By using the data measured by Hill and Ricketson, we can express the anomalous specific heat CV of solid hydrogen at sufficiently high temperatures approximately as CVT2 / R = αc + βc2, α = 1.1, β = 15.7, where c is the concentration of ortho-hydrogen molecules, T the absolute temperature, and R the gas constant. It is an aim of this paper to inquire into the origin of these two terms. Through calculations by the method of moment expansion, the magnitude of β can be explained from the quadrupolar interactions among ortho-molecules, while the anisotropic nature of the valence and van der Waals forces is shown to be effective only as corrective terms. On the other hand, the appearance of α shows that the molecular rotation of an ortho-molecule surrounded by para-molecules should also be quenched. A possible mechanism of this phenomenon may be the rotation-vibration coupling, for which the valence and van der Waals forces should be exclusively responsible. However, we are not yet able to get a complete understanding of this quenching process. Deviation from the above formula, i. e. the linear dependence on c of the the quantity CVT2/R at temperatures not high enough is also derived and compared with experiment. Further, a more exact treatement than the moment expansion method is given for the case of low ortho-concentrations and is applied to the case of 7% ortho.