MarcH 12, 1914| 
phorus is brought towards the lamp, the loops will 
diverge and strike the sides. Or if the displacement 
is only partial, the loops will swing back to their 
original place of rest directly the charged plate is 
removed to a distance. If, however, the metal disc 
of the electrophorus, positively charged, is brought 
towards the still lighted lamp, there is no movement 
of the loops. Equilibrium of potential is attained by 
emission of electrons from the filament. But as the 
disc with its positive charge is being moved away the 
loops diverge and may strike the glass. 
What is most remarkable is this, that if the dis- 
placement of the loops is only partial, and not up to 
the glass, then when the disc is removed, the loops 
retain their displaced position and very slowly creep 
back to their original place of rest. It is this last 
phenomenon which clearly indicates the great difficulty 
of negative electricity returning to the glowing fila- 
ment, or of positive ions leaving it. 
The Beta rays from a few milligrams of radium 
near the lamp produce in it an ionisation current which 
accelerates the creep into a rapid motion, to the natural 
position of the filament. 
These experiments with the electrophorus can all be 
carried out through a dry wooden drawing-board more 
than half an inch thick. When projected by a lens 
on a screen the motions of the filament afford interest- 
ing lecture-room illustrations of the thermionic current. 
The valve action inside high vacuum lamps was 
explained by Fleming (Proc. Roy. Soc., 1890, vol. 
xIvii., p. 122). An account of his work is given in his 
well-known book on ‘Electric Wave Telegraphy’”’ 
(second edition, p. 478). 
So far as I know, the experiments described in this 
letter, with an electric force, produced outside the 
lamp, have not been previously published. 
Ages. SVE. 
McGill University, Montreal, January 29. 
The Densities of the Planets. 
THE prominence you give to M. F. Ollive’s note in 
Comptes rendus, tome 157, No. 26, induces me to 
point out that M. Ollive’s so-called empirical formula 
is really a simple statement about the densities of the 
planets. The formula is r?>=kRR'v”?, where r is the 
mean radius of any planet, R its mean distance from 
the Sun, R’ the mean distance of any satellite from its 
primary, and v’ the mean orbital velocity of the satel- 
lite. v’?R’ for any satellite can be replaced by yM, 
where y is the gravitation constant, and M is the mass 
of its primary, since we can ignore the mass of the 
planet as compared with its primary. We get then 
v3 =k'RM, where k’ is a new constant. But M=47p74 
where p is the mean density of a planet. Thus we 
get Rp=constant. This is what M. Ollive’s formula 
amounts to. In other words, his formula does not 
derive any generality by the introduction of the satel- 
lites. The fact that his results for the various satel- 
lites of any given primary agree inter se is merely 
Kepler’s third law. 
The value of M. Ollive’s ‘empirical’ formula is 
thus to be measured by the extent to which the formula 
pR=constant is true of the planets of the solar 
system. As it happens, this is at all approximately 
correct only for Earth, Mars, Jupiter, and Saturn. 
The densities as generally accepted are, taking the 
planets from Mercury outwards, 0:85, 0-89, I-00, 0-71, 
0-24, 0-13, 0:22, 0-20. The density of the earth is 
taken as the standard. M. Ollive’s formula gives 2-58, 
I-39, I-00, 0-66, 0-19, 0-10, 0:05, 0:03. It is evident that 
M. Ollive’s ‘‘empirical’’ formula is quite wrong for 
all but the four planets mentioned, and even for these 
the agreement is by no means encouraging. 
It may be urged that the densities are not observed 
NO. 2315, VOL. 93] 
NATURE 
22 
rere) 
directly, but are inferred from the masses and the radii 
of the planets, so that a small inaccuracy in the 
observed radius of any planet may well account for a 
considerable error in the inferred density. But I very 
much doubt whether astronomers will be ready to 
admit possible errors of 50 per cent. in the radius of 
Uranus and too per cent. for Neptune. They will 
certainly decline to concede an error of 50 per cent. 
in the radius of Mercury and of 12 per cent. in the 
radius of Venus. SELIG BRODETSKY. 
University of Bristol, March 3. 
An Optical Representation of Non-Euclidean Geometry. 
Let us suppose Euclidean space to be filled with a 
medium of variable refractive index. Then to an 
observer in that medium the curved path of a ray 
of light will present all the appearances of a straight 
line, and, further, if the observer estimates the distance 
between two points by the time light takes to pass 
between them, this path will appear to be the shortest 
distance between the two points. 
Suppose now that one or more such observers con- 
duct an Ordnance Survey of the region occupied by 
the medium, using theodolites to measure angles, and 
imagine them to be equipped with instruments capable 
of measuring the time interval occupied by optical 
signals in transmission from one station to another, 
this interval being used as a measure of the distances 
between the stations. It is clear that these observers will 
obtain what to them must be a convincing proof that 
the sum of the three angles of a triangle cannot 
possibly be always equal to two right angles. And it 
would not be easy for an individual whose methods 
of observation of the geometrical properties of such a 
region were limited to those here assumed to believe 
that the space in which he lived could contain a 
Euclidean geometry. G. H. Bryan. 
NATURE RESERVES. 
ie is Only too true that man is slowly but surely 
destroying the beautiful wild animals and 
plants of the world, and is substituting for them 
queer domesticated races which suit his conveni- 
ence and his greed, or else is blasting whole 
territories with the dirt and deadly refuse of his 
industries, and converting well-watered forest 
lands into lifeless deserts by the ravages of his 
axe. It is not too late to rescue here and there 
larger and smaller areas from this awful and 
ceaselessly spreading devastation. In remote 
lands there are large tracts which may be taken 
in charge by the local government and rescued 
from destruction, and to some extent this has been 
done. Even in our over-crowded European states 
' there are still lovely bits of forest, marsh-land, 
_and down which man has not yet irretrievably 
befouled, and from which he has not yet driven 
by assault nor removed by slaughter the beautiful 
living things which nature has guided and nur- 
tured in their seclusion. There is yet time! 
Some of these little scattered fragments of our 
great mother’s handiwork can still be preserved 
even in England, Wales, Scotland, and Ireland, 
so that future Britons may not utterly curse us, 
but enjoy, with gratitude to those who saved 
them, the precious living relics of the world as it 
was before man destroyed it. 
There must be many who have in these days 
