Section I.

...pretended that our assumptions are exactly realized in nature. On the contrary, we have hitherto placed the greatest weight on the fact that the calculations linked to them are exactly correct—that is, that they are logically necessary consequences of the assumptions. The development of mathematical methods achieved through this was our main purpose. By having the consequences of various types of assumptions available, the discovery of experiments to test them should be facilitated; at the same time, this ensures that with every advance in our knowledge, the mathematical methods for processing new laws are as ready as possible.

Unfortunately, van der Waals Johannes Diderik van der Waals (1837–1923), a Dutch physicist famous for his equation of state for gases and liquids. must also abandon this mathematical rigor on one point that has so far not been manageable through calculation. Yet it certainly proves the high value and great utility of van der Waals’ theory that his formula generally provides a fairly good picture of the behavior of gases up to their liquefaction, even if it does not entirely agree quantitatively with experience. One is also well justified in concluding from this that its fundamental features will hardly ever be replaceable by something completely different.

In this section, I intend to derive the equations of van der Waals in the simplest and shortest possible way, and will provide supplements to them only in Section V.

§ 2. External and Internal Pressure.

Let an arbitrary vessel of volume V contain n molecules of the same nature, which are perfectly elastic, infinitely slightly deformable spheres of diameter $σ$. Let the volume occupied by these spheres themselves be quite small, but not completely negligible compared to the total volume V of the vessel. It will be shown that the formulas we obtain are also approximately applicable to states of the substance contained in the vessel in which it must no longer be described as a gas, but as a "drippable" liquid The author uses the term "tropfbare Flüssigkeit" to distinguish common liquids from aeriform fluids or gases.. We shall therefore simply refer to it in the following as the "substance," not as a gas, although we primarily still have in mind those cases where its state closely approaches that of a gas.