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

657

With reference to fig. 31, this élévation aa0 (fig. 32) of a above the ground plane is found by projecting a upon P'P0 ( = a in fig. 32) ; tbe corresponding point on the principal line revolved about P0 into the platting plane is (a) and its orthogonal projection upon the principal plane, the latter revolved into the platting plane about S'P0, fig. 31, is (a) ; hence, the élévation of A above the ground plane is = (or) a0 — h, to be measured in the platting scale.

If P = distance of the platted point from 8', taken from the platting sheet, H == élévation of



A

..-o

1

1

1

1H I

—ô

Fig. 33.

the point A above the ground plane GG, h = (a) a0 — aa0, fig. 32, = («) a0, fig. 31, = aa0, fig. 33 S'a0 = d (fig. 31), taken from the platting sheet, the élévation H of the point A may be found either graphically from a diagram, fig. 33, or it may be computed from the relation :

IV. APPLICATION OP PROFESSOR HAUCK’S METHOD.

The constructions just described for locating the horizontal directions to points photographed on inclined plates may be greatly simplified by applying Professor Hauck’s method, by utilizing the properties of the “kernel points” of two photographs obtained from different stations but comprising the same ground.

With reference to fig. 34: 8 and 8' = the two caméra stations.

80 and 80! = the foot points of 8 and 8' respectively.

MN and M'N' = inclined picture planes 5 both contain the image a and a' of a point A and the pictures s' and « ( “kernel points”) of the stations 8' and 8. a0 and aQ' = orthogonal projections (in the ground plane GG) of a and a' respectively.

A0 = orthogonal projection of A in the ground plane.

2, s' and tc — kernel points for picture plane MN. s and n' = kernel points for picture plane M'N'.

These “kernel points” are of importance, inasmuch as—

The horizontal direction 80A0 (or 80'A0) intersects the ground line gg' of MN (or M'N') in a0 (or a'o). The line connecting a and s' (“kernel point”) in MN and the connection of a1 and s in M'N1 intersect each other in the same point il of the line of intersection of the two picture planes, and also intersect the ground lines gg' of the picture planes in the “kernel points” n and n', respectively. Ail lines in MN, connecting s' with pictured points, and those in M'N', connecting s with the pictures in M'N' of the same points, intersect each other in points £1 of the line of intersection of the two inclined picture planes. The kernel points 2 and 2' are the intersections of the verticals passing through the caméra stations (S and S'), with the inclined picture planes. They are the “ vanishing points” for the pictures of ail vertical lines shown on the négatives, and when-ever the pictures contain images of vertical lines the intersections of these would locate 2 and 6584---------------42

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