Page:Mind (Old Series) Volume 9.djvu/471

 w. WUKDT'S LOGIK, n. 459 occupied by the well-known treatises of Mill and Jevons. Thus it begins with a discussion upon the analysis of natural pheno- mena preliminary to Inductive processes, and then proceeds to give the following logical rule as a substitute for the more numerous mles of Herschel and Mill : " Amongst the circum- stances which accompany any phenomenon those are to be regarded as essential conditions upon whose removal the pheno- menon itself is removed, and whose quantitative alteration V^ produces a quantitative alteration in the phenomenon ". This rule points to two experimental methods which may be briefly designated as those of Elimination, and Graduation of Conditions. A moderate criticism of Mill's well-known five methods follows, resting in great part on the ground that several of them &i'e~, merely specialisations of others. After the qualitative determination of phenomena and their conditions, follows in natural order their quantitative determina- tion, for without this little progress is attained in physical inquiry. Mill has scarcely touched at all upon this depart- ment. Some of the principal considerations to which it leads are those of the various physical adjuncts and improvements to Observation and Experiment such for instance as micro- scopes, telescopes, &c., which are briefly indicated and described but still more important, from a logical point of view, are the very intricate questions of the establishment of units for physical investigations. Such units are naturally divided into those of Space, of Weight or Mass, and of Time. The qualifications to be demanded of these, and the nature and extent of their mutual independence, are discussed ; and it is shown how in the progress of modern science the two latter kinds of unit tend almost invariably to become dependent upon the former ; as when (to take familiar instances) intervals of time are measured by the movement of the hands of a clock, or differences of weight by the position of the index of a balance. This chapter concludes with a discussion of some of those border-questions of philosophy and physics, as to the limits^ (Gr-rnzheyriffe) to be admitted in either direction : viz., in the one* direction, whether the atom or molecule is to be considered as of finite size, and in the other whether the physical universe itself is to be considered as limited. Discussions of this kind have become to some extent popularised in England through such works as the Unseen Universe. Prof. Wundt recognises six dis- tinct assumptions on this topic which deserve separate discus- sion : viz., that the hypothesis of absolute limitation may be considered to embrace time only, mass and space being unlimited ; or time and mass, space alone being unlimited ; or all three alike. And the same division may be made in respect of the hypothesis of absolute infinity. The discussion, in his treatment of it, involves the distinction noticed above between the merely' infinite and the absolutely transfinite. He considers that Kant's