46 NATURE 

Letters to the Editor. 
[The Editor does net hold himself responsible for 
opinions expressed by his correspondents. Neither 
can he undertake to return, or to correspond with 
the writers of, rejected manuscripts intended for 
this or any other part of NatuRE. No notice is 
taken of anonymous communications. | 
The Spectrum of Neutral Helium. 
In a letter to Nature of November 25, p. 700, 
concerning my first communication (NATURE, August 
19) on this subject, Prof. Raman expresses the opinion 
that the representation of helium lines derived from 
my assumption of the mutual apathy of the two 
interatomic electrons has a purely arithmetical char- 
acter and would thus be deprived of any “ real 
physical basis.”’ pees 
Disregarding a number of remarks reducible to the 
laceration of the empirically established series, a 
regrettable feature pointed out by myself (Astrophys. 
Journ., September 1922), it will be enough to reply 
here to Prof. Raman’s chief and apparently strongest 
objections. These are two: first, that the numerous 
coincidences yielded by my formula are simply ex- 
plicable as so many “ fortuitous arithmetical co- 
incidences,’ and, second, that the particular value 
(109723) of the Rydberg constant N used in that 
formula is, in general, inadmissible, this value belong- 
ing legitimately to He*, with a single electron, but 
not to the neutral atom with its two electrons. 
Now it so happens that precisely these two points 
have steadily occupied my attention since the formula 
was first published, and I am therefore able to reply 
to both of them without delay. The corresponding 
details of reasoning and numerical data being all 
given in a paper just communicated to the American 
Physical Society (for its Boston meeting, December 
27-29), to which readers may be referred, it will 
suffice to describe here the bare results. 
1. Consider only those lines for which the final 
quantum numbers lie between 3 and 8, and the initial 
ones between 4 and 20, which fall within the interval 
v=17,000 to 37,850. The total number of such dis- 
tinct lines is »=680. Among these there are k=45 
lines covering observed helium lines, with a mean 
deviation |6»|=2-57. In the considered »v-interval 
there are in all 97 observed lines. Whence, the mean 
(geometric) probability of hitting an observed line in 
a single trial by mere chance, p=o0-0182, and the 
probability P of hitting # or more such lines in 7 (680) 
trials, by Bernoulli’s theorem, P=1-—0(*), where 
@(x) is the error-function and 
A 
4, A= |h—pn]. 
/2p(1-p)n be 
In our case pn=12:40, A=32:60, and therefore 
the probability that our set of 45 coincidences should 
be “ fortuitous ”’ is 
P=1-0(6-61), 
which is a little less than 1-7. 10-!%—small enough to 
discard every suggestion of the play of blind chance, 
This conclusion is considerably strengthened when 
other groups of coincidences tabulated in the Astrophys. 
Journal are similarly treated. 
Of particular interest, in this and other respects, 
are the 18 lines of the type (™a-me), and another 
group of three lines, each of the type i= ; mm) and each 
, 

covering an empirical “‘ combination » “line of the 
“ doublet system.” 
2. Let m be the mass of each of the two electrons, 
NO. 2776, VOL. 111] 

[JANUARY 13,1923 

M that of the nucleus, and «=m/M. Taking account 
of the wobbling of the nucleus, through which the 
otherwise indifferent electrons perturb each other 
indirectly, and rejecting terms in «*, etc., the energy 
of the system in any stationary state, say 7,=., 2,=k, 
is found with comparative ease. This divided by ch 
gives the corresponding ‘‘ term,” say T.x, our » being 
the difference of two such terms. If this be written 
1 
Tue=4Nuc( 2+), 
then Nix, the ““ Rydberg constant ’’ belonging to the 
particular pair (««) of electronic orbits, is a certain 
symmetrical function of the integers 1, «, and of the 
mutual orientation of the two orbits. For the case 
of quasi-circular orbits (i.e. such as would become 
circular for «=o or no wobbling) the investigation 
given in the Boston paper leads to the interesting ~ 
result 
84 6 : 
Nu=N,[ 1-« - ote 5 . (1) 
where N,, (about 109737) is the constant for M/m 
=, and y the time-average of the cosine of the angle 
between the radii vectores of the two trabants. This 
formula holds for any inclination (7) of the two orbits 
and for any phase difference (a) of the two electrons 
describing them. 
Now, a purely kinematical reasoning gives for «-+« 
the value y=0, and for «=x, 
Y=Yer=$CoSa(I+cosz),. . . (2) 
where a is the angular distance of one electron from 
the ascending node when the other electron just passes 
through it. 
Since for .=« the arithmetical expression in (1) 
becomes equal to unity, we have 
Na«=N,, [1— €— eyee], (1a) 
which, by (2), can assume any value from N,, down 
to N, (1-2), with N,(1-«), the desirable Het 
value, just in the middle of the interval. If, e.g., the 
orbits are coplanar and a=180°, we have Nee=N,, 
for then there is no wobbling; if a=o, Nx would 
reach the other extreme value, about 109709, and for 
a=g9o0° we should have the mean value (109723), 
which might even be made the only value if the lines 
of the type ‘=« are not to be very broad. There is 
thus no essential difficulty. Moreover, very few 
among my tabulated lines have «=x. ; 
For the overwhelming majority of those lines we 
have «+x, when y vanishes, and (1) becomes, no 
matter what the inclination of the orbits and the 
phase difference of the electrons, 
Nuw=N,, (1-6), . aie (1d) 
which is precisely the value (109722 to 23) used in my 
formula. This in itself seems to be a strong support 
for that formula. LupDWIK SILBERSTEIN. 
December 6. 
Returning to my letter of December 6, I beg to 
supplement the same by a result of my last week’s 
work, which seems to give the proposed theory a 
much stronger support than all probability estimates, 
for it represents 7m toto and orderly some empirical 
series of helium. In fact, guided by a few coherent 
items of my original table, I find that the whole 
diffuse series of singlets, denoted by 1P-mD, is 
represented by 
ne a.) =H i) ? 


two final and one initial quantum numbers being 
—E—————— 
