6 Lord Rayleigh on Reflexion from Liquid Surfaces 



For water 



/to = 1-3336, ^ = tan-V=53°8' ? ^ = 36° 52'; 

 and 



T/S = 1-627 80, (4) 



T 2 /S 2 = 2-649 (hd) 2 (5) 



Let us calculate the ratio corresponding to the upper or 

 lower limb of the sun when the spot is central ; that is, let 80 

 he the angular radius of the sun, whose value in minutes is 

 16. Thus 



°^ = 10800' 



and corresponding thereto from (5) 



T 2 /S 2 = 5'74xl0- 5 (6) 



The width of the band actually observed had been estimated 

 at about -J- of the solar diameter, so that at its limits 



T 2 /S 2 = 2xl0- 6 . 



The band was thus about as narrow as Fresnel's formula? 

 would lead one to expect, and its deterioration by a film of 

 grease might be anticipated as at least probable from the 

 rough estimate above given of the effect of such a film. 



The results so far obtained were already sufficient to show 

 that Jamin's value of k, viz. — -00577, must be (numerically) 

 much in excess of the truth. For according to it, since 

 P = 3'33xl0 -5 , the minimum illumination at the centre of 

 the spot should be half as great as Fresnel's formulas make it 

 at the limb of the sun, so that the whole diameter of the sun 

 would be almost equally obscured. The observed narrowness 

 of the band, even in the absence of all precise measures, thus 

 constitutes a proof that Jamin's k is several times too great, 

 and suffices to render it almost certain that the water-surface 

 with which he worked was highly contaminated. 



It has already been mentioned that a well-formed band was 

 attended with a marked appearance of colour. The account 

 of this rendered by Fresnel's formula? is quite satisfactory. 

 Let us calculate the illumination at the centre of the band 

 corresponding to /jl, due to a change from \l to fju + S/u, com- 

 paring it, as usual, with S 2 . In the differentiation is to be 

 treated as constant, and the change in l5 viz. 80 1? is due to 

 8/4. From (2), 



T/S 



cosdir + be^ _ -80 t 

 ~cos(0- 0,-80^ ~cos(0-0i) 5 



