May 5, 1923] 
NATURE 
601 

of molecules “‘ rigidly ’’ attached to each other as in 
a solid, and in of molecules which are relatively 
mobile as in the gaseous state (NATURE, April 21, 
3592). 
fhat the supposition made regarding the constitu- 
tion of liquids is prima facie a reasonable one is, I 
think, clear from thermodynamical considerations. 
The liquid stands midway between the solid and the 
fas and has affinities to both. The volume of a 
iquid at temperatures slightly higher than the 
melting — is only moderately different from that 
of the solid, and hence the probability that many of 
the molecules are at any instant at the same distance 
_ from each other as in a solid is considerable. This 
probability may indeed be found from the latent heat 
of fusion of the substance. If W be the heat of fusion 
in ergs per mol, the number of molecules in the 
“rigid "’ and ‘‘ mobile’’ states should be approxi- 
- mately in the ratio e'/*": 
The mechanism of viscous flow of a liquid is 
aig clearest if we consider the case of a thin 
er enclosed between two parallel plates, one of 
which slides over the other. When a steady state 
is reached, the “‘rigid’’ parts of the liquid move 
practically as complete wholes, and hence the effect 
of their existence is to diminish the thickness of the 
layer through which momentum has to be trans- 
rted by the ‘“‘ mobile ’’ molecules, and thus to 
_ imcrease the viscosity. As a rough approximation, 
this increase is in the proportion of the numbers of 
the two types of molecules. A more exact theory 
should take into account also the volumes occupied 
by the two types of aggregation and their changes 
with temperature. 
The effect of pressure on viscosity of liquids would 
arise in two distinct ways. In the first place, we have 
a change of volume on fusion, and hence, by the 
Le Chatelier-Braun principle, the assumed dissociation 
from the “ solid "’ to the ‘‘ mobile ’’ aggregation would 
be retarded by pressure, so that the viscosity should 
be increased. Witb substances such as ice which 
contract on melting, we have the opposite effect. 
In the second place, pressure diminishes the volume 
occupied by the “ mobile’’ molecules, and therefore 
also the distance through which they have to transport 
momentum. This would increase the viscosity. At 
; eee atures not much higher than the melting point, 
the first effect would preponderate. This is strikingly 
illustrated in the case of water, the pressure-coefficient 
of viscosity of which is negative up to 32° C., that is, 
even at temperatures much higher than that of 
maximum density. C. V. Raman. 
210 Bowbazaar Street, 
Calcutta, March 15. 

Green and Colourless Hydra. 
In Nature of April 7 a short account is given of 
the interesting experiments made by Goetsch on the 
conversion of the green Hydra into a pale Hydra. 
Some vears ago I observed what may be called a 
natural experiment of the same kind. At the south 
end of the tunnel that conducts the water supply of 
Manchester from Lake Thirlmere under Dunmail 
Raise to the Grasmere valley there is a small settling 
tank, and on the walls of this tank I found a very 
large assembly of milk-white Hydras. An examina- 
tion with a pocket lens led me to the conclusion that 
they were only a white variety of the common Hydra 
viridis, and were probably the offspring of parents 
living in the tunnel. These white Hydras were 
evidently enjoying the full vigour of life. 
SYDNEY J. Hickson. 
The University, Manchester, April 11. 
NO. 2792, VOL. 111] 

Single Crystals of Aluminium and other Metals. 
Wirth reference to Prof. Porter’s letter in NATURE 
of March 17, p. 362, the accompanying photographs 
(Figs. 1 and 2) may be of interest. They illustrate at 
a magnification of 100 diameters the type of fracture 
obtained when a drawn tungsten wire consisting of a 
single crystal is broken in tension. The fracture is 

Fic. 1.—o'05 mm. single crystal tungsten wire broken in tension, 
showing reduction in diameter. (X 100.) 

Fic. 2.—Same specimen photographed in a plane at right angles to 
that of Fig. 1, showing no reduction in diameter in this plane. 
always of the wedge type, the wire being very greatly 
reduced in diameter in one plane while it suffers no 
appreciable reduction in the plane at right angles. 
The photographs show the same specimen after 
fracture taken from two planes at right angles. The 
diameter of the wire was 0:05 mm. 
C. J. SMITHELLS. 
Research Laboratories, 
General Electric Co., Ltd., 
Wembley, March 20. 

Stirling’s Theorem. 
A sMALL modification of the proof given by Mr. 
Strachan in NaturE of March 24, p. 397, leads to an 
asymptotic series for » ! rather more convergent than 
Stirling’s. The symbol ! standing, generally, for 
T'(m +1), we have 
log (n +4) ! —log (m - 4) !=log (m +4). 
Hence, by Taylor’s theorem, 
3 5 
(D-5 pe «+ +) log n!=log (n +4). 
245! 
3 
Ds :) log (n+ 4). 
I 
qe log n!= (S-a 5760 ri 
n+t 
ow. nl= lan (* 44) 
I 7 ) 
sare (=a eeghteseae ae oes 9 
the constant in the integration being determined as 
before. 
Stirling's first approximation, V2rn n"e-", makes 
1!=o0'922, whilst V2r{(n+})/e}"+! makes 1!=1-028 
and so is a little closer. H. E. Soper. 
8 Causton Road, Cholmeley Park, 
Highgate, N.6. 
s2 
