In 1888, Swedish physicist Johannes Rydberg working from the 1885 Balmer formula noticed that the atomic numbers of the noble gases was equal to doubled sums of squares of simple numbers: 2 = 2·1, 10 = 2(1 + 2), 18 = 2(1 + 2 + 2), 36 = 2(1 + 2 + 2 + 3), 54 = 2(1 + 2 + 2 + 3 + 3), 86 = 2(1 + 2 + 2 + 3 + 3 + 4). This finding was accepted as an explanation of the fixed lengths of periods and led to repositioning of the noble gases from the left edge of the table, in group 0, to the right, in group VIII. Unwillingness of the noble gases to engage in chemical reaction was explained in the alluded stability of closed noble gas electron configurations; from this notion emerged the octet rule originally referred to as Abegg's Rule of 1904. Among the notable works that established the importance of the periodicity of eight were the valence bond theory, published in 1916 by American chemist Gilbert N. Lewis and the octet theory of chemical bonding, published in 1919 by American chemist Irving Langmuir. The chemists' approach during the period of the Old Quantum Theory (1913 to 1925) was incorporated into the understanding of the electron shells and orbitals under current quantum mechanics. A real pioneer who gave us the foundation for our current model of electrons is Irving Langmuir. In his 1919 paper, he postulated the existence of "cells", which we now call orbitals, which could each only contain two electrons, and these were arranged in "equidistant layers" which we now call shells. He made an exception for the first shell to only contain two electrons. These postulates were introduced on the basis of Rydberg's rule which Niels Bohr had used not in chemistry, but in physics, to apply to the orbits of electrons around the nucleus. In the Langmuir paper, he introduced the rule as 2N where N was a positive integer.