where p is the pressure and r the mixing ratio.
Varen's most important contribution to oceanography was probably the discussions in his book about steady currents being driven by the wind, the first time this notion had seen print. This led to motions in the sea finally being considered in terms other than Aristotle's primum mobile. He also attempted to categorize the motions of the sea, separating them into a continuous western flow, an observed periodic rise and fall of the sea surface that is the tide (although their connection with the moon was suspected though not as yet well-known), and various special flows including what are now known as the Florida, Kuroshio and Mozambique Currents.
Varen also discussed varying theories as to the causes of the perceived general westward flow and the tides. The explanations for the former included a magnetic pull from the moon, thermal expansion as a result of moonlight, downward pressure from the moon as trasmitted through an endless atmosphere, the sun pulling the water after it, the inability of the sea to keep up with the earth's rotation, and more. He concluded that the cause was uncertain although he favored the wind as a cause at least of the general westward currents in the tropics as well as of other non-tidal currents flowing counter to the supposed general western flow. He considered the moon as responsible for the tides although via a mechanism as yet unknown (and to be identified by Newton in 1687). See Peterson et al. (1996).
where
is the velocity vector. This equation implies
that
is normal to the equipotential lines and is
directed from high to low potential.
a If there is also liquid water in the air this is modified as
where
is the liquid water mixing ratio (in grams of
liquid water per gram of dry air).
The virtual temperature is thus defined because it allows the
ideal gas law to be used for situations
in which the air is not dry, i.e. moist air of temperature T behaves
identically to dry air of temperature
.