324

ASTRONOMY.

Sect. III. Of calculating the Distances, Magnitudes.&c. of the Celestial Bodies.

(222.) These are obtained by finding out the horizontal paral-lax of the body, whose distance is desired to he known ; that is,the angle under which the semidiameter of the Earth would ap-pear provided we could see it from that body. In general (lieparallax of a planet is the difference between its place seen fromsome part of the surface, and from the centre of the Earth . Thusthe angle A PC, or the angle TS in the heavens, is the parallax aithe altitude P, and Al'C is the horizontal parallax. (SeePlate XXV. tig. 11 .) Many methods have been devised forlinding the parallax. We shall notice three or four: 1. l.et AD,(Plate XXV. tig. 11.) be the Earth , C its centre, P the planet:then ZAP is the complement of the apparent, and ZCP of thetrue altitude, and their difference is equal to APZ, the parallax.If the distance CP be given, the parallax is found by plane trigo-nometry, for as C P: CA: : sine of PAC, or PAZ, to’sine of APC,the parallax. Let AFC be any other parallax of the same planet,then we have CF or CP: CA: : sine of AFC ; hence from thesetwo proportions it follows tiiat the parallaxes of the same planetare as the sines of the co-altitudes : in an horizontal parallax theco-altitude is 90°; hence as sine ZAP : sine of APC, parallax atthat altitude :: Radius : sine of the horizontal parallax. Theparallax being very small may itself be taken lor the sine of it.2. Let S be the star or planet, whose parallax is sought. (Fig. 12.)Observe it when it is in the same vertical circle with any twofixed stars, A, B. Observe again when the same two stars comeinto a position parallel to the horizon at a and b ; and let the pla-net be come to s. Then with an instrument measure the altitudeof a or b, arid likewise the altitude of s; and the difference ofthese altitudes is the parallax. For the real place of the star S issomewhere in the line AB, and therefore it is also somewhere intl.e line ah, and therefore its altitude is the same as that of a or b.Therefore the parallax is the difference of the altitudes of a and .«,or of b and s. 3. The parallax may be found by observing theazimuth and altitude of the planet. Let IIZO, (l’ig. 13,) be themeridian, EQ the equinoctial, IlO the horizon, Z the zenith, Pthe pole, S the star, ZSB a vertical circle passing through it.Observe the altitude BS, and the azimuth BO, and mark the mo-ment ot tune when these observations are made : then observe themoment of time that the star comes to the meridian, and you havethe distance ot time from the observations. Convert this into de-grees, allowing 23 hours, 56 minutes, 4 seconds, to 360°, (which<js the time of the Earth ’s rotation to the same star,) draw the meri-dian PAD, making the angle EPA , or the arc ED, equal to thesedegrees. Then in the spherical triangle ZPA, we have the angleZPA, and angle PZA, equal to BO, and the side ZP, the co-lati-tude, to find the side ZA, the complement of the aliitude; thissubtracted from ZS, know n by observation, the remainder AS isthe parallax. 4. The operation represented in Plate XXV.tig. 14, requires two observers in different places of the Earth , andcan be applied to none of the planets but Mars in opposition tothe Sun, or to Venus on the Sun ’s disk. It is best performed whenthe Sun is about the equinox. Let PERQ be the Earth , PIt itse.xis, EQ the equinoctial, S the planet Mars in opposition to theSmi, and if near the perihelion, it is better. Let two places F,G, be taken, the one in N. lat. the other in S. lat. the furtherfrom the equinoctial the better; and nearly in the same meridian,or rather so placed, that the line F’G, drawn from the one to theother, may be nearly perpendicular to the orbit of Mars . By thisthere is a greater base to work upon. Then let the two observerspitch upon some fixed star; as A, which Mars comes very near atthat time ; and the nearer the belter. Having two good instru-ments perfectly alike, furnished with micrometers, and beingsituated at F and G: let them observe for several nights succes-sively about midnight, the places of Mars at B and C, as he passesby tlie star A; and take the distances AB and AC every night,during his transit by this star. These observations are to be con-tinued till the distances begin to increase, and no longer; for thenlie is past the star. From these observations, the nearest distanceof Mars from the star A may be found, as observed from thelaces F and G ; at least they may be found by interpolation.,et these nearest distances be AB and AC ; then we have the dif-ference BC, or die angle BSC or FSG. And from the situationthe places F and C*, the length and position of I’G will be

known ; and by these, FS may be found. And lastly, the anglewhich the radius of the Earth subtends at the distance FS, or thehorizontal parallax of Mars will be known. If, instead of Mars <in opposition, Venus be observed ou the body of the Sun ; thenher nearest distances from cither limb of the Sim must be taken,w hose difference will give the angle at Venus , subtended by FG ;the rest as before. Thus the parallax of Venus will be obtained.The parallax of Mars, when nearest the Earth , has been found25", 27", and 30", at different times. A star or planet appearslower than it really is, by the quantity of the parallax, which isgreater the lower the star is ; and therefore the horizontal parallaxis the greatest. The parallaxes of two planets are as the cosinesof ilie apparent altitudes directly, and their distances from theEarth ’s centre reciprocally. The parallax of a planet being known,its distance may be found. For tins is only working backward,saying, As sine of the parallax, tothe Earth’sradius ; so sine zenith-distance , to the planet’s di.-lance. Having the parallax of any ofthe planets, the distances of all the planets from the Hun may beknown, in diameters of the Earth , or any sort of measure. Forthe distances of the planets from the Sun , and from one another,are known in some assumed measure; and by the parallax of aplanet, the true distance of the Earth from it is known: and there-fore all the other distances will be known by proportion, 'l'he4tli of these methods has been practised in determining the paral-lax of Venus , from observations made at different parts of theEarth, upon what is called her transit over the Sun ’s disk, a pha’-nomenon that rareh happens; but when it does happen, it affordsthe best method ot determining that most

astronomy, the Sun ’s parallax, or the ang.. .._

Earth’s semidiameter appears from the Sun . The first transit, orpassage of Venus over the SunU-disk, that ever was observed, atleast by modern astronomers, happened in 1639, but perhaps theonly mortals who sasv it were Air. Ilorrox and his friend Mr.Crabtree. Two transits have happened since; the first in 17G1,and the last in 1769. There will be no more before 1874, andthe next to that will happen in I8S2. The two last transits werecarefully observed. From the first of these Mr. Short has com-puted the sun’s parallax to be 8",69 ; and from the last, the bestastronomers have concluded it to be 8",6. This is an observationof the greatest consequence, because it is only by a knowledge ofthe Sun’s distance' from the Earth , in some known measure, thatwe can acquire a knowledge of the true dimensions of the SolarSystem .

"(223.) The apparent diameter of the Sun or a planet, &c. maybe measured by a micrometer with great accuracy ; this beingascertained, together with its distance from the Earth , its true dia-meter may be thus found; let A, (Plate XX. fig. 7,) representthe Earth, C the centre of the Sun or planet; AD, AB, linestouching its surface in D and 13; join CD, CB, and AC , then inthe right-angled triangle DC A are given tlie distance CA, and theangle DCA, being half the apparent diameter; hence (perTrig.) Rad. : sine ot CAD : : CA : CD, which is the semidiameter;and by doubling this we have the true diameter required. FromIbis the circumference, surface, and bulk, are easily found by themethods given in mensuration.

Sect. IV. Of calculating the Periodical Timf.s, Places,&c. of the Celestial Bodies ; constructing Astro-nomical Tables, and delineating the Phases of theMoon .

(224.) These subjects, if fully treated, would nearly compre-hend the whole of Practical Astronomy. However, it will besufficient here to give some general hints, since by the great la-bours of former astronomers, the periodical times, eccentricities,&c. of the planets have been determined, anil accurate tables oftheir motions constructed. To draw a meridian-line is the foun-dation of most astronomical operations: this being drawn for anyplace, the latitude is found by oliserving the altitude of the pole,for the latitude of a place is equal to the elevation of the poleabove the horizon; hut as (here is no star exactly in either of thecelestial poles, to find the altitude of that invisible point, calledthe pole of tlie heavens, observe some star near it, which doesnot set; and find its greatest and least altitudes, and half the sumof these altitudes gives the exact altitude of the pole, or latitudeof the place. T ims, suppose, the greatest altitude of the star ob-served