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A 324-page scanned textbook of the old quantum theory (Bohr-Sommerfeld atom) written by one of its principal creators. Every page was OCR'd (no text layer); prose is mostly readable, but nearly every equation, table and subscript is garbled, so all numerical claims below were taken from page images by the deep readers. Each PDF page is a two-page spread (PDF page N = book pages 2N-20 and 2N-19 in the later part). Chapter I (Introductory facts) covers electrons (e/m, Millikan e = 4.774e-10 esu), cathode, canal and X-rays, the photo-electric effect (Einstein's law, Millikan's h = 6.57e-27), Planck's quantum, Bohr's frequency condition hv = W_a - W_e, and radioactive decay laws. Chapter II (Natural system of elements) covers Rutherford's nuclear atom, nuclear charge = atomic number (Chadwick's 77.4/46.3/29.3 against 78/47/29 for Pt/Ag/Cu), planetary atom, molecular models (H2, H2+, He, all later judged untenable), radioactive displacement laws, isotopes (Aston), nuclear structure (He nucleus as four H nuclei + two electrons; Rutherford's disintegration of nitrogen; mass defect 0.03 per gram-atom and E = mc2), atomic volumes, ionic radii and shells (Kossel, Lewis, Bohr). Chapter III (X-ray spectra) covers Laue diffraction, crystal structures, Bragg and powder methods, rock-salt standard d = 2.814e-8 cm, Moseley's law, K/L/M series, doublets, absorption edges. Chapter IV is the core. Phase-integral quantisation of oscillator and rotator; the Sommerfeld-Wilson rule that each coordinate gets its own condition, integral p_k dq_k = n_k h; Balmer and Ritz; Bohr circles (a1 = 0.532e-8 cm, alpha = 2 pi e2/(hc), alpha2 = 5.3e-5); reduced mass of the nucleus (R_H = 109677.691, R_He = 109722.144, R_inf = 109737.11 +/- 0.06 cm-1; e/m = 1.769e7 emu/g); elliptic orbits with quantum sum n + n' and energy W = -2 pi2 m e2 E2/(h2 (n+n')2); exclusion of n = 0; the admitted gap that polar and parabolic coordinates give different quantised ellipses for the degenerate Kepler problem (Bohr's objection conceded); spatial quantisation cos(alpha) = n1/(n1+n2); the Bohr magneton and Pauli's correction of the Weiss magneton (NO and O2 at 8.7 and 13.7 predicted versus 9 and 14 observed). Chapter V (Wave theory and quantum theory) is where the book states its attitude to the ether and to the wave/quantum dilemma. Sommerfeld quotes Hertz's 1889 certainty that light is a wave and answers 'Has this certainty meanwhile been shattered? Yes and no!'. He says both the wave view and the light-quantum view 'each offer at present only one-half of the truth'. He then adopts the classical wave theory for propagation only as an explicit assumption ('we shall repress all doubts about the idea of a spherical wave that is coherent in itself'), postulates conservation of energy, momentum and angular momentum in the single emission, assumes the atom does not recoil, and derives (Note 9, after Abraham) that a spherical wave of energy W = h nu carries at most angular momentum h/2 pi (N = (W/2 pi nu) 2ab sin(gamma)/(a2+b2)). Equating this with the change of the atom's angular momentum gives the selection principle |Delta n| <= 1 and the rule of polarisation (Delta n = +/-1 circular, Delta n = 0 linear), credited to Rubinowicz (1918). Sommerfeld flags the weak points himself: Delta n = 0 gives no emission only by a step he calls 'not inevitable'; keeping the orbital plane fixed for n_a = n_e needs a standpoint he calls 'certainly rather risky'; in a field only the component along the field is conserved so the rule is 'weakened' and 'rescinded' in high-current discharge tubes; 5 of the 7 determining elements of a spherical wave are fixed, 2 (including coherence length) are 'still in darkness'; his own footnote concedes that the atom and ether cannot be wholly uncoupled in stationary orbits ('The author finds himself compelled to admit that this objection is justified'). His ether is defined as having 'no properties other than such as light itself possesses'. He also presents Bohr's correspondence principle, says it is 'completely superior' on polarisation and intensities, and calls it a 'magic wand'. Note 10 states its intensity ambiguity (use initial, final or intermediate orbit?) in his own words. The Stark effect follows: Stark and Lo Surdo's eight experimental facts, theory by Schwarzschild and Epstein (1916) in parabolic coordinates, first-order energy W = W0 - (3 h2 F/(8 pi2 m E)) (n2-n1)(n1+n2+n3) (the deep reader corrected the printed OCR 'me E' to 'm E'), component Tables 27-34 for H-alpha to H-delta. Sommerfeld reports perfect agreement for H-gamma and H-delta, but for H-alpha predicted components at Delta = 5, 6, 8 were not observed and for H-beta four observed components (p at 4 and 12, s at 0 and 8) are not predicted; Epstein inferred the field from the theory (107,000 V/cm) against Stark's measured 104,000 V/cm (about 3 %). The parabolic quantisation is stated to hold only for strong fields; the zero-field limit 'is not allowable' and the earlier polar method 'remains true'. The deep reader's check shows the first-order formula equals the later wave-mechanical result (3/2) n (n1-n2) e a0 F. The rest of Chapter V (digest only) gives the normal Zeeman triplet from Larmor precession plus the selection rule for the equatorial quantum number (h cancels), and Ehrenfest's adiabatic hypothesis (quantum numbers invariant under infinitely slow, reversible, unsystematic changes), used to link Stark and Zeeman orbits and to fix the orientation of Stark orbits. Chapter VI (digest only) organises series spectra: principal, first and second subsidiary, Bergmann series; Rydberg and Ritz term forms from a supplementary atomic field (Note 13); the azimuthal selection principle; the Franck-Hertz electron-impact method (Hg 4.9 V, He 20.5 V, ionisation 25.3 V against Bohr's 28.75 V model); the continuous passage from X-ray to optical spectra (Kossel's diagram); permanence of multiplicities and inner quantum numbers eta with Delta eta = 0, +/-1; the spectroscopic law of displacement (spark spectrum of an element resembles the arc spectrum of the previous element; Fowler, Fues); the Wechselsatz (cross or exchange law); the anomalous Zeeman effect (Preston and Runge rules, Landé formula, Paschen-Back effect, Voigt's theory) and a model of doublet and triplet atoms (outer valency electron plus trunk, with Heisenberg's help). Chapter VII (digest) treats band spectra: rotator and oscillator, Deslandres, HCl rotation-vibration bands, the missing zero line, cyanogen bands, hydrogen many-lines spectrum, continuous spectra. Sommerfeld says the Chapter VI regularities are 'mainly empirical' and that doubt attaches to the model interpretation. Chapter VIII is the second core. Relativity preliminaries (Lorentz transformation, mass variation m = m0/sqrt(1-beta2), E = mc2, Kaufmann's experiment 'the experimentum crucis'). Relativistic Kepler motion: orbit with advancing perihelion, advance 2 pi (1/gamma - 1) per revolution; in the quantised problem polar coordinates are fixed by the relativistic perturbation, which he says removes the degeneracy and answers Bohr's objection. Energy formula 1 + W/(m0 c2) = {1 + (alpha E/e)2/[n' + sqrt(n2 - alpha2 E2/e2)]2}^(-1/2); expansion to alpha2; doublet interval Delta nu_H = R alpha2/16 = 0.365 cm-1 (book inputs alpha2 = 5.32e-5, R = 1.097e5); multiplicities of 1 : 3 (triplet), 1 : 2 : 6 (quartet), 3 : 5 : 10 : 30 (quintet) were reproduced exactly by the deep reader; the formula equals Dirac's 1928 result with n = j + 1/2 [memory, high]. Evidence: direct hydrogen measurements (Michelson, Fabry-Buisson, Meissner-Paschen, Gehrcke-Lau) give 0.27-0.33 cm-1, all below 0.365; Sommerfeld says the difference is 'partly explained' by which components survive the selection principle (the deep reader computes 0.329 for H-alpha and 0.350 for H-beta, leaving up to about 0.06-0.08 cm-1 unexplained). Paschen's photographs of the 12-component He+ 4686 pattern, with a photometric curve published here for the first time, are said to be 'a striking confirmation'; Paschen derived an indirect Delta nu_H = 0.3645 +/- 0.0045 cm-1 by fitting the theory's own interval scheme to the He+ pattern; the crude intensity rule (2:1, 3:2:1) is 'contradicted by experience' (II b is the strongest component); forbidden components appear weakly, attributed (Kramers) to stray fields of about 100 V/cm (direct current) and 300 V/cm (spark). Bohr's remark, quoted with approval: the failure of the selection principle in Paschen's photographs was 'a piece of good fortune' for the development of the theory. The X-ray part of Chapter VIII: the L-doublet is 'a gigantic magnification' of the hydrogen doublet, Delta nu_L = Delta nu_H (Z - s)^4 with s = 3.49 (mean of 38 elements Z = 41-92; spread 0.043 by the deep reader's computation, none quoted by Sommerfeld), Table 53; Delta nu_H extrapolates toward 0.365 at low Z. Orbital models are abandoned for screening ('hopeless'; 105 species of atom would be needed) and Sommerfeld retracts, in at least two footnotes (QE counts at least five withdrawals in the whole book), positions held in earlier German editions (L1 and L2 in different atoms; Kossel's combination defects). Irregular (screening) doublets obey Hertz's law (sqrt(nu/R) differences constant, 0.66 for L2L3), the full K, L(3), M(5), N(7), O(5) level scheme with the 'ground quantum number' m and Wentzel's complete selection principle is drawn up (Tables 55-57; the deep reader notes a text/table contradiction on 'regular' versus 'irregular' in the definition of m), and the three universal constants are determined spectroscopically: the 'purely spectroscopic' route gives e = 4.766 (1 +/- 1/54) e-10 esu and h = 6.526 (1 +/- 5/162) e-27 erg s, with error bars he calls 'unsatisfactorily wide'; the 'semi-spectroscopic' route using Millikan's e = 4.774 +/- 0.004 gives h = 6.545 +/- 0.009 e-27, which he ventures 'is at present the truest value', alpha = 7.295e-3, Delta nu_H = 0.3650 +/- 0.0005. Modern values ([memory, high]: e = 4.8032e-10, h = 6.62607e-27) lie outside the narrow bars (e by about 7 sigma, h by about 9 sigma) but inside the wide ones; the narrow bars omit Millikan's systematic error. The chapter ends with a test of relativity against the 'absolute' (Abraham) rigid-sphere electron: the latter would reduce all fine structure by 4/5 (Delta nu_H = 0.29), 'in no wise compatible with Paschen's measurements', so 'the absolute theory comes to grief owing to spectroscopic facts' (the deep reader notes that alpha is itself taken from the doublet, so the test needs an independent value of alpha). Mathematical Notes 1-17 (pp.532-616) are the derivations: Larmor radiation, Rayleigh scattering and the Debye cone, crystal tables, canonical transformations, the virial theorem, contour integrals for the radial phase integral, Hamilton-Jacobi separation and action-angle variables, degeneracy, the spherical wave and its angular momentum (Note 9), correspondence principle (Note 10), Stark effect by Hamilton-Jacobi (Note 11), adiabatic invariance (Note 12), non-hydrogenic spectra (Note 13), the Bohr models of He, H2, H2+ (Note 14: He ionisation 28.75 V against 25.3 V observed, 'Bohr's He-model cannot be correct'; H2+ model 'untenable'), relativistic Hamilton theory and Mercury's perihelion (7 arcsec special relativity versus 43 general relativity, 7.16 and 42.98 reproduced) (Notes 15-16), and rotation-vibration of HCl (Note 17). The deep readers verified the main results and found only sign, exponent and typographical slips (Note 4 eq. 22c sign; Note 6 eqs. 27/29 sign; Note 11 eq. 28 sign of beta; Note 13 third-approximation n-powers; Note 17 sign of the b-squared term; cerium c:a 1.62 should be 1.633; antimony angle '563 deg 6 min'; Table 29 and Table 27 entries; 191/32 in X-ray doublet eq. 14 should be 2807/1024 by the deep reader's derivation) plus a few errors of fact (ζ Puppis and Wolf-Rayet objects called nebulae; 'four octaves' for a factor 4 in frequency; Haas date 1900 versus probably 1910). Note 2 records an unexplained experimental anomaly in gamma-ray scattering (s/rho 0.04 against 0.2) that Sommerfeld ascribes to 'the size of the energy quantum', i.e. a departure from wave optics, a year or two before Compton. Translator's preface (Brose) adds the Stern-Gerlach result for silver (one Bohr magneton) as support for spatial quantisation; the translator's date is printed '1928' in the OCR, probably a misread 1923. QE revision (2026-10-09, MINOR). Added after the QE: (1) the book's and Paschen's report of the circular-orbit relativity term (0.569 +/- 0.25 against 0.590 cm-1), which is the measurement that separates relativity from Weber's law, with its caveats; the deep read shows it cannot separate relativity from Abraham because Paschen took alpha from the same fine structure; (2) Paschen's own 1916 statement that his H-alpha doublet spacing is probably too small because of overlapping edges; (3) electron-impact tests of He+ (79.3 against 79.5 +/- 0.3 and 80 V; 75.4 V); (4) field-blamed selection-rule breaks; (5) Barkla's J-radiation, nebulium/coronium, and the Sommerfeld-Debye accumulation theory as reported effects or alternatives set aside by replication or theory; (6) at least five withdrawals in the book; (7) doublet-atom numbers; (8) Birge 1921 and Grossmann 1921 as records named but not examined. Items (3) to (8) were then deep-read (QE revision 2, below). QE revision 2 (orchestrator fix, 2026-10-09). The six remaining QE deep reads were done (Ch. I sections 6-7, Ch. II sections 3 and 6, Ch. III sections 4-7, Ch. VI in full, Ch. VIII section 4 footnotes). They confirmed the digest-based items above and changed no verdict category. They corrected: the 4686 excitation (printed 75.4 V, arithmetic 75.9 V); the He heat of formation (printed 6.3e9, arithmetic 6.4e8 major calories); the list of withdrawals (the A-doublet and its 'false interpretation' are one episode; 'refuted by Hoyt' refers to the Lambda limits; the triplet Runge denominators take the place of the double-counted item, so the count of at least five stands); Birge 1921 (cited only for a centre-of-gravity point); and the half-integer story (the book's Addendum itself uses half-integer m*; the vindicated half-integers are Landé's). Moseley's law, the nebulium/coronium identifications and the half-integer outcome are now [read] plus [web] rather than [memory].

Key claims

• Allowed (stationary) states of an atom are fixed by one quantum condition per coordinate, the integral of p_k dq_k over a cycle equals n_k h, and in a stationary state the electron does not radiate.
• A hydrogen-like atom quantised in polar coordinates has energy W = -2 pi^2 m e^2 E^2/(h^2 (n+n')^2), depending only on the quantum sum n + n' (azimuthal plus radial), with orbit eccentricity sqrt(1 - n^2/(n+n')^2) and the n = 0 orbit excluded because the electron would fall into the nucleus.
• Each Balmer line has several quantum-number pathways ((n+n')(k+k') of them) that coincide in the non-relativistic theory and are separated only when relativity is included.
• Under spatial quantisation the orbit normal makes angle alpha with a preferred direction given by cos(alpha) = n1/(n1+n2), with exactly n allowed orientations for azimuthal number n and the n1 = 0 orientation excluded.
• The atomic magnetic moment is quantised in units of the Bohr magneton (e/m)(h/4 pi), which Sommerfeld computes as about 5584 per mole, almost exactly five Weiss magnetons.
• With Pauli's correction of Langevin's averaging, NO and O2 should show 8.7 and 13.7 Weiss magnetons, close to the observed 9 and 14, supporting one Bohr magneton per O atom (Sommerfeld stresses the diatomic-gas application is 'very doubtful').
• Allowing for the nucleus's motion with a reduced mass, R_H = 109677.691 and R_He = 109722.144 cm-1 give R_inf = 109737.11 +/- 0.06 cm-1 and e/m = 1.769e7 emu/g.
• A spherical light wave of energy h nu can carry at most the angular momentum h/2 pi, with N = (W/2 pi nu)(2ab sin gamma)/(a^2 + b^2) (Note 9, after Abraham 1914).
• Conservation of angular momentum between the atom and the emitted wave requires |Delta n| <= 1 for the azimuthal quantum number, with circularly polarised light for Delta n = +/-1 and linear polarisation for Delta n = 0 (principle of selection and rule of polarisation, due to Rubinowicz 1918).
• In a field-free atom the case Delta n = 0 produces no emission, an inference Sommerfeld calls 'not inevitable', and the invariable orbital plane is preserved only under an assumption he calls 'certainly rather risky'.
• In an external field only the component of angular momentum along the field is conserved, so the selection principle acts only on the (unobservable) equatorial quantum number, and it is 'rescinded' in discharge tubes of high current density.
• The wave theory may be used for propagation of light while quantum rules govern emission; the atom is assumed not to recoil; neither the wave view nor the light-quantum view alone is complete ('each offer at present only one-half of the truth').
• Of the 7 determining elements of a spherical wave only 5 are fixed by the conservation conditions; coherence length and one further element remain undetermined ('5/7ths ... solved').
• Sommerfeld's 'ether' has no properties other than those of light itself; it is the carrier of the optical field, with its own reference system for each observer under relativity.
• The first-order Stark shift of a hydrogen level is Delta W = -(3 h^2 F/(8 pi^2 m E)) (n2 - n1)(n1+n2+n3), giving components at integer multiples of C = 3 h F/(8 pi^2 m E) (about 6.66 cm-1 for F = 104,000 V/cm), and it accounts for the polarisation (p and s) and the component positions found by Stark and Lo Surdo.
• Theory and observation of the Stark components agree 'absolutely perfectly' for H-gamma and H-delta, and for H-alpha up to Delta = 4; theory also predicts weak H-alpha components at Delta = 5, 6, 8 that were not seen, and four H-beta components were observed that the theory does not predict.
• The absolute scale of the Stark check is a consistency to about 3 % between Stark's measured field (104,000 V/cm) and the field Epstein inferred from the theory (107,000 V/cm), not an independent test.
• Parabolic-coordinate quantisation is correct only for strong fields; passing to zero field is not allowed and the polar-coordinate (Chapter IV) quantisation remains true for the field-free atom.
• The Kepler problem is degenerate, so polar and parabolic coordinates give different quantised orbits with the same energy; Sommerfeld concedes Bohr's objection and answers that relativity (which lifts the degeneracy) selects polar coordinates.
• The normal Zeeman triplet follows from Larmor precession of the quantised orbit with the equatorial quantum number changing by 0 or +/-1, and Planck's constant cancels from the result (digest only, Ch. V section 6).
• Quantum numbers are invariant under infinitely slow, reversible, unsystematic changes of the system (Ehrenfest's adiabatic hypothesis), which does not hold for passage through a degenerate state (digest and Note 12; proof incomplete for near-resonances).
• Bohr's correspondence principle determines the polarisation and intensity of spectral lines from the classical Fourier amplitudes, exactly for large quantum numbers and approximately for small ones, but is ambiguous about whether to use the initial, final or an intermediate orbit.
• Because the mass of the electron varies with velocity, the relativistic Kepler orbit is an ellipse whose perihelion advances by 2 pi (1/gamma - 1) per revolution, where gamma^2 = 1 - (e E/(p c))^2.
• The energy of the relativistic hydrogen-like atom is 1 + W/(m0 c^2) = {1 + (alpha E/e)^2/[n' + sqrt(n^2 - (alpha E/e)^2)]^2}^(-1/2), with alpha = 2 pi e^2/(h c) (alpha^2 = 5.3e-5), and this one formula 'includes all the spectral phenomena that the hydrogen atom is capable of exhibiting'.
• The n = 2 level of hydrogen splits into a doublet of Delta nu_H = R alpha^2/16 = 0.365 cm-1, the n = 3 level into a triplet with interval ratio 1 : 3, n = 4 into a quartet 1 : 2 : 6, and n = 5 into a quintet 3 : 5 : 10 : 30.
• With the selection principle only 5 of the 12 possible components of the He+ 4686 line should survive in a weak discharge, and Paschen's direct-current photographs show those 5 plus weak 'forbidden' components that Sommerfeld attributes to stray electric fields.
• Paschen's indirect value Delta nu_H = 0.3645 +/- 0.0045 cm-1, obtained from the He+ 4686 pattern, agrees with the theoretical 0.365 (0.3648 recomputed), although direct measurements of the hydrogen doublet give only 0.27 to 0.33 cm-1.
• Sommerfeld's crude intensity rule (2:1, 3:2:1, 4:3:2:1 from circular to eccentric orbits) is contradicted by Paschen's photographs (component II b of 4686 is the strongest) and needs the correspondence principle (Kramers) to be repaired.
• The measured-versus-theoretical hydrogen doublet shortfall is 'partly explained' in the book by which components survive the selection principle (about 0.329 cm-1 for H-alpha by the deep reader's computation). [Revised after arbiter correction 2 and QE] The arbiter's seven-component Dirac-plus-Lamb Doppler recomputation indicates the shortfall is largely explainable as a blend of seven fine-structure components (apparent splitting about 0.26-0.32 cm-1 depending on temperature and unmeasured level populations); the residual for Gehrcke and Lau is open. Paschen himself wrote in 1916 that his measured H-alpha spacing (6562.853 and 6562.732 A, 0.121 A = 0.281 cm-1, against 0.1571 A from theory) is 'wahrscheinlich ... zu klein' because of the overlapping edges of the blurred components; Meissner's interferometric values were 6562.849 and 6562.725 A (0.124 A = 0.288 cm-1). The book itself names Doppler and Stark broadening as the cause of the blurring (book p.~485).
• Special-relativistic perihelion advance of Mercury is only about 7 arcsec per century (7.16 recomputed), whereas general relativity gives six times as much, 43 arcsec (42.98 recomputed), the observed anomaly according to Newcomb.
• Sommerfeld's relativistic fine-structure formula was confirmed in the sense that its numerical values (0.365 cm-1) survive in modern theory; his formula is algebraically identical to Dirac's 1928 level formula with n = j + 1/2 [memory, high].
• The L-doublet of X-ray spectra follows Delta nu_L = Delta nu_H (Z - s)^4 over Z = 41 to 92 with s = 3.49 (rows scatter by +/-0.043), and the 'hydrogen doublet' read off the table rises from 0.38 to 0.50 cm-1, which Sommerfeld attributes to higher relativistic terms.
• 'Irregular' X-ray doublets obey Hertz's law: the difference of the square roots of the wave-numbers sqrt(nu/R) is independent of Z (0.66 for L3 - L2 over Z = 55 to 60), so Delta nu rises linearly with Z and Delta lambda falls as Z^-3.
• Orbital models cannot explain the screening numbers: the L-doublet must be a 'macroscopic copy of the microscopic hydrogen doublet' with levels L1, L2, L3 in the same atom, and the problem of the arrangement of the electrons 'becomes hopeless' from an elementary point of view.
• The X-ray term scheme has 1 + 3 + 5 + 7 + 5 = 21 levels for K, L, M, N, O; with the azimuthal number n and the 'ground quantum number' m, strong lines obey n -> n-1 and m -> m-1 (Wentzel's complete selection principle), and Kossel's combination defects are the irregular doublets.
• Moseley's law as printed (eq. 7, book p.157) is nu/R = (3/4)(Z-1)^2, i.e. sqrt(nu/R) = 0.866 (Z - s) with s 'almost equal to 1', for K-alpha; it shows that atomic number, not atomic weight, orders the elements (Co before Ni, Te before I) and that 'the number of gaps must be five' (Z = 43, 61, 75, 85, 87). The author says it is not exact ('a small curvature for larger Z's', assigned to relativity); a modern measurement over Z = 29-92 finds the same relativistic curvature, fitted by a relativistic Bohr-Sommerfeld model. [read: deep/Sommerfeld-AtomicStructureAndSpectralLines-0c4636.ch3.md, page images PDF pp.85, 88; web: arXiv 1809.10480]
• Nuclear charge equals atomic number: Chadwick (1920) found 77.4, 46.3, 29.3 elementary charges for Pt, Ag, Cu against Z = 78, 47, 29 from scattering of alpha rays.
• Isotopes are the rule among elements, differing in mass (Aston's mass spectrograph) but identical in chemistry and in X-ray line positions, so the whole atomic structure is fixed by nuclear charge.
• A He nucleus built of four hydrogen nuclei and two electrons has a mass defect Delta m = 4 x 1.0077 - 4.00 = 0.03 per gram-atom; the book prints its heat of formation as Q = 0.03 c^2/(4.19e10) = '6.3 x 10^9 major cals', which is ten times too large (the arithmetic gives 6.4 x 10^8 kcal [computed]); either way it is far above the roughly 100 major calories of chemical combinations. Rutherford's alpha-ray experiments shattered N, B, F, Na, Al, P (Li, Be, Mg, Si, Cl, K uncertain; none from C, O, S, Ca, Ti, Mn, Cu, Sn). Lenz's He-nucleus model ('an inverted oxygen molecule') is reported 'without committing ourselves', its data 'admittedly rather unconvincing'. [read: deep/Sommerfeld-AtomicStructureAndSpectralLines-0c4636.ch2-s6.md, page images PDF pp.56-58]
• The spectroscopic displacement law holds: the spark spectrum of an element has the line structure (doublet or triplet) of the arc spectrum of the preceding element, with the Rydberg number R replaced by 4R for the singly ionised atom.
• Terms of a series carry inner quantum numbers eta with selection rule Delta eta = 0, +/-1 (strong, less strong, weak), which explains composite doublets and triplets and why combinations such as the p_i d_j with i > j are missing (digest only).
• The anomalous Zeeman effect obeys Preston's and Runge's rules and Landé's result, printed as W = W0(n_i) + m h (n_i/r) Delta nu_norm with r = 2n - 1 (level spacings 2, 4/3, 2/3, 6/5, 4/5, 8/7, 6/7 times the normal splitting for s, p1, p2, d1, d2, b1, b2), and passes to the normal effect in strong fields (Paschen-Back; about 180,000 gauss calculated for full effect on Na D). The inner quantum number obeys n_i -> n_i +/- 1 or n_i, with 0 -> 0 excluded 'by a special convention' from Landé. [read: deep/Sommerfeld-AtomicStructureAndSpectralLines-0c4636.ch6-part2.md, page images PDF pp.192, 204, 206-208]
• Doublet atoms are an outer valency electron plus an atomic trunk, each with mean moment of momentum 1/2 in the ground orbit (a 'fundamental assumption, which is justified by its success'), the trunk's magnetic moment being half a Bohr magneton; the author says the model would scarcely be 'inevitable' without its link to the Zeeman effect and calls the regularities 'a representation of the empirical facts ... rather than a true theory'. [read: deep/Sommerfeld-AtomicStructureAndSpectralLines-0c4636.ch6-part2.md, book pp.369, 406-409]
• Bohr's early models of He, H2 and H2+ fail (He ionisation potential 28.75 V against the observed 25.3 V; the H2+ model 'untenable'); Sommerfeld says the true structure of neutral atoms other than H, He+, Li++ is 'only provisional'. (The book prints Bohr's He figures three ways: 28.8 against 25.4 V in Ch. II, 28.7 against 25.3 in Ch. VI, 28.75 against 25.3 in Note 14 [read: deep/Sommerfeld-AtomicStructureAndSpectralLines-0c4636.ch1-2.md].)
• In the Franck-Hertz electron-impact test, mercury shows a first inelastic loss at 4.9 V (line 2537 A) and ionisation at 10.4 V, helium at 20.45 V and 25.3 V, matching spectroscopic term differences.
• The 'purely spectroscopic' determination from the hydrogen doublet gives e = 4.766 (1 +/- 1/54) e-10 esu and h = 6.526 (1 +/- 5/162) e-27 erg s, with error bars Sommerfeld himself calls 'unsatisfactorily wide'.
• The 'semi-spectroscopic' route combining spectroscopic e/m0 and R_inf with Millikan's e = 4.774 +/- 0.004 e-10 gives h = 6.545 +/- 0.009 e-27 erg s, alpha = (7.295 +/- 0.005) e-3 and Delta nu_H = 0.3650 +/- 0.0005 cm-1, offered as 'at present the truest value'; modern values lie outside these narrow bars because Millikan's e carried an unrecognised systematic error [memory, high].
• The rigid-sphere 'absolute' (Abraham) electron would cut every fine-structure interval by the factor 4/5 (hydrogen doublet 0.29 cm-1), which is incompatible with Paschen's measurements, so the fine structure is a spectroscopic 'experimentum crucis' in favour of relativity. [Revised after the Paschen 1916 deep read] The 4/5 test needs an alpha fixed independently of the doublet: Paschen's alpha^2 = 5.3146e-5 was itself read from the measured He+ splitting (0.3645), so his 4686/4339 comparison cannot see the Abraham factor; Abraham is excluded only through the absolute scale (alpha with e and h: Paschen 1916 e = 4.776e-10, h = 6.553e-27; Glitscher 1917 alpha^2 = (5.32 +/- 0.22)e-5 for relativity against (6.65 +/- 0.28)e-5 for Abraham, measured against the independent e, h value 5.30e-5).
• Gamma-ray scattering coefficient s/rho falls to 0.04 for very hard rays instead of the classical 0.2, a departure from wave optics 'probably due to the size of the energy quantum' (Note 2, an experimental anomaly Sommerfeld could not explain).
• Band spectra of diatomic molecules are explained by a rotator and an anharmonic oscillator coupled, with lines spaced 2B apart and a missing zero line, and HCl isotopes Cl35/Cl37 give subsidiary maxima (digest only).
• The circular-orbit (l-independent) relativity term, the one that separates relativity from Weber's law, was reported measured once: the book (p.~488) says deviations from the Balmer formula 'are of the order of magnitude of our relativity correction R alpha^2/64 ... and bear the correct sign', and Paschen 1916 (Ann. Phys. 50, p.933) gives N_He(4686) - N_He(4339) = 0.569 +/- 0.25 cm-1 against 0.590 calculated from Bohr's relativity term. [read: IA OCR lines 42967-42984; deep/Paschen-1916 read, page image p.933] Caveats beside the figure: one source; the author of the measurement worked with the theory's creator ('mit freundlicher Hilfe ihres Schoepfers', an interested party in the sense of SOURCE HONESTY); the +/-0.25 is a linear-sum 'possible error' on two wavelength settings only and omits the assignment of one weak component at 4339 and the 0.003 A shift chosen for 4686; Paschen calls it 'the right order of magnitude', not a precision test. By computation, Weber's law predicts zero for a circular orbit (0.569 is 2.3 times the possible error from zero), relativity 0.590 and Abraham 4/5 of that (0.472), and the test cannot separate relativity from Abraham because alpha was taken from the same fine structure. Sommerfeld's draft of 29 Dec 1915 found the absolute Balmer differences off by more than a factor of two (0.102 against 0.24), counter-evidence that stays in the record. [computed by QE and deep reader]
• In hydrogen Paschen applies the circular-orbit term (0.526 to 0.405 cm-1, line by line) to get N_H = 109677.691 +/- 0.06 but does not test it; a refit of his own Balmer table with the coefficient free gives 0.51 +/- 0.48 times the relativity term, so the Balmer lines alone are consistent with the full term, the 4/5 term or none. [computed by the deep reader from Paschen p.935]
• Electron-impact tests treat He+ as hydrogen-like (book Ch. VI section 3): second-order ionisation potential of He predicted I + 4 x 13.5 = 79.3 V (25.3 + 54), observed 79.5 +/- 0.3 V (Franck and Knipping, Phys. Zeitschr. 20, 481, 1919) and 80 V (Horton, Proc. Roy. Soc. 95, 408, 1920); excitation of He+ 4686 from neutral He printed as 25.3 + 50.1 = 75.4 V (the arithmetic gives 50.6 and 75.9 V [computed]), observed by Rau absent at 75 V and at full intensity at 80 V. These are independent, non-spectroscopic checks of the Z^2 energy formula; the rest of the He table is partly built on the observed 20.45 V. [read: deep/Sommerfeld-AtomicStructureAndSpectralLines-0c4636.ch6-part1.md, page images PDF pp.182, 184-185. Digest .16 p.182 prints 79.8 V; the book prints 79.3 V.]
• The book attributes many selection-rule breaks to electric fields, with no field strength quoted for any: the anomalous He series (2p-mp, 2s-md, 2s-ms) appear 'only when strong electric fields are applied' (Stark, Liebert, Hardtke: a deliberately applied field); for b-p combinations in Li, Na, K, Al, Tl, Zn, Cu, Ag a field is 'quite possible'; He 1S-2S at 585 A is 'presumably to be expected only in intense electric fields'; Na/K 1s-3d at high current density (Foote, Meggers, Mohler); in Ch. V Bohr ascribes faint Zeeman components at twice (and three times) the normal splitting to 'the unintended simultaneous action of an electric field'; Paschen's forbidden p_i d_j lines are 'called forth by a magnetic field'. The Hg 1S-2p1 and 1S-2p3 collision steps are excused differently: the selection principle 'restricts only ... monochromatic emission'. Many are allowed or field-induced lines in the modern scheme [memory, medium]. [read: deep/Sommerfeld-AtomicStructureAndSpectralLines-0c4636.ch6-part1.md, .ch6-part2.md; IA OCR lines 28030-28100]
• Barkla reported in 1917 a 'J-radiation' harder than K-radiation; the book says 'Repeated tests by other observers have, however, not been able to confirm the existence of this radiation. Nor has the theory a place for such radiation, so that we must regard K-radiation as the hardest possible radiation'. Replication and theory are the two reasons given. [read: IA OCR lines 10913-10920] (Footnote: Richtmyer, Phys. Rev. 17, 433, 1921 [read: deep/Sommerfeld-AtomicStructureAndSpectralLines-0c4636.ch3.md, book p.145].)
• The nuclear model is used to exclude claimed elements of atomic weight 2 or 3 based on unassigned nebular and coronal lines ('Nebulium, Coronium, and Protofluor'; Bourget, Fabry and Buisson 1914): He would then need nuclear charge 4 or 5, 'irreconcilable with our general experiences of a-rays'. The book does not say what the lines are, and leaves isotopes of H or He of mass 2 or 3 open. Later: Bowen (1927) showed the nebulium lines are forbidden lines of doubly ionised oxygen, and Grotrian and Edlén traced the coronal lines to highly ionised iron (green line Fe XIV); protofluor not checked. [read: deep/Sommerfeld-AtomicStructureAndSpectralLines-0c4636.ch1-2.md, page image PDF p.45; web: https://en.wikipedia.org/wiki/Nebulium, https://en.wikipedia.org/wiki/Walter_Grotrian]
• Sommerfeld and Debye's accumulation theory (Ann. Phys. 41, 873, 1913), the author's own classical alternative to light quanta: the atom 'piles up' radiation energy to a limit set by h, deriving Einstein's law only 'under certain conditions (chosen in rather an artificial manner)'; for X-rays it gives 'impossible accumulation times ... of the order of magnitude of years', whereas emission 'commences immediately'. [read: deep/Sommerfeld-AtomicStructureAndSpectralLines-0c4636.ch1-2.md, book pp.44-45]
• The book records at least five withdrawals of the author's earlier positions: the L1/L2 levels in different atoms; Kossel's defects; the 'A-doublets', disproved by G. Hertz's L-absorption limits (confirmed by Smekal and Coster) and owed to 'a false interpretation by the author', together with the extra L-limits Lambda1, Lambda2 that are 'refuted by Hoyt's measurements'; the identification of theta with chi' (after Friman); and his first Runge-denominator scheme for triplets ('erroneous'). It also reports others' withdrawals (Franck's 11 V H2+ interpretation; Rutherford's He of mass 3). The author rejects Fues's half-integer s-term constants (book p.377), while his own Addendum uses half-integer phase integrals and magnetic numbers m*; the half-integer angular momenta later vindicated by spin are Landé's j and m. [read: deep/Sommerfeld-AtomicStructureAndSpectralLines-0c4636.ch3.md, .ch6-part1.md, .ch6-part2.md, .ch2-s6.md; digests .23 p.262, p.272; web: arXiv 2203.07833]
• The doublet-atom model (Addendum, with Heisenberg) gives Li Delta nu = 0.32 cm-1 (p-term) and 0.035 cm-1 (d-term), said to 'agree excellently'; the p-value is compared with Kent's 0.306 and 0.326 and 0.34 from the II N.S., while the d-value has no measurement in the book (a prediction). With its half-Bohr-magneton trunk it is a forerunner of spin [memory, high]. [read: deep/Sommerfeld-AtomicStructureAndSpectralLines-0c4636.ch6-part2.md, page image PDF p.214]
• Records the book names but this project has not examined: R. T. Birge, Phys. Rev. 17, 589 (1921), cited only for testing 'again very carefully in detail' that the weak satellite does not shift the centre of gravity of the long-wave H-alpha group (no Birge number given) [read: deep/Sommerfeld-AtomicStructureAndSpectralLines-0c4636.ch8-notes.md, book p.487]; Birge's alpha^2 = 5.308e-5 (digest .23 p.274); E. Grossmann's 1921 criticism of Newcomb's Mercury numbers (digest .21 p.244; Z. Phys. 5, 280, 1921); Richtmyer, Phys. Rev. 17, 433 (1921) on J-radiation.
• Sommerfeld himself flagged the error bar of the key datum: 'If, then, Paschen has not under-estimated the accuracy of his measurement of Delta nu_H, the idea of purely spectroscopic units must for the present remain an intention' (e/h passage). The English text also contains a translation or print slip, 'the higher the temperature the lower the velocities due to heat motion' (should read 'higher'). [read: IA OCR lines 47878-47882 and 42415-42416]

Relevance: The only document in the project. It is the standard exposition of the Bohr-Sommerfeld old quantum theory by its main author, and the source text for four things the reader may want to study: how quantum rules were fitted to spectra before quantum mechanics (including the places where it was unjustified and admitted), how the wave theory and light quanta were reconciled through conservation laws, how relativity was first tested by fine structure, and how an ether is defined and then dropped inside mainstream physics. Its candour about gaps, retractions and mismatches makes it a good primary source for what the 1921 evidence actually showed. The book is mainstream, not a work of an outsider; the project is presumably in the pool because of its ether language, its status as a superseded theory, and its historical data (Paschen's He+ photographs, the Stark tables, the spectroscopic e, h) that can be checked.

Mainstream conflict: The framework is the old quantum theory, which mainstream physics has superseded by wave and matrix mechanics (1925-26), spin and Dirac theory. What survives: the Bohr energies, the first-order Stark energy (identical to Schrodinger's), the fine-structure level formula (identical to Dirac's with n = j + 1/2), the doublet value 0.365 cm-1, the Moseley law, Hertz's screening law, Kramers/Bohr intensity ideas, the virial theorem and the angular momentum h/2 pi carried by circular light (photon spin). What does not survive: electron orbits with trajectories; the exclusion of n = 0 states (modern l = 0 states exist); the spatial-quantisation count s(s+1)/2 states per level (modern s^2); the selection principle stated for n rather than for l and j (the deep reader notes Lyman alpha is in fact a doublet, contrary to the book's 'strictly simple lines'); the claim that the He+ 4686 weak 'forbidden' components (III d) need a stray field (the deep reader's inference, medium confidence, is that some are allowed by Dirac rules); the ether picture; the Bohr models of He, H2, H2+ (all rejected in the book itself); the atom/ether decoupling and 'no recoil' assumption (Sommerfeld concedes the first in a footnote, the second contradicts Einstein's directed quanta, which later experiments on Compton recoil support [memory, high]); the electron model with radial plus azimuthal numbers for X-ray levels (the deep reader maps n = j + 1/2 and m = l + 1 [memory, high]); the 'semi-spectroscopic' h and e values (about 1 % low); the treatment of the Weiss magneton in O2/NO (agreement is partly coincidental; the right explanation is spin S = 1 [memory, medium]); Kossel-type ionic atom models partly survive in chemistry. The angular-momentum derivation of the selection rule is replaced by parity (Laporte) and dipole matrix elements in modern theory. No claim in the book conflicts with relativity or Maxwell's equations as then understood; the ether is defined so as not to conflict. Weber-type electrodynamics, which predicts no circular-orbit relativity shift, is not excluded by the fine-structure splittings; the one reported measurement of the circular-orbit term (Paschen 1916, He+) is an interested-party result at about 2.3 times its possible error from zero, never repeated.