The passage discusses the additional absorption of radiation over the entire half-width $\gamma$ in addition to the ordinary absorbed radiation of half-width $C / 4 \pi$. This additional absorption is much less intense and is proportional to the square of $G / 4 \pi \gamma^{3}$. When $H$ equals zero, this ratio simplifies to the ratio of the normal half-width $C / 4 \pi$ to the half-width $\gamma$ of the incident radiation. In general, this ratio is small, allowing for the usual analysis that assumes $F(z)$ to be a constant $C$. The formulas provided give the order of magnitude of the effects involved. When $\gamma$ is much smaller than $\Gamma$, the consideration of transitions $A$ to $B$ alone becomes an approximation. The double transition $A$ to $B$ to $A$ can be treated by applying the foregoing analysis, provided the ordinary approximations are made for the spontaneous jumps $B$ to $A$. The most important result is that $\gamma+\Gamma$ replaces $\gamma$ in the square root, leading to no shift in the absorbed line, which agrees with Weisskopf's conclusion when the frequency of his strictly monochromatic radiation coincides with the line center. The second part of the passage discusses the static solutions of Einstein's field equations for spheres of fluid. It introduces a method to treat these equations, providing explicit solutions in terms of known analytic functions. Several new solutions are obtained, and their properties are examined in detail. The aim is to help understand stellar structure, particularly in the context of stellar interiors and the behavior of fluids under various conditions. The solutions are derived by solving the nonlinear differential equations that describe the gravitational equilibrium of perfect fluids, and the properties of the fluid are connected to the gravitational potentials and the energy-momentum tensor. The paper also discusses the connection between interior and exterior solutions, particularly for spheres of fluid surrounded by empty space, and provides detailed considerations of specific solutions, including their physical implications and stability.The passage discusses the additional absorption of radiation over the entire half-width $\gamma$ in addition to the ordinary absorbed radiation of half-width $C / 4 \pi$. This additional absorption is much less intense and is proportional to the square of $G / 4 \pi \gamma^{3}$. When $H$ equals zero, this ratio simplifies to the ratio of the normal half-width $C / 4 \pi$ to the half-width $\gamma$ of the incident radiation. In general, this ratio is small, allowing for the usual analysis that assumes $F(z)$ to be a constant $C$. The formulas provided give the order of magnitude of the effects involved. When $\gamma$ is much smaller than $\Gamma$, the consideration of transitions $A$ to $B$ alone becomes an approximation. The double transition $A$ to $B$ to $A$ can be treated by applying the foregoing analysis, provided the ordinary approximations are made for the spontaneous jumps $B$ to $A$. The most important result is that $\gamma+\Gamma$ replaces $\gamma$ in the square root, leading to no shift in the absorbed line, which agrees with Weisskopf's conclusion when the frequency of his strictly monochromatic radiation coincides with the line center. The second part of the passage discusses the static solutions of Einstein's field equations for spheres of fluid. It introduces a method to treat these equations, providing explicit solutions in terms of known analytic functions. Several new solutions are obtained, and their properties are examined in detail. The aim is to help understand stellar structure, particularly in the context of stellar interiors and the behavior of fluids under various conditions. The solutions are derived by solving the nonlinear differential equations that describe the gravitational equilibrium of perfect fluids, and the properties of the fluid are connected to the gravitational potentials and the energy-momentum tensor. The paper also discusses the connection between interior and exterior solutions, particularly for spheres of fluid surrounded by empty space, and provides detailed considerations of specific solutions, including their physical implications and stability.