ASTRONOMY. 



[ERROR or AZIMUTH. 



iUn to the south of the icnith are observed before they 

 come to the true meridian, and thoM north of the tt&ith 

 altar they p*" the true meridian. 



. T. 



Let N or S (Fig. 208) be the azimuths! error, O 

 the observed place of the star, then S i X sin. Z o - op, 

 draw the great circle 1' o K from the pole to the equator, 

 pasting through the star O, then E Q is the correction in 

 k Aso. in arc, which, being divided by 15, will give the 



correction in time ; but E Q = O p X gijj p o ; 



therefore, E Q i - S X 15 '" fl Z p o - azimuthal erroi 



rin.ZD south g . noe th(j gign of th(j correct ion to 



M. N P D 

 the north of the zenith is contrary to that of the south, 



if zenith distances with have the sign ;i'iw, and those to 

 the north the sign mintu, the above expression will givo 

 the oorrection in either case. 



or 



_toos. (L 



a sin. (LT8)+e 

 cos. 8 



The preceding corrections for errors of level, azimuth, 

 and collimation being all supposed positive, may be re- 

 presented by 



I o.n. 7 n a sin. 7. D e 



sm7NPl>~ l ~siu. NPD + sin. N P t> 



where I represents the error of level, a that of azimuth, 

 and c the error of collimation. By introducing the lati- 

 tude L, the expression for the sum of these corrections 

 may be written thus (S being the declination), 



* 

 I (cos. L cos. 8 + sin. L sin. 8) 



cos. 8 



* 4- a (sin. L cos. 8 + cos. L sin. 8) 

 cos. 8 



_ I cos. L-f I sin. L tan. 8 + a sin. L aoos. Ltan. 8 + e sec. 8. 

 (I cos. L + a sin. L) + ( a cos. L + a cos. L) ten. 8 + e sec. 8. 



m + n sin. 8 + e sec. ?, which is the form of these 

 corrections Bessel gives in the Tabula Rtgiomontana. 



To Find 0* AzinwOuU Error* by Trannti of a 



Cirevmpolar Star. 



Let T the time of superior transit, supposed too 

 late ; ( the time of an inferior transit, which will be 

 too early ; then, since the difference between these tran- 

 sits corrected for motion in R, A. should be 12h., all the 

 other corrections being made, we shall have 



o sin. Z D o sin. Z IX 



T ~16sin.NP"D" +15sin.NPD 



Let T t - 12h. -|- 6, then 



a (sin. Z D + sin. Z IX) 



15 sin. N P D 

 .11. (colat. - N P D) + sin, (colat + N P D) ) 



art. 



15 sin. N P D 

 2 a sin. colat cos. N P D 



15 6 X tan. N P D 



I., MI, N I' 1 1 2 sin. colatitude 



In a future page we shall afford numerical examples of 

 the determination of azimuthal errors. 



The preceding factors for collimation, level, and azi- 

 muth, vis. 



Error of collimation X fg -r "> vr i> T 

 15 sin. star s N P D 



cos. Z D south 



Error of level X 

 Error of azimuth x 



15 sin. N P D 

 sin. Z D south 

 15 sin. N P D 



are tabulated for different north polar distances at the 

 principal observatories, the multiplication being easily 

 made by means of a sliding ruler. Several other contriv- 

 ance* have been invented for forming these corrections by 

 mechanical methods, by the Astronomer Royal, Professor 

 Challis, and Mr. Carrington, for which we beg to refer to 

 the Memoirs of the Royal Astronomical Society. 



Having thus explained the formuUe and methods of 



determining the three preceding errors, we shall now 

 proceed with the investigation for a determination of 

 the equatorial intervals of the wires, which arc immedi- 

 ately necessary for the reduction of imperfect transits. 



When a heavenly body is observed with a transit in- 

 strument at a distance from the meridian, if this distance 

 be known, and also the distance of the object from the 

 Pig. jog. equator, the time to 



s be added to or sub- 



tracted from the si- 

 dereal time of obser- 

 vation can be com- 

 puted thus : Let P 

 be the pole, Q E a 

 portion of the equa- 

 tor, O the object 

 at the distance OS 



measured on a great circle. (It may be well to remark 

 that to whatever part of the heavens a transit instrument 

 is pointed, the distance from any wire to the middle wire 

 is an arc of a great circle ; it is the same as if the 

 equator had been moved into that position). Now in the 

 triangle we have O S and O P given to find SP O, which 



sin. S O 

 expresses the time ; therefore sin. S P O = gj^i or *f 



h = the distance 5=the declination, c angle S P O ; then 

 sin. c = nin. h sec. i. 



Now it frequently happens, especially in cloudy 

 weather, that an object has not been, or cannot be, ob- 

 served at all the wires of the transit instrument ; but if 

 the intervals of the wires bo known that is, the times 

 employed by an equatorial star in passing from the first 

 to the second, from the second to the third, <fcc. tho 

 true time at which an object, which has been observed on 

 any wire or wires, would transit the meridian, can bo 

 found. The manner in which the equatorial intervals 

 are given, is the distance of the first wire from the mean 

 of wires, which is called the first interval ; the distances 

 of the second and third from the same point are tho 

 second and third intervals that is, the distance of the 

 uiuan of all the wires from each wire is the interval : tho 



