Chap. VIII.

GEOMETRY.

865

Fig. 1103.

if the salient angle BUG is required, take it between the limbs of the instrument, andobserve on the deini*circle which is at the head, how many degrees are covered, and thenumber, as 93°, will be the required angle. Sometimes cords are attached to the severalpiquets, that the recipient may be more accurately applied where the angles are to betaken.

To draw out the Plan after the Angles are taken, commence with the line A B, whichserves as a scale, and draw it of any length convenient, divided into any number of parts,as 150°; then at the upper part of the paper drawthe line C D, on which set off 150 parts fromthe scale, to answer to the 150 feet of thescale A B : at the point E draw an angle of121° equal to BCD on the ground, by placingthe centre of the protractor at the point E, andits radius turned towards the side to be drawn,on the plan, and its diameter along the sideCD; count from this line 121°, as to F, anddraw through it a line, FG, which will formwith CE an angle CEG, equal to BCD on theground. To determine the side E G, take81 parts from the scale All, answering to the81 feet from C to D on the ground, and setthem off on the line E G, from E to H. At thepoint FI draw an angle of 113°, answering to the angle C D E on the ground, and set offon the line III, 73 parts of the scale, from II to K, to correspond with the 73 feet from Dto E on the ground; then, at the point K, draw an angle II KL, with the protractor of89° equal to D E F, and set off .55 parts of the scale A B from K to M, answering to the35 feet of E F: from the point M, draw a re-entering angle, K M N, 110°, equalling EFG,by placing the centre of the protractor at M, its radius towards the plan to be drawn, andits diameter along KM, to count 110° from this line on the protractor: continue theseoperations for the sides dnd angles already set down on the rough plan, and the work willbe complete.

To take the Plans of Streets and various other Places, §*c.—To take the plan of a quay nearthe river side, draw a scale, as I K, and on a sheet of paper of any length, draw an obliqueline, as at ab , to unite the quay,

AL, which is skewed, the length ofwhich is to be measured : set off thesame quantity of feet taken from thescale, from c on the line ab ; the lineac will represent the border of thequay, A L ; after having measuredon the ground how far the descent,

R, is from the barrier, A, take alike distance from the scale, andset it off on ab, which will representthe descent of the point R: then re-mark that the border of the quay, A L,makes an angle with the other border,

INI N, which angle may be formed bystretchingtwocords, ALS and MNP,along the two borders, which willintersect at Q, and form the requiredangle, LQN, which will serve as afixed point: then measure the dis-tance from the point Q, to the bor- Fig -

der of the quay, L, and from the point, Q. to the border, N, and measure the angle, LQN :then take from the scale IK, the value of the distance L Q, and set it off on the line abfrom c to d, and from this point, d, draw with a protractor adc, equal to LQN, and bymeans of the scale set off the distance G N on the line de, from d t of: measure also theborder of the quay, NM ; take a like distance from the scale, set off on fe, from f to g ,and do the same for the other parts of the quay. To have the breadth of the quay, placea square against the parapet, at the openings and descent, R L, M N, &c.» opposite thestreets which lead to the quay, with the other side of the square towards the houses, sothat by stretching a cord, RS, along the square, the exact width of the quay may beobtained: then draw perpendicular lines on the paper representing the quay, and itsdescents, hefgnj set off the distances on them of the different breadths of the quay, atthe points i,k 3 l,m,o , through which draw the line to indicate the width of the street*

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