An element is defined by the number of protons in the nucleus of its atoms, but its chemical reactivity is determined by the number of electrons in its outer shell—a property fundamental to the organization of the periodic table of the elements.

In the second half of the nineteenth century, data from laboratories in France, England, Germany, and Italy were assembled into a pamphlet by Stanislao Cannizzaro (1826–1910), a teacher in what is now northern Italy. In this pamphlet, Cannizzaro demonstrated a way to determine a consistent set of atomic weights, one weight for each of the elements then known. Cannizzaro distributed his pamphlet and explained his ideas at an 1860 international meeting held in Karlsruhe, Germany, that was organized to discuss new ideas about the theory of atoms. When Russian...