The slow-moving stars, such as Polaris and 8 Crew 31inoris, are those best suited for determining the interval of the wires, and this is one of the first points to which en observer should direct his attention, for he will observe a slow star as well et starting as afterwards. and as he will probably make a good many broken transits, the sooner ho acquires the means of reducing than the better. The declination of these stars is perfectly known for every day from the Nautical Almanac, but there is a precaution to be taken here, which is unnecessary with quick moving stars, as the path of the star being sensibly curved in moving from the outer to the inner wires, the motion between the wires is nut uniform. The exact formula is sin distance of any wire from mean =sin time from mean x cos. deelin. 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, as In other stars. Or if the following quantities be first subtracted from the intervals observed, the ordinary rule may be followed This table may also be used when the broken wires of a close cir cumpolar aro 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 position. 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 is 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 Bet is similarly reduced to the mean wire, at the horizontal position. The difference between the two results, if the ft3 have not been altered by lifting the instrument and setting it down again, is 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 Vs. When the time is wanted with great nicety, it is convenient to observe a serial, of stars before reversing upon Polaris or 8 Unite Minoris, and 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. Tho
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 Kinnebrook, who observed a star 0e.7 later than the Astronomer Royal. Bessel and Argelander have a still larger difference ; and we found, on deter mining the longitude of Bruxelles chronometrically, that 31. Quetelet, the director of that observatory, noted a transit about earlier than Mr. Henry, one of the transit observers at Greenwich : so that if the time at each place had been simply taken from their observations without ail allowance, the longitude would have been erroneous on that account alone 0'.9, 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 arc, or unless the relative personal equation of the observers at each end is carefully determined. [EQUATION, PERSONAL.] It would be advisable per haps, where the result is very important and the distance considerable, to reverse the observers, as it seems that fatigue will, in sonic cases at least, cause a variation in the personal equation, and 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 which might bo established mechanically) to a class, and habituating them, like an orchestra, to keep the same time; and such a piece of mechanism 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 dend-beat scapement, springs forward simul taneously with the sound of the beat. Where there is a good deal of noise, and the clock has a low beat, it is found necessary to have a second clock called a journeyman, which strikes loudly and speaks as it were for the transit clock. The observer makes them beat pretty nearly together, and then listening at the principal clock and noting the difference, he either pushes forward or delays the pendulum of the journeyman to make the coincidence perfect, and this ought to be continued until he cannot distinguish between the two beats when standing close to the transit clock. Let a person try to make this coincidence by looking at the transit clock and listening to the journey man, and if he can, or can very nearly do this, it is evident that he notes an appearance at the time it happens. Perhaps by trying the same thing when fatigued, he might detect a change in his perceptions, for the coincidence of sounds, as judged of when equalised by standing near the weaker source, is one in which a tolerable ear can scarcely be more than 0..01 or 0'02 out at farthest.