Chap. VIII.
839
To measure the Heights of inaccessible Places, as that of B C : plant three piquets D, E, F, atany distance convenient, but in such a manner that their summits are in a horizontal line,or that a cord passed through theirheads may be level, and lookingalong it some point G may be esta-blished. Measure the distance be-tween the two piquets D, F, as 27feet, in order to divide on the planetable the station line HI into 27equal parts, to serve as a scale, andto answer to the 27 feet. Havingmounted the plane table on its standwith its plane perpendicular to thehorizon, place the point I on thestation line IH, precisely againstthe level of the piquet F, in such amanner that the station line IIIshould be in the visual ray, whichpasses above the piquets D, E, F, oralong the cord D F. Place the endof the rule against the pin I, lowering or elevating it until you see the point C, and drawalong the rule a line I K. Place the plane table perpendicular at the station D, in such amanner that the point II on the station line H I cuts against the head of the piquet D, andthat the station line H I shall be in the same line with the heads of the piquets D, E, F.Then place the rule against the pin H, elevating or depressing it until we discover thepoint C, drawing on the plane table the line H L cutting I K in M.
From the point M let fall a perpendicular M N, on the station line H I, which measuredon the line II I, which serves as a scale, gives 30 feet, to which 5 is to be added for theheight the station line is above the ground, making altogether 35 feet for the height of
Height of inaccessible Places , when they are at a considerable elevation, asB C, situated on the slope B D. Plant two piquets E and F in such a
c.SsrV^C?
H . '
K .
N /
i. r .
L..
*- r /yK | k x
lie.
To measure thethat of the line
manner that their summits arein a right line with the point B.
Measure the distance between thetwo piquets E and F, as 68 feet;divide the station line GH into68 parts, and place a pin at eachextremity of the station line.
Place the point H in the stationline, precisely over the piquet F,and make the station line GIIcoincide precisely with the visualray passing over the heads of thetwo piquets E, F. Place the ruleagainst the plane of the tableuntil we get the point C, draw-ing along the rule a line III.
In like manner bone the point Band D, drawing along the side ofthe rule the lines II K and HL.
Then transport the plane tabicto the piquets E, placing the point G on the station line GII, precisely above the head ofthe piquet E, and make the station line coincide with the visual ray of the two piquets Eand F. Place the rule against the pin G, in order to elevate and depress the rule till wediscover the point C, drawing along the rule a line G M, and boning also the points Band D; draw the lines G N and G O, and observe where the lines G M of this stationcut HI of the first in P, where GN cuts GK in Q, and GO cuts II L in R: drawthe right lines PQ and QR. The line PQ will represent the height B C, and QRthat of the slope 13 D, so that if we measure PQ and QR, we shall obtain the entireheight.
Fig. 1003.
By the mensuration and protraction of lines and angles are determined the lengths,heights, depths, and distances of objects. Accessible lines are measured by applying tothem some certain measure a number of times, as a foot, yard, or chain; but inaccessiblelines can only be measured by angles, for taking which, when the plane table is used, thelines are calculated from the principle of similar triangles, or some other geometrical pro-perty, without regard to the measure of the angles: this method is not so accurate for
3 h 4