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at the time; the opinions of most of us, including myself, were of course largely guided by those of the eminent mathematicians who were also members of it, and by the result of private inquiries. The opinions in favour of Sylvester prevailed ; Cayley received the Medal a few years subsequently.

Never was a man whose outer physique so belied his powers as that of Cayley. There was something eerie and uncanny in his ways, that inclined strangers to pronounce him neither to be wholly sane nor gifted with much intelligence, which was the very reverse of the truth. Again, he appeared so frail as to be incapable of ordinary physical wuurlk ; ilot r1 bit of it, One morning lie coached us as usual and dined early with us at our usual hour. The next morning he did the same, all just as before, but it afterwards transpired that he had not been to bed at all in the meantime, but had tramped all night through over the moors to and about Loch Rannoch. As to memory, I found by pure accident that he could repeat poetry by the yard so to speak, and that of many kinds. His shy, retiring ways did no justice whatever to his gigantic mental capacity.

I was, in a very humble way, able to compare the work of various mathematical teachers with that of Cayley. The latter moved his symbols in battalions, along broad roads, careless of short cuts, and he managed them with the easy command of a great general. The very look of his papers, written in firm handwriting and well proportioned lengths of line, bore thoroughness and accuracy on their face. This is not over fanciful. William Spottiswoode (18251883), himself a mathematician and President of the