. The Astrophysical journal. - in the arrangement of the lines of force, and their projectionon the plane of the whirls. First case: two identical whirls.—Let us consider the compo-nents Px and Py and their resultant P/i in a plane parallel to theplane of the wliirls. Let C (Fig. 23) be the middle point of theline AB joining points A and B where the axes of the whirls cut theplane. Let M and M be two points in the plane situated sym-metrically with regard to C, and let us denote by accents theletters corresponding to the point M. We then have Kr , Sr , 3 86 CARL STORMER which gives P^= —Hr sin
. The Astrophysical journal. - in the arrangement of the lines of force, and their projectionon the plane of the whirls. First case: two identical whirls.—Let us consider the compo-nents Px and Py and their resultant P/i in a plane parallel to theplane of the wliirls. Let C (Fig. 23) be the middle point of theline AB joining points A and B where the axes of the whirls cut theplane. Let M and M be two points in the plane situated sym-metrically with regard to C, and let us denote by accents theletters corresponding to the point M. We then have Kr , Sr , 3 86 CARL STORMER which gives P^= —Hr sin a-{-H4> cos « —Aj? sin /^—K^ cos (3= —PxP[.= —Hr cosa—H^, sin h-\-Kr cos (3—K^ sin ft=—Py, , the component P/, in the point M is obtained by turning thecomponent P/, in the point M through an angle of i8o° around C In Fig. 25 are seen the directions of the components Pj, ina plane, corresponding to the level 20,000 km over the twowhirls in the suns atmosphere. For the two identical whirlswe have chosen case No. 5 of Fig. 8, with A =500 km, CO =20° Pi = 5ookm, c= P2= 50,000 km , r= 100,000 km. RESEARCHES ON SOLAR VORTICES 387 Second case: two whirls corresponding to cases Nos. 5 and 8 inFig. 8.—For the whirl A we have e negative and co and v positive,and for the whirl B, £=£, (o=—w, v =? — V , consequently c=pzv=—c. Further, for both whirls /?, p,, and p^ are supposed to be the same. Let us consider (Fig. 24) as before a given level above the planeof the two whirls, and let CD be the perpendicular through thecentral point C of the line AB. Let M and M be two pointssituated symmetrically with respect to this line, and let us denoteby accents the letters corresponding to the point M. We have Further by formula (11), //j? positive, E^ negative and we find and P = ^Hr sin a-H^ cos
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Keywords: ., bookcentury1800, bookdecade1890, booksubjectspectru, bookyear1895
