Chap. VIII.

GEOMETRY.

819

Fig. 1005.

By the rule of three, place for a first term the parts on the alhidade, in the second thedistance in feet from V to T, and in the third the number of parts in the instrumentcounted from C to Z. The quotient thus obtained, added to that found by the first opera-tion, gives the height of R to T.

Of the Sector , and its uses for mea-suring distances, &c. This is a morecomplicated instrument than theothers previously described, and isusually made of either ivory, wood,brass, or silver, having its twolimbs D B and D C 6 or 8 inches inlength, when used for drawing, and12, 15, or more, for making sur-veys ; the largest sectors are themost accurate, on account of theirdivisions being larger. The limbsof the sector are perfectly flat, andcontain all the lines necessary to bedrawn on them; they are united atone end by a rule joint with a dotin the centre of the screw, roundwhich it works: when the in-strument is closed, the two limbs arccalled the upper and lower : eachface of the sector has a particularname, as that which has the line ofequal parts is called the face ofequal parts, and another the face ofchords. By the line of chords, theopening of angles is ascertainedin making a survey, and upon thisthe sights F, F, are placed withscrew's for directing the visual rays.

For surveying, the instrument isplaced upon a staff by means of ajoint with one or more screws, bywhich any motion may be given it,and a plumb bob is attached, w'hichindicates on the ground the precisecentre after an observation has beentaken. The sector has two faces,one of which is that of equal parts,the other that of chords, and eachface has two branches, which areagain divided by three lines ; be-sides the lines of equal parts whichit contains, there are also the lineof plans and polygons; on theface B, which is the reverse ofA, the line of chords is addedto those of solids and metals.

The lines of equal parts is generallydrawn from the centre of thesector to the third part of thefour into which the end of eachbranch is divided, and its length isthat of the sectors, which is dividedgenerally into 200 equal parts ormore. This length is first dividedin half, so that it may have the 100marked in the middle ; and each ofthese 100 is again divided in 50points, and so on until the 200 parts are set out.

The division of the line of plans is set out from the calculations of equal sides of equalsquares, as it comprises between its points the lengths of equal sides of a certain number ofsquare planes, which commonly are enumerated up to 64, and a tolerable skill in the useof the square root is required to find the distances of these points: the first point on the

3 g 2

Fig. 100G.