Barkla's first experimental work under J J Thomson related to the velocity of electric waves along wires, and the results were published in June 1901. It was in 1902 that he began under Thomson the researches on X-rays that were to occupy him for the rest of his life. In the same year he returned as Oliver Lodge Fellow to Liverpool, where Wilberforce had succeeded Lodge as Professor of Physics.
During the next few years Barkla made a series of fundamental discoveries relating to the secondary radiations from substances traversed by X-rays. He found that there are two types of secondary radiations, "scattered" and "characteristic"; he showed that X-rays, like light, maybe polarised. In 1909 he was appointed Professor of Physics at King's College, London. He now made use of the characteristic X-radiations which he had discovered to investigate the absorption of X-rays and their ionising and photographic effects.
In 1912 Barkla was elected a Fellow of the Royal Society, and in the following year he was appointed to the Chair of Natural Philosophy in the University of Edinburgh. In spite of the great difficulties which the outbreak of war put in the way of his own experimental work he was soon able with the aid of some of his pupils to make further advances, especially regarding the relation between the characteristic X-radiations and the accompanying corpuscular rays. In his Bakerian lecture, given before the Royal Society in 1916 and published in the Phil. Trans. in 1917, Barkla brought together the results of his work on X-rays up to that date and discussed their theoretical bearings. By this time the work of Laue and the Braggs had made it possible to measure X-ray wave-lengths, and Moseley had investigated the X-ray spectra of a large number of the elements; the Bohr-Rutherford conception of the atom had been introduced, and the nature of ionisation by X-rays had been made clear by the cloud method. Barkla was thus able to give a more definite picture of the nature of the secondary X-radiations than had been possible in his earlier publications. As regards scattering of X-radiation, his experiments had shown that the radiation scattered at right angles to the primary beam is polarised (just as ordinary light is polarised when scattered by small particles), that the distribution of the radiation scattered agrees closely with that calculated on the assumption that X-rays are electromagnetic waves; and that the fraction of the energy scattered per centimetre of path agrees closely with what is to be expected if the number of scattering electrons per atom is equal to the atomic number. Barkla concluded that the phenomena of scattering may all be explained on the electromagnetic theory and are difficult to reconcile with the view that X-rays travel as localised quanta. He believed that the facts relating to the characteristic radiations could also best be explained without bringing in the idea of localised quanta. Barkla's earlier work had proved the existence of two series of such characteristic radiations, the K and L series. He was now able to assign the origin of the K-radiation to the fall of an outer electron of an atom to fill the vacancy left by the ejection of a K-electron. Barkla studied the corpuscular rays associated with the characteristic X-radiations; it is perhaps only in the light of the much later experiments of Auger in which the effects of individual quanta could be followed that Barkla's results can be satisfactorily interpreted. Barkla considered that he had found definite evidence of the existence of a series of characteristic radiations, the "J" radiations, of higher frequency than the K series. There can be little doubt that the phenomena interpreted by Barkla in this way were really connected with the Compton effect to be discovered some years later.
Barkla was awarded the Hughes Medal by the Royal Society in 1917, and he received the Nobel Prize for Physics for that year.
Barkla was slow in accepting Compton's discovery of the occurrence of scattering accompanied by change of wave-length, with its implication that X-rays travel in localised quanta. He continued to believe that the generally accepted theories did not account for all the phenomena associated with the scattering and absorption of X-rays; he spent much time in subsequent years in trying with the help of his pupils to interpret certain baffling irregularities which constituted the "J phenomenon".
Barkla was a very good lecturer; his fine voice made it easy for him to hold the attention of a large class. He was always accessible to the ordinary students and ready to give up his time to advising them in their difficulties. He had an unusually wide experience as an examiner and excelled in that work.
Barkla married in 1907 Mary Esther, the elder daughter of J T Cowell of Douglas, Isle of Man. They had three sons and one daughter. The youngest son, who had entered upon what promised to be a distinguished career in medicine, was accidentally killed while on active service in North Africa in 1943.
Barkla was elected a Fellow in 1914 and died on October 23, 1944.