Regular Reflexion of Light hy Gas Molecules. 91 



by (13), and the refractivity (as far as the first order of 

 xV 1 , XP' 1 ) is 



^ 2 u -1 = 7r^L'~ 3 sin 2y = v\ B sin 2y/8ir 2 , . . (40) 



while the coefficient of extinction, to the same order of 

 approximation, is 



^ 1 = 27T^f" 2 sin 2 7 = ^A, 2 sin 2 7/277. . . . (11) 



36. Up to this point the relations obtained belong to two 

 classes : those which are peculiar to the case of simple aerial 

 vibrators excited by sound-waves, and those which are true 

 for swarms of similar vibrators of any type excited by plane- 

 waves of corresponding type ; this latter, more general, 

 class comprising the results" of § § 17-22, 28-31, 33, 31. The 

 special features of the optical (or electromagnetic) problem 

 remain to be considered. 



37. In dealing with the excitation of an electromagnetic 

 secondary vibrator by plane-waves, we shall have to apply 

 Poynting's theorem, involving the vector-product of two 

 vectors, so that the use of imaginary exponents is no longer 

 admissible : only real quantities must appear in our equa- 

 tions *. The state of things close to a radiating atom is as 

 yet involved in obscurity, and it will be well to avoid all 

 assumptions as to intra-atomic conditions, the activity of a 

 radiating atom being specified by the expression for the 

 disturbance which it produces at a distance. The typical 

 radiator, situated at the origin, and vibrating periodically in 

 a mode symmetrical with respect to the axis of z, produces 

 at distant points a variable vector-potential 



a' = 0, 0, Cr- 1 cos (pt-vr-y); . . . (12) 



where as before p/^ir is the frequency and 2tt/v the wave- 

 length, while r is the distance from the vibrator to the point 

 at which a' is measured f. For the magnetic vector h' 



* In the simpler case of an aerial resonator, Lord Rayleigh avoids the 

 necessity for evaluating the time-average of the product pressure x 

 suilace-integral-of-normal-velocity ; instead he introduces the condition 

 that the two factors of this product (each represented by a complex 

 exponential) must be in quadrature. The present case is rather more 

 complicated, and a more laborious treatment seems to be required. 



+ The Ileaviside system of units, as adopted by Lorentz and other 

 authorities, is here used ; the relations of the various electromagnetic 

 quantities being- as stated. It may be observed at once that our tinal 

 equations, dealing as they do with relative amplitudes or energies of 

 incident, transmitted, reflected, and scattered radiation, will remain 

 unaffected by any change in the uuits adopted for electromagnetic 

 measurements. The only formula) required are those belonging to the 

 free aether, for the influence of any matter which may be present takes 

 the form of secondary radiations, which are assumed throughout to have 

 the same frequency as the primary waves. 



