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Dove first observed that from two tuning-forks, one held beside each ear, beats would arise, though neither fork were sounding loudly enough to be heard in the remoter ear. S. concludes that the interference takes place in the central organ. He also shows that difference tones, which disappear under similar circumstances, can be heard together with beats when one fork is set before one ear and the other on the head, or when both forks are set on the head.

The article is, for the most part, a mathematical discussion of the method of right and wrong cases, and of the author's allied method of equal and unequal cases.

Taking Gauss’s theory of observation errors as a basis, M. finds formulae for the probable positive and negative errors and for the measure of accuracy for the m. of r. and w. cases where equal stimuli are used, as well as for the distribution of the ‘equal’ cases with stimuli of different intensities. Formulae are also found for the elimination of the constant errors of the method.

Distinguishing between the method of mean gradations with minimal changes when the object is to find a ‘middle’ between two given stimuli, and his own method of mean gradations when ‘middle’ judgments are avoided, the author shows that such ‘middle’ judgments as do occur are to be distributed according to the formulae of his method of equal and unequal cases. A similar plan of distribution is to be followed in case of judgments of ‘double’ in the author’s method of “doubled stimuli.” The relations of the threshold values in the several methods of r. and w. c., of equal and unequal c., and of minimal changes, are also mathematically deduced.

Spencer holds that our knowledge, not less than the outer world, has evolved from a condition where its elements were still homogeneous and united. In the course of development they gradually become separated and opposed to each other ; the ultimate reality remains however in spite of all differentiating, the unconditioned in which the conditioned factors of knowledge are united. P. divides his discussion into (1) the original unity; (2) the negation of the unity; (3) the restoration of unity. He holds that neither of the two factors, subject and object,