A B K 



ABE 



Use op TitE TAni.rs. 



ji^Lihe right afcenfionl r , ,, 

 /J=;tne declination J 

 i'^the longitude of the fun. 



Entcv Tabic I. with the arn-ument y!— S, and Table II. 

 with yl-}-S, and the fum of the two coiTefpoiiding numbers 

 multiplied by the fecant of I) wiU be the alernilioii in Ri^ht 

 Ajcenfwn. 



Enter Table I. with the argument y/—.S-l- 3 figns, and 

 Table II. with A-\-S-\-2, figns, and the funi of the two 

 coiTefponding numbers multiplied by the line of D will be 

 the firft part of the abcrraUon in cfic/itur/ion. 



Enter Table III. with the arguments S-\-D and S — D, 

 and you will have two other parts of the alerration in de- 

 clination ; and the fum of thefe three parts will give the 

 wliole alcrrntinn in Declination. 



If the declination of the liar be fouth, add fix figns to 

 S-^D and S-n. 



Ex. To find the alen-ation of a AquiLf, on May 10, 

 1795, at 12 o'clock in the evening. 



y/=9' 25° 12' 

 5=1. 20. 12 



A~ S= 8. 5. o Table I. 

 y1+S=iu 15. 24 Table II. 



Z>=8°. 20' fecant 

 yiberration in Right Afcenfion 



+0,8 



+8.9 

 I, 01 1 



+8, 998 Produa. 



v^- 5+3 figns If. 5°. o'Table I. -I7",38 

 ^-|- 5+ 3 figns 2. 15 24 Table II. +0, 21 



J?. 17 

 o, 145 



D=o'. 8°. 20' fine . . - 



5=1. 20. 12 



- 2, 49 Produ(!l. 



5+Z)= I'. 28°. 32' Table III. - -2, 08 

 S-B= I- Mj 52 Table III. - -2, 97 



Aberration in Declination 



-7. 54 



If the ftar's declination had been fotith, then 



S-\-D+6C^gns=j\ 28°. 32' Table III. - + 2",o8 



.S-Z)-i-6 figns=7. II. 52 Table III. - -f- 2. 97 



Firft Part - - - - — 2, 49 



Aberration in Declination 



+ 2, 5^ 



The alerration of a ftar applied to its apparent place gives 

 the true place. On the fubjeft of this article, iee Dr. Mafiie- 

 lyne's rules for finding the alerration of a ftar, and Vincc's 

 Aftron. vol. i. chap. 22. p. 311 — 330. 



Aberration of a planet, in A/lronomy, is its geocentric 

 motion, or the fpace through which it appears to move as 

 feen from the earth, during the time of light's pafiTing from 

 tlie planet to the eai-th. Let S (Astrok. pi. i. fig. 4.) be 

 the fun, T the earth, P the correfponding place of the 

 planet ; and let the earth be fuppofed to move in the direc- 

 tion T/, parallel to which draw PQ, and let it be equal to 

 the fpace through which the earth has moved, whilft light 

 pafles from P to T, and Q^ will be the apparent place of 

 the planet. If Yp reprefent the motion of the planet in the 

 iame time, Q^ being the apparent, and p the correfponding 

 true place, the angle Q^ p ^vill be the aherratiori arifing 



from the progrcffive motion of light and the motion of the 

 planet. Since P(^and P/> reprcfent the motions of the eaitli 

 and planet, (^ p will reprefent their relative motions ; and 

 hence the motion of the planet about the eartii in the time 

 wliicii light takes to pafs from the planet to tiie earth in the 

 aberration. With rclpttl to tiic fun, the abrrralion in lon- 

 gitude is conftantly 20", that being the fpace moved tlirougli 

 by tlic fun, or by the earth ir. tiie time of 8' 75.", which u 

 the time in which light pafTes from the fun to the eaith. In 

 like manner, if we know the diftance of any planet from 

 the earth, wc fliall obtain iXi aberration. Foi letST = i, 

 PT=i-/, and m := the angle defcribed by the planet about 

 the earth, or its geocentric motion, in latitude, longitude, 

 right afcenfion or declination, in 24 hours : then i : d : : 

 8' 7" ,5 : 8' 7",5(/, the time in which light moves from P to 

 T ; confequently 24 h : %' f',^d::m: the aberrations. 



8' 7" >5 dm 



=zo,00564<^m. Thus by taking tlie geocentric 



24Z1 

 motion from the Na\itical Almanac, and eftimating the 

 diftance, in doing which no great accuracy is required, we 

 fiiall find the aberration of a planet in latitude, longitude, 

 right afcenfion or declination. When m is =^ 0, or the 

 planet is ftationary, the aberration is evidently equal to 

 nothing. 



Ex. I. On May I, 179 1, at noon. What is the aberra- 

 tion in longitude of Mars ? Here SP=i,5237 the mean 

 diftance, the longitude of the fun is V 11°, and the geo- 

 centric longitude of Mars is o" 29'^ 19' ; and therefore the 

 angle PTS = iI°4i', and confequently PT=2,489=f/; 

 and w;=44' 5o" = 269o", taken from the Nautical Alma- 

 nac; hence 0,00564 (?m = 37-}-" the alerration in longitude. 



Ex.2. For the Moon, ^=0,00253 the mean diftance, 

 «(z=:i3° 'o' 35" = 47435" the mean diurnal motion: hence 

 o,oo564<-/w=o",67 the aberration, which is fo fniall that it 

 may be negletled. 



It is evident that the aberration will be great eft in the 

 loni-itude, and very finall in latitude, becaufe the planets de- 

 viate ver)- little from the plane of the ecliptic, fo that this 

 aberration is almoft infenlible and difregarded : the grcateft 

 ill Mercui-)' being only about 4^", and much lefs in the 

 other planets. As to the aberrations in declination and right 

 afcenfion, they muft depend upon the fituation of the planet 

 in the zodiac. The alerration in longitude being equal to the 

 geocentric motion, will be greater or lefs according to this 

 motion. It will be greateft in the fuperior planets Mars, Ju- 

 piter, Saturn, &c. when they are in oppofition to the fun ; but 

 in the inferior planets Venus and Mercury, the aberration is 

 greateft at the time of their fuperitirconjunftion. Thefe maxi- 

 ma of aberration for the ieveral planets, when their diftancefrom 

 the fun is leaft, are as foUow, via. Georgian or Herfchell 25", 

 Saturn 27", Jupiter 29", Mars 36", Venus 43" ,5, Mer- 

 cun' 59" >5> and the Moon |. Between thefe numbers and 

 nothing the aberrations in longitude vary according to the 

 fituation of the planets. That of the Sun, however, is in- 

 variable, being conftantly 20" : and this may alter his de- 

 clination by a quantity which varies from o to near 8", be- 

 ing the oreateft, or 8", about the equinoxes, and vaniftiing in 

 the folttices. The methods and fcrmulx of computation arc 

 given by M. Clairaut in the Mem. Acad. Scienc. for I 746, 

 and by Mr. Euler in the Berlin Mem. vol. ii. for 1746. 

 M. de la Lande has calculated a table fhewing the alerratious 

 of the planets at various degrees of elongation from the fun, 

 by means of which the apparent place may be determined 

 from the true place. When the planet is ftationar)', there is 

 no aberration ; when the planet's motion is direft, the aber- 

 ration is negative, and when retrograde, pofitive. This table 

 is publid'.cd bv Mr. Viiice. It has been already ftatcd, that 



^ ' the 



