This inaugural dissertation, titled "A New Determination of Molecular Dimensions," is presented by Albert Einstein to obtain the philosophical doctorate from the University of Zurich. The work aims to determine the size of molecules in a solution using the internal friction of the solution and the diffusion of the dissolved substance. Einstein argues that the volume of a molecule in a solution is much larger than that of a molecule in the solvent, and he models the dissolved molecule as a rigid sphere. He derives hydrodynamic equations to describe the motion of the solution and the sphere, considering the sphere's influence on the solution's movement. The dissertation includes detailed mathematical derivations to calculate the friction coefficient of a liquid containing many small spheres and the diffusion coefficient of a non-disassociated substance in a liquid solution. Finally, Einstein uses these results to determine the molecular dimensions, specifically the radius and number of molecules in a gram molecule of sugar in water, finding that the molecular radius is approximately \(9.9 \times 10^{-8} \text{ cm}\) and the number of molecules is \(2.1 \times 10^{22}\).This inaugural dissertation, titled "A New Determination of Molecular Dimensions," is presented by Albert Einstein to obtain the philosophical doctorate from the University of Zurich. The work aims to determine the size of molecules in a solution using the internal friction of the solution and the diffusion of the dissolved substance. Einstein argues that the volume of a molecule in a solution is much larger than that of a molecule in the solvent, and he models the dissolved molecule as a rigid sphere. He derives hydrodynamic equations to describe the motion of the solution and the sphere, considering the sphere's influence on the solution's movement. The dissertation includes detailed mathematical derivations to calculate the friction coefficient of a liquid containing many small spheres and the diffusion coefficient of a non-disassociated substance in a liquid solution. Finally, Einstein uses these results to determine the molecular dimensions, specifically the radius and number of molecules in a gram molecule of sugar in water, finding that the molecular radius is approximately \(9.9 \times 10^{-8} \text{ cm}\) and the number of molecules is \(2.1 \times 10^{22}\).