Martha spent much of her scientific career interested in the quantitative analysis of various elements. Specifically, she studied the composition of ammonium phosphates in magnesium, zinc, and cadmium. Her study of ammonium phosphates was later used as a tool in her later analytical work. Martha spent much of her research career developing several analytical procedures for metal estimations and separations, with a special focus on gravimetric estimations of manganese and magnesium. Her other work included the analysis of prehistoric bronzes without major disruption to the metal composition and the study of organic esters.
While in graduate school at Yale, she worked for Andrew Gooch in the Kent Chemical Laboratory. Throughout her time in graduate school, she published nine papers in the American Journal of Science and in Zeitschrift für anorganische und allgemeine Chemie for her work in analytical chemistry. Four of the nine papers she published individually and the other five in collaboration with Gooch. After her marriage to Issac King Phelps in 1904, she collaborated with her husband to study ester synthesis. The work resulted in six more publications. In total, she published fifteen papers throughout the span of her ten year career as a chemist.
Martha's work is primarily recognized for her development of a protocol estimating arsenic as ammonium magnesium arsenate. The paper detailing the procedure was published in 1900. The protocol became a standard method of arsenic estimation in quantitative analysis studies and was written into textbooks for several years.