It is named after the Austrian physicist Johann Josef Loschmidt, who was the first to estimate the physical size of molecules in 1865.
Being a measure of number density, the Loschmidt constant is used to define the amagat, a practical unit of number density for gases and other substances: such that the Loschmidt constant is exactly 1 amagat.
Loschmidt did not actually calculate a value for the constant which now bears his name, but it is a simple and logical manipulation of his published results.
To derive this "remarkable proportion", Loschmidt started from Maxwell's own definition of the mean free path (there is an inconsistency between the result on this page and the page cross-referenced to the mean free path; here appears an additional factor 3/4): where n0 has the same sense as the Loschmidt constant, that is the number of molecules per unit volume, and d is the effective diameter of the molecules (assumed to be spherical).
Dividing both sides of the equation by n0πd3/6 has the effect of introducing a factor of Vliquid/Vgas, which Loschmidt called the "condensation coefficient" and which is experimentally measurable.
The equation reduces to relating the diameter of a gas molecule to measurable phenomena.
The number density, the constant which now bears Loschmidt's name, can be found by simply substituting the diameter of the molecule into the definition of the mean free path and rearranging: Instead of taking this step, Loschmidt decided to estimate the mean diameter of the molecules in air.
This was no minor undertaking, as the condensation coefficient was unknown and had to be estimated – it would be another twelve years before Raoul Pictet and Louis Paul Cailletet would liquify nitrogen for the first time.