other angle 85°, which is 0' 28", to the error of the glass corresponding 12"; and in this manner a table of errors may be made, not only for the cross observations, but alsc for observations to the right or to the left.*

It may be remarked that the errors are much less in the cross observations than m the observations to the right, which are those made with a quadrant or sextant; so that the circle has, in this respect, greatly the advantage of those instruments.

The angle between the plane of the horizon glass and axis of the telescope produced being nearly the same in all observations and adjustments of the circle, no sensible error can arise from the want of parallelisin in the surfaces of that glass.

Verification of the parallelism of the colored glasses.

Place one of the dark-colore glasses at C, and another at D; fix the central index at 0, direct the telescope to the sun, and move the horizon index till the limbs of the direct and reflected image coincide; then turn the dark glass placed at C, so that the surface which was farthest from the horizon glass may now be nearest to it, and if the contact of the same two limbs be complete, the surfaces of the glass placed at C are parallel; but if the limbs lap over or separate, the central index must be moved to bring them again in contact; then half the arc passed over by that index will be the error arising from the want of parallelism of the glass C. If great accuracy is required, the operation may be repeated by setting out from the point where the indices the are, and taking 4 or 6, &c., observations; then the are passed over by the central index, being divided by 4, 6, &c., will be the sought error. The other small glass may be verified in the same manner; and, by placing one of the larger glasses befc the central index at a, a, and one of the smaller ones at D, the former may be verif as above. The green glasses may be verified by observing the diameter of the t moon, or by some bright terrestrial object.

It may be remarked, as one of the greatest advantages of the circle, that, in measuring an angle by the cross observatious, no error can arise from the want of parallem in the surfaces of the smaller dark glasses; for if these glasses give too great an ale by an observation to the right, they will give too little by the same quantity } an observation to the left. It is not so with the large glasses placed at a, a, becau he incidence of the rays on these glasses is more oblique in one observation than in the other, so that the errors do not wholly balance each other; however, as these glasses are used only in measuring angles less than 35°, where the errors are nearly the ame as if the incidence of the rays were perpendicular, the errors of these glasses will also nearly compensate each other in the cross observations; and if such obserations only are used, it will be unnecessary to verify the dark glasses. Even when taking observations to the right, or observations to the left, the error of the dark glasses will be destroyed, if the glass is turned at each observation, and the number of observations is even; but there are some cases in which an angle can only be measured by one observation; then it will be necessary to allow for the error of the dark glass, if the distance is required to be found within a few seconds.

If the inclination of the plane of the horizon glass and the a tis of the telescope differ from 80°, you may find the tabular numbers by the method given in the explaration of Table XXXIV. affixed to the

tables

DESCRIPTION AND USE OF A PORTABLE

TRANSIT INSTRUMENT.

A TRANSIT INSTRUMENT is of no service on board of a vessel, but is much used ashore, in seaports, for regulating chronometers for sea voyages, and in making observations to determine the longitude. We have, therefore, thought it would be useful to give a brief description of it, with the methods of adjustment; particularly as it may be considered as a valuable accession to the apparatus of a good navigator, who, while remaining in port a few days, can, by means of it, adjust and fix the rate of going of nis chronometer with ease and accuracy, and also obtain the best data for determining the longitude of the place, by observing the times of the moon's transit or passage over the meridian.

The figure in Plate XI., figure 1, represents this instrument, according to the usual construction of Mr. Troughton, with a telescope of about twenty inches foca length. The telescope tube AA is in two parts, connected together by a sphere B which also receives the larger ends of the two axes C, C, placed at right angles to the direction of the telescope, and forming the horizontal axis. This axis terminates in two cylindrical pivots, which rest in Y's fixed at the upper end of the vertical standards D, D. One of the Y's possesses a small motion in azimuth, communicated by turning the azimuth screw a. In these Y's, the telescope turns upon its pivots; but, that it may move in a vertical circle, the pivots must be precisely on a level with each other; otherwise the telescope will revolve in a plane oblique to the horizon, instead of being perpendicular to it. The levelling of the axis, as it is called, is there. fore one of the most important adjustments of the instrument, and is effected by the aid of a spirit level E, which is made, for this purpose, to stride across the telescope, and rest on two pivots.

The standards DD are fixed by screws upon a brass circle F, which rests on three screws b, c, d, forming the feet of the instrument, by the motion of which the operation of levelling is performed. The two oblique braces GG are for the purpose of steadying the supports, it being essential for the telescope to have not only a free but a steady motion. On the extremity of one of the pivots, which extends beyond its Y, is fixed a circle H, which turns with the axis, while the double vernier, ee, remains stationary in a horizontal position, and shows the altitude to which the telescope is elevated. The verniers are set horizontal by means of a spirit level f, which is attached to them, and they are fixed in their position by an arm of brass g, clamped to the supports by a screw h; the whole of this apparatus is movable with the telescope, and, when the axis is reversed, can be attached, in the same manner, to the opposite standard.

Near the eye-end, and in the principal focus of the telescope, is placed the diaphragm, or wire-plate, which has five vertical and two horizontal wires. The centre vertical wire ought to be fixed in the optical axis of the telescope, and perpendicular to a line drawn through the pivots of the axis. It will be evident, upon consideration, that these wires are rendered visible, in the day-time, by the rays of light passing down the telescope to the eye; but at night, except when a very luminous object (as the moon) is observed, they cannot be seen. Their illumination is therefore effected by piercing one of the pivots, and admitting the light of a lamp fixed on the top of one of the standards, as shown at I. This light is directed to the wires by a reflector placed diagonally in the sphere B. The reflector, having a large hole in its centre, does not interfere with the rays passing down the telescope from the object, and thus the observer sees distinctly the wires and the object at the same time. When, however, the object is very faint (as a small star), the light from the lamp would overpower its feeble rays. To remedy this inconvenience, the lamp is so constructed that, by turning a screw at its back, or inclining the opening of the lantern, more or less light may be admitted to the telescope, to suit the circumstances of the case.

The telescope is furnished with a diagonal eye-piece, by which stars near the zenith may be observed without inconvenience.

Adjustments of a transit instrumen..

In fixing the instrument, it should be so placed that the telescope, when level, should point north and south as near as can possibly be ascertained. This can at first be done only in an approximate manner, as the correct determination of the meridian can only be obtained by observation, after the other adjustments are completed.

To adjust the line of collimation.

The first adjustment is that of the line of collimation, or line of sight. Direct the telescope to some distant, well-defined object (the more distant the better), and bisect it with the middle of the central wire; then lift the telescope very carefully out of its angular bearings or Y's, and replace it with the axis reversed; point the telescope again to the same object, and, if it be still bisected, the collimation adjustment is correct; if not, move the wires one half the error, by turning the small screws which hold the diaphragm near the eye-end of the telescope, and the adjustment will be accomplished; but as half the deviation may not be correctly estimated in moving the wires, it becomes necessary to verify the adjustment by moving the telescope the other half, which is done by turning the azimuth screw a; this gives the small azimuthal motion to the Y, before spoken of, and consequently to the pivot of the axis which it carries. Having thus again bisected the object, reverse the axis as before, and, if half the error was correctly estimated, the object will be bisected upon the telescope being directed to it; if not quite correct, the operation of reversing and correcting half the error, in the same manner, must be gone through again, until, by successive approximations, the object is found to be bisected in both positions of the axis; the adjustment will then be perfect.

To adjust the wires in the telescope.

It is desirable that the central or middle wire (as it is usually termed), should be truly vertical, as we shall then have the power of observing the transit of a star on any part of it, as well as the centre. We may ascertain whether it is so, by elevating and depressing the telescope; for when directed to a distant obje "'t is bisected by every part of the wire, the wire is vertical; if otherwise, it shou.a be adjusted by turning the inner tube carrying the wire-plate until the above test of its being vertical be obtained, or else care must be taken that observations are made near the centre only. The other vertical wires are placed, by the maker, equidistant from each other and parallel to the middle one; therefore, when the middle one is adjusted, the others are so too; he also places the two transverse wires at right angles to the vertical middle wire. These adjustments are always performed by the maker, and are but little liable to derangement. When, however, they happen to get out of order, and the observer wishes to correct them, it is done by loosening the screws which hold the eye-end of the telescope in its place, and turning the end round a small quantity, by the hand, until the error is removed. But this operation requires very delicate handling, as it is liable to remove the wires from the focus of the object-glass.

To fix the axes or arms, upon which the telescope revolves, in a hv izontal position The axes on which the telescope turns, must then be set horizontal. To do this, apply the level to the pivots; bring the air-bubble to the centre of the glass tube, by turning the foot-screw b, which raises or lowers that end of the axis, and consequently the level resting upon it; then reverse the level, by turning it end for end, and, if the airbubble still remain central, the axes will be horizontal; but if not, half the deviation must be corrected by the foot-screw b, and the other half by turning the small screw i, at one end of the level, which raises or lowers the glass tube (containing the airbubble) relative to its supports, which rest upon the pivots. This, like most of the adjustments, frequently requires several repetitions before it is accomplished, on account of the difficulty of estimating exactly half the error.

This adjustment may also be made by means of the polar star; first by observing directly its transit over any one of the vertical wires of the telescope, and immediately afterwards observing the reflected image of the same star from a basin of quicksilver. For if the star appear on the same wire, the axis is properly adjusted; if not, you must bring the wire half way towards it by the small screw i, and then, by the azimuth