826

THEORY AND PRACTICE OF ENGINEERING.

Book II.

Fig. 1026.

divide 12, the number of parts into which the staff 31 O is graduated, by 3, the division ofthe altimetric scale on which is the alhidade : the quotient will give 4, for the number oftimes that the staff 31 O would measure in the length 31 N, and as this staff is 5 feet outof ground, the distance 31 N will be 20 feet.

When a great length is to be measured, the observer must be mounted at a considerableheight, as the astrolabe can only measure twelve timesthe length of the staff added to the height on whichit is mounted.

The width of the river from P to It may be ascer-tained by placing the observer at S, which we willsuppose to be 12 feet above the level of the water ; thensuspending the astrolabe, raise or tower its alhidadeuntil the point It is seen ; remark at what pointof the scale the alhidade stands, as in this case itis found at 1 : divide the height 12 by 1, and thequotient will be 12, which denotes that P It contains12 times the height of PS, or 144, which is thewidth P R.

Measuring Heights , whose foot is accessible with the astrolabe, as the height K L. Placethe alhidade of the astrolabe in such a position that the line of the alhidade which answersto the visual ray of the two sights shall beexactly in one of the right angles of the alti-mctric scale, which is found by one of the versedshadows and one of the right shadows. Thensuspend the astrolabe from a staff, and holding itin the hand, look at the point L from the endof another staff’, through the sights of the alhidade,moving the staff nearer or farther from the lineK L, until the point N is seen : lay the staff N,down on the ground in a right line with K N, asat NV, the length VK will be precisely theheight of K L.

Measuring inaccessible Heights with the Astrolabe .

— It may happen that in taking up the two dif-ferent stations for measuring inaccessible heights,the alhidade, which serves to guide the sight, may• in the same operation fall in four different wayson the sides of the altimetric scale, viz. : when intwo stations the alhidade is on the same side asthe versed shadow; then observe at the first station,which is generally the nearest to the object, atwhat point on the side versed shadow the alhidadestands; with this number divide 12, and write downthe quotient separately: remark at the secondstation B at what point on the same side versedshadow the alhidade stands, and with this numberdivide 12 again, and subtract this from the first,or vice versa if it is greater, and with the re-mainder divide the number of feet between thestations, and the quotient will give the heightrequired by adding that of the staff’to it.

Secondly. —When the alhidade at the firststation stands at the point 12, or the angle inwhich the right shadow and the versed shadow

Fig. 1027.

meet, and at the second station on the side versed shadow; then remark the number atwhich the alhidade stands on the side versed shadow at the second station, and withthis number multiply the distance between the two stations, and divide this product by theremainder of the points which the alhidade makes on the side versed shadow, to make 12of the division; this quotient added to the height of the staff will give the requiredheight.

Thirdly -When the alhidade stands at the first station on the right shadow, and at the

second on the versed shadow ; then divide 12 by the number to which the alhidadepoints at each station, subtract the quotients from each other, the remainder will mark thatthe distance to be known is as many times greater as there are parts to be added tothe remainder, besides the height of the staff.

Fourthly -When the alhidade stands on the ombra at both stations, divide 12 by the

number at which the alhidade stands at both stations, and subtract one from the other;