CHAPTEE III.

PHOTOTOPOGRAPHIC METHODS.

I. ANALYTICAL OR ARITHMETICAL METHODS.

(1) Method of Prof. W. Jordan.—In 1874 Professor Jordan made a raap of tlie oasis “Dachel,7 including the village “ Gassr-Dachel,” based on photographs taken witli an ordinary caméra by Eeinelé, obtained on Gerhard Bohlf’s African expédition during the winter of 1873-74. Care was exercised to expose tlie plates in vertical plane, and horizontal directions to at least three points for each photograph were instrumentally measured to obtain the data needed for the proper orientation of the pictures. Vertical angles to at least two such points (for every pieture) were also observed to give the means for locating the horizon lines of the pictures and thus enabling the draftsman to dednce the élévations of other points pictured on the photographs.

With reference to flg. 35 we hâve: OO1 — horizon line, ff' = principal line, P = principal point, SP = focal length =/, variable for different pictures.

The ordinates au7, bb', and ce' = yx, 3/2, and y3, respectively.

The abscissæ of the three points a, 6, and c be xx, x2, and x3 respectively. ,

The horizontal angles included between the principal ray and the horizontal directions Sa', SI/, and SP = aly a2, and a3 respectively.

The azimuthal angles (between the meridian SN and the horizontal directions Sa', Sbf, and SP) = cp\, cp2, and <p3

Then a2 — «1 = cp2 — <p\= £1 and a3 — a2 = cp3 — cp2 — e2 The élévations of the points A, B, and G above the plane of

FiG. 35

reference or above the ground plane = Hi, H2, and R3

As the photographie plate MN had been exposed in vertical plane, it will be évident that for the three points a, b, and c pictured on the perspective MN, fig. 35—

X\ —f tan a x2 =/tan a2 x3 = f tan a3

or,

sin (a2 — Æi) cos ai cos a2

x2 — Xi=f (tan a% — tan ax) = /

and

sin (a3 — <^2) cos a3 cos a2

x3 — x2 = f (tan a3 — tan a2) = f

The values x2 — x\ and x3 — x2 may be scaled off directly on the photograph, and the values for a2 — ai and a3 — a2 may be taken from the field records of the observed angles.

Hence cos 012 may be computed from the équation cos ai

Xi — Xi _ cos sin (a2 — <*x)

x3 — x2 cos «1 sin (a3 — a2)

If we substitute tan y for — s <a'3

cos ai

and as

659

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