PROF. A. FOWLER ON SERIES LINES IN SPARK SPECTRA. 
257 
The astrophysical and experimental data have as yet given no proof of the existence 
of the lines adjacent to those of hydrogen, but there is no evidence against the 
supposition that they exist. 
The assignment of these lines to proto-helium is supported by the observations of 
magnesium, which have shown analogous series associated with the “ 4481 ” 
series. The series A of magnesium, given by the combination 3 d—mf, would become 
4D— mF in proto-helium—the numeration being slightly different in the two cases*— 
and this would be identical with the formula for the extended Pickering series. 
Series B of magnesium, given by 3 f—mf, would similarly become 4F—mF and would 
also coalesce into the Pickering series. Alternate lines of series B are in fact not far 
removed from the Balmer lines, while intermediate lines are near the observed 
Pickering lines, as will be seen by comparing Tables XIII. and XV.; lines near these 
positions might also be derived from the F series of other elements in which mF 
approximates to 4N/m 2 . The relative weakness of the Pickering series of proto-helium, 
as compared with 4686, is matched in magnesium by the relatively low intensities of 
the analogous combination series A and B. 
The close relations between the lines of hydrogen (real and hypothetical) and some 
of those of proto-helium are simply accounted for by Bohr’s theory of the origin of 
these spectra. The general formulae, in which p and m can only take integral values, 
may be written 
Hydrogen : 
p = 2 for Balmer series. 
Proto-helium : n = N'( ——-5 
\p 2 m. 
fp — 3 for “ 4686 ” series, 
\ p — 4 for Pickering series. 
If N' were exactly equal to 4N, alternate lines of the Pickering series would 
evidently coincide with the Balmer series ; and the hypothetical P series of hydrogen, 
given by p = 1'5 in the first formula, would fall 011 alternate lines of the “4686” series. 
The hydrogen lines, according to the theory, are produced during the binding of an 
electron by an atomic nucleus having a single positive charge, and those of proto- 
heliuin during the binding of an electron by a nucleus having four times the mass and 
a double positive charge. If the mass of the electron were negligible in comparison 
with that of the nucleus, N' would be equal to 4N, but Bohr has shown that when 
correction is made for the mass of the electron, the theoretical ratio for these constants 
is in nearly perfect agreement with that of the values deduced from the spectroscopic 
observations.! His expression for the constant of the hydrogen series may be 
written 
Nh = 
109,675 = 
10 8 27 r"EVMm 
ch 3 (M + m) 
* The numeration would be the same if m in the proto-helium formula were written (m+l) to 
correspond with (m + 0-99) of magnesium, 
t ‘Nature,’ 1913, October 23, p. 231. 
2 L 
VOL. CCXIV.-A. 
