1904.] Lens- Systems, including Rotation of Images. 2SS- 



but the field of view is small. The abscissae are magnified two and a 

 half times and the ordinates diminished in the same proportion, so that 

 the total effect is the same as if the original photograph had been 

 taken on a plate moving 25/4 times as fast, and the resulting curve; 

 can be easily analysed. 



It should, however, be noted that fig. 1, being a curve with polar 

 co-ordinates, is not properly adapted for this process, which requires, 

 to be accurate, curves with rectangular co-ordinates. It serves, never- 

 theless, to illustrate the method, and as the portion photographed 

 occupies not more than an angle of 2° of arc, the error involved is 

 hardly noticeable although great enough to render it not worth while 

 to spend time over a minute analysis of the modified curve. 



It is not necessary that both lenses should be of the same focal 

 length. If they are, the image is magnified as much in one direction 

 as it is diminished in the other. If it is desired to preserve the 

 dimensions in one direction unaltered — as, for instance, in comparing 

 the time relations of two electrical responses of different intensity — 

 e.g., nerve under the influence of C0 2 , and in a normal condition — one 

 lens may be put midway between the object and the screen. 



If m be the magnification required in the other direction, the focal 



length necessary for the other cylindrical lens is / = - ™ . I and its 



distance from the object is — - — 

 J 1+ra 



In practice it is more convenient to employ a pair of lenses of rather 

 more than the required power when close together, and to adjust the 

 distance between them until the right magnification is obtained. 



The image thus modified by the cylindrical system is projected on to 

 the curve with which the comparison is to be made, and examined with 

 a lens. 



The principal difficulty is the smallness of the field of view, which is 

 elliptical in shape, the major axis being limited by the diameter of the 

 lenses and the ratio between the axes being as 1 : m 2 . Unfortunately 

 the use of lenses of larger aperture introduces errors of chromatic 

 and spherical aberration which spoil the definition. 



Owing to the fact that each cylindrical lens has to be separately 

 focussed, and that no image is formed until both are correctly adjusted, 

 not only as to distance but also as to the direction of the axes of 

 curvature, focussing is a matter of some difficulty. I have found the 

 following method answer very well : — 



Two lines, one vertical and the other horizontal, are ruled, across the 

 middle of a glass plate — a spare negative answers very well, and the 

 lines can be ruled with a needle on the film. This is placed in the 

 object holder. The first cylindrical lens is inserted in its cell and the 

 horizontal line focussed with it sharply on the screen. The first lens 



