CLAUSIUS ON THE BLUE COLOUR OP THE SKY, ETC. 327 



generally accepted. On the contrary, another mode of explana- 

 tion, that for example of Brandes in Gehler's Worterbuch, ac- 

 cording to which the particles of air themselves reflect the blue 

 light in a greater proportion than the red, seems to have ob- 

 tained more general recognition than the other. 



After the foregoing considerations, a few words upon this 

 subject will doubtless appear justifiable. 



As every vesicle of vapour consists of a filament of water 

 curved spherically, if it be assumed as very thin in comparison 

 with its diameter, it exerts upon a ray of light passing through 

 it twice the influence that would be experienced by a ray in 

 passing through a plane layer of water of the same thickness. 

 We may therefore apply in this case the known theory of thin 

 plates. 



Let such a plate, of the thickness S, be given ; and upon it, 

 at the angle i, let a sheaf of homogeneous light of the wave 

 length \, of the intensity a% and hence of the amphtude a, be 

 supposed to fall. Further, let the strength of the reflexion 

 which corresponds to the angle i be expressed by the factor r, 

 so that the elongations of the incident and of the once-reflected 

 ray may be to each other in the ratio 1 : r, then the intensities 

 (b^ and c^) of the whole light transmitted and reflected by the 

 plate, taking into account the repeated reflexions within it, will 

 be expressed by the formulae 



b^ = aK- ^^ -/^ r;^, ... (1) 



{l-rj 

 (l-r^f-^4rhm^{2J-^y 



^^=«^- ^-^V^w^.. ... (2) 



where i' denotes the angle of refraction corresponding to i, and 

 X' is the length of an undulation within the plate. 



From this we see, that, when 8 cos i' is determined, both in- 

 tensities depend on V. If, therefore, the incident light, instead 

 of being homogeneous, consist of difierent colours, the action of 

 the plate is not the same on all, and hence the reflected, as 

 well as the transmitted light, will appear coloured ; according to 



