Upon her return to London, Ayrton earned money by teaching and embroidery, ran a club for working girls, and cared for her invalid sister. She also put her mathematical skills to practical use – she taught at Notting Hill and Ealing High School, and was also active in devising and solving mathematical problems, many of which were published in "Mathematical Questions and Their Solutions" from the Educational Times. In 1884 Ayrton patented a line-divider, an engineering drawing instrument for dividing a line into any number of equal parts and for enlarging and reducing figures. The line-divider was her first major invention and, while its primary use was likely for artists for enlarging and diminishing, it was also useful to architects and engineers. Ayrton's patent application was financially supported by Louisa Goldsmid and feminist Barbara Bodichon, who together advanced her enough money to take out patents; the invention was shown at the Exhibition of Women's Industries and received much press attention. Ayrton's 1884 patent was the first of many – from 1884 until her death, Hertha registered 26 patents: five on mathematical dividers, 13 on arc lamps and electrodes, the rest on the propulsion of air.