On the basis of the spectrum term of a electronic rotational-vibrational energy level, the law of vibrational band sequences and progressions in diatomic molecules was analysed. According to the law, the Deslandres table and its nature were summarized. How to indicate the measured values of a electronic-vibrational spectrum was illustrated by taking the Swan band spectra of the C2 molecule as an example. In the example, the measured values were put in order which formed the Deslandres table in terms of the law of vibrational structure. The authors can gain some important data, such as anharmonicity constants and harmonic oscillator frequencies in different vibrational states, concerning the band spectra of molecules. Furthermore, the formula of wave numbers of every band spectrum was derived.
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