"But on the 16th day of the same month--which happened to be Monday, and a Council day of the Royal Irish Academy--I was walking in to attend and preside, and your mother was walking with me along the Royal Canal, to which she had perhaps driven; and although she talked with me now and then, yet an UNDERCURRENT of thought was going on in my mind which gave at last a RESULT, whereof it is not too much to say that I felt AT ONCE the importance. An ELECTRIC circuit seemed to CLOSE; and a spark flashed forth the herald (as I FORESAW IMMEDIATELY) of many long years to come of definitely directed thought and work by MYSELF, if spared, and, at all events, on the part of OTHERS if I should even be allowed to live long enough distinctly to communicate the discovery. Nor could I resist the impulse--unphilosophical as it may have been--to cut with a knife on a stone of Brougham Bridge as we passed it, the fundamental formula which contains the SOLUTION of the PROBLEM, but, of course, the inscription has long since mouldered away. A more durable notice remains, however, on the Council Books of the Academy for that day (October 16, 1843), which records the fact that I then asked for and obtained leave to read a Paper on 'Quaternions,' at the First General Meeting of the Session; which reading took place accordingly, on Monday, the 13th of November following." Writing to Professor Tait, Hamilton gives further particulars of the same event. And again in a letter to the Rev. J. W. Stubbs:-- "To-morrow will be the fifteenth birthday of the Quaternions. They started into life full-grown on the 16th October, 1843, as I was walking with Lady Hamilton to Dublin, and came up to Brougham Bridge--which my boys have since called Quaternion Bridge. I pulled out a pocketbook which still exists, and made entry, on which at the very moment I felt that it might be worth my while to expend the labour of at least ten or fifteen years to come. But then it is fair to say that this was because I felt a problem to have been at that moment solved, an intellectual want relieved which had haunted me for at least fifteen years before. "But did the thought of establishing such a system, in which geometrically opposite facts--namely, two lines (or areas) which are opposite IN SPACE give ALWAYS a positive product--ever come into anybody's head till I was led to it in October, 1843, by trying to extend my old theory of algebraic couples, and of algebra as the science of pure time? As to my regarding geometrical addition of lines as equivalent to composition of motions (and as performed by the same rules), that is indeed essential in my theory but not peculiar to it; on the contrary, I am only one of many who have been led to this view of addition."