Sir Arthur Schuster was born Franz Arthur Friedrich Schuster on 12 September 1851 at Frankfurt-on-Main, Germany into a family of textile merchants. His parents were converts from Judaism. He was educated at Frankfurt Gymnasium from 1863-8, and Geneva Academy from 1868-1870. In 1869, Schuster's father relocated the business to Manchester, wishing to avoid Prussian nationality, following the annexation of Frankfurt in 1866. Schuster followed him in 1870, and was originally intended for the family business. However, disliking this prospect, he enrolled at Owens College, where he was influenced by Henry Roscoe, professor of chemistry. He completed his studies at Heidelberg, where he was awarded a Ph.D. in 1873. Thereafter, he was a honorary demonstrator at Owens, and researched at the Cavendish Laboratory, Cambridge , where he worked with James Clerk Maxwell and J W Strutt (Lord Rayleigh).
Schuster's early interests were in spectrum analysis (originally influenced by Roscoe). His first published paper was "On the spectrum of nitrogen" (1873), and in 1881 he published an important article "On the harmonic ratios in the spectra of gases", where he refuted G J Stoney's proposed law which claimed to identify harmonised ratios within gas spectra of different elements; Schuster showed statistically that spectra confirmed more closely to random distribution. In 1897 the Rydberg-Schuster law proposed a formula to describe regularities in spectral line distribution. Schuster also participated in scientific expeditions to Siam, Arizona, Egypt and the West Indies in the 1870s and 1880s to observe coronal spectra during solar eclipses. In the 1880s he undertook important research on the discharge of electricity through gases in evacuated tubes, which demonstrated that electricity passed through gases as ions, and that once a gas was ionized a current could be maintained using a small potential. This discovery formed the subject of his Bakerian lectures in 1884 and 1890. Schuster's research lay some of the foundations for the later discovery of the electron. Later in his career, he also developed the periodogram, an important tool for measuring statistically important regularities in a time series of observations.
In 1881 Schuster was appointed professor of applied mathematics at Owens College, and in 1888 he became Langworthy Professor of Physics. For almost the next two decades Schuster was the dominant figure in Manchester science. As departmental head, he laid down ambitious plans for physics teaching and research, and his labours culminated in the opening of the new Physical Laboratories in 1900, which when they opened were the largest in the UK and the fourth largest in the world. The new buildings reflected Schuster's belief in the importance of intradisciplinary research within physics, and a symbiotic relationship between pure and applied science. Staff and students were encouraged to undertake original research and to share their ideas for mutual benefit. The layout of the labs reflected this, with communal working areas and a limitation on private research rooms. Schuster also ensured that newer subjects such as electrical engineering and electro-chemistry were developed at Manchester, and he established the Whitworth Observatory in 1892 for the study of astronomy and meteorology. Among staff and students studying physics at Manchester during Schuster's headship were Joseph Petavel, G C Simpson, G A Hemsalech, Arthur Eddington, Albert Griffiths, Robert Hutton, Robert Beattie, C H Lees and C T R Wilson. In 1904, after the Victoria University of Manchester was established, he became the first Dean of the Faculty of Science.
In 1907 he retired as Langworthy Professor to devote himself to the administration of the Royal Society and the organisation of international cooperation in science. He was succeeded at Manchester by Ernest Rutherford, who owed this post to Schuster's efforts.
Schuster was the author of several books including An intermediate course of practical physics with C H Lees, (1896), An introduction to the theory of optics (1904), The progress of physics during 33 years (1875-1908) (1911) and over 150 papers. He was interested in many different aspects of scientific research including terrestrial magnetism, optics, solar physics, the mathematical theory of periodicities and meteorology. Schuster was very active in the public world of science serving as Secretary of the Royal Society, and on the councils of the Meteorological Office and the National Physical Laboratory.
Schuster was elected FRS in 1879, and was knighted in 1920. He married Caroline Emma Loveday in 1887; they had a son and four daughters. In 1913 he moved with his family to Twyford, Berks. Possessed of private means, he was a generous benefactor of various scientific and educational causes. Schuster died on 14 October 1934.