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HEREDITY   305

The mathematician who most frequently helped me later on was the Rev. H. W. Watson, who moreover worked out for me the curious question of the " Probability of the Extinction of Families" [40]. It appeared in 1875 in the Proceedings of the Royal Society as a joint paper, at his desire ; but all the hard work was his : I only gave the first idea and the data. He helped me greatly in my first struggles with certain applications of the Gaussian Law, which, for some reasons that I could never clearly perceive, seemed for a long time to be comprehended with difficulty by mathematicians, including himself. They were unnecessarily alarmed lest the well-known rules of Inverse Probability should be unconsciously violated, which they never were. I could give a striking case of this, but abstain because it would seem depreciatory of a man whose mathematical powers and ability were far in excess of my own. Still, he was quite wrong. The primary objects of the Gaussian Law of Error were exactly opposed, in one sense, to those to which I applied them. They were to get rid of, or to provide a just allowance for errors. But these errors or deviations were the very things I wanted to preserve and to know about. This was the reason that one eminent living mathematician gave me.

The patience of some of my mathematical friends was tried in endeavouring to explain what I myself saw very clearly as a geometrical problem, but could not express in the analytical forms to which they were accustomed, and which they persisted in misapplying. It was a gain to me when I had at last won over Mr. Watson, who put my views into a more suitable shape. H. W. Watson was Second Wrangler of his

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