560 
miade here and at University College indicate that its specific 
gravity is about 9, and this figure agrees fairly well with 
that required for a mineral containing 75 per cent. of thoria. 
T. A. HENRY. 
Scientific and Technical Department, Imperial 
Institute, S.W., April rr. 
Attraction between Concentric Hemispherical Shells. 
By the usual method of Legendre’s functions I have 
arrived at the following result. If two thin attracting 
hemispheres, masses M and M’, radii a and a! (aa’), are 
placed so that the rims lie in one plane and the centres 
coincide, the resulting attraction is } M.M’/a?. 
M 
From this result we conclude that we may replace M’ 
by any number of thin hemispherical shells (radii=a) sub- 
ject to the conditions that the density of any shell is uniform, 
and that the total mass of all the shells is M’. 
The result is so remarkable and simple that one looks 
for an elementary proof. 
Perhaps some of your readers may be able to suggest 
one. GEORGE W. WALKER. 
Physical Laboratory, The University, Glasgow, March 28. 
Mr. G. W. Wacker tells me that he has sent to NATURE 
his interesting problem of the mutual attraction between 
two uniform concentric hemispherical shells, bounded by 
a common diametral plane. The following elementary solu- 
tion has occurred to me. Call the outer shell A and the 
inner B. Now let another hemisphere A’ be added to A 
so that instead of the hemisphere A we have a complete 
and uniform spherical shell surrounding B. The attraction 
between the complete sphere and B is zero, if, as is here 
understood to be the case, the attraction between the 
particles follows the Newtonian law. Hence the attraction 
F of A on B is equal and opposite to the attraction of A’ 
on B. But the force exerted by A’ on B is obviously equal 
and opposite to the attraction which would be exerted by 
A on a hemisphere added to B so as to convert it into a 
complete spherical shell. Hence the force exerted by A on 
the inner sphere thus completed would be 2F, and this 
attraction is the same as that which would be exerted on 
a particle of double the mass of B placed at the centre. 
The attraction F of A on B is therefore that which would 
be exerted by A on a particle of mass equal to B placed at 
the centre, and the same thing holds for the reaction of B 
on A. Mr. Walker’s result is therefore established. 
W e may go a step beyond the problem as proposed. Let 
the diametral plane bounding B, the shells remaining con- 
centric, make any angle with the diametral plane bounding 
A Then, by the same process of completing the sphere 
by adding A’ to A, we see that the attraction exerted by 
A’ on B is equal, and opposite in direction, to that which 
would be exerted by A on a hemisphere added to B to 
complete it in its new position. But the attraction of A on 
the inner sphere thus completed is equal to that which would 
be exerted by A on a particle of mass equal to twice that of 
B situated at the centre, and therefore the whole pull 
exerted on B by A, in any direction, is equal to the force, 
in that direction, exerted by A, on a particle of mass equal 
to that of B situated at the centre. A. GRay. 541 
The University, Glasgow, April 6. 
Curious Formation of Coal. 
In Nature of January 14 (p. 250) Mr. Henry Hall de- 
Scribes a vertical deposit of a carbonaceous mineral in a 
Wooden trough into which water from a coal mine had been 
delivered for three years. This interested me very much, 
as many years ago I described a similar carbonaceous 
mineral lining . vertical cracks in a sandstone near 
NO. 1798, VOL. 69] 
NATURE 
[APRIL 14, 1904 
Whangarei, in New Zealand (Trans. N.Z. Institute, vol. 
ili. p. 250, 1871). 
I hope that Mr. Hall will make further observations and 
experiments on this singular phenomenon to see whether he 
is right in his explanation. F. W. Hutton. 
Museum, Christchurch, New Zealand, February 25. 
Photographic Effect of Radium Rays. 
Ir is interesting to note how pictures of the portions in 
relief on coins, medals, &c., can be obtained by means of 
radium rays. The coin or other object is placed directly 
in contact with a photographic plate which is enclosed in 
an envelope opaque to light. A few milligrams of radium 
bromide, contained in the usual mica-covered box, are placed 
some distance above the plate, and the whole left for several 
days. After development it is found that a clearly defined 
picture is obtained of the portions in relief on the under 
sides of the coins. Pictures have thus been obtained of the 
portions in relief on silver coins (half-crown, sixpence, 
threepence), also of a name engraved on a mother-of-pearl 
seal. Ten days was the time of exposure when ten milli- 
grams of radium bromide were placed six inches above the 
plate, and the coin was a threepenny bit. Ten days also 
in the case of a half-crown when five milligrams were placed 
1} inches above the plate. 
This radium effect was first shown at my last lecture 
on radium at the College of Science, Newcastle, on January 
16, and has been shown at my subsequent lectures. 
HENRY STROUD. 
Durham College of Science, Newcastle-on-Tyne, April 9. 
ON THE MEASUREMENT OF CERTAIN VERY 
SHORT INTERVALS OF TIME. 
CCORDING to the discovery of Kerr, a layer of 
bisulphide of carbon, bounded by two parallel 
plates of metal and thus constituting the dielectric of 
a condenser or leyden, becomes doubly refracting when 
the leyden is charged. The plates, situated in vertical 
planes, may be of such dimensions as 18 cm. long, 
3 cm. high, and the interval between them may be 
0-3 cm., the line of vision being along the length and 
horizontal. If the polarising and analysing nicols be 
set to extinction, with their principal planes at 45° to 
the horizontal, there is revival of light when the leyden 
is charged. If the leyden remain charged for some 
time and be then suddenly discharged, and if the light 
under observation be sensibly instantaneous, it will be 
visible if the moment of its occurrence be previous to 
the discharge; if, however, this moment be subsequent 
to the discharge, the light will be invisible. The 
question now suggests itself, what will happen if the 
instantaneous light be that of the spark by which 
the leyden is discharged? It is evident that the con- 
ditions are of extraordinary delicacy, and involve the 
duration of the spark, however short this may be. 
The effect requires the simultaneity of light and double 
refraction, whereas here, until the double refraction 
begins to fail, there is no light to take advantage of. 
The problem thus presented has been very skilfully 
treated by MM. Abraham and Lemoine (Ann. de 
Chimie, t. xx., p. 264, 1900). The sparks are those 
obtained by connecting the leyden with a deflagrator 
and with the terminals of a large Ruhmkorff coil fed 
with an alternating current. It is known that if the 
capacity be not too small, several charges and dis- 
charges occur during the course of one alternation in 
the primary, and that while the charges are gradual, 
the discharges are sudden in the highest degree. If, 
as in the present case, the capacity is small, it is 
necessary to submit the poles of the deflagrator to a 
blast of air, otherwise the leyden goes out of action 
and the discharge becomes continuous. Under the 
blast, the number of sparks may amount to several 
thousands per second of time. In this way the in- 
