392 



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 in- 

 tensity of the light reflected by metals. The formulas for 

 computing this intensity 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 sappose \p and xp' to be two angles, such that 



, M ,, , . 



cotan \p ■= —, cotan \p' = M/x, (o) 



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



cos w = sin 2^ cos X. cosw'zr sin2i//'cosx, (p) 



we shall have 



r — tan | a>, t' = tan | w', (q) 



where t 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 polarized perpendicularly to that plane ; the 

 amplitude of the iucident vibration being in each case sup- 

 posed to be unity. Hence when common light is incident, if 

 its intensity be taken for unity, the intensity i of the reflected 

 light will be given by the formula 



I = J(tan^| w -)- tan'^l w'). (r) 



If with the values of m and x determined by my experi- 

 ments we compute, by the last formula, the intensity of re- 

 flexion for speculum metal at a perpendicular incidence, in 

 which case ju nz 1, we shall find i =. .583. This is consider- 

 ably lower than the estimate of Sir William Herschel, who, 

 in the Philosophical Transactions for 1800 (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 



