perfect of the class of reflecting instruments, a short description of the method of using it, is here given.

Set the vernier, which moves on the circumference of the inner circle (as do also the horizon glass and telescope at the extremities of arms having one common centre), to zero (or 720°), on the graduated outer circle, and clamp it. Unclamp the vernier at the end of the arm carrying the index-glass, which, when the two glasses are parallel, should read zero. Take the required altitude or angular distance by moving the index forwards till a perfect contact is obtained, and clamp it to the outer circle, noting the time if required, but merely reading approximately the angle.

Unclamp the arm to which the telescope is attached, and, reversing the instrument, make the contact again on the other side, by moving forward this arm concentric with that carrying the horizon glass, (which can be done very rapidly by setting it nearly to the approximate angle already read, but on the other side of the zero of the inner circle, which is graduated each way to 180°,) and perfect the observation by the tangent screw. The angle now read on the outer circle is evidently double that observed for the mean of the times, freed from any index error by the reversal of the instrument. This process may be repeated over and over again all round the circle as aften as required, and the last angle shown by the vernier of the horizon glass is the only one which requires to be read, and divided by the number of observations, for the mean angular measurement answering to the mean of the times.

Instead of setting the vernier at first to 720°, it may be read off at any angle, as with the theodolite; but the method described above is preferable.

The terms answering to terrestrial longitude and latitude, when referred to the celestial sphere, are right ascension and declination;

being affected by the movement of those about it, to ensure which, a sort of detached platform upon posts will be found efficient. Solid rock is considered not so suited for the foundation of this sort of pedestal as sand, or other species of earth, on account of its more readily conveying tremulous vibrations to the instrument. Transits of from 20 to 30 inches focal length were thus used upon the survey (in 1845) of the North American Boundary, a tent made of fine canvas being contrived to protect the lights from the wind.

the former being measured on the equinoctial (or the plane of the equator produced to the heavens) commencing from the first point of Aries, which for many reasons has been taken as the conventional point of departure in the celestial sphere; and the latter on great circles perpendicular to the equinoctial and meeting at the poles, being reckoned north or south of this plane.

A confusion is caused, often puzzling to beginners, by the introduction of the terms longitude and latitude in the celestial nomenclature, having a different meaning from the same expressions as applied to the situation of places on the earth; they have reference to the ecliptic instead of the equinoctial; celestial longitudes commence also from the intersection of these two planes, called the "first point of Aries." This point having a constant gradual retrograde motion on the ecliptic, from causes which will be found clearly explained in the third chapter of Woodhouse's " Astronomy," under the head of "Precession of the Equinoxes," and at p. 282 of the work of Sir J. Herschel, already alluded to, it is evident that the longitudes, as well as the right ascensions and declinations, even of the fixed stars, are constantly undergoing a slight change, though imperceptible to measurement in short intervals of time. The corrections for their places on this account, as well as on that of their annual variations, aberration, and nutation, are all allowed for in the "catalogue of the hundred principal stars," given in the Nautical Almanac for every tenth day.

Great circles perpendicular to the horizon, and meeting in the zenith and nadir, are called vertical circles; on these the altitudes of objects above the horizon are measured; the complements to these altitudes are termed zenith distances; and the arc of the horizon contained between a vertical circle, passing through any object, and the plane of the meridian, is termed the azimuth of that object. The altitude and azimuth of any object being known, its place in the visible heavens at that moment is determined; whereas the latitude and longitude, or the right ascension and declination, fix its place in the celestial sphere.

The right ascension and declination of any celestial object can evidently be determined from its latitude and longitude, and vice versâ; the obliquity of the ecliptic, or the angle it forms with the equinoctial, being known.

The sensible horizon is an imaginary plane tangential to the earth, at the place of the observer; whereas the rational horizon (to which all altitudes must be reduced by the correction for parallax) is a plane parallel to the former, passing through the centre of the globe an altitude requires also another correction for the effects of refraction *, which it has been already explained, in page 71, causes the apparent place of any object to be always elevated above its real place; the correction is therefore subtractive.

The first correction alluded to,-that for parallax +,-is always additive. This term, as applied in its limited sense to altitudes of celestial objects, is meant to express the angle subtended by the semi-diameter of the earth at the distance of the object observed. Altitudes of the moon, from her proximity to the earth, are most effected by parallax: it is also always to be taken into account in observing altitudes of the sun, or any of the planets; but the fixed stars have no appreciable parallax, owing to their immeasurable distance from our globe.

In the figure below, HO is the sensible, and R L the rational horizon; S the real place of the object, and S' its apparent place, elevated by refraction; S'OH is the angle observed; SOH the

altitude corrected for refraction, and SLR the same altitude corrected both for refraction and parallax, being equal to the angle SOH + OSL, the parallax.

* See the tenth chapter of Woodhouse's "Astronomy" for the explanation of the method of obtaining the constant of refraction, and the different values of this quantity, generally estimated at 57".

For a further explanation of Parallax in a more general sense, see Sir J. F. Herschel's Astronomy," p. 47.

At least 5000 million times the diameter of the globe.

It is evident that the equatorial parallax of any object (which is that given in the Nautical Almanac), being subtended by the semi-diameter of the earth at the equator, is always the greatest, and that at the poles the least. The diminution, according to the latitude of the place of observation, can be obtained from tables constructed for the purpose. The parallax in any latitude is also greatest at the horizon, and diminishes as the object approaches the zenith, where it vanishes.

Another correction that must be applied to the observed altitudes of the sun or moon is that for their semi-diameters, plus or minus, according as the upper or lower limb has been taken *: this quantity is found for each day of the month in the Nautical Almanac.

When observations are made at sea, an allowance must be made for the height of the eye above the horizon: this correction, termed the dip, is evidently always subtractive; and in observing with a sextant, it is always necessary to ascertain and apply its index error, which term is meant to express the deviation of the reading of the instrument from zero, when the direct and reflected images of an object are made exactly to coincide, in which case the horizon and index glasses are parallel.

The usual method of ascertaining the amount of this error of the instrument in astronomical observations, is by measuring the diameter of the sun on different sides of the true zero, and is done as follows:-Set the vernier at about half a degree from zero on the graduated limb, and perfect the contact of the two limbs with the tangent screw†, noting the reading: unclamp the index, and set the vernier again to about the same distance on the other side of zero, termed the arc of excess (which is divided for a few degrees for this purpose), observing also this reading, when the contact has been again perfected; half the difference will evidently be the index error, + when the reading of the arc of excess is the greatest, and - when that of the limb: thus, .

* When several observations are taken, the necessity for this correction can be obviated by observing alternately the upper and lower limb.

+ In using the tangent screw, a perceptible difference is found between a progressive and a retrograde motion—the latter had better always be avoided. A difference is also found in different parts of the length of the screw.

These definitions are rendered more evident by reference to the figure below, taken from Sir J. Herschel's Treatise on Astronomy, published in the Cabinet Cyclopædia.

"Let C be the centre of the earth, NCS its axis; then are N and S its poles; EQ its equator; A B the parallel of latitude of the station A on its surface; A P, parallel to S Cn, the direction in which an observer at A will see the elevated pole of the heavens; and A Z, the prolongation of the terrestrial radius C A, that of his zenith; NAES will be his meridian; NGS that of some fixed station, as Greenwich; and G E, or the spherical angle G N E, his longitude, and EA his latitude. Moreover, if ns be a plane

touching the surface in A, this will be his sensible horizon; nAs, marked on that plane by its intersection with his meridian, will be his meridian line, and n and s the north and south points of his horizon."

"Again, neglecting the size of the earth, or conceiving him stationed at its centre, and referring everything to his rational horizon, let the next figure represent the sphere of the hea