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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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 24 of 33)
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work on photographic surveying.

We have seen that the plotted position in the ground plan of
a point may be found from its perspective by locating the inter-
section of the horizontal projection of the ray: "station pic-
tured point" with the line of direction found by revolving this
ray with its vertical plane into the ground plane (about the trace
of the vertical plane in the ground plane as axis of revolution).

With reference to Fig. 1 74, Plate XCII,
S may represent the camera station;

M the position of a point plotted on the ground plan GG;
jj. its perspective in the vertical picture plane MN]
s the foot of the station 5;
XY the ground line of the picture plane MN.

If we draw through the foot of the station a line parallel to
the ground line XY and make its length, s(S), equal to sS, join
the plotted point M with (5), then it will follow, from the simi-
larity of the triangles O^M and sSM, that

The triangles s(S)M and O(jj)M being also similar, we find


As we had made sS=s(S)j the last equation can only prevail if

To find, therefore, the perspective, /*, of a point, M, given on
the ground plan, we first draw through the plotted station, on
the ground plan, a line s(S) parallel to the ground line XY,
making s(S)= height of the station 5 above the ground plane.
Draw the lines sM and (S)M, which will intersect the ground
-ine, XY, in O and (/*), Fig. 175, Plate XCIII. On the ground


line X'Y', drawn in another place of the working-sheet, we assume
a point O', representing O of the ground plan, and erect o/j. per-
pendicular to X f Y' in O f and equal to O(/i), when /z will be the
perspective of M in the reverse position of the 'perspective. The
perspective of any other point N on the ground plan may be
found in the same way, making O'Q f = OQ and Q'v = Q(vJ.

Ritter devised the perspectograph with reference to the pre-
ceding relation between the visual ray, SM t Fig. 174, Plate XCII,
to a point M , the horizontal projection of the ray, and the plotted
position of such point M, the perspectograph performing the
preceding construction, Fig. 175, Plate XCIII, mechanically.

The general arrangement of this instrument is shown in Fig.
176, Plate XCIII: sM and (S)M are two slotted wooden arms
carrying the tracer, M, at their point of intersection. The con-
nections at s, o, (s), and (//) are such that the rulers sM and (S)M
may slide through these points. The slide connections s and
(5) may be moved along the groove or slot of the wooden ruler
RT. The sliding piece O is secured to a rod which may slide in
the groove shown in the wooden ruler XY, being connected at
its other end D with a system of arms, joined together afte* the
manner of a pantograph. The distance OD is maintained
unchanged while the instrument is in use.

The center of 5 is placed over the point which marks the
plotted camera station on the ground plan, and the ruler RT is
placed parallel to the ground line of the picture plane, s and
RT are then secured in this position on the ground plan.

When the arm sM is moved, s being held in a fixed position,
the point O will follow the motions of the arm sM, also applying
its motion directly to the arm OD (which slides in the groove of
XY) and indirectly to the arms of the pantograph system.

The fourth sliding piece (/*) is connected with the point A of
the pantograph system by means of a separate piece which insures
a permanent distance between (//) and A while the instrument is
in use, and which may slide on the rod OD. The pantograph
system is composed of six pieces: four straight arms, AB, AC, F '//,


and Fp', and two double arms, CDE and BDG, which are bent at
right angles in their points of junction D. The sides of the two
parallelograms ABDC and DGFE are all of equal lengths, and
the six arms are joined in A, B, C, D, E, F, and G. The lengths
of the arms F/a and Fp! are twice that of the side of the parallelo-
grams. The pencil which describes the perspective may be
attached to the free end of either arm Fju or Ftf.

The angles GDB and EDC being each equal to 90, the sum
of the two other angles CDB and GDE must be equal to 180.
The sum of two adjacent angles in a parallelogram being also
equal to 180, it follows that

CDB + GDE = CDB + DC A ,
or GDE = DCA,

which shows that the two parallelograms are .also equiangular,
and as their sides are equal in length it follows that the parallelo-
grams themselves must be equal, but they are placed in different
directions. The diagonals FD and GE of the one are equal to
BC and DA of the other, respectively. The two long arms
Ffj.' and Fji being of the same length, /*// will be parallel to GE,
both will be perpendicular to the direction of XY, and /*// will
pass through D. We have, therefore,

Use oj the Perspectograph. The sliding piece s is secured
to the working-board over the plotted position of the camera
station on the ground plan, still permitting a gliding movement
of the arm sM in the direction sM. The center line of RT is
brought into a position parallel to the plotted ground line and
its position is also secured to the board. The sliding piece (5),
finally, is moved from 5 (in the groove of RT) until s(S) is equal
to the elevation of the station S above the ground plane, also
securing (S) in this position, when it will still permit a gliding


movement of the arm (S)M in the direction of (S)M. The
center line of the wooden ruler XY is placed upon the ground
line (picture trace) on the ground plan.

The manipulation of the instrument and its general working
will now readily be understood. For instance, when the tracer M
is moved in a direction parallel to RT or XY, the arm sM will
also move the slide OD in the same direction. The distance
O(/j) remaining unchanged as long as s(S) undergoes no change,
(ft) A will also remain of a constant length. Hence, AD and
also GE as well as Z)/i undergo no changes, and the pencil in /*
or in // will trace a parallel line to XY, representing the perspec-
tive of a line of the ground plan (the one traced by M) and parallel
to the picture plane.

When M is moved in the direction of sM, away from XY,
the positions of O and D remain the same, but O(//) will be
lengthened, (/*) moves to the right away from O carrying the
point A with it (A(p) being a constant length) and increasing
the length of the diagonal DA in proportion to the increase of
the length O(/JL). DA, being equal to GE, equal to >/*(=>//),
the latter will also be lengthened and // will move down away
from XY by the same amount as (/*) is moved to the right.
The relation between the construction made in Fig. 175, Plate
XCIII, and the mechanical plotting with the perspectograph,
Fig. 176, Plate XCIII, will now be evident.

VII. Prof. G. Hauck's Trikolograph and its Use in Iconometric


This instrument has been described by Dr. G. Hauck in a
memorial commemorating the opening of the new building of
the Royal Technical High School at Charlottenburg, near Ber-
lin, Nov. 2, 1884. It serves to reconstruct an object from two
perspectives obtained from two different points of view.

The principles which underlie the construction of this instru-
ment hold equally good for the construction of an instrument


which could serve to plot mechanically the ground plan of any
object represented on two photographs obtained from different

Prof. F. Schiffner, in 1887, suggested the changes to be made
to Dr. Hauck's instrument in order to render it available as an
instrument of precision for the use of the photo topographer; still,
it seems that mechanical difficulties in its manufacture are yet
to be overcome, as the writer has not met with any record of
such an instrument having been in use or even constructed.

In Chapter IV it has been shown that a point, A, photo-
graphed from two stations, S and Si, may be plotted in hori-
zontal plan, if the two picture traces gg and gigi, and the two
camera stations S and Si, are given on the horizontal plan, Fig.
177, Plate XCIV.

The two picture planes may be revolved about their ground
lines, gg and gig\, into the horizontal or ground plan, when (a)
and (fli) will be the two images of the point, A, revolved into
the ground plane. If we draw lines through (a) and (#1) per-
pendicular to the corresponding ground lines gg and gigi, then
a' and a! \ (Fig. 177, Plate XCIV) will be the projections of the
pictured points a and di into the horizontal plan and the inter-
section of the radials drawn from S and Si to a! and a/, re-
spectively, will locate the position A' of the point A pictured
on the two plates as a and a\.

This graphical determination of the plotted position A' of
the point A may be accomplished mechanically by placing
slotted rulers with their center lines upon gg and gig Fig. 178,
Plate XCIV, and indicating the directions of the perpendiculars,
dropped from the pictured points (revolved into horizontal plan)
upon the ground lines, by two arms, (a)bc and a'6, of a panto.
graph combination, where

The points (a)a f and c will always be situated on the pe-
riphery of a semicircle described about b as the center, and as


the points c and a' are permanently held on the line gg, the angle
aa'c (angle of the periphery subtending the semicircle) will be
equal to 90 for all inclinations that may be given (a)c against gg.

The directions of the radials Sa' are laid down mechan-
ically by means of two slotted rulers Sa' and Si#i', held in posi-
tion by the studs in S and a' (in Si and a/), both rulers being
revolvable about the fixed points 5 and Si.

This instrument, of which the characteristic features are
shown in Fig. 178, Plate XCIV, performs the constructions
mechanically which were made graphically or geometrically in
Fig. 177, Plate XCIV.

The slotted rulers gg and gigi are secured to the plotting-
toard (with their center lines on the picture traces) by means of
thumb-tacks T. The pantograph-arms (a)c(a\) c\ and a'b a\b\
are connected with these rulers by means of sliding joints c
(and Ci) and a' (and a/), while the studs which mark the sta-
tions S and Si end in cylindrical projections which fit into the
slots of the rulers Sa' and Siai', the latter fitting also over similar
cylindrical attachments to a' and 0i', in such a way that the
rulers Sa' and Si^i' may freely glide over the points S and a' (or
Si and 0i'), and at the same time may revolve about the fixed
points S and Si respectively.

The points (a) and (#1) are provided with tracers and a pencil-
slide is attached to the intersection of the rulers Sa' and Si a/
(in A') in such a way that the pencil point may freely slide either
way in the grooves of Sa' and Si^i'.

A comparison between Figs. 177 and 178, Plate XCIV, will
plainly show that A' will always represent the plotted position
of two images (a) and (#1) (revolved into horizontal plan) of
the identical point A.

It may not always be possible to identify both images of the
same point A on the two pictures, and in order to apply Prof.
Hauck's method, to identify the second image (on the second
photograph) by means of the so-called "kernel points" the
instrument, shown in Fig. 178, Plate XCIV, must be modified


in such a way that the point of the second tracer will always be
upon the image (on the second picture) which the point of the
first tracer designates on the first picture (revolved into the
ground plane).

We had seen in Chapter IV that the line connecting the
image of any point A on the first picture with the image of the
second station (kernel point (si), Fig. 179, Plate XCV) and
the line connecting the image of the same point A on the se ond
picture with the image of the first station (kernel point (s), Fig.
179, Plate XCV) will bisect the same point o of the line of
intersection of the two picture planes. The picture planes being
vertical, this line of intersection will be the vertical line passing
through the point Q of the ground plane (point of intersection
of the two picture traces or ground lines gg and gigi). The
picture planes having been revolved about their ground lines
as axes into the horizontal plan, this line of intersection oQ, also
revolved into the ground plane (and about gg and again about
gigi), will appear twice, once as Q(o), perpendicular to gg in Q y
and again as Q(a\), perpendicular to gigi in Q. As the points
(a) and (<TI) represent the same point cr, revolved into the hori-
zontal plane, once about gg and again about gigi as axes, the
lengths (a)Q and (o\)Q must be equal.

In order, therefore, that this instrument (Fig. 178, Plate XCIV)
may work in harmony with the principles which underlie Prof.
Hauck's method, it will have to be modified to fulfill the follow-
ing conditions:

A line drawn through the kernel point Si and any point pictured
on the first photograph, and a line drawn through the kernel
point s and the image on the second photograph of the same
point, are to intersect the line of intersection of both picture
planes in the same point a, or, the two lines revolved into the
horizontal plan (with the picture planes) must bisect the re-
volved lines (a)Q and (a\)Q in points (<j) and (01), which are
equidistant from Q.

The complete instrument is represented in a general way


in Fig. 179, Plate XCV. The two slotted rulers gg and
of Fig. 178, Plate XCIV, have been supplied with additional
arms Q(a) and Q(o\), each arm including an angle of 90 with
its ruler. These rectangular elbow-pieces are secured to the
plotting-board by four thumb-tacks T after the rulers gQ and
giQ had been placed with their center lines upon the picture
traces gg and gigi, respectively, in such a way that the intersections
of the center lines of the elbow-rulers, at the rectangular elbow
end of the rulers, coincide with the intersection Q of the ground
lines or picture traces gg and gigi. The pantograph- arms, repre-
senting the ground lines of the pictures, are attached to the rulers
the same as in Fig. 178, Plate XCIV. Studs are inserted into
the kernel points (si) and (s), and the arms Q(d) and Q(<JI) sup-
port a ruler (a)(ai), which may glide freely over these arms
of the . elbow-pieces. To cut off equal lengths on the elbow-
arms Q(a) and Q(o\) by this ruler (a)(o\) the angle d(a)e is ad-
justable, and it should be regulated for each set of two picture
traces to make

When (a)d is moved along the slot of (o)Q the slide point
will move along (a\)Q t Q(a) always being equal to Q(ai).
The screw d serves to clamp the angle d(a)e for any opening
corresponding to the angle [email protected] included between the picture
traces. Slotted rulers are now placed over the studs marking
the kernel points (si) and (s), the slots also receiving the cylin-
drical prolongations of the tracers (a) and (#1) and those of the
slide points (a) and (a\) respectively. Finally two slotted
rulers RS and R\Si are placed over the studs S and Si (they
mark the plotted positions of the two stations) and over the
sliding joints a! and a\ (which are the same as those in Fig. 178,
Plate XCIV). At their point of intersection, A' , the sliding
pencil point is inserted into the slots, and this completes the
instrument. If we now move the tracer (a) on the first photo-
graph, the pantograph arms (a)c and ba f will change the position


of the ruler SR into the direction of the radial from 5 to the hori-
zontal projection on the picture trace of the pictured point
designated by the tracer point (a) on the first photograph and
the ruler (a) (s) is moved, locating the point (a). This change
in the position of (<r) produces a corresponding change in the
sliding point (<TI), which in turn changes the position of the tracer
(ai), causing the pantograph-arms (di)c and ^a/ to move, and
a change in the position of a\ will cause the radial ruler R\S\
to assume a new position also and the intersection of RS with
the new position of RiSi locates the plotted position in hori-
zontal plan of the point under the tracer on the first photo-
graph without actually having identified the corresponding
image as the identical point under the tracer (#1) on the second

If a line on either photograph is followed out by one of the
tracers (a) or (ai), the pencil point A' will draw the horizontal
projection of the pictured line, the second tracer being watched
merely for the sake of obtaining a check or to aid its course,
if necessary, by a gentle tapping, when the movements of the
various parts of this instrument should retard its motion owing
to too much friction or lost motion.

Until now no perfect perspectograph has been constructed,
and no matter how accurately such instruments like the one
just described may be made by the mechanician, there will
always remain some unavoidable imperfections in the piaterial
or in the workmanship of the instrument, producing more or
less error in the results. For accurate and precise work, there-
fore, all iconometric plotting (when applying the radial or so-
called plane-table method) should be accomplished with the
aid of graphical or geometrical constructions, at least for all con-
trol points of the survey, relegating the use of perspective instru-
ments to the filling in of such details, which in an instrumental
survey of like character would be sketched by the topographer.


VIII. The Carl Zeiss Stereoscopic Telemeter and the Stereo-
comparator, including the Stereophotogrammetric Survey-
ing Method, Devised by Dr. C. Pulfrich.

Stereoscopic surveying, when employed for phototopography,
has many advantages, especially if the stereoscopic views of
the terrene may be transferred into the orthogonal horizontal
projection of the plan or map by means of stereoplanigraphs,
or stereoscopes that are supplied with the necessary details
and means for adjustment that may be required for the semi-
mechanical plotting of topographic control points.

The idea of using two stereoscopic views of the ground, ob-
tained from two properly selected stations, in a specially devised
stereoscope and projecting the selected characteristic terrene
points of the stereoscopic image directly on the plotting-sheet,
by means of a movable projecting index mark, occurred to
Capt. Deville about ten years ago. Owing to the pressure of
other official duties, however, Capt. Deville had to suspend the
continuance of his experiments in this direction. This inter-
ruption is greatly to be regretted, as he had practically solved
the problem of stereoscopic plotting by using a modification
of the Wheatstone stereoscope. A description of Capt. Deville's
interesting instrument may be found in:

Transactions of the Royal Society of Canada, Second Series, 1902-1903,
Vol. VIII, Section III, " On the Use of the Wheatstone Stereoscope in
Photographic Surveying." E. Deville.

Also in

A. LAUSSEDAT. "Recherches sur les Instruments, les Methodes et le Dessin
topographiques." Tome II. Paris, 1903. "La Stereoscopic appliquee
a la Construction des Plans."

Dr. C. PULFRICH. "Ueber eine neue Art der Herstellung topographischer
Karten und ueber einen hierfuer bestimmten Stereoplanigraphen."
Zeitschrift fuer Instrument cnkunde, Heft V (Mai), 1903, XXIII Jahrg.


Dr. Pulfrich has devised a stereoplanigraph which is being
made by the Carl Zeiss firm in Jena, a description of which may
be found in the last- mentioned paper by Dr. Pulfrich. This
instrument seems to be planned on the lines suggested by Capt.

A perfected stereoplanigraph would be the ideal instrument
for the rapid plotting of topographic features and details if the
terrene is controlled by a close network of triangulation.

A. The Stereoscopic Telemeter, or Range-finder.

The stereoscopic telemeter, or aerial distance measure,
manufactured by the Carl Zeiss Optical Works in Jena, Ger-
many, was first brought to general notice in a lecture delivered
by Dr. C. Pulfrich before the Society for Natural Research,
Munich (Sept. 19, 1899).

This telemeter, devised by Dr. Pulfrich, is the outgrowth of
ideas that had been suggested in a measure by Prof. Porro to
break the straight course of the light-rays in a telescope, by means
of a series of prisms, into a zigzag path and thus reduce the length
of the ordinary telescope.

The Carl Zeiss Optical firm not only succeeded to improve
on the quality of the prism telescopes heretofore in use, but it
succeeded also to combine two such telescopes into a binocular
set. The relief effect produced by the Zeiss prism binoculars,
based on the difference between the two retinal images, is ac-
centuated by an optical increase of the interocular distance,
simply by setting the two objectives of the binoculars farther
apart. The ratio between the ocular and the objective distance
gives the "stereoscopic power" of these stereobinoculars.

The great practical success of this combination, however,
is mainly due to the recent discoveries made in the optically
worked glass compositions produced by the now world-famed
Jena Optical Glass Works. Dr. Pulfrich could now realize
H. Grousillier's idea of the aerial distance scale, and aided by


the excellence of the mechanical equipment of the Carl Zeiss
firm, the present form of the " stereotelemeter " has been manu-
factured and placed on the market.

With this portable stereoscopic telemeter distances may be
read off directly, the degree of accuracy attainable in the meas-
ures being almost entirely independent of the shapes of the
objects determined, which, furthermore, may be stationary or in
motion. A special transverse scale is also provided for measur-
ing the width or length and the height of any distant object, for
making measurements in " frontal planes."

The Carl Zeiss firm has placed three distinct types or grades
of stereotelemeters on the market, differing in range, magnifi-
cation, and weight, and, of course, also in price.

The so-called " total relief effect " may be expressed by the

product ,

where E= distance between objectives ( = 510 mm.);
e= distance between eyepieces (= 65 mm.);
G = magnification (= 8.).

The middle- size telemeter, to which the figures just given refer,
will have a total relief effect of 63. That is to say, if differences
in relief on the single plate are not observable beyond 450 meters,
the stereoscopic image, as it appears to the observer through
this stereotelemeter, will show differences in depth or relief
at 63X450 m. =28.3 km. This, however, does not mean that
any such distances may be read with its aerial distance scale;
it simply gives the extreme limit for recognizing terrene forms,
all points beyond that distance appearing as infinitely far off.
If we direct the stereotelemeter to a point P at infinite dis-
tance (Plate CIX) the component images of the point P will
be at p and f. If we now consider a second point P', just in
front of P, its image will still coincide with p in the left image
plane, but in the image plane of the right binocular tube it will
appear at /', to one side of p'.


The distance //' , spoken of as the linear parallax of the two
points P and P', is directly proportional to the distance between
the two points. The rays (/fl and o'tf' include the angle of
parallax = d, and as the triangles o'p'^' and P'OO' are similar
we will have the proportion


where /= focal length of 0;

E = interobjective distance, or telemeter base;
D = distance of point P from O, PP being negligible in com*
parison with OP.

Hence the linear parallax

E and / being constants, we find by differentiation

dD= - da,

and substituting the above value for a we find

D 2

The error in linear parallax, da, is directly proportional
to the product of the focal length and the angular parallax 8,
and inversely proportional to the magnification G.

fXd Gxda

and we may now write

D 2


If we now designate by r the range of stereoscopic vision
by unaided eyes in other words, if r is that distance at which
an object must be placed to be seen under an angle of parallax = d
we will have the relation

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 24 of 33)