In the realm of pure chance it is impossible to fix the limits of coincidence. Mr. Proctor's recent work, " Chance and Luck," quotes from Steinmetz this fact:

In 1813 a Mr. Ogden wagered one thousand guineas to one that seven could not bo thrown with a pair of dice ten successive times. Tho wager was accepted (though it was egregiously unfair); and, strange to say, his opponent threw seven nine times running. At this point Mr. Ogden offered four hundred and inference being that they were cured by them. Now wider generalization and more accurate induction establish either that they were inert, or that the patient recovered in spite of them. Great modifications have taken place in the most enlightened medical opinion in regard to the use of water in different diseases, and the relative value of bleeding and the occasions in which it is indicated. The growth of the idea that one or two remedies are sufficient for every disease is one, and the list of thousands of specifics for ten times that number of symptoms another, illustration of deception by coincidence. In 1813 Sir Benjamin Brodie published a work on diseases of the spine and joints, lauding the advantages of calomel, setons, blisters, and bleeding, with long confinement to a recumbent position. In 1834, in a new edition, he confirmed what he had enforced twenty-one years before. In 1850 he thus recants:

A more enlarged experience has satisfied me that, in the very great majority of instances, this painful and loathsome treatment is not oidy not useful, but absolutely injurious. For many years I have ceased to torment my patients thus afflicted in any manner.

Commenting on this, Mr. Proctor says:

Now here we have an instance of a most remarkable series of throws, the like of which has never been recorded before or since. Before they had been made it might have been asserted that the throwing of nine successive sevens with a pair of dice was a circumstance which chance would never bring about; for experience was as much against such an event as it would seem to be against the turning up of a certain number ten successive times at roulette. Yet experience now shows that the thing is possible, and if we are to limit the action of chance we must assert that the throwing of seven ten times in succession is an event which will never happen.

The late Astronomer Royal of England, Prof. Airy, once devoted a considerable part of every day for a week to tossing pennies with special reference to coincidences. During the time he had a run of twenty-eight successive " tails." By the law of chance this could not occur more than once in many hundred millions of times.

I will present one more, which I think will justify the assertion that no coincidence more wonderful has been recorded. The article was found by me in an Italian paper while Louis Napoleon was in prison at Wilhelmshohe.