390 Royal Irish Academy. 



divided by the tangent of 2/3 , gives 7° 19' for the mean value of s, 

 the error of the mica-plate corresponding to that part of the spec- 

 trum which was observed at the incidence of 60°. 



At incidences nearer the angle of maximum polarization, the errors 

 are probably much greater. Beyond that angle they again diminish, 

 and in some cases they almost vanish. Thus, at the incidence of 85° 

 upon steel, with the value of 2 O and the value of 2 Q corresponding 

 to a = 20°, we get, by computation, a value of 2 fi 0> which differs 

 only by a few minutes from that given by M. de Senarmont. Nearly 

 the same thing happens at the same incidence when we take a=25°. 

 In these cases therefore the results belong to that particular ray for 

 which the thickness of the plate was exact. 



The observations of M. de Senarmont on speculum metal were 

 not carried beyond the incidence of 60°. He states that he was un- 

 able to observe at higher incidences, on account of the uncertainty 

 arising from the dispersion of the metal ; but though this cause ope- 

 rated in some degree, his embarrassment must have been really oc- 

 casioned by the increasing magnitude of the difference d'—d", as he 

 approached the angle of maximum polarization ; that difference being 

 perhaps twice as great as in the case of steel. My own experiments 

 on speculum metal were all made, as has been seen, at incidences 

 greater than 60°. 



The experiments of M. de Senarmont do not at all agree with the 

 formulae ; and therefore I have been obliged to analyse his method 

 of observation, and to show that it could not lead to correct results. 

 It is to be regretted that his method was defective, as the zeal and 

 assiduity which he has displayed in the inquiry would otherwise have 

 put us in possession of a large collection of valuable data. 



I shall conclude by saying a few words respecting the intensity of 

 the light reflected by metals. The formula? for computing this in- 

 tensity have been given in the Transactions of the Academy, in the 

 place already referred to ; but they may be here stated in a form 

 better suited for calculation. If we suppose ^ and \p' to be two 

 angles, such that 



cotan \p = — , cotan \p' — M ju,, .... (O.) 



and then take two other angles w, tu', such that 



cos w = sin 2 \p cos %, cos w' = sin 2 ip* cos %, . . (P.) 

 we shall have 



r = tan|w, r' = tan^u>' (Q.) 



where r is the amplitude of the reflected rectilinear vibration, when 

 the incident light is polarized in the plane of incidence, and t' is the 

 amplitude of the reflected vibration when the incident light is polar- 

 ized perpendicularly to that plane ; the amplitude of the incident 

 vibration being in each case supposed to be unity. Hence when 

 common light is incident, if its intensity be taken for unity, the in- 

 tensity I of the reflected light will be given by the formula 



I = | (tan 2 i w + tan 2 i w') (It.) 



Tf with the values of M and % determined by my experiments we 



