32 The Flow of Energy in the Electromagnetic Field. 



according as the plane of observation is in front of the 

 cylindrical "edge" or behind it. x, y are the coordinates of 

 any point, the origin being the " edge " of the cylinder, e is 

 a small angle which for large values of y becomes equal to 7r/4. 



(b) The visibility of the fringes varies in an interesting 

 manner with the position of the part of the field under 

 observation. It is practically constant over the entire plane 

 of observation when this coincides with the plane passing 

 through the (l edge " ; bat it falls off when it is moved 

 farther away from the source of light, the decrease being 

 greatest for the regions farthest from the surface. When 

 the part of the field under observation is between the "edge" 

 and the source of light, the visibilility of the fringes reaches 

 the maximum value at the surface of the cylinder, falling 

 off slowly as we recede from it. 



(c) The loci of maxima and minima of illumination are 

 given by r6 2 —m\j^ and the " mean lines of flow" of energy 

 are given by r0 = const, and are for small values of 6 less 

 inclined to the direction of the incident rays than the former 

 set of curves. The actual lines of flow crinkle about these 

 mean lines ; the " wave-length " of the crinkles increases as 

 we move along the direction of the incident rays, and 

 decreases as we move in a direction at right angles to it 

 away from the cylinder. The "amplitude" of the crinkles 

 decreases as r and 6 increase, and vanishes at sufficiently 

 large distances from the cylinder. A good conception of 

 the actual phenomena is obtained, if we imagine energy as 

 flowing through tubes which widen and contract periodically, 

 the widened parts of successive tubes lying on the loci of 

 minimum illumination, and the contracted parts on the loci 

 of maximum illumination (see fig. 6). When the radius of 

 the cylinder is very small, the results are practically identical 

 with those obtained in the case of diffraction by a straight 

 edge. 



No reference has so far been made to the phenomena 

 noticed within the region of the geometrical shadow of the 

 cylinder. The writer has made some preliminary obser- 

 vations on this subject, and hopes to continue the work, 

 which might prove of interest m relation to the general 

 problem of the diffraction of electromagnetic waves by 

 cylindrical or spherical surfaces of large radius. 



In conclusion, the writer wishes to express his best thanks 

 to Prof. C. Y. Raman, who suggested the investigation and 

 iook much interest in its progress. 



Calcutta, 

 .November 15, 1917. 



