10 Lord Rayleigh on Reflexion from Licjuid Surfaces 



the light by the introduction of a parallel plate of quartz. 

 With the aid of this the analysing nicol could be set, and 

 then the mica. If, with the quartz plate in action, the spot 

 is dark and central, all is well adjusted. On removal of the 

 quartz, the band is now seen in full perfection. 



One of the difficulties in these experiments lay in the 

 extreme sensitiveness of the liquid surfaces to tremor, a sen- 

 sitiveness aggravated by the perfect cleanliness required. It 

 had been thought that it would suffice to mount the apparatus 

 upon a shelf attached to the walls of the building, and isolated 

 from the floor* But it appeared that the slightest touch upon 

 the tangent-screw of the divided circle, such as it is necessary 

 to make at the moment of observation, entailed a most dis- 

 tracting tremor. A remedy was found in suspending the dish 

 containing the liquid under examination independently from 

 the roof. 



The work has been greatly retarded by want of sunshine. 

 In order to be more independent, I tried to work at the Royal 

 Institution by the electric light. But it appeared impossible 

 to make any observations of A*alue on account of the tremor 

 by which London is pervaded. Moreover the arc-light is 

 very inferior to sunshine for such a purpose. 



The theory of the experiment is as follows. According to 

 Fresnel's formulae the ratios of the reflected to the incident 

 vibrations are, for the two planes of polarization, T and S ; 

 in which the reality of T and S indicates that there is no 

 change of phase in reflexion (other than 180 c ). The ellip- 

 ticity is represented by the addition to T of iM, where M is 

 small and i= \/( — l). Thus if the incident light be polarized 

 in the plane making an angle a with the principal planes, the 

 reflected vibrations may be represented by 



(T-f-iM)cosa, Ssina. 



By the action of the mica, or other compensator, a relative 

 change of phase y is introduced. This is represented by 

 writing for $ sin a, 



S sin a (cos y + i sin 7). 



Thus the vibration transmitted by the analyser, set at angle ft, 

 is 



cos a cos J3 (T + iM) + S sin a sin ft (cos y + i sin 7) ; 



and the intensity of this is 



(T cos « cos + S sin a sin /3 cos 7) 2 



+ (M cos a cos /3 + S sin « sin /3 sin 7) 2 . . (10) 



