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Proceedings of the Royal Society 
mena in doubly refracting plates by the aid of an analysing Nicol 
only. 
And, moreover, the nature of the vibration can have no periodic 
changes of a kind whose period amounts to a moderate fraction of a 
second. Nor can it have a slow progressive change. Either of 
these would lead to its resolution into rays of different wave-lengths. 
Airy suggests, as consistent with observation, some thousand waves 
polarized in one plane followed by a similar number polarized in a 
plane at right angles to the first. But no physical reason can be 
assigned for such an hypothesis. 
The difficulty, however, disappears if we consider the question 
from the modern statistical point of view, as it is applied for instance 
in the kinetic theory of gases. We may consider first a space 
average taken for the result due to each separate vibrating particle 
near the surface of a luminous body. When we remember that, for 
homogeneous light, of mean wave-length, a million vibrations occupy 
only about one five hundred millionth of a second ; it is easy to see 
that the resultant vibration at any point may not sensibly vary for a 
million or so of successive waves, though the contributions from in- 
dividual particles may very greatly change. But when we consider 
the time average of about a hundred millions of groups of a million 
waves each, all entering the eye so as to be simultaneously percep- 
tible, — in consequence of the duration of visual impressions, — we see 
that the chances in favour of a deviation from apparently absolute 
uniformity are so large that, though possible, such uniformity is not 
to be expected for more than a very small fraction of a second. 
The improbability of its occurrence for a single second is of the 
same nature as that of the possible, but never realised, momentary 
occurrence of a cubic inch of the air in a room filled with oxygen or 
with nitrogen alone. 
[Added ; May 1, 1882. — I am indebted to Professor Stokes for a 
reference to his paper “ On the Composition and Besolution of 
Streams of Polarized Light from Different Sources” ( Camb . Phil. 
Trans ., 1852), in which the nature of common light is very fully 
investigated. I find I was not singular in my ignorance of the 
contents of this paper, as the subject has quite recently been pro- 
posed as a Prize Question by a foreign society.] 
