The compleat surveyor containing the whole art of surveying of land by the plain table, theodolite, circumferentor, and peractor ... : together with the taking of all manner of heights and distances, either by William Leybourn.

CHAP. V. How to take an inaccessible Distance at two sta∣tions by the three forementioned Instruments, and first, by the Plain Table.

YOu are taught in the last Chapter how to make ob∣servation of any angle in the field by the severall In∣struments before mentioned, as the Plain Table, Theodolite, and Circumferentor, and also an angle of Altitude by the Index, and the Labell there∣unto annexed. I conceive it now convenient to shew how all manner of heights and distances may be readily and exactly measured, severall wayes, whether they be accessible or inaccessible: and first of distances.

¶ You may remember that I formerly intimated, that the mea∣suring of a Height or Distance is only to resolve a Triangle, so that when you make any observation either of Height or Distance, the observation of angles which you make are the angles of some Triangle, and the lines which you measure on the ground, are the sides of the same Triangle, and these are the given parts of the Triangle.

The manner how to take a distance by the Plain Table is thus. Suppose you were standing in a field at R, and that at S were some eminent mark (as a Tree, Church, House, or such like) and that it were required to finde the distance between R and S.

First, place your Table at R, and thereon assigne any point at pleasure, unto which point apply the edge of your Index, turning it about upon that point, till through the sights you espie the mark at S, and draw a line by the side of ••he Index, as RS.

Then in some other convenient place of the field (as at Q) let a staffe or other mark be erected, and the Table remaining as before, turn the Index about, till through the sights you espie the mark at Q, drawing a line by the side thereof, as RQ, so have you de∣scribed upon your Table an angle equall to the angle QRS. Then (with your Chain) measure the distance QR, which let be 176 foot, then take with your Compasses 176 out of any Scale, and set it upon your Table from R to Q, so shall this point Q upon your Table, represent the mark at Q in the field.

This done, set up a staffe a R, and remove your Table to Q, lay∣ing the Index upon the line QR, and holding it fast there, turn the whole Table about till through the sights you espie the mark set up at your former place of standing at R: then screw the Table fast, and lay the Index on the point Q, turning it about, till through the sights you espie your mark at S, then draw a line by the side of the Index, which will cut the line RS (first drawn) in the point S.

[illustration]

By this means shall you have upon your Table a Triangle equall to the Triangle QRS, the correspondent sides and angles thereof being proportionally equall with those in the field: therefore, if with your Compasses you take the length of the side RS, and apply that distance to the same Scale from whence you tooke the side QR, you shall finde it to contain 400 foot, and that is the distance between R and S. Likewise, if you take with your Compasses the length of the line QS, and apply it to the same Scale, you shall finde it to contain almost 303, and so many foot is the distance QS.

¶ In this manner may the distance between any two places be measured, although they be so scituated, that by reason of water or other impediments you cannot approach neere unto them. And here note, rhat when you take your second station, that you take it as large as the ground will permit,

so shall your work be so much the truer, by now much the distance taken is the larger.