ABBE'S MODE OF TESTING 385 



the focal plane of the image at the widest possible angle. As many 

 distinct images will be perceived as there may be zones or portions of 

 the front face of the objective put in operation by separate pencils of 

 light. If the objective be perfect all these images should blend with 

 one setting of focus into a single clear, colourless picture. Such a 

 fusion of images into one is, however, prevented by faults of the 

 image-forming process, which (so far as they arise from spherical 

 aberration) do not allow this coincidence of several images from 

 different parts of the field to take place at the 

 same time, and (so far as they arise from dis- 

 persion of colour) produce coloured fringes 

 on the edges bordering the dark and light 

 lines of the test-object and the edges of each 

 separate image, as also of the corresponding FIG. 329. FIG. 330 

 coincident images in other parts of the field. 



It is to be borne in mind that the errors which are apparent with 

 two or three such pencils of light must necessarily be multiplied 

 when the whole area of an objective of faulty construction is in 

 action. This would appear to us to be the strongest reason for 

 utilising the whole area, because what we are seeking is the defects 

 the errors of the objective and to make these as plain as possible 

 is a sine qua non. Dr. Abbe proceeds, however, to consider 



2. The means by which such isolated pencils can be obtained. 



As a special illuminating apparatus, the condenser of Professor 

 Abbe is recommended, or even a hemispherical lens. But we are 

 convinced that the illuminating apparatus should be as nearly apla- 

 natic as it can be. This is certainly not true of Abbe's chromatic 

 condenser or a hemispherical lens. The reason is obvious : the 

 spherical aberration wholly prevents the rays passing through the 

 holes in the diaphragm from being focussed on the object the 

 silvered plate of lines at the same time. In the lower focal plane 

 of the illuminating lens must be fitted diaphragms (easily made of 

 blackened cardboard) pierced with two or three openings of such a 

 size that the images, as formed by the objective, may occupy a 

 fourth or sixth part of the diameter of the whole aperture (i.e. of the 

 field seen when looking down the tube of the instrument, after re- 

 moving the ocular, upon the objective image). The required size 

 of these holes, which depends, first, on the focal length of the illumi- 

 nating lens, and, secondly, on the aperture of the objective, may be 

 thus found. A test-object being first sharply focussed, card dia- 

 phragms having holes of various sizes (two or three of the same size 

 in each card) must be tried until one size is found, the image of which 

 in the posterior focal plane of the objective shall be about a fourth 

 to a sixth part of the diameter of the field of the objective. Holes 

 having the dimensions thus experimentally found to give the required 

 size of image must then be pierced in a card, in such a position as 

 will produce images situate in the field, as shown by figs. 329 and 330 ; 

 the card is then fixed in its place below the condenser. We are, 

 however, strongly inclined to believe, partly from experiment, that 

 better results would be obtained by putting sections of annular slits 

 at the back of the objective. If the condenser be fitted so as to 



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