660

UNITED STATES COAST AND GEODETIC SUEVEY.

we may now write

^ cos «3

tan (46» + y) =_______008 a> = 008 + 008

1 — C0S a3 C0S al ~ C0S a3 COS (Xi

cos^ + ^cos"1--^

2 2i

sin sin ^ ~ g°

cot

“> + cot "> - “>

2

and tan *** a'3 = cot (45° + y) cot 013

2i 2

From this équation we compute ai + a3, and after subtracting

from

a3 — a2 = cp3 — q)2 — e2

we find

— ai = qh — cp\ — £1

<*1 — = <£>1 — <^3

knowing «i -f «3 and <*1 — we can readily find ai and a3, also,

a2 = a-! + fi or

We had found:

= a3 — f2

_Ta _ Tl -/ sin (”* - "0 -/ sin gl . bence l#2 - ^1) cos cos n2 J cos ax cos a2 J cos ai cos a2 J sin fi

7 sin • «»:, — a,) =f_sinjj_ whence/ = (*3 - «0 cos cos or,

cos a2 cos a2 cos a3 cos a2 sin e2

Tbus the abscissæ xu x2, and x3, (tbe principal line//7) and tbe focal length/may be found.

Witb the aid of the observed vertical angles fi the horizon line 00' may be located on the photograph. For example, if the vertical angle fi3 = c S c‘ had been observed to the point O, we find :

y3 = S& tan fi3

= 55iVan#>

f

The horizon line 00' will fall below the pictured point c by the vertical distance cQg — tan /?3, and for the point a the vertical distance to the horizon line would be

V i=

/

cos a i

tan fii

At least two vertical angles having been observed for each plate, the horizon line 00' may thus be located and marked upon the négative, when the principal point P may also be marked on 00' by means of the abscissæ Xi, x2, and x3 = a'P, b'P, and Pc', respectively.

(3) Method of Dr. O. Le Bon.—Dr. Le Bon, who used his instrument chiefly for the draughting of ancient buildings and monuments in India, provided the ground-glass plate of his caméra with a net of squares, each square having sides 1 centimeter long, the latter béing drawn parallel with the horizon—and principal lines, which latter two were subdivided into millimeters.

This arrangement enabled the operator to obtain the measurements of objects directly by inspection of the image on the (graduated) ground-glass plate. To détermine the dimensions of

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