Between 1911 and 1913, Hess undertook the work that won him the Nobel Prize in Physics in 1936. For many years, scientists had been puzzled by the levels of ionizing radiation measured in the atmosphere. The assumption at the time was that the radiation would decrease as the distance from the earth, the then assumed source of the radiation, increased. The electroscopes previously used gave an approximate measurement of the radiation but indicated that at greater altitude in the atmosphere the level of radiation might actually be higher than that on the ground. Hess approached this mystery first by greatly increasing the precision of the measuring equipment, and then by personally taking the equipment aloft in a balloon. He systematically measured the radiation at altitudes up to  during 1911–1912. The daring flights were made both by day and during the night, at significant risk to himself.
The result of Hesss meticulous work was published in the Proceedings of the Viennese Academy of Sciences, and showed the level of radiation decreased up to an altitude of about , but above that the level increased considerably, with the radiation detected at , being about twice that at sea level. His conclusion was that there was radiation penetrating the atmosphere from outer space, and his discovery was confirmed by Robert Andrews Millikan in 1925, who gave the radiation the name "cosmic rays". Hesss discovery opened the door to many new discoveries in particle and nuclear physics. In particular, both the positron and the muon were first discovered in cosmic rays by Carl David Anderson. Hess and Anderson shared the 1936 Nobel Prize in Physics.