At Cambridge he was chosen, in the autumn of 1880, President of the Philosophical Society, and in the December of that year a brilliant company were gathered together at the Annual Dinner to do honour to their new young President. Otherwise nothing as yet had been done for him in his own University in the way of recognition of his abilities and services; and he still remained a Lecturer of Trinity College, giving lectures in a University building. An effort had been made by some of his friends to urge the University to take some step in this direction; but it was thought at that time impossible to do anything. In 1881 a great loss fell upon the sister University of Oxford in the death of Prof. George Rolleston; and soon after very vigorous efforts were made to induce Balfour to become a candidate for the vacant chair. The prospect was in many ways a tempting one, and Balfour seeing no very clear way in the future for him at his own University, was at times inclined to offer himself, but eventually he decided to remain at Cambridge. Hardly had this temptation if we may so call it been overcome when a still greater one presented itself. Through the lamented death of Sir Wyville Thomson in the winter of 1881-2, the chair of Natural History at Edinburgh, perhaps the richest and most conspicuous biological chair in the United Kingdom, became vacant. The post was in many ways one which Balfour would have liked to hold. The teaching duties were it is true laborious, but they had in the past been compressed into a short time, occupying only the summer session and leaving the rest of the year free, and it seemed probable that this arrangement might be continued with him. The large emolument would also have been grateful to him inasmuch as he would have felt able to devote the whole of it to scientific ends; and the nearness to Whittinghame, his native place and brother's home, added to the attractions; but what tempted him most was the position which it would have given him, and the opportunities it would have afforded, with the rich marine Fauna of the north-eastern coast close at hand, to develop a large school of Animal Morphology. The existing Professors at Edinburgh were most desirous that he should join them, and made every effort to induce him to come. On the part of the Crown, in whose hands the appointment lay, not only were distinct offers made to him, but he was repeatedly pressed to accept the post. Nor was it until after a considerable struggle that he finally refused, his love for his own University in the end overcoming the many inducements to leave; he elected to stay where he was, trusting to the future opening up for him some suitable position. In this decision he was undoubtedly influenced by the consideration that Cambridge, besides being the centre of his old friendships, had become as it were a second home for his own family. By the appointment of Lord Rayleigh to the chair of Experimental Physics his sister Lady Rayleigh had become a resident, his sister Mrs Sidgwick had lived there now for some years, and his brother Gerald generally spent the summer there; their presence made Cambridge doubly dear to him.

At the close of the Michaelmas term, with feelings of relief at having completed his Comparative Embryology, the preparation of the second volume of which had led to almost incessant labour during the preceding year, he started to spend the Christmas vacation with his friend Kleinenberg at Messina. Stopping at Naples on his way thither he found his pupil Caldwell, who had been sent to occupy the University table at the Stazione Zoologica, lying ill at Capri, with what proved to be typhoid fever. The patient was alone, without any friend to tend him, and his mother who had been sent for had not yet arrived. Accordingly Balfour (with the kindness all forgetful of himself which was his mark all his life through) stayed on his journey to nurse the sick man until the mother came. He then went on to Messina, and there seemed to be in good health, amusing himself with the ascent of Etna. Yet in January, soon after his return home, he complained of being unwell, and in due time distinct symptoms of typhoid fever made their appearance. The attack at first promised to be severe, but happily the crisis was soon safely passed and the convalescence was satisfactory.

While yet on his sick bed, a last attempt was made to induce him to accept the Edinburgh offer, and for the last time he refused. These repeated offers, and the fact that the dangers of his grave illness had led the University vividly to realize how much they would lose if Balfour were taken away from them, encouraged his friends to make a renewed effort to gain for him some adequate position in the University. This time the attempt was successful, and the authorities took a step, unusual but approved of by the whole body of resident members of the University; they instituted a new Professorship of Animal Morphology, to be held by Balfour during his life or as long as he should desire, but to terminate at his death or resignation unless it should be otherwise desirable. Accordingly in May, 1882, he was admitted into the Professoriate as Professor of Animal Morphology.

During his illness his lectures had been carried on by his Demonstrator, Mr Adam Sedgwick, who continued to take his place during the remainder of that Lent Term and during the ensuing Easter Term. The spring Balfour spent partly in the Channel Islands with his sister Alice, partly in London with his eldest brother, but in the course of the Easter Term returned to Cambridge and resumed his work though not his lectures. His recovery to health was steady and satisfactory, the only drawback being a swelling over the shin-bone of one leg, due to a blow on the rocks at Sark; otherwise he was rapidly becoming strong. He himself felt convinced that a visit to the Alps, with some mountaineering of not too difficult a kind, would complete his restoration to health. In this view many of his friends coincided; for the experience of former years had shewn them what a wonderfully beneficial effect the Alpine air and exercise had upon his health. He used to go away pale, thin and haggard, to return bronzed, clear, firm and almost stout; nor was there anything in his condition which seemed to forbid his climbing, provided that he was cautious at the outset. Accordingly, early in June he left Cambridge for Switzerland, having long ago, during his illness in fact, engaged his old guide, Johann Petrus, whom he had first met in 1880, and who had always accompanied him in his expeditions since.

His first walking was in the Chamonix district; and here he very soon found his strength and elasticity come back to him. Crossing over from Montanvert to Courmayeur, by the Col du Géant, he was attracted by the peak called the Aiguille Blanche de Peuteret, a virgin peak, the ascent of which had been before attempted but not accomplished. Consulting with Petrus he determined to try it, feeling that the fortnight, which by this time he had spent in climbing, had brought back to him his old vigour, and that his illness was already a thing of the past.

There is no reason to believe that he regarded the expedition as one of unusual peril; and an incident which at the time of his death was thought by some to indicate this was in reality nothing more than a proof of his kindly foresight. The guide Petrus was burdened by a debt on his land amounting to about £150. In the previous year Balfour and his brother had come to know of this debt; and, seeing that no Alpine ascent is free from danger, that on any expedition some accident might carry them off, had conceived the idea of making some provision for Petrus' family in case he might meet with sudden death in their service. This suggestion of the previous year Balfour carried out on this occasion, and sent home to his brother Gerald a cheque of £150 for this purpose. But the cheque was sent from Montanvert before he had even conceived the idea of ascending the Aiguille Blanche. It was not a provision for any specially dangerous ascent, and must be regarded as a measure prompted not by a sense of coming peril but rather by the donor's generous care for his servant.

On Tuesday afternoon, July 18, he and Petrus, with a porter to carry provisions and firing to their sleeping-place on the rocks, set out from Courmayeur, the porter returning the same night. They expected to get back to Courmayeur some time on the Thursday, but the day passed without their appearing. This did not cause any great anxiety because it was supposed that they might have found it more convenient to pass over to the Chamonix side than to return to Courmayeur. When on Friday however telegrams dispatched to Chamonix and Montanvert brought answers that nothing had been seen of them, it became evident that some accident had happened, and an exploring party set out for the hills. It was not until early on the Sunday morning that this search party found the bodies, both partly covered with snow, lying on the Glacier de Fresney, below the impassable icefall which separates the upper basin of the glacier from the lower portion, and at the foot of a couloir which descends by the side of the icefall. Their tracks were visible on the snow at the top of the couloir. Balfour's neck was broken, and his skull fractured in three places; Petrus' body was also fractured in many places. The exact manner of their death will never be known, but there can be no doubt that, in Balfour's case at all events, it was instantaneous, and those competent to form a judgment are of opinion that they were killed by a sudden fall through a comparatively small height, slipping on the rocks as they were descending by the side of the ice-fall, and not precipitated from the top of the couloir. There is moreover indirect evidence which renders it probable that in the fatal fall Petrus slipped first and carried Balfour with him. Whether they had reached the summit of the Aiguille and were returning home after a successful ascent or whether they were making their way back disheartened and wearied with failure, is not and perhaps never will be known. Since the provisions at the sleeping-place were untouched, the deaths probably took place on Wednesday the 19th. The bringing down the bodies proved to be a task of extreme difficulty, and it was not till Wednesday the 26th that the remains reached Courmayeur, where M. Bertolini, the master of the hotel, and indeed everyone, not least the officers of a small body of Italian troops stationed there, shewed the greatest kindness and sympathy to Balfour's brothers, Gerald and Eustace, who hastened to the spot as soon as the news of the terrible disaster was telegraphed home. Mr Walter Leaf also and Mr Conway, friends of Balfour, the former a very old one, who had made their way to Courmayeur from other parts of Switzerland as soon as they heard of the accident, rendered great assistance. The body was embalmed, brought to England, and buried at Whittinghame on Saturday, Aug. 5, the Fellows of Trinity College holding a service in the College Chapel at the same time.

In person he was tall, being fully six feet in height, well built though somewhat spare. A broad forehead overhanging deeply set dark brown eyes whose light shining from beneath strongly marked eye-brows told all the changes of his moods, slightly prominent cheek-bones, a pale skin, at times inclined to be even sallow, dark brown hair, allowed to grow on the face only as a small moustache, and slight whiskers, made up a countenance which bespoke at once strength of character and delicacy of constitution. It was an open countenance, hiding nothing, giving sign at once, both when his body was weary or weak, and when his mind was gladdened, angered or annoyed.

The record of some of his thoughts and work, all that he had given to the world will be found in the following pages. But who can tell the ideas which had passed into his quick brain, but which as yet were known only to himself, of which he had given no sign up to that sad day on which he made the fatal climb? And who can say whither he might not have reached had he lived, and his bright young life ripened as years went on? This is not the place to attempt any judgment of his work: that may be left to other times, and to other hands; but it may be fitting to place here on record a letter which shews how much the greatest naturalist of this age appreciated his younger brother. Among Balfour's papers was found a letter from Charles Darwin, acknowledging the receipt of Vol. II. of the Comparative Embryology in the following words:

"July 6, 1881.