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Ufe of the Common, or Surveying Quadrant.
( 92-4)
Q.UA
i. y*o take the Height \ or Z)epth of an ObjeB, with the fixed Sights and Plummet flace the Quadrant vertical- ly, and the Eye under the Sight next the Arch of the Qua- drant ; Thus djre£t the Instrument to the Object, v.gr. the Top of a Tower, till the vifual Rays thereof ilnke thro' the Sights upon the Eye.
This done, the Portion of the Arch intercepted between the Thread and the Semidiameter, whereon the Sights are fatlen'd, /hew the Complement of the Object's Height a- bove the Horizon, or its Diftance from the Zenith 5 and the other Portion of the Arch intercepted between the Thread and the other Semidiameter, ihews the Height itfelfof the Object above the Horizon.
The fame Arch likewife gives the Quantity of the Angle made by the vifual Ray, and a horizontal Line parallel to the Bafe of the Tower.
Note, to obfervc Depths, the Eye muft be placed over that Sight next the Centre of the Quadrant.
From the Height, or Depth of the Object, in Degrees thus found, which fuppofe 35°, 35', and the Diflance of the foot of the Objecf from the place of Obfervation care- fully meafur'd, which fuppofe 47 Foot 5 its Height or Depth in rect,Yards,£5fc. is eafily determin'd by the moft common Cafe in Trigonometry. See Triangle.
For we have here, in a Triangle, one Side given, visb the Line meafured j and we have all the Angles: for that of the Tower is always fuppofed a right Angle, the other two therefore are equal to another right Angle j but the Angle obferved is 35 Q , 35'$ therefore the other is 54 , 25'. See Angle.
The Cafe then will be reduced to this 5 as the Sine of 54. , 25', is to 47 Feet; fo is the Sine of 35°, 35', to a 4th Term, viz. 33^ Feet: to which add the Height of the Obferver's Eye, fuppofed 5 Foot, the Sum 3$* Feet, is the Height of the Tower required.
2. 9fo farther Ufe of the Quadrant in taking of Alti- tudes of Objefts, both acceffibk and inaccejfible ; fee under the Article Altitude.
3. Ufe of the Quadrant in taking Heights and "Diftances
by the Index and Sights. To take, e.gr. a Height, as
that of a Tower, whofe Bafe is acctffibie Place the
Plane of the Inftrument at right Angles to the Plane of the Horizon, and one of its Edges parallel thereto, by means of the Plummet, which in that cafe will hang down along
the other In this Situation turn the Index, till thro* the
Sight you fee the top of the Tower 5 and the Arch of the Limb of the Quadrant between that fide thereof parallel to the Horizon, and the Index, will be the Height of the Tower in degrees: whence, and from the Diflance mea- fured as before, its Height in Feet, &G. may be found by Calculation, as in the former Cafe; or without Calculation, by drawing, from the Data, on Paper, a Triangle fimilar to the great one, whofe Bafe is the Diftance, and its Per- pendicular meafured on the Scale, the Height of the Tower. See Scale.
4. Ufe of the Quadrant in meafuring horizontal %)if
tances Tho the Quadrant be a lefs proper Inftrument
for this purpofe than a Theodolite, Semicircle, or the like by reafon Angles greater than Quadrants cannot be taken hereby 5 yet Neceffity fometimes obliges Perfons to have recourfe to it*
The Manner of its Application herein is the fame with that of the Semicircle; all the difference between the two Inftruments confifting in this, that the one is an Arch of -180 , and can therefore take an Angle of any Quantity j and the other only an Arch of $o°, and therefore confined to Angles of that Quantity. See, therefore, Semi-cir- cle.
jytrouomicalQyA.vKt.Kr, is a large Quadrant, ufually made of Brafs, fometimes of wooden Bars, only faced with Plates of Iron, or the like 5 having its Limb curioufly di- vided, diagonally or otherwife, into Degrees and Minutes and even Seconds, if poffible; with plain Sights fixed to one fide of it, or inftead thereof, a Telefcope ; and an In- dex moving about the Centre, carrying either plain Sights, Or a Telefcope.
Thefe Quadrants are of principal ufe in taking Obferva- tions of the Sun, Planets, or fixed Stars. See Observa- tion.
The Antientsufed only plain Sights, but the Moderns have found it ot great benefit to ufe Telefcopes inftead of them. See Sight and Telescope,
ted, would afford a very dry and intricate, as well as ufe lefs Detail ; which we /hall omit, as being fufficientlv known among the Inftrument-Makers : And in lieu thereof content ourfeives with giving a Figure or Reputation; (Tab. Astronomy, fig. 53.) '
The Ufe of this Inftrument is obvious — Being adiufled as above, and turned horizontally round on its Axis tilt thro" the moveable Telefcope the Object be Teen to fall in with the Point of Interfeclion of the crofs Bars, the De grees cut by the Index give the Altitude requir'd. Ser Telescofe.
The HorodiBical Quadrant, is a pretty, commodious Inftrument, thus call'd from its Ufe in telling the Hour of the Day ; which is its only Ufe.
Its Conftruclionis fo fimple and eafy, and its Application fo ready, that we mall defcribe both, for the Ufe of f ome who may want other Conveniencies.
Confirutlion and Ufe of the Horoditlkal Qoaerant.
From the Centre of the Quadrant C, (Tab. Astrono- my, Fig. 54.) whofe Limb A B is divided into 5.0° 5 de. fcribe feven concentric Circles at Intervals at pleal'ure ; and to thefe add the Signs of the Zodiac in the Order they are reprefented in the Scheme. 2. Applying a Ruler to the Centre C, and the Limb A B, mark upon the feveral Pa- rallels the Degrees correfponding to the Altitude of the Sun when therein, for the given Hours 5 connect the Points be- longing to the fame Hour with a curve Line, to which add
the Number of the Hour To the Radius CA, fit a
couple of Sights, and to the Centre of the Quadrant C, tie a Thread with a Plummet, and upon the Thread a Bead to Hide.
If now the Bead be brought to the Parallel wherein the Sun is, and the Quadrant directed to the Sun till a vifual Ray pafs thro' the Sights, the Bead will fhew the Hour.
For the Flummetin this fituation cuts all the Parallels in the Degrees correfponding to the Sun's Altitude : Since, then, the Bead is in the Para' 1-1 which the Sun then de- scribes, and thro' the Degrees of All : tude to whkh the Sun is elevated every Hour, there pafs flour-Lines j the Bea.l
muft fhew the prefent Hour Some Perfpns who are nut
mighty nice, reprefent the Hour-Lines by Arches of Circles, or even by flraight Lines; and that without any fenfible Error.
Gimter's Quadrant, is akind of Quadrant (reprefented Tab. Astronomy, Fig. 55.) invented by our Countryman Edm. Gunter.
This, befide the graduated Limb, fixed Sights, and 1 Plummet, as the other Quadrants ; has, likewife' a Sie- reographical Projeflion of the Sphere on the Plane of the Meridian, with the Eye placed in one of the Poles; by which, befides the common Ufes of other Quadrants, fe- veral ufeful Queftionsin Aftronomy, i§c. are eafily folv'ed.
Ufe of Gimter's Qj; a d r a n t .
1. 'to find the Sun's Meridian Altitude for any given Day ; or the Day of the Month for any given Meridian Al- titude Lay the Thread to the Day of the Month in the
Scale next the Limb ; the Degree it cuts in the Limb is the Sun s Meridian Altitude.
Thus, the Thread being laid on the 15th of May, cuts
59^ 30', the Altitude fought And contrarily, the Thread
being fet to the Meridian Altitude, will /hew the Day of the Month. '
a, To find the Hour of the Day Having put the
Bead (which Hides on the Thread ) to the Sun's Place in the Ecliptic, obferve the Sun's Altitude by ihe Quadrant ; then ,f the Thread be laid over the fame in the Limb, the Bead will fall upon the Hour requir'd. _ Thus, fuppofe on the icth of April, the Sun being then in the beginning of Taurus, I obferve the Sun's Altitude bv the Quadrant, tobe 3* . I place the Bead to the begin- ning of Tanrusm the Ecliptic, and lay the Thread over -4° of the Limb ; and find the Bead to 'fall upon the Hour- Line mark'd 3 and 9 ; accordingly the Hour is either 9 i n the Morning, or 3 in the Afternoon Again, laying
— — o> — a — - — uwu™ "gain, laying
the Bead on the Hour given, (having firft reaify'd or put it to the Sun's Place) the Degree cut by the Thread or the Limb, gives the Altitude.
Note, the Bead may be rectify 'd otherwife, v j z b y bringing the Thread to the Day of the Month, and the Bead to the Hour-Line of ii. Add that the Contrivance of moving the Index, by the 5. To find the Sun's Declination from his <Place then ■
elp of a Screw on .'he Edge of the Limb, and of readily and comrariwife Ser the Bead to the Sun's pface in the
Ecliptic ; move the Thread to the Line of Declination E T and the Bead will cut the Degree of Declination requir'd— Contrarily, the Bead being adjufted to a given Declination, and the Thread moved to the Ecliptic, the Bead will cut the Sun's Place,
and eafily directing it, and the Quadrant upon its Pedeftal to any defired Phenomenon, by means of the Screws and dented Wheels, is a flill greater Improvement of the In- flrument. The Particulars of the Mecbanifm whereby this i s e ff K .
4. The
