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William Band was born in Liscard, Cheshire, England, on August 27, 1906, one of two sons born to William D. Band and Amy L. Cooke. He attended Liscard High School, where he excelled in Mathematics, and graduated in 1922 after satisfying the exams for the Higher School Certificate. At the University of Liverpool, which he entered in the fall of 1923, he concentrated in the study of physics and graduated with honors in 1926, winning the Oliver J. Lodge Prize. He became a candidate for the MsSc degree and graduated in 1927.

Upon graduation, Band served in China at Yenching University, a position he favored over study for a PhD at Cambridge. While on a short trip back to England in 1931, he married Claire May Edwards, whom he had met while teaching Sunday School at Liverpool. They arrived at Yenching on August 31, 1931, shortly before the Japanese invaded Manchuria on September 18. He was Chairman of the Physics department at Yenching until 1944, where, besides teaching quantum mechanics and relativity, he developed a research program for the MS degree.

Yenching University was founded in 1916 by John Leighton Stuart as a missionary institution in the continued effort to spread Christianity through education in China, under auspices of the Board of Foreign Missions of the Presbyterian Church in the United States and the Division of Foreign Missions of the Board of Missions of the Methodist Church of the United States and the United Kingdom.

Band's service at Yenching was interrupted as a result of the outbreak of war between the United States and Japan. Band and his wife were evacuated by the Chinese Communists with whom they spent over two years on a thousand mile journey to freedom until they reached Chunking in 1944. A book, Dragon Fangs, based on their diaries of wartime experiences in China, was published in 1947. It was published later in the United States under the title Two Years with the Chinese Communists.

Back in England on furlough, William Band was awarded his PhD by the University of Liverpool as a result of his research in physics. In 1946 he was granted a fellowship at the Institute for the Study of Metals of the University of Chicago where he stayed until 1949. In 1949 he moved to Washington State College as Professor of Physics. During each summer between 1955 and 1966 he worked as Senior Physicist at the Poulter Laboratories of the Stanford Research Institute, on the theory of shock propagation in solids. He was appointed Chairman of the Department of Physics at Washington State in 1960, and served in this position in 1968, continuing his research activities until well after his retirement in 1971, and publishing extensively in all the major professional journals. In 1972 he was honored by colleagues from all over the world for his Physical Cluster Theory. He also published an introduction to mathematical physics and an introduction to quantum statistics. He was a Fellow of the Institute of Physics and Physical Society, London, and Fellow of the American Physical Society. William Band died in 1993.