Edgar was born on September 25, 1871, in Farmington, New York, the son of Amos C. and Emma L. (Smith) Brown. He was a graduate of Union College in Schenectady, New York, and earned his PhD degree in 1895. Arthur began working for the U.S. Department of Agriculture as a botanist in the Seed Testing Laboratory in the 1890s and was the principal botanist from 1902 to 1938.
Edgar was author or first author of over 20 U.S. Department of Agriculture publications that were important to the burgeoning field seed business, both to seeds men and farmers. Among his publications are his 14-page bulletin on alfalfa seed (1904); germination, growing, handling and adulteration of bluegrass seeds (1905); germination of packeted vegetable seeds (1912); how seed testing helps the farmer (1916); and what the farmer should expect from the seeds man (1920). He was the founder of the Official Seed Analysis Association and an honorary fellow of the International Institute of Agricultural Botany of Cambridge, England. His most important works involved testing techniques and standards, such as a quick method for determining moisture in grain in 1907, with Joseph Duvel, and a seed counter in 1928.
He married Elizabeth V. Tefft on August 14, 1902. His second marriage was to Elizabeth D. Gould on June 6, 1936. He died on November 10, 1969, at the age of 98 in Frederick, Maryland.
Edgar was a 1900 founder of the Washington Biologists’ Field Club and was awarded an honorary membership in 1960. Edgar served as secretary/trearsurer from 1900 to 1901.