38 HANDBOOK OF PHOTOGRAPHY 



practical possibility. At once the distortion of the landscape lens and the limited 

 field of the portrait lens became strongly noticeable and objectionable. In 1859, 

 J. T. Goddard attempted to remove the distortion of the landscape lens by intro- 

 ducing a cemented doublet between the lens and the diaphragm. Within the following 

 few years many other nondistorting or "orthoscopic" lenses were introduced, most of 

 which comprised two identical lenses placed symmetrically about a central stop, such 

 as Steinheil's "periscopic" lens of 1865 (Fig. 4). The argument here was that if the 

 lens is in front of the stop, pincushion distortion arises, whereas if the stop is in front 

 of the lens, the distortion is barrel-shaped. Thus, when both lenses are used together, 

 their distortions will neutralize each other. Some extremelj^ wide-angle lenses were 

 made at this time, notably the Harrison and Schnitzer Globe lens, Sutton's panoramic 



Fig. 4. — Steinheil's peri- Fig. 5. — Busch Pantoskop 



scopic lens. wide-angle lens. 



lens containing water inside a hollow thick glass sphere, and the Busch Pantoskop lens. 

 This latter coA^ered a field of 100° at// 30 (Fig. 5). 



The Effects of Shifting the Stop. — The real advantages of the symmetrical con- 

 struction were not at first realized. These follow from a consideration of the laws 

 governing the changes of aberrations as the stop is moved longitudinally along the 

 lens axis. These changes may be represented symbolicallj^ by the equations: 



Sph* = Sph ) 



Coma* = Coma -h X X Sph \ (1) 



Ast* = Ast + 2K X Coma + K^ ^ Sph) 



The asterisk (*) indicates the value of each aberration after the stop has been shifted 

 by an amount represented by K. Thus, shifting the stop does not affect spherical 

 aberration at all, but it changes the coma if spherical aberration is present, and it 

 changes the astigmatism if either spherical aberration or coma or both are present. 

 In the landscape lens, the stop is placed at such a position that the coma is just neu- 

 tralized by the {K X Sph) term in the second equation above. Thus a landscape 

 lens must have spherical aberration if it is to be coma-free, and, of course, coma is a 

 much worse defect than spherical aberration since coma increases as the field increases, 

 whereas spherical aberration is constant over the entire 

 field. The field of a landscape lens must then be flattened 

 by a suitable choice of lens shape. 



The Rapid Rectilinear Lens. — In 1866, Dallmeyer and 

 Steinheil simultaneously and independently realized that, 

 if two identical lenses are mounted symmetrically about 

 Fig. 6. Rapid rectihnear ^ central stop, the three transverse aberrations-distortion, 

 chromatic difference of magnification, and coma, are 

 automatically removed (or drastically reduced), and hence each component of such 

 a symmetrical system need not be corrected for any of these three aberrations. 

 They therefore constructed a symmetrical lens, each half of which was corrected for 

 longitudinal chromatic and spherical aberration; the astigmatism was then removed 

 by placing the stop at the correct position relative to each component to make use of 

 the {2K X Coma) term in the third equation above. In this way they produced the 



