rusch_1923#
M. Rusch, Ann. Physik (4) 70, 373 (1923)
Source record · Catalogue · Review register
Source kind: measurement
Recorded technique: Michelson interferometer (Hilger, fluorite optics) and the pressure-change method (Loria and Patkowski): the fringes passing while the pressure in one of two fluorite-windowed tubes (double gas length L = 1052.8 mm) is changed by Delta p, read to 0.05 mm Hg on a microscope manometer. Visible: Hg 5461.0, 5769.5, 5790.5 and H 6563.0 A lines from a Geissler tube, fringes counted on a Zeiss monochromator. Infrared: the reststrahlen of four calcite plates cut perpendicular to the optic axis (Nernst filament), fringes on a vacuum thermocouple; in the infrared the product n lambda was replaced by the measured double mirror displacement 2s (Eq. (1)). Argon: raw gas from Linde (about 1 % O2, 14 % N2) purified in the apparatus (Ca + 5 % Ca3N2 at 350 C for N2, glowing Cu for O2, CuO for H2, absorbers for CO2, PH3, hydrocarbons, NH3, H2O, P2O5) until spectroscopically pure but for a trace of H2 (pp. 384-386). 15 single measurements per wavelength for argon, 12 (visible) and 9 (infrared) for air. Dissertation, Breslau (1922); measurements helped by B. Quarder.
Materials in structured entries: Ar
Dataset quantities: refractivity
Contents: 6 datasets; 5 formulas.
Curation notes#
Only AIR and ARGON were measured (‘Als Versuchsgase wurden Luft und Argon gewählt’, p. 374); air is not a curated species and is skipped (Tabellen 3, 4, 7 first part, 8, 9). No H2, N2, O2 or CO2 values are in this paper (it discusses J. Koch’s infrared H2 and O2 work only). Wavelengths are printed as lambda x 10^7 cm, i.e. in nm; German decimal commas.
Reduction (p. 381-382, translated): the refractive index follows from Loria’s formula nu_0 - 1 = n lambda / (L Delta p) x 760 x (1 + alpha t) (Eq. (2)), ‘derived on the assumption of the validity of the Gladstone-Dale formula (nu - 1)/d = const (d = density) and of the ideal gas equation’. ‘nu_0 is the refractive index at 760 mm Hg pressure and 0 deg C, n the number of fringes that passed, lambda the wavelength used, for vacuum, L twice the length of the gas column in the tube R_2, Delta p the pressure change in mm Hg reduced to 0 deg C and 45 deg latitude, t the temperature of the gas in R_2, alpha the pressure coefficient of the gas.’ ‘For alpha the pressure coefficient of the gases was used; earlier work [V. v. Lang, Benoit, Walker] showed that a value alpha* somewhat different from the pressure coefficient must be taken; but the corrections disagree not only in size but even in sign’ (p. 383). Hence state 1 atm, 0 C with an ideal-gas (Gladstone-Dale) reduction: density ‘ideal’.
Accuracy (p. 384, translated): ‘With 1/10 fringe-width accuracy the error in n was below 0.1 % in each single measurement, in Delta p below 0.05 %, in the factor (1 + alpha t) likewise below 0.05 %. Since errors that could affect the results only in one direction, such as errors in L, in lambda, in reducing Delta p to 45 deg latitude, were pressed below 0.01 %, the error limit of the means must be taken as 0.02 %.’ Argon (p. 387): ‘the refractive indices averaged from 15 single measurements each (the probable errors are 0.3 to 0.4)’ in units of 10^-7.
Why the argon values ‘cannot be properly corrected to STP’ (Leonard 1974, p. 4): the paper reports only the reduced nu_0, obtained with the ideal-gas law and Gladstone-Dale and with the pressure coefficient alpha in place of the disputed alpha*, and gives neither the gas temperature t nor the absolute pressures at which the pressure changes were made (only L, the precision of Delta p and the error budget). A real-gas (second virial) reduction, which needs the actual pressures and temperature, therefore cannot be redone; argon’s non-ideality at 1 atm (about 0.1 %) is five times Rusch’s stated 0.02 % limit. The same applies to his visible values. In addition, the infrared wavelength is uncertain (below).
Infrared wavelength (pp. 377-381): the centroid of the calcite reststrahlen band, lambda_K = Sum(m lambda_m)/Sum(m) = 6763.2 mu mu +- 0.4 (mean error), from three series at room-temperature plates (Tabelle 1; the band has 7-8 partial maxima). The vacuum correction is included in the mirror-displacement calibration: ‘A correction to vacuum need no longer be applied here, since it was already made in the calibration curve of the mirror displacement, and the dispersion of air between 546 and 6763 mu mu need not be considered, as the error it causes is below 0.01 %’ (footnote, p. 377): a VACUUM wavelength. But the centroid grows when the plates are heated by continuous irradiation (Tabelle 2: five series 6.779-6.822 um, qualitative only, p. 381), and the refraction measurement irradiates the plates continuously; the infrared result was obtained from the measured 2s, independent of lambda, and is assigned to 6763.2 nm. The effective wavelength may lie up to about 0.06 um higher; argon’s dispersion there is negligible (the formula changes n - 1 by < 0.01 x 10^-7). Leonard’s Table II lists this point at 67628.5 A in standard air, which is not Rusch’s 6763.2 nm (vacuum) converted; unexplained.
Visible wavelengths: the lines are printed as 546.10, 576.95, 579.05, 656.30 nm (text: ‘Hg grün 5461,0 A, Hg gelb1 5769,5, Hg gelb2 5790,5, H2 rot 6563,0’, p. 383), the customary air wavelengths rounded (Hg 546.07, 576.96, 579.07, H-alpha 656.28 nm in air); recorded as standard air. Eq. (2) is said to use the vacuum wavelength; which values were actually inserted is not stated.
Tabelle 5 repeats the observed and ‘ber. II’ argon columns and prints the Hg yellow line as ‘567,95’ for 576,95 (image checked; not extracted, see the extraction script). The dispersion constants (Tabelle 6, formula (3)) are recorded as formulas; Tabelle 6 prints n_0^2 = 18 348 for ‘diese Arb. I’, a misprint for 16 348 (below).
Comparison (computed 2026-09-24): with the ideal-gas density at 1 atm, 0 C the infrared value corresponds to alpha = 11.104 a.u., 0.24 % above 11.078 (Gaiser and Fellmuth’s static value with Lesiuk and Jeziorski’s dispersion and chi_0, lesiuk_2023 formula ‘recommended’), and the 546.1 nm value (546.25 nm vacuum) to 11.327 a.u., 0.45 % above 11.276. Both are high, as Leonard found for the Breslau absolute values; Rusch’s ratio (n - 1)(546 nm)/(n - 1)(6.76 um) = 1.0201 exceeds the modern 1.0179 by 0.2 %: his visible values are further from the modern scale than his infrared one, which Leonard calls “in excellent agreement with other work”.
Not in the library: Rusch’s erratum, Ann. Physik (4) 85, 581 (1928), cited by Leonard; it may correct these values.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
rusch_1923/experiment_Ar#
{
"id": "experiment_Ar",
"material": "Ar",
"file": "Ar/rusch_1923__experiment_Ar.csv",
"table": "tbl_1f78cf25d43e",
"quantity": "refractivity",
"scale": 1e-07,
"abscissa_unit": "nm",
"wavelength_medium": "standard_air",
"state": "1atm_0C",
"density": "ideal",
"use": "primary",
"uncertainty": {
"absolute": 0.4,
"level": "probable error",
"systematic_relative": 0.0002
}
}
Tabelle 7 (argon, ‘beob.’), also Tabelle 5 column 2: (nu_0 - 1) x 10^7 at the H-alpha and Hg lines, means of 15 measurements. Probable errors 0.3-0.4 (x 1e-7, p. 387), error limit of the means 0.02 % (p. 384). Leonard (1974) finds the Breslau absolute values hard to reconcile with others (Rusch at 5462 A about 0.3 % above his recommended value) and uses only their dispersion (leonard_1974/rusch_1923_Ar, rescaled): the scale of this dataset is doubtful.
rusch_1923/experiment_ir_Ar#
{
"id": "experiment_ir_Ar",
"material": "Ar",
"file": "Ar/rusch_1923__experiment_ir_Ar.csv",
"table": "tbl_1f78cf25d43e",
"quantity": "refractivity",
"scale": 1e-07,
"abscissa_unit": "nm",
"wavelength_medium": "vacuum",
"state": "1atm_0C",
"density": "ideal",
"use": "primary",
"uncertainty": {
"absolute": 0.4,
"level": "probable error",
"systematic_relative": 0.0002
}
}
Tabelle 7 (argon, ‘beob.’) first row: (nu_0 - 1) x 10^7 = 2778.0 at 6763.2 nm (6.76 um), the calcite reststrahlen centroid (vacuum; the effective wavelength during the measurement may be up to about 0.06 um longer, source notes). The only mid-infrared argon refractivity known; absolute, ‘cannot be properly corrected to STP’ (Leonard), though Leonard finds it ‘in excellent agreement with other work’. Probable error 0.3-0.4 (x 1e-7), limit 0.02 %.
rusch_1923/fit_I_Ar#
{
"id": "fit_I_Ar",
"material": "Ar",
"file": "Ar/rusch_1923__fit_I_Ar.csv",
"table": "tbl_1f78cf25d43e",
"quantity": "refractivity",
"scale": 1e-07,
"abscissa_unit": "nm",
"wavelength_medium": "standard_air",
"state": "1atm_0C",
"density": "ideal",
"use": "check"
}
Tabelle 7 (argon, ‘ber. I’): formula (3) with the constants fitted to the four visible values only (formula hk_I); reproduced exactly (formula notes).
rusch_1923/fit_I_ir_Ar#
{
"id": "fit_I_ir_Ar",
"material": "Ar",
"file": "Ar/rusch_1923__fit_I_ir_Ar.csv",
"table": "tbl_1f78cf25d43e",
"quantity": "refractivity",
"scale": 1e-07,
"abscissa_unit": "nm",
"wavelength_medium": "vacuum",
"state": "1atm_0C",
"density": "ideal",
"use": "check"
}
Tabelle 7 (argon, ‘ber. I’) at 6763.2 nm: the visible-only formula extrapolated to the infrared gives 2781.8, 3.8 x 10^-7 above the observed 2778.0 (‘Delta I’ = -3.8), the paper’s evidence that formula (3) holds only over a small range (p. 389).
rusch_1923/fit_II_Ar#
{
"id": "fit_II_Ar",
"material": "Ar",
"file": "Ar/rusch_1923__fit_II_Ar.csv",
"table": "tbl_1f78cf25d43e",
"quantity": "refractivity",
"scale": 1e-07,
"abscissa_unit": "nm",
"wavelength_medium": "standard_air",
"state": "1atm_0C",
"density": "ideal",
"use": "check"
}
Tabelle 7 (argon, ‘ber. II’), also Tabelle 5 column 3: formula (3) with the constants fitted to all five values (formula hk_II); reproduced exactly.
rusch_1923/fit_II_ir_Ar#
{
"id": "fit_II_ir_Ar",
"material": "Ar",
"file": "Ar/rusch_1923__fit_II_ir_Ar.csv",
"table": "tbl_1f78cf25d43e",
"quantity": "refractivity",
"scale": 1e-07,
"abscissa_unit": "nm",
"wavelength_medium": "vacuum",
"state": "1atm_0C",
"density": "ideal",
"use": "check"
}
Tabelle 7 (argon, ‘ber. II’) at 6763.2 nm; formula hk_II.
Formulas#
rusch_1923/hk_II_Ar#
{
"id": "hk_II_Ar",
"material": "Ar",
"equation": "Eq. (3), p. 386, constants p. 387 and Tabelle 6 ('diese Arb. II')",
"printed": "nu_0 - 1 = C / (n_0^2 - n^2); C = 4,216 x 10^27, n_0^2 = 15177 x 10^27 (Tabelle 6: 2C x 10^-27 = 8,4321, n_0^2 x 10^-27 = 15 177, (nu_0 - 1)_inf 10^7 = 2778)",
"variable": "n: frequency in s^-1, n = c/lambda with c = 3 x 10^10 cm/s and lambda as printed in cm (implied: it reproduces the table; not stated); C in s^-2",
"state": "1atm_0C",
"density": "ideal",
"range": "546.1-6763.2 nm (the five fitted values)",
"coefficients": {
"C": "4.216e27",
"n0_squared": "15177e27",
"two_C_table6": "8.4321e27"
},
"check": "With n = 3e10/lambda (lambda: 6763.2, 656.30, 579.05, 576.95, 546.10 nm as printed) it gives 2778.2, 2816.7, 2827.9, 2828.3, 2834.2 x 10^-7, Tabelle 5/7 'ber. II' exactly (c = 2.99796e10 changes the visible values by 0.1). Static limit C/n_0^2 = 2777.9 x 10^-7, Tabelle 6's 2778. Checked 2026-09-24."
}
The Helmholtz-Ketteler formula for one resonance, fitted by least squares to all five argon values; a single-oscillator form n - 1 = C/(nu_0^2 - nu^2) in frequency (Hz) that fits none of the package’s forms without converting the printed coefficients (with s = 1/lambda in um^-1, B = C/(c^2 1e8) and C’ = n_0^2/(c^2 1e8) in dn_sigma2). The fitted resonance lies at n_0 = sqrt(15177e27) = 3.896e15 s^-1, lambda_0 = c/n_0 = 77.0 nm (computed). Tabelle 6 prints 2C (doubled ‘with Cuthbertson, to compare with diatomic gases’).
rusch_1923/hk_I_Ar#
{
"id": "hk_I_Ar",
"material": "Ar",
"equation": "Eq. (3), p. 386, with Tabelle 6 ('diese Arb. I'), p. 388",
"printed": "nu_0 - 1 = C / (n_0^2 - n^2); Tabelle 6: 2C x 10^-27 = 9,0942, n_0^2 x 10^-27 = 18 348, (nu_0 - 1)_inf 10^7 = 2781",
"variable": "n: frequency in s^-1, n = c/lambda with c = 3 x 10^10 cm/s and lambda as printed in cm; C = (2C)/2 in s^-2",
"state": "1atm_0C",
"density": "ideal",
"range": "546.1-656.3 nm (the four visible values; 'the constants valid for the visible region, labelled I', p. 389)",
"coefficients": {
"two_C": "9.0942e27",
"n0_squared": "18348e27"
},
"check": "As printed it does not reproduce: C/n_0^2 = 4.5471/18348 = 2478 x 10^-7 against the printed (nu_0 - 1)_inf = 2781, and 2520 at 546.1 nm against 'ber. I' 2833.8. With n_0^2 = 16348e27 it gives 2781.4 (static) and 2781.8, 2817.5, 2827.9, 2828.2, 2833.8 at the five wavelengths, Tabelle 7 'ber. I' exactly. Checked 2026-09-24.",
"corrections": [
{
"term": "n0_squared",
"index": 0,
"printed": "18348e27",
"corrected": "16348e27",
"reason": "Tabelle 6 prints n_0^2 x 10^-27 = 18 348 for 'diese Arb. I'; with 2C = 9.0942e27 this gives a static refractivity of 2478 x 10^-7, not the printed 2781 in the same row, and 'ber. I' values 11 % too low. 16 348 reproduces both.",
"evidence": "Tabelle 6 image tbl_3de15b358ae0.jpg prints 18 348; Tabelle 7 (tbl_1f78cf25d43e) 'ber. I' (2781.8, 2817.5, 2827.9, 2828.2, 2833.8) and Tabelle 6's (nu_0 - 1)_inf = 2781 are reproduced to the printed digit with 16 348 (computed 2026-09-24)."
}
]
}
Fitted to the visible values only; used in Tabelle 7 to show that formula (3) fails beyond a small range (Delta I = -3.8 x 10^-7 at 6.76 um). The printed n_0^2 = 18 348 is a misprint for 16 348 (one digit, 6 read or set as 8); corrected below.
rusch_1923/cuthbertson_Ar#
{
"id": "cuthbertson_Ar",
"material": "Ar",
"equation": "Tabelle 6, p. 388",
"printed": "Cuthbertson: 2C x 10^-27 = 9,4326, n_0^2 x 10^-27 = 17 009, (nu_0 - 1)_inf 10^7 = 2773",
"variable": "as hk_II_Ar",
"state": "1atm_0C",
"density": "unknown",
"range": "the visible (Cuthbertsons' data)",
"coefficients": {
"two_C": "9.4326e27",
"n0_squared": "17009e27"
},
"check": "Static limit (2C/2)/n_0^2 = 2772.8, the printed 2773. Checked 2026-09-24."
}
Reproduced: C. and M. Cuthbertson’s constants for argon (Proc. Roy. Soc. A 84, 13 (1911); cuthbertson_1910), as the Cuthbertsons computed them; kind reproduced, not Rusch’s.
rusch_1923/burton_Ar#
{
"id": "burton_Ar",
"material": "Ar",
"equation": "Tabelle 6, p. 388",
"printed": "Burton: 2C x 10^-27 = 9,124, n_0^2 x 10^-27 = 16 335, (nu_0 - 1)_inf 10^7 = 2799",
"variable": "as hk_II_Ar",
"state": "1atm_0C",
"density": "unknown",
"range": "the visible (Burton's data)",
"coefficients": {
"two_C": "9.124e27",
"n0_squared": "16335e27"
},
"check": "Static limit (2C/2)/n_0^2 = 2792.8 against the printed 2799 (0.2 %); no single-digit correction found. Checked 2026-09-24."
}
Reproduced: constants computed by the Cuthbertsons for W. Burton, Proc. Roy. Soc. A 80, 404 (1908).
rusch_1923/ahrberg_Ar#
{
"id": "ahrberg_Ar",
"material": "Ar",
"equation": "Tabelle 6, p. 388",
"printed": "Ahrberg: 2C x 10^-27 = 7,437, n_0^2 x 10^-27 = 13 516, (nu_0 - 1)_inf 10^7 = 2751",
"variable": "as hk_II_Ar",
"state": "1atm_0C",
"density": "unknown",
"range": "the visible (Ahrberg's data)",
"coefficients": {
"two_C": "7.437e27",
"n0_squared": "13516e27"
},
"check": "Static limit (2C/2)/n_0^2 = 2751.2, the printed 2751. Checked 2026-09-24."
}
Reproduced: constants computed by the Cuthbertsons for F. Ahrberg, Dissertation, Halle (1909); Rusch: ‘Ahrberg, whose method does not give the necessary accuracy’ (p. 389).
Corrections#
No dataset errata are recorded in this source record.
Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.