convexity of the ovals is turned towards the north pole of the ecliptic ; but their inclination, or rather the inclination of the straight lines joining their extreme points, to the plane of the ecliptic continues to diminish, and about the beginning of March disappears ; so that the points at which they seem to enter and leave the sun s disk are equally elevated, as in fig. 25. From this time the curvature of the ovals diminishes ; they become narrower and narrower till about the end of May or beginning of June, when they again appear under the form of straight lines (fig. 26) ; but their inclination to the ecliptic is now precisely in a contrary direction to what it had been six months before. After this they begin again to expand, and their convexity is now turned towards the south pole. Their inclinations also vary at the same time, and about the commencement of September they are seen as repre sented in fig. 27 ; the points at which they enter and dis appear being again equally elevated. After this period the ovals begin to contract and become inclined to the ecliptic, and by the beginning of December they have exactly the same direction and inclination as they had the previous
year.These phenomena are renewed every year in the same order, and the same phases are always exhibited at cor responding seasons. Hence it is evident that they depend on a uniform and regular cause, which is common to all of them, since the orbits described by the various spots are exactly parallel, and subject in all respects to the same variations. The true explanation of the phenomena was early recognised by Galileo, who maintained that the spots belong to the surface of the sun, and that the sun uniformly revolves round an axis inclined to the axis of the ecliptic.
From four different combinations of equations, derived from eleven observations of the same spot, Delambre com puted the following table of the elements of rotation:—
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No. Node. Inclination. Revolution. Synodic Kevol. 1 2 3 4 80 45 7" 79 21 35 80 33 40 79 47 55 7 19 17" 7 12 37 7 16 33 7 29 4 251 o h 17 m 26 d 4 h 17 ra Mean 80 7 4 7 19 23 Diurnal motion 14 391
With regard to observations of the sun s spots, for the purpose of determining the rotation, Delambre remarked that he attached little value to them, first, because it is impossible to make them well ; and secondly, because (as he erroneously supposed) they could only lead to results of little importance. He discussed a hundred different spots, each observed at least three times by Messier, and deduced thirty different determinations of the elements of rotation. The more he multiplied his calculations, the more certain he became of the impossibility of a good solu tion ; of which, indeed, there is no other chance than in a compensation of errors, little probable on account of their enormous magnitudes. These discrepancies have been accounted for in recent times, chiefly through the labours of Mr Carrington. It had been suspected that the spots, besides partaking of the general motion of the solar globe, have also proper motions occasioned either by displacement or by a change of form. Carrington not only succeeded in proving that both these causes operate, but also in recognising systematic proper motions of the spots at rates depending on their solar latitude. It would not be possible to assign definitely the nature of such proper motions, simply because we do not know the normal rotation rate of the sun ; and therefore we are compelled, in describing Carrington s results, to speak of varying rotation rates, although it can hardly be doubted that the sun s globe, as a whole, has a definite rate of rotation, and that all the seeming variations from this rate are due to proper motions of the spots. Adopting, however, the only available method of describing Carrington s results, the following table repre sents the various rotation rates for different solar latitudes in both hemispheres:—
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Deg. 50 N. lat. 30 20 15 10 5 PJquator 5 S. lat. 10 15 20 30 45 Sun s Rotation Period, d. h. m. 27 10 41 26 9 46 17 9 3
2 23 5 13 17 12 11 25 25 25 25 24 24 25 25 25 26 28 8 10 29 42 11 18 35 31 52 50 Rotation per Day. 787 824 840 851 859 863 867 865 856 845 839 814 759
It is noteworthy that in each southern latitude the rotation is less than in the corresponding northern latitude, yet the difference is too small to admit of our attaching at present any considerable importance to this indication. Taking the mean between the results for the northern and southern hemispheres. Mr Carriugton has deduced the fol lowing empiric formula for the rotation rates in different solar latitudes:—
Let be the angle through which a part of the sun in latitude A rotates in one day; then
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Spërer, who has made similar observations, deduces the law
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=!G-8475 - 3-3812 (sin. A + 41 13 )
The following elements have been deduced from the results by Carrington and Spërer (for the year 1869):—
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Elements. Carrington. Sporer. Longitude of node of solar equator 73 57 74 37 Inclination of solar equator 7 15 6 57 Mean diurnal rotation 14 18 14 26 G4 Mi-an rotation period ... 25? 28 25<r234
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Fig. 28.—Sun Spots seen Sept 25, 1870.
