From a new perspective, we re-examine self-gravity and turbulence jointly, in hopes of understanding the physical basis for one of the most important empirical relations governing clouds in the interstellar medium (ISM), the Larsons Relation relating velocity dispersion ($sigma_R$) to cloud size ($R$). We report on two key new findings. First, the correct form of the Larsons Relation is $sigma_R=alpha_v^{1/5}sigma_{pc}(R/1pc)^{3/5}$, where $alpha_v$ is the virial parameter of clouds and $sigma_{pc}$ is the strength of the turbulence, if the turbulence has the Kolmogorov spectrum. Second, the amplitude of the Larsons Relation, $sigma_{pc}$, is not universal, differing by a factor of about two between clouds on the Galactic disk and those at the Galactic center, evidenced by observational data.
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