94 Dr. C. V. Burton on the Scattering and 



phase-lag 7 depends- on the "tuning"; the response being 

 greatest when 7= ~, that is, whence there is resonance. 



The vibrator or radiator of type II. is specified in § 42. 



41. Consider next a multitude of vibrators of type I., all 

 ]ying in the plane of yz, and within a square whose sides are 

 formed by the lines y=+b,z=+b. It these vibrators are 

 distributed with complete irregularity, and are all vibrating 

 with the same amplitude and in the same phase, the vibra- 

 tions of each being symmetrical about an axis parallel to the 

 axis of z, the method of §§ 4-7 can be applied to determine 

 the ratio of the plane-wave energy propagated (say) in the 

 direction of ^-decreasing to the energy irregularly scattered. 

 The notation need not be changed, if a is now understood to 

 be the amplitude of the electric vector due to a sino-le 

 vibrator at a point distant /from it, the direction of / being 

 perpendicular to the ^-axis. The expression a 2 b 2 a 2 \ 2 f 2 

 represents as before, on an arbitrary scale, the energy-flux 

 in the diffraction pattern ; while the average value of sin 2 d 

 enters as a new factor into the corresponding expression 

 47rcr6 2 ay 2 av . sin 2 6 for the scattered energy ; 6 being the 

 co-latitude of any point on a complete spherical surface. 

 The average value of sin 2 6 is §, and hence the plane-wave 

 energy, reckoned in one direction only, bears to the scattered 

 energy the ratio 



[TypeL] 3<7\ 2 /8tt = 3tt<7/2i/ 2 (50) 



42. A radiator of type II. has an axis fixed in it, with 

 respect to which its vibrations are understood to be always 

 symmetrical. Let such a radiator be exposed to the action 

 of a primary plane-polarized disturbance, with electric vector 

 parallel to the e-axis, the angle <p between the axis of the 

 radiator and the £-axis being in general finite. The ampli- 

 tude of vibration will be only cos <j> times as great as if the 

 two directions had agreed ; and we can, moreover, resolve 

 the secondary disturbance into two components : one with 

 electric vector parallel to the plane of xy, the other with 

 electric vector parallel to the axis of z. The amplitude of 

 this latter component is only cos 2 (/> times as great as if 

 <f) had been zero. Let the problem of § 41 be now modified 

 by substituting secondary radiators of type II. for those of 

 type L, the axes of the radiators being oriented indiscrimi- 

 nately ; and suppose that plane-polarized plane-waves such 

 as those represented by (45) are incident upon the sheet of 

 secondary radiators. Then evidently the only regular waves 



