596 FROCEEDTXGS OF SECTION H. 



Angles are found from the photngraph by the use of a 

 pair of dividers, a scale, and a table of natural tangents. This 

 may be done approximately with any photograph by ruling a 

 line across the middle from left to right, and another at right 

 angles to it, from top to bottom, called the co-ordinaling lines. 

 The intersection of these lines should correspond to the optical 

 axis of the lens ; and all angles derived from paper measurements 

 taken parallel to the horizontal line left to right of the vertical 

 one will, if the camera has been set up truly, be correct horizontal 

 angles; Avhilst those derived from measurements above or below 

 the horizontal line will be true angles of elevation or depression 

 from the centre of the lens. 



Two factors, however, are required before these angles can be 

 worked out to correspond with what they would be if read with a 

 theodolite placed Avhere the camera stood. They are the offsets 

 from the co-ordinating lines, and the focal length of the lens, 

 Calhng the offsets taken left or right of the middle P, Pj, P,,, the 

 offsets taken above or below the horizon line (/+) or {/—), the 

 focal length F, and the required angle A; the formula is 



P 

 tan. A ==■ -p + r ; P, P, & ./ being of course taken in the same 



unit of measure; thus, let P as measured upon the negative = 



30 

 -roin., F = 8in.,y^ ml, then tan. A = j-rr =. 'OoTo = tan. of 



2° 9'. Again, if P be 4in., F = Sin. as before, and_/'= lin. above 



the line ; tan. A = g^^ = -4444, = tan. of 23° 58'. It may be 



well at this point to remark upon the characteristics vif various 

 lenses in order to avoid being misunderstood, and to prevent 

 disappointment to anyone who might attempt this kind of work 

 with a lens ill adapted to photogrammetrical purposes. 



The so-called single lens (Avhich is really compound, and gener- 

 ally of a meniscus or new moon form) is good for ordinary land- 

 scape work, but not for architectural subjects, as when used with a 

 stop in front of the lens the image of a scpiare becomes barrel- 

 shaped, but with the stop placed behind, it gives a cushion or hour- 

 glass form. 



Portrait lenses are constructed to give a brilliant image of 

 objects in one plane only, and should not on any account be used 

 for the purposes discussed in this paper, where the great desidera- 

 tum is a common focus for near and distant objects. The.se 

 conditions are fulfilled by the rectilinear or symmetrical lenses. 

 They are doublets, and consist of two single meniscus glasses 

 placed at a suitable distance apart, with their concave surfaces 

 inwards and the stop between. We thus have a combination with 

 the lens in front of the stop, giving cushion-shaped distortion, and 

 the second similar lens behind the stop, giving barrel-shaped 

 distortion to an equal extent. It follows that one distortion 



