Sir John Herschel, in commenting on the theory of Mr. Redfield before the British Association, convened at Newcastle in 1838,[35] suggested an analogy to terrestrial hurricanes, from a suspected rotation and progressive motion in these spots. From their rapid formation, change of shape, and diameter, this view is allowable, and, taken in conjunction with the action of the ethereal currents, will account for all the phenomena. The nucleus of the spot is dense, like the nucleus of a storm on the earth, and surrounded by a penumbon precisely as our storms are fringed with lighter clouds, permitting the light of the sun to penetrate. And, it has been observed, that these spots seem to follow one another in lines on the same parallel of solar latitude (or nearly the same), exactly as we have determined the action of the vortices on the surface of the earth from observation. These spots are never found in very high latitudes—not much above 30° from the solar equator. If we consider this equator to be but slightly inclined to the plane of the vortex, this latitude would be the general position of the lateral solar vortices, and, in fact, be confined principally to a belt on each side of the equator, between 15° and 30° of solar latitude, rather than at the equator itself. This, it is needless to say, is actually the case. But, a more capital feature still has been more recently brought to light by observation, although previously familiar to the author, who, in endeavoring to verify the theory, seriously injured his sight, by observing with inadequate instrumental means. This is the periodicity of the spots.
We have already observed, that there is reason to suppose that the action of the inner vortex of the earth is probably greater than that of the outer vortex, on account of the conflicting currents by which it is caused. And the full development of this vortex requires, that the central vortex or mechanical axis of the system shall be nearly tangential to the surface. In this position, the action of the central vortex is itself at a maximum; and, when the planets of the system are so arranged as to produce this result, we may expect the greatest number of spots. If the axis or central vortex approaches to coincidence with the axis of the sun, the lateral vortices disappear, and the central vortex being then perpendicular to the surface, is rendered ineffective. Under these circumstances, there will be no spots on the sun’s disc. When, on the other hand, all the planets conspire at the same side to force the sun out from the mechanical centre of the system, the surface is too distant to be acted on by the central vortex, and the lateral vortices are also thrown clear of the sun’s surface, on account of the greater velocity of the parts of the vortex, in sweeping past the body of the sun. In this case, there will be but few spots. The case in which the axis of the vortex coincides with the axis of the sun, is much more transient than the first position, and hence, although the interval between the maxima will be tolerably uniform, there will be an irregularity between a particular maximum, and the preceding and subsequent minimum.
The following table exhibits the solar spots, as determined by Schwabe, of Dessau:
Previous to the publication of this table, the author had inferred the necessity of admitting the existence of another planet in the solar system, from the phenomenon of which we are speaking. He found a sufficient correspondence between the minima of spots to confirm the explanation given by the theory, and this was still more confirmed by the more exact determination of Schwabe; yet there was a little discrepancy in the synchronous values of the ordinates, when the theory was graphically compared with the table. Previous to the discovery of Neptune, the theory corresponded much better than afterwards, and as no doubt could be entertained that the anomalous movements of Uranus were caused by an exterior planet, he adopted the notion that there were two planets exterior to Uranus, whose positions at the time were such, that their mechanical affects on the system were about equal and contrary. Consequently, when Neptune became known, the existence of another planet seemed a conclusion necessary to adopt. Accordingly, he calculated the heliocentric longitudes and true anomalies, and the values of radius vector, for all the planets during the present century, but not having any planetary tables, he contented himself with computing for the nearest degree of true anomaly, and the nearest thousand miles of distance. Then by a composition and resolution of all the forces, he deduced the radius vector of the sun, and the longitude of his centre, for each past year of the century. It was in view of a little outstanding discrepancy in the times of the minima, as determined by theory and observation, that he was induced to consider as almost certain the existence of a theoretical planet, whose longitude, in 1828, was about 90°, and whose period is from the theory about double that of Neptune. And for convenience of computation and reference, he has been in the habit of symbolizing it by a volcano. The following table of the radii vectores of the sun, and the longitude of his centre, for the years designated in Schwabe’s table, is calculated from the following data for each planet:
| Planets. | Masses. | Mean distances. | Eccentricities. | Long. of Perihelion. |
|---|---|---|---|---|
| ♃ | 1 ⁄ 1648 | 494.800.000 | 0.0481 | 11° |
| ♄ | 1 ⁄ 3310 | 907.162.000 | 0.0561 | 89° |
| ♅ | 1 ⁄ 23000 | 1824.290.000 | 0.0166 | 167° |
| ♆ | 1 ⁄ 20000 | 2854.000.000 | 0.0088 | 0° |
| ⊿ | 1 ⁄ 28000 | 4464.000.000 |
It is necessary to observe here, that the values of the numbers in Schwabe’s table are the numbers for the whole year, and, therefore, the 1st of July would have been a better date for the comparison; but, as the table was calculated before the author was cognizant of the fact, and being somewhat tedious to calculate, he has left it as it was, viz., for January 1st of each year. Hence, the minimum for 1843 appears as pertaining to 1844. The number of spots ought to be inversely as the ordinates approximately—these last being derived from the Radii Vectores minus, the semi-diameter of the sun = 444,000 miles.
In passing judgment on this relation, it must also be borne in mind, that the recognized masses of the planets cannot be the true masses, if the theory be true. Both sun and planets are under-estimated, yet, as they are, probably, all to a certain degree proportionally undervalued, it will not vitiate the above calculation much.
The spots being considered as solar storms, they ought also to vary in number at different times of the year, according to the longitude of the earth and sun, and from their transient character, and the slow rotation of the sun, they ought, ceteris paribus, to be more numerous when the producing vortex is over a visible portion of the sun’s surface.