FOOTNOTES:
[1] It might be suggested that the appearance of this blazing comet among the stars drove the more superstitious of the Israelites at that time to the worship of star-gods, as we read how, during the judgeship of Jair, they "served Baalim, and Ashtaroth, and the gods of Syria, and the gods of Moab, and the gods of the Philistines, and forsook the Lord and served not Him." To a people like the Jews, who seem to have been in continual danger of returning to the Sabaistic worship of their Chaldean ancestors, the appearance of a blazing comet may have been a frequent occasion of backsliding.
[2] I do not say we can in any way avoid this far greater difficulty. Our own material universe cannot even be conceived as limited in any way save by void space of infinite extent; and it is as impossible for us to conceive an infinite void as to conceive the infinite extension of matter. Some modern mathematicians, indeed, assert that space is not necessarily infinite, but they accompany the assertion (very justly) with the admission that we cannot possibly conceive any boundary to space; and as one of the things they ask mathematicians to admit is the possibility that a straight line indefinitely produced both ways will at length re-enter into itself, while another is the possibility that in other parts of the universe two and two may make three or five, they are not likely, I conceive, to persuade most mathematicians (profoundly mathematical though they are themselves) that the mystery of infinity has been as yet entirely expounded.
[3] Of course the reader will understand that when I here speak of the earth's weight, I mean simply the pressure which would be exerted by the quantity of matter contained in the earth, if each portion were only subjected to an attractive force equal to that of gravity at the earth's surface. The actual force with which the earth is drawn in any direction, as a weight at the earth's surface is drawn downwards, depends on the distance and mass of the attracting body as well as on the mass of the earth; and strictly speaking, we ought not to say that the earth weighs so many millions of tons, but that she contains so many million times as much matter as a mass which at her surface weighs a ton.
[4] The words of Newton, "Hypotheses non fingo," have been often quoted in such sort as to give an entirely incorrect idea of his real opinion as to the relation between theoretical and practical science. As too commonly understood, they would, in fact, make his discovery of gravitation a great exception to his own rule. They must be taken in connection with his definition of a hypothesis, as "whatsoever is not deduced from phenomena." It is a part of true science, nay, it is the highest office of the student of science to deduce theories from phenomena. Such research stands as high above the simple observation of phenomena as architecture stands above brick-making or stone-cutting. But to frame hypotheses as the old Greeks did, trusting to the power of the understanding independently of the observation of phenomena, is to make bricks without straw and to build with them upon the sand.
[5] The point is explained in a paper called "Our Chief Timepiece Losing Time," in the first series of my "Light Science for Leisure Hours."
[6] In the popular, but incorrect way of speaking, the balance between the centrifugal and the centripetal force will no longer be maintained: the increase of velocity will give the centrifugal force the advantage, and it will slowly draw the body away from the centre. In reality there is no centrifugal force, the only force acting on the earth in her course round the sun being the sun's attraction upon her, which, however, must keep bending her course from the straight line, if she is to maintain her distance. In the case above imagined it would not bend her course actively enough.
[7] Its place is indicated in my School Atlas, as well as (of course) in my Library Atlas, from the latter of which the small maps illustrating the present article have been pricked off. The new star is marked T in the Crown (Map VIII.), and must not be confounded with the star τ, as in Roscoe's Treatise on Spectral Analysis, and in some astronomical works. The star τ is a well known fifth magnitude star, which has shone with no perceptible increase or diminution of splendour since Bayer's time certainly, and probably for thousands of years before.
[8] This chapter was first published in February, 1877, when the star was already invisible to the naked eye.
[9] It will be remembered by those familiar with the history of solar observation, that when the spectrum of the solar prominence was first observed, the orange-yellow bright line was supposed to be the well-known double sodium line. It is so near to this pair of lines, that while they are called D 1 and D 2, it has been called D 3; and in a spectroscope of small dispersive power the three would be seen as one.
[10] It has been thought by some that, in the beginning, the moon was always opposite the sun, thus always ruling the night. Milton thus understood the account given in the first book of Genesis. For he says,—
Less bright the morn,
But opposite in levell'd west was set
His mirror, with full face, borrowing her light
From him; for other light she needed none
In that aspect; and still that distance keeps
Till night, then in the east her turn she shines,
Revolv'd on Heav'n's great axle.
It was only as a consequence of Adam's transgression that he conceives the angels sought to punish the human race by altering the movements of the celestial bodies—
To the blank moon
Her office they prescribe—
It is hardly necessary to say, perhaps, that this interpretation is not scientifically admissible.
[11] Brown is not the right word for the tint of red where the visible spectrum begins. I know, however, of no word properly expressing the colour.
[12] Suppose there are two planets A and B of equal density, of which A has a diameter twice as great as that of B. Then the volume of A is eight times greater than B's volume. So that if the volume of its atmosphere exceed the volume of B's air in the same degree, the planet A has eight times as much air as the planet B. But the surface of A is only four times as great as the surface of B; so that if A had only four times as much air as B, there would be the same quantity of air above each square mile of A's surface as above each of B's surface. Since then A has eight times—not merely four times—as much air as B, it follows that A has twice as much air over each square mile of surface as B has. And similarly in all such cases, the general law being that the larger planet has more air over each square mile of surface in the same degree that its diameter exceeds that of the other.
[13] By age here I do not mean absolute age, but relative age. I speak of Mars and the Moon as older than the earth in the same sense that I should speak of a fly in autumn as older than a five-year-old raven.
[14] Who assigned to him, as his representative metal, lead—a metal "heavy, dull, and slow," as Don Armado puts it, in "Love's Labour's Lost."
[15] Attention has lately been called, by the astronomers of the Washington Observatory, to the fact that the statement usually made in our books of astronomy, that Sir W. Herschel's latest determination of Saturn's rotation period was 10h. 29m., is incorrect. His only determination of the period gave 10h. 16m. 44s. for the Saturnian day.
[16] "The altar, bearing fire of incense, pictured by stars." A remarkably bright and complex portion of the Milky Way lies near the constellation Ara, giving the appearance of smoke ascending from the altar, only the altar must be set upright, as in my Gnomonic Atlas, not inverted as in all the modern maps. (It is shown properly in the old Farnese globe).
[17] There is, however, a much more perfect way of determining this proportion, by applying the law which Kepler found to connect the distances of the planets from the sun with the times in which they complete the circuits of their orbits. The law is that, if we take any two planets, and write down the numbers expressing their periods of circuit (say in days), and the numbers expressing their distances from the sun (say in miles) in the same order; then if we multiply each number of the first pair into itself, and each number of the second pair twice into itself, the four numbers thus obtained will be proportional; that is to say, as the first is to the second, so will the third be to the fourth. Now, as every one knows who has worked sums in the rule of three, when any three are given out of four proportionals, the fourth can always be found; but we know the periods of circuit both of the earth and Venus (365·2564 days and 224·7008 days respectively) very exactly indeed, because they have traversed their orbits so many times since they began to be observed by astronomers. We can call the earth's distance 100, and then applying the rule just stated, we get Venus' distance relatively to the earth's. The reader who cares to work out this little sum will find no difficulty whatever—if at least he is able to extract the cube roots of any number. The proportion runs thus:—
365·2564 × 365·2564 : 224·7008 × 224·7008
:: 100 × 100 × 100 : (Venus' distance cubed.)
Work out this sum and we get for Venus' distance 72·333. The ratio of Venus' distance to the earth's is almost exactly expressed by the numbers 217 and 300.