168 Prof. J. D. Everett on the Theory of 



X, denoting the wave-length in the first medium which 

 corresponds to \ in air. This value for y l9 the distance 

 between points or lines which can be barely separated, has 

 been extensively adopted. Helmholtz in the Jubelband of 

 Pogg. Ann. 1874, p. 557 adopts it in the form last written. 

 Abbe calls fa sin a l the numerical aperture of the objective, 

 and adopts the formula wave-length divided by twice the 

 numerical aperture. Drude (Lehrbuch der Optih) adopts it as 

 the limiting distance for oblique illumination, and its double 

 as the limiting distance for direct illumination. 



Microscopic test-objects are not self-luminous like double 

 stars, but are viewed by transmitted light. If no condensing 

 arrangement is employed, the pencil of light sent by a point 

 of the object to the objective consists of rays from different 

 parts of the source, that is, in effect, from different sources. 

 An orthogonal section of such a pencil does not possess the 

 characteristic properties of a wave-front. Different portions 

 of it have no definite relation of phase, and are incapable of 

 mutual interference. Our formulae are therefore no longer 

 applicable. Practically we may regard such an orthogonal 

 section as made up of a number of small parts, each of which 

 is a wave-front, giving by reason of its smallness a very 

 large diffraction image of a point of the object. These 

 separate images of the same point overlap without inter- 

 ference, and as they do not exactly coincide, compose a 

 larger and more blurred image of the point represented. 



The cure for this evil is furnished by employing a con- 

 denser of high quality, to throw upon the part of the object 

 under examination a very sharp image of the source of 

 illumination. If the image were perfectly sharp, each point 

 of the object would get its light from its own special point 

 of the source, and the effect would be to make the object act 

 as if it were self-luminous. Each point of the object would 

 send to the objective a pencil whose orthogonal sections would 

 be true wave-fronts, to which our previous reasoning would 

 be applicable ; so that the diffraction spot which represents a 

 point would have the small size due to the largeness of the 

 entire aperture. 



This appears to me to be the chief benefit conferred by 

 sharply focussing the source on the object ; but it has not so 

 far as I am aware been pointed out by any writer on the 

 microscope hitherto. Abbe in his great paper on microscopic 

 perception (Archiv fiir mikr. Anat. ix. p. 413, 1873) regards 

 the condenser merely from the point of view of geometrical 

 optics, and recommends the use of one which is not achromatic. 

 Microscopic observers long ago ascertained, as an empirical 

 fact, that achromatic condensers gave better results than non- 



