TRANSIT CIRCLE ery places of the stars that have served as our guides. The errors of instrument and clock having been thus determined, it is possible, by the aid of formulas and methods which have been so thoroughly developed and systematized as to be applicable with the greatest facility, to obtain by a single observation of any new bject its right ascension within a very small action of a second of time. But, as we have timated, the chief value of the instrument sists in its power of furnishing at the same Imination not only the right ascension but the declination of the object, and it ac- implishes the latter most simply in the fol- owing manner. While the observer is noting the progress of the star across the transit threads, he at the same time, by a delicate movement of the telescope in altitude, places it so that the star appears to run along the fixed horizontal thread ; and then, the transit observation having been completed, he reads, even to the fraction of a second, from the cir- cle microscopes the precise point correspond- ing to the apparent altitude of the star. Or, a still more accurate determination is obtained by placing the telescope so that the star will traverse the field at a little distance above or below the fixed thread ; and there is ordinarily time enough to bring the movable thread sev- eral times into coincidence with the star's image by means of the micrometer screw, al- ways noting its indications and afterward taking the mean of all. The small distance from the fixed thread, as thus measured, must of course be duly applied as a correction to the readings of the microscopes, and thus we de- rive one extremity of the desired arc, and then proceed to find the other. In order to know the star's declination, we must first have its altitude above the horizon. This can some- times be obtained by a double observation of the star's image, first as reflected from a quick- silver surface, and then as seen directly, in which case the arc included between these two directions is obviously equal to twice the alti- tude of the star ; but this course is not always applicable. We have however a readier and exquisitely beautiful method of obtaining with very great accuracy the direction of the ver- tical line, from which we can count the star's zenith distance. The telescope being turned so as to look directly downward, we place im- mediately beneath it a vessel of quicksilver ; and if then, by means of a small plate of thin glass held at an angle of 45, we reflect a strong light down the telescope, it will be reflected back by the quicksilver, and, looking through the glass from above, we shall see not only the threads in the eye piece, but also the re- flected image of each ; and by moving the in- strument carefully until the fixed horizontal thread coincides with its own image, we shall have the telescope mathematically vertical, and may read from the circle the corresponding second point of the desired arc, whereby we obtain the apparent altitude, and thence, cor- TRANSYLVANIA 845 recting for refraction, the true altitude, and finally the desired declination. A few words must be added respecting the use of transit instruments in the prime vertical, that is, so placed that the great circle described by the collimation axis is in the prime vertical. Bes- sel first suggested this method of mounting a transit instrument, for the purpose of deter- mining with special accuracy the latitude of the place of observation. It is manifest that any star which has a north declination less than Z, where I is the latitude, crosses the prime vertical at equal altitudes on the eastern and western quadrants. If the interval in time between these passages be noted as=2, it is manifest from the right-angled spherical triangle having for its angles the pole, the ze- nith, and the star's place in either quadrant of the prime vertical, that tan Z=tan 6 sec t. This method of determining the latitude has a great advantage in the readiness with which instrumental errors may be got rid of, by using the instrument alternately in opposite positions as respects the rotation axis. The adjustments for a transit instrument in the prime vertical relate, like those of the meridional transit in- strument, to the three points, collimation, level, and azimuth. In collimation the adjustment resembles that of the ordinary transit instru- ment. The instrument is brought nearly into the prime vertical by directing it to a star of small northerly declination at the calculated time of the star's passage of the prime verti- cal. When this has been done, the rotation axis must be carefully levelled, and a fresh adjustment made by means of another star. For the small adjustment thus rendered ne- cessary provision is made by allowing one of the V's a small motion in azimuth. Another method is to have the instrument provided with a graduated horizontal circle, and then, having adjusted it in the meridian, to revolve it through 90 in azimuth. When the rota- tion axis is in the meridian but inclined to the horizon, a correction can be readily made for this inclination, because the great circle de- scribed by the collimation axis crosses the horizon at the true east and west points, but passes slightly to the north or to the south of the true zenith ; and the latitude found by means of the instrument corresponds to the latitude of the point where the great circle thus swept out crosses the meridian. Thus the only required consideration of the level correction is that this correction should be applied directly to the latitude found from the instrument used as if correctly adjusted. But if the rotation axis is neither in the meridian nor level, or if the middle thread is not in the collimation axis, the correction is less simple. (See Chauvenet's " Spherical and Practical As- tronomy," vol. ii., p. 242.) TRMSUBSTANTIATION. See LORD'S SUPPER. TRANSVAAL REPUBLIC. See BOERS. TRANSYLVANIA (Hun. Erdely ; Ger. Sieben- lurgeri), a grand duchy of the Austro-Hun-
