ASTRONOMY.

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served is 80°, and its least 20°, we then know, that the latitude ofthe place, where the observation was made, is exactly 50°.

(225.) Having found the latitude, the obliquity of the eclipticis easily obtained by the following method : Observe, about thesummer-solstice, the Sun ’s meridian-distance from the zenith,which is easily done by a quadrant, with a moveable index, fur-nished with sights; if this distance be subtracted from the latitudeof the place, provided the Sun is nearer the equator than theplace of observation is, the remainder will be the obliquity of theecliptic: but, if the place of observation is nearer the equatorthan the Sun at that time, the zenith-distance must be added.The obliquity of the terrestrial ecliptic hath been determin-ed by Bradley to be 23° 28' 19" for 1750. Here it is proper toobserve, that the obliquity of the ecliptic to the equinoctial isfound, at present, to be above the third part of a degree less thanPtolemy found it. And most of the observers after him foundit to decrease gradually, down to Tycho Brake’s time. If it beobjected, that we cannot depend on the observations of the an-cients, because of the incorrectness of their instruments, we haveto answer, that both Brahfi and Flamsteed are allowed to havebeen very good observers; and yet we find, that Flamsteedmakes this obliquity 2 \ minutes of a degree less than Brahfi did,about 100 years before him ; and as Ptolemy was 1324 years be-fore Tycho Brahe , so the gradual decrease answers nearly to thedifference of time between these three astronomers. If we con-sider that the Earth is not a perfect sphere, but an oblate sphe-roid, having its axis shorter than its equatorial diameter ; and thatthe Sun and Moon are constantly acting obliquely upon thegreater quantity of matter about the equator, pulling it, as it were,towards a nearer and nearer coincidence with the ecliptic ; it willnot appear improbable, that these actions should gradually dimi-nish the angle between those planes. Nor is it less probable, thatthe mutual attractions of all the planets should have a tendency tobring their orbits to a coincidence : but this change is too small tobecome observable in many ages.

(226.) The declination of the Sun from the equator, for anyday, may be found by the same method by which we find theobliquity of the ecliptic: and thus, a table of his declination forevery day in the year might be constructed : thus, also, the de-clination of the stars might be found. Having found the declina-tion of the Sun , his right ascension, and place in the ecliptic, maybe geometrically found, by the solution of a case in spherical tri-gonometry. For let EQ, in Plate XX. fig. 10, represent thecelestial equator, Y the Sun , and Y X the ecliptic ; then, in theright-angled spherical triangle EC Y, we have the side E Y, equalto the Sun ’s declination: the angle EC Y 23° 28', being the angleof the ecliptic with the equator ; and the angle Y EC is arightangle. From these data, we can find the side EC, the right ascen-sion ; and C Y, the Sun ’s place in the ecliptic, or his distance fromthe equinoctial point; and thus, a table of the Sun ’s place, forevery day in the year, answerable to his declination, may be formed.

(227.) The right ascension of the stars may be found by theSun ’s place in the ecliptic, and a good pendulum clock: for whichpurpose, the motion of the clock must be so adjusted, that thehand may run through the 24 hours, in the time that a star, leav-ing the meridian, will arrive at it again; which time is somewhatshorter than the natural day, because of the space the Sun movesthrough in the mean time eastward. The clock being thus ad-justed, when the Sun is in the meridian, fix the hand to the pointfrom whence we are to begin to reckon our time ; and then ob-serve when the star comes to the meridian, and mark the hourand minute that the hand then shews: the hours and mi-nutes described by the index, turned into degrees and mi-nutes of the equator, will give the difference between the rightascension of the Sun and stars; which difference, being added tothe right ascension of the Sun , will give the right ascension of thestar. If we know the right ascension of any one star, we may fromit find the right ascensions of all the others which we see, bymarking the time upon the clock between the arrival of a star,whose right ascension we know, to the meridian, and another star,whose ascension is to be found. This time, converted into hoursand minutes of the equator, will give the difference of right ascen-sions; from whence, by addition, we collect the right ascension ofthe star which was to be found out.

(228.) When the right ascension and declination of a star isfound, its longitude and latitude may thence be easily found; andvol. r.— no. 21.

the places of the fixed stars being all marked in a catalogue, ac-cording to their longitudes and latitudes, it may thence be con-ceived, how the longitude and latitude of a planet or comet may-be found for any particular time, by comparing its distance fromthem, and its apparent path may thus be traced ; and thus, thepaths of Mercury and Venu • were traced by M. Cassini.

(229.) To find out the periodical times of the planets, we mustobserve when they have no latitude. At that time the planet is inthe ecliptic, and consequently, in one of its nodes ; so that, by-waiting till it returns to the same node again, and keeping an ex-act account of the time, the periodical time of its revolution roundthe Sun , may be known pretty exactly. By similar observations,from the theory of the Earth ’s motion, we can find the positionof the line of the nodes ; and when once the position of this lineis found, the angle of inclination of the planet’s orbit to theEarth may also be known.

(230.) The eccentricity of the Earth ’s orbit may he determinedby observing the apparent diameters of the Sun at different times :when the Sun’s diameter is least, the Earth is at the greatest dis-tance ; and, when this diameter is greatest, the Earth is at itsleast distance from him. But, as this method must necessarily beprecarious, another is recommended by Keil, by observing thevelocity of the Earth in its orbit, or the apparent velocity of theSun , which is demonstrated to be always reciprocally as the squareof the distance. The eccentricities of the orbits of the other pla-nets may be likewise found, by observing their velocities at differ-ent times; for all of them observe the same proportions, with re-gard to the increase or decrease of the velocity, that the Earth does; only, in this case, care must be taken, to observe thereal, not tire apparent, velocities of the planets, the last dependingon the motion of the Earth at the same time. Their aphelia, oroints of their orbits where they are farthest from the Sun , maye known, by making several observations of their distances fromhim, and thus perceiving, when these distances no longer in-crease.

(231.) The position of the aphelion being determined, the pla-net’s distance from it, at any time, may also be found by observa-tion, which is called its true, or cnequuted anomaly; but, by sup-posing the motion of the planet to be regular and uniform, tablesof that motion may easily be constructed. From thence, the pla-net’s mean place in its orbit may be found for any moment oftime ; and one of these moments being fixed upon, as an epochaor beginning of the table, it is easy to understand, that fromthence tables of the planet’s place in its orbit, for any number ofyears, either preceding, or consequent to that period, may be con-structed. Astronomical tables are to be constructed according tothe meridian of equal time, and not true or apparent time, becauseof the inequalities of the Earth ’s motion, as well as that of the pla-net, and equations must be made, to be added to, or subtractedfrom, the mean motion of the planet, as occasion requires ; w hichwill be readily understood from what w r e have already mentionedconcerning the unequal motion of the Earth in its orbit. Whenall the necessary tables are constructed, by this or similar methods,the calculating of the planetary places becomes s. mere mechanicaloperation, ana consists only in the additions and subtractions, ac-cording to the directions given along with such tables. But itmust be observed, that the accidental interference of the planetswith one another, by their mutual attractions,’renders it impossibleto construct any tables that shall remain equally perfect : andtherefore, frequent actual observations and corrections of thetables will be necessary. This disturbance, however, is inconsi-derable, except in Jupiter and Saturn , and they are in conjunctiononly once in about 20 years.

(232.) The above rules, with regard to the planets, are also ap-plicable to the Moon ; but with more difficulty, on account of thegreater inequalities of her motions. From these irregularities, itmay well be concluded, that the calculation of the Moon ’s placein her orbit is a very difficult matter; and indeed, before New-ton, astronomers in vain laboured to subject the lunar irregularitiesto any rule. By his labours, however, and those of other astro-nomers, these difficulties are in a great measure overcome ; andcalculations, with regard to this luminary, may be made, with asgreat certainty, as concerning any other. Her periodical timemay be determined from the observation of two lunar eclipses, atas great a distance from one another as possible ; for, in the mid-dle of every lunar eclipse, the Moon is exactly in- opposition-to4 0 the