NA TURE 



[July 22, 19: 



Letters to the Editor. 



[The Editor does not hold himself responsible for 

 opinions expressed 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 twtice is 

 taken of anonymous communications.'] 



Cosmical Theory and Radioactivity. 



Sir Ernest Rutherford in his book " Radio- 

 active Substances and their Radiations " has sug- 

 gested the possibility that solar heat may be supplied 

 from radioactive energy derived from elements which 

 had become radioactive under the extreme thermal 

 conditions prevailing. 



As possibly having bearings on cosmical theory 

 (formation of nebulae, planetary genesis, etc.) I 

 would direct attention to the probability that such 

 induced radioactivity would be attended with 

 explosive phenomena on a very great scale and of 

 extreme intensity. 



Let it be assumed that in some deep-seated region 

 of the sun the temperature has attained a potential 

 critical for some element present — that is to say, 

 adequate to disturb the atomic stability of this 

 element. Now normal radioactivity results from 

 internal atomic causes and the radioactive constant 

 is statistical in origin, like a death-rate. But here 

 instability is induced from without inwards. It 

 seems, therefore, difficult to imagine that a normal 

 radioactive constant can control the resultant effects. 

 What will happen must resemble no mere death-rate 

 based on statistics, but rather the mortality brought 

 about by earthquake or flood. A large number of 

 the specific atoms would be affected and a very great 

 local rise in temperature would follow. There is, 

 now, the further probability that this sudden rise 

 will involve yet other elements in the catastrophe. 



If this inference is justified, explosive phenomena 

 in suns and nebula; so far from being unaccountable 

 must be regarded as inevitable, as being associated 

 with gravitative attraction and the internal properties 

 of the atom. 



It is to be expected that such explosive phenomena 

 would diminish in frequency and intensity as time 

 advanced and elements of higher atomic weight 

 became degraded. Thus, in primeval times, our sun 

 may have been many times rent by such explosions. 

 There appears to be evidence that central explosions 

 of great violence occasionally occur even to-day. 



How would the principle of the conservation of 

 moment of momentum fare under conditions involv- 

 ing the translation of internal atomic energy into 

 molar forms ? J. Joly. 



Trinity College, Dublin, July 9. 



Gas Pressures and the Second Law of 

 Thermodynamics. 



In the June Philosophical Magazine Mr. Fairbourne 

 endeavours to prove that in certain easily attainable 

 cases the second law of thermodynamics might be 

 circumvented. He attempts to show that if an en- 

 closure be divided by a partition, the chance that a 

 molecule of a rarefied gas will pass the partition, 

 from the space I to the space II, may be modified, 

 by a funnel, without affecting the chance of passing 

 from II to I, so that a pressure difference will arise. 

 He considers the simple case, shown in Fig. 1, of a 

 right-angled " funnel " in two dimensions only, trun- 

 cated so that the diameter at the end BC is twice 

 that at AD. Taking a point O on BC he shows 



NO. 275 I, VOL. I 10] 



that, of the molecules passing through O, on the 

 whole more than half will be reflected by AB or CD 

 and less than half will pass through AD, since they 

 can approach from an angle w while the angle be- 

 tween the limiting paths by which they can get 

 through is in general less than jt/2. He deduces that 

 of 2N molecules striking BC in a given time less than 

 N will pass through AD, while all of the N molecules 

 reaching AD from the other side in the same time 

 will cross it, so that on the whole more will come 

 from II to I than vice versa. 



The error in this argument lies in the fact that it 

 is impossible to construct a line BC out of a number 

 of points O ; it is necessary to define the tolerance 

 before one can say whether molecules have passed 

 through O or not. As soon as this is done (by taking 

 an element of length dl at O, and defining passage 

 through O as passage through this length), it is clear 

 that the chance of " passing through O " is not 

 independent of the angle of incidence 8, but is pro- 

 portional to cos 0, since dl is foreshortened for ob- 

 liquely moving molecules. In any given case it will 

 now be found that the total number of paths leading 

 through AD is the same on both sides of the partition 

 ZZ'. However, the following general proof of this 

 equality should save the trouble of integrating par- 

 ticular cases. It applies to three dimensions and any 

 shape of funnel. 



It is clear that before the funnel (AB.DC) was 

 added to the partition the chances of passing from 



II 



II to I and from I to II were equal, and that adding 

 the funnel does not alter the chance of passing from 

 II to I. If it is to have an effect then it must decrease 

 the number of paths from I to II. But for every 

 such path XY which it blocks it introduces a new 

 path X'Y, and this is true of every point in any 

 funnel. This result is of course well known in geo- 

 metrical optics ; if it were incorrect any temperature 

 and energy density of radiation would be obtainable 

 without work. 



It may also be remarked that there is not only 

 molecular roughness in even a polished wall, but 

 thermal agitation of all the molecules of the wall ; 

 the argument that if the wall reflects light it should 

 " reflect " a molecule is vitiated by the fact that the 

 wave-length of visible light is about a thousand 

 molecular diameters ; and the argument that even if 

 the direction of rebound is fortuitous the funnel 

 should have an effect defies elementary hydrostatic 

 theory. 



Lastly, the mean free path of the molecules is 

 irrelevant. Mr. Fairbourne assumes that his theory 

 would not apply if there were a large proportion of 

 encounters between gaseous molecules ; but it is clear 

 that if the effect of the funnel is to give on the whole 

 a bias away from II to the average molecule striking 

 it, it cannot matter whether that molecule retains 

 the bias or hands it on to another in an encounter. 



