Section I. [Equation 3]

The portion of the spheres of exclusion original: "Deckungssphären"; refers to the space around a molecule's center into which no other molecule's center can enter of all molecules which lies within the cylinder $γ$ relates to the total volume $4 π n σ^3 / 3$ in the same way as the volume $Ω d h$ of the cylinder $γ$ relates to the total volume $V$ of the gas. It would therefore be:

$A = \frac{4 π n σ^3}{3 V} Ω d h.$

Of all the molecules whose sphere of exclusion reaches into the volume of cylinder $γ$, one can neglect the number of those whose center lies within the cylinder $γ$ itself, since the height $d h$ of this cylinder is infinitely small. The centers of all molecules whose spheres of exclusion reach into the volume of cylinder $γ$ would therefore—if this cylinder were located in the middle of the vessel—lie evenly with one half on one side and the other half on the other side of cylinder $γ$.

Since the cylinder $γ$ we are considering is not in the middle of the vessel's interior, but rather at a distance of $\frac{1}{2} σ$ $σ$ represents the molecular diameter from the wall of the vessel, the centers of the $n - 1$ molecules can only lie on one side of it, but not on the other. Thus, half of the molecules are omitted whose spheres of exclusion previously carved out the volume $A$ from the entire cylinder $γ$; and that part of the volume of cylinder $γ$ which is filled by the spheres of exclusion of any of the $n - 1$ molecules is only:

$\frac{A}{2} = \frac{2 π n σ^3}{3 V} Ω d h .^1)$

$^1)$ This formula can also be derived in the following, somewhat more detailed manner. We shall call the end face of the cylinder $γ$ that faces the vessel wall the "base." A center of one of the spheres of exclusion can, of course, only lie on that side of the base which faces away from the vessel wall. On this side, we construct two planes parallel to the base of cylinder $γ$, both with surface area $Ω$, at distances $ξ$ and $ξ + d ξ$ from the base. Let the space between these two planes be called cylinder $γ_1$; its volume is $γ_1 = Ω d ξ$. The number of those $n - 1$ spheres of exclusion whose centers lie within cylinder $γ_1$ at the given time is:

$\frac{γ_1 (n - 1)}{V - \frac{4 π (n - 1) σ^3}{3}},$