William received his early education in Chicago in the public schools. He served an apprenticeship of three years to a pharmacist and then entered the Chicago Medical College, where he received his medical degree in 1869. Quine served an internship in the Cook County Hospital and for ten years thereafter was gynecologist and obstetrician to that institution.
William Edward Quine began his long teaching career in 1870 when he was appointed professor of materia medica and therapeutics at the Chicago Medical College. In 1883 he joined the faculty of the newly organized College of Physicians and Surgeons of Chicago as professor of the principles and practice of medicine, a post which he held for thirty years thereafter. He was made president of the faculty in 1892. In 1897 when the college passed under the control of the University of Illinois, he occupied the same position under the title of dean. Quine's ambition was to be a great teacher of medicine, and he realized that ambition fully. He is rated among the first half-dozen teachers that served Chicago's medical schools in his branch of teaching, a rank he achieved despite the didactic methods that he inherited from the instructors of an earlier generation. He held the attention and interest of his classes by his exceptionally forceful and arresting delivery of words. He was active in the negotiations that brought about the affiliation of the College of Physicians and Surgeons with the University of Illinois in 1897, and the absorption of the medical school into the university in 1913.
Wiliam founded and for ten years supported the library of the school, which is called the Quine Library. In 1872, three years after his graduation, he was elected president of the Chicago Medical Society, and in 1904 president of the Illinois State Medical Society. From 1885 to 1889 he was president of the Illinois state board of health. A large and remunerative practice came to him early. While teaching at the Chicago Medical College he was on the staff of Mercy Hospital. Later he served on the staffs of St. Luke's and Michael Reese hospitals. He wrote many articles on professional topics, in which zeal for human welfare was always conspicuous.
After his wife's death, on June 14, 1903, Quine built a hospital for women, of one hundred beds, in Chin Kiang, China, and founded four schools for girls in different cities in that country, all named for his spouse. In memory of a daughter Wiliam founded the Ruth Quine Deaconate in a charitable institution in Normal, her mother's old home. He died suddenly at his residence in Chicago of angina pectoris. His fine house on Blackstone Avenue, in a section where many colored people had come to live, he bequeathed to the Chicago Missionary and Church Extension Society of the Methodist Episcopal Church for use as a community house for Negro Methodism.
William Quine was a member of the Chicago Academy of Sciences, of the Chicago Society of Medical History, and of the American Neurological Association.
Wiliam Edward Quine was short and of powerful frame, with a large head and strong, well-cut features. He had few intimates, was introspective, imaginative, sensitive, temperamental, impulsive, and fanatical in his loyalties. Wiliam was of a deeply religious nature, he affected a clerical cut to his dress that gave him the appearance and air of a clergyman.
On November 14, 1876, Wiliam Quine married Lettie A. Mason of Normal, Illinois, who had been a missionary in China, none of their three children long survived.