Convection of Light in Moving Gases. 449 



moving air conducted by Michelson and Morley that 

 Thomson's value for the convection coefficient could not be 

 correct. 



Wbile, therefore, all the available evidence is strongly in 

 favour of Fresnel's value or, rather, Lorentz's corrected value, 

 at least in the case of solids and liquids, it is highly desirable 

 that it should be confirmed in the case of gases also. A 

 special grant secured from tin* Calcutta University through 

 the kind offices of Sir Asutosh Mookerjee has enabled the 

 writers to undertake this research, and it is proposed to give 

 here a preliminary account of the progress of the work and 

 of the difficulties encountered. 



But before we do so it might be of interest to deduce 

 Fresnel's law for gases from slightly different considerations. 

 The late Lord Ravleigh * in discussing the scattering of 

 light by small particles and in referring the blue colour 

 of the sky to the molecules of air, deduced an expression for 

 the refractive index of the gas in terms of the molecular 

 constants. Following the same line of argument, we may 

 also deduce on Doppler's Principle an expression for the 

 altered refractive index when the air molecules are set in 

 motion with a constant velocity v in a definite direction. 

 On this principle, the incident light of wave-length A, is 

 received by the molecules as light of wave-length 



1 



H 



where b is the velocity of light in the medium without these 

 scattering molecules. Thus, in the notation of Lord Ravleigh, 

 the expression for the vibration scattered from the molecule 

 in a direction making an angle 6 with that of the primary 

 vibration is 



D'-D 77-T/. vY . n 2 



(l^|)%ih*cos£(fc-r). 



And considering the particles which occupy a thin stratum 

 dx perpendicular to the primary ray <r, the resultant, at a 

 point on the incident ray, of all the secondary vibrations 

 which issue from this stratum is 



" dj: ) x -D-;^?( 1 -6.) ^-{bt^ry^rdr 



* Sc. Papers, vol. iv. p. 395. 

 Phil. Mag. S. 6. Vol. 43. No. tbb. March 1922. 2 G 



