On his return to Manchester in 1875, he began research on electricity and then went on to spend five years at the Cavendish Laboratory of the University of Cambridge.
His status there was quite unofficial; he was neither a student nor a fellow.
He worked with James Clerk Maxwell and with Rayleigh.
In 1881, he was appointed to the Beyer Chair of Applied Mathematics at Owens, by now one of the colleges of the new Victoria University.
He succeeded his teacher Balfour Stewart as professor of physics in 1888.
This appointment gave him the opportunity to establish a large, active teaching and research department.
In 1900 a new laboratory, for which he had fought and which he had designed, was officially opened.
It was the fourth largest in the world.
The laboratory quickly became a serious rival to the Cavendish; see Manchester Science Hall of Fame.
Much of this later fame was associated with Ernest Rutherford who succeeded Schuster as Langworthy Professor in 1907.
Schuster resigned from the chair, partly for health reasons and partly to promote the cause of international science.
He ensured that Rutherford would succeed him.

Schuster is credited with coining the concept of antimatter in  two letters to Nature in 1898.
 He hypothesized antiatoms, and whole antimatter solar systems, which would yield energy if the atoms combined with atoms of normal matter.
His hypothesis was given a mathematical foundation by the work of Paul Dirac in 1928, which predicted antiparticles and later led to their discovery.

Schuster is perhaps most widely remembered for his periodogram analysis, a technique which was long the main practical tool for identifying statistically important frequencies present in a time series of observations.
He first used this form of harmonic analysis in 1897 to disprove C. G. Knott's claim of periodicity in earthquake occurrences.
He went on to apply the technique to analysing sunspot activity.
This was an old interest.
In 1875 Stewart's friend and Roscoe's cousin, the economist Jevons,  reported, "Mr. A Schuster of Owens College has ingeniously pointed out that the periods of good vintage in Western Europe have occurred at intervals somewhat approximating to eleven years, the average length of the principal sun-spot cycle."

Schuster is credited by Chandrasekhar to have given a fresh start to the radiative transfer problem.
Schuster formulated in 1905 a problem in radiative transfer in an attempt to explain the appearance of absorption and emission lines in stellar spectra.
This was the first use of the two-stream approximation that underpins the treatment of radiative transfer in virtually all weather and climate models.

In 1912 he bought Yeldall House near Twyford, Berkshire.

Following the outbreak of World War I in 1914, the Schuster family was subjected to anti-German prejudice in the press and, in Arthur's case, in some quarters of the Royal Society.
His brother Sir Felix Schuster had to issue a statement pointing out the family's loyalty to Britain and that they all had sons serving in the British army.
On the day Arthur gave his presidential address to the 1915 British Association meeting, he learned that his son had been wounded.

Schuster was regarded by his contemporaries as a mathematical physicist of exceptional ability but also as a capable administrator and teacher, and an advocate for the role of science in education and industry.

He died in Twyford on 14 October 1934.
He is buried in Brookwood Cemetery in outer London.
On his return to Manchester in 1875, he began research on electricity and then went on to spend five years at the Cavendish Laboratory of the University of Cambridge. His status there was quite unofficial; he was neither a student nor a fellow. He worked with James Clerk Maxwell and with Rayleigh. In 1881, he was appointed to the Beyer Chair of Applied Mathematics at Owens, by now one of the colleges of the new Victoria University. He succeeded his teacher Balfour Stewart as professor of physics in 1888. This appointment gave him the opportunity to establish a large, active teaching and research department. In 1900 a new laboratory, for which he had fought and which he had designed, was officially opened. It was the fourth largest in the world. The laboratory quickly became a serious rival to the Cavendish; see Manchester Science Hall of Fame. Much of this later fame was associated with Ernest Rutherford who succeeded Schuster as Langworthy Professor in 1907. Schuster resigned from the chair, partly for health reasons and partly to promote the cause of international science. He ensured that Rutherford would succeed him.
Schuster is credited with coining the concept of antimatter in  two letters to Nature in 1898.  He hypothesized antiatoms, and whole antimatter solar systems, which would yield energy if the atoms combined with atoms of normal matter. His hypothesis was given a mathematical foundation by the work of Paul Dirac in 1928, which predicted antiparticles and later led to their discovery.
Schuster is perhaps most widely remembered for his periodogram analysis, a technique which was long the main practical tool for identifying statistically important frequencies present in a time series of observations. He first used this form of harmonic analysis in 1897 to disprove C. G. Knott's claim of periodicity in earthquake occurrences. He went on to apply the technique to analysing sunspot activity. This was an old interest. In 1875 Stewart's friend and Roscoe's cousin, the economist Jevons,  reported, "Mr. A Schuster of Owens College has ingeniously pointed out that the periods of good vintage in Western Europe have occurred at intervals somewhat approximating to eleven years, the average length of the principal sun-spot cycle."
Schuster is credited by Chandrasekhar to have given a fresh start to the radiative transfer problem. Schuster formulated in 1905 a problem in radiative transfer in an attempt to explain the appearance of absorption and emission lines in stellar spectra. This was the first use of the two-stream approximation that underpins the treatment of radiative transfer in virtually all weather and climate models.
In 1912 he bought Yeldall House near Twyford, Berkshire.
Following the outbreak of World War I in 1914, the Schuster family was subjected to anti-German prejudice in the press and, in Arthur's case, in some quarters of the Royal Society. His brother Sir Felix Schuster had to issue a statement pointing out the family's loyalty to Britain and that they all had sons serving in the British army. On the day Arthur gave his presidential address to the 1915 British Association meeting, he learned that his son had been wounded.
Schuster was regarded by his contemporaries as a mathematical physicist of exceptional ability but also as a capable administrator and teacher, and an advocate for the role of science in education and industry.
He died in Twyford on 14 October 1934. He is buried in Brookwood Cemetery in outer London.
Arthur Schuster