PLOTTING QUADRANT, LEVEL, AND CALCULATOR. g^J 



when the required distance will be given. This is a case of 

 our first problem. 



Fourthly. — To leveU or measure the altitude of any object. 



It is only neces«*ary to set the plane of the instrument ver- To measure 

 tical, instead of horizontal, by means of the joint under the '^^ object. ^ 

 instrument, whence it is evident every case may be known as 

 on the horizon; and to level, it is onlv requisite to set the 

 spirit level at the back of the instrument, the base line and 

 every object cut by the same will be level thereto. 



Fifthly. — To take angles or altitudes at sea, where the instru- 

 ment cannot be made statiof/ari/. 



For this purpose, it is first requisite to chanp^e the sight a. To take angles 

 Mg, 1, and substitute the ond b, Fig. 2; which being firmly or^ltiiudes at 

 fixed and adjusted at right angles with the upper limb, it is 

 evident that when by reflection any object is brought to co- 

 incide on the mirror, at the extremity of the base Hue, with 

 another object seen in the dire( tion of such base, the angle 

 will then be known, being double what the uup'^r limb de- 

 notes on the arch, to which true angle, or ?ts double, the 

 loiver limb may be fixed, leaving the oc.e with the mirror 

 again at liberty to take another observation and angl<% a^ any- 

 distant place, or time; which being ^o taken, thi;s li^nb may 

 be also moved and fixed to double its appar/ent angle, and 

 the altitude or distance be then determined, by sctt ?;g the 

 perpendicular and parallel as in other common caa^ is on land. 



From this mode of determining distances, as the use o( cal- Su; '^r^edefthe 

 culations and of tables of sines and tangents is supeseded, use of calcula- 

 itis presumed that much convenience will arise to th^ unlet- 1,;^',^ of s .. T 

 tered who may have occusion to use it, and thereb} the errours ^'^^ t.u geats. 

 of calculations will be avoided. 



As well as the before-mentioned purposes to which the in- '^ arions other 

 strument appHes, it is presumed there will be i'ouuti oiher """'^ 'o vv^^^hJi 

 things which it will pes f urn, some it is hoped useuii, and 

 jBome amusing, amongst which may be enumerated. Multipli- 

 cation, Division, Rule of Three, Double Kuh of Thee, &c. ; 

 d'Ctermining the area or s-.des of any sort o^ fia^jgle i\om any 

 jnoperdata; determining the inscribing or inscribed circle 



YuL. XVIU— Nov. 1807. Q of ' 



