Lands, published his important work on photographic surveying, which remains a complete exposition of the subject if we exclude some recent departures. Between 1886 and 1892 photographic surveys were confined to the Rocky Mts. in the neighbourhood of the Canadian Pacific railway, but in 1893-4 the method was used by Mr. W. F. King in the survey of the Canada-Alaska frontier. In 1901-2 Mr. A. O. Wheeler carried out a very successful photographic survey of the Selkirk range, British Columbia, on the scale of 1/60,000; this was published, with an interesting account of the range, in 1905.
In the U.S. photo-topographic surveys had been made use of on the International Boundary Survey and reports made by Mr. M. A. Flemer of the U.S. Coast and Geodetic Survey in 1897-8. Stereo-photo surveys (see below) were employed in the survey of Tutuila, Samoa, by the U.S. Hydrographic Office in 1916; and an innovation in the shape of a panoramic camera was first used by Mr. C. \V. Wright in Alaska in 1904 and ex- tended by Mr. J. W. Bagley who wrote an important treatise on the subject in 1917 (Washington, Government Printing Office).
In 1907-8 Lt. M. Weiss, of the expedition commanded by Duke Adolphus of Mecklenburg, made a photo-survey of the volcanic Mfumbiro Mts. to the N. of Lake Kivu. Other fragmen- tary surveys in various parts of the world have been carried out by the aid of photographic methods; most of them, as well as those mentioned above, were in mountainous country.
Outline of the Method. Assuming that a photograph is a true per- spective view, that the plate was vertical when exposed, and that the horizon-line and focal length of the lens are known, it is clearly possible to determine the horizontal and vertical angles from the point where the camera was set up to all objects represented in the photograph, the horizontal angles being measured from some known, represented object. If two such photographs are taken from two points, at known distance apart, we have the means of determining the distance and height of all points shown on both photographs.
It will therefore be necessary in planning a photographic survey, to arrange for a triangulation to fix the relative positions of points at which the camera will be set up, and the first stage in the office work will consist in the plotting of the triangulation. A camera
