The thermodynamic relations between the melting point (MP) and the size of crystals are derived by the use of the Kelvin equation. The results show that the MP depression increases with a decrease in size of a crystal and that there exists the lowest MP when the partial derivative of the surface tension with respect to particle radius (partial derivative sigma/partial derivativer)(T.p)=sigma /r. If the size of a crystal is not too small then the depression is inversely proportional to the radius.