54 
but has 
istan. (Brandis, ‘* Forest Flora of North-West and Central 
India,” p. 511). Our thanks are due to Sir Joseph Hooker for 
pointing out that the statement as it stands suggests a wrong 
inference. THE WRITER OF THE NOTE, 
The Kinetic Theory of Planetary Atmospheres. 
THE much-debated question of the applicability of the 
kinetic theory to decide what gases can and what gases cannot 
exist in the atmospheres of planets is necessarily once more raised 
by a somewhat striking paper by M. E. Rogovsky in the 4s¢vo- 
physical Journal for November, 1901. In performing certain 
calculations contained in this paper which are embodied in 
Table III. (p. 254), the author bases his work on the assump- | 
tion (p. 252) that-**. . . the equation 
s/(2a¢) 
10°22 
W = 
where W is the most probable velocity of the molecules of a gas, 
gives the minimum most probable velocity in a gas which 
escapes from the surface of the given celestial body.” 
This is equivalent to assuming that a gas will escape if the 
velocity required by a molecule in order to overcome the planet’s 
attraction and fly off to infinity (if it does not collide with other 
NATURE 
| 
not been found between Macedonia and Afghan- | \ ] 
| atmosphere, its escape must be due to entirely different causes, 
[May 15, 1902 
If helium is actually at the present time escaping from our 
and has to be investigated by entirely different methods from 
those contained in M. Rogovsky’s paper. At all events, a most 
probable molecular velocity of not more than one-tenth, cor- 
responding to a kinetic energy of not more than one-hundredth 
of that required to carry a molecule of the gas to infinity cannot 
have much influence in helping a gas to escape from a planet’s 
atmosphere. And so soon as outside influences are invoked, the 
ratio of velocities which forms the basis of that portion of M. 
Rogovsky’s work here considered ceases to be the determining 
factor of the problem. G. H. Bryan. 
Bangor. 
On Prof, Arrhenius’ Theory of Cometary Tails and 
Aurore, 
THE letter of Dr. J. Halm in your number of March 67is 
based on two misunderstandings into which the writer could not 
have fallen if he hadseen Arrhenius’ original papers (PAys¢kal- 
| dsche Zeitschrift, November 1900), or my description of them 
molecules) is not more than 10°22 times the most probable | 
velocity. 
Now if we calculate the probability of a molecule attaining a 
speed of ro times the most probable velocity (to use round 
numbers), we find that the expression for this probability involves 
a factor of the form e~}, that is about 1074%, and this alone is 
sufficient to show that it is so rare for a molecule to attain a 
speed of 10 times the most probable velocity that such events 
cannot possibly have any appreciable effect on the planet's 
atmosphere. 
Let us examine the matter a little closer, and 
instance Jet us calculate the average proportion of molecules in 
any gas which have at any instant speeds of wot /ess than 10 
times the most probable velocity. The numerical result we 
obtain is 
10”. 
To interpret this result, let us suppose we are dealing with a 
gas one cubic centimetre of which contains 107! molecules ; this 
figure giving a rough estimate of the number of molecules in a 
cubic centimetre of air of ordinary temperatures and pressures. - 
Then a volume of this gas equal to 2°4 times a cube the side of 
which is 100 £z/omedves will have to be taken in order that there 
may be an average of ove molecule moving with a speed of 
10 times the most probable velocity. 
So far our calculations do not involve any considerations of 
time, although this must necessarily enter into the problem of 
escape of gas from a planet’s atmosphere. Let us therefore now 
suppose the mass of gas under consideration to be bounded bya 
surface S, and let it further be supposed that every molecule which 
impinges on S with a speed greater than 10 times the most 
probable velocity escapes. Let the most probable velocity of 
the molecules be 1093 metres per second, the number assumed 
by M. Rogovsky for helium on p. 252 of his paper. 
Then in order that the number of molecules removed in this 
in the first © 
| ordinary tails pointing away from it. 
way may be equal to the removal of a layer of the gas 1 milli- | 
metre thick all over the surface S, it will be necessary for about 
2°8 x 10° years to elapse. 
Next suppose the surface S to be equal in area to the surface 
of our earth, namely a sphere 4 x 104 kilometres = 4 x 10° centi- 
metres in circumference. How many years would it take for a 
cubic centimetre of gas to escape? The answer comes out to be 
about 5°371 x 10!” years. 
The only conclusion which can be drawn, not only from the 
present calculations, but also from others of a similar character ! 
which have been made, is that a gas cannot escape from the at- 
mosphere of a planet by the motion of its molecules among 
themselves without the aid of extraneous causes unless the most 
probable velocity of the molecules is considerably greater than 
one-tenth of the velocity required to overcome the planet’s 
attraction. 
1 Phil. Trans. A, vol. cxcvi., pp. 1-24 (t901); also S. R. Cuok, Aséyo- 
physical Journal January, 1900. 
NO. 1698, VOL. 66] 
in the Popular Sceence A/onth/y (January 1902), instead of the 
friendly but erroneous notice of my paper in the Osservatory. 
(1) Dr. Halm quotes Prof. Schwarzschild to show that 
Arrhenius’ theory ‘‘appears to be incompatible with any 
assumption which regards the cometary matter as being of a 
gaseous constituency.” 
Arrhenius never suggested that gaseous mo/eca/es could be 
propelled by the pressure of light. “To quote my account of 
his theory :—‘‘ As the comet approaches the sun, the intense 
heat causes a violent eruption of hydrocarbon vapours on the 
side towards the sun. The hydrogen boils off, and the vapours 
condense into small drops of hydrocarbons with higher boiling 
points, or ultimately solid carbon is thrown out, finely divided 
as in an ordinary flame. The largest of these particles fall 
back to the comet, or if they are not condensed till at a great 
distance from it, they form tails turned towards the sun. The 
smaller are driven rapidly from the sun by the pressure of its 
light, with a speed depending on their size, and form the 
That particles of different 
sizes should be formed from the same comet is natural, since 
the comet is likely to be formed of heterogeneous materials, 
and there must be great variety in the circumstances of con- 
densation.” 
Dr. Halm does mention the idea of condensation into drops, 
and remarks, ‘‘ Whether such an assumption can be justified” 
appears to me very doubtful.”’ This, of course, is merely his 
opinion, and receives no authority from the calculations of 
Prof. Schwarzschild. Indeed, in a_ recent letter to me, 
Arrhenius points out that these results fit the theory remark- 
ably well. As Dr. Halm says, Prof. Schwarzschild reckons 
that ‘‘the corpuscles thrown off in the tails of comets should 
have diameters not smaller than 0’o7u and not exceeding 1°5m, 
supposing the specific gravity of the corpuscle to be that of 
water.” ; 
Now Arrhenius, in his original paper (November 1900), 
taking the specific gravity of the hydrocarbon drops to be o°8, 
calculates the size of the particles required by his theory to 
account for the curvatures observed in the case of four different 
comets’ tails, and finds them to be O*Ip, 0°59u, O°O4u, I°25u. 
These values are distributed almost exactly over the interval 
within which light could exert a pressure greater than gravita- 
tion, according to the ‘‘ exhaustive mathematical investigation ”* 
of Prof. Schwarzschild published a year later. 
(2) Dr. Halm says :—‘‘ At any rate Prof. Schwarzschild’s 
profound mathematical investigation makes it absolutely clear 
that the idea of minute electrically-charged corpuscles—about 
one-thousandth the size of a*hydrogen atom (see Observatory) — 
being propelled by the sun’s light towards the earth and causing 
the various phenomena of aurorze, Gegenschein, &c., receives 
no support from the mathematical point of view.” 
A reference to Arrhenius’ paper and to my article will show 
that it is carefully explained in both that the charged (negative) 
particles are known to form excellent nuclei for condensation. 
It is the small drops so formed, and not the corpuscles, which, 
according to Arrhenius, are supposed to be driven off as far 
as the earth, and beyond it, giving rise to the aurorze, &c. 
As was seen above, Prof. Schwarzschild’s results support such 
a view. JoHN Cox. 
McGill University, Montreal, March 19. 
