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SUMMARY OF CURRENT RESEARCHES RELATING TO 



of a small particle. But how is be to gain the practice to explain 

 diffraction phenomena in objects of complicated structure, and which he 

 cannot, like a drop of mastic, reproduce artificially? It is scarcely 

 possible either as the result of practice, or on the basis of theoretical 

 treatment, to arrive at a clear explanation of all the images produced 

 by different focusing, thickness of fibre, illumination, &c. The conditions 

 are too complicated, but I will endeavour to make the essential points 

 more clear. 



Let a b (fig. 33) be the boundary of a muscle-fibre, and m g f n the 

 visible portion of a disc of the same which has a different refractive 

 index from that of the next disc. If A is a point outside the fibre, the 

 intensity of vibration at A of a plane wave of light which traverses a b 

 is, according to Iluyghcns's principle of the elementary zones of spherical 



WL--b 



waves, the result of the interference of g h with q f, of f g with ef, of 

 ef with d e, of de with cd, and of similar portions on the other side 

 which reach A. If the path from g h to A is a half wave-length smaller 

 than that from h i to A, and similarly in the romaining parts, the result 

 of the interference is the extinction of the portion of the wave which 

 is the more remote from A g, and the rectilinear propagation of the ray 

 g A. The shaded portions may represent those parts where wave-troughs 

 reach A at the same moment at which wave-crests arrive from the 

 unshaded parts. If the pencils whose inclination is that of I A, or of 

 the rays beyond I A which are not represented in the figure, do not 

 enter the Microscope, then the above-mentioned case of an incomplete 

 image is realized, which is of course in the present example without 

 signification, since no part of the structure is included. 



If the cylindrical form of the fibre is neglected this method of treat- 

 ment may be applied to any point g of a line which is perpendicular to 

 the axis of the fibre, and Huyghens's elementary zones become elementary 

 stripes parallel to this line. 



Consider next the case (marked B in fig. 33) in which the point g falls 

 on the boundary between two discs of different index. Let the shaded 

 parts represent as before the wave-troughs which reach B, and the 



