ss 



EQUATORIAL INSTRUMENT, 



EQUATORIAL INSTRUMENT. 



834 



The reader will have no difficulty in following out the rules with 

 regard to the signs of the correction in each particular case, but it will 

 be much safer and quite accurate enough to take the value of F 

 from the figure and to multiply it by ^ tan. i for the correction. As 

 .1 practical direction we have found this convenient. Join rp, and 

 produce it both ways. Then according to this figure, the correction is 

 additive to the hour circle reading for all stars having north decli- 

 nation which are observed on the south side of rji produced, and 

 dec rend lor stars on the north side. The tangent of declination is 

 negative when the star is south of the equinoctial, and the rule is 

 reversed. There is no correction for stars in the direction of rp, that 

 is for stars having an east hour angle from the south or a west hour 



angle from the north, such that its tangent = - . After this correction 



has been applied, the index error of the hour circle may be deduced 

 in the manner pointed out. 



It sometimes happens that an observer, from carelessness or want 

 of time or knowledge, does not determine the position of the pole of 

 the instrument by the best means, viz., by observations in the meridian 

 and at six hours from it, but that this position is to be deduced from 

 a higgledy piggledy mass of observations made in different parts of 

 the heavens. To form equations such as we have just given for each 

 observation, and to s Ive them by the method of minimum squares, 

 might possibly be the most accurate mode ; but the labour would be 

 very great, and on such an object very much misspent. We have 

 found the graphical process quite sufficient, and it has the further 

 advantage of exhibiting to the eye those observations which, from 

 their extravagance, are probably errors in bisecting the star or in 

 reading off the verniers. Suppose such a set of observations to be 

 given for reduction. Draw w E and N z, at right angles to each 





/\ 







\ 



other, and intersecting at r, and then draw from r lines such as 

 rs, ps' for each known star observed, making the angles SPZ, s'pz 

 equaf to the observed hour angles of the stars. If the instrumental 

 polar distance be less than that of the catalogue, as in ', take p A'= 

 the difference ; if the instrumental distance be greater, as in s, prolong 

 p and take pA = the difference. Through h and K draw perpen- 

 diculars to PS and PS', and these will intersect at p, the place of the 

 instrumental pole. Repeating this process for each known star, the 

 eye will show pretty nearly where p should be chosen among the 

 various intersections. The place of p being determined, the observations 

 of an unknown star or comet may be corrected as shown above ; and 

 by dropping perpendiculars on PW and TV, the azimuthal and vertical 

 errors of the pole of the instrument may be determined. 



It seems scarcely necessary to caution any person into whose hands 

 nuch observations may come, against relying upon intersections which 

 are made at very acute or very obtuse angles. If, for instance, we 

 wore to attempt to deduce the place of p as to azimuth by a pair of 

 observations near the meridian, or its place as to altitude by observa- 

 tions near the 6 hour meridian, we should only have our own folly to 

 blame for the inaccuracy of the result. From the nature of the case, 

 the unavoidable errors of observation would be multiplied by the 

 process, and a result of any kind might be obtained, just as by observing 

 the sun near noon for time and near the prime vertical for latitude, a 

 tailor might cause his sextant to be guilty of any assignable error. 

 This is evident from the form of the analytical equation, but any non- 

 algebrawt may satisfy himself by drawing lines PS and PS', making an 

 angle of 6 or 10, and by finding what the effect of an error of 10" in 

 the observation* will be on the position of p. If three observations of 

 stars without reversion should be employed, and the index error of the 



declination circle be deduced at the same time, the blunder will be 

 complete. 



Though the errors of an unadjusted equatorial may be detected and 

 the corrections rigorously computed, it would be an abuse of time and 

 calculation to do so. In two of the ordinary constructions of the 

 instrument and probably in the third, the instrumental errors are not 

 and cannot be expected to be accurately the same in all positions of 

 the instrument. In those equatorials of Ramsden's construction which 

 have five feet telescopes and declination circles of three feet diameter, 

 variations of adjustment between the meridian and six hours from 

 it may be expected to amount to 10" or 20", and in the largest equa- 

 torials, which are necessarily more imperfect, discrepancies of 1' or 

 even 2' may arise. We shall now point out the rational mode of using 

 an equatorial instrument, when the object is to determine the place 

 of any phenomenon in the heavens. 



The first thing is to adjust the instrument with great care, and 

 especially to make the pole of the instrument agree with the celestial 

 pole. The permanence of this adjustment depends solely upon the 

 steadiness of the upper and lower supports, which should therefore be 

 fixed very solidly. This being done, suppose a comet is to be deter- 

 mined. Turn the telescope upon it, and having clamped the hour 

 circle very firmly, note the transit of the comet over the vertical wires, 

 bisecting it at the same time in N.P.D. by the horizontal wire. Wait 

 till some other star passes over the field, note its transit, and bisect it 

 in N.P.D. by moving the micrometer screw only. In this case the 

 declination circle is supposed to be firmly clamped between the 

 observations. Then the difference of the times of observation gives 

 the difference of R.A. between the comet and star, and the difference 

 in declination is taken from the micrometer. It is the same thing, of 

 course, whether the star precedes or succeeds the comet. Observations 

 of this kind are amongst the most perfect which can be made, for the 

 errors of the instrument being the same in each case, and the refraction 

 almost the same, no error can creep in except that of noting the 

 phenomenon. The star which is sometimes called the determining 

 star, or the star of comparison, is afterwards observed by meridian 

 instruments, and then the place of the comet is deduced with the 

 greatest accuracy. Frequently, however, there is a dearth of stars of 

 comparison, and the time before a proper star enters the field is too 

 long for the patience of the observer, or he may not have a micrometer. 

 In this case the instrument is kept clamped in R A., and after 

 observing the comet, the telescope is moved up or down a little, and 

 stars above and below the comet are observed, in R.A. by noting the 

 clock, and in declination by reading the circle. The instrument 

 should then be turned half round in R A., and the operation repeated. 

 By combining both sets, as good a place of the comet will be deduced 

 as the division of the declination circle will allow. The stars of com- 

 parison are taken above and below, so that the mean of the instru- 

 mental errors at the stars may be pretty nearly equal to that at the 

 comet, and as the effect in R.A. of an error of collimation or inclination 

 is changed in sign by reversion, it is therefore eliminated from the 

 mean. The instrument must on no account be moved in R.A. between 

 the observation of the comet and the stars of comparison. In this way 

 Halley's comet was observed at Greenwich and Cambridge, the stars 

 of comparison were subsequently observed with the meridan instru- 

 ments, and the apparent places of the comet finally settled. The details 

 will be found in the observations of the respective observatories for the 

 year 1835. 



If the utmost accuracy be not required, it is sufficient, after careful 

 adjustment, to note the transit of the comet over the vertical wires, 

 and to read off the declination and hour circle, and then turning the 

 instrument upon one or more neighbouring stars, to observe them in 

 like manner. The nearer the stars of comparison are to the comet, 

 the greater probability there is that there is no change, or" only a 

 slight change of instrumental error in moving from one to the 

 other. This mode of observation, however, is only to be tolerated 

 in cases of necessity, when, either from haste or uncertain weather, 

 the observer cannot wait for stars coming to the same meridian with 

 the comet. 



Suppose the following observations to have been made of Arcturus 

 and of an unknown star or comet, after correcting each for refraction. 



Time by Clock. Hour Circle. North Polar Diet. 



Arcturus 17 17 9'9 3 10 15'5 69 54 46 

 Comet 17 27 11 '5 2 50 38-1 62 11 1 



To determine the index errors of both circles by Arcturus, we 

 have 



h. m. s. " 



Time by clock 1717 9'9 lustruml. N.P.D . 695446 

 Hour angle west 3 10 15'5 Ditto Naut. Aim. . 69 57 37 



Instrument. R.A. 

 R.A. Naut. ) 

 Aim. ( 



Instrumenl. R.A. 

 too small 



.A. 1 



3 10 15-5 



14 6 54-4 

 14 8 10'6 



1 16-2 



Instruml. N.P.D. 

 too imall 



2 51 



