462 M. E. Jochmann on the Reflection and Refraction 



find that the value of D 2 with perpendicular incidence is to be 

 multiplied by a numerical factor which, as the thickness increases, 

 approaches the limiting value 1*747 for Fraunhofer's line D, and 

 2*2556 for the line H ; so that the greater transparency for rays 

 of higher refrangibility is thereby rendered more apparent. 



Quincke found {Opt. Unters. § 52) that silver of 0*09 millim. 

 thickness, gold of 0*16, and platinum of 0*40 still appeared 

 transparent. The succession of degrees of transparency is, with 

 regard to the optical constants of these metals, that which, from 

 the theory, was to be expected ; and the value 0'09 for silver 

 may be regarded as a limiting value satisfactorily in accordance 

 with the theory, since the extinction at this thickness has pro- 

 ceeded to about 200 °f ^he original intensity. 



Although the phenomena hitherto discussed have revealed de- 

 viations from the theory which could only be explained by the 

 assumption of certain molecular differences in the metallic sur- 

 faces, occasioning a variation in the optical constants, yet the 

 general character of the phenomena was in accordance with the 

 theory. On the contrary, a fundamental difference between 

 theory and experiment occurs in the Newton's colour-rings ob- 

 served by Quincke on thin metallic lamellse {Opt. Unters. 

 §§ 49-64). Silver, gold, and platinum undoubtedly belong to 



the group of metals for which the condition e-f w> — is fulfilled, 



for which therefore, as was above shown, in the transmitted light 

 generally no maxima and minima can occur. As regards the 

 maxima and minima of the reflected light, there are of course 

 an infinite number of them, which yet, as may easily be shown, 

 escape observation through their small intensity. Considering 

 that, for 0*1 millim. thickness of silver, only variations of inten- 

 sity of the order of about ? -J^ of the total can be expected, only 

 the number of maxima and minima which as far as this thickness 

 are, according to the theory, to be expected need be counted. 



•n a r, i -it ^x 4tTC 9 6, COS (e + U) ~ , .„. T 



For A=01 milhm., 2L = * \- J . 0*1 millim. In 



the simplest case of perpendicular incidence, c 2 — 1, u—0; 

 further, for Fraunhofer's line D, \ = 0*5888 millim., so that we 

 obtain 



2L = 0*lS25.27r=65°42', 



As far as this thickness, therefore, the periodic terms of the 

 function have not yet run through one fifth part of their period, 

 and, independently of the bright or dark centre, in the favour- 

 able case perhaps only one maximum or one minimum will have 

 been observed. 



More remarkably, the breadth of the bright and dark streaks 



