Thomas Edison of the Edison patent to charge a more reasonable rate for the use of the Edison patent rights and lowering the price of the electric lamp. On October 8, 1883, the US patent office ruled that Edison's patent was based on the work of William E. Sawyer and was, therefore, invalid. Litigation continued for nearly six years, until October 6, 1889, when a judge ruled that Edison's electric light improvement claim for "a filament of carbon of high resistance" was valid. To avoid a possible court battle with Joseph Swan, whose British patent had been awarded a year before Edison's,
Thomas Edison was to expand Edison's mathematical methods. Despite the common belief that Edison did not use mathematics, analysis of his notebooks reveal that he was an astute user of mathematical analysis conducted by his assistants such as Francis Robbins Upton, for example, determining the critical parameters of his electric lighting system including lamp resistance by an analysis of Ohm's Law, Joule's Law and economics. Nearly all of Edison's patents were utility patents, which were protected for a 17-year period and included inventions or processes that are electrical, mechanical, or chemical in nature. About a dozen were design patents, which protect an