8M

THEORY AND PRACTICE OF ENGINEERING.

Book II.

Then by aid of a scale up the base line, Z Y, set out the angles so taken at a and Y, asca YyfYa, and draw the line gf from the point where the lines e.J> cross, to where the linesc,d intersect each other, and this line gf measured by the scale will be the height required.

E\ D

Fig. 985.

The height of the tower A B may be ascertained from the station at D in a similarmanner. First take the height of the towerCD, and then place the demicircle at I), insuch a position that its diameter shall be paral-lel to the wall of the tower, D C : turn thealhidade towards the point A, at the foot ofthe great tow’er, and measure the angle C 1) A,the angle DC A being a right angle. Keep-ing the demicircle at D, place it in such amanner that its graduated limb shall be up-permost, its plane perpendicular, and its dia-meter parallel with the horizon, as well aswith the ray DE: then turn its alhidadeuntil the top of the tower B is seen : thedegrees intercepted between the diameter andthe alhidade will be those of the angle E I) B.

Construct a scale K, and set out the figureNIK on the base line FG : make GI on the line II, the height of the small tower; andthe height KN, on the line KL, will be the height by the scale.

The height of the tower O P may also be obtained by placing the demicircle at R,on the top of a low’er p

building, the height ofwhich must be measured.

Having observed the twoangles P R T and T R O,keeping T II as a levelline, and setting off thesame angle from Z bythe scale, making XZ theheight of the low build-ing, and raising a perpen-dicular on the line Y Z,where the angle cuts theground: where this cutsthe line 4Z, as at 8, will

be by the scale the height Fig 9g6 Fig . 987 .

of the tow'er O P.

We must always bear in mind when measuring angles, that the circumferences ofdifferent circles are proportional to their radii, and that similar arcs of circles are alsoproportional to their radii, and vice versa. Two arcs of different circles, which bearthe same ratio to their respective radii, must be similar, and therefore consist of thesame number of degrees, minutes, and seconds; it follows, then, that an arc of onesecond of all circles is contained the same number of times in their radii, and from thecalculation of the ratio of the circumference of a circle to its diameter, it is ascertained thatthis number differs from 206265 by only a fraction; therefore the radius of any circle