. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. (3.) Tlie distance between tlie second and fourth of four stations, fig. C, taken in tlie same plane, forming a trapezium, (as in tlie next diagram,) togetlier with the angular distances taken at the first and third stations, measured from an unknown diagonal, heing given to find the remaining linear and angular distances connecting those stations. In this prohlem the best position for the point 0, is the second or fourth station. Let A he the 1st station, 1) the 2nd, C the 3
. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. (3.) Tlie distance between tlie second and fourth of four stations, fig. C, taken in tlie same plane, forming a trapezium, (as in tlie next diagram,) togetlier with the angular distances taken at the first and third stations, measured from an unknown diagonal, heing given to find the remaining linear and angular distances connecting those stations. In this prohlem the best position for the point 0, is the second or fourth station. Let A he the 1st station, 1) the 2nd, C the 3rd, 0 the 4lh ; and the angle O A C = x, angle A C O then will = 180°âa âi-a-, or eâ\SO-a-/i, e â 108° 15'. Having thus far premised we shall now applv the general ' O A : 0 B :: sin O B A ⢠sin 0 A. B :: sin c : sin (a + c) O B : 0 C :: sin 0 C 15 : sin 0 B C :: sin (S ^- rf) : sin (/ 0 C : 0 A :: sin 0 A C : sin O C A :: sin r : sin (eâ x) .â . sin c sin (* + (/) sin r = sin d sin (a + e) sin (e â.»). â¢. cot .r = cot e+ cosec (a + c) sin (A + d) sin c cosec d cosec e. From which we liave the following practical logaritlimic Utile.âJdd tor/el/ier the log cosecant of (a + c), the log sine of {h + d), the log nine of c, the log cosecant of d, and the log cosecant of e. the natural number corresponding to this sum, when a proper allowance is made in the index, added to the natural cotangent of e, will give the natural cotangent ofx. GivenâLineal distance from 1st to 3rd station, A C = 19712 feet = n. Angular distances at 2nd station, A 0 B = 39° 47' = a; B 0 C = 31° 58'» 4. Angular distances at 4th station, A B 0 = 25° 17'= c ; 0 B C = 30° 25' = d. To find X. log cosec (a + c) = log cosec 65° 4' =10-0424890 log sin (6 + d) = log sin 68° 23' = 9-9083285 log sin c = log sin 25° 17' = 9-6305243 log cosec d = log cosec 30° 25' = 10-2264073 log cosec e = log cosec 108° 25'= 10-02-24140 Rejecting 50-49-8902231 we have
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