﻿its Polarization and Colour. 115 



of the incomplete polarization of sky-light at right angles to the 

 solar beams; but it must be remembered that an insufficient 

 fineness in some of the particles of foreign matter would have a 

 like result. 



By many physicists, from Newton downwards, the light of the 

 sky has been supposed to be reflected from thin plates, and the 

 colour to be the blue of the first order in Newton's scale. Such 

 a view is fundamentally different from that adopted in this paper, 

 though it might not at first seem so. In support of this asser- 

 tion, it may be sufficient to notice that the two theories are 

 at variance as to the law connecting the intensity with wave- 

 length. By an argument from dimensions similar to that already 

 used, it is easy to find how the intensity of the light reflected 

 from a thin plate (thin, that is, compared with any of the wave- 

 lengths) varies with X. Instead of our former quantities, T, r, A,, 

 we now have merely A, and 8 the thickness of the plate. Since 

 the reflected vibration necessarily varies as 8, it must also be 

 proportional to A, -1 , and so the intensity of the reflected light 

 QcX -2 instead of \~ 4 . The ordinary analytical expression for 

 the reflected light leads readily to the same conclusion (Airy's 

 Tracts, p. 297). There can, I think, be no question that the 

 composition of the light of the sky agrees more nearly with the 

 latter than with the former law. 



The principle of energy makes it clear that the light emitted 

 laterally is not a new creation, but only diverted from the main 

 stream. If I represent the intensity of the primary light after 

 traversing a thickness x of the turbid medium, we have 



dl=-kl\- 4 dx, 



where k is a constant independent of X. On integration, 



if I correspond to # = 0, — a law altogether similar to that of ab- 

 sorption, and showing how the light tends to become yellow and 

 finally red as the thickness of the medium increases. Fig 2 shows 

 a series of curves representing the composition of the originally 

 white light after passing through thicknesses in the ratio of 1, 2, 

 4, 8, 16, 32. The reader will observe how little of the violet 

 light remains when the red is still in nearly its original force. I 

 cannot but think that this rapid diversion of the rays of short 

 wave-length has a good deal to do with the absence of light of 

 the highest refrangibility from the direct rays of the sun. For 

 the line A at the extreme red and R near the upper limit of the 

 photographic spectrum the wave-lengths are 7617 and 3108. 

 The ratio of the fourth powers is about 36:1; so that, whatever 



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