450 
LETTERS TO THE EDITOR. 
[The Editor does not hold himself responsible for 
opinions expressed by his correspondents. Neither 
can he undertake to return, or to correspond with 
the writers of, rejected manuscripts intended for 
this or any other part of Nature. No notice is 
taken of anonymous communications.] 
Reflection of Light at the Confines of a Diffusing 
Medium. 
I suppose that everyone is familiar with the beau- 
tifully graded illumination of a paraffin candle, extend- 
ing downwards from the flame to a distance of 
several inches. The thing is seen at its best when 
- there is but one candle in an otherwise dark room, 
and when the eye is protected from the direct light 
of the flame. And it must often be noticed when a 
candle is broken across, so that the two portions are 
held together merely by the wick, that the part below 
the. fracture is much darker than it would otherwise 
be, and the part above brighter, the contrast between 
the two being very marked. This effect is naturally 
attributed to reflection, but it does not at first appear 
that the cause is adequate, seeing that at perpendicular 
incidence the reflection at the common surface of wax 
and air is only about 4 per cent. 
A little consideration shows that the efficacy of the 
reflection depends upon the incidence not being limited 
to the neighbourhood of the perpendicular. In con- 
sequence of diffusion! the propagation of light within 
the wax is not specially along the length of the candle, 
but somewhat approximately equal in all directions. 
Accordingly at a fracture there is a good deal of 
“total reflection.”” The general attenuation down- 
wards is doubtless partly due to defect of transparency, 
but also, and perhaps more, to the lateral escape of 
light at the surface of the candle, thereby rendered 
visible. By hindering this escape the brightly illu- 
minated length may be much increased. 
The experiment may be tried by enclosing the candle 
in a reflecting tubular envelope. I used a square 
tube composed of four rectangular pieces of mirror 
glass, 1 in. wide, and 4 or 5 in. long, held together 
by strips of pasted paper. The tube should be lowered 
over the candle until the whole of the flame projects, 
when it will be apparent that the illumination of the 
candle extends decidedly lower down than before. 
In imagination we may get quit of the lateral loss 
by supposing the diameter of the candle to be in- 
creased without limit, the source of light being at the 
same time extended over the whole of the horizontal 
plane. 
To come to a definite question, we may ask what 
is the proportion of light reflected when it is incident 
equally in all directions upon a surface of transition, 
such as is constituted by the candle fracture. The 
answer depends upon a suitable integration of Fres- 
nel’s expression for the reflection of light of the two 
polarisations, viz. :— 
deel ae ar 
sin*(@+ 6’) tan*(6+ 6’) 
where 6, 6’ are the angles of incidence and refraction. 
We may take first the case where @>6', that is, when 
the transition is from the less to the more refractive 
medium. 
The element of solid angle is 27 sin 6¢6, and the 
area of cross-section corresponding to unit area of the 
refracting surface is cos @; so that we have to consider 
rhe 
2 | sin Ocos 6 (S* or T?)d0, . . . (2) 
uD: 
1 To what is the diffusion due? Actual cavities seem improbable. Is it 
chemical heterogeneity, or merely varying orientation of chemically homo- 
geneous material operative in virtue of double refraction ? 
NO. 2303, VOL. 92] 
NATURE 
[|DecEeMBER 18, 1913 
the multiplier being so chosen as to make the integral 
equal to unity when S* or T* have that value through- 
out. The integral could be evaluated analytically, at 
any rate in the case of S*, but the result would 
scarcely repay the trouble. An estimate by quad- 
ratures in a particular case will suffice for our pur- 
poses, and to this we shall presently return. 
In (2) @ varies from o to $m and @' is always real. 
If we supppose the passage to be in the other direc- 
tion, viz. from the more to the less refractive medium, 
S? and T*. being symmetrical in @ and 6’, remain as 
before, and we have to integrate \ 
2 sin 6 cos 6’ (S* or T*)dé’. 
The integral divides itself into two parts, the first 
form o to a, where a is the critical angle corresponding 
to @=47. In this S*, T? have the values given in (1). 
The second part of the range from 6’=a to @=47r 
involves ‘total reflection,’ so that S? and T? must be 
taken equal to unity. Thus altogether we have 
2 sin 6' cos 6'(S? or T?) db’ +2 [sin 6' cos 6'd6', (3) 
0 EM 
in which sin a=1/, » (greater than unity) being the 
refractive index. In (3) 
2sin 6’ cos 6'd6’=d sin °6’=y~*d sin °6, 
and thus— 
(3)=n-2x (2)+1—p-? 
chr 
Sl Pe + |” sin 20 (S? or T?) d6\, (4) 
pl 0 
expressing the proportion of the uniformly diffused 
incident light reflected in this case. 
Much the more important part is the light totally 
reflected. If ~=1°5, this amounts to 5/9, or 0°5556. 
With the same value p, I find by Weddle’s runle— 
‘hr 
| sin 26. S*¢d@=0'1 460, 
Thus for light vibrating perpendicularly to the plane 
of incidence— 
(4) =0:5556+ 0:0649 =0:6205 ; 
while for light vibrating in the plane of incidence— 
(4) =0-5556 + 0:0151=0:5707. 
The increased reflection due to the diffusion of the 
light is thus abundantly explained, by far the greater 
part being due to the total reflection which ensues 
when the incidence in the denser medium is somewhat 
oblique. RAYLEIGH. 
dr 
“ *" sin 20. T2d0=0'0339. 
0 
The Pressure of Radiation. 
Tue theory of radiation at present accepted is based 
on Maxwell’s result that the pressure of any com- 
ponent frequency is one-third of its energy density, 
which appears to result from an assumption analogous 
to Boyle’s law, according to which the excess pressure 
due to vibration, in the case of a gas, would be one- 
third of the energy density of the vibration. 
Lord Rayleigh (Phil. Mag., 1905) has shown that 
this cannot be true in the case of a gas, since the 
vibrations are adiabatic, and Boyle’s law does not 
hold. For a monatomic gas, where the reasoning 
based on the kinetic theory is fairly certain, he deduces 
that the excess pressure should be two-thirds of the 
energy density. 
In a recent note on radiation and specific heat (Phil. 
Mag., October, 1913) I gave an outline of a new 
theory, showing good agreement with experiment, 
from which I deduced the result that ‘‘the total pres- 
sure of full radiation should be one-third of the in- 
| trinsic energy density, but this could not be true for 
