44 t 



Major L. Darwin. On the Method of 

 FIG. 20. 



the point of light can be made to appear, first as a fine vertical 

 line, and then, as the focus is lengthened, as a fine horizontal line. 

 The focal scale is read off at each of these positions, and the dif- 

 ference, 7, between the two readings gives a measure of the astig- 

 matism. But, in order to judge of the amount of astigmatism that 

 can be tolerated, the diameter, <r, of the disc of diffusion caused 

 thereby should be calculated. This is done by multiplying 7, the 



difference of focal distance of the focal lines, either by 4^ 



, / /\ 2 COS 



or by (j, j 2Uv/(C.I. No. of stop)' where e 1S the efEectlve aperture, 

 / the principal focal length of the lens, and /' the focal distance 

 when the observation was made. As the thermometer bulb is placed 

 at the same distance from the testing camera as was the object in the 

 examination for achromatism, the ratio ///' is exactly the same as in 

 that case. The same result may be obtained by the use of the table 

 on p. 427 in the following manner : Find the value of 8, the diameter 

 of the disc of diffusion, on the supposition that the fi of the tables has 

 the value just obtained for 7 ; multiply the value thus obtained for 



/A 2 



y \f) COS ^' and we get ff > the re( l u i re<i valu e of the disc of 

 diffusion due to astigmatism. This is the quantity recorded in the 

 Certificate of Examination. 



That this is the case can readily be seen by reference to fig. 21. 

 Here AB represents the effective aperture, F! and F 2 the positions of 

 the focal lines, and PH the position that the photographic plate 

 would occupy. At F 3 the image appears as a fine line perpendicular 

 to the plane of the paper, and at F x it is represented by the line ab ; 

 half way between these two points the rays cut the plate in the form 

 of a disc, of which a'V is a diameter. Any movement of the plate 

 from this position must lengthen out the disc of diffusion in one 



