## Abstract

The absolute *f*-values of rotational lines in the positive and negative branches of the 2*ν*_{3} overtone band of CH_{4} have been derived from absorption measurements in the laboratory by two independent methods. The first method involves the use of the curve of growth and requires the observation of weak lines for which the total absorption is independent of the damping constant. In the second method the lines are broadened artificially, by the introduction of about 3 atmos of air, to half-widths that are about five times the slit width. The *f*-values are then determined by integration of the logarithm of the percentage absorption over the line profile. On the average, the *f*-values obtained by the two methods agree within 10 percent.

© 1952 Optical Society of America

Full Article |

PDF Article
### Equations (16)

Equations on this page are rendered with MathJax. Learn more.

(1)
$${I}_{\nu}/{I}_{0}={e}^{-\tau \nu},$$
(2)
$${\tau}_{\nu}={n}_{J}l{\alpha}_{\nu}.$$
(3)
$${\alpha}_{\nu}={\alpha}_{0}\frac{\gamma /4{\pi}^{2}}{{(\nu -{\nu}_{0})}^{2}+{(\gamma /4\pi )}^{2}},$$
(4)
$${\alpha}_{0}={\int}_{0}^{\infty}{\alpha}_{\nu}d\nu =\frac{\pi {\u220a}^{2}}{mc}{f}_{J{J}^{\prime}},$$
(5)
$${f}_{J{J}^{\prime}}=\frac{1}{\pi {\u220a}^{2}/mc}{\int}_{0}^{\infty}{\alpha}_{\nu}d\nu =\frac{1}{{n}_{Jl}(\pi {\u220a}^{2}/mc)}{\int}_{0}^{\infty}\text{ln}\frac{{I}_{0}}{{I}_{\nu}}d\nu .$$
(6)
$${n}_{J}=\frac{n}{b(T)}{g}_{J}{e}^{-BhcJ(J+1)/kT},$$
(7)
$$\mathrm{\Delta}\nu ={\int}_{0}^{\infty}\left(1-\frac{{I}_{\nu}}{{I}_{0}}\right)d\nu .$$
(8)
$$W=\frac{{\mathrm{\lambda}}^{2}}{c}\mathrm{\Delta}\nu .$$
(9)
$${\tau}_{0}=\frac{4}{\gamma}\frac{\pi {\u220a}^{2}}{mc}{f}_{J{J}^{\prime}}{n}_{J}l,$$
(10)
$$\delta =(\mathrm{\lambda}/4c)\gamma .$$
(11)
$$W/\mathrm{\lambda}=\delta {\tau}_{0},$$
(12)
$$W/\mathrm{\lambda}=2{(\delta /\pi )}^{{\scriptstyle \frac{1}{2}}}{(\delta {\tau}_{0})}^{{\scriptstyle \frac{1}{2}}}.$$
(13)
$$\text{log}\delta {\tau}_{0}-\text{log}l=\text{log}\left(\frac{\pi {\u220a}^{2}}{m{c}^{2}}\mathrm{\lambda}{f}_{J{J}^{\prime}}{n}_{J}\right).$$
(14)
$$\frac{\gamma}{2\pi}=2N{\sigma}^{2}{\left[\frac{2RT}{\pi}\left(\frac{1}{{\mu}_{1}}+\frac{1}{{\mu}_{2}}\right)\right]}^{{\scriptstyle \frac{1}{2}}}.$$
(15)
$${n}_{J}=\frac{p}{kT}\frac{{g}_{J}}{b(T)}{e}^{(-{B}_{0}hc/kT)J(J+1)},$$
(16)
$$b(T)=1.027{(T/{B}_{0})}^{{\scriptstyle \frac{3}{2}}},$$