42 



NATURE 



[March io, 192 i 



may therefore be of interest. There are two sets of 

 data. In one the density and atomic weight of lead 

 from thorite have been compared with the values of 

 ordinary lead, and in the other a similar comparison 

 has been made for the lead derived from two uranium 

 minerals. These two sets, of course, cannot be compared 

 together, as the densities of specimens are compar- 

 able only when they have been prepared under iden- 

 tical conditions. With due attention to this point the 

 relative densities are, in the case of lead, capable of 

 determination to a very high degree of accuracy. 



In the first set of data (Nature, February 4, 1915) 

 the density determinations agreed in the case of three 

 determinations on 73 grams of ordinary lead to within 

 eight units, and in the case of two determinations on 

 65 grams of thorite lead to within four units in the 

 fourth place of decimals. The first two values of the 

 atomic weights in the following table are single deter- 

 minations by a modification of Stas's method, the 

 lead being converted into chloride, via the nitrate, 

 in a quartz vessel without transference, and the ratio 

 Pb : PbCL determined. The third value is that ob- 

 tained by O. Honigschmid in Vienna on another 

 fraction of the same thorite lead used in the density 

 determination by the silver titration method from 

 four determinations of the ratio PbCU : 2.Ag and four 

 of PbCL : aAgCl, and the probable error is given as 

 ±0014 (Zeitsch. Elektrochem., 1917, vol. xxiii.. p. 161). 

 The second set of data is that of T. W. Richards 

 and C. Wadsworth (Journ. .Amer. Chem. Soc, iqi6, 

 vol. xxxviii., pp. 221 and 1658). The atomic weights 

 are also by the silver titration method. The value 

 207-20 for the atomic weight of ordinary lead has also 

 been obtained by G. P. Baxter and F. L. Grover 

 (Journ. Amer. Chem. Soc, 1915, vol. xxxvii., p. 1027), 

 and the value 207-18 by O. Honigschmid and Mile. S. 

 Horovitz (Monatsh., 1915, vol. xxxvi., p. 351;) by 

 similar methods. (Compare also Ann. Rep. Chem. 

 Soc., iqi6, vol. xiii., p, 247.) 



Varietv of lead Atomic Density Atomic Difference 



' ' weight. at 20°. volume. from mean 



Ordinary 207-199 ir3465 18*2619 +00009 



Ceylon thorite 207*694 ii'376o i8-2572 -0*0038 



20777 l8'2639 + 0*0029 



Mean i8'26io 



Ordinary 207*20 ii*337 182765 -0*0026 



Australian uranium ore 206*34 11*288 18*2796 +0*0005 

 Norwegian cleveite ... 206*085 11*273 18*2813 +0*0022 



Mean 18 •2791 



The differences in the atomic volume are thus 

 exceedingly small, and, moreover, they are not sys- 

 tematic. Rejecting the single determination of the 

 atomic weight of thorite lead, it appears that ordinary 

 lead with the intermediate atomic weight has an 

 atomic volume slightly below that of the others. It 

 seems quite safe to conclude that the atomic volumes 

 cannot differ by so much as three parts in ten 

 thousand and the atomic diameters by so much as 

 one part in ten thousand. Frederick Soddy. 



Relativity and the Velocity of Light. 



In his article in Nature of February 17 on the 

 general physical theory of relativity Mr. J. H. Jeans 

 refers to recent experiments of Majorana, and his 

 remarks imply that these experiments rendered it 

 "possible to watch the progress of the ripple directly" 

 and to measure the velocity of light in its unidirec- 

 tional course from source to receiver, with the result 

 that this velocity was shown to be constant. He 

 contrasts these experiments with the original experi- 

 ments of Michelson and Morley, in which the mean 

 velocity of light in its outward and return journey 

 NO. 2680, VOL. 107] 



after its reflection from a mirror was dealt with. As 

 the point in question is a fundamental one, and as a 

 statement to this effect has been made before, I think 

 the matter should not be passed over. 



The experiments of Majorana referred to are doubt- 

 less those described in Comptes rendus (No. 14, 

 tome clxv., 1917, and No, 2, tome clxvii., 1918) 

 designed to show the constancy of the velocity of light 

 relative to the observer when reflected by a moving 

 mirror or when issuing from a moving source. I 

 venture to suggest that these experiments do not 

 bear the interpretation that Mr. Jeans puts upon 

 them, and that the experiment has not yet been 

 devised that will enable a comparison to be made 

 between the velocity of light on its outward and 

 return journeys along the same path, or that will 

 give a measure of the velocity on a single journey. 

 The author of these papers makes no claim to have 

 done this. I fear such an experiment is impossible. 



C. O. Bartrum. 



32 Willoughby Road, Hampstead, 

 February 24. 



I had not intended to make the statement which 

 Mr. Bartrum considers is implied in my words, and 

 am sorry that in aiming at brevity I appear to have 

 achieved only ambiguity. It need scarcely be said 

 that I agree that no experiment has been, or can be, 

 devised which can measure the velocity of light in 

 any unidirectional course. The impossibility of any 

 such experiment is, in effect, the primary postulate 

 of the theory of relativity. 



It is, nevertheless, possible to compare two velo- 

 cities along the same unidirectional course, and this 

 is what Prof. Majorana claims to have done. 



The Michelson-Morley experiment gave us the sum 

 onlv of the times of two separate journeys — from A 

 (light) to B (mirror) and back from B to A. We 

 cannot even speak of comparing the time on AB with 

 that on B.\ until we have defined time at B in terms 

 of the time at A. If this is defined in terms of the 

 relativity relation t! = ^{t - ux j c") , then the Michelson- 

 Morley experiment is consistent with the two journeys 

 being performed with the same velocity c, and there- 

 fore in equal times, but it does not of itself estab- 

 lish equality either of velocity or of time. The addi- 

 tional information provided by the experiments of 

 Majorana does, I believe, enable this equality to be 

 proved. 



Consider the problem in terms of an aether and a 

 FitzGerald-Lorentz contraction. According to the 

 Michelson-Morley experiment, the time on the double 

 journey is equal to 



<-m.-«^-fJ 



(I) 



but there is so far no justification for identifying 

 the two terms in this sum with the times of the 

 separate journeys. The distributed expression for the 

 time of the double journey might, in general, be of 

 the form 



where c+o, c+yS are the velocities through the aether 

 on the two journeys. For this to conform to the 

 results of the Michelson-Morley experiment, expres- 

 sions (i) and (2) must be equal, requiring that 



2c + a + P _ 1C / X 



(^-« + a)(f +« + /:<) C^-U^ 



Now impose a further velocity v on the whole 



Michelson-Morley apparatus, so that its velocity 



through the eether becomes u-\-v. The first result 



of Majorana (Phil. Mag., vol. xxxv., p. 173) shows 



