fitted upon the cadastral framework by one or other of the methods
described below. When this is complete the map is contoured in the
field, names are added and the topography examined for omis-
sions or mistakes.

The most difficult case arises when the area to be mapped is
rugged and mountainous, and the inhabitants hostile: the positions
and heights of a few peaks in it, visible from accessible ground,
have been fixed trigonometrically, but no reliable map exists.

As a preliminary measure oblique photographs are taken from a
variety of points of view. The positions of the camera in space are
calculated, and from measurements on each photograph a number of
rays are drawn to noteworthy points in the valleys and on the hills.
Positions and heights are thus determined for a subsidiary control.
With the axis vertical a series of photographs of valleys and of
watersheds are taken, pasted together, and fitted to the control.
When the map has been thus built up, form-lines are added from the
oblique photographs and upon the fixed heights. In the majority of
surveys difficulties will be of an order intermediate between those
of the foregoing two cases.

Applications of Air-photography. In any particular survey air-
photographs may be used then for any or all of the following
processes, viz.: (i) Air-photo control, (2) Air-photo-topography,
(3) Air-photo contouring.

In taking vertical photographs for air-photo control, exposures
are so regulated as to ensure a substantial overlap, generally amount-
ing to 50% at least. Each successive photograph may therefore be
fitted to its predecessor, and lines or traverses of photographs may
be mounted and scaled between fixed points. Any two or more
traverses of different and independent lines may be made to inter-
sect over some topographical object, the position of which may be
determined as the simple, or weighted, mean of the individual posi-
tions from each traverse. Traverses may also be made to converge
and end upon some prearranged and hitherto unfixed object. This
method has given fairly accurate results in flat country on the scale
of 1/40,000, and is dependent upon the ability of the pilot to main-
tain an even keel and a constant height.

In broken and hilly country no method can be regarded as trust-
worthy which does not take into account differences of altitude.
We must then lie content to limit the use of each photograph to the
measurement of horizontal and vertical angles and to fix the posi-
tions of hew points by intersection from two or more photographs.
Where this principle is decided upon there remains no advantage to
be derived from the vertical photograph, and oblique photographs
are used in preference as covering larger areas and allowing greater
refinement in the measurement of vertical angles.

The first stage of this photo-topography from the air is to inter-
polate the position of exposure in space from three or more points,
the positions of which on the earth s surface are known, and which
appear on the photograph. If we consider the pyramids whose
apices are the lens and the bases of which are the triangles formed by
the three fixed points respectively on the ground and on the photo-
graphic plate (see fig. 2), we see that (a) the angles at the apex are
a function of the lengths ab, ac, be (which can be measured upon
the plate), and of the focal length, (b) the inclination of the ground
pyramid to its base is determined by the direction and magnitude
of tilt ; at the present time there are no means of measuring accurately
the tilt of the plate at the moment of exposure, and calculation
follows by successive approximations from a preliminary estima-
tion ; (c) the position of O in space can be calculated and plotted in
its correct projection on the plane of A, D, C; (d) angles may be
measured upon the plate and rays drawn to additional points from O.

From the nature of the case air-photo control must be limited to
the provision of a few supplementary points.

Where the area to be mapped contains a sufficiently close control
the filling in of topographical detail is more easily done from vertical
than from oblique photographs, providing that the area in question



is not markedly hilly. The scale on which photographs are taken
may be larger or smaller than that of the map, but it must be suffi-
ciently large to allow of clear identification of detail.

The area to be mapped is photographed from a prearranged height
in strips allowing for an overlap in all directions. Much depends
upon the training of the pilot in maintaining his height and his over-
lap. It is usual to arrange for a mechanical control of exposures
regulated according to the ground speed of the aeroplane.



Photo
Pyramid



Ground
Pyramid




Intersected Point



FIG. 2.



The plotting of detail from these photographs would be simple if
the axis of the camera could be maintained in a vertical position. It
would then be necessary only to bring the photograph to the scale
of the map. No means of ensuring this verticality has, as yet, been
evolved. It often becomes necessary, therefore, to fit photographs
individually upon the control points. This can be done graphically,
or optically by the camera lucida, or by the enlarging camera.

The graphic method depends upon the principle that as straight
lines on one plane remain straight lines on any perspective of that
plane the position of a point which lies upon the intersection of
two lines common to the ground and to the photograph may be
readily determined. Within narrow limits the proportional compass
set to the difference of scale between map and photograph at this
point may be used to fix additional points. It is more accurate,
however, to maintain the straight line principle and to cover the map
and photograph with a "grid" of corresponding lines, as in fig. 3.




PHOTO



MAP



FIG. 3.

The photograph is mounted on a sheet of paper a, b, c, d and
A, B, C, D are four points the positions of which are known and
are also identifiable on the photograph. Subsidiary common points
at oO are established by drawing the diagonals, and four subsidiary
quadrilaterals may then be formed by drawing lines through oO
from vV and wW the intersections of the prolonged sides of the
quadrilaterals. The same principle may be applied to any poly-
gons formed by joining up any number of points (more than four)
which are fixed on the ground and identifiable on the photograph.
Detail may be sketched in by eye.

A useful method of plotting, known as the four-point method, is
as follows (fig. 4) : It can be proved that the cross ratios of four
points which lie upon a straight line are the same upon any perspec-
tive view of that line, hence we can readily plot the position of a
fifth point (S) if we know the positions of four points A,B,C,D.

Let A, B, C, D be four known points on the photograph and
o, b, c, d their positions on the map, and let S be a point on the photo-
graph the position of which on the map is to be found.

Join A B, AC, A S, and A D, a b, a c, and a d.



SURVEYING



625



Lay a piece of paper with a straight edge, in any position cutting
the lines A B in B', A C in C', A S in S' in A D in D' and mark
these cutting points on the paper.

Now lay the paper strip on the map and fit it upon the lines
a b, a c, and a d, so that B', C' and D' lie upon these lines.

Mark on the map the position of a point s' opposite the mark S'
on the paper strip. Join a s'. Then s, the position of point S, upon
the map, lies upon the line a s'.





V\



FIG. 4.



Repeat this proceeding from B, C, or D, and another line b s',
c s', or d s', will be secured, the intersection of which with a s' will
define the position of S.

The camera lucida (see 5.104) has been used extensively for plot-
ting. The upright carrying the prism is mounted on a stand upon
which are also mounted two boards roughly at right angles to each
other called respectively the map and photograph boards. Move-
ments are added to allow of rotating the photograph in its own
plane, of tilting the map (or tracing of control points) around an
axis parallel to a marked horizontal line on the photograph board,
and of increasing or decreasing the distance between the prism and
the photo board (fig. 5).



Mill-headed Screur
actuating pinion for raising,
and lowering Photo-carrier



Slide and Rack
tarrying the Prill



Mill-headed Screui actuating
and oinion for rotating
Photo- carrier



Hilt. headed Screat actuating
Slide carrying Pritm




The movement! peculiar to thlt Instrument
are indicated oy dotted lines and arrwt



FIG. 5.

^Graphic and optical methods are tedious and lengthy compared
with a photographic rectification. The ordinary enlarging camera
can be made to answer the purpose with little modification. It must
provide, in addition to its focussing movements, as follows:

1. The negative must be capable of rotation in its own plane
around its centre.

2. The copying board and negative carrier must be capable of
rotation around parallel axes which are at right angles to the optical
axis of the lens.

3. The copying board and negative carrier must be capable of
movement along the line axis of the lens.

> 4. The negative carrier must be capable of a movement bodily at
right angles to its axis of rotation.

By means of these movements a coincidence can be obtained
between the four control points on the map and on the photograph,
and a " rectified " print may be obtained.






Little contouring has as yet been based on air-photographs. It
must be recognized at the outset that it is impossible to calculate
relative heights from measurements taken from a single photograph ;
for the accurate determination of relative heights we must have at
least two photographs taken from different places. An outline of
photogrammetry from the air has already been given and mention
has been made of interpolation in space, and of the survey of new
points by intersecting rays. A short additional step the measure-
ment of vertical angles on the plate makes it possible to calculate
the height of these new points.

Stereo-photogrammetry from the air may develop in the future,
but has not been made use of hitherto. On the other hand much use
has been made of the stereoscopic effect visible on two photographs
of the same area taken from different positions. Such information is
not of an exact nature but gives a valuable indication of ground forms
and brings out the system of drainage.

Until 1920 mapping from air-photographs had been confined almost
entirely to war time, and to areas already covered by a trigonomet-
rical control, hence there had been little opportunity of comparing
the cost of this method with that of any other, or of laying down
definitely its possibilities and limitations. Clearly its greatest value
lies in the mapping of inaccessible country.

So far as can be judged, the chief fields of usefulness open to air-
photo-topography are, the surveying of native towns on scales of
about 1/10,000, or 6 in. to I m. ; the surveying of deltas and intricate
water channels; and the surveying of ancient sites, on which the
indications of a former civilization become far more evident in the
air than on the ground. Topography on ordinary small scales, and
accurate large scale cadastral mapping are, so far, ruled out. But it
appears that developments may very well be looked for in each of
these directions.

Photographic Surveying

The idea of applying photography to surveying was originally
due to Col. Laussedat (1819-1907), who made some experiments
in the matter in 1859, and continued during his long life to
expound and develop the method. Although the system origi-
nated in France not much was done in that country in the way of
its practical application, and, if we except some minor work by
MM. J. and H. Vallot in the Mont Blanc regionin 1892 and some
similar mapping by M. Flusin in 1905, it is to Canada that we
must go for its first use on any considerable scale.

In 1895 Mr. E. Deville, surveyor-general of Dominion Lands,
published his important work on photographic surveying, which
remains a complete exposition of the subject if we exclude some
recent departures. Between 1886 and 1892 photographic surveys
were confined to the Rocky Mts. in the neighbourhood of the
Canadian Pacific railway, but in 1893-4 the method was used
by Mr. W. F. King in the survey of the Canada-Alaska frontier.
In 1901-2 Mr. A. O. Wheeler carried out a very successful
photographic survey of the Selkirk range, British Columbia, on
the scale of 1/60,000; this was published, with an interesting
account of the range, in 1905.

In the U.S. photo-topographic surveys had been made use
of on the International Boundary Survey and reports made
by Mr. M. A. Flemer of the U.S. Coast and Geodetic Survey in
1897-8. Stereo-photo surveys (see below) were employed in
the survey of Tutuila, Samoa, by the U.S. Hydrographic Office
in 1916; and an innovation in the shape of a panoramic camera
was first used by Mr. C. \V. Wright in Alaska in 1904 and ex-
tended by Mr. J. W. Bagley who wrote an important treatise on
the subject in 1917 (Washington, Government Printing Office).

In 1907-8 Lt. M. Weiss, of the expedition commanded by
Duke Adolphus of Mecklenburg, made a photo-survey of the
volcanic Mfumbiro Mts. to the N. of Lake Kivu. Other fragmen-
tary surveys in various parts of the world have been carried out
by the aid of photographic methods; most of them, as well as
those mentioned above, were in mountainous country.

Outline of the Method. Assuming that a photograph is a true per-
spective view, that the plate was vertical when exposed, and that
the horizon-line and focal length of the lens are known, it is clearly
possible to determine the horizontal and vertical angles from the
point where the camera was set up to all objects represented in the
photograph, the horizontal angles being measured from some known,
represented object. If two such photographs are taken from two
points, at known distance apart, we have the means of determining
the distance and height of all points shown on both photographs.

It will therefore be necessary in planning a photographic survey,
to arrange for a triangulation to fix the relative positions of points at
which the camera will be set up, and the first stage in the office
work will consist in the plotting of the triangulation. A camera



626



SURVEYING



station need not, however, be a trigonometrical point, provided that
its trigonometrical position can be measured from the photograph.
To use the photographs for plotting the detail, from each camera
station A draw, at its correct angle, the central line of view. Along
this line draw Ax, equal to the focal length of the lens; through x
draw a line at right angles to A x and plot from * the projections of
the distant points, as measured on the horizon-line of the photograph.
The intersection of rays from A to the points so obtained, with rays
to the same objects from other stations, will give their positions.

It is an almost universal rule of photographic surveying from the
ground to maintain the photographic plate in a vertical position,
because any inclination of the perspective plane of the plate adds
difficulties to the plotting.

A supplementary order of triangulation is usually added contem-
poraneously with the field work of photogrammetry, both to fix
camera positions and to add a few bearings and vertical angles
from which the photographic data may be checked.

For many years cameras specially designed for surveying work
have been available, a good example being the Bridges-Lee photo-
theodolite. The essential features of these are, that the focal length
should remain constant (for which purpose the sensitized surface
of the plate should be pressed firmly against the frame of the camera) ,
that the position of the optical centre, and of the horizon and prin-
cipal planes should be deducible from marks on the plate, and that
the lens should be free from distortion and aberration. It is also
important to provide levels by means of which to ensure the vertical-
ity of the plate. The later photogrammetric cameras are either
interchangeable with transit theodolites on the same portable stands,
carry eccentric telescopes, or else combine the two instruments by
substituting a telescopic lens for the usual photographic lens, and
by inserting an eyepiece in the back of the camera. The field work
demands a high standard of topographic training, for it is not easy
to select the minimum number of views sufficient to cover the coun-
try whilst leaving no gaps. Valleys and low-lying areas constitute
the main difficulty. One or two stations per diem are all that have
been occupied by the same party in the photogrammetric surveys of
the Canadian N.W. frontier, whilst a supplementary triangulation
was carried on concurrently.

The office work takes two or three times as long as the field work
and consists in plotting positions, calculating heights, and drawing
contours from data measured on the developed plates.

The picture trace will naturally assume the form of the arc of a
circle if a panoramic camera is used such as that employed during
1910-6 by Mr. J. W. Bagley in Alaska.

There are several plotting devices on the market, such as the
perspectograph, but they have not been largely employed. On the
other hand vanishing scales and perspectometers (grids showing
the perspective on a vertical plane of a series of squares on a hori-
zontal and lower plane) can be readily constructed.

Stereo-photo Surveying. The most recent development of photo-
graphic surveying consists in the employment of the stereoscopic
principle. The stereoscope as a toy has long been known, but Dr.
Pulfrich of the firm of Zeiss of Jena, and Col. von Hiibl of the Aus-
trian military ^geographical service, conceived the idea of applying
the stereoscopic principle to the service of exact surveying. Other
pioneers in 1907-8 were the late Capt. F. V. Thompson, R.E., and
Mr. Conrady. In 1913 Mr. G. Muller carried out a successful stereo-
photo survey for part of the proposed Hankow-Ichang railway. In
order to carry out a normal photographic survey successfully it is
necessary to arrange for stations far apart and for intersections of
some 30 degrees or so. But in stereo-photo surveying two stations
can be occupied on the same hill-top and their distance apart need
only be some 50 to 300 feet.

In the simplest case let two vertical photographic plates be ex-
posed from two points, say 100 ft. apart; let the plates be in the
same plane and their centres on the same level. Then if these plates
are put into a stereoscope provided with a system of lenses and
prisms such that the eyepieces are brought to a convenient distance
for seeing, we shall clearly get a very much magnified stereoscopic
effect as_ compared with what is obtainable with the naked eyes.
In the diaphragm of each eyepiece let there be a similar movable
mark, or line on glass. On looking through the eyepieces the
marks in question will appear as a single mark floating in space, and
by vertical and horizontal adjustments this mark can be made to
touch any given object in the picture. We have, thus, a means of
measuring small parallaxes and vertical angles, and these can be
read off graduated micrometer heads.

A stereo-comparator as above described gives angles from the
centre of the plate, distances and vertical angles; but the reading is
laborious and the map has to be constructed point by point.

In 1907 Lieut, von Orel, of the Military Geographical Institute
of Vienna, attempted the construction of a machine which should
quasi-automatically draw the map, and in 1909 such an instrument
was made by Zeiss of Jena. A further model of 1911 permitted the
automatic drawing of contours and the outline of detail. The in-
strument _is called the stereo-autograph ; several have been made and
are in existence in Austria, Germany and France. A stereo-auto-
graph is, of course, an expensive instrument and requires a skilled
operator and good plates of even density. But, given these condi-
tions, practical results have been obtained and the method is one



to be reckoned with in the future. Generally with stereo-photography
we are not limited to a country with marked features, as is the case
with normal photo-topography. Provided that the view is clear,
gently undulating or flat country can be as well surveyed and con-
toured as a mountainous region. The method has some obvious
applications, but it is useless in forest-clad country or in towns
and its value largely depends upon good view points. The old,
photographic surveying has as its chief field of usefulness a well-
marked mountainous region. The new is not so limited but its
r&le has not yet been fully determined.

Bibliography of Photographic Surveying. In 1895 Mr. E. Deville
was able to quote the titles of 26 works on photographic surveying;
in 1911 Dr. Pulfrich in his Stereoskopisches Sehen und Messen men-
tions 276 works, chiefly in German, on stereo-photography alone!
The following books may be recommended: Photographic Survey-
ing, E. Deville, Ottawa, 1895; Hints to Travellers, vol. I. R.G.S.,
1906; The Use of the Panoramic Camera in Topographic Surveying,
James W. Bagley, Washington, 1917; Revue Generate des Sciences,
March 1914, Paris, for stereo-photo-topography.

Longitude by Wireless Telegraphy

The chief technical difficulty which explorers and surveyors
in new countries have hitherto experienced has been in the
determination of longitude in regions unprovided with a telegraph
system. This applies to almost all the unexplored, or little
explored, parts of the world. Since 1910, however, the great
advance made in the transmission of signals by wireless telegraphy
has completely done away with this source of difficulty and error. I
Wireless " receiving " sets are now made of a very portable
character; so much so, that one mule or one porter can carry the
whole apparatus. Frequent practical use is being made of this
method of obtaining time signals, as the following instances will
show. In the year 1912 Comm. Edwards fixed positions during the ,
Bolivia-Brazil boundary commission by wireless signals from
Washington and intermediate stations; in 1913-4 Cav. Dr.
Filippo de Filippi in an expedition to the Karakoram used
wireless signals from Lahore and from Italy; Major A. J. '
Woodroffe in 1913-5 determined longitudes on the Peru-Brazil
boundary commission by wireless signals sent from Senna Madu-
reira, Brazil; in 1914-7 the French explorer, Lt.-Col. J. Tilho,
used wireless signals from Paris to determine longitudes in his
explorations of Tibesti, Borku, Erdi, and Ennedi; in 1917
Capt. A. J. Bamford determined the longitudes of Bagdad
and Kermanshah by wireless signals from Fao, which had '
previously been connected with Basra; in 1910-20 the American
traveller, Dr. A. Hamilton Rice, made use of wireless signals from
Annapolis, Washington and Darien, to determine longitudes
during his Amazonas expedition. Fig. 6 illustrates the wireless
receiving set used by Dr. Hamilton Rice in 1919-20; it was
designed by Mr. J. W. Swanson and Mr. P. F. Godley, and was
found quite satisfactory and very portable.

It is safe to say that, in future, no properly equipped exploring
expedition will be without its wireless receiving set. The designs
of these sets will change from time to time and, no doubt, improve-
ments will be made; but the method has proven to be thoroughly
practical, and the extra amount of transport required is already
of a negligible character. One of the greatest difficulties of the
explorer has thus been removed.

Levelling

Since 1910 much progress has been made in the development
of a sound system of levelling, especially with regard to pre-
cise, or geodetic levelling, i.e. that levelling which provides the
framework on which all national levels depend. The now defunct
International Geodetic Assn. laid down some wise rules on the
subject of the precision of work of the highest standard. The
admirable treatise of M. Ch. Lallemand, Nivellement de haute
Precision, marked a great advance on previous text-books; and
the production of the modern geodetic levelling instruments of
France, the U.S. and Switzerland afforded the means of greatly
increasing the accuracy of observation. To this should be added
the introduction, by the Ordnance Survey of the United Kingdom,
of a specially devised kind of permanent bench-mark, which did
away with a weak element in the old levelling, the instability