Aprit 28, 1923] 
‘ Letters to the Editor. 
[The Editor does not hold himself responsible for 
opinions expressed by his correspondents. Neither 
can he undertake to return, nor 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 Crossed-orbit Model of Helium, its Ionisation 
Potential, and Lyman Series. 
_ Taxrnc for granted the dynamical legitimacy of 
the crossed-orbit model as originally proposed by 
Bohr (Zeits. fiiy Physik, ix., 1922, p. 1) for normal 
_ helium, I find for its negatived total energy, with the 
_usual Coulomb law of force, and treating the two 
_ orbits as ‘‘ circular” in the literal sense of the word, 
-E=7Nqch| 1 - -F(sin 2) ] Se Eee), 
where F is the complete elliptic integral of the first 
kind, i the inclination of the planes of the two 
one-quantic orbits, in Bohr’s case 120°, and the 
Temaining letters are the usual symbols of the uni- 
versal constants. In accordance with symmetry, the 
electrons are assumed simultaneously to pass the 
nodes, that is, the opposite ends of the common 
diameter. (Details of deduction of (1) are given in 
a paper to be published shortly.) If one of the 
electrons be removed to “ infinity,’’ the energy of the 
remaining ionised atom He* is - 4Nch, where N=N,,: 
(1 +m/M). The small difference N,, -N being irrele- 
vant for our purpose, the ionisation work thus be- 
comes, by (1), W=Nch(3 -7F/47), or, the equivalent 
-wave-number (of the flash emitted at the return of 
the removed electron), 
»=N[3 - ZF (sin 2) | Pra ri fee C2) 
_ For Bohr’s model i=120° and, to four decimals, 
F=2'1565. Thus »=1-7987N, and since N is equiva- 
lent to 13°54 volts, the corresponding ionisation 
potential, 

Mi 24°35 VOLES;. hoe) ren (3) 
which is remarkably close to 24°5, the latest value 
observed and corrected by Lyman. The wave-length 
corresponding to (3), or the limit of Lyman’s new 
series, would amount to \,, =506°8 A. 
Thus far Bohr’s (idealised) model, corresponding 
to -cos i=}, a value supported in Bohr’s paper 
(l.c., p. 32) only by a terse reference to the quantum 
condition for atomic angular momentum. 
Now, suppose for the moment that there are 
dynamically ible states of the system also for some 
inclinationsdiffering from 120°. Thenthewave-number 
emitted at the passage from He* to such an i-model will 
be given by (2), with N=1'097;.10° as a sufficiently 
correct compromise value. It has seemed especially 
interesting to apply (2) to simple rational values of 
—cos i other than }, with a particular view of cover- 
ing, perhaps, some of the observed members of 
Lyman’s series, which are four, 
hy =584°4, Xo =537°1, Xs =522°3, 4 =515°7, 
with the conjectured \,, corresponding to 24°5 volts 
or, very nearly, to (3) as limit. The results thus 
obtained were as follows : 
The “‘normal’’ value -} being already treated, 
the next simple rational value cos i= -%, to which 
corresponds F =2-3404, gave, by (2), 
A=537°2, 
encouragingly close to the observed \,. The very 
next, however, cos i= - }, yielding \=561'9, was, for 
NO. 2791, VOL. 111] 
NATURE 

567 
the present, without interest. Further, cos i= -4, 
with the semi-inclination 71°585° and F =2°5892, gave 
\=585'0, 
close enough to the observed ,, and cos i= -}, 
1/2 =63°435°, F =2'2571, yielded 
X= 522°9, 
equally close to \;. But one observed member of 
the series, 515°7, remained uncovered. Working back 
from this, by (2), the required semi-inclination is 
found to be 61°97°, whence -cos i=0'558, while the 
nearest simple fraction § is 0°555. . . . But whether 
5 and 9g are still ‘‘ small”’ integers must be left to 
every one’s own judgment. In fine, the formula (2), 
regardless of its significance or deduction, gives the 
correct ionisation potential for -cos i=4, and at the 
same time, for 

-—cos i=§, #, 4, #, 
the observed Lyman lines },, Az, 2, \;, respectively, 
the initial state being always that of He’, and the 
final energy level being each time given by (1) with 
the corresponding inclination. Notice that for i=o, 
F=7/2, and (1) gives 49/8 Nch, the familiar energy 
level of Bohr's older (untenable) ring model. 
Whether the model of normal helium (i=120°), 
with almost circular orbits, is dynamically legitimate, 
seems doubtful. Finally, a decision with regard to 
the dynamical possibility of the remaining four con- 
figurations, leading to remarkable coincidences, would 
require a thorough and complicated analysis, which 
the writer is not in the position to offer. Unless some 
new lines are discovered beyond 500 A., the domain 
worthy of investigation in this respect, on either the 
accepted or modified dynamical and quantic principles, 
would extend only from i=120° to less than 177°63°, 
the latter being the inclination for which the right- 
hand member of (2) vanishes, when the system is 
ready to break up of its own accord. 
L. SILBERSTEIN. 
Rochester, N.Y., March 1. 

The Nature of Light-Quanta. 
In a letter to NaTurE of April 21, 1921 (vol. 107, 
p. 233), Sir Arthur Schuster pointed out that a 
uantum radiation could not, on account of the 
niteness of its energy, «=/v, be regarded as homo- 
geneous light of frequency », for homogeneity implies, 
strictly, the existence of an infinite train of waves of 
constant amplitude. 
Since all attempts to find a type of nearly homo- 
geneous light with total energy hy have been com- 
paratively unsuccessful, it seems worth while to 
consider the hypothesis that an approximately homo- 
geneous type of light is the result of the interference 
of two or more quantum radiations of an elementary 
character. 
Let us assume that an elementary quantum radia- 
tion, in the form of a plane wave travelling in the 
direction of the axis of x, is specified by an electro- 
magnetic field in which the electric vector E is trans- 
verse to the direction of propagation and represented 
by a vector of type f(x—ct)F, where F depends only 
on z and y and represents in magnitude and direction 
the electric force in a two-dimensional electrostatic 
field, of finite energy W, arising from positive and 
negative charges situated within a small finite area 
A in the yz-plane. 
If f(x) =n Pe the total energy in this electro- 
magnetic field is pW and is thus finite in spite of 
the fact that there are electric charges travelling in 
