TRANSIT CIRCLE, or MERIDIAN CIRCLE, an instru-ment for observing the time of a star's passing the meridian, at the same time measuring its angular distance from the zenith. The idea of having an instrument (quadrant) fixed in the plane 'of the meridian occurred even to the ancient astronomers, and is mentioned by Ptolemy, but it was not carried into practice until Tycho Brahe constructed a large meridian quadrant. This instru-ment enabled the observer to determine simultaneously right ascension and declination, but it does not appear to have been much used for right ascension during the 17th century, the method of equal altitudes by portable quad-rants or distance measures with a sextant being preferred (see OBSERVATORY and TIME). These methods were, how-ever, very inconvenient, which induced ROEMER (q.v.) to invent the transit instrument about 1690. It consists of a horizontal axis in the direction east and west resting on firmly fixed supports, and having a telescope fixed at right angles to it, revolving freely in the plane of the meridian. At the same time Roemer invented the altitude and azimuth instrument for measuring vertical and horizontal angles, and in 1704 he combined a vertical circle with his transit instrument, so as to determine both coordinates at the same time. This latter idea was, however, not adopted elsewhere, although the transit instrument soon came into universal use (the first one at Greenwich was mounted in 1721), and the mural quadrant continued till the end of the century to be employed for determining declinations. The advantage of using a whole circle, as less liable to change its figure, and not requiring reversal in order to observe stars north of the zenith, was then again recog-nized by RAMSDEN (q.v.), who also improved the method of reading off angles by means of a micrometer microscope as described below. The making of circles was shortly afterwards taken up by TROUGHTON (q.v.), who in 1806 constructed the first modern transit circle for Mr Groom-bridge's observatory at Blackheath, but he afterwards abandoned the idea, and designed the mural circle to take the place of the mural quadrant. In the United Kingdom the transit instrument and mural circle continued till the middle of the present century to be the principal instru-ments in observatories, the first transit circle constructed there being that at Greenwich (mounted in 1850), but on the Continent the transit circle superseded them from the years 1818-19, when two circles by REPSOLD (q.v.) and by REICHENBACH (q.v.) were mounted at Göttingen, and one by Reichenbach at Königsberg. The firm of Repsold was for a number of years eclipsed by that of Pistor and Martins in Berlin, who furnished the observatories of
Copenhagen, Albany, Ley den, Leipsic, Berlin, Washington, and Dublin with first class instruments, but since the death of Martins the Repsolds have again taken the lead, and have of late years made transit circles for Strasburg, Bonn, vViVlmshafen, Williamstown (Massachusetts), Madison (Wisconsin), <fcc. The observatories of Harvard College (United States), Cambridge, and Dun Echt have large circles by Troughton and Simms, who also made the Greenwich circle from the design of Airy.


We shall describe the principal features of a transit circle, referring for smaller transit instruments and altazi-muths to the article SURVEYING (vol. xxii. p. 719).

wards they let the piers be made narrower, so that the microscopes could be at the sides of them, attached to
through the pier, but after-

In the earliest transit instrument the telescope was not placed in the middle of the axis, but much nearer to one end, in order to prevent the axis from bending under the weight of the telescope. It is now always placed in the centre of the axis. The latter consists of one piece of brass or gun-metal with carefully turned cylindrical pivots at each end. The centre of the axis is shaped like a cube, the sides of which form the basis of two cones which end in cylindrical parts. The pivots rest on V-shaped bearings, either let into the massive stone or brick piers which support the instrument or attached to metal frameworks bolted on the tops of the piers. In order to relieve the pivots from the weight of the instrument, which would soon destroy their figure, the cylindrical part of each end of the axis is supported by a hook supplied with friction rollers, and suspended from a lever supported by the pier and counterbalanced so as to leave only about 10 pounds pressure on each bearing. Near each end of the axis is attached a circle or wheel (generally of 3 or 3J feet diameter) finely divided to 2' or 5' on a slip of silver let into the face of the circle near the circum-ference. The graduation is read off by means of microscopes, generally four for each circle at 90° from each other, as by taking the mean of the four readings the eccentricity and to a great extent the accidental errors of graduation are eliminated. In the earlier instru-ments by Pistor and Mar-tins the microscopes were fixed in holes drilled
Transit Circle.
radial arms starting from near the bearings of the axis. This is preferable, as it allows of the temporary attachment of auxil-iary microscopes for the purpose of investigating the errors of graduation of the circle, but the plan of the Repsolds and of Simms, to make the piers short and to let the microscopes and supports of the axis be carried by an iron framework, is better still, as no part of the circle is exposed to radiation from the pier, which may cause strain and thereby change the angular distance between various parts of the circle. Each microscope is furnished with a micrometer screw, which moves a frame carrying a cross, or


better two close parallel threads of spider's web, with which the distance of a division line from the centre of the field can be measured, the drum of the screw being divided to single seconds of arc (0". 1 being estimated) while the number of revolutions are counted by a kind of comb in the field of view. The periodic errors of the screw must be investigated and taken into account, and care must be taken that the microscopes are placed and kept at such a distance from the circle that one revolution will corre-spond to 1', the excess or defect (error of run) being determined from time to time by measuring standard intervals of 2' or 5' on the circle.
The telescope consists of two slightly conical tubes screwed to the central cube of the axis. It is of great importance that this connexion should he as firm and the tube as stiff as possible, as the flexure of the tube will affect the declinations deduced from the observations. The flexure in the horizontal position of the tube may be deter-mined by means of two collimators or telescopes placed horizontally in the meridian, north and south of the transit circle, with their object glasses towards it. If these are pointed on one another (through holes in the central cube of the telescope), so that the wire-crosses in their foci coincide, then the telescope, if pointed first to one and then to the other, will have described exactly 180°, and by reading off the circle each time the amount of flexure will be found. M. Loewy has constructed a very ingenious apparatus for determining the flexure in any zenith distance, but generally the observer of standard stars endeavours to eliminate the effect of flexure in one of the following ways :—either the tube is so arranged that eye-piece and object-glass can be interchanged, whereby the mean of two observations of the same star in the two positions of the object-glass will be free from the effect of flexure, or a star is not only observed directly (in zenith distance Z), but also by reflexion from a mercury trough (in zenith distance 180° - Z), as the mean result of the Z. D. of the direct and reflexion observations, before and after reversing the instrument east and wrest, will only contain the terms of the flexure depending on sinlZ, sin4i?, &c. In order to raise the instrument a reversing carriage is provided which runs on rails between the piers, and on which the axis with circles and telescope can be raised by a kind of screw-jack, wheeled out from between the piers, turned exactly 180°, wheeled back, and gently lowered on its bearings.
Tlie eye end of the telescope has in a plane through the focus a number of vertical and one or two horizontal wires (spider lines). The former are used for observing the transits of the stars, each wire furnishing a separate result for the time of transit over the middle wire by adding or subtracting the known interval between the latter and the wire in question. The intervals are determined by observing the time taken by a star of known declination to pass from one wire to the other, the pole star being best on account of its slow motion. The instrument is provided with a clamping apparatus, by which the observer, after having beforehand set to the approximate declination of a star, can clamp the axis so that the telescope cannot be moved except very slowly by a handle pushing the end of a fine screw against the clamp arm, which at the other side is pressed by a strong spring. By this slow motion the star is made to run along one of the horizontal wires (or if there are two close ones, in the middle between them), after wdiich the microscopes are read off. The field or the wires can be illuminated at the observer's pleasure ; the lamps are placed at some distance from the piers in order not to heat the instrument, and the light passes through holes in the piers and through the hollow axis to the cube, whence it is directed to the eye-end by a system of prisms.
The time of the star's transit over the middle wire is never
exactly equal to the actual time of its meridian passage, as the
plane in which the telescope turns never absolutely coincides with
the meridian. Let the production of the west end of the axis
meet the celestial sphere in a point of which the altitude above the
horizon is b (the error of inclination), and of which the azimuth is
90° - a (the azimuth being counted from south through west), while
the optical axis of the telescope makes the angle 90° + c with the
west end of the axis of the instrument, then the correction to the
, , _t. . , .t .„ , sin(¿-8) , cos(<p-S)
observed time of transit will be a —- + b , + c sec S,
cos o cos 8
where <p is the latitude of the station and 8 the declination of the
star (see GEODESY, vol. x. p. 166). This is called Tobias Mayer's
formula, and is very convenient if only a few observations nave
to be reduced. Putting b sin <j> -a cos <p = n, we get Hansen's for-milla, which gives the correction = 6 sec <p + n (tan 8 - tan <p) + c sec S, which is more convenient for a greater number of observations. The daily aberration is always deducted from c, as it is also multiplied by . sec 8 (being 0".31eos<f>sec 8). The above correc-tions are for upper culmination ; below the pole 180° —8 has to be substituted for 8. The constant c is determined by pointing the instrument on one of the collimators, measuring the distance of its wire-cross from the centre wire of the transit circle by a vertical wire movable by a micrometer screw, reversing the instrument and repeating the operation, or (without reversing) by pointing the two collimators on one another and measuring the distance of first one and then the other wire-cross from the centre wire. The inclin-ation 6 is measured directly by a level which can be suspended on the pivots. Having thus found b and c, the observation of two stars of known right ascension will furnish two equations from wdiich the clock error and the azimuth can be found. For finding the azimuth it is most advantageous to use two stars differing as nearly 90° in declination as possible, such as a star near the pole and one near the equator, or better still (if the weather permits it) two successive meridian transits of a close circumpolar star (one above and one below the pole), as in this ease errors in the assumed right ascension will not influence the result.
The interval of time between the culminations or meridian transits of two stars is their difference of right ascension, 24 hours corresponding to 360° or 1 hour to 15°. If once the absolute right ascensions of a number of standard stars are known, it is very simple by means of these to determine the P.A. of any number of stars. The absolute R.A. of a star is found by observing the interval of time between its culmination and that of the sun. If the inclination of the ecliptic (e) is known, and the declination of the sun (8) is observed at the time of transit, we have sin a tan e = tan 8, which gives the R. A. of the sun, from wdiich together with the observed interval of time corrected for the rate of the clock, we get the R.A. of the star. Differentiation of the formula shows that observations near the equinoxes are most advantageous, and that errors in the assumed e and the observed 8 will have no influence if the Act is observed at two epochs when the sun's R. A. is A and 180-A or as near thereto as possible. A great number of observations of this kind will furnish materials for a standard catalogue ; but the right ascensions of many important catalogues have been found by making use of the R.A.'sof a previous catalogue to determine the clock error and thus to improve the indi-vidual adopted R.A.'s of the former catalogue.
In order to determine absolute declinations or polar distances, it is first necessary to determine the co-latitude (or distance of the pole from the zenith) by observing the upper and lower culmination of a number of circumpolar stars. The difference between the circle reading after observing a star and the reading corresponding to the zenith is the zenith distance of the star, and this plus the co-latitude is the north polar distance or 90° - 8. In order to determine the zenith point of the circle, the telescope is directed vertically downwards and a basin of mercury is placed under it, forming an absolutely horizontal mirror. Looking through the telescope the observer sees the horizontal wire and a reflected image of the same, and if the telescope is moved so as to make these coincide, its optical axis will be perpendicular to the plane of the horizon, and the circle reading will bo 180° +zenith point. In observations of stars refraction has to be taken into account as well as the errors of graduation and flexure, and, if the bisection of the star on the horizontal wire was not made in the centre of the field, allowance must be made for curvature (or the deviation of the star's path from a great circle) and for the inclination of the hori-zontal wire to the horizon. The amount of this inclination is found by taking repeated observations of the zenith distance of a star during the one transit, the pole star being most suitable owing to its slow motion.
Literature.—The methods of investigating the errors of a transit circle and
correcting the results of observations for them are given in BrUnnow's and
Chauvenet's manuals (see TIME). For detailed descriptions of modern transit
circles, see particularly Annalen der Sternwarte in Leydm (vol. i.), the Washingtoit
Observations for 1SG5, and the Publications of the Washburn observatory (vol. ii.).
The Greenwich circle is described in an appendix to the Greenwich Observations
for 1S52. (J. L. E. D.)



Footnotes

The most notable exception was the transit instrument and

vertical circle of the Pulkova observatory, specially designed by the elder Struve for fundamental determinations.


This instrument differs in many particulars from others : the important principle of symmetry in all the parts (scrupulously followed in all others) is quite discarded ; there is only one circle ; and the instrument cannot be reversed. There is a similar instrument at the Cape observatory.


On Reichenbach's circles there were verniers instead of micro-scopes, and they were attached to an alidade circle, the immovability of which was tested by a level.