In recent years, scientists have made sizable gains in what was once considered an impossible art — reconstructing the history of Earth’s atmosphere back into the dim past. They can now peer across more than a half billion years. The scientists have learned about the changing makeup of the vanished gases by teasing subtle clues from fossilized soils, plants and sea creatures. They have also gained insights from computer models that predict how phenomena like eroding rocks and erupting volcanoes have altered the planet’s evolving air. “It’s getting a lot more attention,” Michael C. MacCracken, chief scientist of the Climate...