ON APERTURE AND DEFINITION OF MICROSCOPE OBJECT GLASS. 449 



angles of incidence) moderate diffraction. '^ Definition," therefore, 

 instead of improving ''with the chord of the aperture," depends^ 

 rather upon a compromise between magnifying power and aperture 

 which shall give the greatest brightness of image, compatible with 

 good focussing function and least diffraction. The first and most 

 important condition under which it is possible to maintain good 

 definition is the counteraction of that spherical aberration which 

 increases with power and aperture of a lens- system, by the proper 

 calculation of curves and refraction of its constituent parts, and 

 compensation for residual aberrations. And the difficulty of con- 

 struction and compensation is increased with every addition ta 

 aperture beyond 110 '^^S 



That the physical limit of resolution, computed from any formula 

 based on such assumed perfection of the microscope as is needed 

 to realise every theoretical possibility, must be in excess of what 

 the eye itself can perform, will be obvious to all who have studied 

 physiological optics. A few observations on this part of the subject 

 will be appended to the present paper, but attention may here be 

 directed to the fact that far more minute details may be delineated 

 in a photograph than on the retina. Undulations of shorter wave 

 length than will affect the retinal nerves can act powerfully upon 

 photograph materials, so that chemical rays delineate lines too 

 closely approximate for the eye to distinguish when looking at the 

 same object through the same objective. Here then the resolution 

 is entirely physical, and the physiological limit of eye performance is 

 surpassed. This fact is indeed but an extension of the principle 

 that " resolution " is associated with the different wave length of 



* It is true that lenses of equal magnifying power, but different aperture, 

 perform very unequally, and th.at definition will often be best in the image 

 formed by the objective of larger angular aperture (excepting cases of 

 extreme angle), provided that correction of spherical aberration be perfect for 

 those parts of the objective through which pencils of large divergence angle 

 pass, so that their points shaU not become dispersion circles. But mere 

 aperture, without suitable construction, confers no defining power. In 

 Professor Helmholtz's essay the mathematical demonstration is based on the 

 assumption of a perfectly constructed immersion lens, where, as Abbe has con- 

 clusively shewn, the correction of spherical aberration is not attended with such 

 difficulties as is the case with large angled " dry " objectives. 



