. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. 274 THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. [Skpt Fig. posed to be drawn from L lo S, it is evident that the point E falls within the triangle LPS, the angles of which are found by problem (3) to be as follows:â ylSPL = 112' or 27" = a; ZPLS = 15 21 32 ^ h; Z PSL = 52 37 01 = c; we have also Z PES = 112 30 00 = »« = 10 points, or '. / PEL = 78 45 00 = n = 7 points, or N. by E., and Z LPE = X. Then by the general rule we have, log. cosec. a â =10-0339082 lo
. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. 274 THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. [Skpt Fig. posed to be drawn from L lo S, it is evident that the point E falls within the triangle LPS, the angles of which are found by problem (3) to be as follows:â ylSPL = 112' or 27" = a; ZPLS = 15 21 32 ^ h; Z PSL = 52 37 01 = c; we have also Z PES = 112 30 00 = »« = 10 points, or '. / PEL = 78 45 00 = n = 7 points, or N. by E., and Z LPE = X. Then by the general rule we have, log. cosec. a â =10-0339082 log. sin. c =9 9001454 log. cosec. m =10 0313847 log. sin. (m + n) =9 2902357 log. cosec. (6ân) = Reject 50 and 49'30G2953= 1-3062953 = log. of 0-2024395 ; from which substract â -5002568, the natural cotangent of (6ân), and we have, 0-7033003 for the natural cot. of a-, .â¢. ^â =54''52'40"=L P E. The dis- tances L E, S E, C E, can be found by Plane Trigonometry, and are 53-11906; 17-1334; and 1391746 miles respectively. John Topham makes them 53-04; 17-36 ; and 14333 respectively. II. Being at a town in Kent I observed three objects on the other side of the river Medway, a castle (C), a windmill (W), and a spire (S), whose distances from one another are known; from the castle, (the nearest object seen,) to the spire, (CS) is 10 furlongs ; from the castle to the windmill (W C), 23 furlongs ; and from the windmill to the spire (W S), 25 furlongs. I took with a theodolite, the angular distance between the castle and the spire (CT S) and found it to be 28° 34', and between the castle and the windmill (C T W) 57° 45'; what dis- tance did I stand from each of these objects ? From having the three sides of C S W we can find the three angles by problem 3 ; hence we have. Being calculated independant of each other, and making 180° affords a proof. Fig. Please note that these images are extracted from scanned page images that may have been digitally
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