418 Transactions of the Society. 



unresolved, may want nothing but enlargement of scale, to be seen 

 fully resolved. 



The second criticism is, that the experiment itself indicates that 

 the limit which Helmholtz thus discovered was a physiological 

 rather than a physical limit of resolving power. For it is to be 

 observed that he reduced the aperture of his eye by nearly one- 

 half, from 3 mm. to 1 • 72 mm., in order to produce " a noticeable 

 deterioration of the image." Proceeding pari passu with the re- 

 duction of aperture there must have been a corresponding increase 

 in the diameter of the antipoint, and no marked physical change 

 would supervene when it reached the dimensions which sensibly 

 modified his retinal picture. It is true, as he says, that if the 

 limit of the discriminating power of the optic nerve be taken at 

 one minute of angle, the smallest separately visible objects would 

 be flanked by separately visible images at just about that distance, 

 which he noted by observation. Thus a noticeable change would 

 occur at this stage in the development of the antipoint ; but it is 

 a change related to the structure of the optic nerve, not of the 

 image, and has therefore no direct bearing on the limit of resolving 

 power in an optical instrument, of which the retina is no com- 

 ponent part. The fact that Helmholtz could reduce the diameter of 

 his pupil from 3 mm. to 2 mm. without detecting any deterioration 

 of the image argues that the normal antipoint of the eye is much 

 too small to affect the apparent resolution of the picture produced 

 on the retiua. 



It is not very clear — at least it is not very clear to me, in 

 reading Helmholtz' paper — what is the inference which he himself 

 proposes to draw from these experiments upon the diminished 

 pupil. But I rather gather that his idea was to find a more accu- 

 rate measure than the mere average diameter of the pupil (3 mm.) 

 for the aperture of the conventional eye upon which to calculate 

 normal magnifying power. He actually says : 



" Calculated by means of equation (12) the diameter of 1 * 89 mm. 

 of the beam received into the eye corresponds for an angle of 180° 

 aperture in the incident beam in air to a magnification of 2C4 * 5 times. 

 For Microscopes with narrower angular aperture the corresponding- 

 magnification would be less. In accordance with this conclusion 

 we find in Hugo v. Mohl's Micrography that amplifications between 

 300 and 400 times yield the best detail; while Harting in his 

 newest Microscopes with very nearly 180° of angular aperture found 

 magnifications of 430 to 450 times the best for the purposes of 

 measurement." 



Yet even so the argument seems very loose. The conformity 

 is not at all strikingly close of Mohl's result, that amplifications of 

 between 300 and 400 times yield the best detail, and of Harting's 

 that 430 to 450 times are the best magnifications for the purposes 

 of measurement, with Helmholtz' conclusions that deterioration of 

 the image sets in when a normal magnifying power is exceeded which 



