. The Astrophysical journal. instance. Appell, TraiU de Mecanique Rationnelle, 3, chap. xxxv. CARL STORMER in question can be only a very small fraction of the diameter indi-cated by the hydrogen flocculi whirl in the upper levels. This isalso analogous to terrestrial cyclones, whose thickness is very smallcompared with their diameter. In other words, h must be verysmall compared with p,. As to the size of pi compared with hand p,, we can make a probable assumption by starting from thefact observed by Hale, namely, that the magnetic effect of thevortex decreases very rapidly upward along the a
. The Astrophysical journal. instance. Appell, TraiU de Mecanique Rationnelle, 3, chap. xxxv. CARL STORMER in question can be only a very small fraction of the diameter indi-cated by the hydrogen flocculi whirl in the upper levels. This isalso analogous to terrestrial cyclones, whose thickness is very smallcompared with their diameter. In other words, h must be verysmall compared with p,. As to the size of pi compared with hand p,, we can make a probable assumption by starting from thefact observed by Hale, namely, that the magnetic effect of thevortex decreases very rapidly upward along the axis of the vortex,so that there is only a very small fraction of its original valuewhen we come to the level of 5000 miles above the order to do this, we will start from the formula ^20= — 2 7rcOSw/« (z-h+v^ {z-hy-\-pl)(z-{-V z+pl){z-h-{-^ (z-hy+p;)(z+ Vz^+pl) This givesdH,o dz = 2TTC cos (li \ Vz^+pi \/{z-hy+pi Vz^+p\ V{z-hy+p\) The geometrical signification of the radicals will be seen in Fig. 13. <f-^. Fig. 13 On studying this figure, it will be seen that if we choose hsmall compared with the elevation of the high levels of the sunsatmosphere, and, on the other hand, suppose pi to be of the samesize as, or smaller than, /?, the magnetic force at these high levelswill be only a very small fraction of what it is at the level z=h. RESEARCHES ON SOLAR VORTICES 373 We will choose as a numerical example h = pi — ^oo km=5Xio cm , /32= 50,000 km=5Xio> cm . The last value is chosen to correspond with the size of the observedhydrogen whirls around sun-spots. Further, we take co= 20°. With regard to the constant c, wewill start from the value of about 3000 gausses observed in sun-spots by the Zeeman effect, and suppose that this is the value ofHzo for z = h. We then get c= — 583. i. Starting from these valueswe find the following values of Hzo along the Z-axis: z in km H^,^ in Gausses 500 3000 1000 19OI 2000 916. 7 3000 583-2 5000 2 in km B.^ in Gauss
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