usual to take several measures each way; "and half the difference of their means will give a result more to be depended on than one deduced from a single observation only on each side of zero.” A proof of the correctness of observations for index error is obtained by adding the above numbers together, and taking one-fourth of their sum, which should be equal to the sun's semidiameter, as given in the Nautical Almanac. When the sun's altitude is low, not exceeding 20° or 30°, his horizontal instead of his perpendicular diameter should be measured, (if the observer intends to compare with the Nautical Almanac, otherwise there is no necessity); because the refraction at such an altitude affects the lower border (or limb) more than the upper, so as to make his perpendicular diameter appear less than his horizontal one, which is that given in the Nautical Almanac: in this case the sextant must be held horizontally.

To make the Line of Collimation of the Telescope parallel to the Plane of the Sextant.

This is known to be correct, when the Sun and Moon, having a distance of 90° or more, are brought into contact just at the wire of the telescope which is nearest the plane of the sextant, fixing the index, and altering the position of the instrument to make the objects appear on the other wire; if the contact still remains perfect, the axis of the telescope is in proper adjustment; if not, it must be altered by moving the two screws which fasten, to the up-and-down piece, the collar into which the telescope screws. This adjustment is not very liable to be deranged.

Having now gone through the principle and construction of the sextant, it remains to give some instructions as to the manner of using it.

It is evident that the plane of the instrument must be held in the plane of the two objects, the angular distance of which is required: in a vertical plane, therefore, when altitudes are measured; in a horizontal or oblique plane, when horizontal or oblique angles are to be taken. As this adjustment of the plane of the instrument is rather difficult and troublesome to the beginner, he need not be surprised nor discouraged, although his first attempts may not answer his expectations. The sextant must be held in the right hand, and as slack as is consistent with its safety, for in grasping it too hard the hand is apt to be rendered unsteady.

When the altitude of an object, the sun for instance, is to be observed, the observer, having the sea horizon before him, must turn down one or more of the dark glasses, or shades, according to the brilliancy of the object; and directing his sight to that part of the horizon immediately beneath the sun, and holding the instrument vertically, he must with the left hand lightly slide the index forward, until the image of the sun, reflected from the index-glass, appears in contact with the horizon, seen through the unsilvered part of the horizon-glass. Then clamp it firm, and

gently turn the tangent-screw, to make the contact of the upper or lower limb of the sun and the horizon perfect, when it will appear a tangent to his circular disc.* If an artificial horizon is employed, the two images of the sun must be brought into contact with each other; but this will be explained when speaking of that instrument. To the angle read off apply the index error, and then add or subtract the sun's semidiameter, as given in the Nautical Almanac, according as the lower or upper limb is observed, to obtain the apparent altitude of the sun's centre. Before we can use this observation for determining the time, the latitude, &c., it must be further corrected for refraction and parallax, to obtain the true altitude, subtracting the former and adding the latter; and when the sea horizon is employed, a quantity must also be subtracted for the dip, which is unnecessary when the altitude is taken by means of an artificial horizon.

Tables for obtaining the above corrections may be found in Mr. BAILY'S Astronomical Tables, &c. in the Requisite Tables, or in any modern work on navigation.

Dip of the horizon, for an elevation of 18 feet,

True altitude of the sun's centre

60 52 18,7

If the observer is ignorant of the precise moment of the object's being on the meridian, he should, by a slow and gradual motion of the tangent-screw, keep the observed limb in contact with the horizon as long as it continues to rise; and immediately on the altitude's appearing to diminish, cease from observing, and the angle then read on the instrument will be the meridian altitude.

After what has been advanced, little need be said about observing lunar distances, whether of the moon and the sun, or the moon and a fixed star or planet, except that the instrument must be held in

*If the observer knows his latitude approximately, he may find the meridional altitude nearly, to which he may previously set his instrument; when he will not only find his object more easily, but have only a small quantity to move the index to perfect the observation.

Take from the Nautical Almanac the declination of the object, and if it be of the same name with the latitude, add it to the co-latitude; if of a different name, subtract it the sum or difference will be the meridian altitude.

† An observation of a star requires no correction for either parallax or semidiameter.

the plane of the two objects; and it is generally preferable to direct the telescope to the fainter object, particularly if a star, as it can be more easily kept in view when seen directly than it can when seen by reflection. If the brighter object is to the left, the sextant must be held with the face downwards.

The enlightened limb of the moon is always to be brought into contact with the sun or star, even though the moon's image is made to pass beyond the sun or star before the desired contact can be obtained.

Perhaps the best method of taking a lunar distance is, not to attempt to make the contact perfect by the tangent-screw, but when the nearest limbs are observed, make the objects overlap each other a little when they are receding, or leave a small space between them when they are approaching, and wait till the contact is perfect, and the reverse when the furthest limbs are observed.

The altitudes of the two objects should be observed at the same instant as the distance, and the time noted by a chronometer, or watch: this would require several observers; but one person may take them all, by having recourse to the following method: "First, observe the altitude of the sun or star; secondly, the altitude of the moon; then any number of distances; next the altitude of the moon; and lastly, the altitude of the sun or star, noting the times of each by a watch. Now add together the distances and times when they were observed, and take the mean of each; and in order to reduce the altitudes to the mean time, make the following proportion: As the difference of times between the observations is to the difference of their altitudes, so is the difference between the time that the first altitude was taken and the mean of the times at which the distances were observed, to a fourth number; which, added to or subtracted from the first altitude, according as it is increasing or decreasing, will give the altitude reduced to the mean time."

The angular distances of terrestrial objects are measured by the sextant in the same manner as those of celestial ones; but if the obects are not in the same horizontal plane, a reflecting instrument will not give their horizontal angular distance. But this may be obtained nearly by measuring their angular distances from an object in or near the horizon, which subtends a great angle with both, and the sum, or the difference of the angles so measured, will be nearly the required horizontal angle.

Of the sextant, it has been said, that it is in itself a portable observatory; and it is doubtless one of the most generally useful instruments that has ever been contrived, being capable of furnishing data to a considerable degree of accuracy for the solution of a numerous class of the most useful astronomical problems; affording the means of determining the time, the latitude and longitude of a place, &c., for which and many other purposes it is invaluable to the land-surveyor as well as the navigator.

The above figure represents this instrument, which in principle and use is the same as the sextant. It has three vernier readings, A B C, moving round the same centre as the index-glass, E, which is upon the opposite face of the instrument. One of the verniers, B, carries the clamp and tangent-screw. D, represents the microscope for reading the verniers; it is similar to the one used in reading the sextant, and is adapted to each index-bar, by slipping it on a pin placed for that purpose, as shown in the figure. The horizon-glass is shown at F. The barrel, G, contains the screws for giving the upand-down motion to the telescope; it is put in action by turning the milled head under the barrel. H is the telescope, adapted to the instrument in a manner similar to that of the sextant. I and J are

two handles fixed parallel to the plane of the circle, and a third handle, K, is screwed on at right angles to that plane, and can be transferred to the opposite face of the instrument by screwing it into the handle, I; the use of this extra handle is for convenience in reading and in holding the instrument, when observing angles that are nearly horizontal; it can be shifted, according as the face of the instrument is held upwards or downwards. The requisite dark glasses are attached to the frame-work of the circle, to be used in the same manner and for the same purposes as those of the sextant. With respect to the adjustments and application of this instrument, we cannot do better than use the words of the inventor, Mr. TROUGHTON, Contained in a paper which he calls

"Directions for observing with Troughton's Reflecting Circle.

Prepare the instrument for observation by screwing the telescope into its place, adjusting the drawer to focus, and the wires

parallel to the plane, exactly as you do with a sextant: also set the index forwards to the rough distance of the sun and moon, or moon and star; and holding the circle by the short handle, direct the telescope to the fainter object, and make the contact in the usual way. Now read off the degree, minute, and second, by that branch of the index to which the tangent-screw is attached; also, the minute and second shown by the other two branches; these give the distance taken on three different sextants; but as yet, it is only to be considered as half an observation: what remains to be done, is to complete the whole circle, by measuring that angle on the other three sextants. Therefore set the index backwards nearly to the same distance, and reverse the plane of the instrument, by holding it by the opposite handle, and make the contact as above, and read off as before what is shown on the three several branches of the index. The mean of all six, is the true apparent distance, corresponding to the mean of the two times at which the observations were made.

"When the objects are seen very distinctly, so that no doubt whatever remains about the contact in both sights being perfect, the above may safely be relied on as a complete set; but if, from the haziness of the air, too much motion, or any other cause, the observations have been rendered doubtful, it will be advisable to make more and if, at such times, so many readings should be deemed troublesome, six observations, and six readings may be conducted in the manner following: Take three successive sights forwards, exactly as is done with a sextant; only take care to read them off on different branches of the index: also make three observations backwards, using the same caution; a mean of these will be the distance required. When the number of sights taken forwards and backwards are unequal, a mean between the means of these taken backwards, and those taken forwards will be the true angle.

"It need hardly be mentioned, that the shades, or dark-glasses, apply like those of a sextant, for making the objects nearly, of the same brightness; but it must be insisted on, that the telescope should, on every occasion, be raised or lowered, by its proper screw, for making them perfectly so.

"The foregoing instructions for taking distances, apply equally for taking altitudes by the sea or artificial horizon, they being no more than distances taken in a vertical plane. Meridian altitudes cannot, however, be taken both backwards and forwards the same day, because there is not time: all therefore that can be done, is, to observe the altitude one way, and use the index-error; but even here, you have a mean of that altitude, and this error, taken on three different sextants. Both at sea and land, where the observer is stationary, the meridian altitude should be observed forwards one day, and backwards the next, and so on alternately from day to day; the mean of latitudes, deduced severally from such observations, will be the true latitude; but in these there should be no application of index-error, for that being constant, the result would in some measure be vitiated thereby.

"When both the reflected and direct images require to be dark