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.

Almost immediately after, the little book on Embryology appeared, on which he and I had been at work, he doing his share even while his hands and mind were full of the Elasmobranch inquiry. The title-page was kept back some little time in order that his name might appear on it with the addition of Fellow of Trinity, a title of which he was then, and indeed always continued to be, proud. He also published in the October number of the Quarterly Journal of Microscopical Science a preliminary account of his Elasmobranch researches.

He and his friends thought that after these almost incessant labours, and the excitement necessarily contingent upon the fellowship election, he needed rest and change. Accordingly on the 17th of October he started with his friend Marlborough Pryor on a voyage to the west coast of South America. They travelled thither by the Isthmus of Panama, visited Peru and Chili, and returned home along the usual route by the Horn; reaching England some time in Feb. 1875.

Refreshed by this holiday, he now felt anxious to complete as far as possible his Elasmobranch work, and very soon after his return home, in fact in March, made his way again to Naples, where he remained till the hot weather set in in May. On his return to Cambridge, he still continued working on the Elasmobranchii, receiving material partly from Naples, partly from the Brighton Aquarium, the then director of which, Mr Henry Lee, spared no pains to provide him both with embryo and adult fishes. While at Naples, he communicated to the Philosophical Society at Cambridge a remarkable paper on “The Early Stages of Vertebrates,” which was published in full in the Quarterly Journal of Microscopical Science, July, 1875; he also sent me a paper on “The Development of the Spinal Nerves”, which I communicated to the Royal Society, and which was subsequently published in the Philosophical Transactions of 1876. He further wrote in the course of the summer and published in the Journal of Anatomy and Physiology in October, 1875, a detailed account of his “Observations and Views on the Development of the Urogenital Organs.”

Some time in August of the same year he started in company with Mr Arthur Evans and Mr J. F. Bullar for a second trip to Finland, the travellers on this occasion making their way into regions very seldom visited, and having to subsist largely on the preserved provisions which they carried with them, and on the produce of their rods and guns. From a rough diary which Balfour kept during this trip it would appear that while enjoying heartily the fun of the rough travelling, he occupied himself continually with observations on the geology and physical phenomena of the country, as well as on the manners, antiquities, and even language of the people. It was one of his characteristic traits, a mark of the truly scientific bent of his mind, of his having, as Dohrn soon after Balfour's first arrival at Naples said, 'a real scientific head,' that every thing around him wherever he was, incited him to careful exact observation, and stimulated him to thought.

In the early part of the Long Vacation of the same year he had made his first essay in lecturing, having given a short course on Embryology in a room at the New Museums, which I then occupied as a laboratory. Though he afterwards learnt to lecture with great clearness he was not by nature a fluent speaker, and on this occasion he was exceedingly nervous. But those who listened to him soon forgot these small defects as they began to perceive the knowledge and power which lay in their new teacher.

Encouraged by the result of this experiment, he threw himself, in spite of the heavy work which the Elasmobranch investigation was entailing, with great zeal into an arrangement which Prof. Newton, Mr J. W. Clark and myself had in course of the summer brought about, that he and Mr A. Milnes Marshall, since Professor at Owens College, Manchester, should between them give a course on Animal Morphology, with practical instruction, Prof. Newton giving up a room in the New Museums for the purpose.

In the following October (1875) upon Balfour's return from Finland, these lectures were accordingly begun and carried on by the two lecturers during the Michaelmas and Lent Terms. The number of students attending this first course, conducted on a novel plan, was, as might be expected, small, but the Lent Term did not come to an end before an enthusiasm for morphological studies had been kindled in the members of the class.

The ensuing Easter term (1876) was spent by Balfour at Naples, in order that he might carry on towards completion his Elasmobranch work. He had by this time determined to write as complete a monograph as he could of the development of these fishes, proposing to publish it in instalments in the Journal of Anatomy and Physiology, and subsequently to gather together the several papers into one volume. The first of these papers, dealing with the ovum, appeared in Jan. 1876; most of the numbers of the Journal during that and the succeeding year contained further portions; but the complete monograph did not leave the publisher's hands until 1878.