M 



CIKCLE, ASTRONOMICAL. 



CIRCLE, ASTRONOMICAL. 



it* greatest elongation, or by the horizontal wire when near the 

 meridian. In the former caw the eye U to be moved on each aide, in 

 the latter up and down ; and if the ttar continue* bisected, and then- 

 is no dn.>ing of the (tar on one aide or other of the wire, the position 

 is correct. When the star move* contrariwise to the eye of the 

 observer, the tube iniut be pulled out, u the imago of the star U then 

 formed between the wire* and the eye, and the wires must be brought 

 to the same place. When they move the same way, the tube is to be 

 pushed in until the image U formed exactly upon the wire. Any error 

 must be corrected by gradually pushing the tube in or out. When 

 this has been once successfully done, a notch for verification should be 

 made to save all future trouble. The vertical wires are now to be set 

 at right angles to the axis. Take any well-defined object, either a 

 sharp distant terrestrial mark, or the wires of a subsidiary telescope 

 [COLLIMATOR], or a circuinpolar star at its greatest elongation. Bisect 

 this at the centre of the middle wire, and move the telescope up and 

 down until you see the object at the top and bottom of the field. If it 

 is not bisected there twist the moreable tube round, and so bisect it, 

 and repeat the operation until you are satisfied. The middle horizontal 

 wire, if a correct position of that is preferred, must be adjusted, by 

 twisting the tube until a star on the meridian runs along the horizontal 

 wire by its own motion, the azimuth circle being fixed ; or by moving 

 the instrument in azimuth after having bisected Polaris or a circum- 

 polar star near the meridian, on that wire. There are screws above 

 and below the tube at the eye end, which should now be tightened. To 

 make the central and vertical wire describe a great circle, bisect a well- 

 defined object, as near the horizon as may be, read the horizontal 

 microscopes, turn the instrument 180 in azimuth, and observe again, 

 reading the same microscopes. If the means of each pair of readings, 

 before and after reversion, differ exactly 180, the wire describes a great 

 circle; if not, move the instrument half way to 180 by the clamp 

 screw, and bisect the object by turning two antagonist and pulling- 

 screws near the eye-piece, which draw the wire plate to either side ; 

 repeat the operation until you are satisfied. If the horizontal clamp is 

 strong enough, the circle may be taken out of its axis and reversed as 

 an ordinary transit [TRANSIT]. The upper microscopes may now 

 be correctly adjusted. Observe any object which does not alter its 

 altitude on the middle horizontal wire, and read the upper micro- 

 scopes ; turn the instrument through 180 of azimuth, and observe the 

 object again. Move the circle to exactly the middle of these two 

 readings (which will be near either 0" or 1)0), when the telescope is 

 in the zenith, and then by the adjusting screws set the crosses of each 

 of the microscopes exactly on or 90, as the case may be ; the micro- 

 scopes are then in a diameter, and the error of collimation in altitude 

 is also destroyed. As this correction is altered by any alteration of the 

 apparatus for levelling the horizontal axis, and as few observers like to 

 meddle with the adjustments of their microscopes, the microscopes 

 can be brought into a diameter after the axis is .made horizontal 

 by raising or lowering each of the levelling screws a small equal 

 quantity; but though it is convenient that the microscopes should 

 read nearly the same angle, it is not at all essential to accuracy, and the 

 error of collimation must always be ascertained or eliminated by the 

 mode of observation. 



We shall always suppose every observation to be a mean of two, one 

 made face cant and the other face west, unless the contrary be said or 

 implied. In this case there is no error of collimation. 



The altitude and azimuth circle was, as has been stated, invented by 

 Kocmer, though a quadrant moving freely in azimuth, and with a 

 graduated horizontal circle, was used by Hcvelius. It in the most 

 universally useful of all astronomical instruments, and is both portable 

 and accurate. In delicate hands, and with some power of calculation, 

 it U capable of performing a great deal of good work. Besides being 

 an excellent geodesical instrument [THKODOI.KT], it is, when placed in 

 the meridian, an accurate, though not very convenient transit. It 

 may be used in this position as a meridian or transit circle, for deter- 

 mining at once the right ascension and zenith distance of any unknown 

 stars. In this case the horizontal point must be got by combining 

 observations taken directly with others by reflection, in the manner 

 already described in the mural circle ; or else several standard star* 

 may be observed, and their instrumental places coin|>ared with their 

 computed places ; the mean of these differences is to be applied as an 

 index error to correct the observations of unknown stars exactly as in 

 Mr. Pond's first method with the mural circle. In this mode of 

 observing there U no reversion. 



The principal merit in the altitude and azimuth circle is, that it con 

 be moved in azimuth without injuring its accuracy as a measurer of 

 zenith distance. Let us suppose a navigator in a strange place with 

 mch an instrument and a time-keeper, of which the error is unknown. 

 This should mark sidereal time. The instrument must first be 

 nearly adjusted, and the approximate meridian selected. This will In- 

 known new enough by nhifting the in/itrument in azimuth till it i 

 found that a star, which is bisected by the horizontal wire, continues 

 to be bisected for a short time. Observe the zenith distance - 

 known star in this direction, and this will give an approximate 

 latitude. The time and the azimuth of the star should also be noted. 

 Now observe the zenith distance of another known star near the i u ime 

 vertical, the time deduced from this and the approximate latitude will 

 be a very cloee approach to the true sidereal time at the place. The 



original latitude from the first observation may now be corrected by a 

 more accurate knowledge of the time, and the azimuth of the star at 

 the tune of observation be deduced, whence the reading convi-|mdiiu{ 

 to the meridian position of the instrument is also known. If these 

 observations have been managed with any skill or discretion, the lati- 

 tude and time are now found near enough for future calculations.* 



To ascertain the latitude with the utmost precision, several standard 

 stars are to be observed near the meridian, and, if it may be. at 

 nearly equal distances from the zenith, north and south, to 70 

 zenith distance. A few minutes before the star comes to the meridian, 

 bisect it near the centre of the middle horizontal wire, noting the 

 time of bisection. It is perhaps more exact to place the wire cl 

 the star, and then, leaving the vertical circle untouched, to move the 

 whole instrument by the horizontal clamp along with the star, until it 

 is bisected upon the wire by its own motion. The ends of th< 

 and the upper microscopes are then read, the instrument U turned 

 gently round 180 in azimuth, and the observation is repeated. Tin: 

 sum of the two angles (when each pair of readings is connected into 

 one zenith distance) is twice the apparent meridian distance of thr 

 star, affected by the want of verticality in the axis, which is known 

 from the level, and by a small correction depending on the time << 

 observation. It is clear, that if the end of the level towards the 

 eye end of the telescope is too high, the foot-screw towards th 

 observer should be lowered, in which cose the telescope would point 

 above the star, that is, show a less zenith distance than the true zenith 

 distance. Hence the rule is, take the reading of the end of the level 

 towards the object end of the telescope from the reading towards the 

 eye end, halve the difference, and add this, when converted into arc, to 

 the instrumental zenith distance. This may be done in each case, or 

 the mean of the whole applied to the mean of the instrumental zenith 

 distance. For the correction to the meridian the formula is. 



Corr.= 



cos. dec. * x cos. lat. 2 sill. * 

 sin. zen. dist. * 



i 

 . 



The first factor must be computed for each star ; the latter is t ik<-n 

 from a table which maybe found iu Schumacher's BQlfltafdn, or /HI////'., 

 Tablet, and in many collections of astronomical tables. The argument 

 is the angle at the pole, that is, the difference between the moment of 

 observation and the transit of the star. This correction is to be tub- 

 tracttd from the zenith distance of stars observed above the pole, and 

 added to those observed Mow the pole. The mode of observing is 

 generally known by the name of circum-meridian. We have hero 

 detailed the process as it refers to a single pair of observations, but 

 several pairs may be taken, as many as can without hurry be cot in a 

 quarter of on hour on each side of the meridian. With a good instru- 

 ment and a careful observer, the latitude thus deduced tV. .m I 

 stars will be very near the truth, if the observer employs a em n H 

 catalogue, such, for instance, as that of 1112 northern stars, publi.-lied 

 by Mr. Pond in 1833, or the catalogue of southern stars, by Lieut. 

 Johnson, 1835 : if he can observe the same circuinpolar M 

 their upper and lower culminations, he may obtain a latitude inde- 

 pendently of any catalogue. If stars near the pole be observed, it is 

 not necessary that they should be near the time of passing tin UK 

 ridian, but the reduction to the meridian zenith distance must be 

 computed by an exact formula. There are special tables of Polaris, for 

 this purpose in the Nautical Almanac. 



The time may be found by two or three methods. The . 

 distances of known stars near the prime vertical, both to the cost and 

 west, may be observed, and the horary angle computed from tin; 

 observed zenith distance and the known colatitude already found. In 

 this case the altitude circle should be kept el. imped, while the In 

 the passage of the star over each of the horizontal wires are nut< 

 mean is to be token, and the instrumental zenith distance is to bo 

 corrected for the indication of the fixed level. Ui peal the operation 

 after reversing the instrument, and take the mean of the /.mth <h 

 tances, which will corresi>ond very nearly with the middle time 

 between the observations. From this zenith distance the error of the 

 time-keeper is found. The mean of the errors deduced from an eqn.-d 

 number of stars on the east and on the west prime vertical will be 

 very nearly correct, and dej>end upon the divisions of the circle and 

 the catalogue employed. Also, the altitude circle being clamped, a 

 star may be observed rising near the east prime vertical, and again, by 

 moving the instrument in azimuth, near the west prime vertical when 

 descending. The middle time will be the meridian passage of the 

 star by the time-keeper, which, when compared with the con 

 right ascension, will show the error of the time-keeper. This method 

 (commonly called that of equal altitude*) is not to be recommended, 

 except for stars near the zenith, which pass quickly from one prime 



* Let 8 be the firit star observed near the meridian, and r the second near 

 thr- prime vertical, r the pole, and z the zenith ; then rr. the colatitude = r r.t 

 nearly. Again, the triangle rr.r bring solved with this approximate vnlm- of 

 t-t w ill Rive the angle n-z, which, if the star Is west, being added to, or If 

 cant, being subtracted from its right ascension computed from the catalogued 

 place, gives the true aldrreal time at the place of observation, and hence the 

 error and correction of the lime-kccpcr. Let thi correction be applied to the 

 time of observing s, then the difference between the time so correct! il nml tin 

 computed right ascension of s gives Iho ^ srz, from which the toi rcctiun of zs 

 to the meridian may be deduced. 



