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. XLXI. To finde the horizontall line of any hill or mountain.

THis proposition differeth nothing from those formerly taught in the taking of Altitudes. Wherefore, suppose you should meet with a hill or mountain as ABD, the thing required is to finde the length of the line BD on which the mountain standeth.

[illustration]

First, place your Instrument at the very foot of the Hill, exactly levell, then let one go to the top of the hill at A, and there place a mark, which must be so much above the top of the hill; as the top of the Instrument is from the ground; then move the Label up and down till through the sights thereof you see the top of the mark at A, and note the degrees cut by the Label on the Tangent line, for that is the quantity of the angle ABC, which suppose 47 degrees, then by consequence the angle BAC must be 43 degrees, the com∣plement of the former to 90 degrees, then measure the side of the hill AB, which suppose to contain 71 Feet, then in the Triangle ABC there is given the side AB 71 foot and the angle BAC 43 degrees, together with the right angle ACB 90 degrees, and you are to finde the side BC, which to perform, say,

• As the Sine of the angle ACB, 90 degrees,
• Is to the side AB 71 feet;
• So is the Sine of the angle BAC, 43 degrees,
• To the side BC: 48½ feet.

Then (because the hill descends on the other side) you must place your Instrument at D, observing the angle ADC to contain 41 de∣grees, and the angle DAC 49 degrees, and the side AD 80 feet: now to finde the side CD the proportion will be,

• As the Sine of the angle ACD, 90 degrees,
• Is to the side AD, 80 feet;
• So is the Sine of the angle CAD, 49 degrees,
• To the side CD 60½ feet.

Which added to the line BC, giveth 109 feet, which you may re∣duce into Chains, by dividing it by 66, and this line must be protra∣cted instead of the hypothenusall lines AB and AD.

Another way.

There is another way also used by some for the measuring of ho∣rizontall lines, which is without the taking of the Hils altitude, or using of any Arithmeticall proportion, but by measuring with the Chain only, the manner whereof is thus.

[illustration]

Suppose ABC were a hill or mountain, and that it were requi∣red to finde the length of the Horizontall line thereof AC. At the foot of the hill or mountain, as at A, let one hold the Chain up, then let another take the end thereof and carry it up the hil, holding it levell, so shall the Chain meet with the hill at D, the length AD being 60 Links, then at D let the Chain be held up again, and let another carry it along levell till it meet with the side of the hill at E, the length being 54 Links: then again let one stand at E and hold up the Chain, another going before to the top of the hill at B, the length being 48 Links, these three numbers being added together make 162 Links, or 1 Chain 62 Links, which is the length of the horizon∣tall line AC. This way of measuring is by some practised, but the other (in my opinion) is far to be preferred before it, only when you are destitute of better helps you may make use hereof.

¶ But if the hill or mountain should have a descent back again on the other side, you must then use the same way of working as before, and adde all together for the horizontall line.