is moved up or down the ruler A B. AB is provided with a milli-
meter graduation also, and by means of the vernier n' the dis-
tance pV of the line pq from the center of V may be read to o.i mm.
When the line pq is brought to the distance = / from F, by
means of the fine ratchet movement at P, the line pq may be
regarded as the axis of abscissae drawn upon the perspective,
while the point p will then -represent the principal point of the
perspective (see Fig. 168).
286 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.
In this case the line pq may also be regarded as the axis of
ordinates of the perspective mn, Fig. 168, Plate LXXXX, pro-
vided the principal plane (containing VP and the axis of ordinates)
is supposed to have been rotated about VP until it coincides
with the horizontal plane VPO f .
The point p is permanently marked upon the line pq (in
the same way as described for the graphic sector) by a small
puncture, which likewise serves to receive one point of the dividers,
when such are used to lay off the coordinates, taken from the
After pq has been secured, at a distance = /, from the center V
and the abscissa x of a point a, taken from the perspective mn,
Fig. 1 68, Plate LXXXX, has been transferred to the line pq
from p, the second point of the dividers, upon pq, will represent
the horizontal projection a' of the point a. If we now move
the alidade dd' until its fiducial edge touches the second point
of the dividers, the triangle formed by the edge of the alidade
d'dj the edge of the ruler AB, and the line a'p will represent
the horizontal triangle VPa' of Fig. 168, Plate LXXXX.
The end d' of the alidade is provided with a steel index mark i y
which may be moved along dd' by means of a revolvable but-
ton, E, ending in a ratchet-wheel below, which rotates in a row
of teeth attached to one side of the groove s's. If this index
mark i is moved to a 1 (the intersection of the fiducial edge of
the alidade dd! and line pq), the distance Va f (cut off on dd')
will represent the horizontal distance of the point a' (of the per-
spective mn) from V (i.e., the value d in Fig. 168, Plate LXXXX)
measured on the scale with which the fiducial edge of dd' is pro-
vided. Maintaining the index mark i (Fig. 167, Plate LXXXIX)
in this position on dd' and revolving d'd about V, until its fiducial
edge coincides with the edge pV of AB, then moving the ruler MM'
away from V (by turning the button P) until the line pq coincides
with .the index mark i, we will have transferred the distance d
(Fig. 1 68, Plate LXXXX) upon the axis of the hypsometer; we
will also have brought the line pq (engraved upon MM') to a dis-
L. P. PAGANINl'S GRAPHIC HYPSOMETER. 28?
tance equal to d from the center of rotation in F, and by trans-
ferring the ordinate y (Fig. 168, Plate LXXXX), measured on
the perspective mn with a pair of dividers, upon the line pq (while
the latter is still in the position just described), by inserting one
point of the dividers into the cavity p and bringing the fiducial
edge of the alidade dd f gently into contact with the other point of
the dividers, resting on the line pq at a' (Fig. 167, Plate LXXXIX),
then the triangle Vpa' of the hypsometer will also represent the
vertical triangle Va'a of Fig. 168, Plate LXXXX, except that
now it has been revolved about Va' into the horizontal plan.
The movable ruler LL', which also remains always perpen-
dicular to the hypsometer axis (Vp) like MM 1 ', consists of two
plates firmly joined together at their ends, between which the
alidade d'd may freely glide when revolved about V. The upper
plate of LL' is slotted like the handle of a penknife and the edges
LI and LI' are beveled and provided with a millimeter gradu-
ation, the numerals of which correspond with a scale of -
(50 m. = i mm.). A ratchet-screw c serves to move a plate
KOK', with two index marks K and K' that may be adjusted
to coincide with the intersections of the fiducial edge of
the alidade dd r and the two graduated and beveled edges LI
and LV. The index plate KOK' has a double vernier, n",
on the opposite side of the ratchet-screw c, graduated to read -
millimeter (i.e., to read single meters for the - - scale) in
connection with the millimeter scales LI and LV.
When the zeros of the double vernier n" coincide with the
zeros of the graduated edges LI and LI', the marks K and K'
of the double index will coincide with the edge Vp of AB (i.e.,
with the axis of the instrument) and also with the fiducial edge
of the alidade d'd, the zero of the vernier n also coinciding with
the zero of -the arc graduation Ggg' (i.e., the fiducial edge of
dd r will fall together with the axis pV of the instrument).
288 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.
In Fig. 1 68, Plate LXXXX, A may represent a point of the
terrene the image of which is designated in the perspective mn
by a. If A' be the orthogonal projection of A in the horizontal
plane passing through the second nodal point F, then A A'
will represent the difference of elevation = L between the points
A and V. A'V will be the horizontal distance = D of the point A
from the camera station V, which distance is represented by
for a scale of map of - .
Returning to Fig. 167, Plate LXXXIX, we now imagine the
hypsometer revolved about the needle center in V until the
hypsometer axis pV passes through a plotted point A' in the
drawing. If the ruler MM' had previously been secured in
such a position that the distance pV oi p from center of station V
is equal to d and if dd f had been set to lay off the ordinate y
upon pq from p } and if we now bring the index mark K in a
position to mark the intersection of the fiducial edge of the ali-
dade dd f with the edge LI of LL', then the triangle VA A' , Fig. 167,
Plate LXXXIX, will also represent (in the scale of i : 50000)
the triangle VA'A of Fig. 168, Plate LXXXX.
The index mark K indicating, on the beveled graduated
edge LI, the length , we find the difference of elevation
between the point A and camera station V by reading the cor-
responding vernier of the double vernier n" .
The triangles Vpa' and' V A' A (Fig. 167, Plate LXXXIX)
being similar, we will have
AA' Pa! y
We know that
L. P. PAGANINl'S GRAPHIC HYPSOMETER. 289
AA' L D
The numerals of the graduation of the edges LI and LI' and
of the double vernier n" give the value A A' already multiplied
by 50000, which is the true difference of elevation.
With reference to Fig. 168, Plate LXXXX, we have
L y AA'
Hence if we know the angle of elevation of a point A of the
terrene we need only to lay off this an le upon the graduated
arc Ggg r by means of the alidade vernier n, from g and place
the index mark K upon the intersection of the fiducial edge of
the alidade dd r and edge LI (the instrument having been placed
upon the plotting- sheet in such a position that the hypsometer
axis pV passes through the station V and the plotted point .4'),
and then read off on LI and corresponding vernier n" the differ-
ence of elevation between camera station and point A.
This case becomes very much simplified when the image A'
of A is bisected by the principal line of the perspective (axis
of ordinates), as then
x = o and d=f.
The alidade dd' is placed so as to lay off the ordinate of the
point a upon pq from p, after the ruler MM' had been secured
in a position at a distance = / from F; then the index mark K
PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.
or K' is brought into the point of intersection of the fiducial
edge of dd', with the edge LI or LI' of the ruler LL' (the axis of
the hypsometer passing through the plotted point A'), and the
difference of elevation between A and V is read off, either on
the vernier corresponding to the graduation LI, or on that cor-
responding to the graduation LV .
The corrections for curvature and refraction, to be applied
to these differences of elevation, are taken from the ordinary
IV. The Centro-linead as Used by Capt. E. Deville.
Reference to this instrument has already been made under
the head of Photograph-board, Chapter VI; it is used in Canada
under Capt. E. Deville.
We had seen that the distance between the principal point
and the vanishing points of lines increases the nearer parallel
to the picture plane such lines would become. Lines parallel
to the picture plane have their vanishing points at infinite dis-
tance from the principal point; practically they have no vanish-
ing points. Their perspectives are parallel with the original
In iconometric plotting it frequently occurs that the vanish-
ing points of some lines fall outside of the limits of the drawing
board, and in order to draw a line which if produced would
pass through the distant vanishing point, special constructions
would have to be made to locate the direction of such a line.
To avoid making such auxiliary constructions on the photo-
graph board Capt. Deville uses the so-called " centro-linead,"
with which a line vanishing at any distant point may be drawn
upon the picture plane no matter how far off from the principal
point of the perspective the vanishing point may be.
This instrument, represented in Fig. 169, Plate LXXXX,
is composed of a straight edge L (of wood) and two wooden
movable arms / and /'. The inclination of these arms / and /'
THE CENTRO-LINEAD AS USED BY CAPT. E. DEVILLE. 2QI
against the straight edge may be varied to any angle. The arms
may also be permanently fixed in any position by means of the
clamp-screws r and r f .
We had seen that the photograph-board, Fig. 68, Plate XXXV,
was provided with four points ABC and , indicating the centers
of the studs against which the arms / and /' of the centro-linead
play or rest when the same is used on the photograph-board.
The distance between these studs may vary. Each two forming
a pair are generally placed from six to eight inches apart, and
the arms of the centro-linead being held in contact with the
studs, the various directions of the ruler L will intersect each
other in one common point.
Referring to Fig. 170, Plate XCI,
A and B may represent one pair of studs, fixed upon the board ;
OA and OB the arms of the centro-linead, clamped in the posi-
tions indicated, and
OC the ruler of the centro-linead.
If we describe a circle through the three points A, O, and B
the angle AOB remaining constant the angle AOB will be
an angle of the periphery AB for any position given the ruler L
(or OC) as long as / and /' (OA and OB) remain in contact
with A and B (the two studs on the periphery of the circle).
When OC is changed to the position O'C f the intersection V
of the two lines OC and O'C' will also be on the periphery of
the circle because the angle AOV (AO'V) remains the same
and must subtend the same arc AV as long as the position of
the studs remains unchanged. Hence for the assumed position
of the studs the directions of all lines drawn along the fiducial
edge of the ruler L (giving O all positions on the arc AOB)
will pass through the point F; they will vanish at V.
In the iconometric work of the Canadian surveys the centro-
linead is used only for drawing the perspectives of horizontal
lines whose vanishing point is on the horizon line. The studs
A and B are placed on the photograph-board on a line AB per-
2Q2 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.
pendicular to the horizon line and at equal distances from the
latter. The horizon line (DD', Fig. 68, Plate XXXV) HH f ,
Fig. 170, Plate XCI, becomes a diameter of the circle AOBV
and VA = VB.
If the arms / and /' of the centro-linead include the same
angles with the ruler L, the line OC, bisecting the angle AOB,
must pass through V midway between A and B.
The distance of the vanishing point V from the principal
point P may be varied at pleasure by changing the inclination
of the arms / and V against the ruler L. When the directions of the
arms / and /' fall together and are perpendicular to L, the vanish-
ing point will fall at infinite distance from the principal point P,
and the lines drawn along the ruler L will be parallel to the horizon
The distance of the vanishing point V from P may also be
varied by changing the distance between the studs A and B,
or C and E, Fig. 68, Plate XXXV; increasing this distance
enlarges the circle AOBV and V moves farther off from P'. reduc-
ing that distance decreases the diameter of the circle AOBV
and V will approach the principal point P. The practice in
Canada, however, is to retain the position of the studs unchanged
on the photograph-board and to change the inclination of the
arms / and /' of the centro-linead instead.
If we gradually close the arms / and /', V will approach the
line AB, and when the angle AOB becomes equal to 90 the
arc AOB will have become a semicircle and the intersection of
AB with HH' will be the center of the circle AOBV, the distance
of both O and V from AB will be equal to - ; continuing to
close the arms / and /', V will approach closer to AB without
ever reaching it.
THE CENTRO-LINEAD AS USED BY CAPT. E. DEVILLE. 293
A. To Set the Arms I and V of the Centro-linead if the Direction
to the Vanishing Point be given by a Line in the Ground
In Fig. 171, Plate XCI,
P = principal point on the photograph-board;
A and B = positions of the two studs;
Sv= given direction of the line on the ground plan, when V will
be the vanishing point for that line.
If we revolve the picture plane about the horizon line as axis
into the horizontal plane the station may fall in S, Fig. 171,
Plate XCI, when SP will represent the horizontal projection
of the principal ray or the distance line (focal length) of the
picture. If the point V would fall upon the drawing-board we
could describe a circle through AB and V and place the fiducial
edge of the ruler upon DP (the horizon line) with the axis of
rotation o of the arms / and /' in D upon the circle, bring the
arms / and /' into contact with the studs A and B and clamp
them in that position. In this case there would be no use for
the centro-linead, however, as V is accessible.
If we join VB, the angle VDB the inclination of the lower
arm /' against the ruler L is equal to VBA, both angles sub-
tending equal arcs of the same circle. Draw the lines CS and
BS. At any point c on CS draw cM and cv parallel to AB
and DP and join b and v. By reason of similarity of triangles
vb must be parallel to VB and the angle
Hence the arms of the centro-linead may be set, in the case
under consideration, by placing the ruler L on Mb, the axis of
rotation, O, coinciding with b and adjusting the lower arm /'
of the centro-linead to coincide with bv. The other arm /, having
the same inclination against the ruler L as /', may be set by placing
2 94 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.
the ruler L upon the horizon line DP and moving it along this
line until the lower adjusted arm /' comes into contact with the
stud B, then moving the other arm / about O until it comes into
contact with the stud A and clamping it also.
The lines BS, CS, Me, and cv are drawn once for all upon
the photograph-board, Fig. 68, Plate XXXV. The only line
to be drawn for setting the centro-linead arms is Sv, which is
the direction of the given line on the ground plan. The line bv
need not be drawn, the points b and v being located by draw-
ing cv parallel with the horizon line and cM or cb parallel to the
distance line SP.
B. To Set the Arms of the Centro-linead if the given Line (VE)
belongs to the Perspective.
Take any point F, Fig. 172, Plate XCI, on the horizon line,
join F with E and F with B, then draw cM parallel to AB.
Through e draw ev parallel to EV and join vb. Owing to the
similarity of triangles vb will be parallel to VB and the angle
which is the inclination of the arm against the ruler L of the
centro-linead. The lines FB and cM are permanently laid
down on the photograph-board, Fig. 68, Plate XXXV, but FE
and ve will have to be drawn for every given line; in this case
two lines will have to be drawn instead of one as in the pre-
Centro-lineads are usually sold in pairs; one serves to work
on the left side of the principal point and the other on the right.
V. The Perspectometer as Used by Capt. E. Deville.
The perspectometer serves to dispense with the con-
struction of the squares on the perspective, when using the
method, of squares (Chapter IV), to draw a figure in the
THE PERSPECTOMETER AS USED BY CAPT. E. DEVILLE. 295
ground plane by means of its perspective. On a thin trans-
parent film (glass, xylonite, isinglass, horn, etc.) two parallel
lines AB and DD', Fig. 173, Plate XCII, are drawn intersecting
the common perpendicular pP. Make DP = PD' = pA = pB = dis-
tance line (focal length) and from p lay off on AB (to both sides
of p) equal distances,
pm = mn = no . . . =p'm' = m'n f =n'o f ....
Join these points of division to P and through the corresponding
intersections of the radials from P with AD and BD f draw lines
rr 1 , tf . . . , which lines will be parallel to AB and DD 1 '.
Use oj the Pers pedometer. The instrument is placed upon a
perspective with P on the principal point and DD' coinciding
with the horizon line. The ground line of the perspective may
fall in X Y\ it is divided into equal parts by the radials from P,
and the trapezoids of the perspectometer represent the per-
spectives of the squares in the ground plane having the equal
parts of XY as sides.
By placing the perspectometer on the perspective in the
manner indicated above, the squares covering the perspective
of the figure, which is to be plotted iconometrically on the ground
plan, are at once apparent and only those needed are drawn
on the ground plan.
The sides of the squares to be drawn on the ground plan
(their side lengths are equal to the divisions on the ground line
between the radials trom P) are laid off from the trace of the prin-
cipal plane on the ground line, and the position of the front line
nearest the picture trace (or ground line) is laid off on the ground
plan either by estimation or by construction. The estimation
of the position of this line (corresponding to ttf) on the ground
plane is made by noting the fraction of a square's side which
represents the distance (between ttf and XY, Fig. 173, Plate XCII)
from the ground line on the perspective.
The perspectometer serves only for perspectives which have
296 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.
the same distance line (like photographs of distant objects taken
with the same lens), different distance lines requiring a new
perspectometer to be constructed for every one.
The width pP should be equal to the height of the horizon
line above the foot of the picture; the radials need not extend
beyond the width of the picture, the distance points D and D r
having been taken as the limit of the perspectometer in the
figure (Fig. 173, Plate XCII) merely to show more fully the
principles involved in its construction. The length of a single
division on the line AB should be selected with reference to the
resultant equal division lengths of the lowest ground line used
for the pictures, as the divisions on the latter give the measure
for the sides of the squares to be drawn on the ground plan.
These division lengths on the ground line should be in har-
mony with the scale of the plan and with the degree of accuracy
that may be required for the delineation of the topographic
features. The smaller the size of the squares on the ground
plan selected the more accurately the transfer to the ground
plan of the figure from its perspective may be made; the same
principles being involved in this method of iconometric plotting
as in the well-known method of reducing (or enlarging) draw-
ings by means of two sets of squares, the ratio of their sides
corresponding to the scale of the required reduction (or en-
Capt. Deville recommends the perspectometer to be made
by first drawing it on paper in a fairly large scale and then
making a negative of it, reduced photographically to the desired
size of the finished perspectometer. A positive copy of said
negative may then be made on a transparency plate, which,
if bleached in a solution of bichloride of mercury, will show
white lines (they were dark before the bleaching took effect)
on clear glass. For the sake of better preservation the per-
spectometer is varnished when completely dry and hard.
When using the perspectometer to transfer figures from
their perspectives to the ground plan, when such figures are
THE PERSPECTOMETER AS USED BY CAPT. E. DEVILLE. 2Q7
situated in planes perpendicular to the picture plane but in-
clined against the horizon plane, the center of the perspec-
tometer is placed upon the principal point P of the picture
plane the same as before, but the perspectometer is now re-
volved about P until the parallel lines of the same are parallel
to the trace on the picture plane of the inclined plane (contain-
ing the figure to be transferred). In this case the trapezoids
of the perspectometer represent the perspective of a net in the
inclined plane composed of squares which are now to be pro-
jected into the ground plane.
This net of squares in the inclined plane, when projected
on the ground plan, will be composed of rectangular figures
of equal size, their long sides being in a direction at right angles
to the picture trace (or ground line) anu of a length equal to
that which is intercepted between two adjoining radials of the
perspectometer on the trace of the inclined plane (on the pic-
ture plane), while the short sides of those rectangles forming
the net of the ground plan will be equal to the lengths obtained
on the ground line by projecting the points of intersection of
the radials of the perspectometer with the inclined plane's
trace on the picture plane upon the ground line of the picture
The construction of the rectangular net on the ground plan
may now be made in an analogous manner to that mentioned
for the squares, and the drawing-in of the figure on the ground
plan with reference to its position within the trapezoids of the
perspectometer is accomplished in the usual manner.
Should the figure be situated in planes that are inclined
to both the picture and the ground planes, then the figure is
first projected upon a plane perpendicular to the picture plane
and having the same trace in the latter as the inclined plane.
298 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.
VI. The Perspectograph, Devised by H. Ritter.
Numerous instruments have been devised for the mechanical
drawing of perspectives from plans (or from nature), or by
means of optical devices, some of which may, inversely, be-
come of use for transcribing perspectives of figures into orthog-
onal projections, and we have seen that Col. Laussedat as far
back as 1849 ma de his first experimental perspective surveys
with the camera lucida or camera clara, devised by Wallaston,
which in this case had been improved by Regnault. The per-
spectograph invented by H. Ritter serves to construct the
orthogonal projection of a plane figure from its perspective
or to draw the perspective from the plans of the object without
referring to the object itself.
Ritter's instrument, manufactured by C. Schroeder & Co.
in Frankfort on the Main, has been patented in Germany,
Oct. 13, 1883, under No. 29002. It was devised primarily
for architectural purposes. For the title of Ritter's descriptive
pamphlet, see Literature, paragraph 2, Chapter I.
This instrument in its present form, composed largely of
wood, is not well suited for surveying purposes, as it contains too
many sources of error, due to lost motion in its bearings ; still,,
its theory being a good one, there is no reason to doubt its ulti-
mate value, even for precise work, if it were carefully made by
an expert mechanician, excluding the use of wood and using
metal throughout, being guided in its construction by the de-
mands of the utmost attainable precision. Since a carefully
constructed instrument based on the present pattern may become
useful in plotting the data of a topographic reconnaissance,
where, in the nature of the work, rapidity in making the results
practically available will often be of greater value than a high
degree of accuracy, the following description of this instrument
may not be out of place here. For its methods of use in photo-
THE PERSPECTOGRAPH, DEVISED BY H. RITTER. 299
topographic surveying we respectfully refer to Capt. Deville's