JULY 28, 1899. 
A simplified problem in which the ele- 
ment of chance is retained may be con- 
structed by supposing the particles of glass 
replaced by thin parallel discs which are 
distributed entirely at random over a cer- 
tain stratum. We may go further and 
imagine the discs limited to a particular 
plane. Each disc is supposed to exercise a 
minute retarding influence on the light 
which traverses it, and they are supposed 
to be so numerous that itis improbable that 
aray can pass the plane without encoun- 
tering a large number. A certain number 
(m) of encounters is more probable than 
any other, but if every ray encountered the 
same number of discs the retardation would 
be uniform and lead to no disturbance. 
It is a question of probabilities to deter- 
mine the chance of a prescribed number of 
encounters, or of a prescribed deviation 
from the mean. In the notation of the in- 
tegral calculus the chance of the deviation 
from m lying between = r is * 
2 T 
vido 
where z=r/./(2m). This is equal to -84 
when st = 1-0, orr = / (2m); so that the 
chance is comparatively small of a devia- 
tion from m exceeding + 4/ (2m). 
To represent the glass powder occupying 
a stratum of 2 cm. thick we may perhaps sup- 
pose that m = 72. There would thus bea 
moderate chance of a difference of retarda- 
tions equal to, say, one-fifth of the extreme 
difference corresponding to a substitution of 
glass for liquid throughout the whole thick- 
ness. The range of wave-lengths in the 
light regularly transmitted by the powder 
would thus be about five times the range of 
wave-lengths still unseparated in a spectro- 
scope of equal (2 cm.) thickness. Of course, 
no calculation of this kind can give more 
than a rough idea of the action of the pow- 
der, whose disposition, though partly a 
* See Phil. Mag. 1899, Vol. XLVIL., p. 251. 
Cmindic 
SCIENCE. 
107 
“matter of chance, is also influenced by me- 
chanical considerations ; but it appears, at 
any rate, that the character of the light 
regularly transmitted by the powder is such 
as may reasonably be explained. 
As regards the size of the grains of glass 
it will be seen that as great or a greater de- 
gree of purity may be obtained in a given 
thickness from coarse grains as from fine 
ones, but the light not regularly transmited 
is dispersed through smaller angles. Here, 
again, the comparison with the regularly 
disposed prisms of an actual spectroscope 
is useful. 
At the close of the lecture the failure of 
transparency, which arises from the pres- 
ence of particles, small compared to the 
wave-length of light was discussed. The 
tints of the setting sun were illustrated by 
passing the light from the electric lamp 
through a liquid in which a precipitate of 
sulphur was slowly forming.* The lecturer 
gave reasons for his opinion that the blue 
of the sky is not wholly, or even principally, 
due to particles of foreign matter. The 
molecules of air themselves are competent 
to disperse a light not greatly inferior in 
brightness to that which we receive from 
the sky. R. 
DISTRIBUTION OF THE KEEWATIN IN MIN- 
NESOTA. 
In Minnesota the lithological characters of 
that part of the Algonkian known as Lower 
Huronian or Keewatin are necessary in the 
recognition of the stratigraphic subdivisions 
of geographically separated localities. The 
Keewatin carries the first clearly defined 
sediments of this portion of the globe. 
Often the clastic origin of the rocks has been 
so completely obliterated by alteration due 
largely to dynamic metamorphism that it 
is difficult to distinguish them from their 
associates. At the bottom of the series is 
usually a quartzite which is locally con- 
* Op. cit., 1881, Vol. XIL., 96. 
