SUB-ATOMIC PHENOMENA AND RADIOACTIVITY.THE important work of the two years (1929-30) under reviewhas for the most part been physical in character. The new wave-mechanics has been applied to the interpretation of the subjectand with increasing success to such processes as the emission ofa-particles from the nucleus and the disintegration of the nucleiof the lighter elements by swift or-particles; it is clearly going toplay an important part in future work. For the first time newisotopes have been discovered from an examination of band spectra ;the new method promises to reveal isotopes at concentrations belowthose ordinarily detected by the mass-spectrograph. Interestingtheories and speculations have been advanced on the nature of theproton, its relation to the electron, and their relative masses, alsoon the connexion between certain of the fundamental constantsof nature.On the chemical side, progress has been made with" the actinium problem," but an important, possibly a decidingdatum, the atomic weight of protoactinium, has still to be deter-mined before the outstanding difficulties of the subject are clearedup. The publication a t the close of the period of " Radiationsfrom Radioactive Substances " by Lord (formerly Sir E.) Ruther-ford, J. Chadwick, and C. D. Ellis has given students of radio-activity an admirable summary of the subject on the physicaland mathematical sides, and one of unique authority. As the titleimplies, however, the book covers a narrower range of subjectsthan earlier works by the senior author ; the chemical and geologicalsides of radioactivity are excellently but only briefly touched upon.A summary of work on p-particles and y-rays, and other subjectstoo purely physical in nature to be reported upon here, is given i n .this book.Isotopes and Mass-Spectra.During the period, knowledge of the isotopic constitution ofnine elements has been extended.The results are summarisedin Table I.The new isotopes of carbon, nitrogen, and oxygen have beenfound by detecting and interpreting isotopic lines in band spectraalong the lines suggested first by R. S. Mu1liken.l The first to befound were those of oxygen. Working on data provided for them1 Ann. Reports, 1926, 23, 284306 RUSSELL :TABLE I.Atomicnumber.Element .Carbon .........................6Nitrogen ........................ 7Oxygen ......................... 8Chromium ...................... 24Krypton ........................ 36Molybdenum .................. 42Xenon ......................... 54Tungsten ........................ 74Mercury ........................ 80Minimumnumber ofisotopes. of intensities.Masses of isotopes in order2 12, 13.2 14, 15.3 16, 18, 17.4 52, 53, 50, 54.6 84, 86, 82 and 83, 80, 78.7 98, 96, 95, 92, 94, 100, 97.9 129 and 132, 131, 134, 136,130, 128, 126 and 124.4 184 and 186, 182, 183.7 202, 200, 199, 201, 198, 204,196.by C. H. Dieke and H. D. Babcock,2 W. F. Giauque and H. L.Johnston ascribed the weak doublets of the atmospheric absorp-tion bands of oxygen to a molecule 0 1 6 0 1 8 .I n a later communica-tion,* they found other lines which are considered to originate fromthe molecule 0 1 6 0 1 7 . The abundance of these new isotopes issuch as not to be detectable by the new mass-~pectrograph.~ Theproportion of 0 1 6 to 0 1 8 is estimated as 1250 : 1 by H. D. Babcockand also by E. Moles,' and as 1075 -J-- 110 : 1 by S. M. NaudB.s Thatof 0 1 6 to 0 1 7 is given as lo4 : 1 by W. F. Giauque and H. L. Johnston4and also by E. Moles.' By a study of the isotope effect in thenitric oxide bands, S. M. Naudd 8 discovered the isotope N 1 5 . Bandheads were observed in the three bands investigated correspondingwith the calculated heads for the molecules W O 1 6 , N15O16, N14O18,and N 1 4 0 1 7 .These indicate the existence of a new isotope N 1 5and confirm 0 1 7 and 0 1 8 . The relative abundance of N 1 4 to "5was found to be 700& 140. This work has been confirmed byG. Herzberg,g who investigated the second positive group of nitro-gen. No evidenceof a third isotope N 1 6 was found. Carbon also is not a simpleelement. A. S. King and R. T. Birge lo found evidence of theexistence of the molecule C12C13 in the Swan spectrum of neutralC,, and R. T. Birge 11 of C13O16 in absorption spectrograms of COYand of C W 1 4 in the furnace (emission) spectrogram of CN.Although the evidence is conclusive for the existence of C13016 and3 Nature, 1929, 123, 318; A., 1929, 369. Ibid., p. 831; A . , 1929, 736.6 Ibid., p.761; A . , 1929, 624; Proc. Nat. Acad. Sci., 1929, 15, 471; A.,His value of the relative abundance is 800 : 1.Proc. Nut. Acad. Sci., 1927, 13, 670, and unpublished.F. W. Aston, ibid., p. 488; A., 1929, 484.1989, 971.Anal, Fis. Quim., 1930, 28, 127; A., 515.8 Physical Rev., 1939, [ii], 34, 1498 ; 1930, 35, 130; 36, 333 ; A., 1232.2. physiknl. Chem., 1930, [B], 0, 43; A., 1084.lo Nature, 1929, 124, 127; A., 1929, 970. 11 Ibid., p. 182; A,, 192'3, 970SUB-ATOMIC PHENOMENA AND RADIOACTIVITY. 307C13N14, it is neutral as to that of C12018, and decisive against thatof C12N15 and C12N16. R. T. Birge concluded that C13 is moreabundant relative to C12 than is N15 or N16 to N14, but no exactdata are given.lla Although further confirmation and extension ofthese interesting new results is desired, the results already obtainedshow that the examination of band spectra afford in certain casesa powerful means of detecting isotopes which are present inrelatively small abundance.In the mass-spectrograph very faintlines must necessarily be ascribed to possible impurities, but aseach molecule has its own spectrum, impurities in spectra, exceptin so far as they obscure the lines desired, are immaterial. On theother hand, however, the mass-spectrograph method has the greatadvantage of giving the absolute masses of isotopes and accuratelymeasuring their relative abundance ; the band spectrum methodgives only the relative masses of two isotopes and, as recent work 12has indicated, the intensities of the bands may not be a true measureof the relative abundance of isotopes.One further result has beenobtained by this method, vix., the possible existence of C139. H.Becker l3 found a third satellite to each absorption line in thehydrogen chloride rotation-vibration spectrum which is satis-factorily explained by the presence of this isotope. This hasrevived an old suggestion of F. W. Aston which was later rejectedby him. Confirmation of the existence of this isotope is highlydesirable, for it would make chlorine the first element of odd atomicnumber to have more than two isotopes and would make 39 thefirst isobare of odd mass-number to be shared by two elements ofodd atomic number.Continuing his work with the new mass-spectrograph, F.W.Aston has determined the isotopes of chromium,14 molybdenum,l5and tungsten,l6 using in each case as source a preparation of thecarbonyl. For chromium the mass numbers are 52, 53, 50, and54 in the relative abundance of 81-6,10-4,4.9, and 3.1% respectively.The packing fraction x lo4 for Cr52 is - 10 & 3 ( 0 1 6 = 0). Thecalculated atomic weight derived from these data is 52.011 & 0.006.For molybdenum the mass numbers are 98, 96, 95, 92, 94, 100, and97 in the relative abundance of 23.0, 17.8, 15.5, 14.2, 10.0, 9.8,and 9.6% respectively. The packing fractions x lo4 for M098and MofOO are both approximately - 5.5. The calculated atomicweight is 95.97 & 0.05. For tungsten the mass numbers are 184,The abundance ratio C13 : CI2 is non given as 1/400 by A.S. King andR. T. Birge; Aetrophye. J., 1930, 72, 19; A., 1931, 15.12 A. Elliott, Nature, 1930, 126, 203; A., 1232.13 2. Physik, 1930, 59, 601; A., 393.1 5 Ibid., p. 348; A., 1338.l4 Nature, 1930, 126, 200; A., 1232.l6 Ibid., p. 913; A., 1931, 15308 RUSSELL :lS6, 182, and 183 in the relative abundance of 30.1, 30.0, 22.6, and17.2% respectively. The packing fraction was not accuratelymeasured but is probably zero. The calculated atomic weight is183.96. In these three cases the atomic weights derived from thedata are, it is seen, in excellent agreement with those obtained bychemical means. In another piece of work,17 however, evidenceis adduced by the same author that the accepted atomic weightsof krypton and xenon (obtained by physical means) are decidedlylower than those obtained from the data furnished by the mass-spectrograph.He gives details of a method by which the relativeabundance of isotopes may be deduced with fair accuracy fromthe photometry of their lines in mass-spectra, and adds numericalresults for the isotopes of krypton, xenon, and mercury. Thenotion of isotopic moment is introduced. This is defined as thesum for all the isotopes of the product of abundance and distancefrom the mean mass number on the mass scale. This constantis not only roughly proportional to the error to be expected in anatomic weight calculated from mass-spectrum data, but is also anaccurate measure of the ease with which the atomic weight maybe altered, per unit, in the laboratory by such methods as diffusionor free evaporation.The isotopic moments for krypton, xenon,and mercury are calculated to be 0.87, 1.71, and 1.40 respcctivelyand the corresponding atomic weights are found to be 83.77 & 0.02,131.27 -+ 0.04 and 200.62 & 0.05 on the (chemical) scale 0 = 16.The value for mercury is in good agreement with the acceptedvalue, but each of the others is approximately a unit higher. Thesediscrepancies cannot be ascribed to impurities : suspicion is thrownon the limiting-density method of deriving the values hithertoaccepted. In this research, the order of abundance of isotopesof both xenon and mercury has been slightly modified and is thatgiven in Table I. One peculiar and possibly important new featuredisclosed is the exact equality in the abundance of certain isotopesof even-numbered elements.Thus Kr82 and Kr83 are each 11-79y0of the whole; Xe124 and Xe126 are each 0-0870, whilst W18* andW 8 6 , as the data given above show, are very close in abundance.Several series of experiments have been carried out t o test theunvarying nature of the atomic weights of naturally occuring com-plex elements. R. K. McAlpine l5has failed with antimony, T. W. Richards and A. W. Phillips l9with copper, G. P. Baxter and S. Ishimaru witn nickel,20 and H. P.All have given negative results.l7 Proc. Roy. Xoc., 1930, [ A ] , 126, 511; A., 393.J. Amer. Chem. Xoc., 1929, 51, 1745; A . , 1029, 071.ID Ibid., p. 400; A,, 1929, 370.2O Ibid., p. 1729; A., 1929, 863SUB-ATOMIC PHENOMENA AND RADIOACTIVITY.309Cady and H. U. Beecher21 with nitrogen. At the present time,therefore, boron remains the only element to be different in itsisotopic composition according to the part of the world whence itcomes.In the laboratory the work of partially separating isotopes hasbeen continued. F. A. Jenkins 22 has succeeded in obtaining chlorinewith so low an atomic weight as 35.418. A. A. S ~ n i e r , ~ ~ however,after 13 evaporations of cadium in a vacuum, in each of which halfthe material was removed, failed to obtain a difference in thisconstant. The same author z4 discusses critically schemes forfractionating complex elements.The first forty elements without exception have now been invest-igated for isotopes.Themasses still unassigned to any element are in the first decade 2, 3,5, and 8 ; in the next two none ; in the fourth 38 ; in the fifth 42,43, 46, 47, and 49 ; in the sixth 57 ; in the seventh 61 and 62 ; inthe eighth and ninth none. Those in the forties may be discoveredwhen F. W. Aston applies to calcium, scandium, titanium, etc.,the intensive examination to which chromium, molybdenum, andtungsten have lately been submitted, but the masses 2, 3, 5, and8 are in different case : 2 and 3 are unlikely ever to be found inhydrogen since they differ relatively so much from the knownisotope 1. There is a possibility of 5, however, for helium, and bothin band-spectrum work and in an examination of a-particles (in theactinium series) a sharp look-out for this possible isotope mightbe repaid.8 is a possibility for beryllium, about which an interest-ing suggestion has been made by Lord R a ~ l e i g h . ~ ~ R. d’E. Atkin-son and F. G. Houtermans,26 in a theoretical investigation of theprobability that a proton which has entered a nucleus will anchoritself there by radiating and so build up heavier elements out oflighter, find this possibility much improved if electrons can alsopenetrate the nucleus. They find that the isotope Be8 will be oneof such products, but will be so unstable as almost certainly tobreak up into two helium nuclei. This statement has led LordRayleigh, who many years ago found that the mineral beryl alwayscontains helium without appreciable quantities of radioactivematter, to suggest that this helium may possibly have arisen fromBe8.If this could be proved, it would indicate that Be8, even ifThe range of masses is from 1 to 94.21 Science, 1928, 68, 594; A., 1929, 863.22 Abstr. Theses Univ. Chicago (Sci. Ser.), 1926-26, 4, 93; A., 1929, 115.z3 Ibid., p. 173; A., 1929, 115.24 J. Physical Chem., 1929, 33, 577; A., 1929, 666.25 Nature, 1929, 123, 607 ; A., 1929, 487.26 Ibid., p. 567; A., 1929, 487310 RUSSELL :it does not now exist, has done so within geological times and sub-sequent to the formation of the mineral.The discovery of the complexity of oxygen necessitates a re-consideration27 of the scale on which the weights of atoms areexpressed. The present chemical standard is greater than themass of its main constituent 0 l 6 by about 1.26 parts per 104.Thisqimntity is of little significance to chemists, partly because i t isvery small and partly because the isotopic constitution of oxygenis probably invariable, but physicists aiming a t an accuracy in themasses of atoms of 1 part in lo5 parts must find the chemical unitunsuitable. The masses of the proton, the neutral hydrogen atom,one-quarter of the neutral helium atom, one-sixteenth of the neutraloxygen atom, 0l6, have been the chief suggestions for the standardmass. It should be pointed out that apart from this difference inthe scale, the atomic weights of nitrogen and carbon cannot nowbe the same as the masses N14 and C12 respectively determined bythe mass-spectrograph.Calculated values of these are given byS. M. Naud6.sRadioactive Constants and Other Data.A new value of the half-period of ionium, 1.9 x lo5 & 3% years,has been obtained by (Mme.) P. Curie and (Mme.) S. Cotelle z8;this is considerably higher than early values. Two values for thehalf-period of radium-D are also considerably higher than earliervalues. (Mme.) P. Curie and (Mme.) I. Curie29 obtained 19.5 yearsby direct measurements over a period of 16 years, and the latter 30obtained 23 years by an indirect method. The value 21 yearsis provisionally adopted. F. JoliotY3l by a slight modification ofJ. C. Jacobsen’s 32 method, obtained the half-period of radium&’’as 3 & 1.5 x 10-6 sec., confirming the order of the period previouslyobtained.A similar experiment with thorium-(?’ showed thatits period is much less than 10-6 sec. The half-periods of potassiumand rubidium have been determined by W. Muhlhoff 33 by countingthe number of p-particles emitted per g. per sec. in a Geiger andMuller sensitive particle counter. The half-period for potassiumis 1.5 x 1013 years, which is ten times greater than that estimatedby A. Holmes and R. W. Lawson 34 ; that of rubidium is 4.3 x lollST F. W. Aston, Nature, 1930,126, 953 ; A. von Grosse, 2. physikat. Chem.,1930, [B], 10, 395; A., 1931, 15.2 8 Compt. rend., 1930, 190, 1289; A., 976.29 J. Phys. Radium, 1929, [vi], 10, 385; A., 8.31 Compt. rend., 1930,191, 132; A., 1086.32 Phil. Mag., 1924, [V;], 47, 23; A , , 1924, ii, 142.33 Ann.Physik, 1930, [v], 7, 205; A., 1496.30 Ibid., p. 388; A., 8.31 An n. Reports, 1928, 25, 308SUB- ATOMIC PHENOMENA AND RADIOACTIVITY. 31 1years. On the assumption that the radioactivity of potassiumis due only to K41, the half-period of this isotope becomes 10l2 years,since K41 is approx. 6.7% of the total potassium (and not 5% asis generally assumed from the atomic-weight determination inignorance of the exact masses of K39 and K41). The new result forpotassium is important in connexion with J. Joly's theory of thesurface history of the earth, and has been briefly discussed by him.35Attempts to accelerate or influence the rate of decay of a radio-active substance by bombarding it with a-particles have neverbeen substantiated.H. Herszfinkiel and L. Wertenstein 36 havepointed out that this unexpected apparent stability may be dueto the fact that the experimenter may have been looking for aproduct which is in fact not produced. For example, the bombard-ment of uranium-I has been expected to produce the quick-changinguranium-X, due to loss of an a-particle, whereas on Lord Ruther-ford's theory36a it might instead produce uranium-I1 by loss ofan a-particle and two p-particles; since uranium11 is a productof long half-period the possible effect of the bombardment mighthave gone undetected. With thorium, however, the transformationwould produce the relatively quick-changing radiothorium, whichwould be much more easily detected. A milligram of thoriumoxide was bombarded by the a-particles from 28 millicuries ofradon for 6 days.No change of activity could be detected by amethod which was sensitive to 0.05 mg. of thorium. It was con-cluded that, if bombardment produced radiothorium from thorium,not more than one a-particle in 8 x lo6 could have been effective.G. I. Pokr~wski,~' however, found with weak sources of activematerial that the probability law for the number of particles ex-pelled was regularly deviated from, and concludes that the dis-integration of one atom is not independent of that of its neighbours.(Mme.) P. Curie 38 has given an account of experiments undertakenunder her direction to influence the values of the disintegrationconstants, and concludes that this cannot be done. She criticises 39adversely the work of L.B. Hogoia~lenski,~~ who claims that polon-ium disintegrates at different rates in different parts of Russia,the rate of decay being least abnormal in the capital.The round value for the constant &, the number of a-particlesemitted per g. of radium (without products) per sec. must now be35 Nature, 1930, 126, 953.36 Ibid., 1928, 122, 504; A., 1928, 1169.37 2. Physik, 1929, 58, 706; 1930,65, 133; A., 1930, 9, 1496.38 J. Phys. Radium, 1929, [vi], 10, 329; A., 1929, 1358.39 Ibid., p. 327; A., 1929, 1368.40 Ibid., p. 321; A., 1929, 1358; Nature, 1929, 123, 872; A., 1929, 737.36a See ref. 70312 RUSSELL :accepted as 3-70 x lolo. By means of the " total charge " method,H. J. J. Braddick and H. M. Cave 41 obtained the value 3.68 x 1O1Ort: 1%.With a new type of electrical counter due to H. Greina~her,~?P. A. B. Ward, C. E. Wynn-Williams, and H. M. C a ~ e 4 ~ obtainedthe value 3.66 x 1O1O & 0.5%. In both these sets of experimentsthe source employed was radium-C, and the value of the standardused was assumed to be accurately known. In the new elec-trical counter, the ionisation produced by a single a-particle islinearly amplified by triode valves, there being no ionisation bycollision. The final deflexion of the recording instrument is pro-portional to the initial ionisation. The ionisation due to p-particlesis too small to disturb the counting, which can be carried out accur-ately a t so high a rate as 500 particles per minute. This valueconfirms that of V.F. Hess and R. W. Lawson44 which has beenopposed for many years to that of H. Geiger and A. Werner45.The 3.7 x 1O1O value has now been got by the electric counting,the total charge, the production of heli~m,~6 the volume of radon,47and the heating-effect methods.48 The half-period of radiumcalculated from this datum is 1600 years.G. I . Harper and E. Salaman49 found the range of poloniuma-particles to be 3.87 cm. in standard air (15" C. and 760 mm.).J. L. Nickerson 50 found that of thorium a-particles to be 2-76 &- 0.1cm. The former is about 0.05 em. less than the generally acceptedvalue, but is in agreement with an earlier determination of (Mlle.)I. Curie 51 ; the latter value is 0.15 cm. less than the accepted value.The first authors also found that the ranges of thorium-C', radium-C', and thorium4 are all smaller than has previously been recorded.The deviation is greatest for thorium-C, and appears to be definitelyoutside of the range of experimental error.Important work on the initial velocities of the a-particles fromradium-C", thorium-C', and actinium-G has been done.G . C.41 Proc. Roy. SOC., 1928, [ A ] , 121, 367; A., 1929, 6.42 2. Physik, 1926, 36, 364; A., 1926, 563; ibid., 1927, 44, 319; A., 1927,43 Proc. Roy. SOC., 1929, [A], 125, 713; A , 7.O4 Sitzungsber. K. Akad. Wiss. Wien, 1918, [2A], 127, 405.4 5 2. Physik, 1924, 21, 187; A., 1924, ii, 226.O 7 L. Wertenstein, Phil. Mug., 1928, [vii], 6, 17; A., 1928, 932.915.(Sir) J. Dewar, P r o c .Roy. SOC., 1910, [A], 83, 404; A., 1910, ii, 376.E. Rutherford and H. Robinson, ibid., 1913, [vi], 25, 312; A.,1914, ii, 789; S. W. Watson, Proc. Rmj. SOC., 1928, [ A ] , 118, 318; A., i928.456.4 p Proc. Roy. SOC., 1930, [ A ] , 127, 175; A., 659.~.1 Ann. Reports, 1926, 23, 291.T r a n s . Nova Scotia I n s t . Sci., 1930, 17, 172 ; A., 659SUB-ATOMIC PHENOMENA AND RADIOACTIVITY. 313Laurence,52 continuing the work of G. H. Briggs,M has found theinitial velocities of the a-particles from radium-C, thorium-C’, andpolonium to be 1.709, 2.054, and 1.592 x lo9 cm. per sec., re-spectively, assuming Briggs’s value for radium-C’, vix., 1.923 X lo9cm. per sec. S. Rosenblum,M using a magnetic deviation method,found the initial velocities of the a-particles from radium-C’,thorium-C’, and radium-A to be 1.923, 2.054, and 1.695 x lo9 cm.per sec.respectively, assuming Briggs’s value for thorium-C, v ~ z . ,1.701 x loQ cm. per sec. The three sets of values are in excellentagreement. S. Rosenblum 55 has also made the remarkable observ-ation that the initial velocity of the ordinary a-particles fromsome radio-elements is not a constant. He examined the finestructure of the a-particles from thorium-C (range 4.8 cm.) by theDanysz focusing method employed in the examination of p-particlespectra. The particles were bent in a circle of about 25 cm. diameterby means of a field of about 36,000 gauss. He found that fourfaint groups accompany the main group of particles. Their veloci-ties were 1.003, 0.975, 0.962, and 0.964, that of the main groupbeing 1, and their relative intensities were 30, 3, 2, and 0.5%respectively of that of the main group.He obtained no certainevidence of additional groups of particles from radium-A , polonium,radium-C‘, or thorium-C’. This new method of attack is clearlyone of interest and importance. Another method of analysis ofgroups of a-particles has been devised by Lord Rutherford, F. A. B.Ward, and C. E. Wynn-Willisms.56 By using a double ionisationchamber with a Greinacher counter,42 they have succeeded in count-ing, not simply the total number of particles exceeding a givenrange, but the number having ranges between x and x + dx, wheredx is a few millimetres only. With this apparatus they haveinvestigated the straggling curves of the 8-6-cm. or-particles fromthorium-C’, the 7.0-cm.particles from radium-C‘, aid the 3.9-cm.particles from polonium. A11 these, in confirmation of S. Rosen-blum’s results, appear to be homogeneous groups of or-particles.They have shown also that the 5-5-cm. particles from actinium-Care in two well-marked groups of ranges 5.51 and 5.09 cm. in theratio of 100: 22. They found for the first time the short-rangeor-particles postulated by tlhe group-displacement law and theGeiger-Nuttall relation, emitted in the dual disintegration of radium-C. There are two sets with ranges of 4.14 and 3-95 cm., assuming52 Proc. Roy. Soc., 1929, [ A ] , 122, 643; A , , 1929, 370.53 Ibid., 1928, [ A ] , 118, 549; A., 1928, 569.54 Compt.rend., 1930, 190, 1124; A., 837.5 5 Ibid., 1929, 188, 1401, 1549; A., 738; ibid., 1930, 190, 19.66 Proc. Roy. SOC., 1930, [AJ, 129, 211; A., 1338314 RUSSELL :the range of the a-particles of polonium to be 3.92 cm. Theirrelative intensities are 3 to 1. The intensity of the two groupstogether is just over 1 in 4000 of the main 7-cm. group of par-ticles from radium-C’. The branching a t radium must now betaken as 4000 to 1 in the directions radium-C‘ and radium-C”respectively, a value in good agreement with those deduced by K.Fajans 57 (3000 : 1)’ and by (Frl.) E. Albrecht 58 (4000 : l), fromthe intensity of the P-particles from radium-C. The experimentalvalues of the ranges are in agreement with that deduced from theGeiger-Nuttall relation (3.9 cm.).Finally, the 4-8-cm. cc-particlesfrom thorium-C were found to be complex, in qualitative agreementwith S. Rosenblum’s work. It is probably significant that thoseproducts, radium-C, thorium-C, and actinium-C, which give com-plex a-particles, are all of odd atomic number, and it will be interest-ing to see whether protoactinium, when it is examined, conformsto this. This heterogeneity is not explained by earlier theories ofthe structure of radioactive nuclei, but an explanation of i t hassince been put forward by G. gar no^.^^New data have been obtained of the relative abundance andranges of the long-range particles from radium-C’ and thorium-C’.Using a special form of Wilson expansion apparatus, R. R. Nimmoand N.Feather 6O find that the long-range particles of thorium-C”fall into two principal groups of ranges 9-82 and 11-62 cm. instandard air, the range of the ordinary a-particle being taken as 8-54cm. The ratio of the abundance 1 : 5-1 differs considerably fromthat obtained by (Frl.) L. Meitner and K. Freitag (1 : 2.8). Afew tracks indicating a-particles of range 12.5 cm. were observed,but the number was too small to allow definite conclusions to bedrawn. The conclusions for radium-C’ were less definite. Thereis a well-defined group with a range of 9.08 cm., but other particleshave ranges fairly well distributed between 7-5 and 12 cm. Thesemay be regarded as groups with mean ranges of 8.0, 11.0, andpossibly also 10.0 cm. The results, however, make it quite clearthat radium-C’ emits more than the two long ranges found in theoriginal scintillation experiments of Rutherford and J.Chad-wick.G2 On the other hand, K. Philipp and K. D ~ n a t , ~ ~ using alsoWilson’s cloud method, find that for every lo6 normal a-particlesfrom radium-C’ there are 29 with a range of 9.2 cm., 4 of 11.0 cm,,5’ Physikal. Z . , 1912, 13, 699; A., 1912, ii, 824.5 8 Sitzungsber. K . Akad. Wiss. Wien, 1919, [2 A ] , 128,925; A., 1921, ii, 675.5s Nature, 1930, 126, 397; A., 1339.6o Proc. Roy. SOC., 1929, [A], 122, 668; A., 1929, 371.6 1 2. Physik, 1926,37,481; A., 1926, 772.62 Phil. Mag., 1924, [vi], 48, 509; A., 1924, ii, 814.63 2. Phy&k, 1929,52, 769; A., 1929,371SUB-ATOMIC PHENOMENA AXD RADIOACTMTY. 315and 0.5 with a range greater still.These data confirm thescintillation experiments. The origin of the long-range particlesis discussed by Rutherford, J. Chadwick, and C. D. Ellis and, forthorium-C’, by E. Stahe1.64H. Zeigert 65 has determined the number of ions produced per=-particle from uranium-I, uranium-11, and radium by detectingsingle a-particles with a very sensitive electrometer and measuringdirectly the total ionisation in air due to each. The values 1.16 x lo5,1-29 x lo5, and 1.36 x lo5 are in good accord with the valuescalculated from the ranges of these elements based on the range ofradium-C‘ and the number of ions it produces.The Actinium Problem.In a mass-spectrograph investigation of uranium-lead tetra-methyl prepared from broggerite, F.W. Aston 66 found the isotopesPb206, Pb207, and Pb208 in the abundance of 86.8, 9.3, and 3.9%respectively. Pb207 in this proportion cannot be due to ordinarylead, and it is concluded that it is the end product of the actiniumseries. This experiment brilliantly establishes a suggestion, manyyears old, based partly on atomic-weight determinations and partlyon the half -periods of disintegration products. Calculated fromthis result, the atomic weight of protoactinium becomes 231 or,if allowance is made for the packing effect by extrapolating thepacking-fraction curve, 231.08. On the basis of this work, Ruther-ford G7 supposes that an isotope of uranium-I, actino-uranium, ofmass 235, is the head of the actinium series proceeding to proto-actinium via uranium- Y .From the half-value period of uranium-I,he calculates the period of actino-uranium to be 4.2 x lo8 years,and deduces that, if the production of uranium in the earth ceasedas soon as the earth separated from the sun (as is likely), the earthcannot be older than 3.4 x lo9 years. Also if the age of the sunbe taken as about 7 x 10l2 years (Sir J. Jeans’s estimate), it followsthat uranium and similar elements were being formed in the sunas late as 4 x lo9 years ago and that probably the process stillcontinues. Although there is agreement that the atomic weightof actinium42 must be accepted as 207, the other points raisedhave received criticism. C. N. Fenner and C. S. Piggot,68 from astudy of the composition and age of the broggerite from which thelead was obtained, regard Aston’s determination of the abundance84 ‘‘ Radiations from Radioactive Substances,” p.94 ; E. Stahel, 2. Physik,66 8. Physik, 1928,46,668; A., 1928,466.86 Nature, 1929, 123, 313; A., 1929, 370.6’ Ibid., p. 313; A., 1929, 373.1930, 63, 149; A., 1233.68 Ibid., p. 793; A., 1929, 620316 RUSSELL :of Pb208 as about 50% too high, since, on his figures, the uranium-thorium equivalence factor (0.38) comes out at 0.57. By inference,the abundance of Pb207 is also 50% too high. A. Holmes G9 hasdirected attention to another line of evidence, from which it canbe inferred that the half-periods of uranium-I and actino-uraniumare probably nearly equal. It has been generally accepted thatthe percentages of atoms disintegrating via protoactinium andradium from uranium are about 3 and 97 respectively. If bothuranium-I and actino-uranium disintegrate a t about equal rates,these should be the percentages of Pb207 and Pb206 in pre-Cambrianminerals. But if Rutherford is right, the percentage of Pb207 shouldbe definitely higher.From composition and atomic-weight dataof four unaltered minerals, Holmes calculates the percentage ofPb207 to be between 2.5 and 3.3. He concludes that Aston's estimateof the abundance of Pb207 in broggerite is too high to be represent-ative, that Rutherford's resulting estimate for the half-period ofactino-uranium is too low, and that, indeed, the half-periods ofuranium-I and actino-uranium are probably of the same order.This agreement in the proportion of corresponding actinium anduranium members at the beginning and a t the end of their seriesis remarkable, but it does not include all the evidence.There areatomic-weight determinations of uranium-lead which suggest thatPb207 is totally absent from it 69, 70. Again, J. E. Wildish 71 foundthat the number of atoms of protoactinium disintegrating pcr 100atoms of uranium varied from 1.47 to 5-16 in different minerals.The lower values could, no doubt, be explained by alteration of themineral, but not the upper. It is difficult to see also how F. W.Aston's result for Pb207 could be cut down to 3 or even 5yo. Also,A. IF. Kovarik,'2 from a survey of evidence not dissimilar from thatconsidered by A.Holmes, considers that actino-uranium has ahalf-period of 2.7 x los years, a value even lower than Ruther-ford's. Initially, he thinks, there has been a definite amount inproportion to the uranium-I, but the relative proportion of thetwo isotopes has decreased with the age of the mineral. The periodof actino-uranium cannot, therefore, be regarded as settled so longas this conflict of evidence and opinion remafiis. The mass of thisisotope must meanwhile be taken as 235, as suggested by LordRutherford. The determination of the atomic weight of proto-actinium (the result of which has not yet been published) or of theconstitution of uranium by the mass-spectrograph method shouldi o Ann. Reports, 1928, 25, 306.7 1 J . Amer. Chem. SOC., 1930, 52, 163; A ., 308.72 Science, 1930, 72, 122; A., 1495; Amer. J. Sci., 1930, [v], 20, 393; A.,Nature, 1030, 126, 348; A., 1339.1552SUB-ATOMIC PHENOMENA AND RADIOACTIVITY. 317settle this point. But, as it has not been settled, it may be said.that it is exceptional that ordinary uranium should have an isotopeof odd mass like 235, possibly in so great an abundance (byweight) as 3% (on A. Holmes’s evidence) when it apparentlycontains no mass of 236 or 240, and when the abundance of uranium-11, of mass 234, is negligible. A. S. Russell V3 has previously givenreasons for regarding 233 as a more likely mass for protoactiniumthan 231. This appeared to require a mass for actinium4 of 209which is certainly wrong, but only if no other massive particle thanthe a-particle is expelled in the series.From general knowledgeof the masses and stabilities of isotopes both of radioactive andinactive elements, it seems simplest to regard actino-uranium ashaving a mass of 238, protoactinium one of 233, and actinium-0one of 207. An experimental value of protoactinium of 233 wouldsupport this view with its consequence that the a-particle is notthe only massive particle expelled; a value of 231 would favourthe much simpler view.The actinium problem is also discussed by G. E l ~ e n , ~ ~ A. vonG r ~ s s e , ~ ~ and T. R. Wilkh1s.7~ The first author supports a view,now out of favour, that the atomic weight of actino-uranium isgreater than 238; and the last worker is in agreement with LordRutherford in regarding its period as less than that of uranium-I.Wave-mechanics and Radimctive Disintegration.A simple explanation of radioactive disintegration and a solutionof the apparent conflict between the radioactive data and the resultsof scattering has been put forward simultaneously by G.Gamow 77and by It. W. Gurney and E. U. Condon 78 on a basis of the newwave-mechanics. It deals with the points such as the exponentiallaw of transformation and the Geiger-Nuttall relation which were leftuntouched by Rutherford’s theory 79 of the structure of radioactivenuclei. The nucleus is pictured as a tiny enclosure surrounded by apotential hill enclosing an a-particle (represented by a standing wave)of which the energy is less than the potential energy a t the top ofthe barrier.On the classical mechanics, the a-particle inside thenucleus cannot surmount the barrier, but, on wave mechanics, i t73 Nature, 1927, 120, 402 ; A., 1927, 1002.74 2. anorg. Chem., 1929,180, 304; A., 1929, 737.75 Ibid., 1930, 186, 38; A., 515.76 Physical Rev., 1927, [ii], 29, 352; A., 1928, 1302.7 7 2. P h p i k , 1928, 51, 204; A., 1929, 7; ibid., 1929, 53, 601; A., 1929,7 8 Nature, 1928, 122, 439; Physical Rev., 1929, [ii], 33, 127; A., 1929, 374.7g Phil. Mag., 1927, [vi], 4, 680; A,, 1927, 1002; Ann. Reports, 1928, 25,484.309318 RUSSELL :will have a finite chance of escape which will be the greater thegreater its energy, the thinner the barrier, and the smaller theheight of the barrier (see these Reports, p.27). There is thus arelation between the energy of the cc-particle and the disintegrationconstant of the nucleus. Gamow expresses this as log 1 = E + bE,where h is the disintegration constant, 7c a constant, b a constantfor all radioactive nuclei, and E the energy of the or-particle. Thiscorresponds approximately to the Geiger-Nuttall relation, and thecalculated value of b corresponds well with the experimental value.Log 1, it is seen, increases less rapidly than E, a relation which isconsistent with the fact that the half-period of a quick-changingproduct like radium-C’ is much less than is anticipated from theGeiger-Nuttall relation. The theory has been developed by G.Gamow and F. G. Houtermans.so They show how the disintegrationconstants of all a-particle elements can be calculated from thenuclear charge and the velocity of the or-particle.The calculatedvalues are in very satisfactory agreement with the experimental,in view of the approximations made in the calculations. Thetheory, though still in a tentative form, is most promising. Itmay be added that it demands such potential barriers round radio-active nuclei as not to be penetrated by any a-particles a t presentavailable, and this is in agreement with experimental work.ArtiJicial Disintegration by or-Particles.between the two series of investigations onthe artificial disintegration of the light elements carried out a tCambridge and a t Vienna have still to be satisfactorily explained.As these relate to the detection of scintillations, it is obvious thatsome of the doubtful points would be cleared up by obtainingphotographs of the disintegration in a Wilson cloud chamber orby using an electrical method of detecting the particles of disin-tegration. First steps in both these directions have already beentaken and, i t is hoped, will lead ultimately to a solution of thedifficulty.While a general description of the phenomena of disintegrationcan be given in terms of the picture of the potential field betweenan or-particle and the nucleus of a light atom obtained from thescattering experiments, there are still a few outstanding difficulties.The data suggest that penetration of the a-particle into the alum-inium nucleus and capture, for instance, would be impossible forvelocities of or-particles less than 2 x lo9 cm.per sec., while actuallythe aluminium nucleus is disintegrated by particles of much smaller2. Physik, 1928, 52, 496; A., 1929, 233.The divergences81 Ann. Reports, 1926, $23, 285SUB-ATOMIC PHENOMENA AND RADIOACTIVITY. 319velocity. An explanation of this, impossible on classical mechanics,is given by G. Gamow 77 and by R. W. Gurney and E. U. Condon 78 onthe basis of wave-mechanics. The agreement between Gamow’scalculations of the chance of penetration and the experimentalnumbers of emitted protons is sufficient to show that, for elementslike nitrogen or aluminium, the probability that a capture of thea-particle results in disintegration is fairly high. Gamow 82 has alsocalculated the probability of disintegration of light elements whenbombarded by or-particles from radium-C’ and from polonium, andshown that the chance of Penetration decreases very rapidly asatomic number increases and is small for numbers greater than 20.The possibility, therefore, that eventually all elements will bebrought into line with the lighter ones in this respect is exceedinglyremote.The bombardment of atoms of aluminium by or-particles of range7 cm.from radium-(B + C ) has been shown by Rutherford andJ. Chadwick 83 to release protons with a definite minimum rangein air of about 10-12 cm. These experiments suggest that theprotons liberated in disintegration possess a certain minimumenergy in addition (as had been shown earlier) to a maximum energy.This energy of release for aluminium is roughly of the same mag-nitude as that corresponding with the potential of LL proton in thefield round the aluminium nucleus.P. W.Aston’s 84 observation that the packing fraction is higherfor light elements of odd atomic number than for those of even,is correlated 85 with the observation that protons emitted fromelements of odd atomic number have greater maximum energiesin general than those emitted from elements of even atomic number.For if the disintegration consists of the capture of an or-particleand the emission of a proton, the odd-numbered element bombardedis changed to an even-numbered element and vice versa. I n theformer case mass is lost, in the latter mass is gained.The loss willappear as an excess of kinetic energy associated with the emittedproton above that which can exist in the latter case. In this argu-ment, the gain in mass of the proton on its release from the nuclearbinding and the kinetic energy of the incident a-particle have notbeen taken into account. These energies, however, nearly balance ;the gain in mass in the former case, 0.00724, being close to the massequivalent of the kinetic energy of the a-particle (of radium-C‘),vix., 0.0082. But the information at present available is not suffi-82 Nature, 1928, 122, 806; A,, 1929, 6; 2. Physik, 1928, 52, 610.83 Proc. Camb. Phil. Soc., 1929, 25, 186.86 J. Chadwick, Proc. Roy. ~ o c . , 1929, [A], 123, 373; A., 1929, 622.Ann. Reports, 1928, 25, 303320 RUSSELL :ciently accurate to test this point more than qualitatively.Forquantitative agreement, the atomic masses of the lighter elementsmust be known with a greater degree of accuracy than a t present,and the motions of the a-particle and the residual nucleus afterdisintegration must also be accurately known. At present theavailable evidence is against quantitative agreement.86The new wave-mechanics has also been applied to explain arti-ficial disintegration by a-particles. 87 It has been suggested byJ. Chadwick and G. Gamow,88 partly on general grounds and partlyon the basis of unpublished experiments a t Cambridge, that theprocess of disintegration of a nucleus by collision with an a-particlemay occur in two ways : (a) by the capture of the a-particle bythe atomic nucleus followed by the emission of a proton, and (6)(a new suggestion) by the ejection of a proton without the captureof the a-particle.In ( a ) the a-particle must penetrate the nucleus;in ( b ) it need not, collisions being responsible for the disintegration.It is deduced that there may be more than one level at which thea-particle may remain after capture and that there will be protonsof “ the line spectrum ” and protons of “ the continuous spectrum.”The former are expected t o be emitted nearly uniformly in alldirections, the latter will be emitted mainly in the direction of thecolliding a-particles. Experimental evidence for the presence ofgroups of different ranges in the disintegration protons has alreadybeenobtained by different experimenter^.^^ When boron, for example,is bombarded by the a-particles of polonium, three groups of protonshave been found with ranges in air of 16, 32, and 76 em.The firstis identified as a “continuous spectrum,” and the other two as“ line spectra.” From energy considerations it appears that B10is the isotope attacked. The continuous spectrum of protons isinterpreted as corresponding with the formation of the nucleus ofBe9 and both the line groups with that of (213. The disintegrationof aluminium by the a-particles from polonium shows similarfeatures. Although such experimental results are still at a tent-ative stage, it is evident that the phenomenon of artificial disin-tegration promises to reveal the intimate structure of the nucleiof the lighter elements in a way not previously thoughtpossible.86 “ Radiations from Radioactive Substances,” p.307.8 7 Ibid., p. 672.Nature, 1930, 126, 54; A., 1085.W. Bothe and H. Franz, Naturwiss., 1928,16, 204; A., 1928, 1302; 2.Physik, 1928, 49, 1; 51, 613; A., 1929, 230; H. Franz, ibid., 1930, 63, 370;A., 1338; Physikal. Z., 1929, 30, 810; A., 130; W. Bothe, 2. Physik, 1928,51, 613; A., 1939, 230; ibid.. 1930, 63, 381; A., 1338; H. Pose, ibid., 64,1 ; A.,1232; Physika2. Z., 1929, 30, 780SUB-ATOMIC PHENOMENA AND RADIOACTIVITY. 321It is interesting to note that the two synthesised nuclei, 0 1 7 andCIS, have been discovered from an examination of band spectra.90The Smtterileg of u-Particles in Helium.An interesting contribution to this subject has been made byJ. Chadwi~k.~1 The problem of the collision of two particles whichact upon each other with forces varying as the inverse square ofthe distance between them has been solved exactly on the basisof the new wave-mechanics, and the solution is the same as thatgiven by the classical mechanics.This agreement, however, asN. F. Mott 92 has pointed out, depends upon the dissimilarity ofthe colliding particles; if the particles are identical, the scatteringlaws given by the wave-mechanics will be very different from thoseof classical theory. a-Particles from polonium were scatteredthrough angles between 40" and 50". The experimental resultswere found to be close to those predicted by the quantum theoryand markedly different from those predicted on the classical theory.The calculations of Mott are therefore verified, and with them theassumption on which they rest, vix., that it is impossible to dis-tinguish one helium nucleus from another.In other words, thehelium nucleus has no spin or vector quantity associated with it.Its field of force is perfectly spherical. The observations alsoindicate that, as the distance between the colliding u-particle andnucleus is decreased, the observed scattering rises slightly abovethat calculated from the quantum theory, then falls, and finallyrises rapidly again. The initial rise and fall may be due to a truechange in the law of force between the particles, but the asymmetryshown at small distances of collision can be due only to a distortionof the structure of the particles.The Age of Iron Meteorites.F.Paneth, W. D. Urry, and W. Koeckg3 have determined theage of 27 different specimens of iron meteorites by ascertainingthe ratio of helium to uranium. The helium was estimated byPaneth's improved method, and the uranium by a radium deter-mination. The ages ca1cula)ted from the experimental data areall less than the age of the earth, and the results agree with theview that the meteorites originated in the solar system. Earlierdeterminations of age by the helium method were shown to be toolow owing to the incomplete evolution of the gas by the methodsemployed.90 Supra, p. 306.92 Ibid., 126,259 ; A., 369.93 Nature, 1930,125,490; A., 871; 2.EEe&rochenz., 1930,38, 727; A , , 1398.91 Proc. Roy. SOC., 1930, [A], 128, 114; A., 1085.REP.-VOL. XXVII. 322 RUSSELL :The Cosmic Rays.Hitherto the penetrating radiation usually knowii as the cosmicrays has been regarded as electromagnetic in character and comingfrom outer space.94 W. Rothe and W. K~lhorster,~~ however, havedone experiments which suggest that i t is corpuscular. Theyarranged two Geiger counters of special design a small distanceapart inside a protecting shield of iron and detected the same p-particle inside each. They concluded from their experiments thatthe primary penetrating radiations are very high-speed P-particles.The number of these is very small, about 1/100 per sq. cm. per sec.,but their individual energies must be very high.E. Regener,g6on the other hand, has measured the absorption coefficient of theradiation in water to such great depths that it is seems very unlikelyit could be corpuscular in character. He made measurements a tdistances from 32 to 231 metres, obtaining seven readings, belowthe level of Lake Constance. The maximum distance he attainedto is about three times greater than the region explored by R. A.Millikan and G. H. Cameron.94 A single absorption coefficient ofvalue about 0.018 per metre of water was found to explain theabsorption a t depths greater than 80 metres, a value which impliesa penetrating power greater than any of those found by Millikanand Cameron. A. Corlin 97 has made a critical examination of thesystematic measurements to determine whether the penetratingradiation is in any way directional. He concludes that the intensityof it is periodic.It is relatively high at 3 p.m. and possibly between5 and 8 a.m. and low at 10 a.m. As V. F. Hess and 0. Mathias 98did not find such periodic fluctuations with their electroscopecovered with 7 cm. of iron, it was concluded that only the softercomponents follow sidereal time. Fluctuations, however, havebeen also found by E. RegenergG at a depth of 78 metres belowLake Constance, so the whole radiation may show this phenomenon.The absorption of the radiation has been studied in media otherthan water by K. Buttner,99 E. Steinke,l G. and L.Myssovski and L. T ~ v i m . ~ The importance of analysing theahsorption curves into two, representing the primary and theg4 Ann.Beports, 1928, %, 321.9 5 2. Physik, 1929, 56, 751 ; Nature, 1929,123, 638; A., 1929, 621.96 Naturwiss., 1929, 11, 183.97 2. Physik, 1928, 50, 808; Nature, 1930, 126, 57.89 Sitzungsber. Akad. Wiss. Wien, 1928, [2 A], 137, 327.99 2. ffeophysik, 1927, 3, 161.1 2. Physik, 1927, 42, 570; 1928, 48, 647.2 Physikal. Z . , 1925, 26, 669; Ann. Physik, 1927, [iv], 82, 413; A., 1927,3 Z. Physik, 1928, 50, 2 7 3 ; A., 1938, 1070.289SUB-ATOMIC PHENOMENA AND RADIOACTIVITY. 323degraded radiation, has been emphasised by L. H. Gray4 and H.Kuhlenkampff - 5The Fine-structure Constant, the Proton, and the Electron.(Sir) A. S. Eddington 6 has called attention to the possibility thatthe reciprocal of the “ fine-structure constant,” 2xe2/hc, which isknown to be dimensionless, is integral and equal to 137.Thestarting point of this work is the observation that the interactionof electrons can now be described by two principles : Coulomb’selectrostatic forces and Pauli’s exclusion principle. If these areregarded as two aspects of the same feature of our world, theremust necessarily be a theoretical connexion between the two con-stants e2 and hc/2x which they respectively introduce. His firstview was that the ratio should be simply the number of symmetricalterms in an array of 16 rows and 16 columns, which is 136. Sincethe experimental value of the ratio is 137.29 0.11, the theorysuggested that possibly the value of e was about 0.5% too small,a suggestion that did not escape comment from those who upheldR.A. Millikan’s 8 value as against one determined by a new X-raymethod due to E. Backling which is approximately right for thetheory. Eddington discovered later,10 however, that in additionto the 136 symmetrical degrees of freedom there was one character-istic of a pair of electrons which, unlike the others, has no analoguein the theory of a single electron, namely, an alteration of the properdistance between them ; thie degree of freedom had been overlookedthrough his not recognising its distinctness from the others. Themost probable values of the e,, h, c, N , and other fundamental con-stants have been discussed by R. T. Birge l1 and R. A.Millikan,8and given as e = 4-770 & 0.005 x 10-10 abs.e.s.u., h = 6.547 &0.011 x erg./sec., c = 2-99796 & 0.00004 x 1O1O cm. sec.-l,and N = 6.064 & 0.006 x 1023. From an examination of theevidence available, they conclude that the ratio hcl2xe2 cannotbe an integer. The value of Eddington’s suggestion (which neces-sarily requires an integral value for the ratio) thus depends uponthe accuracy with which e can be determined, since the value forProc. Roy. SOC., 1929, [ A ] , 122, 647; A,, 1929, 372.Sitzungsber. Akad. Wiss. Wien, 1928, [2 A ] , 137, 327.Proc. Roy. Soc., 1929, [A], 122, 358; A., 1929, 231.R. T. Birge, Nature, 1929, 123, 318; A., 1929, 368; E. BLicklin, ibid.,Physical Rev., 1930, [ii], 35, 1231; A., 977.Dim., Uppaala, 1927.p.409; A., 1929, 369; J. H. J. Poole, ibid., p. 530; A , , 1929, 484.l o Nature, 1929, 124, 840; A., 10; Proc. Roy. SOC., 1930, [ A ] , 126, 696;11 PhyRical Rev., Suppl., 1929, 1, 1.A., 618324 RUSSELL :h happens to be also dependent upon that of e. The new X-raymethod of E. Backlin promises a very accurate value, but his owndetermination of e by it is not regarded as very accurate. A. P. R.Wadlund,12 however, using this method, has obtained a few valuesthe mean of which, 4.774 & 0.007 x 10-10, is close to Millikan's.The value 4.775 x 1O-lo, which is not outside the limits of thesedeterminations, gives with the present accepted values of the otherconstants the value required by Eddington's theory. It may bepointed out that a form of this ratio had earlier been employed byG.N. Lewis and E. Q. AdamsI3 in their theory of absolute units.There it was regarded as being equal t o 8 x ( 8 ~ ~ / 1 5 ) ~ ' ~ , the numericalvalue of which is 137.35.The ratio, M/m, of the masses of the proton and the electron isanother dimensionless constant which has attracted attention.J. Perles l4 has found that this ratio may be expressed as hc(n - l)/e2.This gives a value 1847.4, identical with the best experimentalvalue, vix., 1847 & 2. R. Fiirth l5 has shown that the value ofthe ratio follows from general quantum considerations, and givesa formula which leads to a value of 1836. E. E. WitmerI6 haspointed out that it is very nearly the square of half the atomicnumber of the heaviest known inert gas (i-e., l849), an agreementwhich it is difficult to regard as more than a coincidence.Heexpresses the relation between the masses and the atomic numbersof helium and hydrogen as MHe/ME= (ZHe/ZH)2[l/(l + a)], whereM represents mass and Z atomic number, and a is 2xe2/hc. Thevalue of hc/2xe2, calculated from this equation, i.e., 138.1, is closeto the experimental value, 137.29.A more developed theory on this subject has been put forwardby (Sir) A. S. Eddingt0n.l' He proposes a theory of mass in whichthe representation in a microscopic space-time increases the naturalmass of the proton in the ratio 1361410 and diminishes that of theelectron in an equal ratio, This gives M/m = 1362/10 = 1849.6which is close to the experimental value.He also shows that ifelectrons and protons form a perfectly rigid system, the mass M rela-tive to that of its constituents is reduced in the ratio 136/137.This ratio agrees approximately with the reduction of the mass ofa proton when it enters into a nucleus. Its reciprocal, in fact(1.00735), is intermediate between the atomic weight of hydrogen12 Proc. Nat. Acad. Sci., 1925, 14, 588; Physical Rev., 1928, [ii], 32, 841;13 Ibid., 1914, [ii], 3, 92. l4 Naturwiss., 1928, 16, 1094.1 5 Ibid., 1929,17, 688, 728; A., 1929, 1123, 1209.1 6 Nature, 1929, 124, 180; A., 1929, 973.1 7 PTOC. C a d . Phil. rSoc., 1931, (in press).A., 1029, 227SUB-ATOMIC PHENOMENA AND RADIOACTIVITY. 325expressed in terms of He == 4 (1,00724) and 0 = 16 (140778) :better agreement than this cannot be expected on the assumptionsmade.A novel theory of protons and electrons has been proposed byP. A. M. Dirac.18 The ‘relativity quantum theory of an electronleads to a wave-equation which has solutions corresponding withnegative energies, the energy of an electron being regarded aspositive. If a negative-energy electron is regarded as a proton,several paradoxes arise. This di6culty is escaped by postulatingonly one fundamental particle, the electron. The stable statesof an electron are those of lowest energy. In consequence, allelectrons would tend to fall into the negative-energy states withemission of radiation were it not for Pauli’s exclusion principle,which prevents more than one electron going into any one state.Dirac, however, assumes that there are so many electrons in theworld that all the states of negative energy except perhaps a feware occupied, and supposes that the infinite number of electronspresent in any volume will remain undetectable if they are uniformlydistributed. Only a few “holes” or missing states of negativeenergy consequently remain amenable to observation, and theseholes, these things of positive energy, are identified with the protons.Various obvious difficulties which follow this conception are dealtwith in the theory. One, however, remains, viz., the’difficulty ofexplaining why the proton and the electron differ so widely in mass.According to this theory, they should be of equal mass or, by con-sidering interaction, of slightly different masses. J. R. Oppen-heimer l9 attempts to surmount some of the difficulties in the fore-going theory by supposing that all, and not merely nearly all, ofthe states of negative energy are occupied, so that a positive-energyelectron can never make a transition to a negative-energy state.This implies, however, that there are no holes which can be calledprotons, so that the proton has to be regarded as a particle inde-pendent of the electron. In consequence, the proton will have itsown negative-energy states which must be assumed to be all occupied.The independence of the proton and electron allows them to haveany relative mass they require, but it is inconsistent with thepossibility that a proton can annihilate an electron.A. S. RUSSELL.la Proc. Roy. SOC., 1930, [ A ] , 126, 360; A., 271. Nature, 1930, 126, 606.lD Physical Rev., 1930, [ii], 35, 461, 939; A., 660, 836