in one, and the glafs will be adjufted; then faften the milled fcrew. This adjustment, as well as that of the fore horizon glass, is fubject to a small error, which is chiefly produced in fastening the milled fcrew, in the middle of the lever; it therefore becomes neceffary to find the error of adjustment, which may be done by again examining the coincidence of the objects as before, after the milled fcrew is faftened, and making it perfect by moving the index, and the interval between the beginning of the index fcale, and Zero on the limb, will be the error of adjustment, or the index error for the back obfervation, to be applied as formerly. In the above determination, we have fuppofed the rods to be in the fame ftraight line, which can be very easily effected; however, if thefe rods are not exactly in a right line, the error of adjuftment may be thus found.

Let one of the extreme rods be called the first, and the other the fecond rod; now the obferver being placed at the middle rod as before, let the fight be directed to the first rod, make the reflected image of the fecond rod coincide with it, by moving the index, and mark the divifion pointed out by the scale. Then let the obferver turn half round, direct the fight to the fecond rod, and move the index till the first feen by reflection coincides with it, and again mark the angle shown by the index fcale.* Now if one of these angles be measured on the limb, and the other on the arch of excefs, half their difference will be the error of adjustment, or index error; but if both angles be measured either on the limb, or on the arch of excefs, half their fum is the index error; fubtractive from altitudes given by the quadrant, when the angle, shown on the limb, exceeds that on the arch of excess, or if both angles be measured on the limb: in other cafes, this error is to be added. If the observation is that of the angular distance between any two objects, then the fupplement of that given by the quadrant corrected as above will be the angle required.

Various other methods have been propofed, for effecting the adjustment of the back horizon glass, fome of which we shall briefly mention. ft, In Mr Dollond's method, an index is applied to the back horizon glass, by which it may be moved, so as to be parallel to the index glafs, when O on the index fcale coincides with O on the limb. When this is effected, the index of the back horizon glass is to be moved exactly 90° from its former pofition, which is known by means of a divided arc for that purpose, and then the plane of the back horizon glass will be perpendicular to the plane of the index glafs produced. 2d, In Mr Blair's method, the under edge of the index glass is ground and polished, so as to be at right angles

*Or invert the pofition of the quadrant, by turning its face downwards; hold its plane level as before, and direct the fight again to the first rod; move the index till the fecond feen by reflection coincides with it, and read off the angle flown by the divid ing fcale.

angles to the plane of the glafs, and hence the back horizon glafs ist adjusted, by making the direct and reflected horizons agree, the index being at O, exactly in the fame manner as the fore horizon glafs is rendered parallel to the fpeculum.

Ufe of Hadley's Quadrant in obferving Altitudes at Sea.

The altitude of any object is determined by the pofition of the index on the limb, when by reflection that object appears to be in the horizon. In obferving altitudes, it will be found moft convenient tohold the quadrant with the left hand, and move the index with the right. Hence the left hand is to be applied to the further radius, towards the end of the curved brace, and the right hand to the lower part of the index.

If the object whofe altitude is to be obferved be the Sun, and if fo bright that its image may be feen in the tranfparent part of the fore horizon glafs, the eye is then to be applied to the upper hole in the fore fight vane, otherwife to the lower hole; and in this cafe, the quadrant is to be fo held, that the Sun may be bifected by the line joining the filvered and transparent parts of the glass. Hence one half of the Sun will be reflected from the filvered part of the glafs. The Moon is to be kept as nearly as poffible in the fame pofition, and the image of a star is to be reflected from that part of the filvered part of the glass, which is adjacent to the line of feparation of the two parts.

In obferving the altitude of any object, the quadrant must be held perpendicular to the horizon, and fo, that its plane produced would pafs through that object. In obfervations of the Sun, this latter pofition is easily obtained, by holding the quadrant fo, that the fhadow of the further radius may fall on that next the obferver; in this cafe, the fight is to be directed to the horizon. If the obferved object is not the Sun, it will be proper to direct the fight to the object; the quadrant being held fo, that the image of the object may appear in the filvered part of the glass, as before mentioned, the index is to be moved till either limb of the object appears in contact with the horizon; but becaufe that part of the horizon, which is immediately under the object, is not exactly known, it therefore becomes neceffary to give the quadrant a flow vibrátory motion, the axis of which being that of fight, the observer at the fame time turning himself about upon his heel,* fo as to keep the object always in that part of the horizon glafs, which is at the fame diftance as the eye from the plane of the quadrant. By this means the reflected object will defcribe an arc of a parallel circle round the true Sun, whofe convex fide will be downwards in the fore obfervation, and upwards in the back; and therefore when, by moving the index, the lowest poin

F

* Dr Maskelyne's remarks on Hadley's quadrant, Nautical Almanac, 1774

point of the arc in the fore obfervation, or highest in the back, is made to touch the horizon, the quadrant will stand in a vertical plane, and the altitude above the vifible horizon will be properly obferved.

It is often found, in meafuring the altitude of any object, or the distance between two fixed objects, that a different angle* will be obtained, by finishing the obfervation with a motion of the index in contrary directions. Thus the angle, obtained by moving the index according to the order of the divifions on the limb, is always found greater, than when the index is moved in a retrograde direction, or contrary to the order of the divifions. As this error arifes from the bending of the index, it may be obviated by taking care to move the index the fame way, both in the adjusting and in taking the obfervations. It frequently happens, that, when the object is nearly in contact with the horizon, the obferver, by endeavouring to make this contact better, often pushes the index too far, and thereby renders the contact worse than before. In order to remove this inconvenience, the beft quadrants are provided with a fcrew at the lower end of the index, called an adjusting or tangent fcrew, by which a slow motion may be given to the index. Hence thofe fudden ftarts, to which it is liable when moved by hand, are prevented.

A fmall magnifying glass will be found of great fervice, in reading off the obferved angle; in doing which, the limb may be held towards the obferver, and the eye fhould be in a plane perpendicular to the quadrant, paffing thro' the coinciding divifions.

To take Altitudes by the Fore Obfervation.

I. Of the Sun.

Turn down either of the coloured glasses before the horizon glass, according to the brightnefs of the Sun; and if the Sun is bright enough to be feen in the transparent part of the glass, let the eye be placed at the upper hole in the fight vane, otherwife at the hole next the plane of the quadrant; direct the fight to that part of the horizon which is under the Sun, and move the index till the coloured image of the Sun appears in the horizon glass; then give the quadrant a flow vibratory motion, about the axis of vifion, move the index till the Sun's lower or upper limb, at the lowest part of the arch defcribed by this motion, is in contact with the horizon, and the degrees and minutes, shown by the index on the limb, will be the obferved altitude of the Sun.

II. Of the Moon.

Put the index to O, turn down the green tinged glass, place the eye at the lower hole in the fight vane, and look at the Moon thro'

* An excellent account of this error is given in the Nautical Almanac for 1788.

the

the fight; which being found in the filvered part of the horizon glafs, move the index gradually, and follow the Moon's reflected image, till the enlightened limb is in contact with the horizon, at the lower part of the arch defcribed by the vibratory motion, as in the laft article; and the index will fhow the obferved altitude of that limb of the Moon, which was brought in contact with the horizon. If the obfervation is made in the day time, the coloured glafs is unneceffary.

III. Of a Star or Planet.

Put the index to O, direct the fight to the ftar, thro' the lower hole in the fight vane, and tranfparent part of the horizon glafs; move the plane of the quadrant a very little to the left, and the image of the star will be feen in the filvered part of the glafs; then move the index, and the image of the ftar will defcend; continue this motion of the index till the ftar is in contact with the horizon, at the lowest part of the arch defcribed; and the degrees and minutes shown by the index on the limb will be the obferved altitude of the ftar.

When the horizon, under the object whofe altitude is intended to be obferved, is obfcured or rendered imperfect, by fog or any other impediment, the back obfervation becomes neceffary; we would, however, advise the obferver, before he depends entirely on the altitude taken by the back obfervation, to accuftom himself to this mode of obferving, and to afcertain what accuracy he is capable of attaining, by comparing altitudes taken by this method with those of the fame object, taken at the fame time by the fore obfervation, allowance being previously made for the dip and index error.

To take Altitudes by the Back Obfervation.'

I. Of the Sun.

Put the stem of the coloured glaffes into the hole between the horizon glasses; turn down either, according to the brightness of the Sun, and hold the inftrument vertically; then direct the fight thro' the hole in the back fight vane, and tranfparent flit in the horizon glafs, to that part of the horizon which is oppofite to the Sun; move the index till the Sun is in the filvered part of the glafs, and by giving the quadrant a vibratory motion, whofe axis is that of vifion, the image of the Sun will defcribe an arch whofe convex fide is upwards; now bring the limb of the Sun, when in the upper part of the arch, in contact with the horizon; and the degrees and minutes fhown by the index on the limb will be the altitude of the other limb of the Sun.

II. Of the Moon.

The altitude of the Moon is obferved in the fame manner as that

of the Sun, with this difference only, that the ufe of the coloured glafs is unneceffary, unlefs the Moon is very bright, and that the enlightened limb, whether it be the upper or lower, is to be brought in contact with the horizon. In the day time, the Moon's altitude may be obferved, as directed in the next article.

III. Of a Star or Planet.

Look directly to the ftar, through the vane and tranfparent flit in the horizon glass, move the index till the oppofite horizon, with refpect to the ftar, is feen in the filvered part of the glafs, and make the contact perfect as formerly. If the altitude of the ftar is known nearly, the index may be fet to that altitude, the fight directed to the oppofite horizon, and the obfervation made as formerly.

Unless obfervations are made accurately, the conclufions to be made therefrom cannot be depended on; and fince a fingle altitude is not to be so much relied on, as the mean of feveral, taken at short intervals of time, therefore four or five altitudes fhould be taken at nearly equal intervals of time, and their fum, divided by their number, will be the mean altitude which the object would probably have had, at the mean interval, or the inftant arising from the divifion of the fum of the times of obfervation by their number. If the intervals between the fucceffive obfervations are fhort, and nearly equal, the correfponding differences of alt tude will alfo be either nearly equal, or gradually increafing or decreafing Hence an erroneous altitude may eafily be difcovered; thus, if the altitudes of an object were 19° 58′, 20° 4′, 20° 11', and 20° 15', and the correfponding times of obfervation, 9h. 15' 1", 9h. 15' 45", 9h. 16' 36", and 9h. 17′ 30′′, refpectively, it may hence be prefumed, that the three firft altitudes are tolerably accurate, but that the last should have been about 20° 18', and therefore fuch altitude fhould be abfolutely rejected.

This method of deducing the mean altitude of the fame limb of the Sun is, however, attended with an error arifing from the irradiation, or apparent spreading of its rays, beyond the true limb; and therefore in order to diminish, if not wholly to destroy it, the mean of an equal number of altitudes of each limb, obferved at nearly equal intervals of time, fhould be taken.

Examination of a Quadrant.

If a quadrant be carefully made by a good artift, it may be very fafely depended on; but as many quadrants are made by workmen carelefs of their reputation, it therefore becomes neceffary to examine any inftrument very particularly, before it is purchased-or, if it be already purchafed, to be able to make allowance in fubfequent obfervations for any error to which it may be liable. For this purpose, it is hoped, the following remarks will be found of fervice.

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