646. SCHOLIUM. The aberration of light has been considered by some philosophers, in a manner rather different from that of Dr. Bradley. About the year 1767, Mr. Patrick Wilson, assistant professor of astronomy at Glasgow, entertained an idea that the aberration of the fixed stars indicated the proportion between the orbital velocity of the earth, and the velocity of light in the vitreous humour of the eye. This opinion soon led him into various discussions, and in particular, made him suppose, that the aberration of the fixed stars, when determined by observations made with a telescope filled with water, would be different from the aberration ascertained by cbservations with a common telescope. About the year 1775, Mr. Wilson felt inclined to embrace an opinion (which has been started by various ingenious men at different times), that the centre of the solar system was in motion, and in 1777, communicated to Mr. Professor

aris. This nutation is a kind of libratory motion of the earth's axis, by which its inclination to the plane of the ecliptic is continually varying backwards and forwards, by a small number of seconds. The whole extent of this change in the inclination of the axis, or, which is a consequence of it, in the apparent declination of the stars, is about 19', and the period of the change is little more than nire years; or, the space of time from its setting out from any point and returning to the same again, about eighteen years and seven months, being the same as the period of the moon's motions; on which, indeed, it chiefly depends: being the effect of the inequalities of the joint action of the sun and moon upon the spheroidal figure of the earth, by which its axis is made to revolve with a conical motion, so that the extremity of it describes a small ellipsis, having its diameters 191 and 14'2, each revolution being performed in the time above mentioned. This is a natural consequence of the Newtonian system of universal attraction, and had been hinted at by some, ever since the publication of the Principia; but for Dr. Bradley was reserved the honour of establishing the fact, and thus confirming (in a manner beyond controversy) the truth of the prin ciples which Newton had laid down.

For more on the subject of nutation, see Philos. Transactions, 1748; Dr. Maskelyne's Astronomical Observations, 1776; D'Alem bert Recherches sur la Précession des Equinoxes; and La Lande's Astronomy, vol. III. p. 210—226.

Robison, and others, a paper on this subject. The water-telescope had, by this time, become familiar to his thoughts; and it occurred to him, that it might be employed for deciding this important question, and even for determining the direction and velocity of this motion, by means of the difference between the observed aberration of the fixed stars, and the aberration which should result from the earth's orbital motion alone. But various objections and difficulties occurred in the prosecution of this attempt; and Mr. Wilson soon after thought of a different method, which as it may, perhaps, at some future period, lead to the discovery of some terrestrial or celestial motions with which we are at present unacquainted, is here described.

If the earth be carried towards a fixed star, with a great velocity, and the rays from the star be made to deviate a little by an achromatic prism, it will follow, that a constant angle of incidence will give different angles of total deviation, according to the velocity of the motion, and this difference will be both real and apparent. Therefore, 1. Let the telescope of a meridional quadrant be furnished with a prism, refracting a few degrees in altitude; then search, by meridional observations, for such stars as exhibit altitudes inconsistent with Dr. Bradley's observations; the differences will indicate an aberration caused by a motion of the earth, different from its orbital motion round the sun: if, after the variations occasioned by nutation (Art. 645. note) are allowed for, there still remain some number of seconds, or parts, they will indicate some motion of the earth of which we have, as yet, no knowledge.

2. Furnish a telescope with a plain mirrour, inclined to its axis in an angle of 45°, and a series of achromatic prisms refracting 90°. Suppose the telescope to be directed to a point of the heavens 90° distant from a star which is viewed through it: sup

pose also, the earth to be at rest, and the images of this star, formed by the refracted and by the reflected light, to coincide: then suppose the earth to be in motion towards this star; the images will separate, both on account of a change in the total deviation of the refracted light, and likewise on account of a transverse aberration, to which the refracted image is liable, by the motion of the telescope.

3. If a long achromatic telescope be directed to a fixed star, towards which the earth is moving, the focal distance will be lengthened; and the contrary. The augmentation may indeed be very small, but an observer, well acquainted with optics, will, on a little consideration, be able to apply such means of increasing it, as to render it sensible.

CHAPTER XXIII.

On the Latitude and Longitude.

1

ART. 647. BECAUSE the latitudes and longitudes of most of the principal places in this kingdom are determined with tolerable accuracy, they have been assumed as known in many of the discussions in the preceding part of this treatise: but as there are many places upon the earth, and indeed in England, respecting which these particulars are not ascertained, the determination of them is of considerable importance to geography and navigation as well as astronomy; various methods of finding each are, therefore, here explained.

648. Since the latitude of a place on the earth, is its distance from the equator, measured on an arc of the meridian passing through it (Art. 19.), the most simple method of determining the latitude is, to take the meridian altitude of the sun's centre, when it is in the equator (i. e. in the first point of Aries or Libra), or the meridian altitude of a star which has no declination; then the complement of the meridian altitude is equal to the latitude of the place. For, in fig. 7, Pl. I. if H R represent the horizon, E Q the equator, Z the zenith of the place, ZH AR the meridian; the latitude of the place will be E Z, and this is manifestly equal to the complement of HE, the altitude of the equator. In this method, and likewise in the following ones, the proper allowances

FF

must be made for refraction, dip of the horizon (Art. 680.), and the sun's semidiameter, when the altitude of either its upper or lower limb is taken.

649. But, since the sun is in the equator only on two days in the year (and then, perhaps, not exactly at noon), and there are very few stars in the equator upon which observations can be made; we may more generally find the latitude by means of the correct zenith distance of the sun's centre, when on the meridian, its declination being known; or the correct zenith distance when on the meridian of any star whose declination is known: for, if the zenith distance and declination are both north, or both south, add them together; but if one be north, and the other fouth, subtract the less from the greater, and the sum or difference will be the latitude, of the same name with the greater. The truth of this rule may be shewn by referring to fig. 7, Pl. I. where HR, EQ, and Z, represent as in the last article: then, 1st, when the zenith distance and declination are both north, or both south, let a be the place of the sun, or star, on the meridian, and E a its declination; aZ +a EEZ the latitude: 2dly, when the zenith distance and declination is one north, the other south; if the zenith distance be greater, let c be the place of the sun, or star, on the meridian, then c Z (its zenith distance) E (its declination) EZ the latitude; but if the declination be greater than the zenith distance, as when the star is at y, then Ey (the declination)Zy (the zenith distance) EZ the latitude.

The latitude may be found in a similar manner, from the observed meridional altitude of the moon's upper or lower limb; but farther corrections will be necessary for the moon's parallax, and her altitude, and great care must be used to obtain the declination accurately.

650. The latitude may be found very readily by