414 Prof. Rowland on Spherical Waves of Light 



fracted light around a very small orifice will be proportional 



to (l + cosS) 2 sin 2 <£. 



The presence of the term in <f> indicates that the intensity of 

 the diffracted light at a given point varies as one rotates the 

 plane of polarization. In ordinary light the intensity varies 



as l+cos 2 S. 



Stokes and others have attempted to determine the relation 

 between the plane of polarization and the direction of dis- 

 placement by means of the first relation ; but they have not 

 agreed with one another, and this want of agreement has 

 usually been assigned to the fact that the gratings used have 

 been ruled on glass rather than in free space, as the equations 

 indicate. 



On examining this question from the point of view of 

 the electro-magnetic theory of light, I have been led to 

 entirely different results. But as the elastic-solid theory for 

 an incompressible solid must agree with the electro-magnetic 

 theory, I have been led to examine the theory of Stokes, and 

 believe that I have now discovered an error, which, if it were 

 corrected, would lead to my result. 



The results which I reach are as follows : — 



First. The plane of polarization of the diffracted light is 

 determined as follows : — Draw a sphere around the orifice, 

 and mark the point on the sphere where the incident light 

 enters it. Through this point draw circles on the sphere whose 

 planes are parallel to the electrostatic displacement at the 

 orifice, and these circles give the direction of the electrostatic 

 disturbance in the diffracted beam. Repeat the same for the 

 magnetic disturbance, which is at right angles to the electrical 

 disturbance, and the circles indicate the direction of the mag- 

 netic disturbance in the diffracted beam. These two systems 

 of circles are orthogonal to one another, as they should be. 



Second. The intensity of the diffracted light around a very 

 small orifice is symmetrical around the incident ray prolonged, 

 and is proportional to 



(1 + cosS) 2 , 



and the same expression applies to ordinary light. 



Although the theory of diffraction forms the most inter- 

 esting part of my paper, yet I have thought it worth while 

 to treat of the general problem of spherical waves of light, 

 which I have not seen considered anywhere else. The method 

 is similar to that used in sound and in the theory of heat- 

 conduction. 



