Before applying the transit Instrument to set ual observation, the adjust ment of the level of the vertical circle must be examined, which we will suppose to read altitudes when the illuminated end is west, and zenith distances when the axis is reversed. ]laving levelled the axis spproxi mately, bring the bubble of the small level to the middle by the screws at a which hold the tail.plece, fix these firmly, and then direct the telescope on some point, which is to be placed exactly on the horizontal wire if there is but one, or between the wires if there are two. Read off the vernier, which we will suppose to give an altitude of 4'. Reverse the axis and repeat the former'observation ; and now read the vernier, which we will suppose to give a zenith distance of 87'. The sum of these readings is Pl", while it ought to be U0', showing an excess of a degree in each reading. Now set the vernier at 86' 30', clamp the screw at 1,, and, by the tail-piece screws at a bring the object to its proper place between the wires ; finally bring the bubble of the small level to the middle by the antagonist capstan-headed screws, which are seen towards the end of the level at o. The instru ment will now show true altitudes and zenith distances within I' if the oremtion has been nicely performed. When the vernier reads polar distances, the vernier must be set to the polar distance of a known star, the telescope brought ,to the star, and the bubble of the small level afterwards brought to the middle. The latitude of the place may generally be supposed pretty well known : if not, direct the telescope to the pole star, or a Urine Minoris, when near their upper or lower culminations, or to the sun, or to any star which the observer can identify when it is nearly south or north. The altitude or zenith distance of a known object will give a latitude near enough for finding a star from its catalogued place, or for instrumental corrections.
We will now proceed to the azimuthal correction. If the time is known from any other observations, the middle wire of the transit may be made to bisect a star at the time when by calculation it should pasa ; and if this star be Polaris or a Ursa Minoris, the instrument will be very nearly in the meridian ; but if the observer has nothing but a transit, instrument and a chronometer, he must place it as near as ho can guess in the meridian,* and level the axis pretty carefully. A moderate knowledge of the heavens will tell what known star is likely to pass soon; and the instrument having been set to the proper altitude or sweeping for it), the observer must wait patiently till it enters the field. The observation is then made in the manner already described. If the star is near the zenith, this alone will give an approximate clock-error. Now compute the time a star near the pole or horizon should pass, and bisect the star by the middle wire at the computed time. If the error in the position of the instrument is too large to be corrected by the azimuth screw, the stand must ho shifted bodily a sufficient angle, and the instrument levelled afresh. In two or three trials it is easy to get the error within command of the azimuth-screw ; and the observer, if he dislike calculation, may con tinue getting his clock-error by a star near the zenith, and then bisecting a star near the pole or horizon at the calculated time with the azimuth-serew, until all stars, high and low, give the same clock error. The instrument is then in the meridian, and the clock-error is
the true one. This tentative process may however be considerably abridged by a little easy calculation, which we will proceed to explain, The errors of collimation and inclination being supposed to be annulled, either by adjustment or calculation, the line of eight describes a great circle passing through the zenith and not far from the pole. On drawing the figure, and supposing the deviation to be to the east of the south and west of the north, it will bo seen that the effect of the error is to cause all stars between the south horizon and the zenith to pass too early, as well as all stars sal, polo ; while stare between the zenith and pole pass too late. The effect upon the passage of a star is sin. zenith distance proportional to eosin. decimation zenith star. If x be assumed to be the amount of the deviation to the east of the south, measured in unite of I5', and the latitude of the place and the declination of the otar be denoted respectively by ˘ and a, the correction to be added to the observed passage of each star in respect of the error of deviation is sin (0 – a) x as.-1- Now suppose two stars, a and a', to be observed, coe a ) which differ a good deal in declination, and let the values of sin ( co-11ii for these stars be p and p' : then a + px and + p's are the times nt which the stars would have been observed if the Instrument had been in the meridian. The interval therefore between their transits thus corrected (and also corrected for tho rate of the clock, if necessary) will be equal to the difference of their right ascensions, which may be taken from the ' Nautical Almanac; if the stars are contained in its list, or must be computed from some good catalogue, if they are not Let the right ascensions of the two stars be a and a, and we have the following (I + p'x) – (s + pa') a' – a.
(a' – a)–(s' – I) or x If the value of a revolution of the azimuth screw is known, it is easy to correct for this error at once with considerable accuracy. If x exceed P or 2', it must bo reduced to those limits. Should x be negative, the deviation is to the west of the south.
The accuracy of the determination of x depends, arleris paribus, upon the stars which are used for the computation, that is, upon the value of the denominator of the above fraction, which should be as large as possible. The most favourable condition is, that both stars should be near the pole, one above and the other below : a Ursa Minor-is and Cephei 51 I levelii present this combination. It is always desirable that one of the stars should be pretty near the pole–Polaris, if possible. If the instrument is nearly in the meridian, it is bettor not to touch the azimuth screw, but to determine the value of x by grouping the stars together, in which sin is nearly of the same magnitude with the same sign. The value of x may afterwards be used to correct each otar separately, and the transits thus corrected will be very nearly such as would have been made if the inatrumeut had been exactly placed in the meridian.