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PHYSICS: C. ST5RMER
62
PROC. N. A. S.
h 1 eA cm 2irim ip can be interpreted as the "velocity of the probability," whose mean value is v; the second integral in (12) is then simply the mean value of the classical force per unit charge, E + vXH/c. When the electric and magnetic fields are uniform we have further f#*E,6dx = E, etc., so that =J- V V *V V4dx +-(E + cv X H) dtsn
(13)
which is classical in terms of the electromagnetic field. This result has some importance as indicating that deflection methods of observing elm will yield correct results when evaluated by the classical formulas.6 ' Kennard, E. H., Zeits. Physik, 44, 1927 (326-352). Darwin, C. G., Proc. Roy. Soc., 117, 1927 (258-297). 3 Rabi, I. I., Zeits. Phys., 49, 1928 (507-511). 4Alexandrow, W., Ibid., 56, 1929 (818-837). 5Page, L., Phys. Rev., 36, 1930 (444-456). 6 Cf. Eckart, C., Ibid., 36, 1930 (1514-1515); Kennard, E. H., Ibid., 36, 1930 (16671668). 2
REMARKS ON A PAPER: NOTE ON THE NATURE OF COSMIC RA YS, BY PA UL S. EPSTEIN BY CARL STORMER OSLO, NORWAY
Communicated December 5, 1930
In a recent paper, "Note on the Nature of Cosmic Rays," in the Proc. Nat. Acad. Sci. of the United States of America, October, 1930, Paul S. Epstein solved a problem concerning the motion of electrons in the field of an elementary magnet without being aware that this problem was solved as early as in the year 1904 in my first paper on the Polar Aurora.' In fact, in the case of the Aurora, we meet exactly the same problem, viz., to find the regions of the earth which can be hit by electrons coming from very great distances. Thus Epstein's equation (11) corresponds to my equation (V, 1) and his equations (14) and (15) correspond to my equation (C, y, k) on page 11 of my paper. A discussion of these equations was published in the above-mentioned paper and with further details in my Geneva paper2 of 1907, which also contains the discussion made by Epstein, especially his inequality (18), where 1 + sin2 0 is erroneously printed instead of 1 + sin3 0.
PHYSICS: C. STORMER
VOL. 17, 1931
63
A list of approximate maximum values of the angle O(3) will be found in my second Geneva paper3 (1912), in the table at the beginning of §19. In that table I have found, e. g., the corresponding values of 0() and V = Ha:
160 291,000 170 368,000 180 460,000
300 3,150,000 310 3,550,000 320 3,980,000
and
in agreement with Epstein's results. A complete discussion of the regions of the earth hit by the cosmic rays, and also a study of the trajectories of these rays down to the earth can be made exactly on the same lines of research as those which I have developed in my mathematical theory of Aurora.4'5'6'7 In particular, the surface given in Epstein's paper P7
fL2
A)
sin2G
1 +
x/1 + sin3O
is nothing else than the toroidal surface playing such an essential part in my explanation of the wireless echoes of long delay.8'9 1 Carl Stormer, "Sur le mouvement d'un point materiel portant une charge d'electricite sous l'action d'un aimant elementaire," Videnskabsselskabets Skrifter, 1904, Christiania. 2 Carl Stormer, "Sur les trajectoires des corpuscules electrises dans l'espace sous l'action du magnetisme terrestre avec application aux aurores boreales," Archi Sci. Physiques et Naturelles, Geneve, 1907. 3 Carl St6rmer, "Sur les trajectoires des corpuscles electrises dans l'espace sous l'action du magnetisme terrestre avec application aux aurores boreales, etc.." second memoire, Geneve, 1911-1912. For American readers I give the following references: 4 Carl Stormer, "Corpuscular Theory of the Aurora Borealis," Terrestrial Magnetism and Atmospheric Electricity, March and September, 1917. Carl Stormer, "The Corpuscular Theory of Aurora Borealis," the boo