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Morley was born in the town of Woodbridge in Suffolk, England.
His parents were Elizabeth Muskett and Joseph Roberts Morley, Quakers who ran a china shop.
After being educated at Woodbridge School, Morley went on to King's College, Cambridge ( B. A., 1884 ).
He moved to Pennsylvania in 1887.
He taught at Haverford College until 1900, when he became chairman of the mathematics department at Johns Hopkins University.
His publications include Elementary Treatise on the Theory of Functions ( 1893 ), with James Harkness ; and Introduction to the Theory of Analytic Functions ( 1898 ).
New International Encyclopedia He was President of the American Mathematical Society from 1919 to 1920 and was the editor of the American Journal of Mathematics from 1900 to 1921.
In 1933 he and his son Frank Vigor published the " stimulating volume ", Inversive Geometry.

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