Albert Fall would resign on March 4, 1921 to become Secretary of the Interior. A special election was held in September 1921.
The source for the canvass is New Mexico Election Returns 1911-1969, compiled by the New Mexico Secretary of State in 1970 and available at the state library in Santa Fe.
Source for Popular Vote data: New Mexico Secretary of State, "For U.S. Senator," Tabular Statement of the aggregate vote cast in the State of New Mexico (Santa Fe, 1918)