DIFFRACTION PHENOMENA 63 



directly through the aperture interfere with those passing obliquely 

 at the edge of the disc and produce, at certain distances, a dark 

 spot, at other distances increased brightness, on that part of the 

 shadow which is opposite the aperture in the disc ; so that light is 

 supplanted by darkness, and darkness changed to light, by the discord 

 or concord of the luminous waves. 



Independently of all experiment, the first principles of undulatory 

 optics lead to these experimental conclusions. The laws of recti- 

 linear propagation of the luminous rays of reflection and refraction 

 are not absolute laws. They arise from, and depend upon, a certain 

 relation between the wave-lengths and the absolute dimensions of 

 the objects by which the waves are intercepted, or reflected, or 

 refracted. 



Taking as illustrative the waves of soitnJ, an acoustic shadow i.s 

 only produced if the obstacle be many times greater than the length 

 of the sound-waves. If the obstacle is reduced, the waves pass com- 

 pletely round it and there is no shadow, or if the notes are of higher 

 pitch, so that the waves are reduced, a smaller obstacle than before 

 will produce the shadow. In the case of light there are similar 

 phenomena. If the obstacles to the passage of light be large in 

 comparison with the wave-lengths, shadow effects result ; but if the 

 linear dimensions of objects are reduced to small multiples of the 

 wave-lengths of light, all shadows or similar effects of solidity must 

 cease. As in the instances given above, light and dark, or maxima 

 and minima of luminosity, interchange their normal positions by 

 harmony or disharmony of luminous waves. 



It is then by means of diffraction phenomena that Abbe is 

 enabled to explain the formation of the images of objects containing 

 delicate stria? or structure, and requiring large apertures for their 

 complete or approximate delineation. In the interests of this ex- 

 position we must here for a moment diverge on slightly personal 

 grounds. It has been the good fortune of the present editor to obtain 

 the courteous consent of Dr. Abbe to read and criticise the whole 

 of the present chapter; however careful and earnest a student of 

 such complex and original work as Dr. Abbe has done and recorded 

 in German and English during the last thirty years or more, it is 

 impossible to be wholly satisfied with the most sympathetic and 

 sincere desire to give such work a popular form unless it should 

 have been perused and accepted by the author. Dr. Abbe has read 

 the entire chapter, and, with many generous words besides, relieves 

 the editor in his consciousness of great responsibility by saving that 

 he distinctly approves of the 'lively interest and care which (the 

 present editor) has bestowed on the exposition of his (Dr. AbbeV) 

 views,' and that he feels ' the greatest satisfaction, in seeing (his) 

 views represented ... so extensively and intensively.' 



But beyond this, an original worker like Dr. Abbe would almost 

 inevitably find, in the course of years, reason for slight verbal and 

 other more serious modifications of his inferences, explanations, and 

 views; and the editor has great satisfaction in being able to put 

 these modifications where they occur, with the approval of Dr. Ablie. 

 In the expositions of Dr. Abbe's views on the diffraction theory 



