If we
measure the light, we shall find that the same law holds good as before,
but that the proportion which passes is invariably greater with the red
than the blue. The question then presents itself: Is there any connection
between the amounts of the red and the blue which pass?
Lord Rayleigh, some years ago, made a theoretical investigation of the
subject. But, as far as I am aware, no definite experimental proof of the
truth of the theory was made till it was tested last year by General
Festing and myself. His law was that for any ray, and through the same
thickness, the light transmitted varied inversely as the fourth power of
the wave length. The wave length 6,000 lies in the red, and the wave
length 4,000 in the violet. Now 6,000 is to 4,000 as 3 to 2, and the
fourth powers of these wave lengths are as 81 to 16, or as about 5 to 1.
If, then, the four inches of our turbid medium allowed three quarters of
this particular red ray to be transmitted, they would only allow (3/4)^{5},
or rather less than one fourth, of the blue ray to pass.
Now, this law is not like the law of absorption for ordinary absorbing
media, such as colored glass for instance, because here we have an
increased loss of light running from the red to the blue, and it matters
not how the medium is made turbid, whether by varnish, suspended sulphur,
or what not.
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