Royal Irish Academy. 



383 



ing Table contains the results of observation compared with those 

 obtained by calculation from formulae (F.). The experiments were 

 made upon a small disc of speculum metal ; and in the calculations 

 I have taken M = 2- 94, x — 64 ° 25 '- 



The light used in these observations was that of a candle placed 

 at a short distance, and was admitted through small apertures at the 

 ends of the tubes (see the description of the instrument in the Pro- 

 ceedings, vol. i. p. 159). The Nicol's prism in the first tube having 

 been secured in a position in which its principal plane was inclined 

 45° to the plane of incidence, and the two arms having been set at 

 the proper angle with the surface of the metal, the Fresnel's rhomb 

 and the Nicol's prism in the second tube were moved simultaneously, 

 until the image of the candle became as faint as possible. Had light 

 perfectly homogeneous been employed, the image could have been 

 made to vanish altogether ; but instead of vanishing, it became highly 

 coloured, and our rule in observing was to make the blue at one side 

 of it, and the red at the other, equally vivid, so as to get results which 

 should belong, as nearly as possible, to the mean ray of the spec- 

 trum. When this was done, the angles and /3 (subject however 

 to certain corrections which will be hereafter explained) were re- 

 spectively read off from the divided circles belonging to the rhomb 

 and the prism. The observations were made at large incidences, 

 because it is within the last thirty degrees of incidence that the phe- 

 nomena go through their most rapid changes. 



If we now cast our eyes on the above table, making due allowance 

 for the uncertainty arising from the dispersion of the metal, we shall 

 be struck with the agreement between the calculated and observed 

 numbers. The differences are greatest in the last two observations, 

 which however were really the first ; for the observations were made 

 in the inverse order of the incidences, and their accuracy may have 

 improved as they went on. However that may be, the differences 

 are quite within the limits of the errors of observation ; and they are 

 actually less than those which Fresnel found to exist between calcu- 

 lation and experiment in the much simpler case of reflexion at the 

 surface of a transparent ordinary medium, when he proceeded to 

 verify the formula which he had discovered for computing the effect 

 of such reflexion (see the Table which he has given in the Annates 

 de Chimie, torn. xvii. p. 314). 



It may seem extraordinary that these experiments should have 



