In all the preceding formulæ, the deviation from the meridian is given in time; but, to convert it into angular measure, if desirable, we have only to multiply by 15, and the seconds of time will be converted into seconds of a degree.

When the instrument is by any of the methods explained above brought into the meridian, a distant mark may be set up in the plane of the meridian, by which the adjustment to the meridian may afterwards be tested.

METHOD OF OBSERVING WITH THE TRANSIT.

The adjustments having been completed, in making obser vations with the instrument, the instant of a star's passing the middle vertical wire will be the time of the star's transit; but the time of the star's passing all the five wires must be noted, and the mean of the times, taken as the time of transit, will be a more accurate result than the time observed at the middle wire only.

When the sun is the object observed, the time of the center of his disc passing the middle wire is the time of transit; but, as it would be impossible to estimate the center with accuracy, the time of both his limbs coming into contact with each wire in succession is to be noted, and a mean of all these times will be the time of transit required. This mean may be conveniently taken, by writing the observed times of contact of the first and second limbs underneath each other in the reverse order, when the sums of each pair will be nearly equal *

The time of either limb passing the center wire is recorded in full, but for the other wires, the seconds only are recorded, as the sums of the several pairs only differ by decimals of a second. Half the sum of the times at the middle gives, then, the correct time of transit as far as the seconds, and the decimals are found by removing the decimal point one place to the left in the sum 13.2, which is equivalent to dividing by

10

Then the time of transit, or mean of observations in the above example, is 12h 0m 1s.32. This example is taken from observations made with a large transit; and, if with a smaller This is Dr. Pearson's method.

instrument the sums of the several pairs of observations should differ by more than a second, it will be necessary to take the sums of both figures of the seconds, and the division by 10, performed as above, will give the last figure of the seconds, as well as the decimals.

In taking transits of the moon the luminous edge alone can be observed, from which the time of transit of the center must be deduced by the aid of Lunar tables.

In observing the larger planets, one limb may be observed at the first, third, and fifth wires, and the other at the second and fourth, and the mean of these observations will give the transit of the planet's center.

It will sometimes happen that from the state of weather, or from some other cause, a heavenly body may not have been observed at all the wires; but, if the declination of the body be known, an observation at any one of the wires may be reduced to the central wire, so as to give the time of transit, as deduced from this observation. If an observation be ob tained at more than one wire, the mean of the times of passing the center, as deduced from each wire observed, is to be taken as the time of transit. The reduction to the center wire is given by the formula,

RV Cosec. T,

or log. R= log. v+log. cosec π;

in which R represents the reduction, the polar distance of the body observed, and v the equatorial interval from the wire, at which the observation has been made, to the central wire. The equatorial intervals for each side wire must, therefore, be carefully observed, and tabulated for the purpose of this reduction. The formula R=v cosec. π is only an approximate value of the reduction, and with large instruments capable of giving results within 0"-05, a further correction is necessary for bodies within 10° of the pole. The whole reduction in this case is given by the formula,

The time of any star's passage from one of the side wires to the center wire being observed, the equatorial interval from that wire to the center is obtained by multiplying the observed interval by the sine of the star's polar distance; and the equatorial intervals being deduced in this manner from a great many stars, the mean of the results may be considered as very correct values of the equatorial intervals required.

No star very near the pole should, however, be taken for this purpose.

USE OF THE PORTABLE TRANSIT.

The large transits in permanent observatories are used to obtain, with the greatest possible accuracy, the right ascensions of the heavenly bodies, from which, and the meridian altitudes observed by a mural circle, an instrument consisting of a telescope attached to a large circle, and placed in the plane of the meridian, nearly all the data necessary for every astronomical computation are obtained. For such purposes the small portable transit is not adapted; but it is competent to determine the time to an accuracy of half a second, to determine the longitude by observations of the moon and moon culminating stars, and to determine the latitude by placing it at right angles to the meridian, or in the plane of the prime vertical*.

The transit of the sun's center gives the apparent noon at the place of observation, and the mean time at apparent noon is found by subtracting or adding the equation of time, as found in the Nautical Almanack, to 24 hours†. The difference between the mean time, thus found, and the time of the sun's transit, as shown by a clock or chronometer, is the error of the clock or chronometer for mean time at the place of obser vation.

The time shown by a sidereal clock when any heavenly body crosses the meridian should coincide with the right ascension of that body, as given in the Nautical Almanack. The difference between the time shown by the sidereal clock, at the transit, and the right ascension of the body, taken from the almanack, will, therefore, be the error of the clock, +, or too fast, when the clock time is greater than the right ascension, or too slow, when it is less.

THE PORTABLE ALTITUDE AND AZIMUTH INSTRUMENT.

The bending of an unbraced telescope renders it unfit for the determination of altitudes; but by placing the telescope * The prime vertical is the great circle which passes through the zenith and the east and west points of the horizon.

The astronomical day commences at noon, and contains 24 hours, the hours after midnight being called 13, 14, &c., and the day ends at the next noon. The equation of time is given in the Nautical Almanack for apparent noon at the meridian of Greenwich, and the correction to give the equation of time at any other meridian will be found by multiplying the difference for one hour, as given in the almanack, by the longitude of the place, estimated in time.

between two circles braced together, an instrument may be formed capable of observing both the meridian altitudes and times of transit of the heavenly bodies. The increased weight of the instrument, however, must now be prevented from producing flexure in the horizontal axis, and this has been very ingeniously accomplished by Troughton. By mounting the transit and altitude instrument, as Troughton's transit-circle may be called, upon a horizontal plate or circle having an azimuthal motion round a vertical axis, an instrument is formed by which observations may be made either in or out of the meridian. When constructed of a portable size, the altitude and azimuth instrument may also be used in important surveying operations; for, in fact, it may be considered as a rather large theodolite of superior construction.

The altitude and azimuth instrument may be considered as consisting of three parts: 1, the tripod carrying the vertical axis about which the instrument turns; 2, the horizontal revolving plate carrying the vertical pillars, with their appendages; and 3, the vertical circles with the telescope. The tripod, A A, is supported by three footscrews, by which the vertical axis is brought into adjustment, and carries the lower horizontal plate, which is graduated to show the azimuths or horizontal angles. The vertical axis is a solid metallic cone rising from the center of the tripod to a height about equal to the radius of the horizontal circle.

The upper horizontal plate, or horizontal revolving plate, vv, carries an index, to point out the graduation, upon the lower horizontal plate, or azimuth circle, which denotes nearly the angle to be read off. The graduations upon the azimuth circle, as well as upon the vertical circle, are subdivided by reading microscopes, the construction and adjustments of which we shall presently explain. The reading microscopes of the azimuth circle are attached to the revolving plate, vv, which also carries two upright pillars. From the center of the upper horizontal plate, vv, rises a hollow brass cone which just fits over, and moves smoothly upon the solid metallic vertical axis rising from the tripod stand. A horizontal brace connects the two upright pillars with one another and with the top of the hollow brass cone, and keeps the pillars firm and parallel to one another. On the top of each pillar a gibbet piece is fixed, projecting beyond the pillars, and upon the extreme ends of these pieces are carried the Ys for supporting the pivots of the horizontal, or transit axis. The Ys are each capable of being raised or lowered by turning a milled-headed screw. The top of one of the pillars carries a cross-piece for supporting the two reading microscopes of the vertical circle; and to this cross-piece is attached the level, LL, by which the adjustment of the vertical axis is denoted.

The third portion of the instrument consists of the vertical circle and its telescope. This circle consists of two limbs firmly braced together, and preventing any tendency to flexure in the tube of the telescope, by affording it support at the op posite ends of a diameter. One of the limbs only is graduated, and the graduated side is called the face of the instru ment, and the clamp and tangent screw, for giving a slow motion to the vertical circle, act upon the ungraduated limb, and are fixed to the vertical pillar on the side of that limb The horizontal axis which supports the telescope and vertical circle is constructed exactly as the axis of the transit instrument already described; but, as it might press too heavily on the Ys from the increased load of the vertical circle, a spiral spring, fixed in the body of each pillar, presses up a friction roller against the conical axis with a force which is nearly a counterpoise to its weight. The adjustment of the horizontal axis is denoted by a striding level, as in the portable transit already described.