292 
ward some objections against the assumption that 
the lines are due to helium. In his communication 
Fowler states that the two series of lines, denoted by 
him as the first and the second principal series of the 
hydrogen spectrum, in his opinion cannot be united 
within the limits of error of observation in a single 
series, such as my theory claims. However, I be- 
lieve that it is possible on the theory to account for 
the lines in satisfactory agreement with the measure- 
ments. 
The first and the second columns of the table below 
contain the wave-lengths given by Fowler for the 
new lines and the corresponding limits of error of 
observation. The lines are marked by P,, P., and S. 
according as they belong to the first or the second 
principal series or the Sharp series respectively. The 
figures in the third column are the products of the 
wave-lengths and the quantity 3 = = where n, and 
2 
n, are given in the bracket. 
A. 108 Lainie oF Nar x3) + rol0 
P, 4685-98 O-01 227791 (3:4) 
P, 3203-30 0-05 227790 (3:5) 
P, — 2733:34 0-05 227773 (3: 6) 
Pie eaariesy 0:05 227783 é 37) 
P, 2385-47 0-05 227779 (3:8) 
P, 2306-20 0-10 22777-3, (3:9) 
P, 2252-88 nas 0-10 227791 (3: 10) 
SS 5410°5 se LO 22774 tt 27) 
S 4541-3 0:25 22777 (4:9) 
S 42003 ae O5 22781 (4:11) 
The figures in the third column are very nearly 
equal, and apparently there is no indication of a 
systematic difference in the figures corresponding to 
the lines denoted by P, and P.,. 
The corresponding figures for the first lines in the 
ordinary spectrum of hydrogen (Ames, Phil. Mag., 
Xxx., p. 48, 1890) are :— 
A. 108 A(Za- aan) . 1010 
6563-04 911533 (2:3) 
4861-49 QII52:9 (2:4) 
4340°66 QII53:9 (2:5 
4101-85 + QII52:2 (2:6) 
3970:25 se 911537 (2:7) 
According to the theory in question we have 
K=a( I es + 2) 
ne ne) 2m*Be*M mw’ 
where c is the velocity of light, h Planck’s constant, 
e and m the charge and mass of an electron, and 
E and M the charge and mass of the central positive 
nucleus in the atom. This formula is deduced exactly 
as that given in the Phil. Mag., where, however, in 
order to obtain a first approximation the mass of 
the electron is neglected in comparison with that of 
the nucleus. 
The above tables give for hydrogen and for helium 
respectively 
Ke=01153.10-%, Kye=22779.107 1, 
The ratio between these values is :— 
Ku 
Kue 
From the theoretical formula we get for hydrogen, 
putting E=e and M=1835m, and using recent deter- 
minations of h, e, and m :— 
= 40016, 
Ka oetons- 
The agreement with the experimental value is 
within the uncertainty due to experimental errors in 
h, e, and m. : 
NO. 2295, VOL. 92] 
NATURE 
[OcToBER 23, 1913 
The theoretical value for the ratio between K for 
hydrogen and for helium can be deduced with great 
accuracy, as it is independent of the absolute values 
of h, e, and m. Putting Ene="Eu And My =4Mzy, 
we get from the formula: 
Sse 
ice 4°00163 
in exact agreement with the experimental value. 
It may be remarked that according to the theory 
helium must be expected to emit a series of lines 
closely, but not exactly, coinciding with the lines of 
the ordinary hydrogen spectrum. These lines, hitherto 
not observed, correspond to n,=4 and n.=6, 8, 10 
.., and have the wave-lengths 6560-3, 4859°5, 
43389 - . . The lines are expected to appear together 
with the lines of the Sharp series observed by Fowler 
and to have intensities of the same order as the latter 
lines. N. Bonr. 
The University, Copenhagen, October 8. 
I am glad to have elicited this interesting communi- 
cation from Dr. Bohr, and I readily admit that the 
more exact form of his equation given above is in 
close accordance with the observations of the lines in 
question. It will be seen that the equation now 
introduces a modified value for the Rydberg series 
‘constant,’ 109675, in addition to its multiplication 
by 4 for the particular series under consideration. 
The constant 22779, which is deduced from the wave- 
lengths of the lines is the reciprocal of this modified 
number, and in the usual numerical form, for oscilla- 
tion frequencies corrected to vacuum, the equation for 
the lines would be :— 
5 [ety ean 
(3? mJ 
where m takes the values 4, 5,6.... 
With this modification, the agreement with the 
observations is very close; in only two cases do the 
calculated values differ from those observed by 
amounts greater than the estimated limits of error, 
and I should not like to insist that such errors in 
the measurements are inadmissible. It may there- 
fore be possible to unite the P, and P, series in a 
single equation, as Dr. Bohr’s theory requires, but 
it should be noted that the combination demands the 
recognition of a type of series differing from those 
previously known. The result of this combination is 
to give what may be called a “‘half-step”’ series, such 
as would be obtained by combining ordinary first and 
second subordinate series, in the special case where 
the fractional parts of the terms (m+ ) in Rydberg’s 
equations for the two series differed by exactly o-5. 
Consideration of the relative intensities of the two 
sets of lines would in general prohibit this procedure, 
but this objection cannot be made in the case of the 
lines under discussion. It is possible that the mag- 
nesium spark lines, which I have recently described, 
form another series of the same kind, but I know of 
no others. 
The corrected formula given by Dr. Bohr leads to 
the further important result that alternate members 
of the ¢ Puppis series cannot be superposed on the 
Balmer hydrogen lines, as at first appeared, but 
should be slightly displaced with respect to them. Dr. 
Bohr, however, appears to have inadvertently inter- 
changed the last two figures of the constant 22779 in 
working out the wave-lengths, and the lines should be 
expected, within very narrow limits, at 6560-37, 
4859°53, 4338:86, 4100-22... . This should provide 
a valuable test of the theory, as the lines 
near H& and Hy, at least, should not be very 
difficult to detect, if present, in stars of the ¢ Puppis 
n=(4 X 109,720) 
