mo

ASTRONOMY.

diurnal arc, because the time is after Jan. 1, 1810, the declinationsouth, and the variation in declination negative, the sum, 2h. 55m.13,49734;. will be the correct semidiurnal arc of the star at thetime proposed.

Example 3. Required the apparent semidiurnal arc of the *in the Ram’s following horn, on I' eb. 21, 1704.—In the Table of Se-midiurnal Arcs the difference for 10 minutes of declination at 22°33' 27" N. is 70 seconds. And 600": 70 seconds:: 17,0 seconds,the star’s annual variation in declination,: 2",053, the animal varia-tion of the star’s semidiurnal arc. Also 2”,053 X 45,858 years,the time preceding Jan. 1, 1810 = I m. 34 ,146, the variation ofthe semidiurnal arc from that contained in the 'fable on Feb. 21,1764. This quantity subtracted from 8h. 10m. 33s. the tabularsemidiurnal arc, because the time is before 1810, the declinationnorth, and the variation in declination affirmative, the remainder8h. 8m. 58,853s. was the correct semidiurnal arc of the star atthe proposed time.

E ample 4. Required the apparent semidiurnal arc of the *, avariable star in the Whale’s neck, on lJfec. 2, 1796.—In tlu-Table of Semidiurnal Arcs, the difference for 10' of declination atB 3 .50' 35" S. declination, is 51 seconds. And 600": 51 seconds: : 17",04, the star’s annual variation in declination: 1",448, theannual change of the star’s semidiurnal arc. Also f',448 x13,079 years, the time preceding 1810, = 18",9. This quantitysubtracted from 5h. 44m. 13s. because the time is before 1810,the declination south, and the star’s annual variation- in declina-tion negative, the remainder 5h. 43m. 54,1s. was the apparentsemidiurnal arc of the star on Dec. 2, 1796, as required.

The right ascension and declination of any particular star inthe above Table being known for the beginning of 1810, its rightascension and declination for any other period may be found by-means of the columns of annual difference, thus: Multiply theannual difference by the quantity of time (expressed in years andparts of a year,) that the required period is before or after Jan. 1,

1810, and add the product, according to the tabular sign, to theright ascension or declination of the star in the 'Fable, if the timebe after the beginning of 1810, but if otherwise, with a contrarysign, and the sum will be the right ascension or declination required.

Example 1. Required the right ascension of Sirius for June 25,

1811. —In the 'Fable the annual difference in right ascen-sion of Sirius is + 2",64. This multiplied by 1,482 years, thetime after the beginning of 1810, the product 3”,93 is the quantityof variation in 1,482 years. And Oh. 30m. 40-. the tabular rightascension of Sirius, added to -f- 3",93, because the time is afterJan. 1, 1810, gives 6h. 30m. 49 ,93 for the star’s right ascensionat the proposed time.

Example 2. Required the declination of Capella on Oct. 2,1802.—in the Table the star’s annual variation in declination is+ o",2i. This multiplied by 7,247 years, the time preceding1810, the product 37”,70 is the star’s variation in declination in7,247 years. And 45° 47' 44” N. the star’s tabular declination,added to — 37",76, because the time is before 1810, the sum45° 47' 6',24 N. was the true declination of the star ou the dayrequired.

If the sun’s right ascension be given, the time of 1 he rising,southing, and setting, of any star noted down in the precedingTable may lie readily found as in the annexed example -.

Example. Required the apparent time of the rising, southing, andsetting, of >i Pleiadum on Nov. 17, 1811, at Greenwich; the Sun’sright ascension on the noon of that day being 15hand iiis daily variation in right ascension 4m. 8,75s.

From tlie star’s right ascension on Nov. 17, 1811...

And the remainder is the star’s approximate time

of southing.

Sun’s right ascension at the approximate time sub-tract..

subtract.

i. 27

m.

36s.

H.

M.

s.

3

36

19

15

27

36

12

8

43

15

29

42

12

G

37

8

17

25

Remainder, the true time of the star’s apparent h. m.

rising. 3 49 12

Star’s apparent semidiurnal arc add... 8 17 25

Sum, tlie true time of the star’s apparent Setting. 20 24 2

Star's real semidiurnal arc add and subtract. 8 12 41

Remainder, tlie true time of tlie star’s real rising 3 53 56

Sum, the true time of the star’s real setting. 20 19 18

i. e. The ii Pleiadum apparently sets on the morning of the18th, at 24m. 2s. pyt 8, according .to common reckoning, 4m44s. alter the time of its real setting.

(95.) To explain yet further (lie orbit of a planet or comet, andthe nature of its motion, let All and El I be tlie axes of an ellipse,of which D is the centre, and S tlie focus. (Plate XVI. tig. 6.)Suppose that S is tlie place of the Sun, and P tlie place of a planetmoving in the curve AFBE, and that l’G is drawn to touch thecurve at P. Join SP, and draw SG perpendicular to l’G. 'Pileplanet will move in the curve, so that tlie line SP shall pass overequal areas in equal times. Since the velocity of tlie planet isinversely as the perpendicular upon the tangent, (Central Forces,Art. 2,) and tiie lines SB, SA are perpendicular to tangents at thepoints B and A, tlie velocity at B is to tlie velocitv at A, as SAto SB, and tlie velocity at B is to the velocity at 1’ as SG to SB.Thus at B, which is called the perihelion, the velocity will be tliegreatest, and at A, the aphelion, it will tie tlie least, and at anyother point P, it will be between these two extremes. The force,that, acting upon tlie planet at P, bends it from the tangent, is tothe force that acts upon it at E, any other point, as tlie square ofSE to the square of SP.

(96.) We have hitherto supposed the Sun to remain absolutelyat rest, and that the planet was urged towards it, as to an im-moveable point; but Sir I. Newton lias shewn, that the. tendencyof tlie planets towards tlie Sun arises from a very general law, thatnot only connects the planets with the Sun, but extends from eachindividual particle of matter to every other particle of matter intlie Solar System , so that not only tlie planets gravitate toward tlieSun, but tlie Sun gravitates towards the planets; hence, in stricttruth, botli tlie Sun and planets revolve round a point, which istheir common centre of gravity, which is not far Irom the centreof tlie Sun, because, of tlie quantity of mutter it contains. Thetrutli of this genera] law is proved by a cartful examination ofparticular cases; and, supposing it to be true, the effects it oughtto produce in the planetary motions round the Sun, are in perfectcoincidence with tlie best observations. If all matter gravitatesto, or is attracted by, all other matter, it is evident that the planetsmust also gravitate towards each other ; and thus in some mea-sure the uniformity of their motions round the Sun will be effected.Now this is really found to Uc the ease by the most accurate ob-servations; and the effects produced are precisely what theyought to be, supposing that tlie same law, which regulates tlietendency of the planets towards tlie Sun, also regulates their ten-dency to one another.

(97.) If the planets were acted on by a power directed to tliecentre of the Sun only, varying according to the general law ofgravity, and that centre was quiescent, their motion about itwould be perfectly regular; but since they are acted on by apower directed to every body of the system, in order to .judge ofthe effects of these actions, Newton lirst supposes two bodies re-volving about their common centre of gravity, and gravitat-ing toward. each other, and since the direction of their mu-tual gravitation passes always through that centre, and their dis-tances from it vary always in tlie same proportion as their dis-tances from each other, it follows, that they must describe similarfigures about that point, and about eacli other, and describe equalareas in equal times,about that centre, and about each other; sotliht there will lie no irregularities in tlie motion of tw'o bodiesabout each other, because of their mutual attractions,, whateverthe law of their gravity is supposed to lie; only they will revolvein less time about their centre of gravity, than the one wouldhave done about the oilier quiescent, because the orbit de-scribed about the other centre of gravity is less than that whichis described by any one of them about the other quiescent; theirdistance in both cases being the same, and the orbits similar.

(98.) Jfthrueor more bodies mutually attract each other, the

gravitation