One small correction: Cp is in kJ/(kg.oC) not J/....
A clarification: specific gravity in this case refers to the ratio of the mass of a given volume of oil to the mass of an equal volume of water, both taken at 60oF.
The above formula appears in Engineering Tribology by Stachowiak and Batchelor, as Vol. 24 of Elsevier's Tribology Series. The formula is said to give a rough estimation of Cp values. They quote it from A. Cameron, Basic Lubrication Theory, Ellis Horwood Limited, 1981.