Bache.] ^d4: [May 6, 



zon line of the photographs, will be the positions of the objects on 

 the map, with due relation by scale and angles to the stations of 

 the base line and to one another. The contemplated map will, in 

 a word, be susceptible of being drawn throughout to scale. It is 

 clear that a great number of objects may be thus plotted from two 

 stations representing the ends of a base line, and that if we know 

 the length and azimuth of a base line, and the azimuths of the 

 lines of sight from its termini, the elements of scale and orienta- 

 tion will inhere in all the resulting work that goes to form a map. 

 Used for the function described, the photographic camera is there- 

 fore very aptly cabled the camera-theodolite. 



Adopting the same diagram to illustrate the mode of determining 

 height by the camera-theodolite, we see the steeple, as observed 

 upon from the point of view A, having the ray eA coming from 

 the photographic position of the steeple as projected on the hori- 

 zon line of the photograph taken from A. Draw from the point e 

 the height of the steeple, as derived from the photograph taken 

 from A, perpendicularly to the ray eA, and draw also the hypothe- 

 nuse Ad. Any one intuitively perceives that the pictorial height 

 of the steeple being ed dit e, at the end of the focal length of the 

 camera, its height at S, the horizontal position by scale of the 

 steeple, must be Sf, and that that by scale is the true height. The 

 length of the line Sf may therefore be obtained numerically by 

 applying to it the scale of the base, which may be the scale of a 

 whole map. With a greater degree of precision the same result 



ed ed 

 may be reached by computation, because Sf^^ AS -j-; -r^ bemg 



the tangent of the vertical angle d A e, and AS the distance from 

 the point of view A to the steeple S. 



Of course the height of any natural as well as of any artificial 

 object above the plane of the horizon may be ascertained by simi- 

 lar means. A steeple was chosen to illustrate both horizontal and 

 vertical methods of determination, because it affords points that 

 are so conspicuous as compared with those of many other objects 

 that offer themselves to the sight in most surveys. 



Surveys from this kind of photogrammetry may be plotted to 

 any scale, within reasonable limits of size, by adopting for the base 

 line of the survey the scale desired. In all cases, however, the 

 photographic pictures must, in order to enable them to present cor- 

 rect angles for the map, be placed in the manner already pre- 



