[1] _Essays,_ (Library Edition, 1891), Vol. ii, p. 381. [2] _The Senses and the Intellect,_4th ed., (1894), p. 79. [3] _Grundzüge der Physiologischen Psychologie,_2nd ed. (1880), Vol. i, p. 375. [4] W. James, _Le sentiment de l'effort (Critique philosophique,_ 1880, Vol. ii,) cf. _Principles of Psychology,_ (1891), Vol. ii, chap, xxvi. [5] _Functions of the Brain,_ 2nd ed. (1886), p. 386. [6] _Handbuch der Physiologischen Optik,_ 1st ed. (1867), pp. 600-601. [7] _Le mécanisme de l'attention._ Alcan, 1888. [8] _The Expression of the Emotions,_ 1st ed., (1872), p. 74. [9] "What is an Emotion?_" Mind,_1884, p. 189. [10] _Principles of Psychology,_ 3rd. ed., (1890), Vol. i, p. 482. [11] _The Expression of the Emotions,_ 1st ed., p. 78. [12] _L'homme et l'intelligence,_ p. 36. [13] Ibid. p. 37. [14] Ibid. p. 43. [15] _The Expression of the Emotions,_ 1st ed., pp. 72, 69, 70. [16] C. Féré, _Sensation et Mouvement,_ Paris, 1887. [17] _Grundzüge der Physiologischen Psychologie,_ 2nd ed., (1880), Vol. ii, p. 437. [18] "On the Temperature Sense," _Mind,_ 1885. [19] Rood, _Modern Chromatics,_(1879), pp. 181-187. [20] _Handbuch der Physiologischen Optik,_ 1st ed. (1867), pp. 318-319. [21] _Éléments de psychophysique._ Paris, 1883. [22] See the account given of these experiments in the _Revue philosophique,_ 1887, Vol. i, p. 71, and Vol. ii, p. 180. [23] _Éléments de psychophysique,_ pp. 61, 69. [24] In the particular case where we admit without restriction Weber's Law ΔE/E=_const.,_ integration gives S=C log. E/Q. Q being a constant. This is Fechner's "logarithmic law." [25] Latterly it has been assumed that ΔS is proportional to S. [26] _Revue scientifique,_ March 13 and April 24, 1875. CHAPTER II THE MULTIPLICITY OF CONSCIOUS STATES[1] THE IDEA OF DURATION [Sidenote: What is number?] Number maybe defined in general as a collection of units, or, speaking more exactly, as the synthesis of the one and the many. Every number is one, since it is brought before the mind by a simple intuition and is given a name; but the unity which attaches to it is that of a sum, it covers a multiplicity of parts which can be considered separately. Without attempting for the present any thorough examination of these conceptions of unity and multiplicity, let us inquire whether the idea of number does not imply the representation of something else as well. [Sidenote: The units which make up a number must be identical.]