. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. sin O C B : sin O B C sin O D C : sin O C D sin O E D : sin ODE sin O A E : sin O E A. sin e sin (?—«•) = sin a sin x sin d, by prop. 2. But sin (e—jr) = sin e cos a-—cos e sin x. cos e sin j-) = sin a sin d sin x. Hence sin 4 sin c sin e cos x — sin b sin c cos e sin By dividing by sin x, and transposing, &c., we have sin a sin d cot^' = cote + -:—;—: sin 0 sin c sin e sin li sin c (sin e cos x~ = sin a sin d sin x. •. cot ^ = cot e + sin a cosec b cosec c sin d cosec e.
. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. sin O C B : sin O B C sin O D C : sin O C D sin O E D : sin ODE sin O A E : sin O E A. sin e sin (?—«•) = sin a sin x sin d, by prop. 2. But sin (e—jr) = sin e cos a-—cos e sin x. cos e sin j-) = sin a sin d sin x. Hence sin 4 sin c sin e cos x — sin b sin c cos e sin By dividing by sin x, and transposing, &c., we have sin a sin d cot^' = cote + -:—;—: sin 0 sin c sin e sin li sin c (sin e cos x~ = sin a sin d sin x. •. cot ^ = cot e + sin a cosec b cosec c sin d cosec e. Therefore to find the value of x we have the following Practical Rule.—Add together the logs of the sine of a, of the cosecant of b, of the cosecant ofc, oftlie sine of d, and of the cosecant of e ; the na- tural number corresponding to this sum, rejecting 50 in the index, added to the natural cotangent of e, will give the natural cotangent of x. sin a =sin 23^29' .. .. Iog= 9 C004090 cosec i = cosec 35° 27' .... log= 10-2365778 cosec c = cosec 19° 9' .... log= 10-4810700 sind =sin 35° 51' .. .. log= 9-7676494 cosec e= 66° 4' .... log= 10-0390452 501277514 The natural number corresponding to -1277514 of a logarithm = 1-3419970 to which if nat cot of e =0-4438352 1-7858322 be added we have = the natural cotangent of x = 29° 14' 50" .^ = 30° 49' 10" When x is obtained, the other linear and angular distances may be easily determined hy the rules of plane trigonometry. OA = 17676-01 feet; 0C=^ 18087-388 feet; A 0 = 2881093 feet; B C = 27082-2 feet. (2.) From the first of four stations, figs. 3, 4,5, in the same plane, the an- Fig. 3. Fig. 4. Fig. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original London : [William Laxton]
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