Chap. VIII.

GEOMETRY.

817

Distances between objects whenone is accessible arc measuredby placing the geometric squareat the station U, in such a man-ner that by boning along its sideD A, we can discover the pointT, and by the other side D C ,the piquet or point X at anydistance from it; the line DTwill then make a right anglewith the line DX. Place thecentre of the square at the pi-quet X, and turn it in suchmanner that by boning along theline D A the piquet II is seen,and by the sights of the alhidadethe point T: then remark the

Fig. 1000.

number of equal parts in the angle made on the side C B, as at Y.

Place, in the first term of a rule of three sum, the number of equal parts from the pointC of the square to the point Y. In the second term, place the number of feet between thetwo stations or centres of the geometric squares D, D ; and lastly, for the third term, thenumber 100 for the number of equal parts into which the side C B is divided. The quotientwill give the distance in feet from the piquet II to the point T: if it be desired to findthe length of the hypotenuse X T, place in the first term the value of D C of the square ;in the second the number of feet from It to T, and in the third term the number of partsmarked on the alhidade, which are counted from the centre of the square to the place wherethe alhidade is on the side C B, as at the point Y. The quotient will give the distance X T.

Distances between objects which areinaccessible are found by the geo-metric square, by first placing it atthe point R, where a piquet is fixed,and then boning a line along its sideD A, until the point T is visible.

Then in the visual ray formed bythe side of the square D C plantthe piquet V. Place the geometricsquare at the piquet V in such amanner that by boning along its sideD A the piquet 11 is seen, and by thealhidade the point S; then countthe number of divisions comprisedbetween the points C and Y, wherethe alhidade rests. Then by therule of three proceed as before.

Heights may be measured by the geometric squarewhen the foot is accessible, as by placing the instru-ment at the point It, and fixing its plane perpen-dicular to the horizon, in such a manner that theside C D shall be parallel to it: elevate the alhidade,until the point P is obtained through its sights,and remark when it stands on the side C B of thesquare, as at the point B, where the 100 divisions ofthe side CB are finished.

Then by the rule of three, place for the first term100 for the side of the square CD; in the secondthe number of feet from the centre D of the squareto the point O, and for the third term 100, thenumber of parts comprised from the point C tothe point where the alhidade is at the angle B, asbefore mentioned. The quotient, which in thiscase is the distance, will be the height, to which,however, must be added the height the foot of the square Is from the ground, when theobservation is taken.

If it be required to measure a building with such accuracy that the proportions ofits several ornaments and detail should be expressed in a drawing, the only method thatcan be adopted is, to take the dimensions of each portion in feet and inches with rulesor rods prepared for the purpose.

Fig. 1001.

Fig. 1002.

3 G