With reference to the general question as to the existence of the “willow-leaves,” my conception of the matter is that the features described by Mr. Nasmyth are not new. His drawing of a spot in Sir J. Herschel’s ‘Outlines’ and Chambers’s ‘Descriptive Astronomy’ exhibits objects extremely uniform in shape and size, and this uniformity I have never observed in the penumbra of spots. As to the engraving in the ‘Outlines,’ showing the aspect of the interlaced “willow-leaves” on the general surface, this is also not realized in observation. The “corrugations” and “bright nodules” of Sir W. Herschel aptly represent what is seen, and they are possibly identical with the “very small bright and obscure points” and “lively and sombre streaks” of Scheiner, though seen much better and in more profusion of detail through the improved modern telescopes. The so-called “willow-leaves” are rounded at the ends, and are consistent neither in size nor shape. They encroach upon the umbra of the spots, and give a thatched appearance to the edges. The penumbra also shows this in its outer limits, where it is also fringed with lenticular particles. Drawings by Capocci and Pastorff seventy-five years ago, and published in Arago’s ‘Popular Astronomy,’ show the thatching at the edges of the umbra quite as palpably as it is represented in recent drawings. [Illustration: Fig. 23. Belts of Sun-spots, visible October 29, 1868.] _Rotation of the Sun._—By noting when the same individual spots return to the same relative places on the disk, the approximate time of rotation is easily deduced. This varies according to the latitude of the spots[12]; whence it is evident the solar atmosphere is affected by currents of different velocities, causing the spots to vary in their longitudes with reference to each other. The Earth’s motion round the Sun causes the spots to travel apparently more slowly than they really do; for observations prove that a spot completes a rotation in 27 days 5 hours, whereas the actual time, after making allowance for the earth’s orbital motion, is about 25 days 7-3/4 hours. The period of rotation may be roughly found as follows, supposing a spot to return to precisely the same part of the disk in 27 days 5 hours:— 365^d 5^h 49^m + 27^d 5^h = 392 10^h 49^m. Then 392^d 10^h 49^m (= 565,129^m) : 365^d 5^h 49^m (= 525,949^m) :: 27^d 5^h (= 39,180^m) : 25^d 7^h 44^m (= 36,464^m).