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 24 of 33)**

Online Library → 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 text (page 24 of 33)

Font size

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

s(S):O(/JL)=Ms:MO',

hence

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

300 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

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 '//,

THE PERSPECTOGRAPH, DEVISED BY H. RITTER. 30!

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

302 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

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

Plotting.

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

THE HAUCK TRIKOLOGRAPH. 303

which could serve to plot mechanically the ground plan of any

object represented on two photographs obtained from different

stations.

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

304 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

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

THE HAUCK TRIKOLOGRAPH. 305

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

306 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

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

THE HAUCK TRIKOLOGRAPH. 307

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

picture.

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.

308 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

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.

STEREOSCOPIC TELEMETER AND STEREOCOMPARATOR. 309

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.

Deville.

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

310 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

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

EXG

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'.

STEREOSCOPIC TELEMETER AND STEREOCOMPARATOR. 31 1

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

p'p":!=E:D,

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

312 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

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

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

s(S):O(/JL)=Ms:MO',

hence

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

300 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

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 '//,

THE PERSPECTOGRAPH, DEVISED BY H. RITTER. 30!

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

302 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

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

Plotting.

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

THE HAUCK TRIKOLOGRAPH. 303

which could serve to plot mechanically the ground plan of any

object represented on two photographs obtained from different

stations.

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

304 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

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

THE HAUCK TRIKOLOGRAPH. 305

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

306 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

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

THE HAUCK TRIKOLOGRAPH. 307

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

picture.

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.

308 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

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.

STEREOSCOPIC TELEMETER AND STEREOCOMPARATOR. 309

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.

Deville.

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

310 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

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

EXG

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'.

STEREOSCOPIC TELEMETER AND STEREOCOMPARATOR. 31 1

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

p'p":!=E:D,

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

312 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

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