numerous and so much more exact.

Accordingly,

Hansen, the eminent mathematician and lunarian, announced in 1854, in a letter addressed to the Astronomer Royal, that this method, applied with the aid of his new tables of the Moon, gave a solar parallax considerably exceeding Encke's estimate. In 1863, he assigned the value 8"-9159, corresponding to a distance of 91,659,000 miles.

Another method, depending on the apparent motions of the Sun, was applied (with a very similar result) by Leverrier.

If the Earth had no satellite she would travel on her elliptic orbit round the Sun, with no other perturbations than those produced by the planets. But since she has a satellite, whose mass is an appreciable though small aliquot part of her own, she is disturbed precisely in the same way, though not to the same extent, that the Moon is disturbed. The Moon travels once in a lunar month around her orbit, but the point round which the Moon moves is not the centre of the Earth, but the centre of gravity of the Earth and Moon; and around that centre of gravity the Earth also travels once in a lunar month. Now, precisely as an observer on the Moon would have in effect the range of the Moon's orbit around this centre of gravity, as a baseline by which to estimate the Sun's distance, so the observer on the Earth has the range of the Earth's orbit around the same centre of gravity for the same purpose. The diameter of this last-named orbit is indeed very small-little more, in fact, than three-fourths of the

Earth's own diameter; but by the radius of this small orbit the Earth is sometimes in advance and sometimes behind her mean position. In other words, her motion in longitude (that is, her angular motion round the Sun) is not equable. Over and above the variation of her velocity due to the ellipticity of her path, there is this alternate advance and (relative) retrogression, having for its period a lunar month. Obviously, the observed effect, so far as the astronomer is concerned, is an apparent irregularity in the Sun's motion, having the same period of one lunation. The effect is exceedingly minute: it is less than the displacement of the Sun as seen from different parts of the Earth; and, as we have seen, this effect could never be employed to determine the Sun's distance. Why then, it may be asked, is the other and smaller effect available? For this reason simply, that the daily observations made on the Sun in the meridian supply a fund of materials for estimating the effect in question. Such observations are made (severally) at one station by one telescope, and if not by one observer, yet by a series of observers who are always working together, so that their relative modes and powers of observation are comparable together.*

Leverrier, by the careful study of an enormous number of observations on the Sun, made at the

The great point, however, is that all the observations are meridional. Were extra-meridional observations of the Sun as trustworthy as those made on the meridian, the Sun's distance could have been long since determined through those effects of the Earth's rotation which depend on the length of her diameter.

principal observatories in Europe, came to the conclusion that the Sun's parallax is 8"-95, corresponding to a mean distance of 91,330,000 miles. Mr. Stone, however, has detected a numerical error in M. Leverrier's calculations; and when this error is corrected the value 8"-91 results, corresponding to a distance of 91,739,000 miles. Mr. Simon Newcomb, of America, has, by the application of the same method, deduced the parallax 8"-81, corresponding to a distance of about 92,800,000 miles.

MM. Fizeau and Foucault applied a method differing wholly in character from any that had before been thought of. It seems at first sight incredible that the ingenious combination of revolving wheels or mirrors should serve to determine the Sun's distance; but such

* Every method of solving the problem of the Sun's distance has its special difficulties. In Leverrier's method, the accuracy of the result is wholly dependent on the accuracy of our estimate of the Moon's mass; for clearly on this estimate depends the extent we are to assign to the Earth's monthly orbital motion around the common centre of gravity of the Earth and Moon. But the Moon's mass is only measurable by observations determining the amount of the nutation of the Earth's axis, a quantity of the same minute order as the solar parallax itself. Still, this method has the advantage of depending on a very large number of observations, both as respects the determination of the Moon's nutation, and that of the inequality of the Sun's motion. It is obvious that the latter inequality may be employed either to determine the Moon's mass when the Sun's distance is known, or vice versâ. It has been employed both ways, Delambre having deduced the value of the Moon's mass by this mode. The way in which the inequality is applied will depend on the question whether the Moon's mass or the Sun's distance is supposed to be best known by other methods. At present it is assumed that the Moon's mass is the more accurately determined element; but doubtless after the transits of 1874 and 1882 the inequality in the Sun's motion in longitude will be applied to determine the Moon's mass from the known distance of the Sun.

is the case. The essential point in the new method is the direct measurement of the velocity with which light travels. This velocity had been determined in two ways by astronomers, or rather it had been discovered in one way, and the deduced result had been confirmed in another. When Jupiter is in oppositionat which time he is nearest to us-the eclipses and occultations of his satellites were found to occur a few minutes earlier than had been calculated; whereas when he is near conjunction these phenomena occur after the calculated time. Römer first pointed out the meaning of this observation. He showed that the phenomena really occur at the calculated epochs, but that the light which brings to us the account of those phenomena reaches us more quickly when Jupiter is nearer to us than when he is farther away. Bradley afterwards found in this discovery the explanation of the aberration of the fixed stars. If light travelled with infinite velocity we should see the stars in the same direction whether the Earth was at rest or in motion. But as the velocity of light, though very great, is yet not infinite, the apparent direction in which the light from a star reaches the terrestrial observer is affected by the motion of the Earth, according to a law precisely similar to that which causes the apparent direction of the wind to be affected by the motion of an observer who is rapidly carried onwards in a carriage or other vehicle. And when Bradley determined the amount of the aberration of the fixed stars at different seasons, he found--and astronomers have since abun

dantly confirmed the result-that the precise velocity assigned to light by Römer was that required to account for the peculiarity which affects the apparent place of every star in the heavens, as the Earth sweeps onward on her yearly orbit.

But it will be seen that neither observation supplied the means of directly determining the velocity of light in miles per second. All that was known was-first, that light takes a certain interval of time in crossing the Earth's orbit (or some known chord of that orbit); and, secondly, that the velocity of light bears a certain proportion to the Earth's velocity in her orbit. Until the exact dimensions of the Earth's orbit are known, neither of these facts informs us of the real velocity of light. Judging, however, from Encke's estimate of the Sun's distance, astronomers concluded that light travels at the rate of no less than 192,000 miles in a single second of time.

It might seem altogether hopeless to attempt to estimate directly a velocity so enormous as this. Remembering how the velocity of sound has been measured, and considering only the application of a similar method to the case of light, how utterly futile does the very thought of such an attempt appear! We can make a signal when a sound is heard at one station, and observers at another station can note how long the sound takes in reaching them; because where the stations are at a considerable distance, an appreciable time elapses before the sound travels from one to the other. But the very best signal we can use is some