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 branches, the theory of probability has made very insignificant progress since the time of Laplace. Improvements and simplicationssimplifications [sic] in the mode of exposition have been made by A. De Morgan, G. Boole, A. Meyer (edited by E. Czuber), J. Bertrand. Cournot's and Westergaard's treatment of insurance and the theory of life-tables are classical. Applications of the calculus to statistics have been made by L. A. J. Quetelet (1796–1874), director of the observatory at Brussels; by Lexis; Harald Westergaard, of Copenhagen; and Düsing.

Worthy of note is the rejection of inverse probability by the best authorities of our time. This branch of probability had been worked out by Thomas Bayes (died 1761) and by Laplace (Bk. II., Ch. VI. of his Théorie Analytique). By it some logicians have explained induction. For example, if a man, who has never heard of the tides, were to go to the shore of the Atlantic Ocean and witness on $$\scriptstyle{m}$$ successive days the rise of the sea, then, says Quetelet, he would be entitled to conclude that there was a probability equal to $$\scriptstyle{\frac{m+1}{m+2}}$$ that the sea would rise next day. Putting $\scriptstyle{m=0}$, it is seen that this view rests upon the unwarrantable assumption that the probability of a totally unknown event is $\scriptstyle{\frac{1}{2}}$,|undefined or that of all theories proposed for investigation one-half are true. W. S. Jevons in his Principles of Science founds induction upon the theory of inverse probability, and F. Y. Edgeworth also accepts it in his Mathematical Psychics.

The only noteworthy recent addition to probability is the subject of "local probability," developed by several English and a few American and French mathematicians. The earliest problem on this subject dates back to the time of Buffon, the naturalist, who proposed the problem, solved by himself and Laplace, to determine the probability that a short needle, thrown at random upon a floor ruled with equidistant parallel