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  1. Communicated by Ludwik Silberstein.
  2. It must be a distant object in order that the rays appear to come from infinity in the same manner as when using the microscope.
  3. Cf. St. Meyer, Phys. Zs. 21, p. 124, 1920; and K. Horovitz, Phys. Zs. 21, p. 499, 1920.
  4. This is Hering’s induction.
  5. In the latter case also dioptrics may be of importance as mentioned before.
  6. Cf. E. Hummelsheim, Arch. f. Ophth. vol.  45, 1898, p. 357and K. Horovitz, Ber. d. deutschen physik. Ges.1921,  2, pp. 9–11and Sitz. Ak. Wiss. Wien, vol.  1130, 1921, pp. 405–421.
  7. F. E. Wright, Jour. of the Opt. Soc. 2–3, p. 101, 1919.
    [CrossRef]
  8. A. Gehlhoff, Zs. f. techn. Phys. 66, p. 477et seq.
  9. Cf. Rohr, Brit. Jour. of Phot. 48, p. 454, 1901, and S. Czapski, Grundzüge der Theorie der optischen Instrumente, p. 256, 267, 1904.
  10. J. K. Horovitz, Sitz. Akad. Wiss. Wien. vol.  130, 1921; Beiträge zur Theorie des Sehraums.
  11. It is necessary to mention, that a change of the pupil also entails a variation of visual acuity (but not vice versa).
  12. It is partly due to the influence of limiting the field of view, that the diminution of the object, when seen through concave spectacles, is much more intensely felt (as shown by Isakovitz), than the diminution of the image on the retina alone could bring about. Therefore, the variation of the depth of focus also must be considered: the entire depth being greater than without spectacles, because pσ which determines the distinctness is only pB2σ(B<1).—It may be mentioned here, that also other dysmegalopsies, micropsy after the injection of atropin, macropsy after the use of pilocarpin (eserin) are intelligible if we assume the principle of maximum accommodation. In the first case the innervation is unlimited, the apparatus of accommodation being paralysed: hence micropsy. In the other case the external eye is in a spasm of accommodation, the impulses are arrested: hence macropsy.—For these and also other cases of physiological interest see K. Horovitz, loc. cit. and further an article appearing in “Pflüger’s Archiv” (Grössenwahrnehmung und Sehraumrelief).
  13. As postulated by the invariance of the line of sight. It is not necessary for the visual space to be always symmetrical around the x axis, as in the case of astigmatism.
  14. Cf. Burmester, Grundzüge der Reliefperspektive.
  15. The case d=a was developed by H. Witte, proceeding from experimental facts, without connection with the relief-formulae explained above. Physik. Zs. vol. 19, vol. 20, several articles “Über den Sehraum.”
  16. The present writer is pursuing these investigations in connection with Riemannian geometry.—The observations stated here are qualitative and it would be most interesting to obtain some exact investigations on these points, which it was impossible to undertake here.

1921 (1)

J. K. Horovitz, Sitz. Akad. Wiss. Wien. vol.  130, 1921; Beiträge zur Theorie des Sehraums.

1920 (1)

Cf. St. Meyer, Phys. Zs. 21, p. 124, 1920; and K. Horovitz, Phys. Zs. 21, p. 499, 1920.

1919 (1)

F. E. Wright, Jour. of the Opt. Soc. 2–3, p. 101, 1919.
[CrossRef]

1901 (1)

Cf. Rohr, Brit. Jour. of Phot. 48, p. 454, 1901, and S. Czapski, Grundzüge der Theorie der optischen Instrumente, p. 256, 267, 1904.

1898 (1)

Cf. E. Hummelsheim, Arch. f. Ophth. vol.  45, 1898, p. 357and K. Horovitz, Ber. d. deutschen physik. Ges.1921,  2, pp. 9–11and Sitz. Ak. Wiss. Wien, vol.  1130, 1921, pp. 405–421.

Burmester,

Cf. Burmester, Grundzüge der Reliefperspektive.

Gehlhoff, A.

A. Gehlhoff, Zs. f. techn. Phys. 66, p. 477et seq.

Horovitz, J. K.

J. K. Horovitz, Sitz. Akad. Wiss. Wien. vol.  130, 1921; Beiträge zur Theorie des Sehraums.

Horovitz, K.

It is partly due to the influence of limiting the field of view, that the diminution of the object, when seen through concave spectacles, is much more intensely felt (as shown by Isakovitz), than the diminution of the image on the retina alone could bring about. Therefore, the variation of the depth of focus also must be considered: the entire depth being greater than without spectacles, because pσ which determines the distinctness is only pB2σ(B<1).—It may be mentioned here, that also other dysmegalopsies, micropsy after the injection of atropin, macropsy after the use of pilocarpin (eserin) are intelligible if we assume the principle of maximum accommodation. In the first case the innervation is unlimited, the apparatus of accommodation being paralysed: hence micropsy. In the other case the external eye is in a spasm of accommodation, the impulses are arrested: hence macropsy.—For these and also other cases of physiological interest see K. Horovitz, loc. cit. and further an article appearing in “Pflüger’s Archiv” (Grössenwahrnehmung und Sehraumrelief).

Hummelsheim, E.

Cf. E. Hummelsheim, Arch. f. Ophth. vol.  45, 1898, p. 357and K. Horovitz, Ber. d. deutschen physik. Ges.1921,  2, pp. 9–11and Sitz. Ak. Wiss. Wien, vol.  1130, 1921, pp. 405–421.

Rohr,

Cf. Rohr, Brit. Jour. of Phot. 48, p. 454, 1901, and S. Czapski, Grundzüge der Theorie der optischen Instrumente, p. 256, 267, 1904.

Silberstein, Ludwik

Communicated by Ludwik Silberstein.

St. Meyer,

Cf. St. Meyer, Phys. Zs. 21, p. 124, 1920; and K. Horovitz, Phys. Zs. 21, p. 499, 1920.

Wright, F. E.

F. E. Wright, Jour. of the Opt. Soc. 2–3, p. 101, 1919.
[CrossRef]

Arch. f. Ophth. (1)

Cf. E. Hummelsheim, Arch. f. Ophth. vol.  45, 1898, p. 357and K. Horovitz, Ber. d. deutschen physik. Ges.1921,  2, pp. 9–11and Sitz. Ak. Wiss. Wien, vol.  1130, 1921, pp. 405–421.

Brit. Jour. of Phot. (1)

Cf. Rohr, Brit. Jour. of Phot. 48, p. 454, 1901, and S. Czapski, Grundzüge der Theorie der optischen Instrumente, p. 256, 267, 1904.

Jour. of the Opt. Soc. (1)

F. E. Wright, Jour. of the Opt. Soc. 2–3, p. 101, 1919.
[CrossRef]

Phys. Zs. (1)

Cf. St. Meyer, Phys. Zs. 21, p. 124, 1920; and K. Horovitz, Phys. Zs. 21, p. 499, 1920.

Sitz. Akad. Wiss. Wien. (1)

J. K. Horovitz, Sitz. Akad. Wiss. Wien. vol.  130, 1921; Beiträge zur Theorie des Sehraums.

Zs. f. techn. Phys. (1)

A. Gehlhoff, Zs. f. techn. Phys. 66, p. 477et seq.

Other (10)

This is Hering’s induction.

In the latter case also dioptrics may be of importance as mentioned before.

Communicated by Ludwik Silberstein.

It must be a distant object in order that the rays appear to come from infinity in the same manner as when using the microscope.

It is necessary to mention, that a change of the pupil also entails a variation of visual acuity (but not vice versa).

It is partly due to the influence of limiting the field of view, that the diminution of the object, when seen through concave spectacles, is much more intensely felt (as shown by Isakovitz), than the diminution of the image on the retina alone could bring about. Therefore, the variation of the depth of focus also must be considered: the entire depth being greater than without spectacles, because pσ which determines the distinctness is only pB2σ(B<1).—It may be mentioned here, that also other dysmegalopsies, micropsy after the injection of atropin, macropsy after the use of pilocarpin (eserin) are intelligible if we assume the principle of maximum accommodation. In the first case the innervation is unlimited, the apparatus of accommodation being paralysed: hence micropsy. In the other case the external eye is in a spasm of accommodation, the impulses are arrested: hence macropsy.—For these and also other cases of physiological interest see K. Horovitz, loc. cit. and further an article appearing in “Pflüger’s Archiv” (Grössenwahrnehmung und Sehraumrelief).

As postulated by the invariance of the line of sight. It is not necessary for the visual space to be always symmetrical around the x axis, as in the case of astigmatism.

Cf. Burmester, Grundzüge der Reliefperspektive.

The case d=a was developed by H. Witte, proceeding from experimental facts, without connection with the relief-formulae explained above. Physik. Zs. vol. 19, vol. 20, several articles “Über den Sehraum.”

The present writer is pursuing these investigations in connection with Riemannian geometry.—The observations stated here are qualitative and it would be most interesting to obtain some exact investigations on these points, which it was impossible to undertake here.

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Equations (1)

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x = a 1 x + a 2 y + a 3 z + a 4 ax + by + cz + d , y = b 1 x + b 2 y + b 3 z + b 4 ax + by + cz + d , z = c 1 x + c 2 y + c 3 z + c 4 ax + by + cz + d