REPORT FOR 1897--PART II. APPENDIX NO. 10.

727

(1) To set the arms (l and V) of the centrolinead if the direction to the vanishing point ( F) is given by a line in the ground plan.

With reference to fig. 119 we hâve :

P = principal point on the photograph board. A and B = positions of the studs. Sv = given direction of the line on the ground plan, when V will be the vanishing point for that line.

We revolve the picture plane about the horizon line, as axis, into the horizontal platting plane when the station may fall in S, fig. 119, SP being then the distance line or focal length projected into horizontal plan. Should the point V fall upon the drawing board we could describe a circle through AB and Y and place the fiducial edge of the centrolinead’s straight-edge upon DP (upon the horizon line) with the axis of rotation O of the arms l and V in D upon the cir- H cle, then bring the arms Z and V into contact with the studs A and B and clamp them in this position. Still, in this case there would be no use for the centrolinead, the point Y being accessible.

To set the arms for

an inaccessible point Y we again refer to fig. 119. Join the points Y and B, the angle YDB—the inclination of the lower arm l' against the ruler L—is equal to VBA, both angles subtending equal arcs of the same circle. Draw the lines CS and BS. At any point c on CS draw cM and cv par-allel to AB and DP and join b and v. By reason of similarity of triangles, vb must be parallel to VB and the angle

vbc = VBC = BDY.

Hence, the arms of the centrolinead may be set in the case under considération by placing the ruler L on Mb, the axis of rotation, O, coinciding with b, and adjusting the lower arm V of the centrolinead to coincide with bv. The other arm l, having the same inclination against the ruler L as the arm V, may be set by placing the ruler L upon the horizon line DP and moving it along this

line until the lower adjusted arm V cornes into contact with the stud B, then moving the other arm l about O until it cornes into contact with the stud A and clamping it also.

The lines BS, CS, Mc, and cv are drawn once for ail upon the photograph board, fig. 70. The only line to be drawn for setting the arms of the centrolinead is Sv, which is the direction of the given line on the ground plan. The line bv need not be drawn, the points b and v being located by drawing cv parallel with the horizon line and cM or cb parallel with the distance line SP.

{2) To set the arms ofthe centrolinead, if the given line YE belongs to the perspective:

Take any point F, fig. 120, on the horizon line, join F with E and F with B, then draw cM parallel to AB. Through e draw ev parallel to EY and join vb. Owing to the similarity of triangles vb will be parallel with VB and the angle vbc = YBA, which is the inclination of the arm against the ruler L of the centrolinead.

FB and cM are permanently drawn on the photograph board, but FE and ve will bave to be drawn for every given line. In this case two lines will hâve to be drawn instead of one, as in the preceding case.

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