Born in Springfield, Massachusetts, Anslow attended Springfield Central High School and entered Smith College in 1909.She earned her A.B. in 1914 after studying physics beginning her second year under Professor Frank Allan Waterman. Following graduation, she was hired as a demonstrator (1914-15) and then an assistant (1915-17) in physics and took advanced physics courses, including one in spectroscopy by Janet T. Howell. In 1916 she began her graduate studies under Howell using a new Rowland grating spectrograph acquired by Smith College to research the emission spectra of radium, resulting in her thesis "Spectroscopic Evidence for the Electron Theory of Matter". She graduated in 1917 with her A.M. Following her graduation, she was appointed instructor in physics to replace Howell.
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