July 15, 1920] 



NATURE 



611 



and he gives us a number of curious illustrations, 

 one of which, however, may judiciously have been 

 omitted in a book which claims to be popular. 



The Propagation of Electric Currents in Tele- 

 phone and Telegrapli Conductors. By Prof. 

 J. A. Fleming. Third edition, revised and ex- 

 tended. Pp. xiv + 370. (London: Constable 

 and Co., Ltd., 1919.) Price 215. net. 

 In preparing *a new edition of his well-known 

 study of the propagation of telegraph and tele- 

 phone currents. Prof. Fleming has taken the 

 opportunity of bringing it in line with both the 

 latest theoretical and the latest practical work in 

 this field. The subject presents a very fine ex- 

 ample of mathematical investigation leading to 

 results of far-reaching practical utility, and the 

 author conducts his reader along a logically con- 

 tinuous path from the point where he introduces 

 him in the first chapter to hyperbolic functions of 

 complex angles, to the page near the end where 

 he pauses to show him a picture of a telephone 

 cable with loading coils being laid across the 

 Channel. Telegraph and telephone engineers owe 

 a great debt of gratitude to Prof. Fleming for 

 the way he has, at first in his lectures and then 

 an the volume now befare us, brought together 

 so much valuable work in this complicated subject, 

 to which he himself has been no mean contributor. 

 Perhaps the most valuable feature of the treatment 

 is the way in which he has simplified, so far as 

 possible, the mathematical results of the original 

 investigators, while at the same time facilitating 

 the building of the bridge from the other end by 

 providing the material to extend the student's 

 mathematical resources in the required direction. 



Half-past Twelve : Dinner Hour Studies for the 

 Odd Half-Hours. By George W. Gough. 

 Pp. vi + 77. (London : Sells, Ltd., n.d.) Price is. 



There is abundant evidence that much of the 

 present-day industrial unrest arises from the ready 

 acceptance of fallacious economic ideas by many 

 of those engaged in industry. The need for sound 

 teaching in the first principles of economics of a 

 character within the ready understanding of work- 

 ing men and women, and of all who help to form 

 public opinion, is acute, and Mr. Gough has 

 rendered a valuable service in helping to satisfy 

 this need. 



This inexpensive little book is an attempt to 

 •correct wrong economic ideas and a limited per- 

 spective by providing a series of talks on familiar 

 ■economic topics such as production, capital, 

 profits, wages, the mechanism of exchange, and 

 the principles of taxation. The author deals with 

 these in a brief but extremely lucid manner, and 

 his conclusions, while significantly orthodox, are 

 arrived at without bias or prejudice. His illustra- 

 tions are most apt, and will effectively secure the 

 interest of his readers. It is to be hoped that this 

 publication will be widely read not only by indus- 

 trial workers and students, but also by the public 

 generally. A. P. M. F. 



NO. 2646, VOL. 105] 



0=-loge K-l-loge 



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 manu- 

 scripts intended for this or any other part of Nature. 

 No notice is taken of anonymous communications.} 



The Separation of the Isotopes of Chlorine. 



Prof. Soddy (June 24) and Mr. Core (July 8) have 

 in their romments on my letter in Nature of June 17 

 raised several points of interest. The former asks 

 that all the assumptions from which the equation 



[C1',][CL]=[C1C1']^ 



was deduced may be given. The assumptions are : 



(i) The differences between the vapour pressures of 

 the three varieties of chlorine are negligibly small. 



(2) The vapours are almost perfect gasesi 



(3) The three varieties of gaseous chlorine are 

 separable by semi-permeable membranes or other 

 means, or the equivalent assumption that the thermo- 

 dynamic potential of a mixture of the three varieties 

 is the sum of the thermodynamic potentials of the 

 constituents. 



(4) The work required to convert reversibly i mol. 

 of solid CI'2 and i mol. of solid CU into 2 mols. of 

 solid CICl' is negligible. 



The three last assumptions lead us to the formula 

 {C1C1'}2 

 {a,}{Cl',} 



where the bracket { | indicates concentration of 

 saturated vapour. Whence with the aid of assump- 

 tion (i) we deduce that K=i, 



Assumption (4) follows from Nernst's heat theorem 

 if it be postulated that the energy of the change 

 considered is almost zero. It would appear, there- 

 fore, that if isotopes are inseparable by processes 

 similar to that described in my first letter, one of the 

 assumptions made is not valid. 



Prof. Soddy asks whether there is any step in my 

 argument to prevent its being applied to prove the 

 possibility of the separation of arbitrarily selected 

 atoms from a group of completely identical molecules 

 by chemical means ; for, if there is not, then it 

 follows, as a reductio ad ahsurdum, that the equili- 

 brium equation 



[C1',][C1,]=[C1C1']" 

 is wrong, and it is unnecessary to test its validity by 

 experiment. Concerning this query I am in doubt 

 whether it would be generally admitted that assump- 

 tion (3) could be made in such a case as that con- 

 templated by Prof. Soddy, and therefore I think it is 

 desirable that the question of the validity of the 

 equation should be submitted to the test of experi- 

 ment—so far as it is possible to do this. 



Mr. Core assumes that the isotopes of chlorine are 

 inseparable by chemical means, but does not agree 

 with my conclusion that if such is the case 

 Nernst's heat theorem will be difficult to defend. 

 He admits that at finite temperatures the dif- 

 ference in entropies of the solid reactants and re- 

 sultants is R log, 4, but he argues that it may become 

 zero at zero temperature owing to the effects of the 

 differences in properties of the three solids being more 

 pronounced at exceedingly low temperatures. But 

 even if it be admitted that in the case of chlorine 

 the difference between the entropies of the reactants 

 and resultants can be nothing at zero temperature 

 and Rlogj4 at finite temperatures, it has still to be 

 explained how the same rise in the difference of 

 entropies from zero to the constant value RIog(,4 

 could occur for a change of the same type in the case 



