cuthbertson_1920#
C. Cuthbertson and M. Cuthbertson, Proc. R. Soc. London A 97, 152 (1920)
Source record · Catalogue · Review register
Source kind: measurement
Recorded technique: Jamin refractometer, as in the authors’ earlier work (measured in 1914). The absolute refractivity at the green mercury line (5461 A) from ‘double experiments’ (pressure increasing and diminishing), at room temperature (about 17.5 degrees C for CO2) and 30-50 cm Hg; the dispersion relative to it at eight lines (Li 6708, Cd 6438, Hg 5790, 5770, 5461, Ag 5209, Cd 5085, 4800 A) by counting 500-800 bands (pp. 1-5).
Materials in structured entries: CH4, CO, CO2, H2, N2, O2
Dataset quantities: refractivity
Contents: 16 datasets; 6 formulas.
Curation notes#
The refractivities are mu - 1 itself, NOT the doubled 2 (mu - 1) of the Cuthbertsons’ 1910 noble-gas tables (cuthbertson_1910): Table I’s 45,050 x 10^-8 at 5461 A is the text’s mean absolute value (mu - 1) 10^7 = 4505 for CO2 (p. 1), and Table III’s 44,150 x 10^-8 the methane mean 4415 (p. 5). The formulas are likewise for mu - 1.
Carbon dioxide: ‘at 0 degrees C. and 76 cm.’, eight absolute values 4500-4509 x 10^-7, mean 4505; reduced for temperature with Chappuis’s coefficient (1 + 0.00371 t) and for pressure with Leduc’s formula P0 V0 / PV - 1 = 102 x 10^-6 (P - P0) (p. 1): a real-gas reduction (state 1 atm, 0 degrees C, density real). About 0.1 % of unabsorbed gas (assumed air) was allowed for. ‘Had we used Walker’s temperature coefficient (1 + 0.0038 t), our result would have been 4512’ (p. 2). Table I’s column 5 reduces the observed values to the number density of hydrogen at 0 degrees C and 76 cm ((mu - 1) D / d0 76 = 0.0004471 at 5461 A, p. 2); it is column 2 times a constant (0.99246) and is not extracted, nor column 6 (two values of column 3 so reduced).
Methane: five absolute values 4412-4417 x 10^-7, mean 4415 (p. 5). The paper states neither the state nor the reduction for methane; 1 atm, 0 degrees C is assumed (the CO2 and CO values are at 0 degrees C and 76 cm), density unknown. The gas was purified from hydrogen by Campbell and Parker’s method.
Wavelengths: the lines rounded to 1 A (6708 for Li 6707.85, 5790 and 5770 for Hg 5790.7 and 5769.6, 4800 for Cd 4799.9), air wavelengths: standard air. The rounding moves no value by more than 0.2 printed units.
Uncertainty: not stated. The per-point uncertainties are the rms of the paper’s calc - obs differences (CO2 2.2, CH4 0.71, CO 1.2 printed units x 10^-8); the scale uncertainty the half-range of the absolute determinations (CO2 0.10 %, CH4 0.057 %, CO 0.045 %).
Earlier work: the CO2 values of six observers at 5461 A (p. 2; no references given in the paper, except Koch’s, cited for methane on p. 5) are extracted as reproduced datasets; ‘the discrepancies are, no doubt, largely due to the use of different coefficients of pressure and temperature in the reduction’. The earlier methane values (St. Loria 4468, Kessler 4435, Koch 4407, x 10^-7) state no wavelength and are not extracted; ‘these values are not concordant, probably owing to the difficulty of purifying the gas’. The lambda_0 comparisons (pp. 3, 5, 6) are derived numbers, not extracted.
Carbon monoxide (pp. 3-5): made from formic acid and concentrated sulphuric acid, dried, condensed in liquid air and fractionated; ‘on testing by explosion with oxygen no impurities were found’. Four double experiments at 5461 A gave (mu - 1) 10^7 = 3362, 3365, 3364, 3364, mean 3364, ‘reduced by the formula’ (mu - 1) 76/P T/273 (p. 4): an ideal-gas reduction to 0 degrees C and 76 cm (density ideal), unlike the CO2 reduction. Dispersion from ten experiments of nearly 600 bands each (Table II, p. 4). The earlier values at 5461 A (Mascart, Perreau, Koch, Grueschke; no references given) are extracted as reproduced datasets; ‘our value agrees well with that of the last three’. Their lambda_0 values (p. 5) are derived and not extracted. The ‘carbon atom’ formula ‘from carbon monoxide’ (p. 7) is not recorded, as for CO2.
The ‘carbon atom’ formulas of p. 7 (CO2 minus O2 and so on) are not gas properties and are not recorded; the hydrogen, oxygen and nitrogen formulas quoted on p. 7 from the authors’ 1909 paper (Proc. R. Soc. 83, 151, not in the library) are recorded as reproduced formulas.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
cuthbertson_1920/experiment_CO2#
{
"id": "experiment_CO2",
"material": "CO2",
"file": "CO2/cuthbertson_1920__experiment_CO2.csv",
"table": "tbl_475eaffb74ab",
"quantity": "refractivity",
"scale": 1e-08,
"abscissa_unit": "angstrom",
"wavelength_medium": "standard_air",
"state": "1atm_0C",
"density": "real",
"use": "primary",
"uncertainty": {
"absolute": 2.2,
"level": "rms",
"systematic_relative": 0.001
}
}
Table I, observed (seven experiments, nearly all counting 800 bands). The 5461 A value is the absolute one.
cuthbertson_1920/fit_CO2#
{
"id": "fit_CO2",
"material": "CO2",
"file": "CO2/cuthbertson_1920__fit_CO2.csv",
"table": "tbl_475eaffb74ab",
"quantity": "refractivity",
"scale": 1e-08,
"abscissa_unit": "angstrom",
"wavelength_medium": "standard_air",
"state": "1atm_0C",
"density": "real",
"use": "check"
}
Table I, calculated column (formula co2_1920, which reproduces it only to 1.6 printed units).
cuthbertson_1920/experiment_CH4#
{
"id": "experiment_CH4",
"material": "CH4",
"file": "CH4/cuthbertson_1920__experiment_CH4.csv",
"table": "tbl_ae9680fa9a81",
"quantity": "refractivity",
"scale": 1e-08,
"abscissa_unit": "angstrom",
"wavelength_medium": "standard_air",
"state": "1atm_0C",
"density": "unknown",
"use": "primary",
"uncertainty": {
"absolute": 0.71,
"level": "rms",
"systematic_relative": 0.00057
}
}
Table III, observed (eight experiments, three counting 800 bands and five 500). The 5461 A value is the absolute one. State assumed (see the source notes).
cuthbertson_1920/fit_CH4#
{
"id": "fit_CH4",
"material": "CH4",
"file": "CH4/cuthbertson_1920__fit_CH4.csv",
"table": "tbl_ae9680fa9a81",
"quantity": "refractivity",
"scale": 1e-08,
"abscissa_unit": "angstrom",
"wavelength_medium": "standard_air",
"state": "1atm_0C",
"density": "unknown",
"use": "check"
}
Table III, calculated column (formula ch4_1920).
cuthbertson_1920/mascart_CO2#
{
"id": "mascart_CO2",
"material": "CO2",
"file": "CO2/cuthbertson_1920__mascart_CO2.csv",
"table": "tbl_b6b36b76ac3b",
"quantity": "refractivity",
"scale": 1e-07,
"abscissa_unit": "angstrom",
"wavelength_medium": "standard_air",
"state": "1atm_0C",
"density": "unknown",
"use": "reproduced",
"reproduced_from": [
"Mascart (no reference given by C. and M. Cuthbertson 1920)"
]
}
Earlier-work table, p. 2, at 5461 A; state as the Cuthbertsons’ (0 degrees C, 76 cm), each observer’s own reduction.
cuthbertson_1920/perreau_CO2#
{
"id": "perreau_CO2",
"material": "CO2",
"file": "CO2/cuthbertson_1920__perreau_CO2.csv",
"table": "tbl_b6b36b76ac3b",
"quantity": "refractivity",
"scale": 1e-07,
"abscissa_unit": "angstrom",
"wavelength_medium": "standard_air",
"state": "1atm_0C",
"density": "unknown",
"use": "reproduced",
"reproduced_from": [
"Perreau (no reference given by C. and M. Cuthbertson 1920)"
]
}
As mascart_CO2.
cuthbertson_1920/walker_CO2#
{
"id": "walker_CO2",
"material": "CO2",
"file": "CO2/cuthbertson_1920__walker_CO2.csv",
"table": "tbl_b6b36b76ac3b",
"quantity": "refractivity",
"scale": 1e-07,
"abscissa_unit": "angstrom",
"wavelength_medium": "standard_air",
"state": "1atm_0C",
"density": "unknown",
"use": "reproduced",
"reproduced_from": [
"G. W. Walker (no reference given by C. and M. Cuthbertson 1920)"
],
"uncertainty": {
"column": true,
"level": "not stated"
}
}
As mascart_CO2; printed 4510 +- 5 (level not stated). Walker used the temperature coefficient 1 + 0.0038 t (p. 2).
cuthbertson_1920/stuckert_CO2#
{
"id": "stuckert_CO2",
"material": "CO2",
"file": "CO2/cuthbertson_1920__stuckert_CO2.csv",
"table": "tbl_b6b36b76ac3b",
"quantity": "refractivity",
"scale": 1e-07,
"abscissa_unit": "angstrom",
"wavelength_medium": "standard_air",
"state": "1atm_0C",
"density": "unknown",
"use": "reproduced",
"reproduced_from": [
"Stuckert (no reference given by C. and M. Cuthbertson 1920)"
]
}
As mascart_CO2.
cuthbertson_1920/grueschke_CO2#
{
"id": "grueschke_CO2",
"material": "CO2",
"file": "CO2/cuthbertson_1920__grueschke_CO2.csv",
"table": "tbl_b6b36b76ac3b",
"quantity": "refractivity",
"scale": 1e-07,
"abscissa_unit": "angstrom",
"wavelength_medium": "standard_air",
"state": "1atm_0C",
"density": "unknown",
"use": "reproduced",
"reproduced_from": [
"Grueschke (no reference given by C. and M. Cuthbertson 1920)"
]
}
As mascart_CO2 (printed ‘Grüschke’).
cuthbertson_1920/koch_CO2#
{
"id": "koch_CO2",
"material": "CO2",
"file": "CO2/cuthbertson_1920__koch_CO2.csv",
"table": "tbl_b6b36b76ac3b",
"quantity": "refractivity",
"scale": 1e-07,
"abscissa_unit": "angstrom",
"wavelength_medium": "standard_air",
"state": "1atm_0C",
"density": "unknown",
"use": "reproduced",
"reproduced_from": [
"J. Koch, Arkiv for Mat. Astr. och Fysik 9 (6) (1913) (cited for methane, p. 5; presumably also the CO2 value)"
]
}
As mascart_CO2. ‘Our value agrees well with that of Koch’ (p. 2).
cuthbertson_1920/experiment_CO#
{
"id": "experiment_CO",
"material": "CO",
"file": "CO/cuthbertson_1920__experiment_CO.csv",
"table": "tbl_5e46be9ef072",
"quantity": "refractivity",
"scale": 1e-08,
"abscissa_unit": "angstrom",
"wavelength_medium": "standard_air",
"state": "1atm_0C",
"density": "ideal",
"use": "primary",
"uncertainty": {
"absolute": 1.2,
"level": "rms",
"systematic_relative": 0.00045
}
}
Table II, observed (ten experiments of nearly 600 bands). The 5461 A value is the absolute one (mean 3364 x 10^-7 of four double experiments, p. 4), reduced to 0 degrees C and 76 cm with the ideal-gas formula.
cuthbertson_1920/fit_CO#
{
"id": "fit_CO",
"material": "CO",
"file": "CO/cuthbertson_1920__fit_CO.csv",
"table": "tbl_5e46be9ef072",
"quantity": "refractivity",
"scale": 1e-08,
"abscissa_unit": "angstrom",
"wavelength_medium": "standard_air",
"state": "1atm_0C",
"density": "ideal",
"use": "check"
}
Table II, calculated column (formula co_1920).
cuthbertson_1920/mascart_CO#
{
"id": "mascart_CO",
"material": "CO",
"file": "CO/cuthbertson_1920__mascart_CO.csv",
"table": "tbl_fe180e2332d2",
"quantity": "refractivity",
"scale": 1e-07,
"abscissa_unit": "angstrom",
"wavelength_medium": "standard_air",
"state": "1atm_0C",
"density": "unknown",
"use": "reproduced",
"reproduced_from": [
"Mascart (no reference given by C. and M. Cuthbertson 1920)"
]
}
Earlier-work table, p. 4, at 5461 A; state as the Cuthbertsons’ (0 degrees C, 76 cm), each observer’s own reduction.
cuthbertson_1920/perreau_CO#
{
"id": "perreau_CO",
"material": "CO",
"file": "CO/cuthbertson_1920__perreau_CO.csv",
"table": "tbl_fe180e2332d2",
"quantity": "refractivity",
"scale": 1e-07,
"abscissa_unit": "angstrom",
"wavelength_medium": "standard_air",
"state": "1atm_0C",
"density": "unknown",
"use": "reproduced",
"reproduced_from": [
"Perreau (no reference given by C. and M. Cuthbertson 1920)"
]
}
As mascart_CO.
cuthbertson_1920/koch_CO#
{
"id": "koch_CO",
"material": "CO",
"file": "CO/cuthbertson_1920__koch_CO.csv",
"table": "tbl_fe180e2332d2",
"quantity": "refractivity",
"scale": 1e-07,
"abscissa_unit": "angstrom",
"wavelength_medium": "standard_air",
"state": "1atm_0C",
"density": "unknown",
"use": "reproduced",
"reproduced_from": [
"Koch (no reference given by C. and M. Cuthbertson 1920; presumably J. Koch, Ark. Mat. Astron. Fys. 10 (1914), whose CO dispersion smith_1976 reproduces from the International Critical Tables)"
]
}
As mascart_CO. The same work as smith_1976’s koch_1914_CO (237.9-289.4 nm), if the presumption holds.
cuthbertson_1920/grueschke_CO#
{
"id": "grueschke_CO",
"material": "CO",
"file": "CO/cuthbertson_1920__grueschke_CO.csv",
"table": "tbl_fe180e2332d2",
"quantity": "refractivity",
"scale": 1e-07,
"abscissa_unit": "angstrom",
"wavelength_medium": "standard_air",
"state": "1atm_0C",
"density": "unknown",
"use": "reproduced",
"reproduced_from": [
"Grueschke (no reference given by C. and M. Cuthbertson 1920)"
]
}
As mascart_CO (printed ‘Grüschke’).
Formulas#
cuthbertson_1920/co2_1920#
{
"id": "co2_1920",
"material": "CO2",
"equation": "formula below Table I, p. 3",
"printed": "(mu - 1)_{n.t.p.} = 6.2144 x 10^27 / ((14097) 10^27 - n^2)",
"variable": "n = V/lambda, frequency in s^-1, lambda the air wavelength in cm, V = 3e10 cm/s (implied)",
"state": "1atm_0C",
"density": "real",
"range": "480-671 nm",
"coefficients": {
"C": "6.2144e27",
"n0_squared": "14097e27"
},
"check": "With V = 3e10 cm/s and the printed wavelengths it gives Table I's calculated column only to within 1.6 printed units (x 10^-8; 5461 A 45047.5 against 45049, 5209 A 45145.4 against 45147, 4800 A 45339.5 against 45341); V = 2.99796e10 or the exact line wavelengths do worse. No single coefficient correction explains it: the best one-pole fit to the calculated column itself leaves +-1.2 units, so the printed column is not an exact evaluation of any such formula. Checked 2026-09-25."
}
Labelled (mu - 1)_{n.t.p.} but it gives the observed column 2 (0 degrees C, 76 cm), not the hydrogen-density column 5. lambda_0 = 799 A (p. 3).
cuthbertson_1920/ch4_1920#
{
"id": "ch4_1920",
"material": "CH4",
"equation": "formula below Table III, p. 6",
"printed": "mu - 1 = 5.02763 x 10^27 / (11689.3 x 10^27 - n^2)",
"variable": "n = V/lambda, frequency in s^-1, lambda the air wavelength in cm, V = 3e10 cm/s (implied)",
"state": "1atm_0C",
"density": "unknown",
"range": "480-671 nm",
"coefficients": {
"C": "5.02763e27",
"n0_squared": "11689.3e27"
},
"check": "With V = 3e10 cm/s and the printed wavelengths it reproduces Table III's calculated column to within 0.7 printed units (x 10^-8). Checked 2026-09-25."
}
lambda_0 = 877 A (p. 6).
cuthbertson_1920/co_1920#
{
"id": "co_1920",
"material": "CO",
"equation": "formula below Table II, p. 4",
"printed": "mu - 1 = 3.64067 x 10^27 / (11,124 x 10^27 - n^2)",
"variable": "n = V/lambda, frequency in s^-1, lambda the air wavelength in cm, V = 3e10 cm/s (implied)",
"state": "1atm_0C",
"density": "ideal",
"range": "480-671 nm",
"coefficients": {
"C": "3.64067e27",
"n0_squared": "11124e27"
},
"check": "With V = 3e10 cm/s and the printed wavelengths it exceeds Table II's calculated column by 0.6-1.4 printed units (x 10^-8; 5461 A 33640.7 against 33640, 5790 A 33537.4 against 33536); with V = 2.99796e10 it agrees to within 0.6 units at all eight lines (5461 A 33639.4), the best any single V does (V = 2.998e10, +-0.54). Not an exact evaluation, as for co2_1920. Checked 2026-09-25."
}
lambda_0 = 899 A (p. 5, ‘Cuthbertson’ row of the lambda_0 comparison).
cuthbertson_1920/h2_1909#
{
"id": "h2_1909",
"material": "H2",
"equation": "unlabelled table, p. 7",
"printed": "mu - 1 = 1.692 x 10^27 / (12,409 x 10^27 - n^2)",
"variable": "n = V/lambda, frequency in s^-1 (as above)",
"state": "1atm_0C",
"density": "unknown",
"range": "visible (the 1909 paper's lines; not stated here)",
"coefficients": {
"C": "1.692e27",
"n0_squared": "12409e27"
},
"reproduced_from": [
"C. and M. Cuthbertson, Proc. R. Soc. London 83, 151 (1909)"
],
"check": "Gives 1.3975e-4 at 5461 A (V = 3e10). Not checked against the 1909 values (not in the library)."
}
Reproduced from the authors’ 1909 paper; not doubled.
cuthbertson_1920/o2_1909#
{
"id": "o2_1909",
"material": "O2",
"equation": "unlabelled table, p. 7",
"printed": "mu - 1 = 3.397 x 10^27 / (12,804 x 10^27 - n^2)",
"variable": "n = V/lambda, frequency in s^-1 (as above)",
"state": "1atm_0C",
"density": "unknown",
"range": "visible (the 1909 paper's lines; not stated here)",
"coefficients": {
"C": "3.397e27",
"n0_squared": "12804e27"
},
"reproduced_from": [
"C. and M. Cuthbertson, Proc. R. Soc. London 83, 151 (1909)"
],
"check": "Gives 2.7171e-4 at 5461 A. Not checked against the 1909 values."
}
Reproduced. The O2 values the authors deduct on p. 7 (26,952 and 27,366 x 10^-8 at 6708 and 4800 A) are on the hydrogen-density scale.
cuthbertson_1920/n2_1909#
{
"id": "n2_1909",
"material": "N2",
"equation": "unlabelled table, p. 7",
"printed": "mu - 1 = 5.0345 x 10^27 / (17,095 x 10^27 - n^2)",
"variable": "n = V/lambda, frequency in s^-1 (as above)",
"state": "1atm_0C",
"density": "unknown",
"range": "visible (the 1909 paper's lines; not stated here)",
"coefficients": {
"C": "5.0345e27",
"n0_squared": "17095e27"
},
"reproduced_from": [
"C. and M. Cuthbertson, Proc. R. Soc. London 83, 151 (1909)"
],
"check": "Gives 2.9979e-4 at 5461 A. Not checked against the 1909 values."
}
Reproduced.
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.