Royal Irish Academy. 391 



compute, by the last formula, the intensity of reflexion for speculum 

 metal at a perpendicular incidence, in which case jit = 1, we shall 

 find I = '583. This is considerably lower than the estimate of Sir 

 William Herschel, who, in the Philosophical Transactions for ] 800 

 (p. 65), gives "673 as the measure of the reflective power of his 

 specula. The same number, very nearly, results from taking the 

 mean of Mr. Potter's observations (Edinburgh Journal of Science, 

 New Series, vol. iii. p. 280). It might seem therefore that the 

 formula is in fault ; but I am inclined to think that the metal which 

 I employed had really a low reflective power. Its angle of maxi- 

 mum polarization was certainly much less than that of the speculum 

 metal used by Sir David Brewster (Phil. Trans. 1830, p. 324), who 

 states the angle to be 76°, whereas in my experiments it was only 

 about 73^°; and any increase in this angle, by increasing the value 

 of M, raises the reflective power. On the other hand, the maximum 

 value of /3 (when a=45°) was greater than that given by Sir David 

 Brewster, namely, 32° ; and any increase in /3 tends also to increase 

 the reflective power. Now it is not unreasonable to suppose that 

 the highest values of both angles may be most nearly those which 

 belong to the best specula; and accordingly if we take 76° for the 

 incidence of maximum polarization, and retain the maximum value 

 of fi, namely 34° 37', which results from my experiments, we shall 

 get M = 3*68, x — 66 ° 16 '» and tne value °f * at tne perpendicular 

 incidence will come out equal to '662, which scarcely differs from 

 the number given by Herschel. 



It is clear from what precedes that the optical constants are dif- 

 ferent for different specimens of speculum metal, and this is no more 

 than we should expect, from the circumstance that the metal is a 

 compound, and therefore liable to vary in its optical properties from 

 variations in the proportion of its constituents ; but I am disposed to 

 believe that the same thing is generally true, though of course in a 

 less degree, of the simple metals, so that in order to render the com- 

 parison satisfactory, the measures of intensity should always be made 

 on the same specimen which has furnished the values of M and x- 

 There is dne metal, however, with respect to which there can be no 

 doubt that the experiments of different observers are strictly compa- 

 rable, when it is pure, and at ordinary temperatures ; I mean mer- 

 cury. For this metal Sir David Brewster states the angle of maxi- 

 mum polarization to be 78° 27', and the maximum value of /3, when 

 a =45°, to be 35°; from which I find M = 4-616, x — 68 ° 13 '> and 

 at the perpendicular incidence, I = "734. Now Bouguer observed 

 the quantity of light reflected by mercury, but not at a perpendicular 

 incidence. His measures were taken at the incidences of 69° and 

 78^°, for the first of which he gives, by two different observations, 



637 and "666 ; for the second, by two observations, *754 and "703, 

 as the intensity of reflexion (see his Traitt d' Optique sur la Gradation 

 de la Lumiere, Paris, 1760 ; pp. 124, 126). If we make the compu- 

 tation from the formula, with the above values of M and %, we find 

 the quantities of light reflected at these two incidences to be, as 



nearly as possible, equal to each other, and to seven-tenths of the in- 



