The circle has been supposed to be adjusted before observing; this is a very simple operation. First place the instrument with the foot screws in their cups, and let that footscrew be towards the observer which rests on the slow-motion piece. This is seen at fig. 1, on the right. Place the axis nearly vertical by guess, or, if there is an azimuthal circle, set the plane of that nearly horizontal by a box level. Then place the plane of the vertical circle upright by the cross level, and bring its plane to be parallel with the two footscrews which are from the observer ; that is, if the object is in or near the meridian, set the circle east and west. Bring the bubble of the main level to the same division at each end by its clamp and tangent screws, and then reverse the instrument (turn it 180° in. azimuth). The level is to be brought again to the same divisions, half by its tangent screw, half by screwing the two footecrews an equal quantity in opposite directions. Now turn the circle a quarter round (place it in the meridian according to the supposition), and bring the bubble of the level to its proper position by the third footscrew only. This first attempt at adjustment need only be approximate, but it must be performed over again with considerable nicety. The slow-motion piece is, we believe, due to Borda, and is a very ingenious and useful contrivance for making a coarse screw do the work of a fine one. By placing the footscrew nearer to or farther from the line of the two studs, the elevating power of the screw can be reduced in any proportion, and the finest and slowest motion possible given to the instrument. We have used the slow motion for finally bisecting a star in observing with great comfort. It is inure ready to the hand than any other part of the instrument, and the disturbance of the axis is of no importance,ls the level must be read off at all events. The approximate bisection is performed by the other screws, and if the observer recollects which way the star is moving, the space through which the instrument is thus moved need only be a very few seconds. The cross level must be originally fixed and adjusted, after the plane of the circle is known to be vertical, either by hanging a plumb-line before the limb, or when the telescope bisects at the same time an object and its image reflected from a fluid. When the cross level is adjusted, the horizontal wire of the telescope may be set right by making a star in the meridian run along it, or else by bisecting a fixed object with it, and afterwards moving the circle in azimuth. The object should run along the wire, and by twisting the wire-plate round may be made to do so.
In the astronomical use of the instrument the azimuthal circle is scarcely required, except to see that you have turned the circle 180° at each reversal. It is convenient to have a coarse division to show this ; it is a relief to the eye, and prevents the possibility of catching a wrong star. Any atop which is adjustable and gives notice when the rotation has reached 180° will do. In many of Troughton's repeating circles there is a pin which is pressed by a slight spring against two holes in the azimuth circle, which are 180° apart. This is convenient enough if the observations are confined to Polaris, or a very slow moving star, but wholly insufficient for stars near the equinoctial. It supposes besides that the feet of the instrument are almost exactly placed with to the meridian, which is not to be done at once. A bar moving rather stiffly on the vertical axis, and coming against a stop, seems a better contrivance.
For setting to the approximate zenith distance, there is a graduated semicircle attached to the level, which may be seen in the general view. This has its diameter parallel to the level A slender bar is attached to the object end of the telescope, and passes at the back of the circle ; this points out on the semicircle the approximate zenith distance of the star. In many circles which we have seen there are
two slips of brass which slide with a little force on the semicircle, and the slight bar above mentioned is brought to touch, each of these stops alternately. Nothing can be more convenient, but unfortunately, how ever well the clamps may be made, the contact between the bar and a stop forces the clamp somewhat, and the essential condition of the instrument, that these should be undisturbed, is destroyed. The bar should not be allowed to touch the semicircle at all, but stand freely from it. In this way, by alternately bringing the bar to the equal and opposite divisions, when either the telescope or the level is moved, the telescope will always be at the proper altitude when the level is hori zontal. If any one should wish to use the repeating circle as an altitude and azimuth circle, or as a surveying instrument, the wires of the telescope must be set at right angles to the circle axis, by bisecting a distant and distinct object, reading the azimuthal verniers, turning the instrument half round, again bisecting the object, and reading the verniers a second time. If the object be very distant, the azimuth circle may be set to the mean of the readings, and the object bisected by the horizontal screws, which draw the wire-plate; but if very great accuracy is required, either two marks must be set up having the same distance from each other as lies between the two positions of the axis of the telescope, or the angle which this last space subtends at the distant mark must be allowed for. The instrument is not fitted for nice observation with the azimuth circle.
We have now explained the chief astronomical use of Borda's circle, which is that of determining the altitudes of stars upon the meridian by several observations near the meridian. There is a correction to be applied to the mean result, which is easily computed when the approxi mate latitude and exact time are known. The formulx and tables required may be found in several works on astronomy, in Schumacher's Hfilfstafeln, p. 3S, and Baily's Tables; p. 154. The length of time during which the observations may be carried on depends on the altitude of the star and its proximity to the pole. Polaris might be observed safely beyond 36m on each side the meridian, which is the extent of the present tables, and, in these latitudes, stars in or below the equinoctial for fully half an hour on each side. It is supposed that the error of the clock is well known, but even this may be wrong to a small amount without causing much error, if the number of obser vations on each side the meridian and the hour angles are nearly equal.• The repeating circle may he very well used for getting the time either by equal altitudes, or by absolute altitudes with one or two repetitions. For this purpose there should be three or five horizontal wires, and the instrument should be previously carefully adjusted. The instrument must be moved in azimuth, so that the star passes each wire near the centre, and nothing should be touched which affects the level. For illumination by night,• there is an opening with a reflector in the centre of the telescope. This is objected to as weaken ing the telescope, but the other mode of illuminating by a small central reflector, or outer ring in front of the object glass, is incon venient. Perhaps by taking a longer hold of the telescope and strengthening the intervening portion of the tube, the former con venient arrangement may be preserved without sensible loss of strength. The repeating circle, on Borda's construction at least, cannot be well employed in observing the sun without very careful screening. The level is so perpetually changing its zero, when exposed to the sun, that there is no possibility of saying what the instrumental zenith is.