A S C 



Apoftolical Conftitiitions, I. v, c. 19. Its ongi;i is not 

 known ; and hence fome have been led to imagine, that it 

 was received by tradition from the apoftles. 



Ascension, in AJlronomy, is citlier right or obHque. 

 Ascension, right, ui the Xun, or of a ftar, is that de- 

 gree of the equinodial, accounted from the beginning of 

 Aries, which rifes with the fnii, or ftar, in a ri^ht fphere. 

 Or, right afcenfion is that degi-ee and minute of the equi- 

 noClial, counted as before, which comes to the meridian 

 with the fun, or ftar, or otlur point of the heavens. The 

 teafon of thus referring it to the meridian, is, becaiife it is 

 always at right angles to the equinoiStial, whereas the hori- 

 zon is only fo in a right or diieft fpliere. The right 

 afcenfion ftands oppofed to the right dcfcenfion, and cor- 

 refponds to the longitude of places on the earth. Two 

 fixed ftars, which have the fame right afcenfion, i. e. which 

 are at the fame dillance from the firft point of Aries, or, vvliich 

 amounts to the fame, are in the fame meridian, rife at the 

 fame time in a riglit fphere, or with refpefl; to people who 

 live under the equator. If they be not in the fame meri- 

 dian, the difference between the times of their riling or 

 coming to the meridian is the precife difference of their 

 right afcenfion. In an obHque fpliere, v.'here the horizon 

 Cut3 all the meridians obliquely, different points of the 

 meridian never rife or fct together ; fo that two flars, on 

 the fame meridian, never rife or fct at the fame time ; and the 

 more oblique the fphere, the greater is the interval of time 

 between them. To find the riglit afcenfion of the fun, 

 ftars, &c. trigonometrically, fay, for the fun. As radius is 

 to the cofine of the fun's greatefl declination, or obliquity 

 of the ecliptic, fo is the tangent of the fun's longitude to 

 the tangent of the right afcenfion. 



Let VY.^<\{AJlfonomy, PJatcW.fg. 15.) reprefent the 

 folllitlal colure, the centre of which is "y, and let the dia- 

 meter EQJje the equator and the diameter PS be theequi- 

 noftial colure. Suppofe the obliquity to be E 25 =23° 28', 

 and the diameter 2S V^ to be the ecliptic, in which take 71 

 for the fun's longitude or diftance fiom the point ty^ ^ 43^ 

 16'; and through P0S defcribe a circle of right afcenfion. 

 Then in the right-angled fpherical triangle <Y^OB, we 

 have 



Radius ... 10.00000 

 to t. fun's long. = 43° 16' 9-97371 

 As cof. obi. eel. r= 23° 28' 9.96251 



to t. right afcenfion =40° 48' 9.93622. 

 While the fun is moving from "y to SS, or in the firft 

 quadrant of the ecliptic, the given longitude is the hypo- 

 thenufe in the triangle 'f O B, the declination B is north, 

 and ^ B is the right afcenfion. V/hen the fun has pail the 

 folftice So, and is defcending towards =2=, or in the fecond 

 quadrant, his longitude or diftance froui "y being taken 

 from 180°, the remainder =^ O becomes the hypothenufe, 

 and the declination is Itill north ; but the arc B=^ found for 

 the right afcenfion is only the fupplement, and mult there- 

 fore be taken from lSo°. The fun having pall the point =^, 

 and defcending towards VJ, is in the third quadrant, and 

 his longitude, reckoned from ty? ^'iH be greater than 180° ; 

 in which cafe the excefs above 180°, or his dillance from =2=, 

 will be the hypothenufe =^ © ; the declination will be fouth, 

 and the arc =^ A, found for the right afcenfion, muft be added 

 to 180° in order to obtain the right afcenfion eftimated from 

 •y. When the fun has pafl tlie fofticc yj, and is afcend- 

 ing towards tyjheis then in the fourth quadrant ; therefore 

 the longitude will be greater than 270°, and mull be taken 

 from 360^', for the hypothenufe T©- In this cafe the decli- 

 nation is fouth, and the right afcenfion, found by the above 



A S C 



proportron,_ muft be taken from 360°, in order to havethcr 

 right afcenllon from ^y. 



If the obliquity of the ecliptic, and the fun's declination 

 were given, the proportion for the right afcenfion would be ^ 

 radius to the cotangent of the obliquity of the ecliptic, as 

 the tangent of the fun's dechnation to the fine of the right 

 afcenfion. 



The fun's right afcenfion in time is uftful to the prac- 

 tical aftronomer in regular obfervatorics, who adjufts 

 his clock by fidereal time. It fcrves alfo for converting 

 apparent into fidereal time ; as e. g. that of an eclipfe of 

 Jupiter's fatellites, in order to know at what time it may be 

 expeded to happen by liis clocks. For this puq^ofe, the 

 fun's right afcenfion at the preceding noon, together with 

 the increafe of right afcenfion from noon, muft be added 

 to the apparent time of the plienomenon fet down in the 

 ephcmeris. The fun's right afcenllon in time ferves alfo 

 for computing the apparent time of a known ftar's palFing 

 the meridian : thus, fubtratt the fun's right afcenfion in 

 time at noon from the ftar's right afcenfion in time, the 

 remainder is the apparent time of the ftar's pafting the meri- 

 dian neariy : from which the proportional part of the daily 

 increafe of the fun's right afcenfion from this apparent 

 time from noon being fubtrafted, leaves the corredt. time of 

 the ftar's paffing the meridian. The fun's right afcenfion 

 in time is alfo ufcful for computing the time of the moon 

 and planets paffmg the meridian. 



For finding the right afcenfion of a ftar, fuppofing 

 its latitude and longitude, and alio the obliquity of the 

 ecliptic, to be given the method is as follows. Let PESQ, 

 (fig. 16.) or the primitive circle, be the folftitial colure; 

 EQ_ the equator, PS its poles, and r i a parallel of 

 latitude interfccting a circle of longitude p K q \\\ the 

 place of a ftar. Suppofe the latitude of the ftar to be 

 7° 9' N. and its longitude v 29° l', and the obliquity of 

 the ecliptic 23° 28'. In the triangle PA/>, we have Vp the 

 diftance of the poles of tlie equator and ecliptic, or the 

 obliquity of the ecliptic = 23" 28', /A, or the complement 

 of the latitude =: 82° 51', and the contained angle P/A =: 

 60° 59', or the longitude from the firft point of 25, and we 

 are to find the angle />PA or the right afcenfion. The 

 proportion is as follows: rad. : cofine VpK :: tang. /A; 

 tang. M. Take the difference between the fide adjacent to 

 the required angle and M, and call it N : then fay, fine N ; 

 fine M. :: tang. P/A : tang. /PA. Or, firft find the de- 

 chnation (fee Declination), which is 17° 49' N. Then 

 fay, 8. co-decHn. : S. long. :: S. co-lat.: S. co-right-afcen- 

 fion ; i. e. _S. 72°ll' : S. 60° 59' : : 8.82° 51': S. co- 

 right-afcenfion:— or, 9.97865-54 : 9.9417492 :: 9.99660961 

 9-9597034. the fine of 65° 41' ; and therefore the right 

 afcenfion will be 24° 19'. 



The right afcenfion and declination of a fixed ftar or^planet, 

 whofe longitude and latitude, as well as (O) the obliquity 

 of the ecliptic, are given, may be found by the following 

 problem, communicated by Dr. Mafkelyne to Dr. A. 

 Mackay. 



Tan. lat. — fine long. = tang. A, north or fouth, as lati- 

 tude is. Call. O north in fixfirll figns, and fouth in fix lad 

 figns. 



A+0 = B. 

 A Icfs than 45°, co. ar. cof. A+cof. B-f-tang. long.' 

 A more than 45'', tang. A4-C0. ar. fine A-f-cof. ~ 



-|- tang. long, 

 tang, right afcenfion of the fame kind as longitude ; 

 unlefs B be more than 90°, when the quantity found of the 

 fame kind as longitude muft. be fubftraded from 12 figns. 



AR 



'g-7 



