Henry's great-granduncle was Brevet Brigadier General Daniel Brodhead, who served as colonel of the 8th Pennsylvania Regiment in the American Revolution.

On account of his great experience and thorough knowledge of such subjects, Linderman was appointed by the secretary of the treasury to examine the mint in San Francisco, and to adjust some intricate bullion questions.

In 1871, he was sent by the U.S. government to London, Paris, and Berlin to collect information concerning the mints in those places, and in 1872 made an elaborate report on the condition of the market for silver.

In order to find an outlet for the great amount of silver in the United States, Linderman proposed the trade dollar.

During Linderman's administration, he gathered a choice collection of specimen coins, which were to be sold by auction in New York in 1887, but the U.S. government claimed them.