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Quadralit bringing the thread to the day of the month, and the forming a kind of cross, without touching the circle, Quadrant. bead to the hour-line of 12.

3 To find the sun's decli he showed him that there was not an error of a single
nation from his place given, and contrariwise. Set the second in the go degrees; and that the difference was
bead to the sun's place in the ecliptic, move the thread occasioned by a mural quadrant of Bird, in which the
to the line of declination, and the bead will cut the arc of 90 degrees was too great by several seconds, and
degree of declination required. Contrarily, the bead which had never been rectilied by so nice a method as
being adjusted to a given declination, and the thread that of Nir Ramsden.
moved to the ecliptic, the bead will cut the sun's place. But the quadrant is not the instrument which stands
4. The sun's place being given, to find his right ascen highest in Mr Ramsden's opinion ; it is the complete
sion, or contrarily. Lay the thread on the sun's place circle : and he bas demonstrated to M. de la Lande,
in the ecliptic, and the degree it cuts on the limb is the that the former must be laid aside, if we would arrive at
right ascension sought. Contrarily, laying the thread the utmost exactness of which an observation is capable.
on the right ascension, it cuts the sun's place in the His principal reasons are: 1. The least variation in the
ecliptic. 5. The sun's altitude being given, to find his centre is perceired by the two diametrically opposite
azimuth, and contrariwise. Rectify the bead for the points. 2. The circle being worked on the turn, the
time, as in the second article, and observe the sun's al surface is always of the greatest accuracy, which it is
titude : bring the thread to the complement of that al- impossible to obtain in the quadrant. 3. We may al-
titude ; thus the bead will give the azimuth sought, ways liave two measures of the same arc, which will
among the azimuth lines. 6. To find the hour of the serve for the verification of each other. 4. The first
night from some of the five stars laid down on the qua point of the division may be verified every day with the
drant. (1.) Put the bead to the star you would ob utmost facility. 5. The dilatation of the metal is uni-
serve, and find how many hours it is off the meridian, form, and cannot produce any error. 6. This instru-
by article 2. (2.) Then, from the right ascension of ment is a meridian glass at the same time. 7. It also
the star, subtract the sun's right ascension converted becomes a moveable azimuth circle by adding a hori-
into hours, and mark the difference; which difference, zontal circle beneath its axis, and then gives the refrac-
added to the observed hour of the star from tl:e meri tions independent of the mensuration of time.
dian, shows how many hours the sun is gone from the 6. Hadley's quadrant is an in-trument of vast utility
meridian, which is the hour of the night. Suppose on both in navigation and practical astronomy. It derives
the 15th of May the sun is in the 4th degree of Ge its name from Mr Hadies, who first published an ac-
mini, I set the bead to Arcturus; and, observing his al count of it, though the first thought originated with
titude, fiod him to be in the west about 52° high, and the celebrated Dr Hooke, and was completed by Sir
țbe bead to fall on the hour-line of two in the afternoon; Isaac Newton (see ASTRONOMY, N° 32. and also No 17.
then will the four be ni hours 50 minutes past noon, and 22.). The utility of this quadrant arises from the
or jo minutes short of midnight : for 62°, the sun's accuracy and precision with which it enable us to de-
right ascension, converted into time, makes four hours termine the latitude and longitude; and to it is naviga-
eight minutes; which, subtracted from 13 hours 58 tion much indebted for the very great and rapid advances
minutes, the right ascension of Arcturus, the remainder it has made of late years. It it easy to manage, and of
will be nine hours 50 minutes; which added to two extensive use, requiring no peculiar steadiness of band,
hours, the observed distance of Arcturus from the me nor any such fixed basis as is pecessary to other astro-
ridian, shows the hour of the night to be 11 hours 50 nomical instruments, It is used as an instrument for
minutes.

taking angles in maritime surveying, and with equal fa-
The mural quadrant has been already described under cility at the mast lead as upon the deck, by which its
the article ASTRONOMY. It is a most important instru sphere of observation is much extended; for supposing
ment, and has been much improved by Mr Ramsden, many islands to be visible from the mast head, and only
who has distinguished himself by the accuracy of his di one from deck, no useful observation can be made by
visions, and by the manner in which he finishes the any other instrument. But by this, angles may be ta-
planes by working them in a vertical position. He ken at the mast head from the one visible object with
places tbe plumb-line behind the instrument, that there great exactness ; and further taking angles from
may be no necessity for removing it when we take an heights, as bills, or a ship mast's head, is almost the
observation near the zenith. His manner of suspending only way of describing exactly the figure and extent of
the glass, and that of throwing light on the object-glass shoals.
and on the divisions at the same time, are new, and im It has been objected to the use of this instrument for
provements that deserve to be noticed. Those of eight surveying, that it does not measure the horizontal angles,
feet, which he has made for the observatories of Padua by which alone a plan can be laid down. This objection,
and Vilna, bave been examined by Dr Maskelyne ; and however true in theory, may be reduced in practice by
the greatest error does not exceed two seconds and a half. a little caution ; and Mr Adams has given very good
That of the same size for the observatory of Milan is in directions for doing so.
a very advanced state. The mural quadrant, of six Notwithstanding, however, the manifest superiority
feet at Blenheim, is a most admirable instrument. It of this instrument over those that were in use at the
is fixed to four pillars, which turn on two pivots, so time of its publication, it was man; years before the
that it

may

be put to the north and to the south in one sailors could be persuaded to adopt it, and lay aside minute. It was for this instrument Mr Ramsden in. their imperfect and inaccurate instruments, so great is yented a method of rectifying the arc of 90 degrees, on the difficulty to remove prejudice, and emancipate the which an ahle astronomer had started some difficulties; mind from the slavery of opinion. No instrument bas but by means of an horizontal line and a plumb-line, undergone, since the original invention, more changes VOL. XVII. Part II.

+

than

4 D

state.

Quadrant than the quadrant of Hadley; of the various altera- image is neither raised nor depressed, but continues in

tions, many had no better foundation than the caprice contact with the object below, as before, then the sur.
of the makers, who by these attempts have often ren faces of the darkening glass are true.
dered the instrument more complicated in construction, For a more particular description of Hadley's qua.
and more difficult in use, than it was in its original drant, and the mode of using it, see NAVIGATION,

Book II. chap. i.
It is an essential property of this instrument, derived This instrument has undergone sereral improvements
from the laws of reflection, that half degrees on the arc since its first invention, and among these improvers artes
answer to whole ones in the angles measured: hence an be ranked Mr Ramsden. He found that the essential
octant, or the eighth part of a circle, or 45 degrees on parts of the quadrant had not a sufficient degree of to-
the arch, serves to measure go degrees; and sextants lidity; the friction at the centre was too great, and
will measure an angular distance of 120 degrees, though in general the alidada might be moved several minutes
the arch of the instrument is no more than 60 degrees. without any change in the position of the mirror ; tbe
It is from this property that foreigners term that in. divisions were commonly very inaccurate, and Mr Ramo
strunient an octant, which we usually call a quadrant, den found that Abbé de la Caille did not exceed the
and which in effect it is This property reduces in truth in estimating at five minutes the error to which
deed considerably the bulk of the instrument : but at an observer was liable in taking the distance bet Feti
the same time it calls for the utmost accuracy in the the moon and a star; an error capable of producing :
divisions, as every error on the arch is doubled in the mistake of 50 leagues in the longitude. On this že
observation.

count Mr Ramsden changed the principle of construe. Another essential, and indeed an invaluable, proper. tion of the centre, and made the instrument in sech a ty of this instrument, whereby it is rendered peculiarly manner as never to give an error of more than balís advantageous in marine observations, is, that it is not minute ; and he has now brought them to such a de liable to be disturbed by the ship’s motion ; for provid- gree of perfection as to warrant it not more than sis ed the mariner can see distinctly the two objects in the seconds in a quadrant of fifteen inches. Since the time field of his instrument, no motion nor vacillation of the of having improved them, Mr Ramsden las constructed ship will injure his observation.

an immense number; and in several which have been Thirdly, the errors to which it is liable are readily carried to the East Indies and America, the deficiency discovered and easily rectified, while the application and has been found no greater at their return than it bad use of it is facile and plain.

been determined by examinations before their being ta To find whetlier the two surfaces of any one of the ken out. Mr Ramsden has made them from 15 inches reflecting glasses be parallel, apply your eye at one end to an inch and a half, in the latter of which the minuts of it, and observe the image of some object reflected are easily distinguishable; but he prefers for general is very obliquely from it; if that image appear single, those of 10 inches, as being more easily handled tha: and well-defined about the edges, it is a proof that the the greater, and at the same time capalle of equal surfaces are parallel : on the contrary, if the edge of curacy. See SEXTANT. the reflected images appear misted, as if it threw a A great improvement was also made in the corshadow from it, or separated like tivo edges, it is a struction of this quadrant by Mr Peter Dollond, is proof that the two surfaces of the glass are inclined to mous for bis invention of achromatic telescopes. The each other: if the images in the speculum, particularly glasses of the quadrants should be perfect planes

, and if that image be the sun, be viewed through a small té. have their surfaces perfectly parallel to one another. By Jescope, the examination will be more perfect. a practice of several years, Mr Dollond found out se

To find whether the surface of a reflecting glass be thods of grinding them of this form to great exactplane. Choose two distant objects, nearly on a level ness; but the advantage wbich should bare arisen free with each other: hold the instrument in an horizontal the goodness of the glasses was often deseated by the position, view the left-hand object directly through the index-glass being bent by the frame which contains it transparent part of the horizon-glass, and move the in- To prevent this, Mr Dollond contrived the frames dex till tlie reflected image of the other is seen below it that the glass lies on three points, and the part tha: in the silvered part; make the two images unite just presses on the front of the glass bas also three points of at the line of separation, then turn the instrument round posite to the former. These points are made to conzise slowly on its own plane, so as to make the united images the glass by three screws at the back, acting direct move along the line of separation of the horizon-glass. opposite to the points between which the glass is plaIf the images continue united without receding from ced. The principal improvements, however, are in the each other, or varying their respective position, the re methods of adjusting the glasses, particularly for the flecting surface is a good plane.

back-observation. The method formerly practised for To find if the two surfaces of a red or darkening glass adjusting that part of the instrument by means of the are parallel and perfectly plane. This must be done by opposite horizons at sea, was attended with so many means of the sun wben it is near the meridian, in the fol difficulties that it was scarcely ever used : for so litule lowing manner: hold the sextant vertically, and direct dependence could be placed on the observations taken the sight to some object in the horizon, or between you this

way. that the best Hadley's sextants, made for the and the sky, under the sun; turn down the red glass and purpose of observing the distances of the moon from the move tbe index till the reflected image of the sun is in sun or fixed stars, have been always made without the contact with the object seen directly: fix then the index, horizon-glass for the back-observation ; for want and and turn the red glass round in its square frame ; view which, many valuable observations of the sun and more the sun's image and object immediately, and if the sun's have been lost, when their distance exceede dal 20 de

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Fig. 3.

Quadrant. grees. To make the adjustment of the back-observa- edge of the quadrant, with the characters of the signs Quadrante

tion easy and exact, he applied an index to the back upon them; and the two horizons are drawn from the
horizon-glass, by which it may be moved in a parallel same point. The limb is divided both into degrees and
position to the index-glass, in order to give it the two ad- time ; and, by having the sun's altitude, the hour of
justments in the same manner as the fore horizon-glass the day may be found here to a minute. The qua-
is adjusted. Then, by moving the index to which the drantal arches next the centre contain the kalendar of
back horizon-glass is fixed exactly 90 degrees (which months ; and under them, in another arch, is the sun's
is known by the divisions made for that purpose), the declination. On the projection are placed several of
glass will thereby be set at right angles to the index- the most noted fixed stars between the tropics; and the
glass, and will be properly adjusted for use ; and the next below the projection is the quadrant and line of
observations may be made with the same accuracy by shadows. To find the time of the sun's rising or set-
this as by the fore-observation. To adjust the horizon- ting, his amplitude, his azimuth, hour of the day, &c.
glasses in the perpendicular position to the plane of the by this quadrant : lay the thread over the day and the
instrument, he contrived to move each of them by a month, and bring the bead to the proper ecliptic, either
single screw, which goes though the frame of the qua- of sunimer or winter, according to the season, which is
drant, and is turned by means of a milled head at the called rectifying ; then, moving the thread, bring the
back; which may be done by the observer while he is bead to the horizon, in which case the thread will cut
looking at the object. To these improvements also the limb in the time of the sun's rising or setting before
he added a method invented by Dr Maskelyne, of or after six ; and at the same time the bead will cut the
placing darkening-glasses behind the horizon-glasses. horizon in the degrees of the sun's amplitude.- Again,
These, which serve for darkening the object seen by observing the sun's altitude with the quadrant, and sup-
direct vision, in adjusting the instrument by the sun or posing it found 45° on the fifth of May, lay the thread
moon, he placed in such a manner as to be turned be over the fifth of May, bring the bead to the summer
hind the fore horizon-glass, or behind the back horizon- ecliptic, and carry it to the parallel of altitude 45o; in
glass : there are three of these glasses of different de- which case the tbread will cut the limb at 55° 15', and
grees of darkness.

the hour will be seen among the hour-lines to be either
We have been the more particular in our description 41' past nine in the morning, or 19' past two in the afo
and use of Hadley's quadraut, as it is undoubtedly the ternoon.-Lastly, the bead among the azimuths shows
best hitherto invented.

the sun's distance from the couth 50° 41'. But note,
7. Horodictical quadrant, a pretty commodious in- that if the sun's altitude be less than what it is at six
strument, so called from its use in telling the hour of o'clock, the operation must be performed among those
the day.-Its construction is this : From the centre of parallels above the upper horizon, the head being ree-
the quadrant, C, fig. 3. whose limb AB is divided into tified to the winter ecliptic.
90°, describe seven concentric circles at intervals at 9. Sinical quadrant (fig. 5.) consists of several con. Fig. 5.
pleasure ; and to these add the signs of the zodiac, in centric quadrantal arches, divided into eight equal parts
the order represented in the figure. Then applying a by radii, with parallel right lines crossing each other
ruler to the centre C and the limb AB, mark upon at right angles. Now any one of the arches, as BC,
the several parallels the degrees corresponding to the may represent

may represent a quadrant of any great circle of the
altitude of the sun when therein, for the given bours; sphere, but is chiefly used for the horizon or meridian.
connect the points belonging to the same hour with a If then BC be taken for a quadrant of the horizon,
curve line, to which add the number of the hour. To either of the sides, as AB, may represent the meridian;
the radius CA fit a couple of sights, and to the centre and the other side, AC, will represent a parallel, or lino
of the quadrant C tie a thread with a plummet, and of east and west: and all the other lines, parallel to AB,
upon the thread a bead to slide. If now the thread be will be also meridians; and all those parallel to AC,
brought to the parallel wherein the sun is, and the qua east and west lines, or parallels.- Again, the eight
drant directed to the sun, till a visual ray pass through spaces into which the arches are divided by the radii,
the sights, the bead will show the bour; for the plum- represent the eight poiuts of the compass in a quarter
met, in this situation, cuts all the parallels in the de- of the horizon; each containing 11° 15'. The arch BC
grees corresponding to the sun's altitude. Since the is likewise divided into 90°, and each odegree subdivid-
bead is in the parallel which the sun describes, and ed into 12, diagonal-wise. To the centre is fixed a
through the degrees of altitude to which the sun is ele- thread, which, being laid over any degree of the quad-
vated every hour there pass hour lines, the bead must rant, serves to divide the horizon.
show the present hour. Some represent the hour-lines If the sinical quadrant be taken for a fourth part of
by arches of circles, or even by straight lines, and that the meridian, one side thereof, AB, may be taken for
without

any
sensible error.

the common radius of the meridian and equator ; and
8. Sutton's or Collins's quadrant (fig. 4.) is a stereo then the other, AC, will be half the axis of the world.
grapbic projection of one quarter of the sphere be- The degrees of the circumference, BC, will represent
tween the tropics, upon the plane of the ecliptic, the degrees of latitude ; and the parallels to the side AB,
eye being in its north pole : it is fitted to the latitude assumed from every point of latitude to the axis AC,
of London. The lines running from the right hand will be radii of the parallels of latitude, as likewise the
to the left are parallels of altitude ; and those crossing sive complement of those latitudes.
them are azimuths. The lesser of the two circles Suppose, then, it be required to find the degrees of
bounding the projection, is one-fourth of the tropic of longitude contained in 83 of the lesser leagues in the
Capricorn; the greater is one-fourth of that of Cancer. parallel of 480 ; lay the thread over 48° of latitude on
The two ecliptics are drawn from a point on the left the circumference, and count thenge the 83 leagues on

4 D 2

AB,

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Fig. 4.

ture,

Qurdrant. A B, beginning at A; this will terminate in H, allow. measuring altitudes, amplitudes, azimuths, &c. Sve Quadrast

ing every small interval four leagues. Then tracing out" Astronomy.
the parallel I!E, fron the point Il to the thread ; the QUADRANTAL, in Antiquity, the name of a Quadra-
part AE of the thread shows that 125 greater or equi vessel in use among the Romans for the measuring of
noctial leagues make 60° 15'; and therefore that the 83 liquids. It was at first called amphora ; and afterwards
Jesser leagues AH, which make the difference of longi- quadrantal, from its form, which was square every way
tude of the course, and are equal to the radius of the like a die. Its capacity was 80 libræ, or pounds of
parallel HE, make 60° 15' of the said parallel. water, which made 48 sextaries, two urnæ, or eight

If the slip sails an oblique course, such course, be congii.
sides the north and south greater leagues, gives lesser QUADRAT, a mathematical instrument, called also
leagues easterly and westerly, to be reduced to degrees a Geometrical Square, and Line of Shadows: it is fre-
of longitude of the equator. But these leagues being quently an additional member on the face of the cum-
made neither on the parallel of departure, por on that mon quadrant, as also on those of Gunter's and Sutton's
of arrival, but in all the intermediate ones, we must quadrants.
find a mean proportional parallel between them. To QUADRAT, in Printing, a piece of metal used to fill
find this, we have on the instrument a scale of cross la rip the void spaces between words, &c. There are qua-
titudes. Suppose then it were required to find a mean drats of different sizes; as m-quadrats, n-quadrats, &c.
parallel between the parallels of 40° and 65°; with which are respectively of the dimensions of these leiters, ,
your compasses take the middle between the 40th and only lower, that they may not receive the ink.
both degree on this scale: the middle point will termi QUADRATIC EQUATIONS, in Algebra, those
nate against the 51st degree, which is the mean parallel wherein the unknown quantity is of two dimensions, or
required.

raised to the second power. See ALGEBRA. The principal use of the sinical quadrant is to form QUADRATRIX, in Geometry, a mechanical line, triangles upon, similar to those made by a ship's way by means whereof we can find right lines equal to the with the meridians and parallels; the sides of which circumference of circles, or other curves, and their setriangles are measured by the equal intervals between veral parts. the concentric quadrants and the lines N and S, E and QUADRATURE, in Gcometry, denotes the squaW: and every fifth line and arch is made deeper than ring, or reducing a figure to a square. Thus, the findthe rest. Now, suppose a ship to have sailed 150 leagues ing of a square, which shall contain just as much surnorth-cast, one-fourth north, which is the third point, face or area as a circle, an ellipsis, a triangle, &c. is and makes an angle of 33° 44' with the north part of the quadrature of a circle, ellipsis, &c. The quadrathe meridian : here are given the course and distance tore, especially among the ancient mathematicians, was sailed, by which a triangle may be formed on the in a great postulatum. "The quadrature of rectilineal fistrument similar to that made by the ship's course; and gures is easily found, for it is merely the finding their hence the unknown parts of the triangle may be found. areas or surfaces, i. e. their squares; for the squares of Thus, suppoging tlie centre A to represent the place of equal areas are easily found by only extracting the roots departure, count, by means of the concentric circles along of the areas thus found. The quadratare of curvilinear the point the ship sailed on, viz. AD, 150 leagues: spaces is of more difficult investigation ; and in this rethen in the triangle AED, similar to that of the ship's spect extremely little was done by the ancients, except course, find AE=diference of latitude, and DE=dif the finding the quadrature of the parabola by Archimedes. ference of longitude, which must be reduced according In 1657, Sir Paul Neil, Lord Brouncker, and Sir Christo the parallel of latitude come to.

topher Wren, geometrically demonstrated the equality Fig. 6.

10. Gunner's quadrant (fig. 6.), sometimes called of some curvilinear spaces to rectilinear spaces; and soon gunner's square, is that used for elevating and pointing after the like was proved both at home and abroad of cannon mortars, &c. and consists of two branches ei- other curves, and it was afterwards brought under an ther of brass or wood, between which is a quadrantal analytical calculus; the first specimen of which was arch divided into 90 degrees, beginning from the shorter given to the public in 1688 by Mercator, in a demonbranch, and furnished with a thread and plummet, as stration of Lord Brouncker's quadrature of the hyperrepresented in the figure. The use of the gunner's bola, by Dr Wallis's reduction of a fraction into an inquadrant is extremely easy; for if the longest branch finite series by division. Sir Isaac Newton, however, be placed in the mouth of the piece, and it be elevated had before discovered a method of attaining the quantill the plummet out the degree necessary to hit a propo- tity of all quadruple curves analytically by his fluxions sed object, the thing is done. Sometimes on one of the before 1668. It is disputed between Sir Christopher surfaces of the long branch are noted the division of dia- Wren and Mr Huyghens which of them first discovered meters and weights of iron bullets, as also the bores of the quadrature of any determinate cycloidal space. Mr pieces.

Leibnitz afterwards found that of another space ; and in QUADRANT of Altitude, is an appendage of the arti- 1669 Bernoulli discovered the quadrature of an infinity ficial globe, consisting of a lamina, or slip of brass, the of cycloidal spaces both segments and sectors, &c. See length of a quadrant of one of the great circles of the SQUARZvG the Circle. globe, and graduated. At the end, where the division QUADRATURE, in Astronomy, that aspect of the moon terminates, is a nut rivetted on, and furnished with a when she is 90° distant from the sun ; or when she is in screw, by means whereof the instrument is fitted on the a middle point of her orbit, between the points of con. meridian, and moveable round upon the rivet to all junction and opposition, namely, in the first and third points of the horizon. Its use is to serve as a scale in quarters. See ASTRONOMY Index. 4

QUADRATUS,

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