. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. Let AO = r,qo=x,Co=:c, and the angle qor=:2e. â¢. A 2 = g r := 2 .r sin 6=râx; and x = 1 + 2 sin »' Again C s = V .t- -c' «= i: sin 2 n e, (n being the number of equal parts into which the arc q s has to be divided); And .V- -c' = > - sin 2 )( B x' (1- -sin- 2 n fl>= c" '»â â c- c- 1- sin- 2« 8 cos 2 0 n a . x = c r cos 2« e 1 + 2 sin a' c COS 2 lie -2sin« = 1. (A.) Although tlie general solution of the equation involves sonic diffi- culty, yet the value of H
. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. Let AO = r,qo=x,Co=:c, and the angle qor=:2e. â¢. A 2 = g r := 2 .r sin 6=râx; and x = 1 + 2 sin »' Again C s = V .t- -c' «= i: sin 2 n e, (n being the number of equal parts into which the arc q s has to be divided); And .V- -c' = > - sin 2 )( B x' (1- -sin- 2 n fl>= c" '»â â c- c- 1- sin- 2« 8 cos 2 0 n a . x = c r cos 2« e 1 + 2 sin a' c COS 2 lie -2sin« = 1. (A.) Although tlie general solution of the equation involves sonic diffi- culty, yet the value of H or of 2 n 6, and therefore of .1, may be readily determined in all cases, to any required degree of exactness, by pro- portion; lor from the near approach of A O S to A OB, which is known, two values of e may be readily selected, which wlien substi- tuted in (A), will give results respectively less and greater tlian unity. One or two examples will show the certainty and simplicity of this mode of proceeding. I. Let r = 4, f = 1, and 11 = 9, i = -2500000 = cos A O B = 75 31' nearly. Equation (A) becomes 4 cos lb C â2 sm 8 = 1 âââ= 4 11'= 9 nearly. 18 Let us substitute 4° 10', and 4' for 8 in (A.) then we have 4 cos 72-2 sin 4"0'= 1-0965550 (a) 4 cos 188â2 sin « ^ l-OOOOOOO (6) 4 cos 75°-2 sin 4" 10' = -8899600 (c) f-2065950= (d-c) 75"-72'^= 3'= IbO'-^ 0965550= (a-6) 84'-125= 1° 24''125, which, when c As 206595 t 96555 : : ISO added to 7-2^= 73':24'-125= 18 8. â¢. 8= 4": 4' 1 cos 73": 24'-12 5 = 3-6008 nearly, so that if A O be divided into 8 equal parts, A5 one of them, will divide the arc q, 1, 2, 3, it., into 9 equal A^ajf ' ' ' C O A 9 o^ â ^<i II. Let r= 7, c = 2, and ?i= 7, f = -2857142 = cos A O Ba r'io 24' cos 73° 24' nearly, âr^â = 5"' 14 = 8 nearly. Let us substitute 5" and 5^ 10' for 8 in equation (A,) which be comes J- cos 148â 2 sin 8= 1, and we have i cos 70° : 0' -
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