132 SUMMARY OF CURRENT RESEARCHES RELATING TO 



basis of tlie progress of tlie Microscope in the last forty years), is 

 characterized by the circumstance that by this form of construction 

 the refractive action of the first spherical surface of a system may be 

 obtained, either free from any spherical aberration, or with a very 

 harmless kind of aberration, which admits of exact correction at the 

 upper parts of the system. But there remains still a considerable 

 aberration aifecting the pencils before they reach the spherical surface 

 on their passage from the radiant to the medium of the front lens. 

 In the ordinary case of a crown front this aberration depends solely 

 on the thickness of the layer of deviating refractive index (air, water, 

 &c.), by which the pencils are admitted, and on the difference, defect 

 or excess, of the refractive index of this layer from the refractive 

 index of crown glass, i. e. on the working distance and on the 

 prescribed working medium of the system. In high and even 

 moderate powers working distance must always be a perceptible 

 fraction of the focal length. When an objective works through air, 

 and in less degree when it works through water or glycerine, the 

 aberration in front bears a considerable proportion to the total 

 sjiherical aberration occurring within the system, and in the case of a 

 wide-angled lens it is by far the most obnoxious part, for these two 

 reasons : because it affects the cone of rays where it has its maximum 

 angular extension ; and because every residual passes to the micro- 

 scopical image with the total amplification of the objective. 



Owing to the former circumstance the anterior aberration is 

 subjected to a very disproportionate increase from the axis to the 

 external parts of the cone as soon as we deal with wide apertures. 

 Whilst in the case of small angles the spherical aberration may be 

 expressed with sufficient approximation by a single term, varying with 

 the square of the inclination to the axis, the anterior aberration of a 

 wide-angled system is composed of many terms varying with the 

 successive even powers of the angle, all of which up to the eighth 

 and tenth power acquire considerable values in respect to the most 

 oblique rays. An aberration effect, the components of which are so 

 very disproportionate, cannot be exactly balanced by opposite 

 (negative) aben-ation at the upper surfaces of the system where the 

 pencils are contracted to much narrower angles, for these narrower 

 pencils do not admit sufficiently large terms or components increasing 

 by the eighth or tenth powers of the angle. The correction of the 

 anterior aberration must therefore be effected by a rather coarse method, 

 balancing the higher terms by an excess of lower terms of opposite 

 aberration at the posterior lenses. This method, of course, cannot 

 afford a uniform correction of the whole pencil from the axis to the 

 marginal rays ; there will always remain an uncorrected residuum 

 which rapidly increases with increasing aperture, and which appears 

 in the image amplified by the total system as has been indicated 

 above. 



This residuum of anterior aberration, which is incapable of correc- 

 tion, and the regular chromatic difference of spherical aberration, 

 are the two principal difficulties attendant upon very large aperture 

 angles. Any non-homogeneous working medium (air, water, &c.), being 



