. The Astrophysical journal. P2- Aslog A = \og e In A = :^42gIn A where e is the base of the hyperbolic logarithms, we get approxi-mately *=^:^.jj(). 18 log e Thus the function R{S2—Sj) is a function of R and of z, whichdiffers from the function $ only by a constant factor and this evenif we express R, e, p,, p2, and h with h as unit of length. Thus the curves $= constant are identical with the curves$1= constant, where i=i?(52—5i), if Simpsons formula is assumed RESEARCHES ON SOLAR VORTICES 379 to be accurate enough for our purpose. From this we have thendrawn the curves with R as abs
. The Astrophysical journal. P2- Aslog A = \og e In A = :^42gIn A where e is the base of the hyperbolic logarithms, we get approxi-mately *=^:^.jj(). 18 log e Thus the function R{S2—Sj) is a function of R and of z, whichdiffers from the function $ only by a constant factor and this evenif we express R, e, p,, p2, and h with h as unit of length. Thus the curves $= constant are identical with the curves$1= constant, where i=i?(52—5i), if Simpsons formula is assumed RESEARCHES ON SOLAR VORTICES 379 to be accurate enough for our purpose. From this we have thendrawn the curves with R as abscissa and $i ordinate, and where zhas a constant value for each curve. The points (Roi, So) and {R02, So) where $ has a given value,$0, can then be found graphically by the intersection of the curveand the line $=$0 (Fig. 16). Similar curves have been drawnwith z as abscissa and $ as ordinate, for controlhng the has finally given enough points for the construction of thecurves i= Fig. 16 In order to control the results, the function $1 has also beencalculated for s=o, in which case the integrals can be reduced toelliptic integrals of the first and second kind by a partial integration. The curves $1= constant are seen in Fig. 17, and the directionsof the components of magnetic force in the meridian plane are alsogiven. It will be seen that the agreement is fairly good, in spiteof the approximate method of computation and construction. With the aid of the curves $1= constant and the logarithmic spirals 7^ = 5e-*cotu,^ where 5 is a constant and co==i=2o°, I have constructed wiremodels of the lines of magnetic force in space over the whirl. Thedimensions are the same as for the case already mentioned. ;So CARL STOmiER I /
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Keywords: ., bookcentury1800, bookdecade1890, booksubjectspectru, bookyear1895
