394 



rization to be 78° 27', and the maximum value of (5, 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 Traiie cVOptique sur la Gradation de la Lumiere, 

 Paris, 1760; pp. 124, 126). If we make the computation 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 incident light, the intensity of reflexion being a mini- 

 mum at an intermediate incidence ; and if we suppose these 

 quantities to be really equal at the incidences observed by 

 Bouguer, we must take the mean of all his numbers, which is 

 .69, as the most probable result of observation. This result 

 differs but little from one of the two numbers given by him at 

 each incidence, and scarcely at all from the result of calculation. 

 The angle at which the intensity of reflexion is a mini- 

 mum, when common light is incident, may be found from the 

 formula 



G^ + D {^+'^ = {''- l)^^'-^S')~^'osx, (s) 



which gives the value of ;u,and thence that of «. This incidence 

 for mercury is, by calculation, 75° 15', and the minimum va- 

 lue of I is .693, which is less than its value at a perpendicular 

 incidence by about one-eighteenth of the latter. According 

 to the formulae, the I'eflexion is always total at an incidence 

 of 90°. 



Rev. Charles Graves communicated certain extracts from 



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