Marci 17, 1904] 
NATURE 
theory in connection with functions of real variables is ex- 
plained.—On the unique expression of a quantic of any order 
in any number of variables with an application to binary 
perpetuants: P. W. Wood. ‘The paper contains a new 
proof that the minimum weight of an irreducible perpetuant 
of degree 8 is 28~'—1.—(1) The derivation of generalised 
Bessel coeflicients from a function analogous to the ex- 
ponential ; (2) transformation of generalised Legendre func- 
tions: Rev. F. H. Jackson. In a series of papers the 
author has shown how functions defined by known power 
series may be generalised by replacing the numbers 
1,2, - - - m in the coefficients by the numbers p,,p., - - - fn 
of a chosen sequence. The two papers now communicated 
trace various analogies between Bessel functions and 
Legendre functions and the functions that are derived from 
them by this process.—The singularities of functions defined 
by power series: H. M. Macdonatd.—lIllustrations of 
modes of decay of vibratory motions: Prof. A. E. H. Love. 
‘The ordinary processes for determining the rate of decay 
of vibratory motion by transmission of waves through the 
surrounding medium afford a good approximation when the 
rate in.question is slow, but they are inadequate for deter- 
mining the motion of the medium. It is shown that when 
a sphere vibrates in air the slightly damped harmonic 
wave, with nearly the period of the vibrator, must be 
accompanied in its passage through the air by one or more 
subsidiary waves, of exponential or rapidly damped harmonic 
type, which serve to establish the front of the advancing 
wave. When electrical oscillations are set up on a spherical 
conductor, the waves that travel through the ther are 
analogous to the subsidiary waves in the sound problem. 
Corresponding with any surface harmonic distribution of 
the initial charge a system of such waves advances into the 
initial electrostatic field of the distribution, and all the 
waves of the system must coexist in order that the wave- 
front may advance. The wave-motions cannot be pro- 
pagated independently. As the front of the composite 
system of waves advances the electrostatic energy of the 
initial field is converted into electromagnetic energy, which 
is accumulated in a narrow region at the front of the 
advancing wave. 
EDINBURGH. 
Royal Society, February 1.—Lord Kelvin, president, in 
the chair.—The President read a paper on deep-water two- 
dimensional waves produced by any given initiating dis- 
turbance, which was in continuation of a paper on the 
front and rear of a free procession of waves in deep water, 
read seventeen years ago. In that paper a question had 
been raised and a solution given in symbols which still, 
however, awaited tabulation or graphical calculation. The 
problem of the surface motion of waves in very deep water 
had long been solved, but the problem of waves circling 
out in all directions from the surface disturbance produced by 
the falling of a stone into the water was a far more difficult 
problem, which nothing known in mathematics enabled the 
mathematician to calculate. In the present paper Lord 
Kelvin gave the solution of an analogous though simpler 
problem. Given a certain definitely specified initial disturb- 
ance fitted to generate two-dimensional wave motion, the 
results showed the genesis of waves from a condition in 
which there was nothing undulating whatever.—Dr. G. A. 
Berry read a paper on the relation of visual efficiency to 
visual acuity, being a consideration of the data for deter- 
mining in general the relative loss of efficiency caused by 
accidents which lead to different degrees of interference 
with sight. The object was to get some basis for calcu- 
lating the amount of compensation which should be allowed 
by the Workman’s Compensation Act when sight had been 
damaged to various extent by accident, and thus avoid the 
frequent litigation to which such accidents now give rise. 
The data for establishing a visual efficiency scale were 
somewhat arbitrary, but basing on certain principles, the 
author deduced the following expression for the efficiency :— 
ee ( o 
2 V+V 2 
m—1+2/(V+V’) 
where V, V! were the visual acuities of the better and worse 
eyes respectively, and m a number such that the fraction 
m/(m-+1) represented the reduction in sight due to complete 
NO. 1794, VOL. 69] 
m+ 1I— 
b= — 
479 
loss in one eye with retention of full sight in the other. 
Tables of efficiency were given for different values of m, 
also maximum and minimum curves for m=3. 
February 15.—Dr. Horne in the chair.—Dr. T. J. Jehu 
read a paper on the Glacial deposits of northern Pembroke- 
shire, in which full descriptions were given of (1) the lower 
Boulder-clay ; (2) the sands and gravels; (3) the upper 
Boulder-clay and rubbly drift. Boulders from the south of 
Scotland and the north-west of Ireland were found, show- 
ing that the northern ice-sheet had covered the whole of 
north Pembrokeshire. The results led to a clearer view than 
had been possible hitherto as to limits of the various ice 
sheets which glaciated that region.—In a communication on 
sea temperature and solar radiation, Prof. C. G. Knott 
discussed some of the data furnished by the elaborate observ- 
ations of temperature at various depths in the Mediterranean 
Sea made by the staff of the Austrian warship Pola. It 
was shown that direct solar radiation was not appreciable 
to depths greater than 15 metres, and that the vertical dis- 
tribution of temperature within the upper layers was largely 
conditioned by convection or diffusion of material. An 
estimate was made of the amount of solar heat which gets 
into the water every day and leaves it at night, and it was 
found that about two-thirds of the available solar energy 
incident on the surface of the waters was so entrapped and 
set free. The processes by which this diurnal influx and 
efflux of heat took place were discussed in some detail. 
Paris. 
Academy of Sciences, March 7.—M. Mascart in the 
chair.—The president announced the death of M. Fouqué, 
member of the section of mineralogy.—Researches on the 
gaseous exchanges between the atmosphere and plants de- 
prived of their roots, and kept in the dark: M. Berthelot. 
The gases given off during the maturing of hay were 
measured, together with the rise of temperature. Neither 
methane nor ammonia were given off, the gases containing 
carbon dioxide, oxygen, and nitrogen only.—On_ the 
rhizomes and roots of the fossil ferns and of the Cycado- 
filices: M. Gramd’Eury.—On the formation of glycuronic 
acid in the blood: -R. Lepinme and M. Boulud. The authors 
have shown in a previous paper that glycuronic acid is 
present in the liver, and now give experimental evidence 
that the lavorotatory power of certain extracts of blood 
from the hepatic veins is due to derivatives of this acid.— 
M. Agassiz was elected a foreign associate in the place of 
the late Sir George Gabriel Stokes, and M. Warming a 
correspondant in the section of botany in the place of M. 
Agardh.—The dielectric cohesion of argon and its mixtures : 
E. Bouty. Argon is characterised by the smallness of its 
dielectric cohesion, which is even less than that of hydrogen. 
Minute traces of foreign gases produce a remarkable in- 
crease in the cohesion, this increase being much greater 
than would be indicated by the law of mixtures.—The 
general law of magnetofriction: H. Pellat. In an intense 
magnetic field the particles in motion, the kathode rays, 
undergo an action analogous to an anisotropic friction, 
which is large in a direction perpendicular to the lines of 
force, but almost nothing in the direction of these lines.— 
Experimental proofs of the laws of anomalous propagation 
of light along the axis of an optical instrument: 
G. Sagnac.—An elementary demonstration of the phase 
rule: C, Raveau.—The different conditions of a spark 
fractionated by blowing: J. Lemoine and L. Chapeau. 
When a stream of sparks is allowed to pass over a spark 
gap for some time, there is an abrupt change in the nature 
of the discharge. This is due to the spontaneous oxidation 
of the brass, the formation of oxide causing a lower ex- 
plosive potential than with polished brass balls.—The action 
of certain chemical and osmotic phenomena on phosphor- 
escence: M. Lambert.—On europium: G. Urbain and H. 
Lacombe. The authors have applied their method of 
crystallisation with magnesium and bismuth nitrates to the 
separation of europium (Demargay) from monazite sand. 
The sand contains only about 0-002 per cent. of this oxide, 
which forms a sulphate Eu,(SO,),.8H,O. The atomic 
weight was found to be 151-8.—The action of carbon dioxide 
upon the metal ammoniunis : Etienne Rengade. Carbon 
dioxide reacts with sodium-ammonium and_ potassium- 
ammonium. Below —50° C. the alkaline carbamate and 
hydrogen are the sole products. At a higher temperature 
