368 
NALGOLRLE 
| FEBRUARY I4, 1907 
independently of any supposition or condition of shape 
and density of the shot, provided the spin imparted by 
the rifling is suitable, and that the trajectory is not curved 
too much. A, G. GREENNILL, 
The Atomic Weight of Nickel. 
IN a paper on the absorption of Réntgen rays (Journal 
de Physique, p. 653, 1901) M. Benoist shows the connec- 
tion between the transparency to X-rays of elementary 
substances and the atomic weight of those substances by 
means of, a curve, which in general exhibits a fall of 
transparency with a rise in the atomic weight of the 
absorbing substance. In continuing investigations on 
secondary X-rays, Mr. C. A. Sadler and I have found 
that by replacing Benoist’s primary beam by secondary 
beams from different substances, curves are obtained 
similar to that got by using a beam direct from an X-ray 
tube, except in the region of atomic weights neat to that 
of the radiator. In those regions a strongly marked 
deviation occurs, showing a special transparency to the 
secondary radiation from a substance, by a sheet of the 
same substance, and a less strongly marked abnormal 
transparency of those substances with atomic weights difler- 
ing little from that of the radiator. Also the nearer on 
the same side the atomic weight of the absorbing sub- 
stance is to that of the radiator, the greater is the devi- 
ation from the normal transparency. This effect does not 
indicate that the secondary rays as emitted by the atoms 
of a substance are specially penetrating, but simply that 
in emerging from the interior atoms to the surface a 
selective absorption has occurred, leaving the remainder 
specially penetrating to further layers of the same sub- 
stance and to a less extent to substances of neighbouring 
atomic weights. This is not a property of secondary rays 
alone, for experiments on primary beams which 
passed through thin sheets of metal show the same effect. 
In making such experiments on a number of metals it 
was found that the radiation from nickel was much more 
abnormally penetrating to copper than to iron, indicating 
a proximity of atomic weight to that of copper. On the 
other hand, when cobalt was used as a radiator the rays 
were much more abnormally penetrating to iron than to 
copper, indicating that the atomic weight of cobalt is 
nearer that of iron than of copper. 
The two experiments together furnish what seems to 
us to be the strongest evidence, based, not only on 
empirical law, but on theory, that the atomic weight of 
nickel is not slightly less than that of cobalt (the accepted 
values are Ni 58-7, Cr 59), but is considerably greater. 
The evidence, however, does not end here. In a paper 
on secondary Réntgen radiation I suggested a method of 
determining atomic weights—based on the fact that the 
radiation is purely an atomic property—by graphically 
plotting the absorbability of the secondary radiation pro- 
ceeding from different elements subject to X-rays and the 
atomic weight of the radiator. A periodic curve was 
obtained in many portions of which the slope was so great 
that atomic weights might be obtained by interpolation 
with considerable accuracy. : 
Using a thin plate of aluminium as the absorber, the 
relation between the absorbability of the radiation and the 
atomic weight of the radiator was found to be approxi- 
mately a linear one for a long range of atomic weights 
on both sides of nickel. Nickel itself, however, can only 
be brought into line by assigning it an atomic weight a 
little above 61. Many absorbing substances have been 
used, and all give approximately the same value, the 
maximum variation in the values found from these different 
experiments being about 0:3. 
The experiments on fairly good commercial specimens 
indicated an atomic weight of about 61-4. To make the 
evidence more conclusive and the numerical values as 
accurate as possible—though a 2 per cent. or 3 per cent. 
impurity could not materially affect the result—the purest 
specimens were used, and the atomic weisht found by two 
separate series of observations did not differ by more than 
about o:1 from the value previously obtained. We are 
thus forced to the conclusion that the atomic weight of 
nickel is about 61-3. Details of these experiments we hope 
to publish shertly. Cuartes G, Barkha. 
University of Liverpool, February 6. 
NO. 1946, VOL. 75] 
have | 
ON HOMER LANE’S PROBLEM OF A 
SPHERICAL GASEOUS NEBULA. 
Sys HIGHLY interesting problem of pure 
mathematics was brought before the 
world in the American Journal of Science, July, 1870, 
by the late Mr. Homer Lane, who, as we are told by 
Mr. IT. J. J. See, was for many years connected 
with the U.S, Coast and Geodetic Survey at Washing- 
ton. Lane’s problem is the convective equilibrium, 
of density, of pressure, and of temperature, in a 
rotationless spherical mass of gaseous fluid,? hot in 
its central parts, and left to itself in waveless 
quiescent ether. 
For the full discussion of this problem we 
must, according to the evolutionary philosophy of the 
physics of dead matter, try to solve it for all past and 
future time. But we may first, after the manner of 
Fourier, consider the gaseous globe as being at any 
time given with any arbitrarily assumed distribution 
of temperature, subject only to the condition that it 
is uniform throughout every spherical surface con- 
centric with the boundary. And our subject might 
be the absolutely determinate problem of finding the 
density and pressure at every point necessary for 
dynamical equilibrium. But for stability of this equili- 
brium, Homer Lane assumed, rightly as I believe 
is now generally admitted, that it must be of the kind 
which two years later’ I called convective equilibrium. 
§ 3. If the fluid globe were given with any arbi- 
trary distribution of temperature, for example uniform 
temperature throughout, the cooling, and consequent 
augmentation of density of the fluid at its boundary, 
by radiation into space, would immediately give rise 
to an instability according to which some parts of 
the outermost portions of the globe would sink, and 
upward currents would consequently be developed in 
other portions. In any real fluid, whether gaseous 
or liquid, or liquid with an atmosphere of vapour 
around it, this kind of automatic stirring would tend 
to go on until a condition of approximate equilibrium 
is reached, in which any portion of the fluid descend- 
ing or ascending would, by the thermodynamic action 
involyed in change of pressure, always take the tem- 
perature corresponding to its level, that is to say, its 
distance from the centre of the globe. 
§ 4. The condition thus reached, when heat is con- 
tinually being radiated away from the spherical 
boundary, is not perfect equilibrium. It is only an 
approximation to equilibrium, in which the tempera- 
ture and density are each approximately uniform at 
any one distance from the centre, and vary slowly 
with time, the variable irregular convective currents 
being insufficient to cause any considerable deviation 
of the surfaces of equal density and temperature from 
sphericity. 
§ 5. A very interesting and important theorem was 
given by Prof. Perry, on p. 252 of Narure for July, 
1899, according to which, for cosmical purposes, it is 
convenient to divide gases into two species—species 
P, gases for which the ratio (k) of thermal capacity, 
pressure constant, to thermal capacity, volume con- 
§ 2. 
> 
1 “ Researches on the Physical Constitution of the Heavenly Bodies” 
Astr. Nachr., November, 1905 ) 
2 By a gaseous fluid 1 here mean what is commonly called a ‘perfect 
gas,"’ that is, a gas which fulfils two Jaws:—(1) Boyle's law. At constant 
temperature it exerts pressure exactly in proportion to its density, or in 
inverse proportion to the volume of a given homogeneous mass of it. 
(2) A given mass of it, kept at constant pressure, has its volume exactly 
proportional to its temperature, according to the absolute thermodynamic 
definition of temperature (Preston's ‘Theory of Heat,” Article 290). 
According to the ‘‘Kinetic Theory of Gases,” every gas or vapour 
approximates more and more closely to the fulfilment of these two laws, 
the smaller is the proportion of the sum of times in collision to the sum 
of times of moving approximately in straight lines between collisions. 
1 “On the Convective Equilibrium of Temperature in the Atmosphere.” 
(Literary and Philosophical Society of Manchester, January 21, 1862; 
re-published as Appendix E, Math. and Phys. Papers, vol. iii.) 
