Chap. VIII.

GEOMETRY.

833

Fig. 1047.

length equal to one of the parts the rod is divided into,and when we wish to measure a height, we must addhalf the thickness of the rod to the extremity of half thecursor which is used to take the height. In order tobone more easily along the rod of Jacob’s staff, foursmall holes are pierced aside the hole in the cursor, asshown at K ; this instrument when used is mounted ona stand fixed to the ground.

To measure the Distance between two Objects one ofwhich is accessible . — Place the cursor on the seconddivision of Jacob’s staff, fix a piquet on the ground nearthe accessible object, and place the end of the rod nearthe piquet; bone along it until you discover a point ofthe inaccessible object, and bone with the extremities ofthe cursor two other points, one to the right, the otherto the left of the inaccessible object, and in the sameline with the first inaccessible point: run the cursor tothe third division of the staff, and retire in a right linefrom the first station, and from the first inaccessiblepoint, in such a manner that by boning along the rodyou can discover the piquet and the point in the inac-cessible object, and also the two points to the right andleft of the inaccessible point by boning along the ex-tremities of the cursor; the distance between the latterstation and the piquet at the inaccessible object will behalf the distance between the two objects. The breadthof a river may be found by placing the cursor on thesecond division of the rod or staff, as at II, and thenplacing a piquet at A, against which the end, M, ofJacob’s staff, is required to bone ; which is done byplacing it in such a manner that by looking alongthe staff M N, you can see the point 15, and alsothe two points E and F by the extremities C andD of the cursor : run the cursor on the third pointof the rod, as to G, and retire in a right line fromthe accessible object A, until by boning along thestaff MN, and by the extremities of its cursor C D,you discover the inaccessible point B, and also thetwo others E and F: the distance K A, beingdoubled, will give the breadth of the river from Ato 15, that is to say, if it is 30 feet from K to A, itwill be 60 feet from A to B.

To measure Distances between two inaccessibleObjects. — Fix the cursor on the second divisionof the staff, and place yourself about midwaybetween the two objects which are inaccessible,bone along the staff, and by the two extremities ofthe cursor, which should be placed in a directionparallel to the line between the two objects, untilyou discover the two inaccessible objects by thevisual rays; plant a piquet at the place where theobservation was made: then run the cursor onthe third division of the staff, and retire from thefirst station, boning by the staff and by twoextremities of the cursor until you discover bythe visual rays the inaccessible objects ; the distancebetween the stations will be equal to that betweenthe objects. As, for instance, it is required to as-certain the distance from A to B: run the cursoron the third division of the staff MX as to H;then being at about an equal distance from bothobjects, bone by the staff M N and by the twoextremities of the cursor, C D, which is parallelwith the line A B, the two objects A and B ; that is to say, you must discover by the visualray MC the object A, and by the ray Ml) the object'B, which will be the’case whenyou are at L, where you must place a piquet for the first station. Then run the cursorC 1) on the third division of the staff INI N, as to G, and retiring from the piquet or station

3 H

Fig.1048.