six must begin some time to turn oftener." On the contrary, if, after the twentieth throw, it turns up exactly one-sixth of the times, its frequency approximates indefinitely in the long run toward one-sixth.
The table given in the April number, p. 715, shows that, as the number of throws increases, the difference between the number of sixes and one-sixth of the number of throws generally increases, being proportional to the square root of that number; at the same time the difference between the proportion of sixes and one-sixth generally decreases, in the same proportion that the discrepancy of the number increases.
In 6 throws, the number of sixes will probably lie between 0 and 2; the proportion between 0 and 0.3333. . .
In 60 throws, the number of sixes will probably lie between 8 and 12; the proportion between 0.133 and 0.200.
In 600 throws, the number of sixes will probably lie between 93 and 107; the proportion between 0.155 and 0.178.
In 6,000 throws, the number of sixes will probably lie between 980 and 1,020; the proportion between .163 and .170.
In 60,000 throws, the number of sixes will probably lie between 9,938 and 10,062; the proportion between .1656 and .1677; and so on.
All this relates to independent events; that is, those of which the occurrence of one neither increases nor diminishes the probability of the occurrence of another. If an urn contains a number of balls, of which one-sixth are black and the rest white, every drawing of a black ball decreases the relative number of black balls among those which remain. If there were but one hundred and twenty balls in all, at first, and the first twenty drawn were black, it becomes absolutely certain that all the remaining drawings will be of white balls. The greater the total number, however, the less influence will the run of twenty black drawings have upon those which follow; and, if the total number were endless, the case would be similar to the repeated throwing of a die.
THE recent activity of psychological study, and the many valuable results arising from it, induced some of its leading students, two or three years ago, to found a new periodical entitled Mind: a Quarterly Review of Psychology and Philosophy, to be devoted to the investigation of mental phenomena, especially from the hitherto neglected physiological side. This review has done excellent service. It was a protest against the inadequacy of the old method of metaphysical and purely introspective study, and represented that class of philosophical thinkers who hold that, in treating of mind, its organic conditions are not to be lost sight of, but that mind and body are to be considered together.
A further and. very significant step, in the same direction, has now been taken by the establishment of another quarterly magazine, under the title of Brain: a Journal of Neurology. The starting-point is here physiological, and the brain and nervous system are studied with reference to their various vital and psychical functions and effects. The editors are all eminent medical men, who have either acquired distinction through large experience in the treatment of nervous maladies involving intellectual and emotional derangement, or have achieved eminence in the department of experimental physiology of the nervous system. The method is here thoroughly scientific. The brain is not merely something to be recognized, but it is taken as the pri-
- Brain: A Journal of Neurology. Edited by J. C. Bucknill, M. D., J. Crichton-Browne, M. D., D. Ferrier, M. D., and J. Hughlings-Jackson, M. D. 142 pages quarterly. Price, 3s. 6d. New York: Macmillan & Co.