In this task you will be given a text passage from a trivia quiz. You should choose the category this question belongs to from these categories: History, Science, Social Science, Fine Arts, Literature. You can only choose one category, so if in doubt, please choose the closest match.

This man gives his name, along with that of Francis Sears, to a process in ultrasonic imaging for which the acoustic wavefronts act as optical gratings to diffract the light on either side of the central spot. The distance over which charge carriers in plasmas exclude electric fields via his namesake shielding is also known as his namesake length. With an assistant later famous in his own right for his rule for determining whether ring molecules would show aromatic properties, he developed a mathematical expression to explain characteristics of electrolytic solutions, the famous equation named for him and Erich Hckel. FTP name this man who also gives his name to the SI unit defined as about 3.3 x 10-30 Coulomb meters, which measures the molecular dipole moment.
Science

This entity shares its name with one controlled by the astronomer and investigator of mesmerism, Jean Sylvain Bailly. It saw the execution of General Lecomte, and Marshall MacMahon led a campaign against it that culminated with a mass execution at the Wall of the Federalists. Its aftermath saw a mass deportation to New Caledonia, and it was opposed by Adolphe Thiers. Louis-Auguste Blanqui was its nominal leader despite being imprisoned at the time, and it ended in the "Bloody Week" amidst fierce barricade fighting. Growing out of the Franco-Prussian War, for 10 points, name this socialist government that held power for two months in 1871 in the French capital.
History

Measurements of this quantity are always subject to a Malmquist bias. This property is proportional to the fourth power of the velocity dispersal, and this quantity is calculated using the Faber-Jackson and Tully-Fisher relations for elliptical and spiral galaxies. This quantity is larger for objects with longer periods in systems like (*) Cepheid variables, which have constantly varying values for this quantity. This quantity is known for standard candles. For 10 points, name this quantity that is plotted against temperature in the Hertzsprung Russell diagram, which describes objects' brightness.

Science