Already in 1785, Charles Coulomb pointed out a puzzle that would take more than a century to solve: An electrically charged conductor will lose charge with time, even if the only way to decharge is through air, which was generally considered a good insulator.
In 1900 the two Germans Julius Elster and Hans Geitel, and independently the Scotsman Charles Wilson, offered the explanation that air becomes partly conductive by the presence of ionizing radiation. It was known at this time that the Earth contains slightly radioactive substances that create a natural background radiation. This was believed to be the origin of the ionizing radiation.
The meterologist Franz Linke, with support from Geitel and Elster, set out to test this hypothesis. If the radiation is emitted by the Earth, its intensity should drop with distance from the ground. In 1902 and 1903 Linke, on board of a balloon, found tentative evidence that, after an initial decrease between 1000 and 3000 meters, the intensity of ionizing radiation did increase again. He concluded nevertheless that the origin of ionization in the first line should be sought after on Earth. Linke's research was followed up on by Theodor Wulf, who measured the intensity, among other places, high up in the alps, and found no evidence for the increase of intensity, caused by "cosmic radiation." He was the first to coin the term.
But the situation remained inconclusive. Wulf himself went on to measure the discharge of a charge isolated by air on top of the Eiffel tower. He predicted that in that height (about 300m), the radiation should be about 74% less than on the ground. Instead, he found it to be only 13% less. And in 1910, the Italian physicist Pacini argued that, if the ionizing radiation is emitted by the solids in the Earth, then there should be less of it to find on the sea. That however was not the case either.
On August 7th 1912, Franz Hess and his colleague Kolhorster started for the final one of sevel balloon rides, and this final one lead up to 5350 meter. Despite oxygen mask, Hess reported feeling disoriented, and in fact accidentally turned off one of his detectors already below 4000m. Nevertheless, his measurement clearly showed an increase in the ionization. This was the first conclusive evidence for cosmic radiation.
Then the first world war spelled a time-out for academic curiosity. It wasn't until 1921 that the American physicist Robert Millikan, together with Ira Bowen, got back to this line of research. Their first balloon ride also found an increase in the ionizing radiation, though less pronounced than what Hess found. The New York Times celebrated him as the discoverer of "Millikan radiation." Needless to say, Hess and Kolhorster were not amused.
The measurement of ionizing radiation dramatically improved with the invention of the Geiger counter in 1928 and the spread of bubble chambers. By 1930 there was little controversy left about the existence of cosmic radiation. Franz Hess was awarded the Nobel Prize in physics in 1936.
Today, cosmic radiation is the true high energy frontier, and has lead to a great many discoveries starting with the positron and the muon, and later the Pion, up to the invaluable knowledge that atmospheric neutrinos have brought to the standard model of particle physics. And, who knows, maybe the first evidence for physics beyond the standard model will come from the cosmic ray frontier too.