. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. gular and linear distances of the second and third stations are known, as welt as the angular distances of those three stations observed from the fourth. Determine the remaining Hnear and angular distances of those stations. In any way this problem may be taken,âthe first station is the best for the point O, round which, as before, when we have particularized the distances, we shall compare the ratios. The linear distances from 1 station. 1, 2, = 3755 ffiet = n; 1, 3, = 4000
. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. gular and linear distances of the second and third stations are known, as welt as the angular distances of those three stations observed from the fourth. Determine the remaining Hnear and angular distances of those stations. In any way this problem may be taken,âthe first station is the best for the point O, round which, as before, when we have particularized the distances, we shall compare the ratios. The linear distances from 1 station. 1, 2, = 3755 ffiet = n; 1, 3, = 4000 feet = m. Angular distances at 4 station. 2 4 0 = 44° 33' = a; 0, 4, 3,= 55° 17' = 4. And the angular distance at station I, in fig. 3, or Z 2 1 3 = 180° 0'; in fig. i, 12 1 3 = 23-2° 16'; in fig. 5, /2 1 3 = 127° 44'. It is required to find the linear distances of 2, 4 ; 4, 3 ; and 4, 1 ; as well as the angular distances 12 4 and 13 4. Supposing A, li, and C, to be at the stations 2, 4 and 3. Put the angle OC B=.r, then will 0 A B = 360 âaâ4 âcâj-=dâa:, makingd=3G0-a-4-c = 80''10'(fis. 3); =27° 54'(fig. 4); =132° 26' (fig. 5). Then, as usual, 0 A : 0 B=sin a ; sin {dâx) OB : 0 C = sin J? : sin (J) 0 C : 0 A = m : n . â¢. m sin a sin x=n sin b sin {dâx); but sin (rfâ.r) = sin d cos:râcosrf sin .r. â¢. m sin a sin x= n sin b (sin d cos xâ cos d sin x) Dividing by sin x we have, >n sin a = n sin b (sin d cot a-âcos d) m sin a n sin 4 cos d . â¢. cot X = â:âIâ'â¢âJ -^ 1â'â âJ n sin b sin a n sin b sin a cot a- = cot rf+ â sin a cosec b cosec d. It Which expression in words gives the followingâ Rule.âJdd together the sub log of n, the log of m, the log sine of a, lotf cosecant of b, and the log cosecant of d; the natural number corresponding to this sum, when a proper allowance is tnade in the index, added to the na- tural cotangent of d will give the natural cotangent of x. n =3755 .. .. sub log = 6-4253201 m =4600 .. ..log = 3
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