SECT. V. Of Phenomena arising from the Earth's Magnitude. PARALLAX. 144. None of the heavenly bodies, unless they be in the zenith, appear to have the same place among the stars when seen from the earth's surface, that they would have, if seen from the earth's centre. To a spectator at G, (Pl. VII, fig. 4,) the centre of the earth, the moon at E would appear among the stars at I; but seen from the surface of the earth at A, it would appear at K. The place I is its true place, and K its apparent place; and the difference between them is its parallax, diurnal parallax, or horizontal parallax. As the moon comes above the horizon, say to D, its parallax decreases; for here it is Ha, less than IK. And when the moon comes to the zenith at F, parallax ceases; for it appears at Z, whether seen from G or A. 145. The parallax of a heavenly body is less as its distance is greater. If the moon were at e instead of E, its parallax would be n K instead of IK. The moon's horizontal parallax is about 57'; the sun's 8". The distance of the stars is so great, that no parallax can be discovered. 146. Refraction and parallax both make bodies appear where they are not; but refraction elevates them, and parallax depresses them. They are both greatest in the horizon, and vanish at the zenith. The moon is depressed by parallax near twice as much as it is elevated by refraction; but the sun is depressed by parallax only about as much as it is elevated by refraction. Refraction is the same, whether the light come from the sun, moon, or any other heavenly body; being generally about 33' in the horizon. 147. Parallax or diurnal parallax is to be understood as above explained. But there is an annual parallax ; by which is meant, (the difference in the apparent place of a heavenly body, as seen from the earth in opposite points of its orbit.) As the mean distance of the earth from the sun is 93 millions of miles, it is obvious that the earth, in one part of its orbit, as at, is (293) 186 millions of miles farther eastward, than when in the opposite part, as at . Hence we might suppose, that if a particular star is exactly in the north when the earth is in one part of its orbit, it would deviate somewhat from the north, when the earth comes to the opposite point. (For the earth's axis is always parallel with itself.) But the pole star (and indeed all stars) have no annual parallax, that can be discovered; owing to their inconceivable distance. The nicest instruments, which the most ingenious artists have been able to construct, fail entirely to indicate to us any deviation arising from this cause of any star from its true place. But these instruments would indicate such deviation, were not the stars more than 200,000 times farther off than we are from the sun. (19,600,000 millions of miles.) The probability, is, that the nearest stars are at a much greater distance. The following Numbers of this section cannot be fully understood without a knowledge of plane Trigonometry. They may therefore be omitted by those who are ignorant of that branch of mathematics. 148. The distance of the moon was long since ascertained with the utmost accuracy by means of her parallax. There are several methods of obtaining this parallax, and of applying it. The following is one of the most sure and simple. Let us suppose that two observers are at the points A and B in the same meridian; and let the distance between them, that is, their difference pass off the sun's disk at C; the time of doing which, let us suppose to be the same as the calculated duration of the transit as seen from the earth's centre. But during this time, by the rotation of the earth on its axis, the place D is carried eastward to F, where it is at the end of the transit; so that instead of coming to H, Venus moves only to E in its orbit before it is seen passing off the sun's disk at C, and the transit is ended. 154. Hence it is obvious, that the duration of the transit, as computed for the earth's centre, is shortened by the motion of the place from D to F, by the time it would take Venus to move from E to H. Hence by observing the difference between the computed and observed duration of the transit, we have the time which Venus takes in passing from E to H by the excess of her angular motion over that of the earth; and since this excess is previously known, by turning this difference of time between the computed and observed duration of the transit into degrees and minutes of that excess, we get the number of degrees and minutes between E and H, that is, we get the angle ECH, or DCF. Now the line DF may be readily computed from the latitude of the place and the observed duration of the transit; and may be compared with the semidiameter of the earth. From this comparison would be seen at once the angle at C, which a semidiameter of the earth would subtend; that is, the sun's parallax. Let this parallax be equal to the angle IAL, subtended by the semidiameter of the earth IL. Here then we have a triangle IAL, of which the angle at A is known, and the angle at I a right angle, and the side IL, equal to the earth's semidiameter, is known; whence may be known the angle at L, and the side AI, which is the earth's distance from the sun. 155. Having obtained the absolute distance of the earth from the sun, and the relative distances of all the planets being previously known, their absolute distances may be at once ascertained. For, as the relative distance of the earth is to its absolute distance, so is the relative distance of any planet to its absolute distance. In what has been said of the method of finding the parallax of the earth, and thence the distances of the planets from the sun, none of the difficulties of its execution appear. Incredible pains were taken by astronomers in making accurate calculations, and in providing the means for numerous and accurate observations, previous to the transits of 1761 and 1769. The skilful and scientific of Europe were scattered over the habitable globe, for the purpose of observing this phenomenon under circumstances as various as possible. Some went to India, others to America; some to the north of Europe, others to the south. The truth was arrived at by vast labour in comparing an almost endless variety of obser vations, made at different places; correcting the probable error of one observation by the probable opposite error of another observa tion, thus taking a mean of the whole. For a more full account, the pupil is referred to Ferguson's Astronomy. There will not be another transit of Venus till the year 1874. In of latitude, be previously M also known (by the supposition.) These three things therefore being known, we can readily calculate the length of the side AB, and the magnitude of the angles OAB and OBA. 149. Now the zenith distances ZM and zM, (which have been observed) measure the angles ZAM and zBM. If then each of these angles be taken from 180°, we have the angles OAM and OBM. If from the angle OAM we take the angle OAB, we get the angle MAB; and if from the angle OBM, we take the angle OBA, we get the angle MBA. Here then in the triangle MAB, the angles MAB and MBA, and the side AB are known; and hence can be found the side MB, which is sufficient for our purpose. Now in the triangle MBO, these three things are known, viz. the sides MB and BO, and the included angle MBO; hence may be found the length of the side MO, which is the distance of the moon from the earth. In the same way might the distance of other heavenly bodies be found, were not their distance so great and the parallax so small that accurate observations could not be made. Proper allowance must here be made for refraction. |