"I had been wishing for an occasion of corresponding a little with you on Quaternions: and such now presents itself, by your mentioning in your note... that you "have been reflecting on several points connected with them"... "particularly on the Multiplication of Vectors. ...No more important, or ...fundamental question, in the whole theory of Quaternions, can be proposed than that which thus inquires What is such Multiplication? What are its Rules, its Objects, its Results? What Analogies exist between it and other Operations, which have received the same general Name? And finally, what is (if any) its Utility? ...[R]eferring to an ante-quaternionic time, when you were a mere child, but had caught from me the conception of a Vector, as represented by a Triplet... I happen to be able to put the finger of memory upon the year and month—October, 1843—when... the desire to discover the laws of the multiplication referred to regained with me a certain strength and earnestness, which had for years been dormant, but was then on the point of being gratified, and was occasionally talked of with you. Every morning in the early part of the... month, on my coming down to breakfast, your (then) little brother William Edwin, and yourself, used to ask me, "Well, Papa, can you multiply triplets"? Whereto I was always obliged to reply, with a sad shake of the head: "No, I can only add and subtract them." But on the 16th day of the same month… I was walking… and your mother was walking with me, along the … and although she talked with me now and then, yet an under-current of thought was going on in my mind, which gave at last a result, whereof... 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 , as we passed it, the fundamental formula with the symbols, i, j, k; namely,i^2 = j^2 = k^2 = ijk = -1,"