The examination was over in the early days of Dec. 1873 and Balfour was now free to devote himself wholly to his original work. Happily, the University had not long before secured the use of two of the tables at the then recently founded Stazione Zoologica at Naples. And upon the nomination of the University, Balfour, about Christmas, started for Naples in company with his friend Mr A. G. Dew-Smith, also of Trinity College. The latter was about to carry on some physiological observations; Balfour had set himself to work out as completely as he could the embryology of Elasmobranch fishes, about which little was at that time known, but which, from the striking characters of the adult animals could not help proving of interest and importance.
From his arrival there at Christmas 1873 until he left in June 1874, he worked assiduously, and with such success, that as the result of the half-year's work he had made a whole series of observations of the greatest importance. Of these perhaps the most striking were those on the development of the urogenital organs, on the neurenteric canal, on the development of the spinal nerves, on the formation of the layers and on the phenomena of segmentation, including a history of the behaviour of nuclei in cell division. He returned home laden with facts and views both novel and destined to influence largely the progress of embryology.
In August of the same year he attended the meeting of the British Association for the Advancement of Science at Belfast; and the account he then gave of his researches formed one of the most important incidents at the Biological Section on that occasion.
In the September of that year the triennial fellowship for Natural Science was to be awarded at Trinity College, and Balfour naturally was a candidate. The election was, according to the regulations, to be determined partly by the result of an examination in various branches of science, and partly by such evidence of ability and promise as might be afforded by original work, published or in manuscript. He spent the remainder of the autumn in preparation for this examination. But when the examination was concluded it was found that in his written answers he had not been very successful; he had not even acquitted himself so well as in the Tripos of the year before, and had the election been determined by the results of the examination alone, the examiners would have been led to choose the gentleman who was Balfour's only competitor. The original work however which Balfour sent in, including a preliminary account of the discoveries made at Naples, was obviously of so high a merit and was spoken of in such enthusiastic terms by the External Referee Prof. Huxley, that the examiners did not hesitate for a moment to neglect altogether the formal written answers (and indeed the papers of questions were only introduced as a safeguard, or as a resource in case evidence of original power should be wanted) and unanimously recommended him for election. Accordingly he was elected Fellow in the early days of October.