This hammered home for me how incredibly recent are a lot of the scientific discoveries we take utterly for granted. Even before nuclear energy, atoms themselves were only confirmed to exist in the 20th century. Everyone knows about plate tectonics, but that was confirmed in the 60s or something.
(i.e. he has determined the value of what is now called the constant of Avogadro, which is proportional to the inverse of the mass of an atom; there are various related quantities where knowing one determines all the others, including the constant of Avogadro and the concentration of molecules in a gas at standard pressure and temperature; knowing the mass of any molecule or atom allows the computation of the masses of all other atoms and molecules, using the chemical formulas)
Using the mass of an atom, various other atomic quantities could be computed immediately, e.g. George Johnstone Stoney has computed in 1874 the value of the elementary electric charge, based on the results of Loschmidt. The work of Loschmidt has also allowed James Clerk Maxwell to propose in 1873 a system of fundamental units for the physical quantities which was based only on reproducible atomic properties, instead of unique artifacts like the platinum standard meter and the platinum standard kilogram. (However Maxwell's system was not yet practical at that time, because the accuracy with which the atomic masses were known was too low in comparison with the precision of the weight scales.)
Before Loschmidt, the atoms were indeed just a hypothetical construct that could explain some properties of the chemical reactions and of the gases, but nothing could be said about them quantitatively.
After Loschmidt, the atoms became physical objects with precisely known properties, e.g. you could count how many atoms are in a pebble that you hold in your hand.
By the start of the 20th century, more than a human generation had passed since the last time when scientists wondered whether atoms really exist. At that time already atom beams were routinely manipulated with electric and magnetic fields and unexpected atomic properties like radioactivity and transmutation were already known.