442 Major L. Darwin. On the Method of 



from the ground glass to the nodal point of emergence, or to the pivot 

 which has been made to pass through that point. The difference of 

 focus, lw, noted between the blue and white light is then multiplied 

 by f/f and the result thus obtained is that finally recorded m the 

 Certificate of Examination as if it were the direct result of an ob- 

 servation made on a distant object. Exactly the same process is then 

 repeated with a sheet of red glass, the colour of which has a dominant 

 wave-length of 6250. 



The reason for multiplying the result of the observations by/// is 

 that it would evidently be unfair to test objectives of different focal 

 lengths on a near fixed object, for in some cases the ground glass 

 would be close to the principal focus, and in others far removed from 

 it. It seems, therefore, advisable to reduce all results so as to make 

 them equivalent to observations taken on infinitely distant objects, 

 and this is done by applying this correction. An assumption is here 

 made that the difference of focus between different coloured rays in 

 the same lens varies directly as the focal distance, and this in 

 all probability, though not strictly accurate, introduces an exceed- 

 ingly small error in the results. 



The blue and red glasses, which were selected and measured for 

 colour by Captain Abney, form a perfect contrast, as may readily be 

 seen by placing them together and observing how very nearly com- 

 pletely all light is excluded. 



By simply noting the difference of focus recorded in the certificate 

 between observations made in red and white light, or between observ- 

 ations made in blue and white light (the latter being of far more 

 practical importance), it can at once be told if the lens is or is not 

 well corrected for achromatism. But it would seem desirable, as 

 already remarked, to form an estimate of the actual amount of 

 diffusion produced in the image as a result of any error that may be 

 detected in the chromatic adjustment of the lens. Now there can be 

 no difficulty in determining the size of the disc of radius b'w, for bw 

 has been directly determined by experiment, and, since the cone b'bb' 

 represents the cone of rays of maximum actinic effect, on this disk 

 will be concentrated the bulk of the rays which produce the effect 

 on the photographic plate. But what we want in reality to find is 

 the radius u'w, since that has been shown to represent more accu- 

 rately the radius of the disc of diffusion ; it may, however, be re- 

 marked that no fault can be found on this head with the method of 

 testing, because the probabilities of error are lessened by taking the 

 observation with rays of the maximum actinic effect. With a lens not 

 at all corrected for achromatism the length between the different foci 

 for different coloured rays varies approximately as the difference of 

 the squares of the wave-lengths of the colours in question ; and, taking 

 the wave-lengths as above given, uw will be found to be to bw as 5 to 



