248 



NA TURE 



[August 19, 1922 



the nucleus and the two electrons, are always col- 

 linear with each other, the latter describing two equal 

 and oppositely situated ellipses around the former. But 

 the corresponding spectrum formula, which is again 



49N/ 1 1 \ 

 of the simple Balmer type, namely, " = x g- \^~^)' 



proved to be entirely useless, as (to judge from one's 

 numerous trials extended up to n = 8) it does not 

 cover, even within i-sA, a single observed line of He. 

 This tends to show that such extremely special 

 (collinear) states of motion, or at least passages 

 between them, do not occur within the He-atoms, 

 or if they do, then only so sporadically as to give 

 no light of observable intensity. 



What next suggested itself was the apparently 

 trivial class of motions in which the mutual perturbation 

 of the two electrons is negligible. Though approximate 

 only, this class of solutions, being much broader 

 than that of the collinear motions, would seem more 

 likely to cover some actual spectrum lines. In fact, 

 the very first trials gave encouraging results, as will 

 be shown presently. 



The energy of the system being for such states of 

 motion equal to the sum of the energies due to the 

 nucleus and each of the electrons taken separately, 

 the corresponding spectrum formula for neutral 

 helium is, obviously, 



, = ^(J i+ J i __5 i _JL 1 ). 



^ \n l - n* nil' in,-/ 



or v = v 1 + v 2 , where v 1 and v 2 are any two frequencies 

 belonging to ionised helium, and thus represents a 

 " combination principle " of a new kind. The re- 

 sulting line of He, due to the passage of the two 

 electrons from stationary orbits determined by m lt 

 m 2 to a pair of orbits determined by n v n 2 , may 



, , , , , f»i, . m„\ 



conveniently be denoted by I — " I . 



This simple spectrum formula, the sum of two 

 Balmerian ones, has yielded so far ten or eleven 

 remarkably well-fitting lines, of which it will be 

 enough to quote here a few. 



..11. r , f*Ht . WU\ . 



Thus, to start with lines of the type I — - 1, i.e. 

 3S ( — ) of He + , we 



derivable from the Pickerin 

 have the frequencies (v lt »„) 



9875-1. 



fir 4 )- 



25191-8, 

 the sum of which gives for the frequency of the 



theoretical line ( — — - ) 

 \ 4.4/ 



» = 35 67- 



This agrees very closely with the nearest observed 



line at X (air) 2851 or •' = 35065, which is tabulated 



among the combination lines of neutral helium 



(Fowler, p. 94). Similarly the members ( -) and ( — J 



of the Pickering series of He + give ( ) with the 



frequency 



" = 9875-1 + 26333-6 = 36209, 

 which is in striking coincidence with the observed 

 He-line at X = 276i or v = 36208. 



In these examples both v x and v 2 are frequencies 

 actually observed in He + . But not less interesting 



are lines of the type ( — — - ) , i.e. combinations of 

 Pickering lines with those of a purely theoretical 

 NO. 2755, VOL. I io] 



+ series y = 4A r ( 2 2 ), and yet covering some 



He 



observed lines of neutral helium very closely. Thus, 

 we have (with N= 109723) : — 



(I75). - = 27377,^ = 3651-8, 



\-~). " = 31276, X = 3i96-4, 

 (^y). " = 31579, ^ = 31657, 



the nearest observed lines of neutral helium being 

 X3652-0, 3196-7, and 3166 respectively. 



Finally, an example in which both of the combined 

 frequencies are purely theoretical is 



'6^28^ 

 * 5-5 



), ^ = 22360, X = 447i-oo, 



with the nearest observed He-line at X = 4471-48, 

 tabulated (I.e., p. 93) among the diffuse doublets. 



Other examples of well-fitting lines and some 

 further details are being given in a paper on this 

 subject to appear in the September issue of the 

 Astrophysical Journal. 



Similarly one could try to cover some Li-lines by 



three pairs of terms, i.e. by v = 9AM — - z -\ H 1 



I I I \ \ n l n i" "3 



-„ . ;), and some spectrum lines of the 



m* m 2 ~ m 3 -/ 



higher atoms by four and more pairs of terms. But 

 since, with increasing number of independent term- 

 pairs, even a thorough agreement would appear more 

 and more likely as the work of chance, it does 

 not seem worth while to push the procedure much 

 beyond lithium. For the latter element I have 

 thus far found (with ^=109730) eight well-fitting 

 lines, of which the most interesting lines are 



(ftTfnf )' ' = 2 3394'4 and (j^fg), " = 26046-6, 

 which are remarkably close to the lithium lines ob- 

 served at v = 23394-7 and 26046-9. But by far more 

 interesting seem, for the present at least, the coinci- 

 dences obtained for neutral helium. These would 

 seem to justify the conclusion that there is a good deal 

 of independence between its electrons. 



LlIDWIK SlLBERSTEIN. 



July 18. 



In my letter of July 18 I considered the formula : 



„ =4N r,L + JL_ i__ jli 



^ LMj n,~ mf m,~-i 



constructed as if the two electrons did not influence 

 each other at all, and I mentioned that this spectrum 

 formula had yielded ten or eleven well-fitting lines, 

 of which six were actually quoted, the remaining 

 lines being given in the full paper appearing in the 

 Astrophysical Journal. 



I now write to say that, to my own surprise, the 

 same formula has since covered more than thirty 

 further lines of neutral helium, and that when the 

 whole ground is swept (by means of an auxiliary 

 arithmetical table), almost the whole observed 

 spectrum of helium is likely to be thus represented. 

 While a complete list will be found in the paper 

 referred to, some of these further lines may be quoted 

 here so as to give an idea of the closeness of the 



fm, . m.,\ 

 agreement. Losing the short symbol ( —r- J as 



already explained, we have, to five figures : — 



