26 REPORT — 1841. 



Results of some Investigations on the Phcenomena of Tliin Plates in Polarized 

 Light. By the Rev. Professor Lloyd, F.R.S. 



Professor Lloyd stated, that his attention had been drawn to this subject by a 

 letter which he had recently received from Sir David Brewster, describing a large 

 class of hitherto unobserved phsenomena. Sir David Brewster having expressed his 

 desire, in this letter, to know whether the wave-theory could furnish an explanation 

 of the facts which he had observed. Prof. Lloyd was thus led to undertake the inves- 

 tigation which formed the subject of the present communication. 



Mr. Airy had long since inferred, from a consideration of the form of Fresnel's 

 expression for the intensity of reflected light, that when light, polarized perpendicu- 

 larly to the plain of incidence, was incident upon a thin plate bounded by media of 

 unequal refractive powers, a remarkable change in the reflected light should take 

 place, when the angle of incidence was intermediate to the polarizing angles of the 

 two surfaces of the plate. This theoretical anticipation was fully verified by experi- 

 ment. When a lens of low refracting power was laid upon a plate of high refracting 

 power, the rings which were formed appeared with a hlack centre, when the angle of 

 incidence was less than the polarizing angle of the low refracting substance, or 

 greater than the polarizing angle of the high refracting substance ; while, when the 

 incidence was intermediate to these two angles, the rings were white-centred, and the 

 whole system was complementary to what it had been before. At the polarizing angle 

 itself the rings disappeared, there being no light reflected from one of the surfaces 

 of the plate, and therefore no interference. 



The examination of this subject has recently been resumed by Sir David Brewster ; 

 and he has repeated the experiments of Mr. Airy in a more general form, the in- 

 cident Wghth^mg polarized in any plane. He has thus been led to many new results. 

 The rings are found to disappear under circumstances in which light is reflected from 

 hoth surfaces of the plate ; and there are many remarkable peculiarities in the transi- 

 tion of the rings into the complementary system. 



It was to the theoretical explanation of these phasnomena that Prof. Lloyd now 

 invited the attention of the Section. In the conduct of the investigation he has 

 generalized the methods followed by M. Poisson and Mr. Airy on the same subject. 

 The incident vibration being resolved into two, one in the plane of incidence, and 

 the other in the perpendicular plane, each portion will give rise to an infinite series 

 of reflected vibrations, into which it is subdivided at the bounding surfaces of the 

 plate. The expression of the resultant intensity, for each portion, being then de- 

 duced, the actual intensity of the reflected beam is the sum of these intensities ; 

 and it is found that the part dependent on the phase will vanish, and therefore the 

 rings disappear, when the plane of polarization is connected with the incidence of 

 the following formula : — 



2 _ cos (6 - 6') cos {ff — ff') 

 '^ ~" cos {6+ $') cos {&' + n ' 

 in which d is the angle of incidence on the first surface ; 6' the angle of refraction at 

 first surface, or the angle of incidence on second ; and 6" the angle of refraction at 

 second surface. 



On Simultaneous Changes of the Magnetic Elements at Different Stations. 

 By the Rev. Professor Lloyd, F.R.S. 



Professor Lloyd laid upon the table of the Section a series of curves prepared by 

 Lieut. Riddell, representing the simultaneous changes of the magnetical elements, 

 observed at Toronto, Dublin, Brussels, Prague, Milan, St. Helena, and Van Diemen's 

 Land, on the 29th of May and 29th of August 1840. 



He said, that one of the chief objects kept in view in the arrangement of this great 

 system of combined observation now in operation, was the extension of the plan of 

 simultaneous observations at short intervals of time, first laid down by Gauss. The 

 results of this system had been, that the observed changes of the magnetical elements 

 were strictly simultaneous at the most remote stations at which observations had 

 been hitherto made ; and that these changes followed in all cases the same laws, the 

 representative curves being similar to one another in all their inflexions, and differing 

 only in the magnitude of the change. This similarity had been found to extend to 



