There are, in addition, as De Mairan proved in his classical memoir of the year 1746, longer periods common to both the number of sun-spots and the number of auroras. According to Hansky, the length of this period is 72 years; according to Schuster, 33 years. Very pronounced maxima occurred at the beginning and the end of the eighteenth century, the last in the year 1788; afterwards auroras became very rare in the years 1800-1830, just as in the middle of the eighteenth century. In 1850, and particularly in 1871, there were strong maxima; they have been absent since then. The estimates of the heights of the polar lights vary very considerably. The height seems to be the greater, on the whole, the nearer the point of observation is to the equator, which would well agree with the slight deflection of the kathode rays towards the surface of the earth in regions which are farther removed from the pole. Gyllenskiöld found on Spitzbergen a mean height of 55 km.; Bravais, in northern Norway, 100 to 200 km.; De Mairan, in central Europe, 900 km.; Galle, again, 300 km. In Greenland, Paulsen observed northern lights at very low levels. In Iceland he fixed the apex of the northern arch which may be considered as a point where the charged particles from the sun are discharged into the air at about 400 km. Not much reliance can be placed upon the earlier determinations; but the heights given conform approximately to the order of magnitude which we may deduce from the height at which the solar dust will be stopped by the terrestrial atmosphere. The polar lights possess, further, a pronounced yearly periodicity which is easily explicable by the aid of the solar dust theory. We have seen that sun-spots are rarely observed near the solar equator, and the same applies to solar faculæ. They rapidly increase in frequency with higher latitudes of the sun, and their maximum occurs at latitudes of about fifteen degrees. The equatorial plane of the sun is inclined by about seven degrees towards the plane of the earth’s orbit. The earth is in the equatorial plane of the sun on December 6th and June 4th, and most distant from it three months later. We may, therefore, expect that the smallest number of solar-dust particles will fall on the earth when the earth is in the equator of the sun—that is, in December and June—and the greatest number in March and September. These relations are somewhat disturbed by the twilight, which interferes with the observation of auroras in the bright summer nights of the arctic region, while the dark nights of the winter favor the observation of these phenomena. The distribution of the polar lights over the different seasons of the year will become clear from the subjoined table compiled by Ekholm and myself: Iceland and United Southern Sweden Norway Greenland States auroræ (1883-96) (1861-95) (1872-92) (1871-93) (1856-94)