May 18, 1899] 
NATURE 
65 
for glass, the choice is restricted by the presumed necessity of 
avoiding appreciable double refraction. Common salt is singly 
refracting, but attempts to use it were not successful. Opaque 
patches always interfered. With the idea that these might be 
due to included mother liquor, the salt was heated to incipient 
redness, but with little advantage. Transparent rock-salt 
artificially broken may, however, be used with good effect, but 
there is some difficulty in preventing the approximately rect- 
angular fragments from arranging themselves too closely. 
The principle of evanescent refraction may also be applied to 
the spectroscope. Some twenty years ago an instrument had 
been constructed upon this plan. Twelve 90° prisms of 
Chance’s ‘‘dense flint” were cemented ina row upon a strip 
of glass (Fig. 1), and the whole was immersed in a liquid mix- 
ture of bisulphide of carbon with a little benzole. The dis- 
persive power of the liquid exceeds that of the solid, and the 
difference amounts to about three-quarters of the dispersive 
power of Chance’s ‘‘extra dense flint.” The resolving power 
of the latter glass is measured by the number of centimetres of 
available thickness, if we take the power required to resolve the 
D-lines as unity. The compound spectroscope had an available 
thickness of 12 inches or 30 cm., so that its theoretical resolving 
power (in the yellow region of the spectrum) would be about 22. 
With the aid of a reflector the prism could be used twice over, 
and then the resolving power is doubled. 
One of the objections to a spectroscope depending upon bi- 
sulphide of carbon is the sensitiveness to temperature. In the 
ordinary arrangement of prisms the refracting edges are vertical. | 
If, as often happens, the upper part of a fluid prism is warmer 
than the lower, the definition is ruined, one degree (Centigrade) 
of temperature making nine times as great a difference of refrac- 
tion as a passage from D, to D,. The objection is to a great 
extent obviated by so mounting the compound prism that the 
refracting edges are horizontal, which of course entails a 
| encountering a large number. 
and liquid that would more nearly assimilate the two cases. If, 
for example, the glass consisted of equal spheres resting against 
one another in cubic order, some rays might pass entirely 
through glass and others entirely through liquid, and then the 
quarter wave-length of relative retardation would enter at the 
same total thickness in both cases. But such an arrangement 
would be highly unstable ; and, if the spheres be packed in 
close order, the extreme relative retardation would be much 
less. The latter arrangement, for which exact results could 
readily be calculated, represents the glass powder more nearly 
than does the cubic order. 
A simplified problem, in which the element of chance is 
retained, may be constructed by supposing the particles of glass 
replaced by thin parallel discs which are distributed entirely at 
random over a certain 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 it is improbable that a ray can pass the plane without 
A certain number (vz) 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 determine the chance of a 
prescribed number of encounters, or of a prescribed deviation 
from the mean. In the notation of the integral calculus the 
chance of the deviation from mm lying between + 7 is (see Phd. 
Mag., 1899, vol. xlvii. p. 251) 
2 ie -a 
cee GES oho. 
NJ o 
where t=7//(2). This is equal to 84 when t=1'0, or 
r= ./(2m); so that the chance is comparatively small of a 
deviation from 7 exceeding + ,/(2 72). 
To represent the glass powder occupying a 
ie 
| stratum of 2cm, thick, we may perhaps suppose 
Fic. 1. 
horizontal slit. The disturbance due to a stratified temperature 
is then largely compensated by a change of focus. 
In the instrument above described the dispersive power is 
great—the D.-lines are seen widely separated with the naked eye 
—but the aperture is inconveniently small (4-inch). In the 
new instrument exhibited, the prisms (supplied by Messrs. 
Watson) are larger, so that a line of ten prisms occupies 20 
inches. Thus, while the resolving power is much greater, the 
dispersion is less than before. 
In the course of the lecture the instrument was applied to 
show the duplicity of the reversed soda lines. The interval on 
the screen between the centres of the dark lines was about 
half an inch. 
It is instructive to compare the action of the glass powder with 
that of the spectroscope. In the latter the disposition of the 
prisms is regular, and in passing from one edge of the beam to 
the other there is complete substitution of liquid for glass over 
the whole length. For one kind of light there is no relative 
retardation ; and the resolving power depends upon the question 
of what change of wave-length is required in order that its 
relative retardation may be altered from zero to the quarter wave- 
length. All kinds of light for which the relative retardation is 
less than this remain mixed. In the case of the powder we 
have similar questions to consider. 
medium is optically homogeneous, 2z.e. the retardation is the 
same along all rays. If we now suppose the quality of the 
light slightly varied, the retardation is no longer precisely the 
same along all rays; but if the variation from the mean falls 
short of the quarter wave-length it is without importance, and 
the medium still behaves practically as if it were homogeneous. 
The difference between the action of the powder and that of the 
regular prisms in the spectroscope depends upon this, that in 
the latter there is complete substitution of glass for liquid along 
the extreme rays, while in the former the paths of all the rays 
lie partly through glass and partly through liquid in nearly the 
same proportions. 
rays is thus a question of a deviation from an average. 
For one kind of light the | 
The difference of retardations along various | 
that #2 = 72. There would thus be a moderate 
chance of a difference of retardations equal to, 
say, one-fifth of the extreme difference corre- 
sponding to a substitution of glass for liquid 
throughout the whole thickness. 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 spectroscope of equal (2 cm.) 
thickness. Of course, no calculation of this kind can give more 
than a rough idea of the action of the powder, whose disposition, 
theugh partly a matter of chance, is also influenced by 
mechanical 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 degree of purity may be obtained in a given 
thickness from coarse grains as from fine ones, but the light not 
regularly transmitted 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 presence 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 (of. cét., 1881, vol. xii. p. 96). 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. 
UNIVERSITY AND EDUCATIONAL 
INTELLIGENCE. 
OXx¥FORD,—The honorary degree of M.A. was conferred in 
Convocation on Tuesday upon Mr. Roland Trimen, F.R.S. 
Convocation has passed the decree accepting the offer of the 
Royal Geographical Society of 400/. for five years for the 
furtherance of geographical studies in Oxford, and providing an 
equal contribution from the funds of the University. 
CAMBRIDGE.—The following is the speech delivered on 
It is true that we may imagine a relative distribution of glass | May 11 by the Public Orator, Dr. Sandys, of St. John’s 
NO. 1542, VOL. 60] 
