is

portion as it is more diftant; for the nearer g to S, the greater is the angle Sg T; hence mathematicians prove, that when the altitudes are the fame, the parallax of altitude is in the inverse ratio of the distance.

The horizontal parallax of the moon, which s the greatest of all the planets, does not exceed a degree.

The parallax of a planet increases also with it's apparent diameter; in fact, the further a planet is off, the lefs is it's apparent diameter, and the diameter diminishes like the parallax in an inverse ratio of the diftance; therefore the parallax is as the diameter. If the parallax was leffened one half, the diameter would be one half lefs; and the fame relation fubfifts, whatever be the diftance. Thus the diameter of the moon is always of it's parallax, and the cube of this fraction, marks it's fize with respect to the earth.

When the horizontal parallax of a celeftial object is known, it is eafy to difcover, by the rules of trigonometry, the diftance of the object; for in the right angled triangle S T G, you have the femidiameter of the carth S T known, the angle S TD 90 degrees, and the parallactic angle T G S given, from whence it is eafy to obtain the reft. It is indeed difficult to determine the horizontal parallax with accuracy, on account of the effects of refraction. But the parallax of an object at any altitude being obferved, it's horizontal parallax may be computed.

The diurnal parallax of an object according to the different fituation of the ecliptic and equator in respect to the zenith, will fometimes caufe an apparent change or parallax of the latitude, longitude, declination, and right afcenfion thereof.

In finding the parallax of the fun, or which is the fame, the angle under which the earth's femidiameter would appear at that diftance, the angle

is fo exceeding fmall, that a mistake of one fecond would occafion an error of about feven millions of miles, from whence you tnay judge the exactness neceffary in finding the parallax of any celestial object.

The annual parallax is the change in the apparent place of an object, which is caused by it's being viewed from the earth in different parts of it's orbit.

The annual parallax of all the planets is very confiderable, that of the fixed ftars infenfible.

The fun's parallax being fo fmall as to be fcarcely fenfible to the beft obfervers when ufing the most accurate inftruments, various indirect methods have been propofed: of thefe, that fuggefted by Dr. Halley is allowed to be the most perfect. It was to observe the tranfit or paffage of Venus over the fun's difc; a phenomenon which happened in the years 1761 and 1769, and by which this difficult problem was refolved with an accuracy unlooked for by aftronomers of ancient times.

OF THE APPARENT MOTION OF THE FIXED STARS, OCCASIONED BY THE ABERRATION OF LIGHT.

The aftronomers of the last century, in their endeavours to difcover the parallax of the fixed ftars, found annual variations in the ftars, following a law contrary to what would have happened, had it arifen merely from the earth's fituation in his orbit.

These variations threw them into great perplexity, from which they were not relieved till Dr. Bradley, by applying himfelf to obferve accurately thefe variations, at laft difcovered the true caufe thereof; and has given rules for calculating the changes, and fhewn what allowances are to be made in confequence thereof, in obfervations of the stars. VOL. IV.

L

He

He has also proved clearly, that this aberration of the fixed stars, or the motion which makes them appear to describe ellipfes of 40 feconds diameter, arifes from the motion of light combined with the annual motion of the earth.

This I fhall now endeavour to explain, and place in as clear a point of view as poffible, defiring you only to recollect the idea of decompofition of forces into parallelograms, as explained in our Lectures on Mechanics. Let E, fig. 1, pl. 15, be a ftar darting a ray of light, which I fhall confider here as a fingle particle going from E to B. Let A B be a fmall portion of the earth's orbit, of 20 seconds, for example; and C B the space that the ray of light has paffed through, while the earth moved from A to B; thus the particle was at C when the earth was at A, and arrives at B the fame time as the earth. Hence CB and A B exprefs the velocity of light and the earth during 20 feconds.

Draw CD parallel to A B, and finish the parallelogram DBA; now according to the known principle of the compofition and decompofition of forces, we may confider the velocity EB of the light, as refulting from the two velocities in the directions CD, CA; the velocity CD being the fame in quantity and direction as the velocity A D of the earth, cannot be perceived, is therefore destroyed with respect to us; the eye cannot fee by a ray moving in the fame direction and with the fame velocity as the eye. So that only the part CA of the velocity of the light will fubfift to us, and the ray will come to the eye in the direction C A, and we shall perceive the ftar in the line AC, or according to BD which is parallel thereto; the angle CBD is what is termed the aberration; it is the quantity that a ftar appears out of it's true place, in confequence of the motion of light and the carth.

Perhaps

H

Perhaps another way of confidering this may render it more clear to your apprehenfions. Suppofe a tube to be erected perpendicular to the horizon at a time when it rains, the drops to fall in a perpendicular direction, and the tube to be of fuch a diameter as to admit but one drop at a time; now it is plain that if a drop of water enter the orifice of the tube, it will fall down without touching the fides. But if the tube be moved along, ftill preferving it's perpendicular direction, any drop that enters the tube will ftrike against the fides, and none could pafs freely through while the tube is in motion, unless the tube has fuch a direction as will compenfate the motion.

Thus let A B, fig. 2, pl. 15, reprefent the horizon, CD the perpendicular tube, and GD the courfe of a drop of rain; then if CD be moved towards A, while the drop is falling within the tube, it is evident that the inner furface of the tube, which is fituated towards B, will be carried against the drop, and prevent it's arriving at the bottom without touching. But if the inclined tube be moved with a fimilar motion to that of the drop from E to D, in the fame time that the drop moves from C to D, the lower orifice of the tube and the drop will be found at the fame inftant at D, and the velocity of the drop will be expreffed by CD, and that of the tube by ED.

The fame reasoning holds good, if instead of drops of rain we fuppole particles of light, and a telescope instead of a tube. For to an obferver, who through the tube C D views the vaftly diftant object C, if the motion of light be inftantaneous or infinitely swift, no finite motion of CD, it's pofition being unaltered, can prevent it's being vifible; becaufe by the fuppofition the light which enters at C, will arrive at D before C D can have moved at all. But if light be propagated in time, and the obferver

L 2

obferver be carried by a motion fimilar as to acceleration to that of light, the tube must be inclined in an angle, whofe fine is to the fine of CED, as the velocity of the obferver is to the velocity of light.

By this theory, which is eftablished by numerous obfervations of ftars of different magnitudes and fituations, it appears, that the fmall apparent motion which the fixed ftars have about their real places, which is called their aberration, arifes from the proportion which the velocity of the earth's motion in her orbit bears to that of light.

This proportion is found to be as 10210 to I; from whence it follows, that light moves or is propagated from the fun to the earth, in 8 feconds, 12 thirds.

This discovery of the aberration of light by Dr. Bradley, is a direct proof of the motion of the earth in it's orbit. The motion of light, combined with the motion of the earth, produces an apparent difference in the places of the fixed stars; and as this motion is found to affect all the ftars differently, according to their fituations, it fully proves the truth of the caufe upon which they were fuppofed to depend, and fhews that the Copernican fyftem is conformable to nature and the order of things.

OF THE PRECESSION OF THE EQUINOXES.

The ftars, which compofe the conftellations, are found to increafe their longitude continually. The whole flarry firmament appears to have a flow motion, from weft to caft, about the poles of the ecliptic, fo that the conftellations feem to have deferted the places firft appropriated to them; infomuch that the fint ftar in the conftellation of Aries, which appeared in the vernal interfection of the equator and ecliptic in the time of Meton,

the