of Refraction, Reflexion, and Extinction. 273 



which makes the rate of transmission a maximum for 

 •directions contained in the equatorial plane and zero along 

 the (positive or negative) direction of the axis. The amount 

 which crosses the area of S in unit time is — § <?r 2 BC. 



§ 2. To put our results in a form suitable for use in 

 further deductions, we follow a well-known method of 

 procedure, due to Rowland and Hertz. We begin by 



assuming 



iAW 

 S$r( r ^ t } = _ i ^_ ( :in{t-ar-bzo + q)^ . . . . (1) 



I 

 w 1 



here n is the frequency of transmitted vibrations and />, 

 A (2) , and q are new constants, characteristic of the secondary 

 radiation. Evidently (1) is an admissible solution. Let us 

 first consider the part of the field that lies nearest to the 

 vibrator; in this region anr may be supposed to be a very 

 small fraction and (2), § 1, reduces to 



E< 2 >=Vdiv¥ (2) 



In order to write out the full expression take (5), § 1, and 

 substitute from (1) above. If we write 



L=-iAWei»(t-^o+<!)l, .... (3) 



the resulting formula, holding true in the immediate proximity 

 of the vibrator, is as follows : 



E«)=Vs(l.v(J)); .... (4) 



and from this we conclude that the electric moment of the 

 vibrator is correctly represented by the vector L localized in 

 the axis 1. 



Reverting now to the general case when M(#, y, z) is 

 an arbitrary point, situated anywhere in the field of the 

 vibrator, we propose to calculate the values of the quantities 

 A, B, C on which, as we have seen, the determination of the 

 secondary field ultimately depends. Using R to denote 1/anr 

 we easily deduce 



rt 2„2A(2) 



+ A= — 6^- ar -^o+9){(i_3R'-')/ + 3R} ; . (5) 



+ B = Ci y Ai2) e in(f-ar-bz 0+q )f (1 - Rg) / + R } , . . (6) 

 r 



_ c= a 2 n 2 A< 2 € ^-ar-^ +g)|R + {| ( 7 ) 



