66 

The geographer, speaking specially of the sandhill, 
says:— ‘The hill of sounding sand stretches 80 li 
east and west and 4o li north and south. It reaches 
a height of 500 ft. The whole mass is entirely con- 
stituted of pure sand. In the height of summer the 
sand gives out sounds of itself, and if trodden by 
men or horses, the noise is heard 10 li away. At 
festivals people clamber up and rush down again in 
a body, which causes the sand to give a loud rumbling 
sound like thunder. Yet when you look at it next 
morning the hill is just as steep as before.” 
Mr. Lionel Giles, from whose translation of the 
Tun-Huang-Lu 
that this sounding sandhill is referred to in another 
old Chinese book, the Wu Tai Shih. 
JOsEPH OFFORD. 
94 Gloucester Road, South Kensington, S.W. 

The Green Flash. 
I can confirm Dr. Schuster’s observation of the 
green flash at sunrise, as in September last I saw a 
green segment herald the sun as it rose from the sea 
into a sky which was free from atmospheric glare 
(see the Observatory, December, 1914). Observations 
had previously been made at sunset, in one of which 
the eye was unquestionably fatigued, and the green 
flash was seen upon turning away from the sun at 
the instant after sunset. In a later sunset experiment 
precautions were taken to prevent retinal fatigue, 
and again the flash was seen. 
My opinion is confirmed by Prof. Porter’s experi- 
ment that ‘‘the reason why doubt has been cast upon 
records of the green flash is that the colour may 
arise in two different ways (complementary colour 
due to retinal fatigue, or dispersion by the atmo- 
sphere), and that the observer has not always been 
careful to avoid retinal fatigue, as was the case in my 
first (sunset) observation,” 
My observation, No. 2 (loc. cit.), is also in agree- 
ment with Dr. Schuster’s experience, that with a 
very red sun no flash is to be seen. 
W. GEOFFREY DUFFIELD. 
University College, Reading, March 6. 

Measurements of Medieval English Femora. 
As the Editor of Nature has insisted upon the great 
pressure at present upon his space I propose to reply 
to Dr, Parsons’s letter, in the issue of March 11, 
adequately elsewhere. Kart Pearson. 

[| 2evE often been impressed by the scanty 
attention paid even by original workers in 
physics to the great principle of similitude. It 
happens not infrequently that results in the form 
of “laws” are put forward as novelties on the 
basis of elaborate experiments, which might have 
been predicted a priori after a few minutes’ con- 
sideration. However useful verification may be, 
whether to solve doubts or to exercise students, 
this seems to be an inversion of the natural order. 
One reason for the neglect of the principle may 
be that, at any rate in its applications to par- 
ticular cases, it does not much interest mathe- 
maticians. On the other hand, engineers, who 
might make much more use of it than they have 
done, employ a notation which tends to obscure it. 
I refer to the manner in which gravity is treated. 
these extracts are made, mentions | 
NATURE 

[Marcu 18, 1915 
makes no appearance, but when gravity does not 
enter into the question at all, g obtrudes itself 
conspicuously. 
I have thought that a few examples, chosen 
almost at random from various fields, may help 
to direct the attention of workers and teachers 
to the great importance of the principle. The 
statement made is brief and in some cases in- 
adequate, but may perhaps suffice for the purpose. 
Some foreign considerations of a more or less 
obvious character have been invoked in aid. In 
using the method practically, two cautions should 
be borne in mind. First, there is no prospect of 
determining a numerical coefficient from the prin- 
ciple of similarity alone; it must be found if at 
all, by further calculation, or experimentally. 
Secondly, it is necessary as a preliminary step to 
specify clearly all the quantities on which the 
desired result may reasonably be supposed to 
depend, after which it may be possible to drop 
one or more if further consideration shows that 
in the circumstances they cannot enter. The fol- 
lowing, then, are some conclusions, which may 
be arrived at by this method :— 
Geometrical similarity being presupposed here 
as always, how does the strength of a bridge 
depend upon the linear dimension and the force 
of gravity? In order to entail the same strains, 
the force of gravity must be inversely as the 
linear dimension. Under a given gravity the 
larger structure is the weaker. 
The velocity of propagation of periodic waves 
on the surface of deep water is as the square 
root of the wave-length. 
The periodic time of liquid vibration under 
gravity in a deep cylindrical vessel of any section 
is as the square root of the linear dimension. 
The periodic time of a tuning-fork, or of a 
Helmholtz resonator, is directly as the linear 
dimension. 
The intensity of light scattered in an otherwise 
uniform medium from a small particle of different 
refractive index is inversely as the fourth power of 
the wave-length. 
The resolving power of an _ object-glass, 
measured by the reciprocal of the angle with which 
it can deal, is directly as the diameter and in- 
versely as the wave-length of the light. 
The frequency of vibration of a globe of liquid, 
vibrating in any of its modes under its own gravi- 
tation, is independent of the diameter and directly 
as the square root of the density. 
The frequency of vibration of a drop of liquid, 
vibrating under capillary force, is directly as the 
square root of the capillary tension and inversely 
as the square root of the density and as the 14 
power of the diameter. 
The time-constant (i.e., the time in which a 
current falls in the ratio e: 1) of a linear con- 
ducting electric circuit is directly as the inductance 
and inversely as the resistance, measured in 
electro-magnetic measure. 
The time-constant of circumferential electric 
When the question under consideration depends ' currents in an infinite conducting cylinder is as the 
essentially upon gravity, the symbol of gravity (g) | square of the diameter. ; 
NO. 2368, VOL. 95] 
rl 
