is the velocity of the shot, the smaller will be the space bB described by the ship while the shot is passing across her, and therefore the smaller will be the angle b CB between the apparent direction of the shot and its real direction.

The same thing happens with regard to the effect of the motion of the earth on the apparent path of light, and it will produce an apparent change in the places of the stars. And if we find that there is such an apparent change, it will be a certain proof that the earth is in motion; but if we find the change to be small, it will prove that the velocity of light is much greater than that of the earth.

Now I will point out to you the visible effect of the aberration of light upon the place of a star. The immediate interpretation of the consideration which I have mentioned is this. In whatever direction the earth is moving, the apparent position of any star which we are looking at, is displaced in the direction towards which the earth is moving. In Figure 53, let C be the sun, E',E",E"",E"", the earth in four successive positions of its orbit (viewed in perspective), its motion at each place being in the direction of the arrow drawn there; S the true place of a star. Then, in consequence of the aberration, when the earth is at E', as its motion is in the direction of the arrow drawn from E', the light coming from the star will enter the eye of a spectator or the tube of a telescope, not as if it came from S, but as if it came from s', the line Ss' being parallel to the arrow at E'; and therefore the observer, when the earth is at E', does not see the star at S but at s'. In like manner, when the earth is at E" he sees the star at s"; when at E" he sees the star at ""; and when at E he sees the star at """. Thus you will see that, in

every position of the earth, the star's place is affected by the aberration of light; and from this cause every

star apparently describes a small circle every year parallel to the earth's orbit. It is a minute circle; its angular diameter, as seen without any foreshortening, is found to be about forty seconds. This quantity is, however, so serious that it cannot be omitted in the computation of any observation whatever.

From the measure of the apparent semi-diameter of the small circle described by the star, corresponding to the angle BCb in Figure 52, we are able to compute the proportion of the earth's velocity to the velocity of light; and we find that the velocity of light is about 10,000 times as great as the earth's velocity in its orbit, or about 200,000 miles in a second: In other words, light travels a distance equal to eight times the circumference of the earth between two beats of a

clock. This is a prodigious velocity, but the measure of it is very certain.

These three quantities, (precession, nutation, and aberration,) are the corrections to a star's apparent place, which it is necessary for us to take into account in every observation of a star, at whatever part of the earth it is observed; and besides these, it is necessary at every place to apply the proper correction for refraction, which may be different at every different place of observation. Having obtained these elements of calculation, we can proceed at once with the measure of the distance of the fixed stars.

In Figure 54, let E',E",E"",E""", be four positions of

the earth in its orbit (seen in perspective), P a place of observation, S a star, (the earth being in such a

part of its rotation that the meridian of P passes through the star); also let S' be another star in the plane of the earth's orbit, and in the direction corresponding nearly to the earth's solstitial position. And suppose (in conformity with the assertion that we have made all along, but which we shall now subject to the severest proof) that the earth's axis remains strictly parallel to itself in its motion round the sun, with no other motion than those which we have described as produced by precession and nutation. And suppose that with a mural circle at P we observe the zenith-distances of the stars S and S' when they pass the meridian of P, and apply the proper corrections for refraction; and then, by applying corrections for the effects of aberration, we find the place in which the star would have been seen, if unaffected by the earth's velocity: and by applying corrections for precession and nutation, we find the zenithdistances which the stars would have had if the position of the earth's axis had not been affected by precession and nutation. Now, if our assumption (that the earth's axis has no motion but those depending on precession and nutation) be correct, the result of the observation of the star S', whatever be its distance, will be, that its corrected zenith-distance when observed on the meridian will be the same whether the earth be at E', E", E"", or E""". This is found to be strictly in agreement with the results deduced from actual observation, so that it is certain that the earth's axis has no motion but those depending on precession and nutation. Moreover, for the vast majority of stars in all parts of the heavens, when the same corrections are applied, the corrected meridional zenithdistances are found to be the same whatever be the position of the earth in its orbit; and this proves,

both that the earth's axis has no motion except those of precession and nutation, and that the stars are at an inconceivable distance.

But there may be other stars, as S, whose distance we have some reason for conjecturing to be not so enormously great. Now, the only way in which we can measure its distance is one strictly analogous to that used for measuring the distance of the moon ; with this difference, that we cannot observe from two places at once. On account of the immense distance of the stars, it would be necessary to observe the place of the star from two positions, as far distant as the breadth of the earth's orbit; but we cannot do that. We can, however, observe the position of the star from the earth when the earth is in two positions, as E' and E"", on opposite sides of the earth's orbit ; that is, at times half a year apart.

I have used, as an elucidation of parallax, the effect of the two eyes in the head. If you have your head in any fixed position, and you shut one eye, you cannot determine accurately the distance of an object; but if you open both eyes, the distance is seen immediately. But with one eye, a person can judge of distance very well, if he moves his head. In like manner, one observer on the earth can observe the 'distance of a star, provided he takes advantage of the change of places at different times; that is, provided he allows his eye to be moved round for him by the revolution of the earth round the sun; it is, however, necessary for us to be fully possessed of every element for correction of the star's place, so as to clear it of every source of change, except the difference of apparent place depending on the star's distance and the earth's place in its orbit. This is the reason why I have deferred the mention of this measure until I had