of Light by thin Layers of Metal. 463 



observed by Quicke was not essentially influenced either by the 

 colour or the angle of incidence. If, however, they are to be 

 regarded as Newton's interference-lines, it will thence follow 

 that Cauchy's theory of reflection cannot, without essential mo- 

 dification, be applied to such thin metallic lamellae ; considerably 

 different values must be assigned to the optical constants; particu- 

 larly the constant e must have a considerably smaller value than 

 for opaque metals, in order to be in accord with experiment. But 

 thence will necessarily result the further consequence that, even 

 in opaque metals, the arrangement of the sether in a superficial 

 layer of measurable thickness is essentially different from that in 

 the interior of the metal, so that the quantities l 2 and e lose their 

 character as constants, and that, as Quincke has assumed, the 

 reflection takes place not in a geometrical bounding surface, but 

 within an intermediate layer of finite thickness. 



The middle of the system of fringes observed by Quincke, cor- 

 responding to A = 0, appeared dark in silver lamellae when the 

 reflection took place in air, bright when in glass — which agrees 

 with the above-developed result of the theory. The action of 

 gold and platinum was somewhat anomalous. 



I refrain for the present from a closer discussion of the expres- 

 sions for the phases, and merely refer to an easily controllable 

 result of experiment which likewise stands in contradiction to 

 the theory. M. Quincke found (Gott. Nachr. Dec. 1870) that 

 the difference between the directions of the rays transmitted 

 through air and through metal amounted to nearly +7T for dif- 

 ferent thicknesses of metal < 0*04 millim. For minute thick- 

 nesses of metal, the condition of a constant direction-difference 

 between metal and air cannot generally be fulfilled by the theory. 

 For greater thicknesses, the phase d in approximates, as before 

 mentioned, to the limiting form L— ty, and the quantity L, in- 

 creasing with the thickness, would be equal to the corresponding 

 quantity for air, if the direction- difference were to assume the 

 constant value yjr. The condition thence following is 



0,cos (e + w) = — • 



C 2 



This cannot be fulfilled for any angle of incidence. Let it 

 hold good for perpendicular incidence, and approximately for 

 small angles of incidence, it will be reduced to 6 X cos e = l, 

 whereas for silver 6 X cos € = 0*5373 was found above. But even 

 in the case of its being fulfilled the constant direction-difference 

 would not be found equal to +vr, because the angle yjr always 

 lies in the first quadrant. 



Leignitz, January 18/1. 



