John Adolphus Flemer. # An elementary treatise on phototopographic methods and instruments, including a concise review of executed phototopographic surveys and of publicatins on this subject online

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and center of projection, with reference to phototopography

we may premise, with reference to Fig. 2, Plate I:

A The picture plane VV (photographic plate) is sup-

posed to be vertical.

B Through the center of projection O (eye-point) a

horizontal plane HH is placed (" horizon plane").

C A vertical plane is laid through the center O, inter-

secting the picture plane at right angles in the line w;

it is the so-called " principal plane."

D A plane GG (" ground plane ") is placed parallel

with the horizon plane HH, but falls below it; the

distance OO between the two planes is equal to the

elevation of the point of view O (in the horizon plane)

above the datum plane (to which all elevations of

the survey are referred). The ground or datum

plane in iconometric plotting is identical with the

plan and it is represented by the surface of the paper

upon which the topographic map is being plotted.

The line of intersection gg, Fig. i, Plate I, of the ground plane

GG with the picture plane VV is known as the " ground line "

of the perspective.

38 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

The line of intersection hh, Fig. i, Plate I, of the horizon

plane HH with the picture plane VV is termed the " horizon

line " of the perspective.

The line of intersection vv of the plane (" principal plane ")

passing through O and intersecting the vertical picture plane VV

at right angles, Fig. 2, Plate I, is called the " principal line "

of the perspective.

The intersection O r of the two lines hh and w, Fig. 2, Plate I,

is the " principal point " of the perspective. It marks the point

of penetration in the picture plane of the " principal ray " OO f .

The principal ray is drawn from the center O (point of view

or nodal point) horizontally to intersect the picture plane VV

at right angles.

The point O\ where the vertical through the station O pierces

the ground plane GG is termed the " foot of the station."

The length of the principal ray OO', equal to the vertical

distance of the point of view O from the picture plane, is termed

the "distance line."

When the point of view coincides with the second nodal point

of a camera-lens this same line, the distance line, is known as

the "focal length" of the camera.

The perspective view a of a luminous point, A, Fig. 2, PL I,

in the vertical picture plane VV is identical with the point of pene-

tration of the visual ray OA, passing from the luminous point A

to the center of projection O (point of view or nodal point).

If we have several parallel vertical picture planes VV, V'V,

V"V", . . . , Fig. 3, PL II, the impression produced on the retina

of the eye at O will remain unchanged, no matter which plane

VV of the series may be retained in its position while the others

are removed.

All planes V'V', V"V",.;., placed parallel to the picture

plane VV are termed "front planes" and any line drawn in a

front plane will be parallel to the picture plane and is called a

"front line." Front planes may be placed either before or behind

the picture plane.

PHOTOGRAPHIC PERSPECTIVES. 39

The perspective view ab of a line AB is found in the vertical

picture plane VV, Fig. 4, PL II, by joining the perspectives a and b

of its end-points. The perspective ab of a line AB coincides

with the trace produced in the vertical picture plane VV by a plane

(so-called "visual plane") passing through O and AB', it is the

intersection of these two planes.

The perspective a, b, c, d, e of a curve A, B, C, D, E is found

by locating the perspectives of a series of its points, a, 6, c, d, e,

Fig. i, PL I, hi the vertical plane VV and drawing a continuous

curve through these points. The perspective of a curve may

also be obtained by locating the perspectives of a series of tangen-

tial lines enveloping the curve. The perspective of a curve

a, b, c, d, e is the intersection with the picture plane of that conical

visual plane which contains the curve A, B, C, D, E as trace

and which has its apex in O.

To draw the perspectives of the superficial planes of bodies,

the figures inclosing the same (f.L, the perspective of the pentagon

A, B, C, D, E, Fig. 4, PL II) are drawn in perspective by con-

structing the central projections of their perimeters.

The perspectives of parallel lines when produced will inter-

sect each other in one point, the so-called "vanishing point."

The perspectives of all horizontal lines (AB and A '', Fig. 5,

PL III) have their vanishing point (D) on the horizon line hh

in the picture plane VV.

Lines perpendicular to the picture plane have the principal

point of the perspective as vanishing point (in the picture plane).

Horizontal lines intersecting the picture plane under an angle

of 45 vanish in the so-called "distance points" on the horizon

line, one on either side of the principal point. Their distances

from the principal point are equal to the distance line of the per-

spective.

The so-called upper and lower distance points are the vanishing

points for lines falling within the principal plane or that are

parallel with it and which intersect the picture plane under an

angle of 45. The distances of these two points from the principal

40 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

point are likewise equal to the distance line of the perspec-

tive.

Lines parallel with the picture plane, lines in front planes,

have no vanishing points in the picture plane. Their perspectives

are lines parallel to the original lines.

Vertical lines (are parallel to the picture plane in our case)

have no vanishing points and their perspectives are parallel with

the principal line vv, Fig. 5, PI. III.

Horizontal lines when parallel with the picture plane have

perspectives that are parallel with the horizon line.

The scale of a front plane is the proportion between the per-

.spective and the original. It is expressed by the ratio between

the distances from the station (point of view) to the picture plane,

the distance line, and that to the figure's front plane (the plane

containing the original figure).

The relationship between object (prism ABCD-A f B'C'D'\

picture plane (VV), and ground plane (GG) may be shown more

clearly with reference to Fig. 5, PL III:

O is the station, eye-point, point of view, nodal point, etc.

A vertical line passing through O will intersect the ground plane

in O\. The point Oi is the orthogonal (vertical) projection in

horizontal plan of the station O and it is called the "foot of the

station" O.

The perspective a\ of a point A i', situated in the ground plane

GG, is obtained by joining the foot of the station O\ with the point

A i', erecting a perpendicular to the ground plane in the point of

intersection a\ of O\A\ with gg and joining O with A\ . The

intersection of the ray OA\ with the vertical a\a\ just mentioned

will be the perspective of the point AI' of the ground plane GG.

AAi being a vertical line in space, its perspective aa\ will be

paraUel with the line w, and, if we draw the ray OA, its inter-

section a with the line drawn parallel to vv through a\, previously

found, will be the perspective of A.

To find the perspective of a line AB, the perspectives a and b

of its terminal points A and B may be located in VV and joined

PHOTOGRAPHIC PERSPECTIVES. 41

by a straight line ab. Frequently it will be more convenient,

however, to use the intersection T of the line AB with the picture

plane VV together with the vanishing point D of the line ab to

locate the perspective ab of the line AB. This vanishing point D

is the intersection with the picture plane VV of a line drawn

through the station O and parallel with the line AB. If AB is

horizontal, the line OD will fall within the horizon plane and

intersect the horizon line hh at D.

The line TT' y which is the trace in the picture plane VV of

the plane ABA 'B', is termed the "vanishing line "of the plane

ABA'B'.

CHAPTER III.

PINHOLE PHOTOGRAPHY.

THE photographic camera produces perspectives upon the

photographic plate through the chemical action of the light

rays upon the sensitized film, and to establish the conditions

that are to be fulfilled, in order to regard a photograph as a true

perspective, we will first consider the so-called " pinhole pic-

tures," which are produced by a camera of the simplest form.

The pinhole camera consists of a box made entirely light-

tight with the exception of a minute hole O, Fig. 6, Plate IV,

in the front wall of the box. The rear side of the box is remov-

able and may be replaced by either a photographic plate-holder

or a ground-glass plate. With such a " camera obscura " photo-

graphs may be obtained without a lens or optical apparatus,

simply by means of the small round aperture O in the thin front

wall of the box.

I. Diameter of the Pinhole.

When exercising some care, the pinhole may be made by

burning it into a thin blackened cardboard with a needle heated

to red heat. The following table gives the diameter in inches

that may thus be burnt into the cardboard with needles of differ-

ent sizes:

Commercial number of sewing-needle 3 6 8 9

Diameter of burnt hole in inches 1/26 1/34 1/44 1/49

42

LENGTH OF EXPOSURE FOR PINHOLE CAMERAS.

43*

The best results, however, have been obtained with a round

hole carefully drilled into a sheet of copper or brass 0.2 mm.

thick. The border of the hole should be perfectly smooth, with-

out " burr," and it should be beveled that the hole forms a

truncated cone, the larger circle or base of the cone to face the

sensitized plate in the camera-box.

II. Length of Exposure.

The following table, published by F. C. Lambert, gives the

corresponding exposures, in minutes, for pinhole-camera expos-

ures, if, with the same plate-brand, identical illumination, same

subject, and a lens working at //i6, the correct exposure would

have been one second.

Distance of

Pinhole from

Diameter of Pinhole, in Inches.

the Sensitized

Plate Surface, in

Inches:

1/5

1/44

I/3S

1/25

6

6

4-5

8

10

8

c

10

16

13

8

12

24

18

12

6

14

3 2

24

15

8

16

40

3 2

2O

IO

18

4i

26

*3

20

32

16

24

24

This table plainly indicates that there is little danger of over-

exposing a plate in the pinhole camera, particularly as these

exposures are not strictly limited to the time given in the table;

they depend greatly on the general character of the plate, on the

developer, and on the general conditions of illumination during

the exposure, thus giving the operator a wide range regarding the

time limit erf the exposure.

44 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

III. Focal Lengths of Pinhole Cameras.

The depth of focus is practically unlimited, as shown in the

preceding table of F. C. Lambert. Still, there will always be a

certain distance between image plane and pinhole that will give

the best result for a given aperture, and Capt. Colson recom-

mends the following focal distances for a set of apertures of

four different sizes:

Diameter of pinhole in millimeters 0.3 0.4 0.5 0.6

The best definition is at a focal length, in centimeters . . . 1 1 20 30 44

Using the focal length corresponding to the size of aperture,

as given in the above table, the time of exposure for a plate in the

pinhole camera, compared with the exposure required when using

a lens under identical conditions and with a medium stop, may

be generally accepted to be:

25 50 100 200 times longer for a diameter of hole of:

0.3 0.4 0.5 0.6 mm.

The size of a pictured object, when photographed in a pin-

hole camera, is proportional to the ratio between the distance

of the object from the camera and the distance from the pin-

hole to the sensitized film surface.

IV. Determination of the Values of the Pinhole-camera Constants.

It will be a simple matter to determine the values of the con-

stants of a pinhole camera that are required to be known for

making iconometric constructions.

If the angles of the box are exactly 90, if the aperture is in

the point of intersection of the diagonals of the camera front,

and if means are provided for setting the camera level (for exposing

the plate in vertical plane), the two lines joining the opposite

VALUES OF THE PINHOLE-CAMERA CONSTANTS. 45

middles of the four sides which compose the rear frame of the

box will represent the horizon line (HH) and the principal

line (VV) of the photographic perspective. The intersection (P)

of these two lines will be the principal point and the distance (OP)

between the aperture and the sensitive film surface will be the

constant focal length or the distance line of the photographic

perspective a, b, c, Fig. 6, Plate IV.

By referring to Fig. 6, Plate IV, it will readily be seen that

the rays of an object A, B, C, after passing through the aper-

ture O, produce an inverted image a, b, c on the photographic

plate. The image obtained in a pinhole camera originates in

the same way as a perspective is drawn, with the exception

that the picture plane V'V is not interposed between the eye-

point O and the original A, B, C, but is here placed behind the

eye-point, at a distance PO equal to OP', producing an inverted

and reduced image a, b, c of the original A, B, C.

By introducing the " negative " with the image a, b, c between

the eye-point O and the original A, B, C at V'V, Fig. 6, Plate IV,

and at a distance from O equal OP' = OP (in- and reverted),

it would become a " positive." P' being in the prolongation

of the distance line OP and VV intersecting the line OP' at

right angles, the line hh of the " positive " will be horizontal

and w vertical. The point a will again be in the point of inter-

section of the light-ray OA, the point b in the intersection of

the light-ray OB, and the point c in the intersection of the light-

ray OC with the plane of the positive VV. A positive copy

of a negative will be as true a perspective of the original as the

negative. Negatives, however, may be used for obtaining any

measurements that may be required from the perspective for

the iconometric plotting. Measurements are often preferably

made on the negatives, as the production of the positives without

distortion requires considerable care and experience, the amount

of distortion depending greatly on the character of the material

on which the positives are made.

The data given in this chapter may prove useful when a

46 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

pinhole camera is selected for phototopographic or photogram-

metric experimental studies in case of an emergency, or when

the cost of the apparatus must be considered, the pinhole camera

being recommendable chiefly on account of its cheapness and

simplicity.

CHAPTER IV.

THE FUNDAMENTAL PRINCIPLES OF ICONOMETRIC MAP-

PLOTTING ("ICONOMETRY").

UNDER " iconometry " we understand the measuring of

dimensions of objects from their perspective views (" Bildmess-

kunst "). It refers to the plotting of terrene forms directly on

the plotting-sheet from the photographs of the landscape.

If a photographic perspective of an object, the focal length

(" distance line "), the second nodal point (" principal point ")

of the camera-lens, and the horizon line of the perspective are

given if the point of view and the central projection of an object

are given these data will be insufficient for the determination

of the object with reference to position and size.

If, however, two such perspectives of the same object, obtained

from two suitably located stations, be given, the dimensions of

the object and its position with reference to the two stations may

be determined iconometrically, very much in a manner analogous

to that in which a point is located (by intersection or by the so-

called radial method) on the plane-table sheet by being observed

upon from two known plane-table stations.

I. Orienting the Picture Traces on the Plotting-sheet.

The positions of two camera stations A and A', their linear

horizontal distance A A' and two photographs, exposed in ver-

tical plane, one from each station, may be given. Each picture

may, furthermore, contain the image / of the same object 7*

and the image a of the other camera station, Fig. 7, Plate IV.

47

48 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

After the base line A A' has been laid down in reduced scale

AiA^ y Fig. 7, Plate IV, and the pictures MN and M'N' are

brought into the same relative positions with reference to the

line AiAi', which they had with reference to the base line AA f

in the field at the time of their exposure, the position T of the

point pictured as / and t' on the respective pictures MN and

M'N' may be located (with reference to the line A\Ai f ) by

drawing the radials A\t and A^ti ', when their point of intersec-

tion will fix the relative position of T with reference to A\ and A.

The position of T on the map, plotted to scale with refer-

ence to the reduced base line or with reference to the plotted

stations A\ and A\', would be found by projecting the point

of intersection T into the plotting or ground plane.

A topographic map being the orthogonal projection of the

terrene forms into horizontal plan, the horizontal projections

into the plotting-plane of the rays A\t, A\a\ f , A\1f, and A\a are

used to locate the plotted positions of pictured points / and a

and the horizontal projections of the picture planes (which now

become " picture traces ") are utilized in this connection, instead

of actually using the pictures in the iconometric plotting as was

indicated in the diagram of Fig. 7, Plate IV.

In order, therefore, to plot the horizontal projection T\ of

a pictured point / with reference to the plotted base line A\A\' >

it will become necessary to ascertain the correct positions of

the picture traces with reference to A\ and -4i' it will become

necessary to " orient " the picture traces hh and h'h', Fig. 8,

Plate V.

This orientation of the picture traces forms a very important

part in iconometric plotting, as the subsequent fixing of loca-

tions of pictured points is accomplished mainly by bringing

the horizontal projections of their radials (lines of horizontal

directions drawn from the different stations to identical terrene

points) to intersect. Any error in the orientation of the picture

trace produces corresponding errors in the plotted positions of

pictured points.

ORIENTING THE PICTURE TRACES ON THE PLOTTING SHEET. 49

A. Iconometric Plotting when using a Surveying Camera only.

A base line measured in the field may have been plotted to

scale, AiAi', Fig. 8, Plate V, and two pictures, MN and M'N',

Fig. 9, Plate V, may have been obtained from the camera sta-

tions A and A' respectively by means of a surveying camera.

The focal lengths of the pictures =/ and /' respectively, the

positions of the principal points P and P f and the horizon lines

HH and H'H' may be known. It is desired to locate T\ with

reference to the plotted base line A\Ai f .

Wehave4iPi=/; 4i'Pi'=/'; the length of the base =4i4i',

and the abscissa /iP = /iPi, *i'P' =/i'Pi', Pa/ =Pia/, P'a l = Pi'a lf

Figs. 8 and 9, Plate V.

The distances A\ai'j and Ai'ai, Fig. 8, may be found graph-

ically by constructing the right- angle triangles A \P\a\ and

Ai'Pi'ai, or they may be computed from

These distances are laid off upon A\A\ from A\ and from A\'

respectively a semicircle is described over each length, A\a\

and Aidi, and two circles are drawn about A\ and A\ with

/ and f respectively as radii. The intersections of these two

pairs of circles will locate the horizontal projections PI and P\

of the principal points P and P' on the two picture traces hh

and h'hf, the latter being represented by the tangents P\a\

and Pi'ai.

B. Plotting the Picture-trace when using a Camera or

Phototheodolite.

In this case the angles a and a', Fig. 8, Plate V, may be

measured directly in the field and plotted on the base line AiAi',

a at A i and a' at A\ . We lay off the distances

and

50 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

(found by construction or computation) and describe circles

about A i and A i with / and /' respectively as radii. The

tangents drawn from a\ and a\ to these circles will locate P\

and PI respectively when PI/I should equal tiP=x, measured

on the picture MN, and PiV = PV=^ on M'N'.

When using a phototheodolite a well-defined point T may

be bisected with the principal lines VV and F'F', Fig. 9, Plate V,

from the two stations A and AI, in which case these angles of

orientation are laid off upon the base line at AI and at AI re-

spectively, and the distances / and /' are laid off on the lines

AiTi and A l r T l respectively (=A 1 P ] _ and =A l 'P l '), when the

perpendiculars to A\P\ in PI and to A\P\ in P\ will represent

the picture traces hh and h'hf in correct orientation with refer-

ence to AI, AI, and T\.

When the pictures of several triangulation points B, C, and D

and the base line are given, the orientation of the picture traces

hh and h'h' upon the plotting-sheet may be accomplished as

follows :

The radials A\B\, Aid, A\D\ . . . , as well as the radials

A\B\, Ai'Ci, Ai'Di . . . , are drawn upon the iconometric plot-

ting-sheet, the points BI, C\, DI . . . being already plotted on

the same. The points 61, ci, P, d\, and a\ are then transferred

from the horizon line OO\ of the photographic perspective MN,

Fig. n, Plate VI, upon the perfectly straight edge of a strip

of paper, which now is placed upon the radials converging to A\,

as a center, Fig. 10, Plate V, and moved about until

bi falls upon the radial line

r tt (i n ( ( tt

c\

" " " " "

" " " base "

The line A\P\ should then be perpendicular to the straight

edge hh of the paper strip, Fig. 10, Plate V, and the line hh,

drawn along the paper strip's edge on the plotting-sheet will

DETERMINATION OF PRINCIPAL. AND HORIZON LINES. 51

i

represent the oriented picture trace of M,N\ A\P\ will be the

distance line and PI the horizontal projection of the principal

point P.

The same having been done regarding the point A\ r , its

picture M'N' and the paper strip OiO/ (Fig. n, Plate VI),

both picture traces hh and h'h' will have been oriented. The

plotted positions of any other pictured points that may be iden-

tified on both pictures MN and M'N' may be similarly located

by plotting their abscissae (measured on the horizon lines OOi

and O'Oi') upon the picture traces hh and h'h r (Fig. 10, Plate V)

on the proper sides of the principal points PI and PI'.

Lines drawn from the station points A\A\ through such

corresponding points, transferred to their respective picture

traces, will locate the relative positions of such points on the

plotting-sheet by their points of intersection.

II. Arithmetical Determination of the Principal and of the

Horizon Line on the Photographic Perspectives.

In the preceding paragraphs it has been assumed that the

photographic perspectives were already provided with the prin-

cipal and the horizon lines. Such, in point of fact, would be

the case with an adjusted surveying camera or phototheodolite.

If the instrument is out of adjustment or if an ordinary camera

be used (one provided with a device for maintaining the image

plane in a vertical position during the exposure of the plate),

the correct positions of the principal and horizon lines, as well

as the length of the distance line, must be ascertained. In photo-

topographic work this may be accomplished in various ways.

A. Determination of the Principal Point and Distance Line of

the Photographic Perspective.

A plumb line suspended in front of the camera in such a

way that the line iru, Fig. 12, Plate VI, may be photographed

52 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

upon the negative will serve to establish the direction of the

principal line on the trial plate. This negative may, further-

more, contain the images a, b, c ... of three or more points A y

B, C, . . . of known positions and elevations. A line hh is drawn

at right angles to the pictured plumb line w on the photographic

perspective and a strip of paper is placed with its straight edge

along this line. The images a, b, c ... of the known points

A, B, C . . . are projected upon the paper straight edge, held

in position at hh, by drawing parallels to vv through these pic-

tured points.

After the radials from the plotted station Si, Fig. 12, Plate VI r

have been drawn through the plotted points A\, BI, C\ . . .

the paper strip is adjusted upon those radials in such manner

that the image projections ai, bi, c\ . . . (previously marked

we may premise, with reference to Fig. 2, Plate I:

A The picture plane VV (photographic plate) is sup-

posed to be vertical.

B Through the center of projection O (eye-point) a

horizontal plane HH is placed (" horizon plane").

C A vertical plane is laid through the center O, inter-

secting the picture plane at right angles in the line w;

it is the so-called " principal plane."

D A plane GG (" ground plane ") is placed parallel

with the horizon plane HH, but falls below it; the

distance OO between the two planes is equal to the

elevation of the point of view O (in the horizon plane)

above the datum plane (to which all elevations of

the survey are referred). The ground or datum

plane in iconometric plotting is identical with the

plan and it is represented by the surface of the paper

upon which the topographic map is being plotted.

The line of intersection gg, Fig. i, Plate I, of the ground plane

GG with the picture plane VV is known as the " ground line "

of the perspective.

38 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

The line of intersection hh, Fig. i, Plate I, of the horizon

plane HH with the picture plane VV is termed the " horizon

line " of the perspective.

The line of intersection vv of the plane (" principal plane ")

passing through O and intersecting the vertical picture plane VV

at right angles, Fig. 2, Plate I, is called the " principal line "

of the perspective.

The intersection O r of the two lines hh and w, Fig. 2, Plate I,

is the " principal point " of the perspective. It marks the point

of penetration in the picture plane of the " principal ray " OO f .

The principal ray is drawn from the center O (point of view

or nodal point) horizontally to intersect the picture plane VV

at right angles.

The point O\ where the vertical through the station O pierces

the ground plane GG is termed the " foot of the station."

The length of the principal ray OO', equal to the vertical

distance of the point of view O from the picture plane, is termed

the "distance line."

When the point of view coincides with the second nodal point

of a camera-lens this same line, the distance line, is known as

the "focal length" of the camera.

The perspective view a of a luminous point, A, Fig. 2, PL I,

in the vertical picture plane VV is identical with the point of pene-

tration of the visual ray OA, passing from the luminous point A

to the center of projection O (point of view or nodal point).

If we have several parallel vertical picture planes VV, V'V,

V"V", . . . , Fig. 3, PL II, the impression produced on the retina

of the eye at O will remain unchanged, no matter which plane

VV of the series may be retained in its position while the others

are removed.

All planes V'V', V"V",.;., placed parallel to the picture

plane VV are termed "front planes" and any line drawn in a

front plane will be parallel to the picture plane and is called a

"front line." Front planes may be placed either before or behind

the picture plane.

PHOTOGRAPHIC PERSPECTIVES. 39

The perspective view ab of a line AB is found in the vertical

picture plane VV, Fig. 4, PL II, by joining the perspectives a and b

of its end-points. The perspective ab of a line AB coincides

with the trace produced in the vertical picture plane VV by a plane

(so-called "visual plane") passing through O and AB', it is the

intersection of these two planes.

The perspective a, b, c, d, e of a curve A, B, C, D, E is found

by locating the perspectives of a series of its points, a, 6, c, d, e,

Fig. i, PL I, hi the vertical plane VV and drawing a continuous

curve through these points. The perspective of a curve may

also be obtained by locating the perspectives of a series of tangen-

tial lines enveloping the curve. The perspective of a curve

a, b, c, d, e is the intersection with the picture plane of that conical

visual plane which contains the curve A, B, C, D, E as trace

and which has its apex in O.

To draw the perspectives of the superficial planes of bodies,

the figures inclosing the same (f.L, the perspective of the pentagon

A, B, C, D, E, Fig. 4, PL II) are drawn in perspective by con-

structing the central projections of their perimeters.

The perspectives of parallel lines when produced will inter-

sect each other in one point, the so-called "vanishing point."

The perspectives of all horizontal lines (AB and A '', Fig. 5,

PL III) have their vanishing point (D) on the horizon line hh

in the picture plane VV.

Lines perpendicular to the picture plane have the principal

point of the perspective as vanishing point (in the picture plane).

Horizontal lines intersecting the picture plane under an angle

of 45 vanish in the so-called "distance points" on the horizon

line, one on either side of the principal point. Their distances

from the principal point are equal to the distance line of the per-

spective.

The so-called upper and lower distance points are the vanishing

points for lines falling within the principal plane or that are

parallel with it and which intersect the picture plane under an

angle of 45. The distances of these two points from the principal

40 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

point are likewise equal to the distance line of the perspec-

tive.

Lines parallel with the picture plane, lines in front planes,

have no vanishing points in the picture plane. Their perspectives

are lines parallel to the original lines.

Vertical lines (are parallel to the picture plane in our case)

have no vanishing points and their perspectives are parallel with

the principal line vv, Fig. 5, PI. III.

Horizontal lines when parallel with the picture plane have

perspectives that are parallel with the horizon line.

The scale of a front plane is the proportion between the per-

.spective and the original. It is expressed by the ratio between

the distances from the station (point of view) to the picture plane,

the distance line, and that to the figure's front plane (the plane

containing the original figure).

The relationship between object (prism ABCD-A f B'C'D'\

picture plane (VV), and ground plane (GG) may be shown more

clearly with reference to Fig. 5, PL III:

O is the station, eye-point, point of view, nodal point, etc.

A vertical line passing through O will intersect the ground plane

in O\. The point Oi is the orthogonal (vertical) projection in

horizontal plan of the station O and it is called the "foot of the

station" O.

The perspective a\ of a point A i', situated in the ground plane

GG, is obtained by joining the foot of the station O\ with the point

A i', erecting a perpendicular to the ground plane in the point of

intersection a\ of O\A\ with gg and joining O with A\ . The

intersection of the ray OA\ with the vertical a\a\ just mentioned

will be the perspective of the point AI' of the ground plane GG.

AAi being a vertical line in space, its perspective aa\ will be

paraUel with the line w, and, if we draw the ray OA, its inter-

section a with the line drawn parallel to vv through a\, previously

found, will be the perspective of A.

To find the perspective of a line AB, the perspectives a and b

of its terminal points A and B may be located in VV and joined

PHOTOGRAPHIC PERSPECTIVES. 41

by a straight line ab. Frequently it will be more convenient,

however, to use the intersection T of the line AB with the picture

plane VV together with the vanishing point D of the line ab to

locate the perspective ab of the line AB. This vanishing point D

is the intersection with the picture plane VV of a line drawn

through the station O and parallel with the line AB. If AB is

horizontal, the line OD will fall within the horizon plane and

intersect the horizon line hh at D.

The line TT' y which is the trace in the picture plane VV of

the plane ABA 'B', is termed the "vanishing line "of the plane

ABA'B'.

CHAPTER III.

PINHOLE PHOTOGRAPHY.

THE photographic camera produces perspectives upon the

photographic plate through the chemical action of the light

rays upon the sensitized film, and to establish the conditions

that are to be fulfilled, in order to regard a photograph as a true

perspective, we will first consider the so-called " pinhole pic-

tures," which are produced by a camera of the simplest form.

The pinhole camera consists of a box made entirely light-

tight with the exception of a minute hole O, Fig. 6, Plate IV,

in the front wall of the box. The rear side of the box is remov-

able and may be replaced by either a photographic plate-holder

or a ground-glass plate. With such a " camera obscura " photo-

graphs may be obtained without a lens or optical apparatus,

simply by means of the small round aperture O in the thin front

wall of the box.

I. Diameter of the Pinhole.

When exercising some care, the pinhole may be made by

burning it into a thin blackened cardboard with a needle heated

to red heat. The following table gives the diameter in inches

that may thus be burnt into the cardboard with needles of differ-

ent sizes:

Commercial number of sewing-needle 3 6 8 9

Diameter of burnt hole in inches 1/26 1/34 1/44 1/49

42

LENGTH OF EXPOSURE FOR PINHOLE CAMERAS.

43*

The best results, however, have been obtained with a round

hole carefully drilled into a sheet of copper or brass 0.2 mm.

thick. The border of the hole should be perfectly smooth, with-

out " burr," and it should be beveled that the hole forms a

truncated cone, the larger circle or base of the cone to face the

sensitized plate in the camera-box.

II. Length of Exposure.

The following table, published by F. C. Lambert, gives the

corresponding exposures, in minutes, for pinhole-camera expos-

ures, if, with the same plate-brand, identical illumination, same

subject, and a lens working at //i6, the correct exposure would

have been one second.

Distance of

Pinhole from

Diameter of Pinhole, in Inches.

the Sensitized

Plate Surface, in

Inches:

1/5

1/44

I/3S

1/25

6

6

4-5

8

10

8

c

10

16

13

8

12

24

18

12

6

14

3 2

24

15

8

16

40

3 2

2O

IO

18

4i

26

*3

20

32

16

24

24

This table plainly indicates that there is little danger of over-

exposing a plate in the pinhole camera, particularly as these

exposures are not strictly limited to the time given in the table;

they depend greatly on the general character of the plate, on the

developer, and on the general conditions of illumination during

the exposure, thus giving the operator a wide range regarding the

time limit erf the exposure.

44 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

III. Focal Lengths of Pinhole Cameras.

The depth of focus is practically unlimited, as shown in the

preceding table of F. C. Lambert. Still, there will always be a

certain distance between image plane and pinhole that will give

the best result for a given aperture, and Capt. Colson recom-

mends the following focal distances for a set of apertures of

four different sizes:

Diameter of pinhole in millimeters 0.3 0.4 0.5 0.6

The best definition is at a focal length, in centimeters . . . 1 1 20 30 44

Using the focal length corresponding to the size of aperture,

as given in the above table, the time of exposure for a plate in the

pinhole camera, compared with the exposure required when using

a lens under identical conditions and with a medium stop, may

be generally accepted to be:

25 50 100 200 times longer for a diameter of hole of:

0.3 0.4 0.5 0.6 mm.

The size of a pictured object, when photographed in a pin-

hole camera, is proportional to the ratio between the distance

of the object from the camera and the distance from the pin-

hole to the sensitized film surface.

IV. Determination of the Values of the Pinhole-camera Constants.

It will be a simple matter to determine the values of the con-

stants of a pinhole camera that are required to be known for

making iconometric constructions.

If the angles of the box are exactly 90, if the aperture is in

the point of intersection of the diagonals of the camera front,

and if means are provided for setting the camera level (for exposing

the plate in vertical plane), the two lines joining the opposite

VALUES OF THE PINHOLE-CAMERA CONSTANTS. 45

middles of the four sides which compose the rear frame of the

box will represent the horizon line (HH) and the principal

line (VV) of the photographic perspective. The intersection (P)

of these two lines will be the principal point and the distance (OP)

between the aperture and the sensitive film surface will be the

constant focal length or the distance line of the photographic

perspective a, b, c, Fig. 6, Plate IV.

By referring to Fig. 6, Plate IV, it will readily be seen that

the rays of an object A, B, C, after passing through the aper-

ture O, produce an inverted image a, b, c on the photographic

plate. The image obtained in a pinhole camera originates in

the same way as a perspective is drawn, with the exception

that the picture plane V'V is not interposed between the eye-

point O and the original A, B, C, but is here placed behind the

eye-point, at a distance PO equal to OP', producing an inverted

and reduced image a, b, c of the original A, B, C.

By introducing the " negative " with the image a, b, c between

the eye-point O and the original A, B, C at V'V, Fig. 6, Plate IV,

and at a distance from O equal OP' = OP (in- and reverted),

it would become a " positive." P' being in the prolongation

of the distance line OP and VV intersecting the line OP' at

right angles, the line hh of the " positive " will be horizontal

and w vertical. The point a will again be in the point of inter-

section of the light-ray OA, the point b in the intersection of

the light-ray OB, and the point c in the intersection of the light-

ray OC with the plane of the positive VV. A positive copy

of a negative will be as true a perspective of the original as the

negative. Negatives, however, may be used for obtaining any

measurements that may be required from the perspective for

the iconometric plotting. Measurements are often preferably

made on the negatives, as the production of the positives without

distortion requires considerable care and experience, the amount

of distortion depending greatly on the character of the material

on which the positives are made.

The data given in this chapter may prove useful when a

46 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

pinhole camera is selected for phototopographic or photogram-

metric experimental studies in case of an emergency, or when

the cost of the apparatus must be considered, the pinhole camera

being recommendable chiefly on account of its cheapness and

simplicity.

CHAPTER IV.

THE FUNDAMENTAL PRINCIPLES OF ICONOMETRIC MAP-

PLOTTING ("ICONOMETRY").

UNDER " iconometry " we understand the measuring of

dimensions of objects from their perspective views (" Bildmess-

kunst "). It refers to the plotting of terrene forms directly on

the plotting-sheet from the photographs of the landscape.

If a photographic perspective of an object, the focal length

(" distance line "), the second nodal point (" principal point ")

of the camera-lens, and the horizon line of the perspective are

given if the point of view and the central projection of an object

are given these data will be insufficient for the determination

of the object with reference to position and size.

If, however, two such perspectives of the same object, obtained

from two suitably located stations, be given, the dimensions of

the object and its position with reference to the two stations may

be determined iconometrically, very much in a manner analogous

to that in which a point is located (by intersection or by the so-

called radial method) on the plane-table sheet by being observed

upon from two known plane-table stations.

I. Orienting the Picture Traces on the Plotting-sheet.

The positions of two camera stations A and A', their linear

horizontal distance A A' and two photographs, exposed in ver-

tical plane, one from each station, may be given. Each picture

may, furthermore, contain the image / of the same object 7*

and the image a of the other camera station, Fig. 7, Plate IV.

47

48 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

After the base line A A' has been laid down in reduced scale

AiA^ y Fig. 7, Plate IV, and the pictures MN and M'N' are

brought into the same relative positions with reference to the

line AiAi', which they had with reference to the base line AA f

in the field at the time of their exposure, the position T of the

point pictured as / and t' on the respective pictures MN and

M'N' may be located (with reference to the line A\Ai f ) by

drawing the radials A\t and A^ti ', when their point of intersec-

tion will fix the relative position of T with reference to A\ and A.

The position of T on the map, plotted to scale with refer-

ence to the reduced base line or with reference to the plotted

stations A\ and A\', would be found by projecting the point

of intersection T into the plotting or ground plane.

A topographic map being the orthogonal projection of the

terrene forms into horizontal plan, the horizontal projections

into the plotting-plane of the rays A\t, A\a\ f , A\1f, and A\a are

used to locate the plotted positions of pictured points / and a

and the horizontal projections of the picture planes (which now

become " picture traces ") are utilized in this connection, instead

of actually using the pictures in the iconometric plotting as was

indicated in the diagram of Fig. 7, Plate IV.

In order, therefore, to plot the horizontal projection T\ of

a pictured point / with reference to the plotted base line A\A\' >

it will become necessary to ascertain the correct positions of

the picture traces with reference to A\ and -4i' it will become

necessary to " orient " the picture traces hh and h'h', Fig. 8,

Plate V.

This orientation of the picture traces forms a very important

part in iconometric plotting, as the subsequent fixing of loca-

tions of pictured points is accomplished mainly by bringing

the horizontal projections of their radials (lines of horizontal

directions drawn from the different stations to identical terrene

points) to intersect. Any error in the orientation of the picture

trace produces corresponding errors in the plotted positions of

pictured points.

ORIENTING THE PICTURE TRACES ON THE PLOTTING SHEET. 49

A. Iconometric Plotting when using a Surveying Camera only.

A base line measured in the field may have been plotted to

scale, AiAi', Fig. 8, Plate V, and two pictures, MN and M'N',

Fig. 9, Plate V, may have been obtained from the camera sta-

tions A and A' respectively by means of a surveying camera.

The focal lengths of the pictures =/ and /' respectively, the

positions of the principal points P and P f and the horizon lines

HH and H'H' may be known. It is desired to locate T\ with

reference to the plotted base line A\Ai f .

Wehave4iPi=/; 4i'Pi'=/'; the length of the base =4i4i',

and the abscissa /iP = /iPi, *i'P' =/i'Pi', Pa/ =Pia/, P'a l = Pi'a lf

Figs. 8 and 9, Plate V.

The distances A\ai'j and Ai'ai, Fig. 8, may be found graph-

ically by constructing the right- angle triangles A \P\a\ and

Ai'Pi'ai, or they may be computed from

These distances are laid off upon A\A\ from A\ and from A\'

respectively a semicircle is described over each length, A\a\

and Aidi, and two circles are drawn about A\ and A\ with

/ and f respectively as radii. The intersections of these two

pairs of circles will locate the horizontal projections PI and P\

of the principal points P and P' on the two picture traces hh

and h'hf, the latter being represented by the tangents P\a\

and Pi'ai.

B. Plotting the Picture-trace when using a Camera or

Phototheodolite.

In this case the angles a and a', Fig. 8, Plate V, may be

measured directly in the field and plotted on the base line AiAi',

a at A i and a' at A\ . We lay off the distances

and

50 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

(found by construction or computation) and describe circles

about A i and A i with / and /' respectively as radii. The

tangents drawn from a\ and a\ to these circles will locate P\

and PI respectively when PI/I should equal tiP=x, measured

on the picture MN, and PiV = PV=^ on M'N'.

When using a phototheodolite a well-defined point T may

be bisected with the principal lines VV and F'F', Fig. 9, Plate V,

from the two stations A and AI, in which case these angles of

orientation are laid off upon the base line at AI and at AI re-

spectively, and the distances / and /' are laid off on the lines

AiTi and A l r T l respectively (=A 1 P ] _ and =A l 'P l '), when the

perpendiculars to A\P\ in PI and to A\P\ in P\ will represent

the picture traces hh and h'hf in correct orientation with refer-

ence to AI, AI, and T\.

When the pictures of several triangulation points B, C, and D

and the base line are given, the orientation of the picture traces

hh and h'h' upon the plotting-sheet may be accomplished as

follows :

The radials A\B\, Aid, A\D\ . . . , as well as the radials

A\B\, Ai'Ci, Ai'Di . . . , are drawn upon the iconometric plot-

ting-sheet, the points BI, C\, DI . . . being already plotted on

the same. The points 61, ci, P, d\, and a\ are then transferred

from the horizon line OO\ of the photographic perspective MN,

Fig. n, Plate VI, upon the perfectly straight edge of a strip

of paper, which now is placed upon the radials converging to A\,

as a center, Fig. 10, Plate V, and moved about until

bi falls upon the radial line

r tt (i n ( ( tt

c\

" " " " "

" " " base "

The line A\P\ should then be perpendicular to the straight

edge hh of the paper strip, Fig. 10, Plate V, and the line hh,

drawn along the paper strip's edge on the plotting-sheet will

DETERMINATION OF PRINCIPAL. AND HORIZON LINES. 51

i

represent the oriented picture trace of M,N\ A\P\ will be the

distance line and PI the horizontal projection of the principal

point P.

The same having been done regarding the point A\ r , its

picture M'N' and the paper strip OiO/ (Fig. n, Plate VI),

both picture traces hh and h'h' will have been oriented. The

plotted positions of any other pictured points that may be iden-

tified on both pictures MN and M'N' may be similarly located

by plotting their abscissae (measured on the horizon lines OOi

and O'Oi') upon the picture traces hh and h'h r (Fig. 10, Plate V)

on the proper sides of the principal points PI and PI'.

Lines drawn from the station points A\A\ through such

corresponding points, transferred to their respective picture

traces, will locate the relative positions of such points on the

plotting-sheet by their points of intersection.

II. Arithmetical Determination of the Principal and of the

Horizon Line on the Photographic Perspectives.

In the preceding paragraphs it has been assumed that the

photographic perspectives were already provided with the prin-

cipal and the horizon lines. Such, in point of fact, would be

the case with an adjusted surveying camera or phototheodolite.

If the instrument is out of adjustment or if an ordinary camera

be used (one provided with a device for maintaining the image

plane in a vertical position during the exposure of the plate),

the correct positions of the principal and horizon lines, as well

as the length of the distance line, must be ascertained. In photo-

topographic work this may be accomplished in various ways.

A. Determination of the Principal Point and Distance Line of

the Photographic Perspective.

A plumb line suspended in front of the camera in such a

way that the line iru, Fig. 12, Plate VI, may be photographed

52 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

upon the negative will serve to establish the direction of the

principal line on the trial plate. This negative may, further-

more, contain the images a, b, c ... of three or more points A y

B, C, . . . of known positions and elevations. A line hh is drawn

at right angles to the pictured plumb line w on the photographic

perspective and a strip of paper is placed with its straight edge

along this line. The images a, b, c ... of the known points

A, B, C . . . are projected upon the paper straight edge, held

in position at hh, by drawing parallels to vv through these pic-

tured points.

After the radials from the plotted station Si, Fig. 12, Plate VI r

have been drawn through the plotted points A\, BI, C\ . . .

the paper strip is adjusted upon those radials in such manner

that the image projections ai, bi, c\ . . . (previously marked