[35] Quoted by G.H.  Lewes, loc. cit., p. 257.

[36] The subject of the perception of movement is too intricate to be dealt with fully here.  I have only touched on it so far as necessary to illustrate our general principle.  For a fuller treatment of the subject, see the work of Dr. Hoppe, already referred to.

[37] The perception of magnitude is closely connected with that of distance, and is similarly apt to take an illusory form.  I need only refer to the well-known simple optical contrivances for increasing the apparent magnitude of objects.  I ought, perhaps, to add that I do not profess to give a complete account of optical illusions here, but only to select a few prominent varieties, with a view to illustrate general principles of illusion.  For a fuller account of the various mechanical arrangements for producing optical illusion, I must refer the reader to the writings of Sir D. Brewster and Helmholtz.

[38] Painters are well aware that the colours at the red end of the spectrum are apt to appear as advancing, while those of the violet end are known as retiring.  The appearance of relief given by a gilded pattern on a dark blue as ground, is in part referable to the principle just referred to.  In addition, it appears to involve a difference in the action of the muscles of accommodation in the successive adaptations of the eye to the most refrangible and the least refrangible rays. (See Bruecke, Die Physiologie der Farben, sec. 17.)

[39] Helmholtz tells us (Populaere wissenschaftliche Vortraege, 3tes Heft, p. 64) that even in a stereoscopic arrangement the presence of a wrong cast shadow sufficed to disturb the illusion.

[40] Among the means of giving a vivid sense of depth to a picture, emphasized by Helmholtz, is diminishing magnitude.  It is obvious that the perceptions of real magnitude and distance are mutually involved.  When, for example, a picture represents a receding series of objects, as animals, trees, or buildings, the sense of the third dimension, is rendered much more clear.

[41] A striking example of this was given in a painting, by Andsell, of a sportsman in the act of shooting, exhibited in the Royal Academy in 1879.

[42] This is at least true of all near objects.

[43] Helmholtz remarks (op. cit., p. 628) that the difficulty of seeing the convex cast as concave is probably due to the presence of the cast shadow.  This has, no doubt, some effect:  yet the consideration urged in the text appears to me to be the most important one.

[44] Populaere wissenschaftliche Vortraege, 3tes Heft, pp. 71, 72.

[45] See, on this point, some excellent remarks by G.H.  Lewes, Problems of Life and Mind, third series, vol. ii. p. 275.

[46] To some extent this applies to the changes of apparent magnitude due to altered position.  Thus, we do not attend to the reduction of the height of a small object which we are wont to handle, when it is placed far below the level of the eye.  And hence the error people make in judging of the point in the wall or skirting which a hat will reach when placed on the ground.