Transactions of the Royal Society of New Zealand . frequently occurs in topographical surveying in the follow-ing form :— Given the height of a station above the surface of a lake, bay, or arm ofthe sea; and the zenith distance, or angle of depression, to a point on theshore ; to determine the distance thereto. Let A be the elevated station, B thepoint on the shore, and C the centre of theearth. Refraction will cause the point Bto appear at D, and the observed zenithdistance will be the angle ZAD, the truezenith distance being ZAB. Draw HE per-pendicular to AH, and HG perpendicularto AB. Subtr
Transactions of the Royal Society of New Zealand . frequently occurs in topographical surveying in the follow-ing form :— Given the height of a station above the surface of a lake, bay, or arm ofthe sea; and the zenith distance, or angle of depression, to a point on theshore ; to determine the distance thereto. Let A be the elevated station, B thepoint on the shore, and C the centre of theearth. Refraction will cause the point Bto appear at D, and the observed zenithdistance will be the angle ZAD, the truezenith distance being ZAB. Draw HE per-pendicular to AH, and HG perpendicularto AB. Subtracting the observed zenithdistance from 180°, or the observed angle ofdepression from 90°, we get the angle BAH,which we will call the observed Nadir dis-tance, and subtracting the refraction from this, we get the true Nadir dis-tance = BAH = GHF. Then the distance HB = HG sec. GHB = AH sin. BAH sec. GHB. Let N be the observed angle from the Nadir = DAH. Let K = the distance HB. Let m = co-efficient of refraction. Let C = the contained arc. 8. 106 Transactions.—Miscellaneous. ^ Let h = height of the station A above the surface of the lake. Then if = /i sin. (N-mC) sec. (iV-mC+iC).= h sin. (N—mC) ,-v cos. {N-mC-\-iO) ^ ^ li Z = the observed zenith distance, then the following will be theformula:— K = h sin. (Z-\-mC) ,^\ COS. {Z-\-m C-^C) ^ ^ If D = the observed angle of depression ; thenK = h cos. (D+mC) cosec. {D+mC-^C)= h cos. {D-\-mC) XQN sin. {D+mC-iC) ^ ^ These 3 formulas require the angle C (or contained arc) to be known, butas this is measured by the distance HB, some method of approximationmust be employed in order to get this distance. This may be done gra-phically by making AH = the height in links, then draw HE perpendicularthereto, and draw AF making the angle HAF = N, then HF will be thedistance required in links nearly, but always less than the true same thing may be done by calculation, by multiplying AH by tan A. A more accurate method may
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectscience, bookyear1881
