[96] For the most recent view of this discussion, with the arguments on either side, see Couturat: _De l’Infini mathématique_ (1896). 2nd part. Bk. III. [97] Cournot, _op. cit._, I., p. 331 et seq. Renouvier, _Logique_, I., pp. 377-394. Poinsot, _Théorie nouvelle de la rotation des corps_, p. 78. [98] For a summary of these investigations, see the chapter “Sensations of Orientation” in Prof. E. Mach’s _Popular Scientific Lectures_, 3rd ed., Chicago, 1898; and for original discussions of the whole subject of space-sensations, see the same author’s _Analysis of the Sensations_, Chicago, 1897.—_Trans._ [99] Münsterberg, _Beiträge zur experimen. Psychologie_, pp. 182 et seq. Wundt, _Physiol. Psychologie_, 4th ed., II. pp. 95-96. [100] This is not the place to enter into the well-known discussion between the “nativists” and the “empiricists.” To the former all sensation, visual or tactile, contains from its outset a _quantum_ of extension which is the primitive element, and the foundation for our spatial constructions. For the others there are only local signs, tactile or visual, and movements whose synthesis suffices to constitute all the modalities of existence. Whichever hypothesis be adopted, the extension in point is always that given by concrete data (not that of space conceived in the abstract)—directly cognised according to some, a genetic construction according to others. This discussion has no direct relation with our subject: for the full debate see Ribot’s _Psychologie allemande contemporaine_, Ch. V. James (_Psychology_, II. Ch. XX.) has recently taken up the nativistic theory, giving new arguments in its favor. [101] Extracted from Spencer’s _Psychology_, Vol. I. § 90. [102] Lotze, _Mikrokosmus_, II. p. 47. [103] Stallo, _Concepts of Modern Physics_, Chap. XIII., p. 225, _Int. Sc. Ser._, third ed. He also gives a very concise criticism of Mill’s theory of induction in geology. [104] _System of Logic_, I. Bk. II., Chap. 15, § 1. [105] The complete history of this question, from its first beginnings to contemporaneous work, may be studied in Nichols’s “Psychology of Time,” _Am. J. of Psychol._, III. pp. 453-530. [106] For these and the following experiments, cf. Wundt, _Physiologische Psychologie_, 4th ed., I. pp. 408 et seq. [107] _Psychol._, I. 642. [108] M. Janet has studied this subject, under the title “Une illusion d’optique interne” (_Rev. Phil._, 1877, III. pp. 497 et seq.) and explains the illusion by supposing that the apparent duration of a certain portion of time, in the life of each individual, is proportional to the total duration of his life. [109] Nichols, _op. cit._, p. 502. [110] _Analysis of the Sensations_, Chicago, 1897, pp. 110 et seq. [111] H. Spencer, _Psychology_, I., § 91, p. 215. [112] Horwicz, _Psychologische Analysen_, III., 145. Guyau, _Genèse de l’idée du temps_, pp. 35 et seq. [113] _Beiträge zur experimentellen Psychologie_, II., 1889.