PROBLEM X. To measure any inaccessible distance by the chain. RULE I. Choose two stations, and measure the distance between them; then ftand at your firft ftation, and lay off a chain towards your fecond ftation, and leave a peg at the end of the chain; then lay off a chain towards your object, and leave a peg at the end of your chain; meafure your diftance between your two pegs, and your work is done at your first station. 2. Then meafure to your fecond ftation, and lay one chain towards your firft ftation, and leave a peg at the end of the chain; then lay off a chain towards your object and leave a peg at the end of your chain; meafure the distance between your two pegs, and your work is done at your fecond station. 3. Look in the Ift, table for the number of links that was between the pegs at each station, add the two numbers together which you find againft füch numbers in the table, and take the fupplement of that fum, that is, fubtract the fum from 180 degrees. Then look in the 2d. table which fhew the natural fines of the firft, and fay thus; As the fine of the remainder is to the distance between the two ftations, fo is the fine of the angle at the firft ftation to the distance of the object from the fecond station; and fo is the fine of the angle. at the fecond ftation, to the diftance of the object from the firft ftation. And thus you have two diftances much more correct than if you had made ufe of the beft theodolite or plaintable that ever was made. Next follows a table of factors to find the area of any plain triangle, by Baving any two fides and the angle included between them. 02 1. 11⁄2 2 2 3 34 4 0.000001.00500 1.010001.015001.01999.025001.02999.034991.03999-04498 10.09987.10485.10983.11479.11975.12475.12972.13469.13966.14462 30.29661.30143.30625.31107.31588.32068.32548.33027 -33.505.33983 40.39192.39660.40129.40596 41063.41529.41995-42459-42922-43387 50 48412.4886449314.49763.50211.50659.51105.51551.51994.52437 70.65573.65975.66376.66775 .67172.67569.67964.68357.68748.69139 90.80373.807018103581363.81688.82012.82334.82654.82972.83287 150.99216.99118.9901498904.98788.98665.98537.98401.98259.98109 160.96000.95762.95517.95264.95002.94731.94452.94165.93864-93562 170.89549.89123.88685.88234 .87771.87295.86807.8630585791.85521 180.78460.77735-77000.76240.75458-74647-7383272984.72113.71216 190.593271.579981.566521.552351.537601.52222.50614.48931-471621.45300 6 9 9 7 F 8 8 2 01.04998.0549805987.06468.06995.07494-079931.08492.08991.09489 10.14958.15453.15949.16441.1693817433.17927.18421.18914.19414 20.24804-25292.25789.26266.26753.27239.27724.28209.28694.29178 303446034936-35412.35887.36361.36835-3730837780.38251.38722 40-43845-44307-44768.45226 .45709.46141.4659747052,47506.47960 50.52879-53319-53758-54197.54636.55072-55487.55941.56374.56567 100.89366.89628.89887.90145.90399.90652.90902.91147 .91390.91630. 110.94087-94274-9449594695.94889-95087.95279.95463-95643.95823 160.93247.92923.92589.92245.91892 .91528.91162.90770.90375.89970 17084721.84166.83595 83010.82410.81794.81169.80512.79846.79162 180.70294 69344.68366.67358.66329.65247.64141.6298061816.60594 1901.433301.41212.390041.36600.33998.31130.27932.24266.198751.14098 EXAMPLE. Suppofe I fee a remarkable object B at a great diftance, and I would know my diftance from it. 1. Measure the dif tance A C which lay off a chain fuppofe 20 chains, A D 20.00 120 from A to D, and alfo from A to E, meafure the dif tance DE, (which fuppofe) 135 € links. 4. Look in the first table for 5 deg. 26 min. 44 fec. and the nearest to it is 5 deg. 26 min. 42 fec. (which is near enough,) and the number of links belonging to it is 9. Then look in the fecond table for 9, and the number be longing is .09489; look for 140% and the number is .99991: Then fay, Ch. 20.00 Ch. .99991: 210.75, which is 2 miles, 5 furlongs, and 16 yards, for the distance AB. Again, Ch. Ch. A's .09489: 20.00 .99664: 210.06 :: of 2 M. 5 F. 1 Y. F. for the dift. B C. Note. If the number of degrees minutes, &c. in the fupplement do not fall out very near to the fame fought in the table, and you would have your fine móré exact; fay, As the difference between any two numbers in the first table is to the difference of the like fines in the fecond table, fo is what is wanting of the first to a number to be added to the fecond, &c. PROBLEM XI. To take a map or plan of any country or kingdom by the chain only. 1. Choofe fome remarkable hill or other place where you can fee a number of towns, villages, parish churches, gentlemen's feats, mills, &c. and choofe alfo a fecond station. |