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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intersections " may be employed with advantage.

GRAPHICAL ICONOMETRICAL PLOTTING METHODS. 143

With this method the base line its horizontal projection

being either too short or more frequently falling into the same

direction with the distant points to be located by the intersec-

tions of lines of direction is projected upon a vertical plane.

The greater the difference in elevation between the two sta-

tions the greater will the length of this vertically projected base

line be and the more accurate will be the iconometric location

of the points by lines of direction.

We have, with reference to Fig. 63, Plate XXXIII, two camera

stations A and 5, two photographs AN and BN obtained from

them and containing the image d A and ds of the identical geodetic

point D. It is assumed that the horizon plane through the

lower station B be the ground or plotting plane, and that the

principal plane of the photograph AN be the vertical plane of

projection which is revolved about its trace into the horizon

plane of B.

a = horizontal projection of station A\

aB= horizontal projection of the base line AB\

H AB H' AB = picture trace of photograph AN in horizon plane

of B (plotting-plane) ;

H B H B ' = picture trace of photograph BN in horizon plane of B\

aP A '=BP B ' = constant focal length of the negatives AN

and B N ]

aP A = trace of principal plane passing through aP A ' in

horizon plane of B.

To plot the position d f of a point D (pictured in AN as d A

and in BN as dp) in the plotting-plane the rays Ad A and Bd B

are projected upon the vertical plane (revolved about aP A ' into

the ground plane), when (di) will represent their point of inter-

section d projected into that same vertical plane (revolved about

aP A r into the plotting-plane).

The ray Ad A =AD intersects or penetrates the picture plane

A N at a distance =d A d f AB vertically above the ground plane

(above the picture trace or ground line H AB H' AB of picture A N ).

144 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

This ordinate is laid off upon P A 'H AB = P A '(d A ), when d A

will be the projection on the vertical plane of pictured point d A .

The vertical through a projected upon the vertical plane is

represented as a(A), and if we make

a(A)=P A P' AB (picture ,4 AT)

= difference in elevation between the two stations B and A,

(A) will be the upper camera station A projected into the ver-

tical plane, and the line (A)(d A ) will be the projection of the

ray Ad A , or AD, upon the vertical plane (revolved about aP A

into the plotting-plane).

The ray Bd B =BD intersects the second picture plane B N

in d B . If we draw through d B (projection of d B on ground line

H B H B ') a perpendicular to aP A =d B 'di B , d\ B will be the pro-

jection in the vertical plane of the horizontal projection in the

picture trace of the pictured point d B . Producing d B d\ B beyond

d\ B and making di B (d B )=d B d B (measured on the negative B N )

will locate at (d B ) the projection of the pictured point d B upon

the vertical plane.

The perpendicular to aP A ' through B locates the projection

into the vertical plane = bi of the plotted station B, hence the

line bi(d B ) will be the projection into the vertical plane of the

ray Bd B =BD.

The intersection (d\) of bi(d B ) with A(d A ) locates the pro-

jection into vertical plane of the point d, and the horizontal pro-

jection of the point D (plotted on the ground plan) will be on

the line (d\)d', which is the vertical through d (perpendicular

to aP A in our case) passing through (d\) and produced beyond

di, and either horizontal line of direction ad A or Bd B , produced

to intersect this perpendicular (di)di, will locate the position d f

(of the point D) on the plotting-sheet with reference to the plotted

stations A (or a) and B.

(The location of d' as the intersection of the horizontal direc-

tions ad A ' and Bd B would not be very accurate in our case,

and far less so for points pictured on the other side of the prin-

GRAPHICAL ICONOMETRICAL PLOTTING METHODS. 145

cipal point P B , the angle of intersection of their horizontal direc-

tions being even smaller than at d'.)

The point d\ being the projection into the vertical plane

of the point d r (the horizontal projection into the ground plane

of the point d), the length (d\)di (measured on the plotting-scale)

will represent the elevation of the point D above station B (or

above the ground plane).

8. ICONOMETRIC DETERMINATION OF THE ELEVATIONS OF PICTURED

TERRENE POINTS.

Generally speaking, one perspective is insufficient to deter-

mine the elevation of a point, although there are exceptions,

like the points on the horizon line of a photograph which have

the same elevation as the camera station. A single photograph

would also suffice if the distance from the camera station to

the point to be determined vertically be known; for instance,

Fig. 64, Plate XXXIV, the horizontal projection d of the point D

being known, its height H above the ground plane will be the

fourth proportional to the three known lines Bdi, Ed\ B and di B (d B ):

Bdi= horizontal distance between the plotted station B

and the plotted point, measured in the plotting-scale

of the working-sheet;

Bdis= horizontal distance between station B and projection of

pictured point d B in the ground line H B H B f , meas-

ured on the plan;

d\B (<fe) = &=ordinate of pictured point d B , measured on the pic-

ture plane (=d B 'd B , Fig. 63, Plate XXXIII, pic-

ture B N ),

and the value for H may be computed from the equation

Bd

IB

If we now project the plotted point di and the pictured point d B

into the principal plane and revolve the latter about the prin-

146 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

cipal line BP into the plotting-plane, we will have with refer-

ence to Fig. 64, Plate XXXIV,

P(d B ')= height of pictured point d B above the horizon plane = h',

(d B ) = pictured point d B) projected into the principal plane

and revolved with the latter into the horizon or plot-

ting plane;

(d')di = vertical distance of the point d above the horizon

plane =*H.

This height, H, is the fourth proportional to the three known

lengths Bdi, Bdi B and h;

P=focal length of the print = /;

P(d B ')=ordmate of the pictured point above the horizon line (to

be measured on the photograph), and

Bdi' = f+Pdi, where Pd\ = vertical distance between the plot-

ted point di and the picture trace H B H B =d\d (to

be measured on the plotting- sheet),

its value may be found with the aid of an ordinary sector, Fig. 65,

Plate XXXIV, in the following manner:

Take with a pair of dividers the (ordinate) distance from

the pictured point d B to the horizon line (on the photograph)

place one point of the dividers on the division c of the sector,

when CO = focal length of the photograph, and open the arms

of the sector until the second point of the dividers coincides with

the corresponding division D of the other sector arm (OD being

equal to OC = focal length). Now take with the dividers the

horizontal distance (di'P = did, Fig. 64, Plate XXXIV) of the

plotted point d t from the picture trace H B H B , place one of

the points in C and note where the second point of the dividers

intercepts the scale OC, say at A. Turn the dividers about this

point A (maintaining the opening of the sector unchanged) and

place the second point of the dividers upon B on the scale OD

B corresponding to A, or OB = OA when AB, measured on

the plotting-scale, will represent the height, H, of the point d

above the horizon plane of the station B.

GRAPHICAL ICONOMETRICAL PLOTTING METHODS. 147

9. ICONOMETRIC DETERMINATION OF THE ELEVATIONS OF PICTURED TER-

RENE POINTS BY MEANS OF THE SO-CALLED "SCALE OF HEIGHTS."

Another method for determining the elevations of plotted

points iconometrically consists in the use of the so-called " scale

of heights," Fig. 66, Plate XXXV.

Make SP equal to the focal length of the photographic per-

spective, erect PA perpendicular to SP in P, and divide both

lines into equal parts. Join the points of division on PA to 5

and through those of SP draw lines parallel to PA.

To use this scale of heights with a pair of dividers, take

from the photographic perspective the (ordinate) distance from

the pictured point to the horizon line and transfer it to the line

PA = P/JL. The point // may be found to correspond to the line 5//,

passing through the division mark 9 of the graduation on PA.

With a pair of dividers take the vertical distance from the hori-

zontal projection of the point to the plotted-picture trace (measured

on the working-sheet) and transfer it to SP to the right or to

the left of P according to the position of the plotted point with

reference to the picture trace, whether beyond the picture trace or

between the same and the plotted station.

In Fig. 66, Plate XXXV, it is shown as falling between the

station and the picture trace, into m. The line mB, parallel

with PA, is intersected by Sp in Af, and the distance mM, meas-

ured on the plotting-scale, will be the height of the point M

above (or below) the station horizon.

A scale, Fig. 67, Plate XXXV, is conveniently pinned, some-

where on the plotting-board, perpendicularly to a line AB; the

division C of this scale, bisected by the line AB, corresponds

to the height of the camera horizon. Placing one of the legs

of the dividers with which the length AB was taken off the

" sector," Fig. 65, Plate XXXIV, or with which the length mM

was taken off the " scale of heights," Fig. 66, Plate XXXV,

in C, Fig. 67, Plate XXXV, the division D of the scale, coincid-

ing with the other point of the dividers, will indicate the height

148 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

of the point above the plane of reference or datum plane This

height is entered in pencil on the plan, inclosed in a small circle

to distinguish it from the number of the point. It is checked

by means of a second photograph, and when the discrepancy

between several values for the elevation of the point falls within

the limits of permissible error, their mean is entered in red ink

on the plan and all pencil figures are erased.

Any marked difference in the values for the height obtained

from two photographs would indicate that the two points of

which the elevations were determined are not identical points

or that an error had been made in plotting the same or in deter-

mining its height.

A third intersection would dispose of the first two alternatives

and a new measurement of the height will show whether an

error has been made, or whether the discrepancy is due to una-

voidable errors.

10. THE USE OF THE SO-CALLED " PHOTOGRAPH -BOARD."

The various constructions described in the preceding pages

if made directly on the photographs would obscure many details

and produce confusion through the intricacy of the auxiliary

lines. Capt. Deville, therefore, had a special drawing-board

prepared on which as many of the construction lines are drawn,

once for all, as would have to be repeated for the different prints

of uniform size (which were, of course, obtained with the same

camera).

This so-called "photograph-board" is an ordinary drawing-

board covered with tough drawing-paper the surface of which

is to represent both the picture plane and the principal plane

(both planes revolved into the 'horizon plane), and it is used in

conjunction with the photographic perspectives, using the nega-

tives when great accuracy is required, or using solar prints for

general plotting.

Two lines DD and SS', Fig. 68, Plate XXXV, are drawn

at right angles to each other; they represent the horizon and

GRAPHICAL ICONOMETRICAL PLOTTING METHODS. 149

principal lines, while PD - PD' = PS = PS' are equal to the

focal length, so that D, D', 5, and 5' represent the left, the right,

the lower, and the upper distance points respectively.

The photographic perspective is placed in the center of the

board, within the rectangle TYOZ, the principal line coinciding

with SS' and the horizon line with DD', and it is secured hi

this position by means of small thumb-tacks, pins, etc. The

four scales forming the sides of the rectangle OTYZ serve to locate

lines parallel with either SS' or DD' on the perspective (with-

out actually drawing those lines).

At a suitable distance from D f a line QR is drawn perpen-

dicular to DD f , and on it are laid off, by means of a table of tan-

gents, the angles formed with DQ by a series of lines drawn

from D as a center. This scale, QR, is employed when measuring

the altitudes or the azimuthal angles of points pictured on the

perspective, as will be explained in a following paragraph.

From 5 as a center with SP as radius an arc of a circle PL

is described and the latter is divided into equal parts. Through

the points of division of PL lines converging to S are drawn

between PL and PD'. The lines MN are drawn parallel to

the principal line, as shown in Fig. 68, Plate XXXV, and these

lines are all used in connection with the scale of degrees and

minutes QR.

The studs of the centro-lineads are fixed in A, B, C, and E,

the lines AB and CE joining their centers, and those needed

for adjusting the centro-lineads are drawn and used in the man-

ner to be explained in Chapter X.

A square, FGKH, is constructed on the four distance points,

Fig. 68, Plate XXXV.

II. ICONOMETRIC PLOTTING OF THE TRACE OF A FIGURE'S PLANE.

If one wishes to use a perspective instrument for converting a

figure situated in an inclined plane of which the perspective

photograph) is given into the projection of the figure into

150 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

horizontal plan it will be necessary to locate the traces of the

figure's plane in both the principal and picture planes.

We may distinguish between two cases frequently met with

in practical work:

(1) The inclined plane containing the figure may be given

by its line of greatest slope.

(2) The inclined plane containing the figure may be given

by three points.

First Case. The inclined plane of the figure may be given

by the line of greatest slope, which may be an inclined

road-bed, the drainage line of a straight valley (thalweg),

the surface of a glacier, etc.

This line of greatest slope may be represented on the plan

by a line ab, Fig. 69, Plate XXXVI, the altitude of a being known.

The photographic perspective is pinned to the photograph-

board, and the ground line XY is drawn, taking the horizontal

plane through a as ground plane.

On the plotting-board aO is drawn through a perpendicular

to the horizontal projection ab of the line of greatest slope AB,

and it is produced to its intersections L and O with the prin-

cipal line S\pi and with the picture trace X\Y\.

On the photograph pE is made equal to pib, at a perpen-

dicular to XY is erected and produced to the intersection /? with

the pictured line a/?, representing the line of greatest slope AB.

If we make pN, on the photograph-board, equal to piO of the

plan and join N with /? on the picture, this line N0 will rep-

resent the trace of the required plane on the picture plane. If

pQ is made equal to p\L and Q is joined with M, MQ will rep-

resent the trace of the required plane, revolved about SS f , oh

the photograph-board, into the picture plane, the station S

falling in D.

Producing MQ to R, DR will represent the vertical distance

of the station S above the plane RM/3.

Second Case. The inclined plane containing the figure

is given by three points.

GRAPHICAL ICONOMETRICAL PLOTTING METHODS. 151

Take for ground plane the horizontal plane containing one

of the points, a, Fig. 70, Plate XXXVII, and draw the ground

line XY on the photograph. Join a on the plotting-sheet to

the two remaining points and produce these lines to their inter-

sections E and F with the picture trace. On the photograph

make p\K equal to pE and draw KL perpendicular to XY] join

the perspectives a and /? of the points shown as a and b on

the plan and produce to the intersection with KL. Take p\T

equal to pF, draw TN perpendicular to XY and produce to

the intersection N with the line joining the perspectives a and 7-.

Join N and L, when NL will represent the trace of the required

plane on the picture plane.

Produce LN to O and take pG equal to piO; join a and G

and make piQ equal to pH. The line MQ will represent the

trace of the required plane on the principal plane revolved about

SS' into the picture plane, the station being in D. Here also DR

is the vertical height of the station above the plane containing

the three given points.

12. ICONOMETRIC CONTOURING.

After the. heights of a sufficient number of points have been

determined to give a good development of the terrene that is

to be mapped, the contour lines are drawn in by interpolation

between the points of which the heights had been established.

In a moderately rolling country a limited number of points

of known elevations will suffice to draw the contour lines with

precision, but in a rocky region, where abrupt changes and

irregular forms predominate, it is almost impossible to plot

enough control points to enable the iconometric draughtsman

to render a faithful representation of the relief of the broken

terrene, and it is here that a close and minute study of the photo-

graphs becomes indispensable to modify the courses of the con-

tours to represent the characteristic features of the terrene.

The value of photographic views for the cartographic delinea-

152 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

tion of the topography of a mountainous area is generally acknowl-

edged by experienced topographers, even when using instrumental

methods exclusively for all the control work. A minute study

of the pictured terrene will always be of great aid to the draughts-

man (when inking the topographic sheet), to draw the contours

of which the main deflections had been located instrumentally,

with a more natural and artistic reproduction of nature's forms,

than could be attained by mechanically inking the pencilled

lines as obtained by instrumental measurements and free-hand

sketching alone.

Instead of drawing the contour lines at once upon the plan,

the draughtsman may begin by sketching them on the photo-

graphs first, following the same rules for their location (by inter-

polation), as if he were drawing them on the plan, for the image

of every plotted point is already marked on the photographs

and its elevation may readily be taken from the working-plan.

By adopting this plan he will be enabled to follow the inequali-

ties of the surface very closely and the perspectives of the con-

tours thus drawn on the pictures will greatly facilitate the draw-

ing on the plan of their horizontal projections. They may also

be transferred to the plan by means of the perspectograph or

perspectometer if accuracy is to give place to rapidity in the

map production.

A sufficient number of tertiary points having been plotted

by the method of intersections, there will be little difficulty in

drawing the contour lines by interpolation between such points.

It may happen, however, that the control points are too few

in number and too far apart to give a good definition of the ter-

rene (in a topographic reconnaissance), and then it will become

necessary to resort to less accurate methods for locating the

contours on the plan. For example, the ridge abed of a mountain

range, pictured on a photograph as a^d, Fig. 71, Plate XXXVIII,

may be divided by the contour planes by assuming it to be

contained in a vertical plane.

On the plan we produce the projection ad of the ridge to

GRAPHICAL ICONOMETRICAL PLOTTING METHODS. 153

the intersection F with the picture trace and draw through the

station Si the line SiC parallel to ad.

The photograph having been pinned to the photograph-

board, take from the principal point on the horizon line PV

equal to p\C and PG equal to p\F. At G place the scale of

equidistances perpendicular to the horizon line HH', the division

at G corresponding to the height of the station, and join the

marks of the scale (corresponding to the elevations of the con-

tour planes) to the vanishing point V.

Having thus located the points of intersection of the ridge

by the contour planes, their distances (abscissae) from the prin-

cipal line are now marked upon the edge of a strip of paper and

their directions plotted in the usual way. The intersections of

the radials (drawn from Si to the points marked on the paper

strip) with ad will give the intersections of the contour lines with

the ridge ad.

When the mountains have rounded forms showing no well-

defined ridges, the visible outline, silhouetted on the photograph,

may be assumed to be contained in a vertical plane perpendicular

to the line of direction drawn to the middle of the ridge outline,

or silhouette.

The construction may be made by drawing, on the photo-

graph-board, SV perpendicular to the direction SM of the middle

of the outline, Fig. 72, Plate XXXIX; p\M\ on the plan is made

equal to PM, and from the projection a of the summit of the

mountain a perpendicular ac is let fall on SiMi, which represents

the projection of the visible outline. It is produced to the inter-

section N with the picture trace. PQ is taken equal to piN and

the scale of equidistances is placed at Q, perpendicular to the

horizon line. The points of division are joined to V, these

radials are produced to intersect a^, and the plotting of the con-

tour points along a.f is done in the same way as described in the

preceding case, or the directions of the intersections of aj- by

the contour planes may simply be plotted and the contour lines

drawn tangent to these directions.

154 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

The horizon line, containing the perspectives of all points

of the same elevation as the camera station, represents the per-

spective of a contour line when the horizon plane coincides with

a contour plane.

The topographic draughtsman should pay particular atten-

tion to geologic forms and to the originating causes of the topo-

graphic features, as without such knowledge the correct inter-

pretation of such forms by means of contours and a faithful

cartographic representation of the various terrene forms would

require the cartographic location of a vast number of control

points.

Although the terrene forms often result from the successive,

or from the combined, actions of many agencies, they will yet

have similar characteristic shapes when resulting from the same

causes, and the cartographic representation of such typical

terrene forms (produced by identical agencies) sliould also show

a corresponding characteristic similarity in the contour forms.

13. THE USE OF THE SO-CALLED "PHOTOGRAPH-PROTRACTOR."

The angle included between the line of direction to a point

of a photographic perspective and the principal and horizon lines

(the altitude and azimuthal angle) is sometimes wanted in arc

measure.

The azimuthal angle of the line of direction to a point A

may be obtained at once on the photograph-board by joining

the station 5, Fig. 73, Plate XL, to the projection a of the pic-

tured point on the horizon line.

If required in arc measure, the distance Pa is transferred

to the principal line=PG, D is joined to G and produced to

intersect the scale of degrees and minutes BC, where the gradu-

ation mark K indicates the value of the azimuthal angle in arc

measure.

When many such angles are to be measured, the horizontal

scales TV and OZ, Fig. 68, Plate XXXV, may be divided into

GRAPHICAL ICONOMETRICAL PLOTTING METHODS. 155

degrees and minutes by means of a table of tangents, using the

focal length SP as radius.

The altitude is the vertical angle at 5, Fig. 73, Plate XL,

of the right-angle triangle, having for sides Sa and aa. To

construct it, take DF equal to Sa, draw FE parallel and equal

to aa, join D and E and produce DE to the scale (BC) of degrees

and minutes.

This construction will be facilitated by the lines previously

drawn on the photograph-board. With a pair of dividers take

the distance (abscissa) from a to the principal line, carry it from P y

Fig. 68, Plate XXXV, in the direction PD', and from the point

so obtained take the distance to the arc ML, measuring it in

the direction of the radials marked on the board, which will be

the distance PF. Then with the dividers carry aa to FE, which

is that one of the series MN of parallel lines, Fig. 68, Plate XXXV,

which corresponds to the point F. The construction may now

be completed in the manner already explained.

GRAPHICAL ICONOMETRICAL PLOTTING METHODS. 143

With this method the base line its horizontal projection

being either too short or more frequently falling into the same

direction with the distant points to be located by the intersec-

tions of lines of direction is projected upon a vertical plane.

The greater the difference in elevation between the two sta-

tions the greater will the length of this vertically projected base

line be and the more accurate will be the iconometric location

of the points by lines of direction.

We have, with reference to Fig. 63, Plate XXXIII, two camera

stations A and 5, two photographs AN and BN obtained from

them and containing the image d A and ds of the identical geodetic

point D. It is assumed that the horizon plane through the

lower station B be the ground or plotting plane, and that the

principal plane of the photograph AN be the vertical plane of

projection which is revolved about its trace into the horizon

plane of B.

a = horizontal projection of station A\

aB= horizontal projection of the base line AB\

H AB H' AB = picture trace of photograph AN in horizon plane

of B (plotting-plane) ;

H B H B ' = picture trace of photograph BN in horizon plane of B\

aP A '=BP B ' = constant focal length of the negatives AN

and B N ]

aP A = trace of principal plane passing through aP A ' in

horizon plane of B.

To plot the position d f of a point D (pictured in AN as d A

and in BN as dp) in the plotting-plane the rays Ad A and Bd B

are projected upon the vertical plane (revolved about aP A ' into

the ground plane), when (di) will represent their point of inter-

section d projected into that same vertical plane (revolved about

aP A r into the plotting-plane).

The ray Ad A =AD intersects or penetrates the picture plane

A N at a distance =d A d f AB vertically above the ground plane

(above the picture trace or ground line H AB H' AB of picture A N ).

144 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

This ordinate is laid off upon P A 'H AB = P A '(d A ), when d A

will be the projection on the vertical plane of pictured point d A .

The vertical through a projected upon the vertical plane is

represented as a(A), and if we make

a(A)=P A P' AB (picture ,4 AT)

= difference in elevation between the two stations B and A,

(A) will be the upper camera station A projected into the ver-

tical plane, and the line (A)(d A ) will be the projection of the

ray Ad A , or AD, upon the vertical plane (revolved about aP A

into the plotting-plane).

The ray Bd B =BD intersects the second picture plane B N

in d B . If we draw through d B (projection of d B on ground line

H B H B ') a perpendicular to aP A =d B 'di B , d\ B will be the pro-

jection in the vertical plane of the horizontal projection in the

picture trace of the pictured point d B . Producing d B d\ B beyond

d\ B and making di B (d B )=d B d B (measured on the negative B N )

will locate at (d B ) the projection of the pictured point d B upon

the vertical plane.

The perpendicular to aP A ' through B locates the projection

into the vertical plane = bi of the plotted station B, hence the

line bi(d B ) will be the projection into the vertical plane of the

ray Bd B =BD.

The intersection (d\) of bi(d B ) with A(d A ) locates the pro-

jection into vertical plane of the point d, and the horizontal pro-

jection of the point D (plotted on the ground plan) will be on

the line (d\)d', which is the vertical through d (perpendicular

to aP A in our case) passing through (d\) and produced beyond

di, and either horizontal line of direction ad A or Bd B , produced

to intersect this perpendicular (di)di, will locate the position d f

(of the point D) on the plotting-sheet with reference to the plotted

stations A (or a) and B.

(The location of d' as the intersection of the horizontal direc-

tions ad A ' and Bd B would not be very accurate in our case,

and far less so for points pictured on the other side of the prin-

GRAPHICAL ICONOMETRICAL PLOTTING METHODS. 145

cipal point P B , the angle of intersection of their horizontal direc-

tions being even smaller than at d'.)

The point d\ being the projection into the vertical plane

of the point d r (the horizontal projection into the ground plane

of the point d), the length (d\)di (measured on the plotting-scale)

will represent the elevation of the point D above station B (or

above the ground plane).

8. ICONOMETRIC DETERMINATION OF THE ELEVATIONS OF PICTURED

TERRENE POINTS.

Generally speaking, one perspective is insufficient to deter-

mine the elevation of a point, although there are exceptions,

like the points on the horizon line of a photograph which have

the same elevation as the camera station. A single photograph

would also suffice if the distance from the camera station to

the point to be determined vertically be known; for instance,

Fig. 64, Plate XXXIV, the horizontal projection d of the point D

being known, its height H above the ground plane will be the

fourth proportional to the three known lines Bdi, Ed\ B and di B (d B ):

Bdi= horizontal distance between the plotted station B

and the plotted point, measured in the plotting-scale

of the working-sheet;

Bdis= horizontal distance between station B and projection of

pictured point d B in the ground line H B H B f , meas-

ured on the plan;

d\B (<fe) = &=ordinate of pictured point d B , measured on the pic-

ture plane (=d B 'd B , Fig. 63, Plate XXXIII, pic-

ture B N ),

and the value for H may be computed from the equation

Bd

IB

If we now project the plotted point di and the pictured point d B

into the principal plane and revolve the latter about the prin-

146 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

cipal line BP into the plotting-plane, we will have with refer-

ence to Fig. 64, Plate XXXIV,

P(d B ')= height of pictured point d B above the horizon plane = h',

(d B ) = pictured point d B) projected into the principal plane

and revolved with the latter into the horizon or plot-

ting plane;

(d')di = vertical distance of the point d above the horizon

plane =*H.

This height, H, is the fourth proportional to the three known

lengths Bdi, Bdi B and h;

P=focal length of the print = /;

P(d B ')=ordmate of the pictured point above the horizon line (to

be measured on the photograph), and

Bdi' = f+Pdi, where Pd\ = vertical distance between the plot-

ted point di and the picture trace H B H B =d\d (to

be measured on the plotting- sheet),

its value may be found with the aid of an ordinary sector, Fig. 65,

Plate XXXIV, in the following manner:

Take with a pair of dividers the (ordinate) distance from

the pictured point d B to the horizon line (on the photograph)

place one point of the dividers on the division c of the sector,

when CO = focal length of the photograph, and open the arms

of the sector until the second point of the dividers coincides with

the corresponding division D of the other sector arm (OD being

equal to OC = focal length). Now take with the dividers the

horizontal distance (di'P = did, Fig. 64, Plate XXXIV) of the

plotted point d t from the picture trace H B H B , place one of

the points in C and note where the second point of the dividers

intercepts the scale OC, say at A. Turn the dividers about this

point A (maintaining the opening of the sector unchanged) and

place the second point of the dividers upon B on the scale OD

B corresponding to A, or OB = OA when AB, measured on

the plotting-scale, will represent the height, H, of the point d

above the horizon plane of the station B.

GRAPHICAL ICONOMETRICAL PLOTTING METHODS. 147

9. ICONOMETRIC DETERMINATION OF THE ELEVATIONS OF PICTURED TER-

RENE POINTS BY MEANS OF THE SO-CALLED "SCALE OF HEIGHTS."

Another method for determining the elevations of plotted

points iconometrically consists in the use of the so-called " scale

of heights," Fig. 66, Plate XXXV.

Make SP equal to the focal length of the photographic per-

spective, erect PA perpendicular to SP in P, and divide both

lines into equal parts. Join the points of division on PA to 5

and through those of SP draw lines parallel to PA.

To use this scale of heights with a pair of dividers, take

from the photographic perspective the (ordinate) distance from

the pictured point to the horizon line and transfer it to the line

PA = P/JL. The point // may be found to correspond to the line 5//,

passing through the division mark 9 of the graduation on PA.

With a pair of dividers take the vertical distance from the hori-

zontal projection of the point to the plotted-picture trace (measured

on the working-sheet) and transfer it to SP to the right or to

the left of P according to the position of the plotted point with

reference to the picture trace, whether beyond the picture trace or

between the same and the plotted station.

In Fig. 66, Plate XXXV, it is shown as falling between the

station and the picture trace, into m. The line mB, parallel

with PA, is intersected by Sp in Af, and the distance mM, meas-

ured on the plotting-scale, will be the height of the point M

above (or below) the station horizon.

A scale, Fig. 67, Plate XXXV, is conveniently pinned, some-

where on the plotting-board, perpendicularly to a line AB; the

division C of this scale, bisected by the line AB, corresponds

to the height of the camera horizon. Placing one of the legs

of the dividers with which the length AB was taken off the

" sector," Fig. 65, Plate XXXIV, or with which the length mM

was taken off the " scale of heights," Fig. 66, Plate XXXV,

in C, Fig. 67, Plate XXXV, the division D of the scale, coincid-

ing with the other point of the dividers, will indicate the height

148 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

of the point above the plane of reference or datum plane This

height is entered in pencil on the plan, inclosed in a small circle

to distinguish it from the number of the point. It is checked

by means of a second photograph, and when the discrepancy

between several values for the elevation of the point falls within

the limits of permissible error, their mean is entered in red ink

on the plan and all pencil figures are erased.

Any marked difference in the values for the height obtained

from two photographs would indicate that the two points of

which the elevations were determined are not identical points

or that an error had been made in plotting the same or in deter-

mining its height.

A third intersection would dispose of the first two alternatives

and a new measurement of the height will show whether an

error has been made, or whether the discrepancy is due to una-

voidable errors.

10. THE USE OF THE SO-CALLED " PHOTOGRAPH -BOARD."

The various constructions described in the preceding pages

if made directly on the photographs would obscure many details

and produce confusion through the intricacy of the auxiliary

lines. Capt. Deville, therefore, had a special drawing-board

prepared on which as many of the construction lines are drawn,

once for all, as would have to be repeated for the different prints

of uniform size (which were, of course, obtained with the same

camera).

This so-called "photograph-board" is an ordinary drawing-

board covered with tough drawing-paper the surface of which

is to represent both the picture plane and the principal plane

(both planes revolved into the 'horizon plane), and it is used in

conjunction with the photographic perspectives, using the nega-

tives when great accuracy is required, or using solar prints for

general plotting.

Two lines DD and SS', Fig. 68, Plate XXXV, are drawn

at right angles to each other; they represent the horizon and

GRAPHICAL ICONOMETRICAL PLOTTING METHODS. 149

principal lines, while PD - PD' = PS = PS' are equal to the

focal length, so that D, D', 5, and 5' represent the left, the right,

the lower, and the upper distance points respectively.

The photographic perspective is placed in the center of the

board, within the rectangle TYOZ, the principal line coinciding

with SS' and the horizon line with DD', and it is secured hi

this position by means of small thumb-tacks, pins, etc. The

four scales forming the sides of the rectangle OTYZ serve to locate

lines parallel with either SS' or DD' on the perspective (with-

out actually drawing those lines).

At a suitable distance from D f a line QR is drawn perpen-

dicular to DD f , and on it are laid off, by means of a table of tan-

gents, the angles formed with DQ by a series of lines drawn

from D as a center. This scale, QR, is employed when measuring

the altitudes or the azimuthal angles of points pictured on the

perspective, as will be explained in a following paragraph.

From 5 as a center with SP as radius an arc of a circle PL

is described and the latter is divided into equal parts. Through

the points of division of PL lines converging to S are drawn

between PL and PD'. The lines MN are drawn parallel to

the principal line, as shown in Fig. 68, Plate XXXV, and these

lines are all used in connection with the scale of degrees and

minutes QR.

The studs of the centro-lineads are fixed in A, B, C, and E,

the lines AB and CE joining their centers, and those needed

for adjusting the centro-lineads are drawn and used in the man-

ner to be explained in Chapter X.

A square, FGKH, is constructed on the four distance points,

Fig. 68, Plate XXXV.

II. ICONOMETRIC PLOTTING OF THE TRACE OF A FIGURE'S PLANE.

If one wishes to use a perspective instrument for converting a

figure situated in an inclined plane of which the perspective

photograph) is given into the projection of the figure into

150 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

horizontal plan it will be necessary to locate the traces of the

figure's plane in both the principal and picture planes.

We may distinguish between two cases frequently met with

in practical work:

(1) The inclined plane containing the figure may be given

by its line of greatest slope.

(2) The inclined plane containing the figure may be given

by three points.

First Case. The inclined plane of the figure may be given

by the line of greatest slope, which may be an inclined

road-bed, the drainage line of a straight valley (thalweg),

the surface of a glacier, etc.

This line of greatest slope may be represented on the plan

by a line ab, Fig. 69, Plate XXXVI, the altitude of a being known.

The photographic perspective is pinned to the photograph-

board, and the ground line XY is drawn, taking the horizontal

plane through a as ground plane.

On the plotting-board aO is drawn through a perpendicular

to the horizontal projection ab of the line of greatest slope AB,

and it is produced to its intersections L and O with the prin-

cipal line S\pi and with the picture trace X\Y\.

On the photograph pE is made equal to pib, at a perpen-

dicular to XY is erected and produced to the intersection /? with

the pictured line a/?, representing the line of greatest slope AB.

If we make pN, on the photograph-board, equal to piO of the

plan and join N with /? on the picture, this line N0 will rep-

resent the trace of the required plane on the picture plane. If

pQ is made equal to p\L and Q is joined with M, MQ will rep-

resent the trace of the required plane, revolved about SS f , oh

the photograph-board, into the picture plane, the station S

falling in D.

Producing MQ to R, DR will represent the vertical distance

of the station S above the plane RM/3.

Second Case. The inclined plane containing the figure

is given by three points.

GRAPHICAL ICONOMETRICAL PLOTTING METHODS. 151

Take for ground plane the horizontal plane containing one

of the points, a, Fig. 70, Plate XXXVII, and draw the ground

line XY on the photograph. Join a on the plotting-sheet to

the two remaining points and produce these lines to their inter-

sections E and F with the picture trace. On the photograph

make p\K equal to pE and draw KL perpendicular to XY] join

the perspectives a and /? of the points shown as a and b on

the plan and produce to the intersection with KL. Take p\T

equal to pF, draw TN perpendicular to XY and produce to

the intersection N with the line joining the perspectives a and 7-.

Join N and L, when NL will represent the trace of the required

plane on the picture plane.

Produce LN to O and take pG equal to piO; join a and G

and make piQ equal to pH. The line MQ will represent the

trace of the required plane on the principal plane revolved about

SS' into the picture plane, the station being in D. Here also DR

is the vertical height of the station above the plane containing

the three given points.

12. ICONOMETRIC CONTOURING.

After the. heights of a sufficient number of points have been

determined to give a good development of the terrene that is

to be mapped, the contour lines are drawn in by interpolation

between the points of which the heights had been established.

In a moderately rolling country a limited number of points

of known elevations will suffice to draw the contour lines with

precision, but in a rocky region, where abrupt changes and

irregular forms predominate, it is almost impossible to plot

enough control points to enable the iconometric draughtsman

to render a faithful representation of the relief of the broken

terrene, and it is here that a close and minute study of the photo-

graphs becomes indispensable to modify the courses of the con-

tours to represent the characteristic features of the terrene.

The value of photographic views for the cartographic delinea-

152 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

tion of the topography of a mountainous area is generally acknowl-

edged by experienced topographers, even when using instrumental

methods exclusively for all the control work. A minute study

of the pictured terrene will always be of great aid to the draughts-

man (when inking the topographic sheet), to draw the contours

of which the main deflections had been located instrumentally,

with a more natural and artistic reproduction of nature's forms,

than could be attained by mechanically inking the pencilled

lines as obtained by instrumental measurements and free-hand

sketching alone.

Instead of drawing the contour lines at once upon the plan,

the draughtsman may begin by sketching them on the photo-

graphs first, following the same rules for their location (by inter-

polation), as if he were drawing them on the plan, for the image

of every plotted point is already marked on the photographs

and its elevation may readily be taken from the working-plan.

By adopting this plan he will be enabled to follow the inequali-

ties of the surface very closely and the perspectives of the con-

tours thus drawn on the pictures will greatly facilitate the draw-

ing on the plan of their horizontal projections. They may also

be transferred to the plan by means of the perspectograph or

perspectometer if accuracy is to give place to rapidity in the

map production.

A sufficient number of tertiary points having been plotted

by the method of intersections, there will be little difficulty in

drawing the contour lines by interpolation between such points.

It may happen, however, that the control points are too few

in number and too far apart to give a good definition of the ter-

rene (in a topographic reconnaissance), and then it will become

necessary to resort to less accurate methods for locating the

contours on the plan. For example, the ridge abed of a mountain

range, pictured on a photograph as a^d, Fig. 71, Plate XXXVIII,

may be divided by the contour planes by assuming it to be

contained in a vertical plane.

On the plan we produce the projection ad of the ridge to

GRAPHICAL ICONOMETRICAL PLOTTING METHODS. 153

the intersection F with the picture trace and draw through the

station Si the line SiC parallel to ad.

The photograph having been pinned to the photograph-

board, take from the principal point on the horizon line PV

equal to p\C and PG equal to p\F. At G place the scale of

equidistances perpendicular to the horizon line HH', the division

at G corresponding to the height of the station, and join the

marks of the scale (corresponding to the elevations of the con-

tour planes) to the vanishing point V.

Having thus located the points of intersection of the ridge

by the contour planes, their distances (abscissae) from the prin-

cipal line are now marked upon the edge of a strip of paper and

their directions plotted in the usual way. The intersections of

the radials (drawn from Si to the points marked on the paper

strip) with ad will give the intersections of the contour lines with

the ridge ad.

When the mountains have rounded forms showing no well-

defined ridges, the visible outline, silhouetted on the photograph,

may be assumed to be contained in a vertical plane perpendicular

to the line of direction drawn to the middle of the ridge outline,

or silhouette.

The construction may be made by drawing, on the photo-

graph-board, SV perpendicular to the direction SM of the middle

of the outline, Fig. 72, Plate XXXIX; p\M\ on the plan is made

equal to PM, and from the projection a of the summit of the

mountain a perpendicular ac is let fall on SiMi, which represents

the projection of the visible outline. It is produced to the inter-

section N with the picture trace. PQ is taken equal to piN and

the scale of equidistances is placed at Q, perpendicular to the

horizon line. The points of division are joined to V, these

radials are produced to intersect a^, and the plotting of the con-

tour points along a.f is done in the same way as described in the

preceding case, or the directions of the intersections of aj- by

the contour planes may simply be plotted and the contour lines

drawn tangent to these directions.

154 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

The horizon line, containing the perspectives of all points

of the same elevation as the camera station, represents the per-

spective of a contour line when the horizon plane coincides with

a contour plane.

The topographic draughtsman should pay particular atten-

tion to geologic forms and to the originating causes of the topo-

graphic features, as without such knowledge the correct inter-

pretation of such forms by means of contours and a faithful

cartographic representation of the various terrene forms would

require the cartographic location of a vast number of control

points.

Although the terrene forms often result from the successive,

or from the combined, actions of many agencies, they will yet

have similar characteristic shapes when resulting from the same

causes, and the cartographic representation of such typical

terrene forms (produced by identical agencies) sliould also show

a corresponding characteristic similarity in the contour forms.

13. THE USE OF THE SO-CALLED "PHOTOGRAPH-PROTRACTOR."

The angle included between the line of direction to a point

of a photographic perspective and the principal and horizon lines

(the altitude and azimuthal angle) is sometimes wanted in arc

measure.

The azimuthal angle of the line of direction to a point A

may be obtained at once on the photograph-board by joining

the station 5, Fig. 73, Plate XL, to the projection a of the pic-

tured point on the horizon line.

If required in arc measure, the distance Pa is transferred

to the principal line=PG, D is joined to G and produced to

intersect the scale of degrees and minutes BC, where the gradu-

ation mark K indicates the value of the azimuthal angle in arc

measure.

When many such angles are to be measured, the horizontal

scales TV and OZ, Fig. 68, Plate XXXV, may be divided into

GRAPHICAL ICONOMETRICAL PLOTTING METHODS. 155

degrees and minutes by means of a table of tangents, using the

focal length SP as radius.

The altitude is the vertical angle at 5, Fig. 73, Plate XL,

of the right-angle triangle, having for sides Sa and aa. To

construct it, take DF equal to Sa, draw FE parallel and equal

to aa, join D and E and produce DE to the scale (BC) of degrees

and minutes.

This construction will be facilitated by the lines previously

drawn on the photograph-board. With a pair of dividers take

the distance (abscissa) from a to the principal line, carry it from P y

Fig. 68, Plate XXXV, in the direction PD', and from the point

so obtained take the distance to the arc ML, measuring it in

the direction of the radials marked on the board, which will be

the distance PF. Then with the dividers carry aa to FE, which

is that one of the series MN of parallel lines, Fig. 68, Plate XXXV,

which corresponds to the point F. The construction may now

be completed in the manner already explained.