ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 365 



The well-known paper, Contributions to the, Theory of the Microscope 

 and of Microscopic Perception, which forms the basis of his work, is here 

 reprinted, and it will be interesting to consider some of the points 

 it raises. 



But first let us contrast what is now possible so far as achromatic 

 correction is concerned with what was possible, say twenty years ago. 

 In those days the ordinary flint and crown glasses only were available. 

 In the case of a telescope object glass with a focal length of one metre 

 for the D line, the variation in focal length will, with such glasses, 

 amount to 1 ■ 4 mm. for A' and 2 ■ 2 mm. for G-'. In an object glass 

 using modern glass, such as that designed by Mr. H. D. Taylor, these 

 errors are reduced respectively to — O'l mm. and +0*3 mm. 



These figures are enough to show how much the optician owes to 

 the art of the glass maker. 



Turning now to some theoretical matters connected with the micro- 

 scope which are dealt with by Abbe in his papers, let us consider first 

 the term " numerical aperture " in its relation to the resolving power of 

 the instrument. We owe to Abbe the introduction of this term, and the 

 realisation of its importance as defining, in certain circumstances, the 

 resolving power of the instrument. By numerical aperture is meant 

 the value of the quantity //, sin a, where //. is the refractive index of the 

 medium in which the object is placed, 2a the vertical angle of the cone 

 subtended at the object glass by the point in which the axis of the 

 instrument meets the object. Let us suppose, then, that an object is on 

 the stage viewed by transmitted light, and to simplify matters let us 

 suppose the source of light at some distance. 



Then, according to Abbe* and his followers, in considering the image 

 formed in the focal plane of the eye-piece, we are not to start from the 

 object as a self-luminous source and consider where the image of such a 

 source would be if formed by the laws of geometrical optics ; we are to 

 start from the source itself, to consider its image formed in the focal 

 plane of the object-glass, and to treat this image as a self-luminous 

 source of light in the microscope tube from which arises the image we see. 



If the object be small, the focal image will be modified by diffraction 

 due to the object, and according to the views enunciated in the paper 

 before us, it is on the nature of the diffraction images and the number 

 of them which are formed that the definition depends. 



We will return later to the question whether it is necessary thus to 

 consider our problem. 



At present let us develop it and examine whether it affords us a 

 satisfactory solution of the problem of resolving power. 



Suppose, now, the Microscope has been focussed on some object on 

 the stage and then this object has been removed ; the parallel rays from 

 the source are brought to a focus in the focal plane of the object glass, 

 forming there a circular patch of light ; rays diverge from each point of 

 this, and reaching the eye produce the sensation of a uniform luminous 

 field. 



Now let the field in the focal plane be limited by diaphragms 



* It was stated recently by Dr. Czapski (Proc. K.M.S. August, 1903, p. 569) 

 that it would be a mistake to suppose that Prof. Abbe had merely given a grating 

 theory of the Microscope ; he has treated the matter more fully. 



June 15th, 1904 2 c 



