Chap. VIII.

GEOMETRY.

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squares with inscribedcircles.

The cone may be showninverted by drawing twolines from the circum-ference of the circle on theupper plane to a point inthe centre of the lower;or it may be exhibited onits base by making theapex terminate in the centreof the upper square, usingthe lower circle for its Yig. 910.

base.

Setting out Points or Lines .—To set out lines on the ground, where the situation isinaccessible, as supposing it were required to draw through the point A a line parallel tothe inaccessible wall B C. Unite two straight edges or rulers about 3 feet in length by ascrew, on which they could be made to open and shut like a pair of compasses. Place theend of this instrument against a piquet at A, and bone along the edge of the tworules, and open them until they cut the inaccessible points B and C ; then secure the open-ing of the two rules, by screwing on a cross piece which shall embrace the two arms.

w c. g

Fig. 911.

Then changing the position, walk to the side through which the parallel is to be drawn,looking along the two open arms of the rules till B C is seen, which will be the case whenthe station E is arrived at.

Then removing the transverse rule from above the two others, and placing their head onthe piquet E, open them, so that by boning along their sides the point B and the piquet Aare discovered, and by which the angle B E A is obtained; this being found, fix the rules, andproceed to the station A, so as to see the point C along the limb of the angle B E A. Thena cord drawn along the other limb at F will be the parallel to the wall required.

If it be required to let fall a perpendicular from any inaccessible place, as at B, fromthe point G, first mark out the parallel line, and then, by means of a square LIII,advance along the line, till the boning edge of the perpendicular comes opposite thepoint G.

Of Levelling and Levelling Instruments. — To the architect, as well as the civil engineer,this term is understood rather to mean the difference which exists between two planes orheights than the idea of a perfectly horizontal surface ; the object generally being to dis-cover how much ground must be elevated or removed to facilitate the running of water, orthe construction of a railroad over valleys or mountains. A level line infers a plane orsurface parallel with the horizon of the place where it exists; so that if water were placedupon its surface, it would remain at rest, having no inducement either to mount or descend.