810

THEORY AND PRACTICE OP ENGINEERING.

Book 11.

the repeating or multiplying circle is so contrived, that the observation made may berepeated or multiplied by reading it off successively on different parts of the graduatedlimb : the number of values thus found afford a mean result.

Distances between places where one only is accessible may also be found. Placethe demicircle at the foot of the tower A, and measure the angle CAB; then placethe instrument at C, and measure the angle A C B ; by setting out these angles on paper,the distance between A and B may be found by a scale of parts, or by calculation.

Fig. 963.

K H SO

Fig. %4.

To ascertain the distance from the piquet atI\I to the angle of the building at N: place thedemicircle at P, and measure the angle MPN;then draw the line RS, of the length or dis-tance that P is from >1, and construct from thepoint It a similar angle to that observed fromP. Suppose it has been found by measure-ment that the angle taken at P was 112°,the length of the line PM was 83 feet, and theangle PMN 30°; if.all these are accuratelydrawn out by a scale, the distance may beeasily ascertained. R to T being the same asthe measured distance from P to M, and R toI that of P to N, it is evident that by thescale the distance from T to I on the line X may be taken off.

Distances between places inaccessible on allsides, as between A and B, may be found by a

placing the demicircle on a point C, where bothobjects may be seen, as well as a piquet at D.

The demicircle is then turned in such a mannerthat the piquet D is visible through the sightsof the diameter, and the steeple B through thesights of the alhidade. The degrees containedbetween the diameter and the alhidade mustthen be read off; keep the diameter in thesame line C D, and move the alhidade untilthrough its sights the tower A is seen; then readoff again the degrees contained between itand the base line ; remove now the demicircleto the piquet D, and measure this distancefrom the new station ; repeat the operation,and lay the angles so taken down upon paperwith a properscale, asKFI M H N,and the dis-tance between A B may be truly ascertained. ^ lg *

If it were required to ascertain how many yards distance it was between the points M, E,of a fortified town, by placing a piquet at N, and then measuring the angle, and the distancefrom N to L, and from N to J\I, the same might be laid down accurately on paper by