EQUATORIAL INSTRUMENT. 



EQUATORIAL INSTRUMENT. 



920 



exactly as iu determining the collimation. Since an elevation of the 

 west end of the declination axis causes the line of sight to describe a 

 circle to the east of the pole, all the transits observed in that position 

 will be too early, and rice rerid all will be too late when the east end 

 is high. Again, if the west end is too high before reversing, the east 

 is too high after reversing ; so that an error of inclination has a 

 different effect upon observations in reversed positions, and thus the 

 interval is increased or diminished by twice the error of a single 

 observation. The law of the error is that it varies as the tangent of 

 the star's declination. Suppose the star observed to have 45 decli- 

 nation, and that the interval between the observations is, according to 

 the clock, 3 8', and according to the hour-circle only 3. It is 

 evident that the first observation was 4 1 too early and the second 

 4 too late, and since the tangent of declination = 1 , the west end of 

 the declination axis was elevated 1' in the first position and depressed 

 1' in the second. If the star had had any other declination, as S, the 

 4" should have been divided by the tangent 8 before it was converted 

 into an arc. There is a second astronomical method which may 

 lierhaps suit some observers better, though less satisfactory, as it 

 depends entirely on the accuracy of the position of the polar axis in 

 azimuth. Having clamped the hour-circle very firmly when the instru- 

 ment is nearly in the meridian, observe the transits of some stars near 

 the equinoctial and others distant from it. If the distant stars agree 

 in giving the same clock error with the stars near the equinoctial, the 

 declination axis is rightly placed in respect of inclination ; but if not, 

 then, taking the clock errors from the equatorial stars, it will readily 

 be seen whether the stars between the pole and the equator pass too early 

 or too late. If they pass too early, the west end is high, if too late, 

 the east end is high, and the inclination of the axis in arc is equal to 



error in time 

 * ' *" ^*h these astronomical modes no error of 





Ian S ' " 

 collimation is supposed to exist. 



The mechanical adjustment varies a little according as the level is 

 applied. [LEVEL.] This may rest with its Ys upon the pivots of the 

 declination axis, as in the altitude and azimuth circle [CIKCLE] and 

 transit [TRANSIT], or hang from two cylinders, which, being fixed on 

 the declination axis and parallel to it, project so far as to allow a level 

 suspended from them to swing clear of the axis in all positions of the 

 telescope. Place the declination axis horizontal by the level, and read 

 the hour-circle ; turn the polar axis half round, and place the declina- 

 tion axis horizontal again, and again read the hour-circle. If the 

 readings are the same (or where the graduation is to 24*, differ exactly 

 12*) in both positions, the declination axis is adjusted ; but if not, 

 place the hour-circle half way between the positions it actually has and 

 that which it ought to have, and make the declination axis horizontal 

 by raising or depressing the screws which adjust it. The swing level 

 requires a preliminary adjustment, that of making the cylinders from 

 which it hangs parallel to the declination axis, which is to be per- 

 formed thus : By turning round the telescope, bring the level directly 

 below the declination axis ; and by turning round the polar axis, bring 

 the bubble into the middle, and clamp the hour-circle. Turn the tele- 

 scope half round, when the level will be directly above the declination 

 axis. Then, if the bubble run towards one end, bring it half way back 

 by the screws which raise one of its supports, and the other half by 

 the tangent screw of the hour-circle. The process must be repeated 

 till it is satisfactory. The level itself is to be adjusted, as all levels 

 are, by reversing it end for end on its cylinders. 



6th. The instrument having been placed in the meridian, and clamped 

 there, the hour-circle verniers, or microscopes, are to be set to mark 

 0*. If the observer have the means of getting his time with tolerable 

 accuracy, he may perfect his adjustment thus : Clamp the instrument 

 approximately in the meridian, observe the transit of one or more 

 known stars not far from the equator, and correct the time of ob-rrva- 

 ti"ii fur the known error of the clock. Then, as the right ascension of 

 the star = true sidereal time of observation ;fc true hour angle from 

 the meridian, the true hour angle is known, and the verniers, or micro- 

 scopes, may be set to mark it. Or the declination axis may be set 

 horizontal by the level, when, if the previous adjustments have been 

 properly performed, the instrument is in the meridian, and the verniers 

 or microscopes set to mark O b . 



By attending to these rultM and repeating the operation (stars near 

 the pole may be safely used the second time), the instrument will be 

 I'otiud to be very nearly in adjustment, and it is desirable that it should 

 be so. The computation of instrumental corrections is tedious aud per- 

 plexing, ami moat ordinary observers would blunder in the attempt ; 

 after all, the results of an equatorial, used as an independent instru- 

 ment, are little to be relied upon. Except for obsei-vations of N.P.D. 

 ucar the meridian, in reversed position* of the polar axis, as described 

 in the first and second adjustment, the best equatorial must always be 

 inferior to an indifferent vertical circle. Out of the meridian the care- 

 will always use it aa a differential instrument, which is its 

 peculiar destination. 



In the rules above given it will be remarked that the observer is 

 directed, in every case but the 3rd, to place the instrument nearly in 

 the meridian. This is the most favourable position of the instrument 

 in its ordinary construction as regards symmetry and strength. Besides 

 this advantage, the computation for refraction in or near the meridian 



ART* ASD KI. DIV. VOL. IIL 



is very simple, being the same in N.P.D. as in zenith distance,* while 

 it is in R.A. For the third adjustment, the formula of computation, 

 where great accuracy is not required, is refraction = 57". 7 x tang. 

 N.P.D. of star, or the ordinary formula for refraction in altitude, using 

 the star's polar distance instead of its zenith distance. The formula in 

 more accurate the nearer the star is to the pole, but in these latitudes 

 will be sufficiently correct if the N.P.D. do not exceed 60. An adjust- 

 ment within 10" may be considered to be close enough for all practical 

 purposes. 



The equatorial, being thus adjusted, is ready for use, and may be 

 turned upon any star at pleasure. Suppose it be required, at sidereal 

 time 13 k 14, to find a star, the R.A. of which is 17" 33", N.P.D. 

 67 28'. As the R A. of the star is greater than the sidereal time, 

 the star has not yet come to the meridian, or the hour angle 

 is east. Subtracting 13 h 14 from 17 1 " 33, we have 4" 10 for 

 the east hour angle. Turn the telescope to the east, and set to 

 the reading 12 h '> 19, or 7 h 41 of the hour-circle ; t then set the 

 declination circle to 67 28' N.P.D., and the star will be nearly in the 

 centre of the field. With a little practice an observer can make an 

 approximate allowance for refraction by taking away a few seconds 

 from the hour-angle, and a minute or two from the N.P.D. If the 

 star be very near the horizon, the usual course is to put on a low 

 power to the telescope, and, having thus found the star, to set the tele- 

 scope exactly upon it, and then to apply the power best adapted to the 

 observation in view. The telescope being clamped in N.P.D. will 

 follow any star by moving the instrument round in R.A. with au 

 angular velocity equal to the apparent motion of the heavens. This 

 motion is best given by clockwork, which is now pretty generally in 

 use ; and, indeed, for the measurement of double stars, the observa- 

 tion of occultations, eclipses of Jupiter's satellites, and all optical 

 and niicrometrieal purposes, is nearly indispensable. 



It is not necessary actually to correct each adjustment before pro- 

 ceeding to the next, and the errors in R.A. may be determined at the 

 same time with those in N.P.D. by any person who understands the 

 mysteries of a simple equation and the law of the errors. As the 

 subject has not, we believe, been treated very satisfactorily, at least 

 in any English publication, we shall proceed to deduce the errors 

 aud corrections of an equatorial every way out of adjustment from 

 observations. We take as an example July 8, 1836. 



The sidereal time is corrected for the error of the clouk, and the 

 mean readings of the hour-circle and declination circle are collected for 

 refraction. 



The instrumental N.P. distances, instrument east, are larger than 

 those, instrument west, and the difference is 



for /3 Ursa: Minoris . 6' 20 

 for S Aquilro. ... 6 15 



Mean ... 6 17'5=:double index error. 



or the index error is 3' 87" to be subtracted inst. E., aud added 

 iust. W. 



Again taking the mean of the N.P.D. iust. E. and W. 



_Int'. JJ.l'.D. N.A. Aim. Differ. 



S Ursic Minoris 

 8 Aquiltc . . . 



15 12 .5-0 15 10 17 1 48 

 87 14 28-5 87 12 23 2 5'5 



Mean .... 1 56- 7 



and as the instrumental exceeds the true N.P.D. and both stars ure 

 above pole, it follows that the pole of the instrument is Mum the pole of 

 the heavens. 



a Ursa; Majoris is nearly in the 6 hour meridian west, aud therefore 

 in a proper position for determining the ludniuthal deviation of the 

 pole : we shall suppose it is exactly at ti hours from the meridian. 



* The refraction in N.P.D. may be taken from any of the tables, us the 

 /.cnitli distance is equal to the N.P.D. of the st.ir, after subtracting the co-lati- 

 tude for the upper culmination and adding it for the lower. The correction is 

 to be added to the instrumental N.P.D., when the star is south of the zenith or 

 sub polo, and to be subtracted when the star is between the pole iind the zenith. 



t The hour angle reckoned from the meridian is always the difference between 

 the sidereal time and the K.A. of the star. When the sidereal time is less than 

 the R.A. of tbc star, add 12h to the sidereal time, and then, aflcr subtracting 

 the E.A. of the star, you have the reading of the hour-circle, according to the 

 graduation into two twelves. If the graduation is from Oh to 21h, add 24u 

 instead of 12h to the sidereal tiuie, and subtract the 11. A. as before. 



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