330 CLAUSIUS ON THE BLUE COLOUR OF THE SKY 



clouds illuminated by white light must appear white, which is 

 indeed the case. 



We now pass over to the consideration of the transmitted 

 light. As it is complementary to the reflected light, it follows 

 that so far as it is sensible it must appear as orange. With 

 regard to the quantity of the white light mixed along with it, 

 however, an essential difference takes place. In the formula 

 (I) the minimum value is =0, and hence, by reflexion from a 

 plate, certain colours might be completely extinguished, so that 

 the entire light may appear highly coloured. In the formula (2), 

 on the contrary, the difference between minimum and maximum 

 is indeed of the same magnitude as in (1), but the minimum is 

 not null. For example, if the plate consists of water, and if 

 the light fall perpendicularly upon it, we have r^ = 0*0203 7, and 

 from this w^e obtain as the extreme values of c the quantities 



0-922 . a^ and a^, 

 while for h^ they are 



and 0-078 . a^. 



In the transmitted light, therefore, the quantity 0*922 . a^ is 

 completely white, and only the remaining portion, which at 

 most amounts to 0*078 . a% is coloured, so that the tint of the 

 entire light must be very feeble. When the incidence is oblique 

 the colouring indeed increases, but with great slowness. For 

 example, for 45° we obtain as minimum and maximum for c^, 

 the values 



0*894 . a^ and a% 



and the obliquity must be very great when a strong colouring 

 takes place. 



Fixing our attention on a vesicle of vapour, all possible angles 

 of incidence are presented to us, but to the greatest and smallest 

 angles, as is readily seen, comparatively small quantities of 

 light belong, so that the medium angles are those to which the 

 principal part belongs. But these produce but a very feeble 

 tinting, and hence the entire light which passes through a 

 vesicle must be but feebly coloured. Hence it is that the sun, 

 when it stands high in heaven and the rays pass through a 

 comparatively short length of atmosphere, appears white, par- 

 ticularly as we have no absolutely white beside it with which to 



