H. Alfv~n's theory envisages a stream of gas shot out from a place on the sun where there is a large magnetic field. The gas, supposed highly conducting, carries the magnetic field H with it, and the field is supposed to be perpendicular to the velocity v. A stationary observer observes an electric polarization perpendicular to H and v, and the potential change across the beam of width h is calculated as Hvh/C. A cosmic ray crossing the beam is supposed to change its energy by Hohe/C, and by making H or h large this change of energy can be made as great as is desired. Alfvdn calculates a 10 per cent change for the energy of a 3 X 10 ~° e.v. ray on crossing a beam of width 5 X 10 TM cm. carrying a magnetic field of 3 X 10 -4 gauss and travelling with a velocity of 2 X 10 s cm./sec.
The present paper recognizes that an observer moving with the beam observes no change of energy, and by a relativity transformation, it is shown that a fixed observer cannot observe a change of energy greater than 2vW/C, where W is the energy of the cosmic ray. This change amounts to only about 1.4 per cent.
The discrepancy between the conclusions from relativity and those drawn by AlfvSn are shown to arise from the fact that the cosmic ray path in the example considered by Alfv~n would have, in the beam, a radius of curvature 15 times smaller than the beam width and so could never cross it. Thus relativity gives for the change of energy of the beam an upper limit of the order 2v/C times the energy of the beam, and this limit can never be exceeded, however large H or h may be chosen.
An analysis of the considerations resulting from the assumption of a finite conductivity for the space external to the beam shows that the existence of such a conductivity does not change the conclusions.