[1] He is noted particularly for "Child's law" (1911), which is an equation that describes the electric current that flows between the plates of a vacuum tube.

[2] Vacuum tubes were the main components in electronics from about 1905 to 1960, when transistors and integrated circuits mostly supplanted them.

[3] Child's Law is still a staple of textbooks treating charged particle motion in vacuum and in solids.

In 1898 he was appointed a professor of physics at Colgate University in Hamilton, New York, where he spent the rest of his career.

The application to electrons was made in 1913 by Irving Langmuir,[10] and the equation is also called the Child-Langmuir Law because of this.