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  1. H. A. Rowland, Phil. Mag. 13, 469 (1882); 16, 197 and 210 (1883).
  2. R. T. Glazebrook, Phil. Mag. 15, 414 (1883).
  3. E. Mascart, J. de Physique 2, 5 (1883).
  4. W. Baily, Phil. Mag. 22, 47 (1886).
  5. C. Runge, in Kayser's Handbuch, Vol. I, p. 450–470; C. Runge and K. W. Meissner, Handbuch der Astrophysik, (Verlagsbuchhandlung Julius Springer, Berlin, 1933). Vol. I, Pp. 235–257.
  6. J. E. Mack, J. R. Stehn, and B. Edlén, J. Opt. Soc. Am. 22, 245 (1932).
  7. I. S. Bowen, J. Opt. Soc, Am 23. 313 (1933).
  8. W. R. Hamilton, Mathematical Papers. (The University Press, Cambridge, England, 1931). Vol. I, p. 17
  9. W. deW. Abney, Phil. Trans. 177, 457 (1886).
  10. A. Eagle, Astrophys. J. 31, 120 (1910).
  11. C. Runge and F. Paschen, Anh, z.d.Abh. d. Berlin Akad. d. Wiss (1902).
  12. B. Hoag, Astrophys. J. 66, 225 (1927).
  13. For instance by M. Siegbahn, B. Edlén, and J. Soederguist. Papers in Zeits. f. Physik (since 1930), J. E. Mack, P. G. Kruger, and I. S. Bowen in Phys. Rev. (since 1930).
  14. F. L. O. Wadsworth, Astrophys. J. 3, 54 (1896).
  15. Compare the results obtained by an approximated treatment of the same problem by D. L. Mac Adam, J. Opt. Soc. Am. 23, 178 (1933).
  16. J. E. Mack, J. R. Stehn, and B. Edlén, J. Opt. Soc. Am. 22, 245 (1932).
  17. D. L. MacAdam, J. Opt. Soc. Am. 23, 178 (1933).
  18. For a small wave-length range, the stigmatic mounting (with the spectrum on the normal) is preferable.
  19. See the photograph in the paper of Mack, Stehn, and Edlén (reference 16).
  20. J. L. Sirks, Astron. and Astrophys. 13, 763 (1894).
  21. It may be emphasized, that these conditions are only fulfilled for the spectral lines appearing at the normal. Sirks treated only this case, because at that time no other than the Rowland mounting was known. For spectral lines appearing far away from the normal, the construction of a tangent does not lead to the outside focus for horizontal lines, as is sometimes erroneously stated. In Fig. 8, the distances of those foci outside of the slit are represented in a diagram.
  22. G. H. Dieke, J. Opt. Soc. Am. 23, 274 (1933).
  23. A. Eagle, Astrophys. J. 31, 120 (1910).
  24. In some treatments the reason given for avoiding large angles is that then the angular aperture of the grating becomes very small. This is not the case however because the width of the grating can be approximated very well by a chord on the Rowland circle, and the angle subtended at any point of a circle by the two end points of a chord is strictly constant. This geometrical property can in fact be used for derivation of the Rowland circle as focal curve of a concave grating. On the other hand, the aperture with respect to the length l of the grating gets much larger with increasing angles, as 1/cos α or 1/cos β respectively.—This conclusion, however, holds only as long as the aperture of the grating is limited by its own size, not by the aberration. (See Section X.)
  25. G. H. Dieke, J. Opt. Soc. Am. 23, 280 (1933); Sister M. I. Bresch, J. Opt. Soc. Am. 28, 493 (1938).
  26. B. Edlén, Thesis, Upsala 1932.
  27. See reference 16.
  28. R. A. Sawyer, Experimental Spectroscopy (Prentice-Hall, Inc., New York, 1944) p. 131.
  29. F. L. O. Wadsworth, Astrophys. J. 3, 54 (1896).
  30. C. Runge and, F. Paschen, Ann. d. Physik 61. 641 (1897).
  31. C. Fabry and H. Buisson, J. de Physique [4] 9, 940 (1910).
  32. W. F. Meggers and K. Burns, Sci. Pap. Bur. Stand. [441] 18, 191 (1922).
  33. A. Poritzky, Proc. of the Fifth Conference on Spectroscopy, p. 38.
  34. Sometimes the opinion is expressed that the focal length of a grating in the Wadsworth mounting is one-half of that in the Rowland circle mounting. This statement is not generally correct. The distance from grating to plate in Wadsworth's mounting lies between R/2 and R, and on the Rowland circle between R and about R/10. An example may illustrate this point—the focus for 4000A in the second order, diffracted by a 30,000 lines/inch grating, lies for the Eagle mounting at 0.88R, for the Wadsworth mounting at 0.77R. Hence, the dispersions in these two cases are only slightly different and the apertures of the grating in the two mountings differ only by 30 percent.
  35. Compare the discussion of the aberration for the Rowland circle, and Eq. (27), Section VI, part b.
  36. This was nearly realized by Fabry and Buisson, reference 31.
  37. A. Poritzky, reference 33.
  38. M. Czerny and A. F. Turner, Zeits. f. Physik 61, 792 (1930).
  39. Since the grating acts as a mirror for α = -β, Eq. (107) gives a very simple formula for the astigmatism of a concave mirror if struck by parallel light.

Abney, W. deW.

W. deW. Abney, Phil. Trans. 177, 457 (1886).

Baily, W.

W. Baily, Phil. Mag. 22, 47 (1886).

Bowen, I. S.

I. S. Bowen, J. Opt. Soc, Am 23. 313 (1933).

Buisson, H.

C. Fabry and H. Buisson, J. de Physique [4] 9, 940 (1910).

Burns, K.

W. F. Meggers and K. Burns, Sci. Pap. Bur. Stand. [441] 18, 191 (1922).

Czerny, M.

M. Czerny and A. F. Turner, Zeits. f. Physik 61, 792 (1930).

Dieke, G. H.

G. H. Dieke, J. Opt. Soc. Am. 23, 280 (1933); Sister M. I. Bresch, J. Opt. Soc. Am. 28, 493 (1938).

G. H. Dieke, J. Opt. Soc. Am. 23, 274 (1933).

Eagle, A.

A. Eagle, Astrophys. J. 31, 120 (1910).

A. Eagle, Astrophys. J. 31, 120 (1910).

Edlén, B.

J. E. Mack, J. R. Stehn, and B. Edlén, J. Opt. Soc. Am. 22, 245 (1932).

J. E. Mack, J. R. Stehn, and B. Edlén, J. Opt. Soc. Am. 22, 245 (1932).

For instance by M. Siegbahn, B. Edlén, and J. Soederguist. Papers in Zeits. f. Physik (since 1930), J. E. Mack, P. G. Kruger, and I. S. Bowen in Phys. Rev. (since 1930).

B. Edlén, Thesis, Upsala 1932.

Fabry, C.

C. Fabry and H. Buisson, J. de Physique [4] 9, 940 (1910).

Glazebrook, R. T.

R. T. Glazebrook, Phil. Mag. 15, 414 (1883).

Hamilton, W. R.

W. R. Hamilton, Mathematical Papers. (The University Press, Cambridge, England, 1931). Vol. I, p. 17

Hoag, B.

B. Hoag, Astrophys. J. 66, 225 (1927).

MacAdam, D. L.

D. L. MacAdam, J. Opt. Soc. Am. 23, 178 (1933).

Compare the results obtained by an approximated treatment of the same problem by D. L. Mac Adam, J. Opt. Soc. Am. 23, 178 (1933).

Mack, J. E.

J. E. Mack, J. R. Stehn, and B. Edlén, J. Opt. Soc. Am. 22, 245 (1932).

J. E. Mack, J. R. Stehn, and B. Edlén, J. Opt. Soc. Am. 22, 245 (1932).

Mascart, E.

E. Mascart, J. de Physique 2, 5 (1883).

Meggers, W. F.

W. F. Meggers and K. Burns, Sci. Pap. Bur. Stand. [441] 18, 191 (1922).

Paschen, F.

C. Runge and F. Paschen, Anh, z.d.Abh. d. Berlin Akad. d. Wiss (1902).

Poritzky, A.

A. Poritzky, reference 33.

A. Poritzky, Proc. of the Fifth Conference on Spectroscopy, p. 38.

Rowland, H. A.

H. A. Rowland, Phil. Mag. 13, 469 (1882); 16, 197 and 210 (1883).

Runge, C.

C. Runge and, F. Paschen, Ann. d. Physik 61. 641 (1897).

C. Runge, in Kayser's Handbuch, Vol. I, p. 450–470; C. Runge and K. W. Meissner, Handbuch der Astrophysik, (Verlagsbuchhandlung Julius Springer, Berlin, 1933). Vol. I, Pp. 235–257.

C. Runge and F. Paschen, Anh, z.d.Abh. d. Berlin Akad. d. Wiss (1902).

Sawyer, R. A.

R. A. Sawyer, Experimental Spectroscopy (Prentice-Hall, Inc., New York, 1944) p. 131.

Siegbahn, M.

For instance by M. Siegbahn, B. Edlén, and J. Soederguist. Papers in Zeits. f. Physik (since 1930), J. E. Mack, P. G. Kruger, and I. S. Bowen in Phys. Rev. (since 1930).

Sirks, J. L.

J. L. Sirks, Astron. and Astrophys. 13, 763 (1894).

Soederguist, J.

For instance by M. Siegbahn, B. Edlén, and J. Soederguist. Papers in Zeits. f. Physik (since 1930), J. E. Mack, P. G. Kruger, and I. S. Bowen in Phys. Rev. (since 1930).

Stehn, J. R.

J. E. Mack, J. R. Stehn, and B. Edlén, J. Opt. Soc. Am. 22, 245 (1932).

J. E. Mack, J. R. Stehn, and B. Edlén, J. Opt. Soc. Am. 22, 245 (1932).

Turner, A. F.

M. Czerny and A. F. Turner, Zeits. f. Physik 61, 792 (1930).

Wadsworth, F. L. O.

F. L. O. Wadsworth, Astrophys. J. 3, 54 (1896).

F. L. O. Wadsworth, Astrophys. J. 3, 54 (1896).

Other (39)

H. A. Rowland, Phil. Mag. 13, 469 (1882); 16, 197 and 210 (1883).

R. T. Glazebrook, Phil. Mag. 15, 414 (1883).

E. Mascart, J. de Physique 2, 5 (1883).

W. Baily, Phil. Mag. 22, 47 (1886).

C. Runge, in Kayser's Handbuch, Vol. I, p. 450–470; C. Runge and K. W. Meissner, Handbuch der Astrophysik, (Verlagsbuchhandlung Julius Springer, Berlin, 1933). Vol. I, Pp. 235–257.

J. E. Mack, J. R. Stehn, and B. Edlén, J. Opt. Soc. Am. 22, 245 (1932).

I. S. Bowen, J. Opt. Soc, Am 23. 313 (1933).

W. R. Hamilton, Mathematical Papers. (The University Press, Cambridge, England, 1931). Vol. I, p. 17

W. deW. Abney, Phil. Trans. 177, 457 (1886).

A. Eagle, Astrophys. J. 31, 120 (1910).

C. Runge and F. Paschen, Anh, z.d.Abh. d. Berlin Akad. d. Wiss (1902).

B. Hoag, Astrophys. J. 66, 225 (1927).

For instance by M. Siegbahn, B. Edlén, and J. Soederguist. Papers in Zeits. f. Physik (since 1930), J. E. Mack, P. G. Kruger, and I. S. Bowen in Phys. Rev. (since 1930).

F. L. O. Wadsworth, Astrophys. J. 3, 54 (1896).

Compare the results obtained by an approximated treatment of the same problem by D. L. Mac Adam, J. Opt. Soc. Am. 23, 178 (1933).

J. E. Mack, J. R. Stehn, and B. Edlén, J. Opt. Soc. Am. 22, 245 (1932).

D. L. MacAdam, J. Opt. Soc. Am. 23, 178 (1933).

For a small wave-length range, the stigmatic mounting (with the spectrum on the normal) is preferable.

See the photograph in the paper of Mack, Stehn, and Edlén (reference 16).

J. L. Sirks, Astron. and Astrophys. 13, 763 (1894).

It may be emphasized, that these conditions are only fulfilled for the spectral lines appearing at the normal. Sirks treated only this case, because at that time no other than the Rowland mounting was known. For spectral lines appearing far away from the normal, the construction of a tangent does not lead to the outside focus for horizontal lines, as is sometimes erroneously stated. In Fig. 8, the distances of those foci outside of the slit are represented in a diagram.

G. H. Dieke, J. Opt. Soc. Am. 23, 274 (1933).

A. Eagle, Astrophys. J. 31, 120 (1910).

In some treatments the reason given for avoiding large angles is that then the angular aperture of the grating becomes very small. This is not the case however because the width of the grating can be approximated very well by a chord on the Rowland circle, and the angle subtended at any point of a circle by the two end points of a chord is strictly constant. This geometrical property can in fact be used for derivation of the Rowland circle as focal curve of a concave grating. On the other hand, the aperture with respect to the length l of the grating gets much larger with increasing angles, as 1/cos α or 1/cos β respectively.—This conclusion, however, holds only as long as the aperture of the grating is limited by its own size, not by the aberration. (See Section X.)

G. H. Dieke, J. Opt. Soc. Am. 23, 280 (1933); Sister M. I. Bresch, J. Opt. Soc. Am. 28, 493 (1938).

B. Edlén, Thesis, Upsala 1932.

See reference 16.

R. A. Sawyer, Experimental Spectroscopy (Prentice-Hall, Inc., New York, 1944) p. 131.

F. L. O. Wadsworth, Astrophys. J. 3, 54 (1896).

C. Runge and, F. Paschen, Ann. d. Physik 61. 641 (1897).

C. Fabry and H. Buisson, J. de Physique [4] 9, 940 (1910).

W. F. Meggers and K. Burns, Sci. Pap. Bur. Stand. [441] 18, 191 (1922).

A. Poritzky, Proc. of the Fifth Conference on Spectroscopy, p. 38.

Sometimes the opinion is expressed that the focal length of a grating in the Wadsworth mounting is one-half of that in the Rowland circle mounting. This statement is not generally correct. The distance from grating to plate in Wadsworth's mounting lies between R/2 and R, and on the Rowland circle between R and about R/10. An example may illustrate this point—the focus for 4000A in the second order, diffracted by a 30,000 lines/inch grating, lies for the Eagle mounting at 0.88R, for the Wadsworth mounting at 0.77R. Hence, the dispersions in these two cases are only slightly different and the apertures of the grating in the two mountings differ only by 30 percent.

Compare the discussion of the aberration for the Rowland circle, and Eq. (27), Section VI, part b.

This was nearly realized by Fabry and Buisson, reference 31.

A. Poritzky, reference 33.

M. Czerny and A. F. Turner, Zeits. f. Physik 61, 792 (1930).

Since the grating acts as a mirror for α = -β, Eq. (107) gives a very simple formula for the astigmatism of a concave mirror if struck by parallel light.

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