we shall at once have the ratio of Q E and E S. Aristarchus thought he had ascertained that the first quarter of the month (from N to Q) was about 12 hours shorter than the second, from which he computed the sun to be about 19 times as distant as the moon. The difficulty
lies in the impossibility of determining the precise moment when the disk of the moon is an exact semicircle. The real difference between the first and second quarters is really not quite 36 minutes, and the sun's distance is about 400 times the moon's.
The different methods upon which our present knowledge of the sun's distance depends may be classified as follows:
1. Observations upon the planet Mars near opposition, in two distinct ways:
(a) Observations of the planet's declination made from stations widely separated in latitude.
(b) Observations from a single station of the planet's right ascension when near the eastern and western horizons—known as Flamsteed's method.
2. Observations of Venus at or near inferior conjunctions:
(a) Observations of her distance from small stars measured at stations widely different in latitude.
(b) Observations of the transits of the planet: 1. By noting the duration of the transit at widely-separated stations; 2. By noting the true Greenwich time of contact of the planet with the sun's limb; 3. By measuring the distance of the planet from the sun's limb with suitable micrometric apparatus; 4. By photographing the transit, and subsequently measuring the pictures.
3. By observing the oppositions of the nearer asteroids in the same manner as those of Mars.
4. By means of the so-called parallactic inequality of the moon.
5. By means of the monthly equation of the sun's motion.
6. By means of the perturbations of the planets, which furnish us the means of computing the ratios between the masses of the planets and the sun, and consequently their distances—known as Leverrier's method.
7. By measuring the velocity of light, and combining the result (a) with equation of light between the earth and sun, and (b) with the constant of aberration.
Our scope and limits do not, of course, require or allow any exhaustive discussion of these different methods and their results, but some of them will repay a few moments' consideration:
The first three methods are all based upon the same general idea, that of finding the actual distance of one of the nearer planets by ob-