PHYSICS 537 



that time there have been a large number of researches, theoreti- 

 cal and experimental, on this question, not only in connection 

 with gaseous and vaporous media, but also for solids and liquids. 

 It is proposed in this note briefly to review the present situation. 

 When light passes through a gaseous medium, each molecule 

 becomes a centre of secondary disturbance. In the direction 

 of propagation of the primary wave, the secondary waves 

 emitted by all the molecules in a given layer are in identical 

 phase, although the phases will be retarded behind the phase 

 of the primary wave by an amount which corresponds to the 

 retardation associated with the passage of light through a 

 refractive medium, and can be related to the index of refraction 

 of the gas. In other directions than that of the primary wave, 

 the phases of the scattered waves do not stand in an invariable 

 relation to one another, since the molecules are distributed at 

 random in the volume. Hence, to find the intensity of the 

 scattered light in any direction we sum, not the amplitudes of 

 the waves scattered by individual molecules, but the squares 

 of the amplitudes, or the intensities. By mathematical reason- 

 ing we find in this way a relation between the intensity of the 

 emerging beam deprived of the scattered light and the index of 

 refraction. In fact the beam is reduced in intensity after 

 traversing a distance x through the gas in the ratio e"^, where 



«=32 7r'(/^-i)V3NV. 



/I, is the index of refraction, \ the wave-length, and there are 

 N molecules per unit volume. 



This formula of Rayleigh's has stood the test of experimental 

 observation very well over wide ranges of pressure and density. 

 The method of deriving it has been criticised by Larmor, but 

 it would appear that the criticisms can be well met. Rayleigh's 

 original memoir appeared in vol. xlvii of the Phil, Mag. (1899), 

 and fairly recent papers by Rayleigh and Larmor discussing 

 the theoretical points raised can be found in the Phil. Mag., 

 December 191 8 and January 191 9. It would seem that the 

 assumption of random phases for the light scattered from 

 individual molecules (which is necessary if we are to add in- 

 tensities and not amplitudes) is justifiable if the probability 

 that a given molecule is found within a small specified volume 

 is independent of the presence of any other molecules, i.e. 

 if the volume occupied by the gas is a sufficiently large multiple 

 of the total volume of the molecules— in short, if there is reason- 

 able agreement with Boyle's law. 



According to Lord Rayleigh not only should the intensity 

 of the scattered light be proportional to (//. - i)', but the light 

 scattered in a direction perpendicular to the incident beam 

 should be completely polarised. As regards the intensity. 



