sit 



TRANSIT. OR TRANSIT INSTRUMKNT. 



TRANSIT, OR TRANSIT INSTRUMENT. 



hare the value of , and that with gnat exactness, if the star* have 

 been well wlectcd, are pretty muneroua, and have been tolerably 

 observed. To reduce the traiuiu of the other object* observed to 

 apparent R. A. nothing more ii required than to add m + it tan J to the 

 observed transit, which, beside* being a good deal ahorter than the 

 method previously described, only require* a table of natural tangent* 

 for computing the correction*. 



If the observations are made on or near the pole, where the sec 8 

 vrie almost a* rapidly at the tangent, a aensihle error of collimation 

 would mix iUelf up in the value of tan S. U the pivot* of the instru- 

 ment are exactly equal, two aerie* might be observed in reversed 

 poaition* of the axis, and a* M and n would have the same value in 

 each, while the aigu of collimation changes, the determination of the 

 Utter would present no difficulty. We have used another plan, which 

 in steady weather, when observations can be made on consecutive nights 

 and in large msrniti. in perhaps the bent for cataloguing. On the first 

 night observe forty or fifty stare, consisting of all the standards which 

 pass and those stars the place* of which you wish to determine. 

 These may now lie scattered all over the heavens, so far as the method 

 is concerned. On the following evening reverse the instrument and 

 observe the same stars. The first night, each obeerved star should be 

 increased by M + tan 8 + e sec 8, while the second night the correc- 

 tion U nT + ' tan t c sec S, the collimation being supposed (as is 

 found to be the case) to be invariable in a well-made instrument, unless 

 violence is used. Now if we add the observed transits of each star on 

 the two nights together, and take a mean, the result requires a 



correction of m + m + " * n ton S; and the collimation is eliminated. 



This new correction for the mean of the two nights is exactly of the 

 same form as the original correction, call it si + N ton S, and M and N 

 ore found by comparing the observed places of the standard stars with 

 t!..-,r known computed places, just as before. If the clock rate is 

 sensible, the values of n, preceding and succeeding the mean of the 

 standard stars, must receive a proportional correction, but it is easy to 

 make the rate of a good clock so small that in ordinary circumstances 

 this may be neglected. The rate may be determined near enough by 

 observing the same high star both nights in the same position of the 

 axis, and measuring the inclination by the level. From some trials of 

 this method, we should strongly recommend it in a steady climate and 

 where a large catalogue of stars is to be formed. An error of 0*-1 

 would, we are convinced, be very rarely found in the it. A. of stars so 

 determined within 40 of the equinoctial ; the computations are very 

 short and can scarcely be wrongly made, and there is only one com- 

 putation of a mean place for two complete observations of an apparent 

 place. Writing the separate results under each other, is an excel- 

 lent check against those provoking small errors which, when they 

 once got admittance, are so difficult of detection. It is a drawback 

 that the computation does not furnish the absolute time or clock 

 error, if that should be required for other purposes, without further 

 calculation. 



In this climate it frequently happens that the star is visible during 

 only a portion of its passage over the wires, or the observer may lose 

 some of the wires ; hence it is necessary to have some means of com- 

 pleting the imperfect transits, and ascertaining so far as possible at 

 what time the star would have pawed the mean of the wires, if all 

 could have been observed. For this purpose a sufficient number of 

 complete and satisfactory observations is selected (suppose the illumi- 

 nated end to be west), and the difference taken between each wire, and 

 the mean of the wires. Multiplying these numbers respectively by 

 the cosine of the corresponding star's declination, we have the differ- 

 ences, such as they would have been if the stars observed had been in 

 the equinoctial. A mean of these is taken for each difference, and the 

 proper sign affixed. If a second series be selected of observations 

 made when the illuminated end is east, and be treated similarly, nearly 

 the same value* will be found as before, but in reversed order, and 

 with different signs. A mean is token when the number is sufficient 

 to give a satisfactory result ; and the logarithms of the intervals be- 

 tween each wire and the mean, for on equinoctial star, are set down 

 for future use, discriminating whether the instrument is Illuminated 

 end K. or W. Now suppose a broken set of wires is to be made up : 

 take the logarithms with the proper sign corresponding to each wire. 

 add to each logarithm the log. secant of the star's declination, and take 

 the natural numben corresponding to the logarithms thus found, and 

 you have the number of seconds and decimals of a second which are to 

 be added (algebraically) to the observation of each wire to reduce it to 

 the mean win. Of these partial results, a final mean is taken. The 

 numbers for reducing each wire to the mean wire are found in the 

 introductions to all the modern observations. 



The slow-moving stars, such as Polaris and S Ursa; Minoris, are those 

 best suited for determining the interval of the wires, and this U one of 

 the first points to which an observer should direct his attention, for he 

 will observe a slow star as well at starting as afterwards, and as he 

 will probably make a good many broken transits, the sooner he acquires 

 the means of reducing them the better. The declination of these stars 

 U perfectly known for every day frum the Nautical Almanac, but there 

 1* a precaution to be taken here, which is unnecessary will. 

 moving stars, as the path of the ktar being sensibly curved in moving 



from the outer to the inner wire*, the motion between the wires is not 

 uniform. The exact formula U 



sin distance of any win from mean = sin time from mean 

 x cos. dedin. star ; 



and the equatorial interval may be computed by taking the log sin of 

 the intervals log sin 15", instead of simply the log interval in seconds 

 of time, a* in other stars. Or if the following quantities be first 

 subtracted from the intervals observed, the ordinary rule may be 

 followed : 



Intfrnl 



Observed. Correction. Observed. Correction. 



4 . 



8 ... 01 11 . 2-0 



11 



IS . 

 14 



IS . 

 16 



17 . 

 18 



K . 

 SO 



This table may also be used when the broken wires of a close cir- 

 cumpolar are to be reduced. Compute the correction for each wire by 

 the ordinary formula, and add to it the number from this table corre- 

 sponding to the interval, before applying the correction to the observa- 

 tion of the wire. 



As the stars sub polo pass the wires in a contrary direction, the 

 numbers for reducing each star to the mean wire must be taken from 

 the table corresponding to the reversed position of the instrument, or, 

 what comes to the same thing, they must be reckoned backward with 

 changed signs from the table which belongs to the existing p. 

 When the interval between the mean wire and the other wires is well 

 established, the collimation error must be referred to the mean wire, 

 after it has been measured for the middle wire. There in a way of 

 measuring the collimation, when the distance of each wire from the 

 mean is well determined, which is very useful in the absence of a 

 meridian or collimating mark. Polaris or 8 Ursa: Minoris, or any 

 slow-moving star, is observed over the first four wires (the inclination 

 error having been previously measured) ; the instrument is then re- 

 versed and the star is observed over the remaining three wires, and the 

 inclination again measured. The first set of observations is reduced to 

 the mean wire by the known intervals at the horizontal position of the 

 axis. The second set is similarly reduced to the mean wire, at the 

 horizontal position. The difference between the two results, if the 

 Y'B have not been altered by lifting the instrument and setting it down 

 again, is the sum of the collimation in two positions ; and when this is 

 divided by twice the secant of the star's declination, the result is the 

 collimation error required. If the pivots are perfectly equal, the 

 levelling may be omitted except as a precaution against altering the Y'S. 

 When the time is wanted with great nicety, it is convenient to observe 

 a series of stars before reversing upon Polaris or 8 Ursie Minoi ; 

 a second series after. If the pole star has been properly observed and 

 reduced, and the' collimation rightly determined, the two series will 

 give nearly the same clock-error, and be a check on each other. The 

 instrument must always be used in reversed positions, for determining 

 the time, when this is practicable. 



There is a curious anomaly sometimes found in transit observations, 

 namely, that two practised observers will make a notable and constant 

 difference in observing the exact moment at which a star passes a wire. 

 Maskelyne first noticed this singularity in his assistant Kiunebrook, 

 who observed a star 0*7 later than the Astronomer Ruyal. Bessel and 

 Argelander have a still larger difference ; and we found, on deter- 

 mining the longitude of Bruxelles chronometrically, that M. Qu 

 the director of that observatory, noted a transit about 0"8 earlier than 

 Mr. Henry, one of the transit observers at Greenwich : so that if th 

 time at each place had been simply taken from their observations 

 without any allowance, the longitude would have been erroneou- on 

 that account alone 0"S, which might have been either way. This 

 shows how insecure all nice chronometrical longitudes are, unless the 

 same observer determines the time at both ends of the are, or unless 

 the relative pcrtonal ry nation of the observers at each end is carefully 

 determined. [EQUATION, PERSONAL.] It would be advisali! 

 haps, where the result is very important and the distance considerable, 

 to reverie the observers, as it seems that fatigue will, in some cases at 

 least, cause a variation in the personal equation. ,m<l that two observers 

 may begin a night with one difference and end with another. 



If it were not for this latter circumstance, it would perhaps be 

 possible to train observers to observe alike, by exhibiting the same 

 phenomena of sound and sight (the relation between wl.irh might be 

 established mechanically) to a class, and habituating them, like an 

 orchestra, to keep the same time ; and such a piece of mecli 

 would be easily made, though there would be a difficulty in getting 

 observers to submit to the drill. We have found the following prac- 

 tice a good exercise for making the eye and ear work together. The 

 pointer of a clock, with dead-beat scapement, springs forward simul- 

 taneously with the sound of the beat. Where there is a good deal of 



