Final answer:
The easiest way to sample atmospheric gases from past eras is through Antarctic ice cores, which provide insights into historical carbon dioxide levels and past climate change.
Step-by-step explanation:
Samples of atmospheric gases from past eras can most easily be done from Antarctic ice cores. These ice cores are drilled from ice sheets or high mountain glaciers and they contain trapped bubbles of air, representing a snapshot of Earth's past atmosphere. Studying these cores provides insight into historical carbon dioxide levels and climate change through the concentration of gases and isotopes such as deuterium. For example, the Russian Vostok station ice cores give a record of atmospheric CO₂ concentrations over 420,000 years, with deuterium levels indicating past temperatures relative to the modern day. Additionally, other methods like the examination of the chemistry of minerals and the stomatal index of plant fossils offer information on the changing concentration of atmospheric oxygen and carbon dioxide over time.