Experiments with light and matter in the late 1800s uncovered a reproducible but puzzling regularity. When light was shown through purified gasses, certain frequencies (colors) did not pass. These dark absorption 'lines' followed a distinctive pattern: the gaps between the lines decreased steadily. By 1889, the Rydberg formula predicted the lines for hydrogen gas using only a constant number and the integers to index the lines. The origin of this regularity was unknown. Solving this mystery would eventually become the first major step toward quantum mechanics.