G. N. Plass, J. Opt. Soc. Am. 49, 821 (1959).

C. C. Ferriso, Astronautics Report AE 61–0910, "High Temperature Infrared Emission and Absorption Studies," September 1961; also published in J. Chem. Phys. 37, 1955 (1962).

R. H. Tourin, J. Opt. Soc. Am. 51, 175 (1961).

D. E. Burch and D. A. Gryvnak, "Infrared Radiation Emitted by Hot Gases and its Transmission Through Synthetic Atmospheres," Aeronutronic Rep. U-1929, October 1962.

M. Steinberg and W. O. Davies, J. Chem. Phys. 34, 1373 (1961).

G. Herzberg, Infrared and Raman Spectra (D. Van Nostrand Inc., Princeton, New Jersey, 1945), p. 380.

W. Malkmus and A. Thomson, Convair Report ZPh-095, "Infrared Emissivity of Diatomic Gases for the Anharmonic Vibrating Rotator Model," May 1961; also published in J. Quant. Spectry. Radiative Transfer 2, 17 (1962).

G. N. Plass, J. Opt. Soc. Am. 48, 690 (1958).

W. Malkmus, "Infrared Emissivity of Diatomic Gases with Doppler Line Shape," Convair Report ZPh-119, September 1961; also to be published in another journal.

Reference 5, p. 211.

Reference 5, p. 215.

This approximation is based on Dennison's values (*x*_{13}= -21.9, *x*_{23}= -11.0) as given by Herzberg,^{13} and used by Plass.^{8} Courtoy's^{14} more recent measurements differ somewhat (*x*_{13}= 19.37, *x*_{23}= 12.53); however, the exactness of the approximation *x*_{13}≈2*x*_{23} is not critical since *x*_{13}υ_{1}+*x*_{23}υ_{2}≡ x¯υ+½(½*x*_{13}-*x*_{23})(2υ_{1}-υ_{2}). The second term is dropped in Eq. (6); its coefficient is small compared with *x*¯ (using either set of data), and the factor |2υ_{1}-υ_{2}| ≤υ. The approximation ω_{1}≈2ω_{2} is very close; however, the same remarks apply to its noncriticality.

Reference 6, p. 276.

C. P. Courtoy, Can. J. Phys. 35, 608 (1957).

Reference 5, p. 503.

S. S. Penner, Quantitative Molecular Spectroscopy and Gas Emissivities (Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, 1959), p. 152.

D. M. Dennison, Rev. Mod. Phys. 3, 280 (1931).

W. S. Benedict and E. K. Plyler, "High-Resolution Spectra of Hydrocarbon Flames," in Energy Transfer in Hot Gases, pp. 57–73, Natl. Bur. Std. Circ. No. 523, 1954.

L. D. Kaplan and D. F. Eggers, J. Chem. Phys. 25, 876 (1956).

R. Herman and R. F. Wallis, J. Chem. Phys. 23, 635 (1955).

R. P. Madden, J. Chem. Phys. 35, 2083 (1961).

D. W. G. Ballentyne and L. E. Q. Walker, A Dictionary of Named Effects and Laws in Chemistry, Physics and Mathematics (The Macmillan Company, New York, 1961), 2nd ed., p. 14; Van Nostrand's Scientific Encyclopedia (D. Van Nostrand Inc., New York, 1958), 3rd ed., p. 181; Encyclopaedic Dictionary of Physics (Pergamon Press, Inc., New York, 1961), p. 388. Also known as Beer-Bouguer or Beer-Lambert Law.

Assume a statistical distribution of lines of intensity *S* with an arbitrary probability distribution *P*(*S*). Then we have^{8} [equation] where *p* is the total pressure, *c* the mole fraction of absorbing gas, and *b*(*p*, ω) the normalized line shape factor. If we assume the line shape to be linearly pressure broadened, but otherwise arbitrary we have *b*(*p* ω) = *p*^{-1}[(ω-ω_{0})/*p*], where f is an arbitrary function of its argument. If we change the lower limit of the integral over ω from 0 to -∞ for mathematical convenience and make the substitution *u*= (ω-ω_{0})/*p*, we find [equation] Thus In(*I*_{0}/*I*) is linear in *p*, although Beer's law is not satisfied in general, as is seen from the complicated functional dependence on *l*.

A. Thomson (private communication).

H. J. Babrov, P. M. Henry, and R. H. Tourin, The Warner & Swasey Company Scientific Report No. 2 under Contract AF19(604)-6106, "Methods of Predicting Infrared Radiance of Flames by Extrapolation from Laboratory Measurements," October 1961; also published in J. Chem. Phys. 37, 581 (1962).

U. P. Oppenheim and Y. Ben-Aryeh, J. Opt. Soc. Am. 53, 344 (1963).