Potential density
Potential density is a dynamically important property: for static stability potential density must decrease upward. If it doesn't, a fluid parcel displaced upward finds itself lighter than its neighbors, and continues to move upward; similarly, a fluid parcel displaced downward would be heavier than its neighbors. This is true even if the density of the fluid decreases upward. In stable conditions (potential density decreasing upward) motion along surfaces of constant potential density (isopycnals) is energetically favored over flow across these surfaces (diapycnal flow), so most of the motion within a 3-D geophysical fluid takes place along these 2-D surfaces.
API gravity
API gravity is thus an inverse measure of a petroleum liquid's density relative to that of water (also known as specific gravity). It is used to compare densities of petroleum liquids. For example, if one petroleum liquid is less dense than another, it has a greater API gravity. Although API gravity is mathematically a dimensionless quantity (see the formula below), it is referred to as being in 'degrees'. API gravity is graduated in degrees on a hydrometer instrument. API gravity values of most petroleum liquids fall between 10 and 70 degrees.
In 1916, the U.S. National Bureau of Standards accepted the Baumé scale, which had been developed in France in 1768, as the U.S. standard for measuring the specific gravity of liquids less dense than water. Investigation by the U.S. National Academy of Sciences found major errors in salinity and temperature controls that had caused serious variations in published values. Hydrometers in the U.S. had been manufactured and distributed widely with a modulus of 141.5 instead of the Baumé scale modulus of 140. The scale was so firmly established that, by 1921, the remedy implemented by the American Petroleum Institute was to create the API gravity scale, recognizing the scale that was actually being used.