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 PHILOSOPHICAL PERIODICALS. 141 n.) d. Hence we may speak of ' difference,' though we may have, later, to take account of ' noticeableness '.] S. Landmann. ' Zur Diagnose psychischer Vorgange, rnit besonderer Bezugnahme auf Hamlets Geistes- zustand.' [Against Bosner : Hamlet was sane. Shows no knowledge of the different sources of the play.] Litteraturbericht. Bd. xi., Heft 3 und 4. M. Meyer. ' Ueber Kombinati on stone und einige hierzu in Beziehung stehende akustische Erscheinungen. ' [Helni- holtz' theory is not adequate to all cases. We must distinguish two difference tones : the tone of m - n, and that of 2n - m. Hermann's theories of the median and duplicate interruption tones will not hold. Five vibrations (instead of Exner's 16) give us tone pitch. Difference tones can be mechanically explained, by peripheral analysis of the curve of the vibration. Wundt's theory of tone perception does not work. A valuable article, both in critical and experimental regard.] A. Meinong. ' Ueber die Bedeutung des "Weber'schen Gesetzes,' etc. [III. Ueber Teilvergleichung und Messung. 12. We can compare divisible magnitudes by their parts. Hence there may be more than one relation of comparison (even if similarity is excluded) between two magnitudes. Comparison by parts is (a) arithmetical (A - B) or (6) geometrical (A : B). The resulting numbers are named, and are not relations : the only relations which are magnitudes are difference and similarity (cf. 8). (c) Proportionality is likeness of differences. 13. Measurement is com- parison by parts, aided by physical operations. The mental process of comparison is always present, however ' exact ' the science. 14. True measurement is direct (line by superposed line) or indirect (scale and weights). 15. Indirect measurement is true or surrogate (distance measured by spatial extent, temperature by expansion, velocity by space and time). Surrogate measurement occurs where the magnitudes to be measured are indivisible (cf. 3). 16. And its possibility here is its justi- fication. As for conditions : there is only one surrogate in each case ; that must be a divisible magnitude, or if indivisible, measurable by a surrogate ; its continuum must be strictly correlated with that of the real object of measurement. IV. Ueber Messung von Grossenverschieden- heiten. 17. Difference, an indivisible magnitude, must be measured by a surrogate. Extent (Strecke) serves for many cases, even for tones and colours, but not for all : indeed, there is no single surrogate for all differ- ence. There may be one, however, for difference of measurable magni- tudes of the same continuum. We must determine the functional relation between these and the magnitude of the difference between them. 18. What of the arithmetical relation ? It breaks down in the case of 1 and : their difference is greater than that between any finite magni- tudes. 19. Moreover, equal arithmetical difference (1 and 2, 1001 and 1002) is compatible with unequal differentness ; 20, while unequal arithmetical differences may give the same differentness (constancy of the relative s. d.). The constancy of the relative difference limen is undisputed ; and j. n. d. are equal differentnesses. In the case of supraliminal differentnesses there are apparently negative instances (Merkel), but these are not strong enough to overthrow our thesis. 21. Hence we must for the future distinguish between difference (arithmeti- cal) and differentness, Unterxchied and Verschiedeiiheit. 22. What of the geometrical relation ? It breaks down in the case of the equality of the compared magnitudes ; in other respects, it does better service. 23. What of the relative difference ? It gives equal vahies for equal, unequal for unequal differentness ; it gives for the differentness of equal magni- tudes ; it does not break down badly when one of the compared magni- tudes is or oo. 24. But it has two forms : either of the compared m.s may be divisor. If we test the matter algebraically, with three magni- tudes, we find that the rel. d. with the smaller magnitude as denominator