Energy in the Electromagnetic Field. 15 



slightly changed the positions of the maxima and minima. 

 The magnitude of the change depends upon e, which is zero 

 when y = (equation 10), and steadily increases with y to a 

 limiting value of (ka0 z -\- 7r/4) or 7r/4, since lead 5 is negligible 

 over the first few bands when y is sufficiently large. By 

 actual calculation it is found that this limit is practically 

 reached when y is over three times the radius of the cylinder. 

 Under these conditions equations (11) reduce to 



x 2 =y\(4:m-l)/4: (12) 



Formula (12) is identical with Schuster's formula for the 

 case of diffraction of plane waves by a straight edge. 



Returning to equation (7) we see that the intensity of 

 illumination of the successive maxima and minima is given 



b ? Ima^a + yS) 2 ") 



Imin=(l-VS) 2 ) ' 



where S is given by equation (8). The intensity-curve for 

 a plane 5 mm. behind the edge is shown in fig. 2 (c). It 

 will be seen that the ratio of the minima to the maxima is 

 considerably greater than in (a) and (&). Calculation also 

 shows that the visibility of successive fringes in this plane 

 of observation should decrease, though somewhat slowly. 

 For still greater distances from the edge of the cylinder the 

 illumination curves become practically identical with those 

 of the Fresnel type due to a straight edge, the intensity of 

 the reflected rays becoming negligible in comparison with 

 that of the incident and the diffracted rays. The ordinates 

 of the curves (a), (&), (c), (though not the abscissae), have all 

 been drawn to the same scale, and the curves illustrate the 

 tact that the luminosity of the field as a whole decreases as 

 we recede from the cylinder. 



3. Photometric Study of the Field. 



The formulae obtained above have been tested by two 

 independent methods, (1) by photometric comparison of the 

 maxima and minima of illumination, and (2) by deter- 

 mination of their relative positions. 



A small polished cylinder of glass, of about 1*5 cm. radius, 

 was used. It was mounted on one of the stands of an 

 optical bench, and a microscope objective mounted on another 

 of those stands was brought up close to the cylinder. Light 

 from a narrow slit was passed through a collimating lens and 

 was allowed to fall grazingly on the cylinder. The field 

 was viewed through a micrometer eyepiece placed at a 

 distance behind the objective. By moving the cylinder 



