32

NAVIGATION.

termined by the position of the index on the limb, when by re-flection that object appears to-be-in contact with the horizon. Ifthe object whose altitude is to be observed be the sun, and if-sobright that its image may be'seen in the transparent-pait of the.fore horizon-glass, the eye is to be applied-to the upper .hole inthe sight-vane; otherwise, to the lower hole: -and in this case, thequadrant is to be held so that the sun may be bisected by the lineof separation of the silvered and transparent parts of the glass.The moon is to be kept as nearly as possible in the same position;and the image-of-thc-star is to be observed in the silvered part ofthe glass adjacent to the line of separation of the two parts. Thereare two different methods of taking observations with the qua-drant. In the first of these the face of the observer is directed to-wards that-part of the horizon immediately under the sun, and istherefore called the fore observation. In the other method,, theobserver’s back is to-the sun, and it is hence called the back ob-servation. This last method of obrorvalion is to be used onlywhen the horizon under the situ is obscured, or rendered indistinctbv fog or any other impediment. In taking (lie sun’s altitude,whether by the fore or back observation, the observer must turnthe quadrant about upon the axis of vision, and at the same time••turn himself about upon his heel, so as to keep the sun always in■ that part of -the horizon-glass which is at the same distance .as the

- eye from the pkne of the quadrant. In this way (he- retleeted sun. iVUI describe an arch of a parallel circle round the (rue. sun, whose

convex side will he downwards in the fore-observation, and.up-

- wards in the back; and consequently, when by moving the index,the lowest point of the arch in the fore observation, or highest in

-the back, is made to touch the horizon, the .quadrant will stand ina vertical plane, and the altitude above the visible horizon will Im-properly observed. The reason of these operations may bethus explained: The-image of the sun being always kept in the-axis of vision, the index will always- sho.w on the quadrant the dis-tance between the sun and any -object sean directly which itsimage appears to touch; therefore, as long ns .the index, remains• unmoved- the image of the sun will dcscribe an arch every whereequi-distant from the sun in the heavens, and consequently.a.pa-railel circle about the sun, as a pole. Such a translation of thesun’s image can only be produced by the quadrant’s being turnedabout upon a line, drawn from the eye to the sun, as an axis. Amotion of rotation upon this line may be resolved into two, oneupon the axis, of vision, • and the other upon a line on-the quadrantperpendicular to the-axis, of vision; and consequently .a propercomhination of these two motions.will.keep the image of the sunconstantly in the axis of vision, and cause both jointly to run over-a parallel circle-about the sun in the heavens: but when the qua-drant is vertical, a line thereon perpendicular to the axis of visionbecomes a vertical-axis; and as a small motion of the quadrantisall that is wanted, it will never differ much in practice from a ver-tical axis. The-observer is directed to perform two motions ra-ther than the single-one equivalent to them on a line drawn fromthe eye to the sun ; because we are not capable, .while looking to-wards the horizon, of judging how to turn the quadrant about- uponthe elevated line going to the sun as an axis, by any other meansthan by combining the two motions above-mentioned, so as tokeep the sun’s image always in the proper part of .the horizon-glass. When the sun is mear the horizon, the line going from theeye to the sun will not he far removed/rom the axis of vision ; andconsequently the principal motion of the quadrant will be per-formed on the axis of vision, and the part of motion made on thevertical axis will be but small. On the contrary, when the sun isnear the zenith, the line going to the sun is not tar removed from avertical line, and consequently the principal motion of the qua-drant will he performed on a vertical axis, by the observer’s turn-in--' himself about, and the part of the motion made on the axis ofvision will be but small. In intermediate altitudes of the sun, themotions of the quadrant on the axis of vision, and on the verticalAxis, will be more equally divided. -Observations taken with thequadrant are liable to errors, arising from the bunding and elasti-city of the -index, and the resistance it meets with in turninground its centre: whence the extremity of the index, on beingpushed along the .arch, will sensibly advance before the index-jr|ass begins to move, .and may be seen to recoil when the forceacting on it is removed. Mr. Hadley seems to have been appre-hensive that his instrument would be liable to errors from this

.

cause; and in order to avoid them, gives particular directions thatthe index be made broad at the end next the centre, and that thecentre, or axis itself, have as easy a motion as is consistent withsteadiness; that is, an entire freedom from looseness, or-shake, asthe workmen term it.- By strictly complying with these direc-tions the error in question may indeed be greatly diminished ; sofar, -perhaps, as to render it nearly insensible, where the index ismade strong, and the proper medium between the two extremesof a shake at the centre on one hand, and too much stiffness thereon the other, is nicely hit: but it cannot he entirely coirectcd ;for to more or less of bending the index will always be subject;and some degree of resistance will remain at the centre, unless thefriction there could be-total!y removed, which is impossible. Ofthe reality of the en-or to-which be ■ is -liable from this cause, thej observer, if he is provided with a quadrant furnished with a screw! for moving the index gradually, may thus satisfy himself. Afterfinishing the observation, lay the quadrant on a table, and note thej angle: then cautiously loosen the screw which fastens the index,

I and it will immediately, if the quadrant is not remarkably wellconstructed, be seen to start from its former situation, more orless according to the perfection of the joint and the strength ofthe index. This starting, which is owing to the index recoilingafter-being released from tin: confined state it was in during theobservation, will sometimes amount to several minutes; and its di-rection will be opposite to that in which the index was moved bythe screw at the time of finishing (he observation. But how far it! affects the truth of the observation, depends on the manner inwhich the index -v.as.moved in setting it to n, for adjusting tile in-strument ; or in finishing the observations necessary lor finding theindex-error. -The easiest.and best rule to avoid these errors seemsto he this: In all observations made hv Hadley’s quadrant, let thej observer take notice constantly to--finish-his observations, by mov-• -mg tire index in the same direction which was used in setting it toi o for adjusting; or.in the observations necessary for finding the! index-error. If this rule is observed, the- error arising from thej spring of the index will he-obviated: .for as -tint index was bent; the same way, and in the same degree in adjusting as in observing,

! the truth of the observations will not be affected by this bending.

I To take Altitudes by the Fore Observation: 1. Of the Ann.Turn down either of the coloured glasses before the horizon-glass,according to the-brighUicss-of the sun ; direct the sight to that partof the horizon which is under.the sun, and move the index untilthe coloured image of the sun appears in the horizon-glass; thenj give tlie quadrant a slow vibratory motion about the axis of vision;

1 move the index unlil the lower or upper limb of the sun is in con-tact with the horizon, at the lowest pact of the arch described bythis motion ;. and the degrees and minutes shewn by the index onthe limb. will be the altitude of the sun; observing to add sixteen> minutes, or the sun’s semi-diameter, if the sun’s upper edge isi used, and subtract the same for the lower edge.

II. Of the Moon . Put the index to o, turn down the greenglass, .place the eye at the lower hole in the sight-vane, and ob-serve the moon in the silvered part of the horizon-glass; move theindex gradually, and follow the moon’s reilected image until theenlightened limb is in contact with the-horizon, at the lower partof the arch described by the vibratory motion as before, and theindex will shew the altitude of the observed limb of the moon. Ifi the observation is made in the day-time, the coloured glass is unne-' cessery.

HI. Of a.Star or Planet. The index being put too, direct thesight to the star through the lower hole in the sight-vane and trans-parent part of the horizon-glass; move the plane of the quadranta very little to the left, and the image of the star will be seen inthe silvered part of the glass. Move the index,.and the image ofthe star will appear to descend; continue moving the index gra-dually until the star is in contact with the horizon at the lowestpart of the arch described, and the degrees and minutes shewn bythe index on the limb will be the altitude of the star.

To take Altitudes by the Back Observation. I. Of the Sun.Put.the stem of the coloured glasses, into the perforation betweenthe horizon-glasses, turn down either according to the brightnessof the sun, and hold the quadrant vertically ; then direct the sightthrough the hole in the hack sight-vane, and the transparent slit u» 'the horizon-glass to that part of the horizon which is opposite U»the sun ; bow move the index till the sun is in the silvered part of

the