Martha was born in Georgia, Vermont on February 13, 1870. She grew up in Easthampton, Massachusetts where she graduated high school. She earned her B.S. degree from Smith College in 1892. Prior to enrolling in graduate school at Yale University, she taught as a science teacher in New York and Massachusetts. She started graduate school in 1896 and graduated with her Ph.D. in chemistry in 1898. After completing her Ph.D., she continued working for her Ph.D. advisor, Andrew Gooch in the Kent Chemistry Laboratory for one year and then transferred to the Rhode Island Experiment Station where she worked as an assistant chemist in 1900. From 1901-1904, she went back to being a science teacher and taught chemistry and physics at Wilson College. In 1904, she also married Issac King Phelps, who was working as a chemistry instructor at Yale and George Washington University at the time. In 1908, the couple moved to Washington D.C. where Martha went to work for the Bureau of Standards as a chemistry researcher and Issac went to work for the U.S. Department of Agriculture. Martha ceased working as researcher in 1909. Martha was one of the first female scientists to be employed by the Bureau of Standards. After 1909, she began her activist work in women's education clubs until retirement. Martha and Issac lived in Washington D.C until 1923, until they moved to New Haven, Connecticut where Martha eventually died on March 15, 1933.