1. The position of a figure influences its view. According to the position in which objects are viewed different muscle-sensations come into play and the impression is altered. To recognise inverted letters as such long experience is required. The best proof of this are the letters d, b, p, q, which are represented by the same figure in different positions and yet are always distinguished as different.[149]

2. It will not escape the attentive observer that for the same reasons and even with the same figure and in the same position the fixation point is also decisive. The figure seems to change during the act of vision. For example, an eight-pointed star constructed by successively joining in a regular octagon the first corner with the fourth, the fourth with the seventh, etc., skipping in every case two corners, a.s.sumes alternately, according to where we suffer the centre of vision to rest, a predominantly architectonic or a freer and more open character. Vertical and horizontal lines are always differently apprehended from what oblique lines are.

[Ill.u.s.tration: Fig. 58.]

3. The reason why we prefer vertical symmetry and regard it as something special in its kind, whereas we do not recognise horizontal symmetry at all immediately, is due to the vertical symmetry of the muscular apparatus of the eye. The left-hand side a of the accompanying vertically-symmetrical figure induces in the left eye the same muscular feelings as the right-hand side b does in the right eye. The pleasing effect of symmetry has its cause primarily in the repet.i.tion of muscular feelings. That a repet.i.tion actually occurs here, sometimes sufficiently marked in character as to lead to the confounding of objects, is proved apart from the theory by the fact which is familiar to every one quem dii oderunt that children frequently reverse figures from the right to the left, but never from above downwards; for example, write [epsilon] instead of 3 until they finally come to notice the slight difference. Figure 50 shows how pleasing the repet.i.tion of muscular feelings may be. As will be readily understood, vertical and horizontal lines exhibit relations similar to symmetrical figures which are immediately disturbed when oblique positions are chosen for the lines. Compare what Helmholtz says regarding the repet.i.tion and coincidence of partial tones.

[Ill.u.s.tration: Fig. 59.]

I may be permitted to add a general remark. It is a quite universal phenomenon in psychology that certain qualitatively quite different series of percepts mutually awaken and reproduce one another and in a certain aspect produce the appearance of sameness or similarity. We say of such series that they are of like or of similar form, naming their abstracted likeness form.

1. Of spatial figures we have already spoken.

2. We call two melodies like melodies when they present the same succession of pitch-ratios; the absolute pitch (or key) may be as different as can be. We can so select the melodies that not even two partial tones of the notes in each are common. Yet we recognise the melodies as alike. And, what is more, we notice the form of the melody more readily and recognise it again more easily than the key (the absolute pitch) in which it was played.

3. We recognise in two different melodies the same rhythm no matter how different the melodies may be otherwise. We know and recognise the rhythm more easily even than the absolute duration (the tempo).

These examples will suffice. In all these and in all similar cases the recognition and likeness cannot depend upon the qualities of the percepts, for these are different. On the other hand recognition, conformably to the principles of psychology, is possible only with percepts which are the same in quality. Consequently there is no other escape than to imagine the qualitatively unlike percepts of the two series as necessarily connected with other percepts which are qualitatively alike.

Since in differently colored figures of like form, like muscular feelings are necessarily induced if the figures are recognised as alike, so there must necessarily lie at the basis of all forms also, and we might even say at the basis of all abstractions, percepts of a peculiar quality. And this holds true for s.p.a.ce and form as well as for time, rhythm, pitch, the form of melodies, intensity, etc. But whence is psychology to derive all these qualities? Have no fear, they will all be found, as were the sensations of muscles for the theory of s.p.a.ce. The organism is at present still rich enough to meet all the requirements of psychology in this direction, and it is even time to give serious ear to the question of "corporeal resonance" which psychology so loves to dwell on.

Different psychical qualities appear to bear a very intimate mutual relation to one another. Special research on the subject, as well also as the demonstration that this remark may be generally employed in physics, will follow later.[150]

FOOTNOTES: [Footnote 147: This article, designed to ill.u.s.trate historically that on Symmetry, at page 89, first appeared in Fichte's Zeitschrift fAr Philosophie, for 1865.]

[Footnote 148: Comp. Cornelius, Ueber das Sehen; Wundt, Theorie der Sinneswahrnehmung.]

[Footnote 149: Comp. Mach, Ueber das Sehen von Lagen and Winkeln. Sitzungsb. der Wiener Akademie, 1861.]

[Footnote 150: Comp. Mach, Zur Theorie des GehArorgans. Sitsungsber, der Wiener Akad., 1863.--Ueber einige Erscheinungen der physiolog. Akustik. Ibid., 1864.]

INDEX.

Absolute, temperature, 162; time, 204; forecasts, have no signification in science, 206.

Abstract, meaning of the term, 240.

Abstraction, 180, 200, 208, 231.

Acceleration, organ for forward, 299 et seq.

Accelerations, 204, 216, footnote, 225-226, 253.

Accident, logical and historical, in science, 160, 168, 170, 213; in inventions and discoveries, 262 et seq.

Accord, the pure triple, 46.

Acc.u.mulators, electrical, 125 et seq.; 132, footnote.

Acoustic color, 36.

Acoustics, Sauveur on, 375 et seq.

Action and reaction, importance of the principle of, 191.

Adaptation, in organic and inorganic matter, 216, 229; in scientific thought, 214-235.

Asthetics, computation as a principle of, 34; researches in, 89, footnote; repet.i.tion, a principle of, 91.

Africa, 186, 234, 237.

Agreeable effects, due to repet.i.tion of sensations, 92, 97 et seq.

Agriculture, transition to, 265.

Air-gun, 135.

Alcohol and water, mixture of oil and, in Plateau's experiments, 4.

Algebra, economy of, 196.

Alien thoughts in science, 196.

All, the, 88.

Amontons, 174, 346.

AmpAre, the word, 314.

AmpAre's swimmer, 207.

a.n.a.logies, mechanical, 157, 160; generally, 236-258.

a.n.a.logy, defined, 250.

a.n.a.lysis, 188.

a.n.a.lytical geometry, not necessary to physicians, 370, footnote.

Anatomic structures, transparent stereoscopic views of, 74.

Anatomy, character of research in, 255.

Andrieu, Jules, 49, footnote.

Animals, the psychical activity of, 190, 231; the language of, 238; their capacity for experience, 266 et seq.

Animism, 186, 187, 243, 254.

Anisotropic optical fields, 227.

Apparatus for producing movements of rotation, 287 et seq.

Arabesque, an inverted, 95.

Arabian Nights, 219.

Arago, 270.

Aral, the Sea of, 239.

ArchAopteryx, 257.

Archimedes, 4, 237.

Arcimboldo, Giuseppe, 36.

Area, principle of least superficial, 10 et seq.

Ares, the bellowing of the wounded, 272.

Aristotelians, 283.

Aristotle, 348, 296.

Art, development of, 28 et seq.

Artillery, practical, 334-335.

Artistic value of scientific descriptions, 254.

Arts, practical, 108.

Ascent, heights of, 143-151.

Asia, 234.

a.s.syrians, the art of, 79.

Astronomer, measures celestial by terrestrial distances, 136.

Astronomy, antecedent to psychology, 90; rigidity of its truths, 221.

Atomic theories, 104.

Atoms, 207.

Attention, the rAle of, in sensuous perception, 35 et seq.

Attraction, generally, 226; of liquid particles, 13-14; in electricity, 109 et seq.

Aubert, 298.

Audition. See Ear.

Austrian gymnasiums, 370, footnote.

Axioms, instinctive knowledge, 190.

Babbage, on the economy of machinery, 196.

Bach, 20.

Backwards, prophesying, 253.

Bacon, Lord, 48, 280.

Baer, C. E. von, 235.

Balance, electrical, 127, footnote; torsion, 109, 168.

Balloon, a hydrogen, 199.

Barbarism and civilisation, 335 et seq.

Ba.s.s-clef, 101.

Ba.s.s, fundamental, 44.

Beats, 40-45, 377 et seq.

Beautiful, our notions of, variable, 99.

Beauty, objects of, in nature, 91.

Becker, J. K., 364, 369.

Beethoven, 39, 44.

Beginnings of science, 189, 191.

Belvedere Gallery at Vienna, 36.

Bernoulli, Daniel, on the conservation of living force, 149; on the vibrations of strings, 249.