78 



NA TURE 



[May 24, 1900 



LETTERS TO THE EDITOR. 



\The Editor does not hold himself responsible for opinions ex- 

 pressed by his correspondents. Neither can he undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of Nature. 

 No notice is taken of anonymous communications. "^ 



Escape of Gases from Atmospheres. 



I ASK for space to reply to Mr. Cook's letter in last week's 

 Nature. 



There are two ways in which the rate at which gases escape 

 from atmospheres may conceivably be investigated, viz. the 

 a priori method, which seeks to determine from the kinetic 

 theory of gas what proportion of molecules attain the requisite 

 speed ; and the a posteriori method, which seeks to ascertain 

 from the observed effects of escape where and on what scale it 

 has actually taken place. 



I tried the a priori method more than thirty years ago, but 

 had to abandon it, having satisfied myself that in the present 

 state of our knowledge it cannot be made to furnish a valid 

 investigation. I came to this conclusion upon grounds which 

 are fully stated in a paper of which the first part will appear in 

 the May number of the Astrofhysical Journal, and the second 

 and more important part probably in the June number. I then 

 turned to the a posteriori method, and endeavoured to develop 

 it in the memoir which Mr. Cook has criticised (see Scientific 

 Transactions of the Royal Dublin Society, vol. vi. {1897), 

 p. 305, or Astrophysical Journal (ox ]a.nn3,ry 1898, p. 25). 



Both methods, if correctly applied, should lead to the same 

 results ; but the a priori method, as handled by Mr. Cook and 

 Prof. Bryan, furnishes a different rate of escape from the 

 a posteriori method. In such cases there must be a mistake or 

 mistakes somewhere, and in the above-mentioned paper sent to 

 the Astrophysical Journal I have endeavoured to trace out 

 where the mistakes are. 



The principal errors seem to be three. 



The number of molecular speeds which lie between v and 

 v-Vdv 



= N(7r + 8)^z; 



where N is the number of molecular speeds whose distribution 

 is under consideration, ir is the probability function (in this case 

 Maxwell's law), and 5 may be called the deviation function, as it 

 furnishes the difference which exists between the actual number 

 and that computed by Maxwell's law. In all cases of prob- 

 ability laws the deviation fuction S is large when N is small ; 

 but when the events whose distribution is sought are independent 

 of one another and have causes all of one kind, then 5 becomes 

 inconspicuous when N is sufficiently large, and the distribution 

 law may iti such cases be reduced to '^irdv without sensible 

 error. This reduction, however, is not always legitimate when, 

 as in gases, the events are so associated with one another and 

 with other agencies that cumulative effects can arise. Then S 

 may become larger than ir in reference to those values of v 

 which make ir small. The first omission seems to be the omis- 

 sion to take this into account. 



Another omission is the omission to take the size of the 

 element of volume dxdydz into account. This, as experiment 

 shows, may at the bottom of the earth's atmosphere be as small 

 as the cube of one-tenth of a millimetre. But in the regions 

 from which the escape of gas is possible, it has a volume of 

 many cubic miles. This circumstance, which largely increases 

 the opportunity which molecules have of escaping from that 

 situation, has not been taken into account. 



But perhaps the most serious error is overlooking the fact that 

 Maxwell's law holds good only of a portion of isotropic gas 

 surrounded by similar gas. That the gas shall be isotropic is 

 one of the data employed by Maxwell in his proof of the law. 

 Another law (which may be, and in fact is, very different from 

 Maxwell's) is the law of distribution of the molecular speeds in 

 a portion of gas as anisotropic as that of the regions from which 

 the actual escape takes effect. The deductions from Maxwell's 

 law may be correctly derived, but the premiss being wrong the 

 conclusion has no significance. 



It would be very satisfactory if we had two ways — the 

 a priori method as well as the a posteriori — of investigating 

 the problem; but with our present limited knowledge of 

 molecular physics, this does not seem to be within our reach. 



Mr. Cook at the end of his letter supposes that "the dis- 

 covery by Ramsay of helium as a constituent of our atmosphere 



only tends to confirm the results of my (Mr. Cook's) calculations 

 of the impossibility of its escape." This is so far from being 

 the case that the quantitative determinations made in Prof. 

 Ramsay's laboratory are now sufficiently advanced to lead with 

 much increased emphasis to the opposite conclusion. This 

 appears from the following data, which have been generously 

 placed at my disposal by my friend. Prof. Ramsay : — 



(i) The proportion by volume of argon in dry atmospheric 

 air is about i per cent, of the whole, the volume of neon (to 

 which the present note will not further refer) may be taken as 

 about a thousandth part of the volume of argon, and the volume 

 of helium as about i/io to 1/20 of the volume of neon. Ac- 

 cordingly, the volume of helium in dry air is something like 

 from 1/10,000 to 1/20,000 of the volume of argon, or from 

 1/1,000,000 to 172,000,000 of the whole volume of the air. 



(2) Both argon and helium are supplied to the atmosphere 

 by hot springs ; argon generally by all hot springs which contair> 

 atmospheric gases, and helium by some of them. 



(3) The argon in such springs, like the oxygen and nitrogen, 

 may be simply gas which had previously been removed from 

 the atmosphere by water. A litre of water under ordinary 

 conditions will absorb about 45 c.c. of the oxygen of the air in 

 contact with it ; about 15 c.c. of its nitrogen ; about 40 c.c. of 

 its argon ; and about 14 c.c. of its helium.' 



Hence in rain we should expect to find the following pro- 

 portions preserved : — 



NO. 1595, VOL. 62] 



He. 



So far as oxygen, nitrogen and argon are concerned, these pro- 

 portions are sufficiently nearly those in which the gases are pre- 

 sent in the springs referred to. But in those springs in which 

 helium also has been detected, it seems to be present in quanti- 

 ties about i/io of the argon — that is, in a quantity which _is 

 nearly from 3000 to 6000 more than we can attribute to its 

 having been derived from the atmosphere. 



(4) This great excess of helium in some springs has doubtless 

 a mineral origin, some minerals, chiefly uranium compounds, 

 containing much helium which they give up when heated. On 

 the other hand, there does not appear to be any comparable 

 mineral source of argon. 



(5) Hence, on the whole, the argon which is being supplied 

 to the atmosphere by hot springs seems to be argon which had 

 previously been withdrawn from the atmosphere and which is 

 being restored to it. Whereas, in contrast to this, there seems to 

 be a continuous transfer of additional helium from the solicl 

 earth to the atmosphere always going on. 



Thus the facts seem to warrant our inferring : — 



(a) That the excessively small quantity of helium in the 

 atmosphere is helium on its way outwards. 



(b) That it would have become a much larger constituent of 

 the atmosphere, by reason of the influx from below, if there had 

 been no simultaneous outflow from above. 



(c) That the rate of this outflow is presumably equal to the 

 rate of supply ; and therefore such as would suffice in a few 

 thousand, or at least in a few million, years to drain away the 

 small stock of helium in the earth's atmosphere, if the source of 

 supply from bdow could be cut off.^ 



1 See the determinations made by Herr Estreicher in Prof. Ramsay's 

 laboratory, as recorded in ih^ Zeitschri/t fur pkysikaliscke Chemie,wo\. 

 xxxi. (1899), p. 184. 



- If the proportion of helium in the atmosphere is assumed to be some- 

 thing between 1/1,000,000 and 1/2,000,000 of the whole atmosphere 

 (which rather tends to be an over-estimate, since it does not take 

 into account the increased diminution of the density of the helium as it 

 ascends, which is a consequence of its escape from the top of the atmo- 

 sphere), then the helium in the whole of the earth's atmosphere would, if 

 reduced to standard temperature and pressure, occupy a volume somewhere 

 between a cube of ten miles, and half that space. Now, so far as can be 

 judged from the imperfect observations as yet made on the rate at which 

 helium is being filtered into the atmosphere, it would appear that the pre- 

 sent rate of supply is such as would yield this quantity of helium in some- 

 thing like one or two thousand years, and perhaps in a less time. 



