382 Royal Irish Academy, 



merly the time of high water at London was an hour hiter than it is 

 at present. 



The Society then adjourned over the Easter recess, to meet again 

 on the 6th of April. 



ROYAL IRISH ACADEMY. 



October 24, 1836. — A paper was read, entitled "■ Contributions 

 to the History of Pyroxylic Spirit, and the derived Combinations." 

 By Robert J. Kane, M.D. M.R.I.A., Professor of Natural Philo- 

 sophy in the Royal Dublin Society*. 



A paper was also read, " On the laws of Reflexion from Metals." 

 By James MacCullagh, M.R.I. A., Professor of Mathematics in the 

 University of Dublin. 



The author observes that the theory of the action of metals upon 

 light is among the desiderata of physical optics, whatever informa- 

 tion we possess upon this subject being derived from the experiments 

 of Sir David Brewster. But, in the absence of a real theory, it is 

 important that we should be able to represent the phaenomena by 

 means of empirical formulae ; and, accordingly, the author has en- 

 deavoured to obtain such formulae by a method analogous to that 

 which Fresnel employed in the case of total reflexion at the surface 

 of a rarer medium, and which, a s is w ell known, depends on a pecu- 

 liar interpretation of the sign ^ — 1. For the case of metallic re- 

 flexion, the author assumes that the velocity of propagation in the 

 metal, or the reciprocal of the refractive index, is of the form 



m{cosx + V - 1 sin;)^)i 



without attaching to this form any physical signification, but using 

 it rather as a means of introducing two constants (for there must be 

 two constants, m and %, for each metal) into Fresnel's formulae for 

 ordinary reflexion, which contain only one constant, namely, the 

 refractive index. 



Then if i be the angle of incidence on the metal, and i the angle 

 of refraction, we have 



sin i'=m (cos % + i/ — 1 sin p^) sin j, (1) 

 and therefore we may put 



cos z'=m' (cos ;^' — V — 1 sin p^') cos 2, (2) 



if m!^ cos * j = 1 — 2m2 cos2 % sin H + rw* sin *i, (3) 



and tan 2y'= — ^- — .-— .. (4) 



^ 1 — wi2 cos 2% sin H 



Now, first, if the incident light be polarized in the plane of re- 



♦ This paper has appeared in our present volume, p. 45 et scq. See 

 also the Proceedings of the British Association, also in Lond. and Edinb. 

 Phil. Mag., vol. vii. p. 397— Edit. 



