Cassini afterwards traced the progress of this spot to the Sun's limb. He remarks, The apparent velocity nigh the centre was such that if it had continued the same, the spots would have arrived almost in four days to the limb of the disque; but in the hypothesis that they are either attached to the Sun's surface or not far from it-this apparent velocity was to lessen according as the spots should remove from the centre; as hath come to pass in effect. The diminution in the length of the misty crown' (a strange name for the penumbra) was in a manner proportionat to the diminution of the apparent velocity; since that when this crown was in the midle, and in a scituation wherein its true figure could be best seen, it appeared oblong and of the form of an human ear, its greatest diameter respecting east and west; but being nigh the limb, this same diameter seemed to shorten; and having appeared greatest in its first scituation, it appeared least in this, because it was almost in a circle that passed through the centre of the Sun, whose equal arches are by so much the more oblique by how much they approach more to the limb of his disque, and consequently appear less according to the rules of opticks; meantime the diameter that was turned from north to south apparently kept the same bigness it had near the centre, because it was in a circle almost parallel to the horizon of the Sun, which formed the representation of its limb, and whose equal arches (by the same optical reasons) do not appear contracted.' It will be seen by this reasoning-which,

6

being interpreted, signifies that the effect of foreshortening was to make the spot seem longest in a direction square to a line from the Sun's centre-that Cassini had on this occasion come very near to the discovery afterwards made by Dr. Wilson, that the nucleus of a spot is at a lower level than the solar photosphere. For had he but noticed an excess of breadth in the penumbra nearest to the Sun's limb, the same just reasoning which he applied to the figure of the spot would have enabled him to pronounce at once respecting the relative level of the nucleus, the penumbra, and the photosphere. He gives a picture of the spot close by the Sun's limb, in which the penumbra is of equal width on the side next the centre and on that next the limb. Most probably no such peculiarity as Dr. Wilson detected, existed in the case of this particular spot. In fact, so far as my own experience of the aspect of Sun-spots is concerned, spots such as the one observed by Cassini seldom exhibit the peculiarity in question in a manner which would enable an observer to theorise safely respecting the level at which nucleus, penumbra, and photosphere actually lie.

In November 1769, Dr. Wilson, of Glasgow, began the careful study of a large spot (visible to the naked eye). The results which he deduced from its changes of appearance are of great interest and importance. When he first examined the spot (November 22) it was situated not very far from the western edge of the Sun's disc. On the next day he found that the spot

had changed in appearance.

*

The penumbra which on the previous day was equally broad on all sides of the nucleus was now very much contracted on the side which lay towards the centre of the disc, while the other parts retained nearly their former dimensions. On the 24th he again observed the spot. The distance from the limb was now only twenty-four seconds, and the contracted side of the penumbra had entirely vanished. The breadth of the nucleus on the same side also appeared to be more suddenly impaired than it ought to have been by the motion of the Sun across the disc.'

Dr. Wilson showed that these results correspond with those which would follow if the spot was a vast cavernous opening, having the nucleus at the bottom, and the penumbra forming its sloping sides. It only remained to be seen whether a corresponding succession of changes occurred when the spot re-appeared on the eastern edge, and thence passed across the solar disc. This actually happened. On December 11, the spot appeared on the opposite side of the disc. It was then distant about a minute and a half from the edge. The side of the penumbra next the edge, which formerly vanished, was now wholly visible, while that turned towards the centre of the disc appeared to be wanting. On December 12 it came into view, and he saw it distinctly, though narrower than the other side. He did not see the spot again until December 17, when it

From Professor Grant's abstract of the original narrative, in his excellent History of Physical Astronomy.

had passed the centre of the disc, and the penumbra now appeared to surround the nucleus equally on all sides.

In fig. 41 the upper row of spots represents the succession of changes actually presented by this spot, while the lower shows what would occur as a spot traversed the Sun's disc, if the spot were simply a surface stain with a penumbral fringe. It will be seen

FIG. 41.

that the difference between the appearances depicted in the two rows is of a sufficiently marked character. It will also be noticed that even without any definite explanation of the peculiarities shown in the upper row, the mind at once recognises the fact that we have here to do with a cavity or depression.

Let us examine, however, the line of reasoning by which Dr. Wilson demonstrated this.

Let A, B, C (fig. 42)* be supposed to represent perspective views of a saucer-shaped depression on the surface of a sphere-the depressions being all of like dimensions (the sloping sides are assumed in these three views to be transparent). Then it is obvious that to an eye, supposed to view them from above, the relative breadth of the black base and of the shaded sides would be indicated by the breadth of the dark and shaded spaces carried vertically upwards from the

spots. Now, suppose the sphere to be rotated on a horizontal axis so that the spots are brought (their edges sliding as it were along the dotted lines) down to the positions A', B', C.' Then the relative breadths of the penumbra and nucleus will be indicated by the

* This figure in essentials closely resembles a figure in Fr. Secchi's recently published work on the Sun. It was drawn by me, however, and employed in illustrating lectures, nearly a year before Secchi's book appeared.