S84> Royal Irish Academy. 



And these two conditions will enable us to determine the constants 

 M and % for any metal, when we know its maximuni polarizing angle 

 and the value of (p ; both of which have been found for a great 

 number of metals by Sir David Brewster. The following table is 

 computed for steel, taking m = 34^, % = 54°. 



The most remarkable thing in this table is the last column, which 

 gives the intensity of the light reflected when common light is in- 

 cident. The intensity decreases very slowly up to a large angle of 

 incidence, (less than 75°,) and then increases up to 90°, where there 

 is total reflexion. This singular fact, that the intensity decreases 

 with the obliquity of incidence, was discovered by Mr. Potter, whose 

 experiments extend as far as an incidence of 70°*. Whether the 

 subsequent increase which appears from the table indicates a real 

 phaBnomenon,or ari.ses from an error in the empirical formulae, can- 

 not be determined without more experiments. It should be ob- 

 served, however, that in these very oblique incidences Fresnel's 

 formulae for transparent media do not represent the actual phaeno- 

 mena for such media, a great quantity of the light being stopped, 

 when the formulae give a reflexion very nearly total. 



The value of ^' — 5, or the difference of phase, increases from 0° 

 to 180°. When a plane-polarized ray is twice reflected from a me- 

 tal, it will still be plane- polarized if the sum of the values of ^' — J 

 for the two angles of incidence be equal to 180^ 



It appears from the formulae that when the characteristic ;)^ is 

 very small, the value of ^' will continue very small up to the neigh- 

 bourhood of the polarizing angle. It will pass through 90°, when 

 w m' = I ; after which the change will be very rapid, and the value 

 of 5' will soon rise to nearly 180°. This is exactly the phaenomenon 

 which Mr. Airy observed in the diamondf. 



Another set of phaenomena to which the author has applied his 

 formulae are those of the coloured rings formed between a glass 

 lens and a metallic reflector ; aad he has thus been enabled to ac- 

 count for the singular appearances described by M. Arago in the 

 Memoires d^ Arcueil,iom.\iu, particularly the succession of changes 



• A notice of Mr. Potter's experiments will be found in Phil. Mag. and 

 Annals, vol. viii. p. 60. — Edit. 



t M r. Airy 's paper, in which this phaenomenon is described, appeared in 

 Lond. and Edinb. Phil. Mag., vol. ii. p. ^0.— Edit. 



