Abstract: During a series of experiments performed between 1907 and 1911, the Italian physicist Domenico Pacini (Marino 1878-Roma 1934), at that time researcher at the Central Bureau of Meteorology and Geodynamics in Roma, studied the origin of the radiation today called cosmic rays, the nature of which was unknown at that time. In his conclusive measurements in June 1911 at the Naval Academy in Livorno, and confirmed in Bracciano a couple of months later, Pacini, proposing a novel experimental technique, observed the radiation strength to decrease when going from the surface to a few meters underwater (both in the sea and in the lake), thus demonstrating that such radiation could not come from the Earth's crust. Pacini's conclusive experiment was performed, and the results published (in Italian), one year before the famous balloon experiment by Victor Hess, who found the ionization rate to increase with height. While Hess is today celebrated as the discoverer of cosmic rays, Pacini's work was largely overlooked. Hess was awarded the Nobel Prize in Physics in 1936, two years after the death of Pacini, who had become a full professor of Experimental Physics at the University of Bari and the Director of the local Institute of Physics. The discovery of cosmic rays --a milestone in science-- involved several scientists in Europe and in the United States of America and took place during a period characterized by nationalism and lack of communication. Historical, political and personal facts, embedded in the pre- and post-World War I historical context, might have contributed to the substantial disappearance of Pacini from the history of science. This article aims to give an unbiased historical account of the discovery of cosmic rays; in the centenary of Pacini's pioneering experiments, his work, which employed a technique that was complementary to, and independent from that of Hess, will be duly taken into consideration. A translation into English of three fundamental early articles by Pacini is provided in the Appendix.