[25] Five of Jupiter's revolutions occupy 21,663 days; two of Saturn's revolutions occupy 21,526 days.
[26] Excircularity is what is meant by this term. It is called "excentricity" because the foci (not the centre) of an ellipse are regarded as the representatives of the centre of a circle. Their distance from the centre, compared with the radius of the unflattened circle, is called the excentricity.
[27] A curve of the nth degree has ½n(n+3) arbitrary constants in its equation, hence this number of points specifically determine it. But special points, like focus or vertex, count as two ordinary ones. Hence three points plus the focus act as five points, and determine a conic or curve of the second degree. Three observations therefore fix an orbit round the sun.
[28] Its name suggests a measure of the diameter of the sun's disk, and this is one of its functions; but it can likewise measure planetary and other disks; and in general behaves as the most elaborate and expensive form of micrometer. The Königsberg instrument is shewn in fig. 92.
[29] It may be supposed that the terms "minute" and "second" have some necessary connection with time, but they are mere abbreviations for partes minutæ and partes minutæ secundæ, and consequently may be applied to the subdivision of degrees just as properly as to the subdivision of hours. A "second" of arc means the 3600th part of a degree, just as a second of time means the 3600th part of an hour.
[30] A group of flying particles, each one invisible, obstructs light singularly little, even when they are close together, as one can tell by the transparency of showers and snowstorms. The opacity of haze may be due not merely to dust particles, but to little eddies set up by radiation above each particle, so that the air becomes turbulent and of varying density. (See a similar suggestion by Mr. Poynting in Nature, vol. 39, p. 323.)
[31] The moon ought to be watched during the next great shower, if the line of fire happens to take effect on a visible part of the dark portion.
[32] Address to Birmingham Midland Institute, "A Glimpse through the Corridors of Time."