rests, light passes through the arm into the telescope where it falls upon a perforated plane mirror placed at an angle of 45 degrees with the optical axis, and from thence it is reflected to the eye of the observer. By this means the wires are rendered visible in the night, the light from the lamp being regulated so as not to efface that of the star, which is seen through the aperture in the mirror. The extremities of the telescope are sometimes capable of being removed from the body and interchanged with one another; and in this case the reflecting mirror is capable of being turned on an axis so that its inclination to the optical axis of the telescope may be reversed, and thus the light from the lamp may be thrown at pleasure towards either extremity: by this contrivance inaccuracies in the form of the cylindrical pivots may be compensated, since different parts of their surfaces may be made to rest on the notches or inclined planes at the tops of the piers or supports. 83. At the extremity of the other arm is usually fixed, in a vertical position, a graduated circle which turns with the telescope upon the axis of motion, and is furnished with an index which is attached to the pier or stand, and consequently is immoveable, except for adjustment. The bar which carries the index sometimes extends across the circle in the direction of a diameter, and at each extremity is a vernier for subdividing the graduations of the circle: a spirit level attached to the bar serves to indicate the exact horizontality of the line joining the opposite indexes. The use of this circle is to obtain roughly the altitude of a celestial body at the time of the transit: or, the meridian altitude being previously computed, the observer is enabled by the circle to direct the telescope to the apparent place of the body on the meridian, preparatory to the observation of the transit. 84. The horizontality of the axis of motion is usually ascertained by means of a spirit level, which is either suspended below that axis from angular hooks passing over the cylindrical pivots, or is made to stand above, the feet being notched so as to rest tangentially on those pivots; and the annexed dia لسلس اساسی سلسلاسل gram represents one of the latter kind. The spirit level may be adjusted, and the axis upon which the transit telescope turns may be rendered horizontal, by methods similar to those which are employed in levelling a common theodolite; but in order to avoid the risk of injuring the instrument by too frequent reversions, it is usual to have a graduated scale adapted to the level so that its middle point, which for sim plicity may be the zero of the graduations, is vertically above the middle of the bubble or column of air, and to determine, by the difference of the readings at the extremities of the line, the error, if any exist, in the horizontality of the axis of motion. When the level is in a horizontal position, the bubble of air is stationary at the middle of the upper surface of the spirit in the tube; but on giving the latter a small inclination to the horizon, the air will move towards the higher end, till the force of ascent is in equilibrio with the adhesion of the water to the glass; and it is assumed that the space which the centre or either extremity of the air bubble moves through is proportional to the angle of inclination. In such angle the number of seconds which correspond to each graduation of the scale may be determined by the maker of the instrument, or the astronomer may determine it himself by placing the level on the connecting bars of a graduated circle which is capable of turning in altitude, and reading the number of minutes of a degree through which the circle is turned, in order to make the air bubble move under any convenient number of graduations on the scale. Now the length of the column of air in the tube will vary with changes in the temperature of the atmosphere, and the axis of the spirit tube may not be parallel to a plane passing through the points on which rest the feet of the level: therefore, though the latter plane were horizontal, the middle of the air might deviate from the zero of the scale. If the number of the graduation above each extremity of the air column be read, the excess of the greater number above half the sum of the two numbers will indicate the inclination of the axis of the spirit tube to a horizontal line, the axis being highest at that end of the scale towards which the air has moved; then, reversing the level on its points of support, and reading the numbers as before, if the excess of the greater number above half the sum of the two should be the same as before, it is evident that the points of support will be in a horizontal plane. But, should the said excess not be the same in thecontrary positions of the spirit level, half their sum, if the two excesses are on the same side of the centre of the scale, or half their difference, if on opposite sides, will be the number of graduations expressing the inclination of the plane passing through the points of support to one which is horizontal. Thus, for example, let the first excess be equal to 2.4 divisions of the scale (which, if each division correspond to 5 seconds of a degree, will be equivalent to an inclination of 12") towards the west; and the second excess equal to 0.8 divisions, or 4", also towards the west; then half their sum, or 1.6 divisions (=8") will be the true quantity by which the west end of the axis is too high: therefore that end must be lowered by means of the screw under the support till the west end of the column of air has moved 1.6 divisions of the scale nearer the middle of the level, when the axis will be in a horizontal position. If the excesses of the readings on the scale above their mean values, in the direct and reversed positions of the level, had been in opposite directions, one towards the west and the other towards the east, half the difference between the excesses would have been the quantity by which the higher end of the air column must have been moved towards the middle, in order to render the axis of motion horizontal. When the level is placed above the axis of the telescope's motion, there should be attached to it horizontally a small level at right angles to its length, in order by the bubble of air in the latter being in the middle, to ensure the vertical position of a plane passing through the axis of the telescope's motion and that of the principal level. N Р 85. The deviation of the axis of motion from a horizontal position being ascertained, the error occasioned by it in the time of the observed transit of a star may be thus determined. Let NZN' represent the plane of the meridian, NZN' half a great circle of the sphere, in which the telescope is supposed to turn, the line NON' in the plane of the meridian being parallel to the horizon, and o being the place of the observer; let also the angle zoz or the arc zz measure the deviation of the telescope from z, the zenith, or the inclination of the axis of the telescope to the horizon, and let P be the pole of the world. Then, for a star which passes the meridian in or very near the zenith, the angle subtended at P by the arc zz, or the arc ab of the equator equivalent to the angle ZPZ expressed in seconds of a degree will (art. 70.) be equal to ZZ or to the number of seconds in zz divided by the sin. ZP' cosine of zb, the latitude of the station. But, for a star which passes the meridian on any other parallel of declination, let sp represent a portion of such parallel between the meridian NZN and the circle NZN': then we have (art. 70.) sp very nearly equal to zz sin. N's, or to the product of the seconds in zz by the cosine of zs, the star's meridional distance from z; and the angle subtended at P by sp, or the arc be of the equator equivalent to SPP, equal to sp that sin. Ps' is, the angle s Pp is equal to zz sin. N's or to zz Cos. (PSPZ) sin. PS This value being divided by 15, since by the rotation of the earth on its axis every point, as s, in the heavens appears to describe about P an angle or arc equal to 15 degrees in one hour, &c., will give the number of seconds which must be added to, or subtracted from the observed time of the transit, according as the circle Nz N' is eastward or westward of the meridian, in order to have the corrected time of the transit. 86. The horizontality of the axis may be verified without a spirit-level, on observing by reflexion from mercury the transit of a star near the zenith or the pole, at the first and second wires; then turning upwards quickly the object end of the telescope and observing the same star by direct view at the fourth and fifth wires (the number of wires being supposed to be five). The intervals between all the wires being equal to one another, if the difference between the times at which the star was observed to be bisected by the first and fifth wire be equal to four times, and the difference between those at which it was observed to be bisected by the second and fourth be twice the difference between the times of being bisected by the first and second, or by the fourth and fifth, it will follow that the axis of motion is correctly horizontal. The error, if any exist, in the horizontality of the axis may be obviated by observing the transit of a star directly on one night, and by reflexion on the next: but in this method it is supposed that the rate of the clock is well known, and that the telescope suffers no derangement between the times of the observations. 87. In order to make the central or meridional wire in the telescope pass through the optical axis, the telescope must be directed so that the wire may coincide with, or bisect some conspicuous object, as a white disk on a post or building at a considerable distance; then, the pivots of the horizontal axis being reversed on their supports, if the wire still coincide with the object the adjustment is complete; otherwise, the wire must be moved towards the object as much as half the observed deviation, by means of the screw in the side of the tube, and the other half by turning the axis a small way in azimuth; employing for this purpose the screw which moves the notched plate at the top of the pier or support of the telescope. It may be necessary to repeat this operation several times before the deviation, or the error of collimation as it is called, is quite corrected. 88. If the transit telescope be provided with a micrometer, the error in the position of the optical axis may be determined in the following manner: By turning the screw of the mi crometer till the wire which was previously in coincidence with the meridional wire of the telescope is made to bisect a well-defined terrestrial mark, ascertain the number of seconds by which that meridional wire deviates from the mark, and having reversed the axis of the telescope, ascertain, in like manner, the deviation in this position. Half the difference, if there be any, between the deviations, is the true deviation of the line of collimation from a line perpendicular to the axis on which the telescope turns. This deviation is supposed to be expressed in divisions of the micrometer scale, and if these denote seconds of a degree, on dividing by 15 as above mentioned, the deviation will be expressed in seconds of time. The observed time of the transit of an equatorial star must be corrected by the quantity of the deviation so found; but for a star having north or south declination, that deviation must (art. 70.) be divided by the cosine, or multiplied by the secant of the declination, in order to obtain the corresponding arc of the equator, or angle at the pole, which constitutes the error of the transit for such star. It must be observed, that if the line of collimation deviate from the south either eastward or westward, it also deviates (the telescope being turned on its axis) from the north towards the same part; and that when the telescope is reversed on its supports, the deviation is from the south or north towards the contrary parts: if the transit of a star below the pole be observed, the correction which, for a transit above the pole, north or south of the zenith, would be additive, must then be subtractive, and the contrary. At the Royal Observatory, Greenwich, the error of collimation is found by means of a telescope placed, for the purpose, in the north window of the Transit Room. See Collimator, art. 125. 89. When it is required to ascertain that the central or meridional wire is in a vertical position, the optical axis being horizontal, it is only necessary to observe that the wire exactly covers or bisects a terrestrial object, as the white disk before mentioned, while the telescope is turned on the pivots of its horizontal axis; or a star which passes the meridian near the pole may be made to serve the same purpose as the terrestrial mark. If the mark or star should appear to deviate from the wire near the upper and lower parts of the field of view, the eye-piece with the wires must be turned on the optical axis of the telescope till the object remains bisected in the whole length of the wire. The horizontality of the wire which should be at right angles to the meridional wire and those which are parallel to it is ascertained by placing it on an equatorial star when the latter enters the field of view, and observing that the star is bisected by the wire during the |