edlen_1966

B. Edlen, “The Refractive Index of Air”, Metrologia 2, 71 (1966)

Source record · Catalogue · Review register

No DOI is recorded.

Source kind: fit

Recorded technique: Review and refit of the refractivity of air: the absolute level from Barrell and Sears (1939) as adopted in 1953; the dispersion from Erickson’s (1961) visible data (normalized at 6058 A) with Rank et al. (1958), Peck and Khanna (1962), Svensson (1960) and Traub (1920) normalized to it (Table 2), fitted by a Sellmeier-type formula with a constant term; the temperature and pressure dependence from the Lorentz-Lorenz equation and the density equation of air, checked on Barrell and Sears’s 320 values; corrections for CO2 and water vapour (pp. 71-80).

Materials in structured entries: CO2

Dataset quantities: None recorded.

Contents: 0 datasets; 2 formulas.

Curation notes

Identity: unverified by the library; the pdf’s cover sheet reads ‘To cite this article: Bengt Edlen 1966 Metrologia 2 71’ and the running heads ‘Vol. 2, No. 2, 1966 ... BENGT EDLEN: The Refractive Index of Air’ with page numbers 71-80 (pdf page N is journal page 69 + N). No DOI is recorded in the library. Air is not a curated species: the record holds no datasets, and the air formulas are given here verbatim.

The dispersion formula for standard air, Eq. (1), p. 76 (also in the abstract, p. 71), checked on the page image: (n - 1)_s x 10^8 = 8342.13 + 2406030 (130 - sigma^2)^-1 + 15997 (38.9 - sigma^2)^-1, ‘where sigma is the vacuum wave-number in reciprocal micrometres (um^-1)’; it represents the observations ‘from 2000 A through the visible region in a very satisfactory way’ (p. 76), the infrared data to 20 587 A falling ‘below the formula by an average of about 0.7e-8’ (p. 76). Standard air (pp. 72, 79): ‘dry air at 760 torr and 15 degrees C’, ‘defined as containing CO2 to 0.0003 parts by volume’. The absolute level is uncertain by about +-5e-8 (abstract; the dispersion, i.e. relative values, is known far better). Check (2026-09-24): Eq. (1) minus Table 2’s ‘1953 formula’ column reproduces Table 2’s printed ‘1965-1953’ column at all 53 wavelengths to within 0.1e-8, the rounding of the printed columns. The formula agrees exactly with the package’s conditions.standard_air_refractivity (1e8 (n - 1) = 8342.13 + 2406030/(130 - s^2) + 15997/(38.9 - s^2), s the vacuum wavenumber in um^-1; standard air dry, 0.03 % CO2, 15 degrees C, 101 325 Pa = 760 torr), which was transcribed from memory (TC-2): the coefficients, the variable and the reference state all agree.

Other formulas, verbatim (not datasets; air and water are not species): - Table 4, approximations to (1): 0.0472300 (173.3 - sigma^2)^-1 for 4050-7050 A (max. error 1.2e-8); 0.0480877 (176.4 - sigma^2)^-1 for lambda > 5800 A (0.7e-8); (27260.6 + 155.7 sigma^2) x 10^-8 for lambda > 7050 A (0.8e-8); (27261.1 + 154.3 sigma^2) x 10^-8 for lambda > 10000 A (0.2e-8). - Eq. (12), p. 78, dry air 5-30 degrees C: (n - 1)_tp = p (n - 1)_s/720.775 x [1 + p (0.817 - 0.0133 t) x 10^-6]/(1 + 0.0036610 t), t in degrees C, p in torr; D_s = 720.775 the density factor of standard air. Eq. (15), p. 78: (n - 1)_tp = (n - 1)_s x 0.00138823 p/(1 + 0.003671 t), within 1.0e-8 of (12) at 15-30 degrees C and 700-800 torr. - Eq. (17), p. 79: (n - 1)_x = [1 + 0.540 (x - 0.0003)] (n - 1)_s for x parts by volume of CO2. - Eq. (22), p. 80: n_tpf - n_tp = -f (5.722_4 - 0.0457 sigma^2) x 10^-8 for f torr of water vapour (visible; near 20 degrees C, 760 torr, f = 10 torr); Eq. (21), p. 79, K’_lambda = (31.59 + 0.2963 sigma^2) x 10^-8; Eq. (23) Delta lambda x 10^5 = 0.457 lambda_2 (sigma_2^2 - sigma_1^2) f.

Carbon dioxide (p. 79): ‘The best information on the refractivity of CO2 appears to be obtained from KOCH (1914) and the CUTHBERTSONS (1920)’; Edlen transferred their 0 degrees C figures to 15 degrees C with alpha = 0.00371 ‘and recalculated their refractivities for different wavelengths on the common basis of (n - 1) = 42676 x 10^-8 for 5462 A at 15 degrees and 760 torr’, giving Eqs. (16) and (18) (formulas below). The 42676e-8 is a normalization chosen by Edlen, not a measurement here; the originals are not in the library.

The temperature and pressure dependence, Eq. (12), p. 78, checked on the page (2026-09-26): ‘(n - 1)_tp = p (n - 1)_s / 720.775 . [1 + p (0.817 - 0.0133 t) x 10^-6] / (1 + 0.0036610 t), where t is in degrees C, p in torr, and (n - 1)_s is given by the dispersion formula for standard air’, for dry air from 5 to 30 degrees C; D_s = 720.775 is the density factor of standard air (Eq. 11), and the formula follows from the Lorentz-Lorenz relation and the equation of state of dry air (Eqs. 3-10). It is the package’s conditions.air_refractivity, used to take solid indices measured relative to room air to vacuum (TC-398).

Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets

No datasets are recorded.

Formulas

edlen_1966/eq16_CO2

{
  "id": "eq16_CO2",
  "material": "CO2",
  "equation": "Eq. (16), p. 79",
  "printed": "r = (n_CO2 - n_s)/(n - 1)_s = 0.5291 + 0.00360 sigma",
  "variable": "sigma: vacuum wavenumber in um^-1; (n - 1)_s the standard-air refractivity of Eq. (1)",
  "state": "1atm_15C",
  "density": "unknown",
  "range": "the wavelengths of Koch's (1914) and the Cuthbertsons' (1920) CO2 data (Fig. 3: visible and near ultraviolet); r varies 'within +-1 %' over the range of interest",
  "coefficients": {
    "r0": "0.5291",
    "r1": "0.00360"
  },
  "check": "Not checked against printed CO2 values (the paper prints none but the normalization 42676e-8 at 5462 A): at 5462 A (sigma = 1.8308) r = 0.53569 and (n - 1)_CO2 = 1.53569 x 27789.9e-8 = 42677e-8 (computed here), consistent with the normalization."
}

n_CO2 - 1 = (1 + r) (n - 1)_s at 15 degrees C, 760 torr: a CO2 dispersion formula derived from Koch (1914) and C. and M. Cuthbertson (1920) (not in the library), transferred from 0 to 15 degrees C with alpha = 0.00371 and normalized to (n - 1) = 42676e-8 at 5462 A. Reproduced, not a measurement of this paper. No form fits (a ratio to the air formula); the ratio is taken ‘as independent of t and p’.

edlen_1966/eq18_CO2

{
  "id": "eq18_CO2",
  "material": "CO2",
  "equation": "Eq. (18), p. 79",
  "printed": "(n_CO2 - n_s) = (14485 + 117.8 sigma^2) x 10^-8",
  "variable": "sigma: vacuum wavenumber in um^-1",
  "state": "1atm_15C",
  "density": "unknown",
  "range": "as Eq. (16) (Fig. 4)",
  "coefficients": {
    "a": "14485",
    "b": "117.8"
  },
  "check": "At 5462 A (sigma^2 = 3.3517) it gives 14880e-8, and with Eq. (1) (n - 1)_CO2 = 42670e-8 (computed here), 6e-8 below the normalization 42676e-8; the equivalent form of Eq. (16)."
}

The same CO2 correction as Eq. (16) in the form n_CO2 - n_s (cf. Fig. 4); ‘gives 0.1178 for the coefficient that MASUI (1957) gave as 0.11’. Reproduced from Koch and the Cuthbertsons as for eq16_CO2.

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.