The interaction between the vibration and rotation of the C${\mathrm{O}}_2$ molecule is discussed. It is shown that the fine-structure lines will exhibit a convergence which depends upon certain of the anharmonic potential constants. The convergence factors are compared with the experimental data of the resolved bands and an excellent agreement is found, which leads to a determination of the anharmonic constants. Combining these results with those of Part I, the complete potential function for C${\mathrm{O}}_2$ is obtained. A simple analytic function for the potential is proposed which contains but four constants. It is shown that this function agrees satisfactorily with the experimental potential for small displacements. The range of the validity of the analytic function is discussed and one of the heats of dissociation of C${\mathrm{O}}_2$ is obtained.

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