A Treatise On Astronomy, for the Use of Colleges And Schools
A Treatise On Astronomy, for the Use of Colleges And Schools
Hugh Godfray
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Thus, let the dark line in the figure represent the first position of the graduated circle when J?, K, are the points of the limb opposite the microscopes Aj By and M the zero of graduation. Let the fine line represent the second position of the circle, its centre, the line HK having come into the position H'K'j and M moved to if. The telescope will have Digitized by Google CHAP, v.] THE MURAL CIRCLE. 73 turned through the same angle as any line rigidly connected s p^ y^ ^ rr^'^'^ with the circ...le ; therefore HGH' is the angle to he found. The two readings of A are respectively {MH or) M'H' and Jf' A, B {MHK or) M'lTK's^niirE'k. The dlflference of the readings at A gives hOE'=2CkH\ B WK'^2CH'k. The sum of these = 2 { CkH' + CH'k] = 2HCH^ and the half sum is the angle between the two positions of the telescope. The centre of rotation, that Is, the point about which the instrument is supposed to have turned in passing from the first position to the second, Is not shewn on the figure ; and the Investigation, being Independent of this centre, shews that, even when the pivots are not cylindrical, and when con- sequently the centre of rotation Is not a fixed point, the readings of ^mch pair of microscopes will give a value of the angle free from errors of centering and from irregularity in the form of the pivots.
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