. The Astrophysical journal. e. co = o corresponds to circles concentric aroundthe origin. If w approaches — 7r/2 or +7r/2 the spirals tend tobecome straight lines through the origin. After this review of the well-known properties of logarithmicspirals, we will consider an ideal vortex defined as follows: The whirl shall be bounded by two cylinders of revolutionwith the Z-axis as axis and with radii equal to pi and p2, by theXF-plane, and by a parallel plane at the distance h above it. Weconsider h small as compared with p, in order to have a flat motion of the gas in the space menti
. The Astrophysical journal. e. co = o corresponds to circles concentric aroundthe origin. If w approaches — 7r/2 or +7r/2 the spirals tend tobecome straight lines through the origin. After this review of the well-known properties of logarithmicspirals, we will consider an ideal vortex defined as follows: The whirl shall be bounded by two cylinders of revolutionwith the Z-axis as axis and with radii equal to pi and p2, by theXF-plane, and by a parallel plane at the distance h above it. Weconsider h small as compared with p, in order to have a flat motion of the gas in the space mentioned is supposed to bepermanent, and the trajectories of the gas particles are supposedto be logarithmic spirals parallel to the XF-plane, whose projectionson that plane are 350 CARL STORMER where to is the same for all particles, and where A is determinedby the position of the spiral. Let us suppose further that thevelocity and electric charge in unit volume are functions of the dis-tance from the Z-axis only. -70 -5S -/S. Fig. 3 It is clear that such a whirl does not exist in reality; there mustbe a source and a sink for the coming and going masses of gas in thewhirl, but in the first approximation we will neglect the electricaction of masses outside this hypothetical whirl; their action willbe calculated later, when we have discussed the formulae for thisfirst simple case. RESEARCHES ON SOLAR VORTICES 351 To fix the motion without ambiguity, we will call the velocityV positive if the motion corresponds to increasing , negative if itcorresponds to decreasing 0. Thus the motion seen from thepositive side of the Z-axis will be clockwise for positive v, counter-clockwise for negative v; and the gas will approach the Z-axis ifthe product o)V is negative, and recede from the Z-axis if it ispositive, as is seen in Fig. 4. Co > 0
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Keywords: ., bookcentury1800, bookdecade1890, booksubjectspectru, bookyear1895
