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

. (page 12 of 33)
Online LibraryJohn Adolphus FlemerAn elementary treatise on phototopographic methods and instruments, including a concise review of executed phototopographic surveys and of publicatins on this subject → online text (page 12 of 33)
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intersections " may be employed with advantage.


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 ).


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-


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).



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



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-


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.



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


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.


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

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


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.


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


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.


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.


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-


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


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.


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

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.


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

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

When many such angles are to be measured, the horizontal
scales TV and OZ, Fig. 68, Plate XXXV, may be divided into


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.

Online LibraryJohn Adolphus FlemerAn elementary treatise on phototopographic methods and instruments, including a concise review of executed phototopographic surveys and of publicatins on this subject → online text (page 12 of 33)