June 24, 1922] 



NATURE 



811 



If we regard the speed of the electron as having 

 been acquired through intermolecular reactions 

 making for the equipartition of energy, the above 

 quantity should be comparable with the energy of 

 molecular agitation. For a temperature of 1000° 

 Abs. the mean kinetic energy of a molecule is 



E(iooo) = 2-o6x 10-^'. . . . (2) 

 Comparing (i) and (2) it is apparent that a gas 

 temperature of about 2500° will be required if an 

 electron of average energy is to develop a Une at 

 3 340 A. That position, however, marks the extreme 

 end of the spectrum, and radiation in the neighbour- 

 hood is therefore to be regarded as due to the capture 

 of electrons of exceptionally high speed. According 

 to Maxwell's law an appreciable proportion of the 

 molecules have three or four times the mean energy, 

 and it is therefore permissible to divide our 2500° by 

 some such figure as that. It accordingly seems 

 reasonable to assume that 1000° Abs. Cent., or even 

 a less temperature, in the presence of the proper 

 degree of ionisation, would suffice to produce the 

 observed spectrum.^ The temperature of the chromo- 

 sphere is of course very much higher than that. With 

 respect to the nebulae, while we have no general 

 knowledge of their thermal states, it will be recalled 

 that Buisson, Fabry, and Bourget have estimated 

 the temperature of the Orion Nebula to be of the 

 order of 15,000° Cent.^ In the light of such an 

 estimate, the theoretical requirement of 1000° cannot 

 be regarded as extravagant. 



The foregoing considerations related to the sug- 

 gestions that the electron acquires its speed through 

 equipartition of molecular energy, according to the 

 kinetic theory ; that is to say, the spectrum has 

 been regarded as a " temperature efiect." It is of 

 course quite conceivable that the electronic velocity 

 might be acquired in some other way, for instance, 

 through the action of an electric field, or photo- 

 electrically, as has been suggested to me by Prof. 

 Frederick A. Saunders in a personal letter. The 

 presence in the Class A stars of absorption beyond 

 the Balmer limit may be taken as evidence that 

 photoelectric ionisation is going on in their atmo- 

 spheres, and as most of the planetary nebulae have 

 nuclei that are powerful radiators of ultra-violet 

 Ught, the suggestion is an attractive one. However, 

 unUke the Class A stars, the nuclei show no perceptible 

 falling off in strength near the head of the Balmer 

 series. If absorption through photoelectric action 

 takes place it is probably higher in the spectrum. 



The above remarks refer very largely to the upper, 

 or more refrangible hmit of the outtying spectrum ; 

 of greater importance is the lower hmit, since here 

 contact is established with the line series. The 

 spectrum fades gradually to invisibiUty at the upper 

 extremity ; at the lower the termination is, on the 

 other hand, quite abrupt, and should, according to 

 what has been said, lie at the theoretical limit of 

 the Balmer series. As a matter of fact it has been 

 found. I believe in every case, to be perceptibly to 

 the redward of that point. We recall that this 

 outlying continuous spectrum comes down to the 

 junction from the more refrangible part of the 

 .spectrum, and the hne series reaches up from the 

 other or redward end. The series limit is at 3646A, 

 while the edge of the outlying spectrum in the 

 chromosphere, according to Evershed, lies at 3668A ; 

 that is to say, the outlying spectrum overlaps 

 the series .limit by about 22 A ; more than that, it 

 extends 7A beyond the highest series line observed 



* A higher estimate of the required temperature was given in the earlier 

 paper. I have not at hand the computations on which it was based, but it 

 seems to have been affected by some numerical error, probably the use of 

 N m place of N74 for the coefficient of A in the equations preceding (i) of 

 this paper. " e v ^ "• 



» Astrophys. Jour., 40, 258, 1914. | 



NO. 2747, VOL 109] 



by Evershed (3661A). In the radiation of the nebulae 

 the end of the outlying spectrum is difficult to measure, 

 but it lies quite certainly to the redward of the 

 Balmer Hmit. In N.G.C. 7009 it has been estimated 

 to be at about 3650A, in other nebulae it is at a 

 greater wave-length. More marked is the discrepancy 

 for the absorption spectrum in the Class A stars. 

 Thus in the spectrum of a Cygni the „ absorp- 

 tion spectrum may be said to, begin at 3710 + A, and to 

 reach full strength at 3660! A,' while for Vega * the 

 corresponding positions are 3800 + A and 3710! A. 

 In the latter case we have then the beginning of 

 absorption 150 A to the redward of the series limit, a 

 disparity between theory and observation that might 

 raise a doubt as to whether the absorption bears in 

 reahty any relationship to the Balmer series. A 

 consideration of the influence of density will, however, 

 show that an inequality of that order is to be expected. 



It is probably significant that in the spectra of 

 a Cygni and of Vega the last of the recorded series 

 lines falls in each case in the neighbourhood of the 

 point where the outlying absorption attains its full 

 value. Thus for Vega the series is lost at 3687A, 

 and the estimated position of the attainment of full 

 absorption is 37101 A; for a Cygni the highest line 

 is 3668 A, with full absorption estimated to begin at 

 3660 ± A. The estimates of the position at which 

 full absorption begins are difficult to make, and the ■ 

 positions given are only roughly approximate, but 

 it is quite evident that the series of dark lines which 

 lie to the redward, and the continuous spectrum 

 which extends in the other direction, merge one 

 into the other, and that the second begins at the 

 actual and not at the theoretical hmit of the first. 



The inference that the continuous spectrum should 

 begin at the theoretical hmit is based on the assump- 

 tion that the atomic orbits extend to infinity. Bohr 

 has pointed out that the size of the orbit system is 

 necessarily limited by the density of the radiating 

 gas, and has explained the absence of Unes of a very 

 high order as a consequence. Applying this con- 

 sideration to the theory of the outlying spectrum it 

 seems necessary to substitute for the " orbit at 

 infinity " adopted in our former reasoning, the largest 

 orbit in effective operation. Into the atomic system, 

 as circumscribed by this orbit, electrons may be 

 conceived to enter with speeds from zero upward. 

 Now an entering electron of speed zero has less 

 energy than one moving in the outer effective orbit — 

 less by just the kinetic energy of orbital motion. 

 In dropping into the second orbit therefore it sets 

 free a smaller amount of energy, and consequently 

 produces a line of lower frequency (or greater wave- 

 length) than that of the series line which corresponds 

 to the outer effective orbit. But the line formed by 

 this electron must mark the more refrangible edge 

 of the outlying continuous spectrum. We should, 

 therefore, expect the continuous spectrum to begin 

 somewhere on the less refrangible side of the highest 

 visible member of the Balmer series. In other words, 

 there should be an " overlapping " of the bright-line 

 and continuous spectra such as is actually found. 

 The margin of overlap should be proportional to the 

 kinetic energy of the electron in the outer effective 

 orbit, and on this assumption is expressible by the 

 relation : 



"2-^3 = *'!- "2. ■ • . . (3) 



* Lick Obs. Bull., 10, 103, Fig. i. 



♦ Publ. Lick Obs., 13, 257, Fig. 2. The positions for both Vega and 

 a Cygni are scaled from the intensity curves in the respective references. 

 They are subiect to great uncertainty. Compare stellar intensity curves by 

 Hartmann, Phys. Zeit., 18, 431. 



' The expression follows at once from the frequency-energy relation 

 assumed by Bohr. Let the nth be the largest effective orbit of one of his 

 atomic systems ; then for the highest line we have : 



v, = N(l/2«-l/««). 



The second term in the parenthesis represents the energy lost during the 



