Although experimental studies continued during the 18th century, a successful quantitative treatment of capillary action was not attained until 1805 by two investigators: Thomas Young of the United Kingdom and Pierre-Simon Laplace of France. They derived the Young–Laplace equation of capillary action. By 1830, the German mathematician Carl Friedrich Gauss had determined the boundary conditions governing capillary action (i.e., the conditions at the liquid-solid interface). In 1871, the British physicist William Thomson, 1st Baron Kelvin determined the effect of the meniscus on a liquid's vapor pressure—a relation known as the Kelvin equation. German physicist Franz Ernst Neumann (1798–1895) subsequently determined the interaction between two immiscible liquids.