On the other hand the vertical component may be deduced from the inclination and the horizontal component.

For further information on this subject see Lee's Tables and Formulæ, and Riddell's Magnetical Instructions. For the theory of magnetism as applicable, see the papers of Gauss, and a late elementary work of Prof. Lamonte, of Munich. Translations of some of the papers of Gauss, Lamonte, and Weber have been published in Taylor's Scientific Memoirs, Parts 5, 6, 11, and 12.

APPENDIX TO PART VI.

INSTRUMENTS FOR EXTRA MERIDIAN OBSERVATIONS.

THE principal of these are the equatorial, and the altitude and azimuth instrument.

THE EQUATORIAL

is a telescope usually of large size, upon an equatorial mounting. The latter consists, 1, of a strong metallic axis, placed in a position parallel to the axis of the earth, so as to point to the pole of the heavens, the lower end of this axis, which is called the polar axis, being enlarged into a circle called the hour circle, the plane of which is parallel to the equator, and the circumference of which is divided into hours and fractions of an hour. 2. Of another axis crossing the upper end of the former at right angles, called the equatorial axis, one end of which is enlarged into a circle called the declination circle, divided into degrees and fractions of a degree, and firmly fastened to the other end of which, at right angles, near the middle of its tube, is the telescope. The instrument must be so adjusted that when the optical axis of the telescope describes the meridian as the instrument moves upon the equatorial axis alone, the index of the hour circle is at the zero, and when the optical axis points to a star in the equator, the index of the declination circle is at zero. Then if the instrument be turned on its equatorial axis till the index or vernier of the declination circle points to the declination of any celestial object as given by the Nautical Almanac or by catalogue, and on its polar axis till the index of the hour circle points to the hour angle, which is the difference between the right ascension and the time by the siderial clock, the object will be seen in the centre of the field of view of the telescope. As it passes out of the field of view by the rotation of the earth on which the instrument stands, the telescope is made to follow it by a rotation of the instrument on its polar axis alone. Attached to this axis is a clamp and screw of slow motion for the purpose. Sometimes the polar axis is made to move by clockwork, the velocity being regulated by friction, and the motion becoming uniform when the friction is equal to the accelerating force of the clock-weights. In the Fraunhofer* mounting, a hollow inverted frustum of a cone contains balls, supported at the ends of a flexible bar at right angles to the axis of the frustum, about which it revolves, carrying the balls which rub against the sides of the frustum. The velocity should be different for the sun, moon, each of the planets, and

So called, from the inventor and first manufacturer, Fraunhofer, of Munich.

for the fixed stars. If the bar be lowered in the frustum, less velocity will make the friction equal to the accelerating force. If raised, more velocity will be required. For each kind of heavenly body the requisite velocity is determined by experiment, and a permanent mark made where an attached index stands.

Approximate adjustment is sufficient for this instrument,'which is ordinarily used as a differential instrument, by means of an appendage which we proceed to describe, called

THE POSITION MICROMETER.

This is an eye-piece which screws on in place of the ordinary eye-piece of the ' telescope, and consists of a circle of brass about four inches in diameter, the plane of which is perpendicular to the optical axis, which passes through its centre. It is graduated on the outer rim, the graduation being numbered to 360°. A rectangular box, about one inch by four, and the eighth of an inch in thickness, is fitted to the circle in the position of a diameter, at the ends of which are micrometer screws, which move each one of two parallel wires along a notched scale, the wires and scale being seen (when the eye is applied to the telescope) at the focus of the object glass, where also the image of the heavenly body is formed. The circle carrying the box has also a motion round the optical axis, by means of a screw projecting perpendicularly to the plane of the circle, which acts as a pinion by cogs, in a cogwheel of less diameter than the circle, attached to the piece which screws into the telescope to which two verniers, 90° apart, marked A and B, are firmly fixed.

To determine the right ascension and declination of a new heavenly body, as a comet, for instance, with this instrument in any part of the visible heavens, let the object be brought into the field of view at the same time with some fixed star, one whose place is given by catalogue, if possible. Bring the star to one of the movable micrometer wires, and turn the micrometer in position, i. e. round the optical axis till the wire threads the star in its motion along its diurnal path. The wire is then parallel to the equator. Let the two wires now be separated by turning the micrometer screws till one of them passes through or bisects the star, and the other bisects the comet; the number of turns of the screw shown by the notched scale, and the fractions of a turn by the screw-head, will indicate the difference in declination between the comet and the star.* Let the micrometer now be turned in position 90°, and the transits of the comet and star across the two wires be observed by the siderial clock. The difference in the times of transit will be the difference of right ascension of the comet and star. The absolute right ascension and declination of the comet thus becomes known, if that of the star of comparison be known from catalogue. If this be not the case, the star must be brought to the centre of the field of view indicated by the point at which a third wire at right angles to the other two crosses them when they are made to coincide at the zero of the notched scale, and the approximate right ascension and declination of the star must be noted by the declination and hour circles and clock, with sufficient accuracy to identify it, in

* It will be found convenient to make the wires coincide before commencing the operation with the screwhead of one of them at the zero, and let this be the only one moved, if possible, and read by its screw.

1 For methods of exact adjustment, see Lond. Ast. Soc. Memoirs, vol. IV. p. 495.

order that its place may be more exactly determined by observation with the meridian instruments, the transit and mural, at some subsequent time.

The micrometer screw head is divided into 100 parts. The value of a single turn of the screw in arc is determined by measuring the diameter of a planet, given by the Nautical Almanac or the known distance apart of a pair of stars, and then by the proportion, as the number of turns and hundredths of a turn of the micrometer screw is to the known distance measured, so is 1 to the value of one turn.

MEASUREMENT OF ANGLES OF POSITION AND DISTANCE OF DOUBLE STARS.

The angle of position of a pair of stars is the angle which the visual plane passing through both the stars makes with the plane of the declination circle passing through the larger star. It is estimated from the s. round by the w. to 360°. The following is Capt. Smythe's method of observing position and distance.

Bring the wires coinciding at the zero of the scale, with the index of one screwhead at the zero, upon the line of the two stars, so as to bisect both, and read one of the verniers; next turn the instrument 90° in position, and measure the distance of the stars apart; finally turn in position till one of the stars runs along either of the wires, and read one of the verniers again, the difference between the first and last vernier reading, will give the angle which the visual plane of the two stars makes with the equator, from which the angle of position may be obtained in an obvious In the transit instrument and instruments of that class the wires are made visible at night by a lamp placed at one end of the supporting axis, which is left open for the purpose, with a piece of glass over it; the light is received by a small plane mirror in the axis of the telescope, and reflected down the tube to the wires. In the equatorial instrument the horizontal tube bearing the lens (colored red) of a small lamp is inserted in the tube of the telescope, near the wires of the micrometer, and a reflector so arranged as to throw the light on the wires.

manner.

When the object to be observed is so faint as not to bear illumination, a ring micrometer is used. This is a black circle on a piece of plane glass in the focus of the object glass, with which differences of right ascension and declination are obtained by noting the times occupied by the two objects to be compared in crossing the circle. Half the sum of the times of either object's making the transit of the circumference on opposite sides will be the time of its passing the middle diameter, and the difference of the time of passing the middle diameter by the two objects will be their difference of right ascension.

For declination it is necessary to ascertain, by experiment, the time of an equatorial star's passing over a diameter of the ring, by observing the time of any other star, and multiplying by the cosine of the declination. Then the ratio of the time occupied by a star in passing over a chord of the ring to the time which it would occupy in passing over the diameter is the cosine of an angle, the sine of which to the radius of the ring is the difference of declination between the centre of the ring and the star. (For the whole theory see Ast. Nach., Vol. 8.).

THE ALTITUDE AND AZIMUTH INSTRUMENT.

This is in effect a large theodolite, with two micrometer microscopes, 1800 apart, on both the horizontal and vertical limb. It may be used as a theodolite, also as a