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struments. A dark glass is also supplied to fit on to the eyeend of the telescope, and a key for turning the adjusting

screws.

To examine the Error arising from the Imperfection of the Dark Glasses.-Fit the dark glass to the eye-end of the telescope, and, all the shades being removed, bring the reflected image of the sun into contact with his image seen directly through the unsilvered part of the horizon glass. Then remove the dark glass from the eye-end of the telescope, and, setting up first each shade separately, and then their various combinations, if the two images do not in any case remain in contact, the angle through which the index must be moved to restore the contact, is the error of the dark glass, or combination of dark glasses, used in the observation, and which error should be recorded for each glass and each combination of the glasses.

The adjustments of the instrument consist in setting the horizon glass perpendicular to the plane of the instrument, and in setting the line of collimation of the telescope parallel to the plane of the instrument.

To adjust the Horizon Glass.-While looking steadily at any convenient object, sweep the index slowly along the limb, and, if the reflected image do not pass exactly over the direct image, but one projects laterally beyond the other, then the reflectors are not both perpendicular to the face of the limb Now the index glass is fixed in its place by the maker, and generally remains perpendicular to the plane of the instru ment, and, if it be correctly so, the horizon glass is adjusted by turning a small screw at the bottom of the frame in which it is set, till the reflected image passes exactly over the direct image

To examine if the Index Glass be perpendicular to the Plane of the Instrument.-Bring the vernier to indicate about 45°, and look obliquely into this mirror, so as to view the sharp edge of the limb of the instrument by direct vision to the right hand, and by reflection to the left. If, then, the edge and its image appear as one continued arc of a circle, the index glass is correctly perpendicular to the plane of the instrument; but if the arc appears broken, the instrument must be sent to the maker to have the index glass adjusted.

To adjust the Line of Collimation.-1. Fix the telescope in its place and turn the eye-tube round, that the wires in the focus of the eye-glass may be parallel to the plane of the instrument. 2. Move the index till two objects, as the sun and moon, or the moon and a star, more than 90° distant from each other, are brought into contact at the wire of the dia

phragm, which is nearest the plane of the instrument. 3. Now fix the index, and altering slightly the position of the instrument, bring the objects to appear on the other wire; and, if the contact still remain perfect, the line of collimation is in correct adjustment. If, however, the two objects appear to separate at the wire that is further from the plane of the instrument, the object-end of the telescope inclines towards the plane of the instrument; but, if they overlap, then the objectend of the telescope declines from the plane of the instrument. In either case the correct adjustment is to be obtained by means of the two screws, which fasten to the up and down piece the collar holding the telescope, tightening one screw and turning back the other, till, after a few trials, the contact remains perfect at both wires.

The instrument having been found by the preceding methods to be in perfect adjustment, set the index to zero, and if the direct and reflected images of any object do not perfectly coincide, the arc, through which the index has to be moved to bring them into perfect coincidence, constitutes what is called the index error, which must be applied to all observed angles as a constant correction.

To determine the Index Error.-The most approved method is to measure the sun's diameter, both on the arc of the instrument, properly so called, to the left of the zero of the limb, and on the arc of excess to the right of the zero of the limb. For this purpose, firstly, clamp the index at about 30' to the left of zero, and, looking at the sun, bring the reflected image of his upper limb into contact with the direct image of his lower limb, by turning the tangent screw, and set down the minutes and seconds denoted by the vernier; secondly, clamp the index at about 30' to the right of zero, on the arc of excess, and, looking at the sun, bring the reflected image of his lower limb into contact with the direct image of his upper limb, by turning the tangent screw, and set down the minutes and seconds denoted by the vernier underneath the reading before set down. Then half the sum of these two readings will be the correct diameter of the sun, and half their difference will be the index error. When the reading on the arc of excess is the greater of the two, the index error, thus found, must be added to all the readings of the instrument; and when the reading on the arc of excess is the less, the index error must be subtracted in all cases. To obtain the index error with the greatest accuracy, it is best to repeat the above operation several times, obtaining several readings on the arc of the instrument, and the same number on the arc of excess; and

the difference of the sums of the readings in the two cases, divided by the whole number of readings, will be the index error; while the sum of all the readings, divided by their number, will be the sun's diameter.

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The readings on the arc of excess being less than those on the arc of the instrument, the index error, 2′ 49′′, is to be subtracted from all the readings of the instrument.

NOTE. In taking off the readings on the arc of excess, the vernier must be read backwards; that is, the division read off on the limb, being the division next to the left of the zero of the vernier, the divisions of the vernier to be added must be reckoned from the other end of the vernier to the division coinciding with a division upon the limb; or the reading of the vernier forwards, according to the usual method, may be subtracted from 10', the limb being divided to 10', and the remainder added to the reading of the division upon the limb next to the left of the zero of the vernier, as before.

The manner of observing with the sextant has been already explained, when treating of the pocket sextant (p. 120).

TROUGHTON'S REFLECTING CIRCLE.

In this instrument, which is the same in principle as the sextant, the limb is a complete circle, L L L. It has three verniers, ▼ ▼ ▼, one of which is furnished with the clamp and tangent screw, s s, for regulating the contacts; and the verniers are read by a magnifier, м, which may be applied successively to all the verniers. In the middle of the frame, and attached to it by a broad base or flanch, is a hollow center, upwards of two inches long, in which an axis revolves. The triple vernier bar, I II, is attached at one end of the axis, and the index glass at the other, so that both turn together, but on opposite sides of the instrument. A secondary frame, B B, carries the telescope, T, the horizon glass, and the dark glasses. H H are two handles, one of them bent, and passing round to the center of the instrument on the other side; and there is a third handle,

which can be screwed on perpendicular to the plane of the in strument, either into the handle at c, or upon the other side of the instrument, at its center. The adjustments and manner of observing with the instrument are explained by the inventor, Mr. Troughton, as follows:

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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 byt he 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 causes, 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

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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 those taken backwards and those taken forwards, will be the truc angle.

"It need hardly be mentioned, that the shades, or dark glasses, apply like those of a sextant, for making the object 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 darkened, as is the case when the sun's diameter is measured, and when his altitude is taken with an artificial horizon, the attached dark glasses ought not to be used: instead of them, those which apply to the eye-end of the telescope will answer much better; the former having their errors magnified by the power of the telescope, will, in proportion to this power, and those errors, be less distinct than the latter.

"In taking distances, when the position does not vary from the vertical above thirty or forty degrees, the handles which are attached to the circle are generally most conveniently used; but in those which incline more to the horizontal, that handle which screws into a cock on one side, and into the crooked handle on the other, will be found more applicable.

"When the crooked handle happens to be in the way of reading one of the branches of the index, it must be removed, for the time, by taking out the finger screw, which fastens it to the body of the circle.

"If it should happen that two of the readings agree with each other very well, and the third differs from them, the discordant one must not on any account be omitted, but a fair mean must always be taken.

"It should be stated, that when the angle is about thirty degrees, neither the distance of the sun and moon, nor an altitude of the sun, with the sea horizon, can be taken backwards; because the dark glasses at that angle prevent the reflected rays of light from falling on the index glass; whence it becomes necessary, when the angle to be taken is quite unknown, to observe forwards first, where the whole range is without interruption; whereas in that backwards you will lose sight of the reflected image about that angle. But in such distances, where the sun is out of the question, and when his

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