[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.

Transcriber's Notes: