828

THEORY AND PRACTICE OF ENGINEERING.

Book II.

Fig. 1031.

were 3, we must triple the distance between the two stations in order to have a sum,to which the length of the staff must be added, to obtain the required height.

To illustrate the fourth remark, select the two stations It and S, in order that theheight from 31 to N may be obtained ; these stations

are 40 feet distant from each other: at the station N

R suspend the astrolabe ; bone through the sights ofthe alhidade the point N, and observe at what divi-sion, and on what side of the altimetric scale, the alhi-dade is, as at the third point of the side right shadow;suspend then the astrolabe at the second station S,and bone the point N through the alhidade, and havingobserved that it stands at the 10 point of the rightshadow, adopt the fourth rule, previously given; ac-cordingly divide 12 by 3 = 4 — 3, being the numberof points on the side right shadow indicated by thealhidade at station R: divide 12 by 10, the num-ber indicated on the side right shadow of the alti-metric scale at the second station S; the quotient 1,rejecting the remainder of this division, which is of littleaccount, must be subtracted from the first quotient 4,and 3 remains: then multiply 40 feet, the distancebetween the two stations by 12, in order to divide theproduct 480 by 8, the remainder from the subtractionof the two quotients; the quotient of this last divisionwill give 160 feet, to which add 5 feet, the height of thestaff, which gives 165 feet for the total height of theline VN; if then we subtract the height from theground to the point 31, viz. V to 31, we shall obtain theheight 31 N.

Measuring Depths by the Astrolabe . — Required the depth of a well, as from P 31 to ON :first measure the opening of the mouth P 31, which is 34 inches; then suspend the astro-labe, disposing it in such a manner that the vertical lineA B of the altimetric scale, which divides the right shadowinto two equal parts, shall be plumb or on the same linewith the wall of the well P O : then turn the alhidade ofthe astrolabe until the bottom of the well N is seen throughthe sights of the alhidade: remark at what point on theright shadow the alhidade stands; if on the 4th point, asin this case, the depth 31 N is half the number 12, whichis half the division of the long square; therefore, if thediameter of the well 31 P is 34 inches, the depth 31N willbe 102 inches, and if we subtract 6 inches for the height ofthe astrolabe, there will remain 96 inches for the depth ofthe well. If the alhidade fell on the 6th point of theright shadow instead of on the 4th, the depth of the wellwould only be twice the diameter of the mouth : if on thepoint 12, where the right and versed shadow makes a rightangle, the depth would be precisely equal to the diameterof the well: if on the 1st point of the right shadow, thedepth of the well would be twelve times the diameter ofthe mouth, and so on with the other points, taking theirrelation to the number 12.

Measuring Heights or Depths u-ith the Astrolabe , whenthe station is either above or below, as to get the heightO P. We must so place ourselves at R that we can seethe point O ; and at R suspend the astrolabe in such amanner that the line A B shall be perpendicular to thehorizon ; then turn the alhidade until by means of its sightswe discover the point O ; observe then where the alhidadestands on the right shadow at the 2 point, counting fromthe vertical line A B, which indicates that the depth orheight O P will be six times greater than the distanceR P, because 2 is the sixth of 12, the division of the side ofthe square used in this operation. Therefore if we measurethe distance RP, and find it 12 feet, we shall have tomultiply 12 by 6, and the product 72 feet will be the heightof OP.

Fig. 1032.

Fig. 1033.