in motion is (pace M. Cremieux) equivalent to a negative current, the passage of electrified particles through the upper atmosphere should affect magnetic instruments on the earth. Sunspots, auroræ, magnetic storms should therefore vary together.
It has long been known empirically that they do agree in a general way. Arrhenius' discussion of the mass of statistics of observed auroræ forms so striking an example of the 'Method of Concomitant Variations' that at the risk of wearying the reader we shall give it in some detail.
(a) Both sunspots and auroræ show marked maxima at the middle of the eighteenth and the end of the nineteenth centuries.
(b) Sunspots, auroræ, and magnetic storms go through a simultaneous increase and decrease in the well-known period of 11.1 years.
The source of these slow variations must be looked for in the little understood variations of the sun's activity.
The number of auroræ is greatest in March and September, and least in June and December; and the mean frequency for both hemispheres is somewhat less in June than in December.
Now the sun's activity, as indicated by the number of sunspots, is a minimum at his equator, the spots occurring principally in belts about 15° north and south of his equator. Since the streams of particles issue radially from the sun, the earth will be most exposed to them, when she is most nearly opposite the active belts. But the earth stands opposite the sun's equator on June 4 and December 6, and is at her farthest north and south of it (7°), i. e., most nearly opposite the sunspot belts, on March 5 and on September 3. Moreover, she is somewhat nearer to the sun in December than in June.
As between the two hemispheres, the same conditions apply as those which regulate the seasons, viz., altitude of the sun above the horizon, and length of time during which he remains above it daily. Auroræ should therefore be more frequent in summer than in winter, a result which is verified by the records. And just as the highest daily temperature occurs from two to three hours after mid-day, so we ought to find a daily maximum of aurorae about 3 p. m. It is not possible to verify this directly, since auroræ are not visible in daylight. But Arrhenius remarks (1) that the majority of them occur before midnight and not after it, which is so far in general agreement with the theory; (2) that Carlheim-Gyllenskiöld, discussing the observations made at Cape Thordsen in Spitzbergen during the winter of 1882-1883, with a view to correcting the numbers recorded for the effect of daylight in concealing them, deduces a probable maximum for the number actually occurring at 2.40 p. m.