Copyright
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 9 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 9 of 33)
Font size
QR-code for this ebook


the Position of the Principal Point.

.: , -..'; .'.)

x = / tan w oc* = }- tan CD'

w = go-r = io 52' 58".9 a/ = 90 -=17 09' 31",!
tog / = 9 - 3 8 44i 23 (mean log) log / = 9 . 38441 23 (mean log)
log tan w = 9. 2 838945 log tan 07 = 9.4896222



log x = 8 . 6683068 log yf = 8 . 8740345

# = 46.59 mm. A/ = 74. 82 mm.



oc meas. on plate = 46. 05 mm. tf meas. on plate = 75. 40 mm.
difference = Ax= 0.54 mm. ^=0.58 mm.

Mean difference =0.56 mm.

From this difference we infer that the principal point P of
the photographic perspective should be transposed toward the
pictured point, of Punta di Nomenon by 0.6 mm.

{ 7-) Computation of the Ordinates (y and y') of Pictured Terrene Points
of Known Elevations to Check the Position of the Horizon Line (OO f )
en the Negative.

y= - tana, y = .tan a f .

' cos co * cos a> f



PHOTOTOPOGRAPHIC SURVEYING METHODS. 99

Where

= angle of elevation of Punta Rouletta = 3 1 1' 30" I" Observed f . ro the trig-
'= anile of elevation of Punta di Nomenon= I? 38' 30" | ^a pTrcia Statl n



log /= 9-3 8 44i 23

log tan a =8. 7463444

colog cos a>= 0.0078820

logy =8. 1386387

y= 13.761 mm.
y measured on plate= 13.75 mm.

Difference = o.oi mm.



lg /= 9-3 8 44i 23

log tan a'= 8.45 7281 2

colog cos w'= 0.0197731

log /= 7.8614666

y'== 7.269 mm.

y' measured^ 7.30 mm..

Difference =0.03 mm.



The correction for y is so small that it may be disregarded;
the length measured on the plate for y should be reduced by
0.03 mm. and the corrected horizon line would fall 7.27 mm.
below the pictured point P. di Nomenon (Fig. 126, Plate LXIII).

() Orienting a Panorama.

The angles of orientation of the perspective (aj and CD') regard-
ing the two pictured triangulation stations had been found to be

w = io 52' 58".9
and a/ =17 09' 31". i

. Owing to the fact that the distance ZXarid D' in the pi&
ceding example are large in comparison with the ordihates
y and /, it may be preferable first to determine / by means of
the abscissae and then to compute the values for \ the ordihates
(y and /) based upon this value of / and the observe/!' angles
of orientation oj and a/.

If we construct the decagon (see Fig. 124,. 'Plate LXtl^ rep-
resenting the horizontal projection of the ten negatives "obtained
at the station Punta Percia by means of the elements, -obtained
by observations only, we will find the direction to the principal
point P of the -perspective containing the pictures \ ojf . Rouletta
and Nomenon to be = 3 50 oo' oo". : rtli; > ' M :< (".ms



IOO PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

Direction to Punta Nomenon (signal) = 33 2 42' oo'.
Direction to Punta Rouletta (signal) = o 44' 30".
From these lines of direction we find the following values for
the angles of orientation:



Direction to Rouletta = 360 44' 30"
Direction to point P =350 oo' oo"



10 44' 30"



Direction to point P =350 oo' oo '
Direction to Cima

Nomenon =332 42' oo"



Which differ from /= 17 18' oo"

the preceding values w= 10 52' 5&"-9

by Jw= 8' 28".9 w'= if 09' 31".!

This small angle Aw (at V) corresponds to an abscissa Ax y
which in turn represents the error in position of the pictured
point P in the horizontal sense. (In the preceding example,
panorama from station Percia, Sept. 19, 1884, ^#=0.56 mm.)

From the right-angle triangle with angle at V = Aa> and the
two sides Ax and / (Fig. 126, Plate LXIII) we find the value
for Ax for our negative from the equation

4x = ) tan AOJ.

log / = log 242 .332 =2 .3844123
log tan o 08' 28".9 = 7. 3922081



log Ax = 9 . 7 766204
Ax= To. 598 mm.,

representing the error in the position of the principal point of
the perspective, which, however, has little influence upon the
precision of the graphical operations (iconometric plotting)
which are to be executed in order to transpose the topographic
relief upon the chart from the photographic perspectives as
long as the error in question (Ax} does not exceed 2 mm. for
the entire panorama of ten plates, each controlling an angle
of 36 horizontally.

4. CHECKING THE VERTICALITY OF AN EXPOSED PLATE.
For mountain work, where the differences in elevation between
the several terrene points (which are pictured on the negative)
and the camera horizon are relatively great, it is important to



PHOTOTOPOGRAPHIC SURVEYING METHODS. IOI

know whether the negative had been exposed while in vertical
plan and whether the photographic perspective has a correct
horizon line OO', since the ordinates of the various terrene
points in question would become too long when the plate is
(inclined) not vertical. Therefore to assure oneself whether
the picture plane (ground-glass or negative plate) of the photo-
theodolite is vertical and also whether the optical axis of the
camera is horizontal (the trace of this axis upon the perspective
plane is represented by the intersection P of the pictured cross-
threads OO' and //') bring the plane containing the optical axis
and the " horizontal wire " OO' representing the horizon line
into horizontal plan and direct the instrument to a well-defined
distant point situated high above the camera horizon, and
at the same time the vertical thread should be visible against
the ground glass, so that the distant point may be bisected by
it. If we now measure the ordinate of the elevated distant
point on the ground -glass plate and repeat this measurement
after revolving the camera in azimuth 180, clamping the hori-
zontal circle, and " transiting " the camera (revolving it about
its horizontal axis of revolution 180), the two lengths thus
obtained for the ordinate of the point in question should be the
same, otherwise the conditions of the apparatus are not satis-
factory and the instrument should be adjusted until the two
measurements give the same results.

With reference to Fig. 127, Plate LXIII, we have

VP = optical axis of the camera made horizontal and the vertical

thread bisecting the distant point 5;

M PA = angle of inclination of the picture plane against the verti-
cal plane;

Po = length of ordinate of pictured point S, measured on ver-
tical thread from P.

The plane of the perspective NM not being vertical to the
optical axis, 'it will assume the position N'M' for the indirect
position of the camera (as described above) and the ordinate Po'



102 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

measured on the ground-glass plate will now be shorter than
when measured ( = Po) before. Had the picture plane . been
vertical originally it would have coincided with AB for both the
direct and reversed observation; the ordinate measured in both
positions would have been = Ps.

The instrument must be adjusted to make



The error in position of the principal point P of the perspective,
considered in the last numerical example, will appear immediately
if one wishes to determine the value of the focal length = / by
means of the abscissae measured on the ground-glass plate (or on
the negative).

.We had found by measurement

x = 46.05 mm. and oS = 75.40 mm.
and the observed correpsonding angles of orientation were
w = io 44' 30" and a/ -=17 18' oo".

The twofold determination of / may be derived from the
relations

f~^- and -/__2l.;:.r.-=

tan a) tan a/



log x= i . 6632296
cplog tan 10= 0.7219207

log /= 2. 385 1503
.-j /=-242 . 745 mm.



log #'=1.8773713
colog tan a)'= 0.5 065903 [\o: ^

log /*= 2. 3839616
/= 242 . 082 mm.



Mean value for /=242.4i mm., differing but slightly from the value /=242.33
mm., previously obtained. Difference=o.o8 mm.

Example No. V. Giving the means .for ascertaining ; the
attainable degree of accuracy of the Italian photo topographic



PHOTOTOPOGRAPHIC SURVEYING METHODS. 103

method the following computation is of greater interest in a general
way, as the panorama station was selected over a trigonometrical
point of the Italian geodetic triangulation system, thus admitting
a direct comparison between the elements of the perspective
and the exact values of these same elements deduced from the
data of the triangulation work.

In the panorama views, obtained on Sept. 21, 1884 (see Ex-
ample No. II), vertically above the trigonometrical point known
as Reale Accampamento there is one plate (P 5 ) which con-
tains the pictures of two triangulation points, Punta Ruja
and Gran Cima di Nomenon (the same points as previously
mentioned). From the geodetic computations we take the follow-
ing data:

Elevation of Punta Ruja (signal-mark) =31 73.5 m.

Elevation of P. di Nomenon (signal-mark) =3488.4 m.

Elevation of camera horizon (Reale Accampa-
mento) = 2191.8 m.

Distance: R. Accampamento-Ruja=D =5804.2 m.

Distance: R. Accampamento-Nomenon=Z)' =5029.6 m

Horizontal angle : V = Ruja-Accampamento-

Nomenon =13 51' 04". 50

It is desired to find <see Fig. 128, Plate LXIV):

(1) The focal length, /, approximately found by reading the
scale attached to the objective tube = 244.50 mm.

(2) The position of the principal point of view P which is
located by the abscissae x and (xf.

The coordinates obtained by carefully executed measurements
on the negative (the same as in the preceding) are for

Punta Ruja: x =54.80 mm.;- y =41.45 mm,

Gran P. di Nomenon: a/ = 34.05 mm.; / = 63.50 mm.



104 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

Computation of the apparent difference in elevation:

Elevation of P. Ruja = 3*73-5 m.
Elevation of camera ho-



rizon



True difference in level = 981.7 m.
Correction for curvature

and refraction 2.3



Apparent difference of

elevation = 979.4 m.

Computation of d= y.
Li

log D= 3. 7637424

log y= 8. 6175245

colog L= 7 . 0090399



Elevation of Nomon = 3488.4 m.
Elevation of camera ho-
rizon = 2 19 1 .8m.



True difference in level= 1296.6 m.
Correction for curvature

and refraction 1.7111.



Apparent difference of

elevation = 1294.9 m.= U

D'
Computation of d'=-y f .

log D'= 3. 7015334

log /= 8. 8027737

colog .'=6.8877638



log d= 9 . 3903068
d= 245 . 644 mm.

d+d'= 492.29 mm.
d'd= i.oomm.
Computation of the angles f and d:

r-d d'-d V

tan 1 = - - cot ;

2 d+d r 2'



log d'= 9. 3920709



r = 13 51' o 4 ". 5 o; -^-=6 55' 3 2".2 5 .

7-+<5=i8o-F=i66 08' 55 '.50
-=Af = 83 04' 27".75

log (d'd)= 7.0000000

y
log cot - =0.9155404

colog (d+d') = 0.3077790



-

log tan -^=8.2233194



li. O o s

M-N=S 4 2 c
Computation of f:
f= d sin f.
log </= 9. 3903068
log sin 7-= 9 . 9976402


i' 5 6". 9 = r
6' 5 8". 7 =a

log d'= 9 . 3920709
log sin d= g. 995875 7


log /= 9 -387947
/= 0.24431 3m.


l g/ = 9-3879466
/=o. 244313m.



PHOTOTOPOGRAPHIC SURVEYING METHODS. 105

Mean value for 7=244.31 mm. is the same as obtained in numerical example
No. i.

Computation of the abscissa x and x' (to check the position of the principal

point P) :



x=f tan a}.
w=go- r =5 58' 03".!

log/- 9-3879468
log tan w= 9.0192462

log*= 8.4071930

#=25.54 mm.

Measured x= 24 . 80 mm.



Diff.



x'=fta.n ft/.
=7 53' oi". 3



log/=
log tan o/= 9.1413601

logx'= 8.5293069

*'= 33 83 mm.

Measured x'= 34 . 05 mm.

Diff. = 0.22 mm.



The mean difference= 0.48 mm. = error in the position of the principal point P
of the perspective P 5 (Accampamento panorama). The true point P 5 is 0.5 mm.
to the right of P 5 , Fig. 122, Plate LXI, and the vertical line //' (the principal line)
on the plate, Fig. 128, Plate LXIV, should be moved towards Punta di Nomenon
(image) 0.5 mm.

The preceding five numerical examples may well serve to
elucidate the relations between the elements of the photographic
perspectives and their corresponding parts of the terrene, as well
as to give the means for forming a correct idea of the degree
of accuracy, attainable in the Italian photographic surveying
method.

In practical work it would be too time consuming to make
such computations (with the necessary minute and careful graph-
ical measurements) for every negative, or even for every set of
panorama views.

If the phototheodolite has been carefully planned and is well
constructed, the optical axis should always remain perpendicular
to the image plane, hence be horizontal when the latter is ver-
tical. The value / for any (or for all) panorama views, obtained
with the same objective and with the same constant focal length
(obtained under the same reading of the scale attached to the
objective tube), may be computed from the formula



_

taniS '



106 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

In the panorama set of Accampamento Reale station we
had one plate, P', Fig. 122, Plate LXI, containing the image of
the signal at Punta Cian del Lei, bisected by the principal
line, VP', and another plate, P 5 , containing the images of two
other points, Punta Nomenon and Punta Ruja.

The horizontal shiftings in azimuth

P'FP 2 , P 2 FP 3 , P 3 FP 4 . . . ,

representing the horizontal swings in azimuth of the camera for
each successive exposure, are all alike, each being = 36, and the
horizontal angles

P'Vm, mVP 2 , P 2 Vm'...

will each be =18.

The horizontal angle, included between the principal lines
FP' and FP 5 (between the horizontal direction to the reference
point P. Cian del Lei and the principal line of perspective
No. 5) will be = 4X36 = i44 (Fig. 122, Plate LXI).

We find in the trigonometrical records, or from direct ob-
servation at the station Accampamento Reale:

Horizontal angle: Cian del Lei-Accampa-

mento-Nomenon = t35 5&' 23".25

Horizontal angle: Nomenon-Accampamento-

Ruja = 13 51' 04".5

Hence the horizontal angles of orientation for the fifth plate:

4 o/ = (P 5 -F -Nomenon) = 8 01' 36^.75

4 <*> = (Nomenon F Ruja) a/ = 5 49' 2 7". 75

13 51' O4".5o

In the computation for the abscissae x and ^ under Example
No. V we had found

a/ = 90 = 7 53' oi"-3
and co = 9 o-r = S 5%' Q3"- 1 -



PHOTOTOPOGRAPHIC SURVEYING METHODS. 107

The differences ' between these values for cu is =08' 35". 35 and
for a/ =08' 35"-45, or the difference in the mean value of to and
a/ is expressed by



being about the same error in azimuth of the principal point P
that . had been found for the panorama obtained from the station
Punta Percia with the same instrument (considered under
Example No. IV, where we obtained Jw=8' 28". 9). This
error, Aa>= 8' 35".4o, corresponds to a horizontal linear dis-
placement, J#, of the principal point P of the photographic per-
spective:

J#= ^0.610 mm.



5. APPLICATION OF FRANZ HAFFERL'S METHOD FOR FINDING THE FOCAL-
LENGTH VALUE OF A PHOTOGRAPHIC PERSPECTIVE FROM THE AB-
SCISSA OF TWO PICTURED TERRENE POINTS.

When the horizontal distances, D and D r , are great com-
pared with the differences in elevation between the pictured
points under consideration and the camera station, the ordi-
nates, y and y, will be rather short and the accurate measure-
ment of their lengths will be difficult.

In such case it may become advisable to determine the value
of the focal length / by means of the abscissae, x and a/, of the
pictured terrene points. To do this L. P. Paganini uses the
following method, suggested by Franz Hafferl of Vienna.

We have with reference to Fig. 129, Plate LXIV:

OO'= horizon line of photographic perspective;

Vs and Vs f = horizontal directions from the camera station V to the

pictured points 5 and s*;
VP= perpendicular to the horizon line OO f .

It is desired to find the length value for /.



108 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

Describe a circle through the three points F, s, and s', the
center of which may be at C. The angle sCs' is double the
angle sVs' and the perpendicular CM to the line ss f will divide
this line and also the center angle sCs' into two equal parts;
hence



If R be the radius of the circle described through the three
points 5, s', and V, we will have, from the triangle sMC, the
following relation :

SM x+x' i x+x*

-~r r : as SM= - .



r

sin V 2 sin V

After having drawn the diameter mn parallel to ss f we find
]=VP=VA+AP.

VA being vertical to mn it will be the middle proportional to mA
and An:

mA:AV=AV:An,



We can replace mA by (mC-AQ^R-] AC=SM-SP;

oc f x
and as An = nC+AC=R + - ,



we will have AV =



and finally AP = CM =SM cot V = ~ cot- F.

Example No. VI. Determination of the value / for a plate
by means of the abscissae of two pictured points.



PHOTOTOPOGRAPHIG SURVEYING METHODS. 109

From the data derived from the computation in Example
No. IV we find

7 = 28 02' 30"

x= 46.05 mm. and ^ = 75. 40 mm.

#+a/ = i2i.45 mm. x? # = 29.35 mm.

x+x* xf-x

= 60.725 mm. - = 14.675 mm.






x+x* i

Computation of R = - - : =7:
2 sin V



x+x*
log ^ = 1.7833675

colog sin 7=0.3277972



log ^ = 2.1111647
^ = 129.171 mm.



Computation of VA =



x / x
R-\ - =143.846 mm.



yf x
R - =114.496 mm.



log &+ =2.1578978

/ ^_^\
log(R - j= 2.0587903

log VA 2 =4.2166881
log VA =2.1083440
VA =128.335 mm.



110 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

x+oc?
Computation of PA= - cot V:

x+x*
log j-= 1.7833675

log cot 7=0.2735641



log PA =2.0569316
PA =114.007 mm.

Hence j=VA +PA =242.342 mm.,

which compares very closely with

mm.,



obtained under numerical Example No. IV.

In practical work, like the great Italian topographic sur-
vey, it would take too much time and labor to determine the
focal length (/), after the method just shown, for each perspec-
tive, or even for each panorama set. If there is no reason for
doubt that the optical axis of the camera intersects the picture
plane at right angles (as it does for the Italian phototheodolite
with a sufficient degree of precision) it will be more simple to
determine the value / for an entire panorama set (and also for
all subsequent panoramas that may be executed with the same
objective, and with the same focal length, which may be veri-
fied at each exposure) by simply checking ^the scale-reading on
the objective tube, which should remain the same for all pictures.
Under this supposition the focal length is computed in the fol-
lowing manner:

Since the azimuthal swings of the camera after each exposure,

P'VP 2 , P 2 VP 3 > P 3 FP 4 ...,

are all alike, and each being equal to 36 (Fig. 122, Plate LXI),
the angles

P'Vm, mVP 2 , P 2 Vm' .



PHOTO-TOPOGRAPHIC SURVEYING METHODS. Ill

will each be = i8. If x m denotes the maximum length of the
abscissae of the plates then

x m = P'm = mP 2 = P 2 m'= . . . =/tan 18,

hence / = ta^8~'

In the preceding (page 93) it has been stated that two adjoining
negatives of a panorama set have a vertical marginal strip of the
pictured terrene in common, and the width of this strip may
be expressed in arc by the angle pVq (Fig. 122, Plate LXI).

If the negatives are sufficiently clear (showing a good defi-
nition) it will be an easy matter to locate a point m, either on
the negative or on the photographic print, that may be identi-
fied on both overlapping strips pq (Fig. 122, Plate LXI) of two
adjoining plates P' and P 2 , which will be on or near the horizon
line OO', and distant from the principal line //' of plate P' by
mP', and distant from the principal line of plate P 2 by mP 2 , mP r
being = mP 2 .

If we now select such points m', m" ', m'" . . . , that can be
readily identified upon two adjoining perspectives,

P 2 and P 3 , P 3 and P 4 , P 4 and P 5 . . . ,

we will obtain ten values for m for the entire set, and the focal
length, /, for the panorama may be determined by means of
the preceding formula,

x m
' = tan 1 8'

where x m is the arithmetical mean of the ten greatest abscissas
P'm, mP 2 , P 2 m' ....

Example No. VII. By means of ten negatives of a pano-
rama station, obtained with Paganini's phototheodolite, described
in " La Fototopografia in Italia," the following values were
found for the distances x m :



112 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.



x m f or pi _p2 = 77 IQ mm

win ^ ^ P2 P3 .-_ >7 ^ T r* ^ ^

~ // J -5

^w '< P 3 P 4 =7700 <(
^m ^ p4 _p5 =77.40 "
^m ^ p5 _p6 =77.40 "

x m il P 6 -P 7 =77.20 "
P9 _pio = 77. 4 o -
pio_pi =76.90 "

log 77.194 = 1.8875835
colog tan 1 8 =0.4882 240



x m



77.194 mm. = mean value.



/ =237.6 mm.

The above values were obtained by using the negative plates
and reading the measurements scaled off (by means of dividers)
on the graduated rulers of the graphical instruments (" icono-
meters ") of the Royal Military Geographical Institute.

Using the positives (albumen prints) of the same panorama
the following results were obtained:

x m f or pi _p2 = 6 <2



-m <



.X m



P2 _p3 =76.20 c<

P 3 -P 4 =76.10 "

P 9 -P 10 = 76.70 (<

plO_pl =76.00 "

log 76.25 = 1.8822398
colog tan 1 8 =0.4882 240



= 76.25 mm. =mean value.



The negatives gave
The positives gave



log/ = 2.3704628

/ = 234.67 mm. = 234.7 mm.
77.i9 mm.
76.25 mm.



Difl. = 0.94 mm.

The evident contraction of the greatest abscissa amounting
to very nearly one millimeter on the prints is due to the shrink-



PHOTOTOPOGRAPHIC SURVEYING METHODS.



age in the 24X18 cm. albumen paper. Whenever " positives "
(prints) are used in the iconometric map construction, this shrink-
age should be ascertained and taken into account. Of course,
the elements of the " contracted " photographic perspectives are
now substituted for those of the glass negatives.



6. SUPPLEMENT.
I. FORMS SHOWING ARRANGEMENTS OF FIELD RECORDS FOR PANORAMA VIEWS.



Station on Punta Bivula (trigon. pt.), on the ridge between the valleys
of the Valsavaranche and Rhemes.


Date, September 18, 1884.


Orientation of the
Panorama.


Perspectives
belonging
to the
Panorama.


Directions
to the Prin-
cipal Points
of View.


Focal
Distance.


Remarks.


Punta Gran Paradise,
78 27' oo"


P 1

P 3
P 4
P 5


78 27'
114 27
150 27
186 27

222 27


244.5 mm -

ET c


Time of exposure:

5te^t

1) &o r 7 agm>


Punta della Grivola,
123 47' oo"


P 8
pi

P 8
P 8
pio


2 5 8 2 7
294 27

33 27
6 27

42 *>


M "3,

'3 c
js tf
c -

c/5


10 s ^

9 s

10 s
10 s
10 s ,


Fine w e a -
ther


Directions and Vertical Angles of the Computation of Elevation of Station and
Trigonometrical Points. Elevation of Line of Horizon.



Station on partly removed signal.

Elevation of instru-
ment = 2 . 30 m.

Geodetic point, ele-
vation = 341 3 . 69 m.



Elevation of lines of
horizon of the
panorama =3415.99=3416 m.



(The adjoining page of the record book may be utilized for topographic
sketches from station, for detailed remarks, names of roads, etc.)



U4



PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.



Station


on Punta Percia, on ridge between the valleys


of the Valsava-




ranche and the Rhemes.


Date,


September 19, 1884.






Perspectives


Directions




Remarks.


Orientation of
Panorama.


the


belonging
to the


to the Prin-
cipal Points


Focal
Distance.






Panorama.


of View.
















Time of exposure:


Punta dell' Erbetet,


P l


170


oo'


244.5 mm -


6 s


" Shorter e x -


282 04' 06"


P 2


206


00




7 s


posure than






ps


242


00


g


8 s


before on ac-






p4


278


00




9 s .


count of the






P 5


314


oo


Jita


10 s


great reflec-






p6


35


oo


& c

O d


8 s


tion from sur-






pi


26 oo


J-J
^ .<


9 s


rounding












'5 C3




L glacier.


'




ps


62


00


rC o3

C -

'


9 s


D iaphraem
. No. 7






P 9
plO


98
184


00

oo


C/3


10 s 1

7 s ,


Fine weather


Directions and Vertical Angles to the Sur-
rounding Trigonometrical Points.


Computation of Elevation
Elevation of Line of


of Station and
Horizon.


Cima di Breuil 220 54' oo"


Elevation of Invergnan= 3607 . 72 m.


Elevation


i 33 oo


Diff. of elev. + corr.


= 406.15



Punta dell' Erbetet 282 04 10
Elevation 3 36 30



Cima di Nomenon
Elevation

Cima di Rouletta
Elevation



>.2 42 oo

i 38 30

o 44 30

3 ii 3



Punta dell' Invergnan 80 07 oo
Elevation 3 42 oo



Cima di Toss
Elevation



34 ii 30
o 30 30



3 20I -S7

Elevation of Nomenon = 3488 . 42
Diff. of elev. + corr. = 284.94



Elevation of Toss
Diff. of elev. + corr.



3202.48

3302 . 24

99.84



3202.40

Elevation of Breuil =3454.62
Diff. of elev. + corr. = 252.64



3201.98

Elevation of Rouletta = 3384 . 10
Diff. of elev. + corr. = ' 182 . 28



3201.82
Elev. of line of horizon= 3202 . 30



PHOTOTOPOGRAPHIC SURVEYING METHODS.



II. FORM USED FOR RECORDING THE ELEVATIONS OF SECONDARY POINTS OF THE

PANORAMA VIEWS.



Names or
Numbers of
Points.



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 9 of 33)