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XXXII. A Diffraction Problem. Supplementary Note. 

 By R. Hargreaves*. 



A CORRESPONDENT writes with reference to my 

 paper in the August number, " Your formula in terms 

 of one potential applies I presume to electric waves as well 

 as sound waves, when oblique/' The formula does apply 

 to electric waves ; the function which for sound is a poten- 

 tial, is for electric waves a stream function. Also where 

 the incident wave implies a third dimension, something 

 more than the normal use of a stream function is involved. 



As no reference to electric waves was made in the paper, 

 it may be of advantage to supplement it by showing how 

 the electromagnetic quantities are derived from the func- 

 tion, and what is the polarization in each case. The plane of 

 polarization is, in general, subject to deflexion : a test could 

 therefore be made by the use of short electric waves and a 

 metallic screen f. 



§1. If independence of z is assumed in Maxwell's equa- 

 tions of types 



and 



1 BX 



v a* 



1 ba 

 Y~dt 



Be 



by 



BY 

 bz 



B& 

 bz 



BZ 



(1) 



GO 



the first two of (1) are equivalent to expressions for cXY in 

 terms of -v|r, viz., 



c=^, X=|t Y=-P; Z = 0, « = 4 = 0. (3a) 



The third equation of (2) then gives 



l B *± _ BV B^ 



V^ B* 2 ~ B* 2 + by 2 ' 



w 



The components Zab are unconnected with <?XY, and may 



* Communicated by the Author. 



f My correspondent is Sir Joseph Larnior, to whom I am indebted for 

 the suggestion of this experimental test, as well as for the reminder that 

 it may be of service to the physicist to make an explicit statement on 

 the electrical problem. 



