Geographical surveying, its uses, methods and results

UC-NRLF

III

$B EST blM

ia\L COMMISSION OF

: Cll. FRED. HARTT, CHTEF.

;APHICAL SURVEYING,

BE YEAUX CARPENTER, C

Geographer to the Commission.

FROM VAN NOSTKAND'S MAGAZINE

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GEOLOGICAL COMMISSION OF BRAZIL,

PROFESSOR CH. FRED. HARTT, CHIEF.

GEOGRAPHICAL SURVEYING,

ITS USES, METHODS Al RESETS,

BY

FRANK DE YEAUX CARPENTER, C.E,

Geographer to the Commission.

REPRINTED FROM VAN NOSTHAND'S MAGAZINE.

NEW YORK:

D. VAN NOSTRAND, PUBLISHER,
23 MURRAY AND 27 WARREN STREET.

1 8 78.

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18T8,

By D. VAN NOSTRAND.
"'

PREFACE.

CHAKLES FKEDERIC HAKTT, Professor
of Geology in the Cornell University,
and Chief of the Geological Commission
of Brazil, died on the eighteenth of March
last, in Rio de Janeiro, where he was
engaged in preparing the reports of his
Survey.

His death and the dissolution of the
Commission, of which he was the founder
and director, have prevented the realiza-
tion in Brazil of the plan of surveying
proposed in the accompanying pages.

F. D. Y. C.

NEW YORK, July, 1878.

GEOGRAPHICAL SURVEYING.

IN this paper I shall present a scheme
for the organization, the gradual develop-
ment, and the prosecution of a geographi-
cal survey in connection with the
Geological Commission, which, in the
efficiency of its results, will satisfy not
only the present demands but also the
future needs of the Empire of Brazil for
very many years to come. In the rapidi-
ty of its progress, this survey will be
especially adapted to a country of so
vast an area and comparatively sparse
population, and as an adjunct to the
above Commission, and in great part
carried on by the members of the same,
without interfering with the ends of
that body, it can be maintained at an
expense so moderate as to be in con-
formity with the present desire for econ-

6

omy and retrenchment in the public
service.

THE PROPOSED PLAN OF SURVEY.

The immense empire of Brazil is yet
without reliable geographical maps.
These are necessary to the national wel-
fare. The question arises as to what
kind of maps will be sufficient to satisfy
the imperative needs of the country and
of science. The plan of survey which I
shall advocate is a mean between that
system which takes cognizance of every
house in a village and every little undula-
tion in the landscape, and that want of
system in which are represented whole
mountain-chains that do not exist, or
actual topographical features are delin-
eated with gross inattention to accuracy.
It is a judicious mean between the slow
and laborious processes used, for in-
stance, in the Ordnance Survey of Great
Britain, and the sketchy and unreliable
information gained by the early ex-
plorers of the New World, from whose
results our first maps were compiled.

These last are scarcely more graphic and
complete than our present maps of the
moon, and in fact, speaking broadly,
they are not so accurate as the latter,
which are, in great part, photographs of
the surface which they represent. With
these mere hints of the geography of its
country a people should not feel obliged
to rest satisfied until it can sustain a
minutely topographical survey.

AN EVOLUTION IN CARTOGRAPHY.

The demand for maps depends upon
the population and civilization of a
country. In the beginning a rough
sketch will answer the purposes of the
pioneer. As the region becomes inhab-
ited better maps are wanted, and finally
the people require the nearest possible
approach to absolute accuracy in the de-
lineation of topographical features. Map-
making in every country must follow a
regular evolution from the incomplete to
the complete.

Reviewing the origin and growth of
the cartography of a country, we see how
faulty it is liable to be. The first ex-

plorer is the first contributor to the
geography of a region. By way of il-
lustration, let us follow one of these
pioneers as he traverses Brazil from
South to North. Following up a branch
of the River Plate, he records the ap-
proximate directions and distances of his
journey, which he obtains, perhaps by
the use of unreliable pocket instruments,
perhaps by an occasional glance at the
sun and his watch, or, more probably,
by estimating at night the latitude and
departure which he has made during the
day. At a certain period of his march
he finds a river entering from an easterly
direction, whose volume he measures
with a glance of the eye. Farther on,
he encounters a tribe of Indians, whose
village is situated upon the west bank of
the river; he counts their houses, and
makes the number of these a key to the
extent of the population. At the fol-
lowing night he camps at the foot of a
cataract. Impressed by its grandeur, and
also by a kind of optimism, common to
early explorers, and which will not allow

him to underrate any of the glories
which he sees, he estimates its height to
be at least twenty meters, when in reality
it is but ten.

At a certain point whose latitude and
longitude he determines in a rude and
hasty way with the sextant which he
carries, he leaves the main stream and
follows a tributary to its head in the
highlands, where he crosses the divide be-
tween the great Parana — Paraguay basin
and that of the Amazon. Upon the
summit of the plateau he te'sts his alti-
tude above the sea by noticing the tem-
perature of boiling water, or by reading
the indication of his single aneroid, un-
reliable methods which have been known
to give results even a thousand meters
wide of the truth.* Continuing down

* Gibbon's observations at the head of the Amazon,
both the mercurial and thenno-barometer being used,
show a discrepancy between the two which is equivalent
to 300 meters of altitude. The height of Mount Hood, in
Oregon, as given by one authority, who determined it by
the boiling point of water, is almost 2,000 meters greater
than that indicated by the cistern barometer and by tri-
angnlation. In the writer's own experience he has en-
countered an aneroid record, upon one of the peaks of

10

the Araguaya, he observes the trend of the
mountain-range along his route, and, de-
scending the Tocantins, he makes, a simi-
lar survey extending to Para.

We do not disparage the work of this
man. Under the circumstances of hard-
ship and peril by which he is surrounded
he does all that is possible, and his re-
port is really of great value until some
more reliable exploration can be made;
still, for all of that, it is none the less in-
correct and incomplete.

It is from such sources as this that the
material for our first maps is drawn. In
later revisions there may be introduced
the results of desultory explorations of
mines, railway routes and navigable
waters, as well as the meagre topograph-
ical data acquired by the land surveyor

the Sierra Nevada Mountains of the United States, which
made the height of this mountain to be 3,000 feet above
its true altitude. It is a noteworthy fact that these pre-
liminary determinations, made with the above faulty
methods, resemble the estimates of the early explorers,
inasmuch as they almost invariably give exaggerated alti-
tudes ; perhaps the opinions and imagination of the ob-
server are allowed to form, in some unaccountable way,
a factor in these results.

11

in running boundary lines of private
estates, but still, taken at its best, a map
constructed in this way falls far short of
its purpose as a picture of the conforma-
tion of the earth's surface, or as a guide to
the traveler, the geologist, or to the capi-
talist who wishes to invest his money in
the development and internal improve-
ment of his country.

FAULTS IN EXISTING MAPS.

In his compilation of the scattered in-
formation at his disposal the cartog-
rapher finds that a certain district of
country has never been entered by the
engineer. He knows, however, that two
rivers rise somewhere in this terra in-
cognita, and he feels it safe to predicate
a divide between them. He also thinks
it safe to presume that this divide is a
range of mountains, of greater or less
height, and, in his desire to give an ap-
pearance of finish to his chart, he does
not scruple to insert at this place an
ideal mountain system, and represent
it as drained by the upper tributaries of

12

the two rivers, concerning|whose head-
waters in reality nothing is known.
These physical features soon come to be
reproduced, with more or less variation,
in other maps, and in this manner errors
are grounded in the national geography,
from which they can only be eliminated
by a systematic geographical survey.
Like national myths they stubbornly
refuse to give way until eradicated by
true scientific research.

Supposing, on the other hand, that
the compiler, accepting the report of the
explorer, who claims to have discovered
a range of mountains between the Rio
Parana and the Rio Araguaya, wishes to
represent them upon the map. He has
no mathematical data to insure their
position, and no sketches or other in-
formation from which to draw their in-
tricate topographical features, and so he
evolves from his imagination an utterly
impossible chain of mountains, out of
place, artificial, conventional, and even
mechanical in their regularity. These
he depicts in that stereotyped form of

13

delineation, which is known in the
modern geographical draughting-room
as the " caterpillar " formation.

THE RELATIONS OF GEOGRAPHY TO GEO-
LOGY.

Upon such an unfaithful map as this
it is impossible to faithfully represent
the geology of a country. If the geolo-
gist attempts to lay down his conclusions
upon a sheet of this kind, its' errors will
continually clash with his truths. The
configuration of the land, as it appears
upon this erroneous drawing, might in-
dicate that it belonged to a certain geo-
logical age, and that, in fact, it could
not be referred to any other; the geolo-
gist, visiting and studying the country
itself, finds that it is of a later and
entirely different period. But if he
paints it as it really is he publishes a
glaring anachronism to the world, for
the color which represents the rock of
one geological epoch overlies, upon the
map, the physical features which are
peculiar to another age. As in the

14

artistic and true delineation of tbe
human figure every feature must be the
exponent of anatomical structure, so in
topography, every representation of
topography must be true to geological
structure. Ranges of mountains mean
disturbance or great erosion of certain
strata, and each has its own characteris-
tic features as sharply defined as those
of an animal. This should be thoroughly
understood, and those immense lines of
sierras which are supposed to separate
certain river basins, or are delineated in
the very heart of regions of which we
have no knowledge whatever, should be
erased from the national maps until
these districts can be explored. In the
course of his travels the geologist may
find some physical feature of great im-
portance, which he wishes to portray,
in area and position, upon his chart, but
the best maps at his disposal represent a
topography utterly at variance with
geological structure, perhaps a sharp
ridge of mountains where there should
be a plain, and so they are of no use to

15

him. Or he may find himself obliged to
color the top of a mountain peak with
the tint conventional to the bed of a
lake, and in this manner science is made
ridiculous.

To take an illustration nearer home,
suppose that the group of mountains that
abut into the sea in the vicinity of Rio
de Janeiro have intervening valleys filled
with alluvium, which is really the truth.
Suppose that the limits of these mount-
ains have never been accurately determ-
ined, which is also true. In this case, it
is easy to be seen that if the geologist
lays down upon the map the alluvial
deposits in their true extent, they will
here and there encroach upon and over-
lap the rugged masses of gneiss, and in
places will extend far up the steep preci-
pices of the mountain side. To avoid
this absurdity the geologist is forced to
be as inaccurate as those who have gone
before him, and, in general, every error
in the geographical map must be con-
tinued and apparently sanctioned in the
geological chart that is based thereon.

16

It becomes therefore absolutely neces-
sary that the work of the geologist
should be preceded by and based upon
that of the geographer, and that he
should work in conjunction with the lat-
ter. In the exploration of a new coun-
try the geological party should make its
own topography ; and in the United
States of North America, where the ex-
periment has been most efficiently tried,
this is always the case.

A good geographical map would give,
with sufficient completeness, all the lead-
ing topographical features of the region
explored, delineating with especial care
those peculiarities of structure which are
the keys to the different formations. It
would display the shape and position of
bodies of water, and show how the di-
rection of a stream is changed and de-
termined by the accidents of a broken
and displaced stratification, and by other
circumstances of its boundaries. If re-
strained by canon walls its route would
be angular; down a steep gradient it
would be direct; and in the level allu-

17

vium near the sea its track would be
tortuous and broken into bayous. This
map would distinguish between the
rounded slopes of a synclinal valley and
the abrupt sides and angular cross sec-
tion of an anticlinal cleft; and between
the sharp edges of the volcanic rock and
the eroded angles of the sand-stone. If
there was exposed a great " fault " in the
stratification, it would show it at a
glance, with its precipitous bluff of ex-
posed strata on one side, and, on the
other, its gentle declivity of tilted sur-
face rock. And, drawn in contour lines,
it would reveal, not only the heights of
peaks and passes and other vertical dis-
tances from plane to plane, but also the
various orographic forms, each of which
is full of meaning to the geologist.

ECONOMICAL USES OF THE PROPOSED
MAPS.

Aside from being quite indispensable
to a scientific commission, in the various
ways that have been mentioned, these
maps can be made a graphic supplement

18

to their report in numerous other par-
ticulars, and can be made to embody the
stores of practical information which
they gather incidentally to their regular
work. Upon it they can display the
valleys of arable land and the plains
adapted to grazing. The forests of tim-
ber can be laid down, and, from this
drawing, their areas and values can be
closely estimated. Advantageous sites
for colonies can be noted here. The
superficial contents of coal-beds and ore-
deposits are given, and not only does a
geological chart reveal where the
precious and useful minerals are, or may
be found, but it also furnishes that nega-
tive information, equally valuable to the
miner, which defines to him the larger
districts in which it is impossible for
them to exist, and in which, consequent-
ly, it is a waste of effort to search for
them; it is here that the science of
palaeontology is especially useful. If
any portion of the country lies at a great
elevation, the altitude limits of the vari-
ous forms of vegetable growth may be

19

traced, and also the limits of the possible
culture of grain, coffee, cotton, and the
other principal products. In this man-
ner the map is made a general statistical
report upon the value of the national
domain.

The economical ends served by a work
of this nature in the development and
settlement of a new country, cannot be
too highly esteemed. Every stream of
importance is surveyed, in all except
those minor branches whose courses can
be traced in from the adjacent mountain
stations. The frequent tests for altitude
along its banks determine the rapidity
of its descent, the amount of water-
power which it represents, and its value
as a motor for machinery, and as an
agent in hydraulic mining and diamond-
washing. This profile of the bottom of
the valley also decides the feasibility of
railways or other lines of communication
by this route, while the sketches of the
adjacent hills show what room there is
for such a road, and, in connection with
this, the geologist's report will give a

20

general idea of the rock or other ma-
terial with which the engineer will have
to contend and work. In the survey of
a range of mountains careful readings
for altitude are made, not only on the
summits of the peaks, but also at the
passes, or low depressions in the divide,
while the slope of the descent from the
summit to the valley will be delineated
in contour lines, drawn at such vertical
distances as circumstances may require.
It must be admitted that these contours
will only approximate to their true
places, yet their number will be correct,
and their positions will be such that they
will give with sufficient certainty the
various gradients that occur in the as-
cent, so that, by counting the meters of
rise for every kilometer of horizontal ad-
vance, as shown by the scale of the map,
the engineer or capitalist, in his distant
office, with this sheet before him, can
form a very satisfactory idea of the
practicability of a proposed railway, and
can select the most advantageous route
for the preliminary survey.

21

The meteorological data accumulated
in the process of this work are valuable,
not only in the determination of the ver-
tical elements of the survey, but also as
an illustration of the general laws of
drought and excessive rainfall. At in-
tervals throughout the country, the de-
clination of the compass needle will be
observed, and will be published for the
guidance of land surveyors who may not
be proficient in astronomical observation.
The positions and supra-marine eleva-
tions of all villages, important fazendas,
medicinal and thermal springs, ancient
ruins or other discoveries in archaeology,
supplies of water in a dry country, or of
pasture in a barren district, and all other
places of interest to the traveler, will
be determined. The roads and trails
already in existence will be surveyed
and mapped, while a leading object of
this enterprise will be to find shorter and
easier lines of travel. The explorer who
opens a new pass through the mountains
is a far greater benefactor to mankind
than he who discovers and names a con-
spicuous peak.

22

Many of the national surveys of
Europe were founded on military
necessity, that is, the necessity of having
correct information to govern the move-
ments of armies in time of war and the
incessant transfer of troops in time of
peace. In some of these countries their
early maps were withheld from the
citizen whose taxes had paid for their
construction, and to as recent a date as
1857, in one or two cases, they were
kept secret for use in some contingent
war. This argument of military necessi-
ty will have but little weight in Brazil,
whose rulers, knowing that a country
strong in peace will also be strong in
war, take the enlightened and advanced
policy of encouraging the peaceful pur-
suits of life, as the surest basis of nation-
al strength. Still it must be acknowl-
edged that these maps would be of
excellent service in the administration
of the affairs of distant provinces, in the
transportation of military supplies, and
in the garrisoning of frontier posts,
although the country is to be congratu-

23

lated that, for every soldier to whom
they would be useful, a hundred immi-
grants would be benefited by them.

THE INTENTS OF THIS ESSAY.

While entertaining no wish to make
this article popular, in the ordinary sense
of the word, I shall seek to exclude from
it all formulas, equations for computa-
tion, and other material, purely mathe-
matical, upon which the surveyor bases
his work, and as far as possible I shall
avoid those technical terms which would
be embarrassing to the reader who is not
an engineer. The fundamental princi-
ples of geographical engineering are the
same all the world over, and in every
mathematical library there are books of
reference which give all the laws and
formulas necessary for a work of this
kind. Therefore, nothing would be
gained by their repetition here. Spe-
cialists in geodesy, astronomy, and
hypsometry have investigated their vari-
ous branches, have published their re-
sults, and these, in their purity, are

24

applicable to any quarter of the globe.
One, for instance, has applied the theory
of least squares to geodetic computa-
tion; another has invented the zenith
telescope for latitude observations; and
a third has traced the horary curve in
the barometric record. All of these dis-
coveries fall within the comprehensive
department of the geographer, who
supplements these studies by utilizing
their results in his labors in the Held
and office; or, if he is about to write a
brief exposition of the subject of geo-
graphical surveying, it is his business to
describe, in a straightforward manner,
the way in which practical application
of these truths is made.

This paper will be, in general, a
description of the most approved meth-
ods, the economical devices, and the
practical results of a successful geo-
graphical survey, working in obedience
to the directions of the chief of the
commission to which it is attached, and
covering such areas as may be designated
by him as most worthy of geological

25

and geographical delineation. From
time to time, as occasion may offer, and
especially at the conclusion, the project
will be adapted to the Empire of Brazil,
as it is quite impossible to propose a
plan of survey which will be applicable
to all countries. Although, as has been
stated heretofore, the general principles
underlying this kind of work are the
same wherever physical laws prevail,
and the face of the country is wrinkled
with mountains and valleys and furrowed
with the river-bed and canon, yet there
are physical conditions peculiar to every
land, as well as circumstances of area,
population, and wealth, which require
that it should have its own type of geo-
graphical survey, and not copy too ex-
actly those of any other nation.

THE BEST TYPE OF SURVEY FOR BRAZIL.

Considering the circumstances of area,
population, and wealth it is evident that
the national surveys of Brazil should be
" geographical " in a very liberal sense of
the word; that is, that they should be

26

comprehensive in their scope, rapid in
their execution, and sufficiently accurate
without being too punctilious and too
excessively minute. It is only within
the present generation of engineers, and
particularly in the western hemisphere,
that there has grown up an important
distinction between topographical and
geographical surveying, and even now it
is hard to define the limit between them.
The latter is an outgrowth and extension
of the former and an adaptation of it to
the mapping of large domains at the
least possible expenditure of money and
time.

DISTINCTION BETWEEN THE GEOGRAPHER
AND TOPOGRAPHER.

As one of the many points of differ-
ence between the geographer and the
ordinary topographer, we may mention
that the former, in his travels and sur-
veys, accommodates himself to the roads,
trails, or other open and easy routes that
already exist, and it is but seldom that
he finds himself obliged to make a path

27

for his survey to follow. In the ascent
of some mountains it may be necessary
to cut a road, and in the measurement of
the base line for his triangulation he may
have to prepare the ground before him,
but these are almost the only instances.
The topographer, however, in tracing a
contour line around the side of a mount-
ain, or in making parallel profile sec-
tions of the land, is not allowed to devi-
ate therefrom, and if the way is not
clear, he must wait, perhaps at great loss
of time, until his assistants have removed
the brushwood, or whatever other obsta-
cles may intervene ; in this respect he
resembles the railway engineer. Again,
in the selection of the stations for his
triangulation, the geographer makes the
best possible use of the mountains
of a country as he finds them, generally
accepting them as they occur; though
their arrangement, it may be confessed
here, is not always in such well-condi-
tioned triangles as he would desire. The
topographer, on the contrary, delays his
work by the establishment of arbitrary

28

stations where natural points are lacking,
and by the erection of artificial signals
on those mountain tops which the former
observes without such aid.

In the end it will be found that the
topographer's notes are so numerous and
in such detail that it may require several
centimetres of map to represent one kilo-
metre of the earth's surface; while to
the geographer, who is satisfied with the
general shape of a mountain- spur, the
approximate width of a valley, and the
more important bends of a stream, a
scale of one centimetre to several kilo-
metres may be sufficiently large for the
portrayal of the earth as he finds it. But
it will also be observed, by an economi-
cal government, that while the topog-
rapher consumes several years in the
survey of a thousand square kilometres,
the geographer will obtain a very satis-
factory knowledge of thousands of
kilometres in one year. And, in general,
the superior accuracy, or rather detail, of
the former, is purchased at an expendi-
ture of time and money so great that

29

only the older and wealthier nations
can afford the investment; while I hope
to demonstrate that the geographer's re-
sults are sufficiently complete for the
needs of Brazil.

THE GEOGRAPHER'S PROFESSION.

The geographer's work is a peculiar
and difficult one, and one for which his
ideas must become enlarged by a special
training. This is a branch of our pro-
fession for which no training-school pre-
pares its student and no text-book yet
published can instruct him. This is a
field in which the experienced topog-
raphical engineer, fresh from his labors
on park and landscape, or on the detailed
surveys of thickly-populated Europe,
finds himself unhandy and incompetent,
for much of the experience and tradition
that he brings with him is an incubus
to retard him. To become efficient in
this new service he must forget much of
the rule and routine that he has learned,
and accustom himself to taking broad
and bird's-eye views of the country.

30

Strange as it may sound, he must
make it a matter of duty and pride to
overlook and neglect much that is near
at hand, and remember that, although a
mole-hill at a distance of a few feet sub-
tends a greater visual angle than a
mountain as many miles away, yet it is
the mountain, and not the mole-hill, that
deserves delineation upon his map.
Hitherto he has been local and narrow in
his range; he must now become geodetic,
else he will accumulate a mass of minu-
tiae, whose representation would be in-
finitesimal on a map of the proposed
scale, and which is hence but an incum-
brance to his books, and even worse than
cumbersome, inasmuch as its presence
excludes other and more valuable data.
In short, the topographer considers the
earth minutely, and with a microcosmic
view, but the geographer is a man of no
such narrow horizon, and trains himself
to look upon it as a macrocosm, or great
world.

31

THE INSTRUMENTS USED.

Of scarcely secondary importance to
the men of a geographical corps, are the
instruments with which they shall work.
The tools which have been devised for the
ordinary surveys of land and landscape
must be left at home with the slow and
tedious methods from which they cannot
be divorced. In a work of geographical
extent the spirit-level, chain, and tally-
pins are out of place, and whosoever,
making accuracy his plea, attempts to in-
troduce them there, will find his own
ends defeated by them. Once upon a
time, for instance, an engineer was in-
trusted with the survey of a large tract
of new country. A certain sum of
money and a limited period of time were
given to him, a stated area of territory
was assigned to him, and in return the
authorities expected of him the most ac-
curate and impartially complete map
that his means would allow.

The time and resources granted him
would permit him to touch the country
but lightly and by swift marches, but, as

32

this was intended to be only a reconnois-
sance, nothing more was expected of him
than to trace the conformation of the
land in a general way. He was an
honest and conscientious engineer, and
so great was his zeal for accuracy, or
nicety rather, that he was scrupulous to
a fault. He abused the maxim which
says that whatever is worth doing at all
is worth doing well. For determining
the altitude of stations along the route
he used the spirit-level, and their inter-
mediate distances were found by stadia
measurements, which system, though
considered incautiously rapid in topogra-
phy, is too laggardly slow for the or-
dinary purposes of geography. In this
manner he crossed his territory with a
few lines of march whose profiles were
as trustworthy as those of a railway sur-
vey, and far more accurate than the pub-
lic interest demanded, while between
them there were large areas untouched
and unseen, and of these the public,
whose agent he was, had commissioned
him to obtain information. The failing

33

of this engineer was a common one; he
neglected to distribute his resources
fairly and impartially, and while half of
his map is reliable the other half is con-
jectural.

It would be too long a task to de-
scribe in detail all the instruments used
in geographical work, or to rehearse all
of the devices employed in its prosecu-
tion; however, the most necessary and
novel features will be noticed here. At
the basis of the work is the transit, or
theodolite, which, with compass-needle
attached, is the engineer's constant com-
panion, without which his occupation is
gone, no matter in what field his labor
may lie. As an appurtenance to this,
not the chain nor the stadia, but the
odometer wheel, has become the recog-
nized means of linear mensuration in the
survey of streams and the determination
of those distances of route and detour
which are so useful in filling in a trian-
gulation chart. Instead of the level, the
cistern barometer gives the heights of
mountains, mines, passes, camps, vil-

34

lages, and other important positions,
while the aneroid barometer, portable as
a watch, and as easily read, will tell the
altitude of minor points and give with
sufficient closeness the data from which
may be plotted the profile of the odome-
ter's itinerancy.

THE PERSONNEL OF A GEOGRAPHICAL
CORPS.

These are the three classes of instru-
ments that are indispensable; the purely
geographical party required to use them
need consist of but three men, the en-
gineer, the meteorologist, and the
odometer recorder. To this corps it
may be deemed advisable to add a fourth
member to act as an assistant to the en-
gineer, and, by personal obervation and
experience acquire that facility in the
practice of his profession which will fit
him, in the course of a brief period of
training, for the responsible position
above him. Such a person should al-
ready have the theoretical education of
an engineer, and some skill in drawing.

35

If it is not practicable to make this ad-
dition to the corps, it is well to choose
as an odometer recorder one who pos-
sesses the acquirements stated above,
and to consider that position, whose
appertaining duties are light, as prepar-
atory to the grade of engineer. As for
the meteorologist, his is an intricate
science which cannot be studied too
thoroughly, and barometric hypsometry
should be regarded as a profession quite
distinct from the engineer's, although
necessarily subordinate to it.

The various duties involved in the
measurement of the base-line, at the
opening of the season, may demand the
services of a larger body of men than
this, but, once in the field, any addition
to the above number, except as muleteers
and servants, will be superfluous, as far
as the geographical work is concerned.
One surveyor can see as far as two, and
one man is able to take note of all of the
country visible from his route of travel.
No axemen are needed, for if there is a
tree in the way, the line must yield to

36

the tree; the resultant error will be trif-
ling and will not be apparent in a map
which represents several kilometres of
territory on one centimetre of space.
Neither is there any necessity for rod-
men, with rods of two targets for mi-
crometer measurements or one target for
levels, who would retard the corps by
the long delays consequent upon their
transfer from the stations in the rear to
those in advance. This party travels as
a unit, moving as fast as its animals can
walk, and is never broken, a considera-
tion which is of value in a country of
hostile people.

Of course the scope of the work may
require the service of a great number of
professional men, but its best progress
demands that they should be divided
into corps of the above size, which shall
work in concord and under one general
liead. This director will assign to each
party its territory for the season, and
tupon the borders of these areas, the va-
rious engineers will make rendezvous
from time to time, as circumstances may

37

admit, with their neighbors of the ad-
joining fields, for the purpose of
reorganization, exchange and issue of
material, and especially for the compari-
son of sketches and geodetic data, so as
to insure the proper union of their sev-
eral schemes of triangulation. In order
to make the different systems of trian-
gles interlock in one grand plan, the
observer will frequently be obliged to
read angles to stations which lie in an
adjacent district, and which will be oc-
cupied by his co-laborers for the purpose
of reciprocal observations. It is there-
fore necessary that they should meet in
occasional conference for the mutual
identification of those stations.

THE STATIONS OF SURVEY.

Guided by these thoughts, let us sup-
pose that we have completed our organi-
zation for a season in the field, and that
we are now on the ground ready for
work, at the place selected as the initial
point of the survey. As with all surveys,
this one will be executed from stations,

38

meaning thereby any points at which a
tripod is planted and an instrument ad-
justed, angles are read and sketches may
be made. Of these we shall occupy
four orders, of which, in importance, and
consequently in accuracy, the astronomi-
cal is first. Then comes the geodetic, or
triangulation station; the topographical
station, so designated for the sake of con-
venience; and, finally, the odometric, or
route station. In addition to the ends
which they are especially intended to
serve, each of these will be a meteorologi-
cal station as well. These five classes,
with the incidental details pertinent to
them, will now be considered in the
order named.

THE ASTRONOMICAL STATION.

Since the positions determined by tri-
angulation, or other system of survey in
which terrestrial objects alone are con-
sidered, are only relative to each other
and to the first station occupied, it is
evident that a map may be completed,
which, in itself, will have all of the ex-

39

actness of perfect truth, but whose place
on a projected surface of the globe will
still be uncertain. A map of a conti-
nent may be made, and this may be of
great use in the guidance of travelers
across the continent, and for the local
information of its inhabitants, but still
it does not play its proper part in the
grand plan of this earth's geography, and
define the situation of this land relative
to the other continents of the earth,
until it is bound into place by the meri-
dians and parallels, which are the warp
and woof of the structure of geography.
Therefore, in order to adjust our map,
when made, into its true place, we must
have the absolute determination of one
or more of its positions.

Now there is but one way of finding
the absolute position of an object on the
earth, and that is by going beyond the
earth, consulting the stars, and ascer-
taining its place relative to them. Hav-
ing two triangulation stations thus
located, the whole chart becomes ad-
justed to its place. Or, having the lati-

40

tude and longitude of our initial point
and the astronomical azimuth of a side
of a triangle leading from this origin, the
former serves to pin the plot to the pro-
jected map, and the latter is instrument-
al in orienting it into the area to which
it belongs.

POSITION OF THE ASTRONOMICAL STATION.

For every base-line measured and
developed there should be an astronomi-
cal station occupied, and as a matter of
convenience and co-operation they should
be in the same vicinity, although it is
not necessary that the station should be
directly over either end of the base.
Indeed, owing to great exposure to
the wind, or to inconvenience of ap-
proach, it may not be found practicable
to locate the astronomical station at any
of the points of the triangulation system,
or, to secure proximity to the telegraph,
whose office may be hidden in the heart
of a town, or the bottom of a valley, it
may be so secluded as to be quite in-
visible from those points.

41

If so, it may be easily connected with
them by running a careful linear survey
from the astronomical station to the
nearest geodetic station. If, owing to
the disadvantageous nature of the
ground, or other obstacles in the way, it
may be impossible to measure the dis-
tance directly between these two points,
the engineer can connect them by a
broken line, reading at the astronomical
station the angle between the meridian
mark, already fixed by the astronomer,
and the direction of his first course, and
afterwards referring the direction of each
measured section of his traverse to that
immediately preceding. From these re-
sults he calculates, in meters, the differ- •
ence of latitude and departure between
the two points, and then, transforming
the meters into seconds of arc, he com-
putes their difference of latitude and
longitude.

NUMBER OF ASTRONOMICAL STATIONS.

For a commission of moderate size, in-
cluding one, two, or three engineering

42

corps, the triangular development of one
base will cover as much territory as can
be surveyed by them in a single cam-
paign, and therefore one astronomical
position a season is all that this survey
would require during the first year or
two of its organization. A series of ob-
servations extending through a couple of
weeks, in favorable weather, or through
a month at the farthest, will determine
the geographical co-ordinates of our
point of departure. These can be made
by the astronomer while the engineers
are measuring the base-line and develop-
ing the same, the director is perfecting
his arrangements, and the purveyors are
preparing and distributing the supplies,
instruments, and all of those numerous
articles of equipment which are the fur-
niture of a scientific field season. At
the same time, the meteorologist, by a
set of hourly barometric and psychro-
metric readings accumulates data whose
digest will give the vertical co-ordinate
of this place with the possible error of a
very few feet, and this completes the de-

43

termination of its position with reference
to a system of co-ordinates whose origin
is at the level of the sea at the point
where the first meridian crosses the
equator.

For so short an annual term of service
it might not be advisable to keep an as-
tronomer constantly in commission, nor,
at present, might it be well to go to the
expense of the costly and elaborate in-
struments requisite for the best astro-
nomical observation, provided that the
co-operation of the Imperial Observatory
could be secured and an astronomer
could be detailed from there for that
purpose. In addition to the gratification
to be derived from the warranted excel-
lence of the results which would be fur-
nished by the skilled assistants of that
institution, this cooperation would be a
matter of economy to the Government?
and also, what is especially to be desired
between any two scientific bodies, a
means of friendly relation and inter-
change of information which would cer-
tainly prove of mutual value.

44

ASTRONOMICAL METHODS.

For the determination of the latitude
of our point of outfit the zenith tele-
scope would be used; while the longitude
would be found by the telegraphic ex-
change of time signals, a method which
has lately been so successfully introduced
by the Astronomical Commission. The
present wide-spread extension of lines
of electric telegraph within the borders
of Brazil is especially favorable for a
survey of this nature, whose longitudes
would be based upon telegraphic commu-
nication with the national observatory.
The lines along the coast afford a gen-
eral connection with the northern and
southern provinces of the Empire, while,
by the numerous branches which accom-
pany the railways into the interior, points
which lie far to the inland could be re-
ferred to the meridian of Eio de Janeiro,
which, in its turn, has communication
by cable with the observatories of Eu-
rope.

Thus it will be seen that the engineer
need not be confined to any unfavorable

45

locality in the selection of the ground
for his base line, nor need the chief of
the commission be restricted in his choice
of areas to be surveyed. From the
railways either constructed or contem-
plated it would probably be possible to
reach any of the settled portions of
Brazil without seriously overtasking the
accuracy of the triangulation, and, if it
were required to carry the survey still
farther, longitudes determined by the
method of moon-culminations would be
sufficiently exact for the less important
regions beyond.

ORIGIN OF THE TKIANGULATION.

An inland survey, based upon trigono-
metrical methods, progresses most suc-
cessfully from an initial source concen-
trically outwards. The most fortunate
location for the initial line is in the cen-
ter of some broad valley or intermontane
plateau, whose level expanse offers fair
ground for the measurement of the base,
and whose open field is favorable for the
gradual and symmetrical development

46

of the same until it shall reach the lines
of the remotest triangles, in which it be-
comes a metrical standard for finding
their length. In an extensive survey,
lasting for years and covering broad ter-
ritory, a series of bases are indispensa-
ble. These act as checks upon each
other, and the net-works of triangles
emanating therefrom are dovetailed into
each other, and, in their adjustment to
fit, each to each, what little error they
may have accumulated is reduced to a
minimum.

For instance, on each side of a range
of mountains there is an open basin. In
each of these an astronomical station is
established and a base is measured. On
the comb of the intervening sierra, one-
hundred miles apart, stand two pre-emi-
nent mountain peaks. The latitude and
longitude of each of these, with the
distance between them, is determined
from the two origins independently.
They check each other, verifying, in
their agreement, the accuracy of both
systems, or showing by their disagree-

ment that there is an error somewhere^
and the long line, drawn by the labor-
saving appliances of trigonometry,
through a hundred kilometres of aerial
route, a thousand meters above the val-
leys and chasms which it spans, is now
ready to be used as a new base in the
primary triangulation.

It may be difficult to find a favorable
locality for the source of a triangulation
immediately upon the sea-shore, as there,
unless there are islands in the adjacent
ocean, one side of the field is quite open
and affords no stations to be occupied.
If it were not for this objection it would
seem best to measure a succession of
bases along the coast of Brazil, and
thence develop them westward. A tri-
angulation is always most accurate in
the vicinity of its origin, and as it be-
comes more and more remote from its
initial ground it becomes less reliable,
owing not only to the continued multi-
plication of the original error of the
base, but also to the accumulation of in-

48

accuracy and mistake * from other
sources. Now, the population of Brazil
is thickest along the sea, and thence, into
the interior, at least in many provinces,
it gradually thins out. The importance
of the country and the necessity of
having truthful maps correspond to the
density of the population. Add to this
the fact that the most interesting geology
of Brazil is on the sea-board, and,
furthermore, the important considera-
tion that the coast of a country, for pur-
poses of navigation, demands a more
rigorous geographical determination than
the interior, and it will be seen that the
triangulation upon which this delineation
depends should not originate too far
away. In a general survey of Brazil,
therefore, the first series of astronomical
stations and bases should be established,
if not upon the sea-shore itself, at least

* There is an important difference in the meanings of
the terms "mistake" and "inaccuracy." If a man,
carelessly reading a vernier whose indication is 38' 45",
calls it 39' 45", he is guilty of a mistake. If from parallax
or some defect in vision or judgment, he calls it 38' 40",
he is inaccurate. Mistakes are due to want of care ; in-
accuracy, to want of precision.

49

upon the first plateaus that are encount-
ered between the mountains of the in-
land.

POSITION OF THE BASE-LINE.

In its direction and position the base-
line should bear judicious relations with
certain hills, knolls, corners of terraces,
or other prominent elevations in the vi-
cinity, which may be selected as sites
for the stations to be occupied in its de-
velopment. The plans for its expansion,
matured before its position is selected,
should include two prominent peaks in
the horizon, remote from the origin and
from each other, whose distance apart
this measured length will be instrumental
in determining. The ground upon which
it is to be measured should be as smooth
and bare as possible. It should be free
from brush, tall grass, or other vegeta-
tion, and also from hillocks and gulches,
which are serious impediments to a work
of delicate mensuration. Whether it is
level or not, provided its slope be grad-
ual and even, is of secondary importance,

50

as corrections may be easily applied to
cancel the effect of its gradients.

LENGTH OP THE BASE.

The length of the base may vary from
two to ten kilometres. In the opinion
of many engineers more than four kilo-
metres of measured length is zeal gone
astray, for the advantages of accuracy
gained by such excess would be obtained
more easily by devoting the extra time
to a more elaborate trigonometrical de-
velopment. No arbitrary rule can be
applied here, however. All must depend
upon the judgment of the engineer, who
will consider his surroundings, and if
they are favorable for a slow and pro-
gressive development, a short base will
answer; but if he is obliged to carry his
triangulation from the base stations to
the distant mountains by an abrupt
transition, a longer one will be required,
to prevent too great acuteness in those
remote angles.

INSTRUMENT OF MEASUREMENT.

Since rapidity, as well as accuracy, is

51

an object, we use a steel tape, ten or fif-
teen metres in length, as a measuring
unit. In the swivel at one end of this
there is a thermometer which tells the
heat to which the tape is exposed at
any time; there is also a micrometer
screw, by which it can be lengthened or
shortened in compensation for any possi-
ble change of temperature; and there is
a dynamometer attached to govern the
tension applied, which should amount to
three or four kilograms, being at every
application the same as it was in the orig-
inal test for length, to which the tape
was subjected.

Thus, as this apparatus is applied, in
the process of measurement, it is under
a constant strain, which preserves it
from the error from sagging, to which
all flexible cords are liable, and its length
is always corrected to meet the contrac-
tion and expansion which the metal is
constantly undergoing as the tempera-
ture varies. Should this micrometer be
but incompletely graduated, so, for in-
stance, as to be adjustable only for every

52

five or ten degrees of thermometric
change, or should it even be wanting
entirely, very good results can still be
obtained with the steel tape by reading
the thermometer at every application,
and, in the final computations for length,
making the necessary temperature cor-
rections. Used carefully and with intel-
ligence, this instrument is one of the
most valuable adjuncts of the geograph-
ical survey, and, in the hands of consci-
entious and interested observers, it is
capable of results that are very near the
exact truth; the error ought not to ex-
ceed one centimeter for every kilometer
of measured distance.

METHOD OF MEASUREMENT.

The mensuration may be made on
wooden plugs, with smooth, flat upper
surfaces. These are driven firmly into
the ground along the alignment at inter-
vals equal to the length of the tape, and
should be allowed to project above the
earth sufficiently to permit this cord to
swing clear of all inequalities in the

53

surface, or other obstacles between the
two stations. Or, instead of these, little
stools of plank may be used; these
should have short, pointed iron legs, to
be forced into the ground, so as to hold
the wooden block firmly in position.

When all things are ready a distance
of one or two kilometers can be meas-
ured in one day. But, on account of any
possible inefficiency in the compensation
for temperature, and also because even
the best assistants are liable to a per-
sonal equation in sticking the marking
pin, some invariably inserting it to the
right of perpendicular, and others the
reverse, it is well that it should be
measured several times, and by different
persons, and a mean of the results taken.
Then it should be leveled, in order that
each tape-length may be corrected for
its gradient, which is done by a simple
trigonometric process, and finally it is
reduced to its corresponding concentric
arc at the level of the sea, when it is
ready for use in the system of triangu-
lation.

54

THE ASTRONOMICAL BASE.

The method of base-measurement by
astronomical observation is sometimes
resorted to in geographical surveying,
but this process will be noticed here
only sufficiently to point out the serious
objections that there are to its use.
Having the latitudes of the two ends of
the base and the azimuth of one from
the other, it is a simple matter to com-
pute their distance apart. This seems to
afford an economy of labor, over the
former method, that involves the determ-
ination of the latitude and longitude of
the first station, the azimuth of the i ase-
line, and its length by direct measure-
ment; this one requires the determina-
tion of the latitude and longitude of the
first station, the azimuth of the base-
line, and the latitude of the second
station. The latter is apparently the
simpler and shorter task, and since both
methods are based upon astronomical
observation they would appear to be
equally reliable. But they are not.

Experience has long since taught the

55

scientific world that the probable error
of any ordinary astronomical result is
several meters at the very least, and that
it is not safe to put absolute reliance in
those reports which give a latitude down
to a very small fraction of a second.
Now, in that system of triangulation
whose position is based upon the astro-
nomical determination of one point only,
an error of a few meters in the latitude
of that point will not do material injury.
It will simply displace the entire trian-
gulation scheme, as a whole, so much to
the north or the south, while, since the
length of the base, or measuring unit of
the proportions of * this scheme, was
accurately found, there will be no error
in these proportions. But, in the astro-
nomical measurement of a base, suppose
its two terminal points to be in their
most favorable position, that is, on the
same meridian. The latitude determina-
tion of the southern station places it
several meters too far to the south of
its true position ; that of the other, per-
haps, makes it an equal distance too far

56

to the north. Hence it follows that
there is an error in the length of the
base equal to the sum of the two astro-
nomical errors, and this, in the develop-
ment, is multiplied almost indefinitely,
being repeated in any side of triangle as
often as the length of the base is con-
tained in the length of that line. This
is supposing the base to be an arc of
meridian; the greater its divergence
from the meridian, the more seriously,
for obvious reasons, will an error in the
astronomical determination affect the
length of the base. An astronomical
base-line, therefore, should only be used
when there are difficulties which make a
direct measurement impossible.

THE DEVELOPMENT OF THE BASE.

In the early stages of the develop-
ment, occurring, perhaps, on the level
surface of the plain, it will be found
necessary to use artificial signals. Great
tripods of frame-work, ten or fifteen
meters high, are constructed, leaving
ample space within for the observer and

5?

his instrument. In erecting these, care
must be taken that none of the legs of
the tripod interfere with the view to-
wards any of the proposed triangulation
stations. Each of the signals terminates
at the summit with a flag-staff, to which
voluminous folds of white muslin are
nailed, while the body of the steeple is
wrapped with the same material and
decked with loose tatters and streamers,
which, by their ceaseless flutter in the
wind, offer occasionally a surface from
which the light is reflected to the eye of
the distant observer. The same purpose
may sometimes be better served by the
use of glittering sheets of tin, or by a
cone of the same material. These meth-
ods all have one very great advantage
over the more accurate heliotrope, that
is, they are always in position, and ready
for observations to be directed upon
them at any time. The use of the re-
fleeting mirror, however, unless there are
a number of heliotropes in the field, in-
volves the loss of much time, as the in-
strument is transferred from one to an-
other of the neighboring stations.

58

The development stations should be
erected in conspicuous places, on high
ground or the salient angles of bluffs,
that the observer may know where to
direct his instrument in searching for
them, as it is extremely difficult to pick
out the faint glint of a few yards of
muslin on the broad light surface of a re-
mote plain. As the development con-
tinues and climbs from the foot-hills into
the high and peaked mountains, these
natural points are sharp and distinct
enough, being projected against the sky
beyond, and the labor of station-building
ceases, except in cases that are very un-
favorable.

True, this triangulation by natural
points is not so precise as it is in some
geodetic surveys, and especially in the
surveys of coasts, where even the phase
of the conical signal is considered too
important an element of error to be neg-
lected; nor is it wise that it should be so,
for a fault of a few meters in the posi-
tion of a mountain-top in the remote in-
terior of Brazil, located by this plan, is

59

at present of no practical consequence,
and the nation cannot afford to purchase
an accuracy imperceptibly greater than
this by an expenditure that would many
times exceed the cost of this method of
survey. Considering a mountain as a
land-mark by which travelers are assured
of their place and are guided as they go,
it will be seen that, to men who travel
by land, a small fraction of a kilometer,
in latitude and longitude, is a deviation
which they cannot notice; to the voya-
ger at sea, however, the exact site of the
sunken rock which he shuns should be
known to him, in order that he may cer-
tainly avoid it. This is why the coast
survey, in most countries, precedes that
of the inland in the degree of accuracy
which characterizes it, as well as in the
amount of expense which attends it.

TRIANGULATION BY NATURAL POINTS.

It must not be inferred, however, that
the use of natural points in triangulation
necessarily involves a serious accumula-
tion of error. In general, the engineer,

60

looking from one station to the next, can
readily cover, with the thickness of the
spider-line of his instrument, the highest
ground of the distant mountain, and
that point is selected as a correlative
station, because that is the spot which
can be most easily identified, either from
a distance, or upon the ground itself.
If this place is uncertain, as where there
are a number of pinnacles of equal alti-
tude, or not sufficiently prominent, as in
a plateau summit, some peculiar object,
as a solitary tree, or an isolated boulder,
should be chosen as a center upon which
to sight. If the profile of the mountain
has but little curvature, its culminating
point is usually determined by a pile of
rock, a clump of vegetation, or other
body upon its crest, which, although it
may not be distinctly visible from a dis-
tance, yet has the effect of increasing
the apparent altitude at that precise
locality. In the same way the useful-
ness of a monument of rock, which a
party should always leave behind it
upon a mountain, as a signal to look

61

back upon, does not terminate at that
distance at which it becomes apparently
invisible. The eye will still be im-
pressed with the superior elevation of
the place where it stands.

If the round top of a mountain is per-
fectly bare, and offers none of these ac-
cidental aids to the observer, it is well
for him, in reading his first angle to it, to
keep the horizontal cross-wire tangent to
the surface, while he makes a careful
and deliberate search for its highest
point. Having decided upon this, he
brings the vertical wire upon it, and then
follows down the thread with his eye
until he finds it bisecting some well-
defined body in the field before him,
such as a corner of rock or the trunk of
a tree, and, in his repetitions of the
angle he fixes the vertical wire always
upon this object, while keeping the hori-
zontal thread tangent to the surface. In
this manner he secures to each of the
following readings the advantages of the
prolonged study given to the first, and
not only are his results more accurate,

62

as a whole, but they also agree better
among themselves, which is always a
source of gratification to the engineer.

THE MOUNTAINS OF BEAZIL.

In those lands which are remote from
the equator the summits of the high
mountains, of an altitude of three thou-
sand metres or more, are above all vege-
tation and in the belt of perpetual snow,
and their occupation is a work of great
privation and exposure. The mountains
of Brazil are exempt from that disad-
vantage to triangulation, as the climate
is never rigorously cold here, and the
elevation of the highest land is less than
three thousand metres. The only ob-
stacles to be feared here are the oppo-
site disadvantages of too much vegeta-
tion, either hiding the tops of the peaks,
or embarrassing the ascent to them, and
too little height, whose result is liable to
be a system of round, well-preserved,
and insufficiently pointed mountains.
But if those in the vicinity of Rio de
Janeiro are to be accepted as a criterion,

63

nothing more could be desired in the
way of natural aids to triangulation.

PROGRESS OF THE TRIANGULATIOX.

In some cases it may be absolutely
necessary to send a party in advance to
erect monuments of stone, or signals of
timber upon proposed stations which are
at the same time important and unfavor-
able for observations ; or, should the
mountain be covered with forest, it may
be necessary to send axemen to clear
away all but the largest and most cen-
tral of these trees. Such action, how-
ever, causes a vexatious delay on the
part of the engineer, and is contrary to
the fundamental principles of this
method of survey, whose work should
be a steady and unretarded progress,
and should be reconnoissance and com-
pletion in itself.

From the top of his first high mountain
station the engineer sees his allotted
territory spread out before him, and he
immediately begins to lay his plans for
the coming season. He selects two dis-

64

tant peaks, which, with his present
station, will form a grand triangle. Be-
yond these, far in the distance, there is
yet another, and these four constitute a
great quadrilateral, the lengths of whose
diagonals may each l>e determined by
two independent sets of observations,
checking each other. In like manner
he makes the circuit of the horizon, util-
izing, as best he can, the peaks which
rise around him.

Although, owing to the many obsta-
cles and unforeseen difficulties which are
experienced in traveling through an un-
known country, he may be compelled to
modify and alter his first plans very
often, yet as soon as he abandons one
feature of his scheme he immediately
adopts a substitute to take its place.
To be provided for such an emergency,
if a distant peak, as,f or instance,one of the
sharp pinnacles of the Organ Mountains,
should appear impossible of ascent, he
will select another in the same vicinity,
and consider that as an alternate to the
first, reading angles to it and treating it

65

in all respects as a regular station as
long as such a reserve may seem neces-
sary.

In proceeding from one mountain to
the next he surveys all of the interme-
diate country, his course being governed
by the advantages and obstacles whieh
present themselves from day to day.
His route should never be an arbitrary
one, determined at a distance and weeks
beforehand, but he should be free to act
upon the spur of the moment, following
a stream to its source here and stuvey-
ing a lake there, according as these geo-
graphical features may be encountered.
If these features are depicted on maps
already made, then there is no need of a
second survey of the country; if they
are not, he is not likely to know of their
existence until he finds them.

EQUIPMENT OF THE PARTY.

Since the terminus of a day's survey
cannot always be advantageously decided
upon, even in the morning on which it is
begun, it is especially desirable that th§

66

party may carry with it its own equipage
and supplies, so as to be prepared to
camp anywhere that night may over-
take it. As it is a part of the policy of
geographical work that the engineer
should never follow the same route
twice, a survey carried on by daily ex-
cursions from fazendas, settlements, or
other fixed points of supply, returning
to this base by the same road in the
afternoon, would cost a great waste of
time and energy. The necessary outfit
of a scientific corps, consisting of instru-
ments, clothing, cooking utensils, and
provisions, can be carried by a train of
pack-mules equal in number to the peo-
ple whom they accompany. With this
equipment the party are independent,
and can camp anywhere that wood for
fuel, forage for the animals, and a sup-
ply of water are found. This arrange-
ment is particularly necessary in the
occupation of a mountain station, upon
which, for successful observation, it may
be imperative to arrive at an early hour
in the morning and to remain through

67

the greater portion of one, two, or three
days. From a camp near the summit
this may be reached in an hour or two;
but from a distant base almost the en-
tire day would be consumed in the jour-
ney to and fro.

THE TRIANGULATION STATION.

The mountain will be ascended by the
engineer, the meteorologist, and such
assistants as may be required to carry
the implements of the work and the food
and water necessary for the maintenance
of the party, and to build the stone
monument, which, if possible, should
always crown the peak, to receive the
records deposited here, to assist in the
future identification of this station, and
to serve as an object upon which to
direct the telescope in subsequent ob-
servations. One day will be a sufficient
time of occupation for the ordinary
triangulation station, provided the
weather be favorable. To the more
important ones, however, it may be
advisable to devote two days, spending

68

one night upon the crest in astronomical
observations for the determination of
the azimuth of some line radiating from
here; this will serve as a check upon its
computed value, as derived from the
original azimuth determination made by
the astronomer at the base-line. In
times of high wind, or cloudy and stormy
weather, especially liable to occur upon
the summits of peaks, it may be several
days before satisfactory results are ob-
tained, and therefore the party should
always go well equipped for a prolonged
stay in their mountain camp.

PROFILE SKETCHES.

As an economy of time, which is of
the greatest value here, the observer
should make all reasonable haste in his
operations. Especially is this so in his
sketches, over which he must not linger,
which, if he is anything of an artist, he
will be sorely tempted to do. He may
see before him broader views and
scenery more grand and impressive than
ever was painted yet, but picturesque

69

effects are no business of his. To the
geographer of artistic tastes there is
great temptation to finish his sketch by
inserting a pine-tree in the foreground,
and, perhaps, an eagle's-nest in the tree;
this is all very wrong, as such dalliance
may cost the omission of that far distant
peak, which is printed like a fine point
against the horizon, and which, insignifi-
cant and low as it appears, is yet of
vital importance to his scheme.

His sketch is perforce but the outline
and skeleton of a picture. Two con-
verging straight lines, with a few strokes
of shading, hastily thrown in, are suffi-
cient to represent the ordinary mountain
peak. Yet, if the peak should possess
any oddity or marked individuality of
shape, this feature should be preserved
and even magnified in the drawing, as a
key to the identification of this point
when seen from elsewhere at some other
time. Since any mountain, from differ-
ent points of view, presents phases that
are quite dissimilar, it is one of% the
greatest difficulties of triangulation to

70

make sure of the identity of a station
previously occupied, or, where there are
a number of observers in the field, to se-
cure uniformity in the choice of the same.

CONTOUR DRAWINGS.

The expert geographer is proficient not
only in rapid profile but also in contour
drawing, and on every mountain station
he executes a contour plot of that scope
of country which he sees beneath his
feet, and of whose conformation he is
reasonably certain. But in the prepara-
tion of this local plot he should not be
too comprehensive, and go beyond the
bounds of certainty into the outer limits
of conjecture. Every mountain is sur-
rounded by valleys, on whose farther
side are other ranges perhaps as high as
this, and they form the limit beyond
which no contour sketch should presume
to go, else it becomes conjectural and
unreliable. It may include those en-
virons of valleys, with a periphery of the
foot-hills which are beyond them, and an
indication of the canons which indent
the same, but no more.

71

In the office a contour sketch is ac-
cepted as truthful evidence of the ground
as it really is, while a profile drawing is
considered only a copy of the country as
it appears to be, when uncorrected for
the illusions of perspective, and is studied
and deciphered accordingly. Looking
abroad from this station, the successions
of distant ranges, which are in reality
separated by broad interspaces of valley
and plain, are projected into a dense and
circular wall, apparently unbroken by
pass or intermission, whose serrated out-
line is seemingly as continuous as the
horizon. It is an error to which the
human sight and judgment are subject,
and so, in orographic delineation, the
impressions of the eye are to be received
with caution, and only the readings of
the theodolite are to be accepted in full
faith.

PHOTOGRAPHS.

As a supplement to the pencil of the
engineer, the photographer's camera can
often be used to good advantage in se-
curing, in their true proportions, the

72

many details of geological structure
which are necessarily omitted from a
hasty sketch. In the best geographical
delineation of a country, a series of
photographs are almost indispensable,
as, aside from affording much material
for the filling in of a map, they reveal
the nature of the surface which they
represent, showing whether it is regular
or broken, well-preserved or eroded,
whether a cliff is impassable or easy of
ascent, and whether a coast is smooth
and sandy, or irregular and rocky. All
of these conditions should be made to
appear in every good map, whether in
contour lines or hachures, and particu-
larly so, when, as in this case, the map is
intended as a basis for geological repre-
sentation.

READING THE ANGLES.

The instrument of triangulation is a
theodolite,- whose accuracy and weight
increase with the minuteness of the
graduation, but, in this work, in which
rapidity and ease of transportation are

73

to be considered, there comes a limit be-
yond which it is imperative to sacrifice
nicety to portability. This is reached
when the limb is graduated so as to dis-
criminate to ten seconds of arc, between
which divisions the observer may esti-
mate to every intermediate five seconds.
With this he reads and repeats the
angles, singly and in combinations, that
lie between the visible points of the
triangulation scheme. It is advisable to
make at least six determinations of each
angle upon each of the two verniers of
the instrument, amounting to twelve
repetitions in all. The greater the num-
ber of readings from which the mean is
derived, the less will be the " probable
error of observation affecting that mean.
The observer may complete the repe-
tition of each angle by itself, or, what is
more convenient, he may read them in
conjunction, by making six complete cir-
cuits of the horizon. In either case the
graduated limb of the theodolite will be
turned 30° in azimuth at every return to
the initial point. In this manner each

74

angle is read upon twelve different and
equi-distarit divisions of the circle, and
the faults arising from eccentricity or
imperfect graduation are reduced to a
minimum.

The most opportune moments of the
day will be devoted to this important
task, and all other duties will be neg-
lected for this. Successful triangulation
demands perfect quiet and a clear hori-
zon. In a dense and hazy atmosphere,
or in a region of low clouds, the observer
may find his opportunity in the evening
or early morning, when the sun is be-
hind the hills, and the rim of the earth
is seen in" silhouette against the rosy
background of the sky.

SUBORDINATE ANGLES.

Upon the triangulation station the
engineer also reads angles for the direc-
tion of the spurs which project from
here and of the streams that debouch
from here, estimating the distances of
geographical features in his immediate
vicinity. How far he may trust to his

75

judgment in this respect, will be determ-
ined by the circumstances by which he
is surrounded. It is the engineer's duty
to make the best map of a country that
is possible with the advantages at his
command, and if he should see before
him a tract of country, distant even ten
or twenty kilometres, which he will
never see again, he should take note of
it on his contour plot; but if he knows
that some future route of his will cross
it, he can afford to neglect it now.

In addition he takes readings to infe-
rior elevations which, although they
may never be occupied for reciprocal ob-
servations, may yet be located by
intersections from two or more triangu-
lation stations. Some point, or "tit,"
standing on the edge of an abrupt bluff,
where the rapid descent begins, is used
as a means of marking the end of a
neighboring mountain range. A solitary
butte on the plain, insignificant in itself,
is very useful in determining the locus
of the stream which flows by the side of
it. A promontory, jutting into the con-

76

fluence of two rivers, is instrumental in
fixing the place of their union. Sights
are also taken to the junctions of
streams, the mouths of canons, and to
the church or other central object of a
distant village. A spot of green on the
desert, evidence of a spring of water
there, is located, for it will perhaps be
camping-ground some day for himself or
his co-laborers. A minute patch of
white lake-bed, or red escarpment, or a
solitary tree, is sighted upon, because on
such a day he made an odometric sta-
tion there, and this sight will serve to
check his position.

NOMENCLATURE.

In his note-book and mind he has
dubbed all of these things with graphic
titles, or designated them by letters of
the alphabet, and by these tokens he will
know them when he sees them again.
But this system of names is only a
transient device for the assistance of
himself and those who work in concord
with him, and should not appear upon

the printed sheet to the exclusion of tae
native and established nomenclature of
the country, which should be investigated
as far as possible, and, upon the final
maps, should be adopted in preference
to the arbitrary naming of any one man.
The usefulness of a map, as a guide to
the traveler, is in a great degree invali-
dated by a nomenclature which is at
variance with that in use upon the ground
itself. Perhaps the modern geographer
is guilty of no more common and high-
handed outrage against right, conven-
ience, and beauty, than by ignoring the
appropriate titles which abound in every
country, however wild and uncivilized,
and attaching his own, or by mutual and
tacit agreement, the names of his com-
rades, to the mountains of that land,
thus announcing themselves to the world
as nostrums are advertised on the pyra-
mids.

THE TOPOGEAPHICAL STATION.

All of the preceding description that
does not refer to the triangulation pro-
cess is also pertinent to the topographical

78

tation. This term is applied to those
isolated stations of survey, apart from
the route of the odometer, and interme-
diate to the points of primary triangula-
tion. They are more numerous than the
primary stations, being usually scattered
over the country at intervals of not
more than twenty kilometres, but are
less important, since there is no great
responsibility of accuracy resting upon
them. The topographical stations cor-
respond, in position and numbers, with
the secondary triangulation stations of a
more elaborate geodetic survey.

A SECONDARY TRIANGULATION.

Even here the topographical station
may be made a point in a subordinate
scheme of triangulation if its situation is
elevated, distinct, and capable of recog-
nition from a distance. Of course, it is
desirable that every occupied station
should subsequently be made an object
of reciprocal observations, and the engi-
neer should neglect no opportunity to
confirm his position in this manner.

79

Each point thus fixed becomes the center
of a plexus of triangles, of each of which
the three angles have been observed;
the total error of observation in these
three angles becomes apparent, and the
computer is enabled to distribute it judi-
ciously among them before he proceeds
to the computation of the sides.

For this reason the observer upon any
topographical station will make careful
search for other points which he may
have occupied or may contemplate oc-
cupying, and will be more than usually
cautious in reading angles to them. On
his return to the office, at the end of the
season, he will pick out from the multi-
tude of his notes as many complete tri-
angles as he may have observed, and
these will be so much gain attained at a
cost of but little extra labor. But if he
makes it imperative upon himself to
carry on a complete and systematic tri-
angulation within the first, the additional
refinement gained will by no means com-
pensate him for the disadvantages of
reconnoissance and delay which this in-
volves.

80

It is safe to say that it is a longer and
more laborious work to accomplish an
unbroken secondary triangulation than
a primary, as the stations are more nu-
merous, less elevated and conspicuous,
and oftener in the shadow. On the
other hand, the results are by no means
so valuable. The primary triangulation
sustains the general and continued accu-
racy of the survey; the secondary does
little more than to insure the individual
positions of its own stations.

POSITION OF THE TOPOGRAPHICAL STA-
TION.

Although not necessarily a point in
the triangulation proper — the site of the
topographical station must afford angu-
lar data sufficient for the determination
of its position by the three-point problem.
After that, its predominant idea is that
it is a means of local geography, or to-
pography, and a center for a series of
contour sketches. In addition to these
detailed plots of the country in the im-
mediate vicinity, profile drawings of the

81

more distant regions are made. Then,
by lines of sight, which shall be intersect-
ed by other rays from other topographical
or triangulation stations, the most
prominent features within a radius of
twenty or thirty kilometres are crossed,
and, as a precaution, angles are also read
to all eminent points visible at a greater
distance, even to the horizon, as they
may come into use in some future di-
lemma in map-drawing.

While the site of the topographical
station should be as elevated and marked
as possible, yet any hill, however humble
and inconspicuous, or even the level sur-
face of a plain, may serve this purpose?
provided that there be three triangula-
tion stations, or other known points, visi-
ble, and there is any useful information
to be gained by lingering here. A few
hours are usually enough for its occupa-
tion, and the route between points of
triangulation should be marked at regu-
lar intervals by the monuments of these
stations. It is a good plan for the en-
gineer to make a practice of diverging

82

from his route at some point in each
day's odometric survey, and, ascending
a suitable eminence close at hand, make
a topographical station there. As far as
a general rule can be given for the oc-
currence of mountain stations, it is advis-
able for the party to advance by linear
survey every second day, remaining in
camp on each alternate day, while the
engineer ascends some peak in the vicin-
ity for the purpose of establishing a
topographical or triangulation station
there.

The - large triangulation theodolite
should be used in the more important
topographical stations, or those which
may possibly be treated as points in a
secondary triangulation, but, for the sake
of convenience, the small route transit
must be made to suffice for those which
are made in the course of the daily
march.

THE ODOMETRIC, OR MEANDER SURVEY.*

The meander survey is useful as an

* Note to the Portuguese Edition.— This term, which is
now firmly grounded in the technical language of

83

adjunct to the triangulation, filling up
its skeleton with that 'detailed informa-
tion which alone can give practical and
popular value to a map. It determines
the courses of valleys and streams, the
routes of roads and trails, the peripheries

geographical surveying in the United States, is a mis-
nomer, and therefore, in introducing a corresponding
one into the Portuguese, it will be well to adopt some
more appropriate expression. For this reason " odomet-
ric survey" will be used to designate line surveys in
which the odometer takes part, and "route survey"
(caminhamento) as a general term, to include not only the
above, but also those in which distances are determined
by time, by the chain where that method is employed, or
by paces, whether of man or horse, and whether re-
corded by the pedometer or by direct counting.

As the meander survey is understood, where this ex-
pression is used, it is simply any survpy following a zig-
zag line, whose angles in general, are alternately salient
and re-entrant, as the line accommodates itself to the
route of travel. But this word " meander," having been
derived from the river of the same name, in ancient
Phrygia, which was celebrated for its winding, sinuous
course, literally means "abounding in curves." It will
thus be seen that the more a survey approaches to a true
meander, the farther it departs from the first principles
of accurate linear surveying, which dictate that it shall
consist of straight lines and angles only. Since it is al-
ways to be regretted when a survey is confined to a true
meand*er line, as for instance, in tracing the course of a
road along and up the Fide of a mountain range, so it is
also a matter of regret that this word should have been
introduced into the language of engineering, apparently
sanctioning a faulty survey.

84

of lakes and basins, and the distances
between springs of water, villages, areas
of pasture, fords of rivers, and other
points of interest to the future traveler.
Finally, it is a commendable occupation
for the engineer while on his way from
one mountain station to the next, and,
since it occasions no delay in the general
progress of the work, as the engineer
can, as a rule, meander as much road as
his pack-train can travel in one day, its
results are net gain to the survey.

In the theoretical journey of this kind,
the engineer would follow the edge of
the dividing ridge from one station to
the next, from which lofty promenade
he could see the earth like an extended
scroll beneath his feet, and make a sur-
vey that would be exhaustive and
complete. But in the real, hard prac-
tice, he finds this path an impracticable
one, for it is broken by precipices and
blocked by abutments often a hundred
metres or more in height. His easiest
route of travel is by the side of flowing
water, whose tendency it is to erode aft-

85

rupt cliffs and soften steep gradients
into an average and even slope. Be-
sides, along the streams there are trails
made by the wild animals which come
here for drink and covert, and by the
people of the country who come hither
to hunt and fish. Therefore, if the* de-
tour be not too great, the most expedi-
ent route from mountain to mountain, is
down one valley and up another, and
the geographer who traverses a valley
without taking some sort of a survey of
it, is culpably negligent of his duty.
On the other hand, if in a block of
mountains the pre-eminent peaks be oc-
cupied, and the streams which emanate
therefrom be meandered, nothing more
is needed for a most excellent geograph-
ical map of that country.

THE MEANDER TRANSIT.

It is supposed that all transportation
of outfit, and all travel, even in the me-
ander survey, is accomplished on the
backs of horses or mules. Riding in
the saddle, the surveyor can devote but

86

one hand to the grasp and protection of
his instrument, the feet of whose tripod
rest in a holster attached to the left
stirrup. To facilitate his secure- hold,
the members of the tripod are thirds of
a cylinder, which fold into the smallest
possible compass, and are easily held in
the grip of one hand.

The instrumental part of the meander
transit is neat, solid, and compactly
constructed. Its graduated limb is of
small diameter, and its horizontal ver-
nier reads to minutes only, which is all
very well, since no smaller divisions can
be plotted on the map. This graduation
is used in the occupation of topograph-
ical stations, at those meander stations
where the view is extended enough to
make it profitable to linger an hour or
so in the accumulation of notes and
sketches, and at all those which are
three-point stations as well. But in the
general survey, not the vernier-plate,
but the compass needle, is used, on ac-
count of its greater convenience. The
compass box is graduated, from zero at

8V

the north, around by the left to 360° at
the north again, so that a reading of 90°
corresponds to magnetic east, and 270°
to west. The field records are kept
in this manner, and in the office the de-
clination of the needle is first applied to
each bearing^ after which it is reduced
to its true direction, preparatory to the
plotting.

THE ODOMETEB.

The distances from station to station
of the meander are measured by the
odometer, an implement of survey which,
in some of its forms, has been long in
use in Europe, and has of late years re-
ceived especial attention and improve-
ments in the reconnoissances and other
geographical surveys carried on by the
War Department of the United States
of North America. In this service it
has been adapted to the severe condi-
tions of travel in a new country. It has
been strengthened so as to withstand
any shock or fall to which it may be
subject. The recording apparatus is

88

made so compact and simple that there
is no danger of disarrangement there.
Instead of the old laborious process of
pushing it by hand, the wheel has been
fitted with shafts, so as to be drawn by
a mule, and so efficient is the method of
attachment that the odometer can follow
any route, however rough, precipitous,
or narrow, that will admit of the passage
of a pack-mule.

In its simplest and best form the
odometer vehicle is a solitary wheel, a
little more than a meter in diameter, or
about the size of a light carriage- wheel.
It is strongly constructed of the best
material, and is braced by opposite in-
clinations of alternate spokes, so as to be
uninjured by the heaviest jars and col-
lisions. A pair of shafts are attached to
it, and into these a strong and steady
mule is firmly harnessed by straps from
above and underneath. The vehicle is
close in the rear of the animal, and the
shafts are made short and heavy, and in
this manner the wheel is preserved in a
plumb or upright position as it runs, not

89

swaying from side to side. The length
of the circumference of the wheel being
accurately known and the number of
revolutions being recorded by the at-
tached apparatus, it is a simple matter
to learn the distance between any two
points.

The recording instrument hangs in a
cylindrical box which is strapped to the
wheel. It consists of a mechanical com-
bination attached to a heavy block of
metal, whose center of gravity is at one
side of the axis to which it is suspended.
As it is free to revolve upon this axis it
always maintains a vertical position,
while its box turns with the wheel, and
the apparatus scores the number of
revolutions, of which it is capable of re-
cording 9900, or a distance of about
forty kilometers, when it begins anew.

USEFULNESS OF THE ODOMETEK.

This detailed description of the odo-
meter is in accordance with the promise,
made in the early part of this article, to
dwell upon the novel features of this

90

work, even to the exclusion and apparent
neglect of others, already well-known,
which are really of greater importance.
Still it would be difficult to over-esti-
mate the usefulness and practical value
of this instrument. It requires but little
technical knowledge to use it and to
conduct the meander survey which ac-
companies it, and any person educated
in the simplest rudiments of surveying
is competent for this kind of work.

For this reason every party of scien-
tific exploration and reconnoissance,
every preliminary survey for railways,
and every marching body of troops
should consider its outfit incomplete
without the implements of an odometric
survey. Aside from the mass of notes
and sketches that would be accumulated
by them, and the itinerary maps that
would result, in the item of distances
alone the country would be more than
repaid for the cost of these surveys. As
a means of mensuration the odometer
will determine distances en route, as the
wagon travels, more truthfully than the

91

chain itself. These, being published,
are of profit, not only to the ordinary
traveler, but also to the general govern-
ment, whose agents and officials, in one
capacity or another, are constantly pas-
sing to and fro.

ERRORS OF THE ODOMETRIC SURVEY.

is there any very great error in
the ordinary surveys which the odome-
ter is likely to be called upon to perform.
Having the geographical positions of
two towns forty kilometres apart, they
may be connected by an odometric sur-
vey, the plot of which can be adjusted
between these two positions so that no
intermediate points will be appreciably
out of place on a map of the usual scale.
Since this is a map for practical use and
for the public good, it fulfills its pur-
pose as well as if its distances had been
measured by the most refined methods.

The great objection to its use is the
tendency towards the accumulation of
error in an odometric meander, and the
farther it is from the known point which

92

is its origin, the greater is the probable
error of any position determined by it.
Therefore, in a prolonged journey, or in
a general survey of the country, the
odoraetric position should frequently be
verified, or checked and rectified, by con-
nection with known points. This can be
accomplished by making a station at
some point on a railway, boundary, or
other line of accurate survey ; by astro-
nomical observation, which, however, if
taken with a sextant, is often less relia-
ble than the meander itself; or by mak-
ing a meander station dependent upon
the accompanying triangulation, by
means of the three-point problem. The
last method, which is by far the most
reliable, will be explained further on.

ERROR OF DIRECTION.

The meander is affected by error of
two kinds, of direction, and of distance.
The former, in its most serious nature, is
incurred in the survey of a tortuous val-
ley, whose general course must be ac-
cepted, or in crossing a timbered coun-

93

try, or a pathless plain, where the sur-
veyor is in a constant state of uncer-
tainty as to whither he is to go, or, tak-
ing a back-sight, as to whence he has
come. Sometimes the engineer is
obliged to keep his eye on the sun and
get a general idea of the course from
that. Or, in traversing a dense forest,
he may find himself compelled to resort
to the paradox of sighting upon a sound;
that is, he allows the pack-train to keep
a certain distance in advance, and from
time to time he directs his telescope to
the tinkling of the bell which is carried by
the horse that leads the train. It must
be confessed that these make-shifts are
loose methods of survey, but they are
better than none, since they give the
prominent directions and the distances
between streams, divides, etc., and
months afterwards, when the engineer
comes to make the map and lay down
upon it the trail of that day's march, he
will find the poorest and most incom-
plete notes more reliable than his present
memory and judgment.

94

Even under the most favorable cir-
cumstances it will seldom be possible to
direct the telescope with greater pre-
cision than to the nearest degree, nor, as
a consequence, will it ever be worth
while to record any fraction of a revolu-
tion in the odometer. A road does not
usually change direction by an abrupt
angle, but by a gradual curve, and the
bearing is made approximately tangent
to that curve. Or, in the survey of a
stream, it is not known on which side
the trail will run at some point a kilo-
metre in advance, and so the approxi-
mate center of the valley is accepted.
But if there should be a solitary tree,
bush, house, rock, or other prominent
object fortunately situated for a station,
the course will be made closely tangent
to that, a reading of instruments will be
taken upon arriving there, and, going on
to the next station, the engineer will
take a back-sight to the same point. In
general the system of back-sights will
be found more satisfactory than that of
foresights, as it is easier, on a strange

95

route, to tell whence you have corne than
to decide where you are going.

ERROR OF DISTANCE.

This error of direction, it will be seen,
is thrown by the law of chance alter-
nately to the right and left of the true
line, and so has a tendency in its elements
towards mutual compensation, and in a
measure it corrects itself. But not so
the error of distance, which is always
plus, and cumulatively so. The test of
the odometer wheel, by which its num-
ber of revolutions per kilometre is ascer-
tained, is made upon a level surface and
along a staked alignment, giving a re-
sult almost absolutely correct. In prac-
tice, however, the vehicle climbs acclivi-
ties of every grade, tacks hither and
thither as it follows the trail up the
mountain, winds incessantly in its route
through the forest, and is disturbed by
frequent jolts and collisions along the
rocky floor of the canon. In a theo-
retical traverse the straight line between
any two stations is determined, but in an

96

odometer survey the measuring imple-
ment usually follows a beaten path, and
the route distance, by road or trail, is
rarely the shortest distance between two
points. Hence an "overrun" in its
record, which can only be remedied, and
that approximately, by the judgment of
the surveyor, who is taught by experience
to estimate very closely the surplus in a
given run, and who applies a correction
accordingly.

Still, to such perfection has the odo-
meter survey been brought, that it is a
common occurrence for a skilled worker
to meander a closed circuit of. one hun-
dred kilometres, and plotting the route,
to find the plot also close within a small
fraction of a kilometre. Even this error,
being judiciously distributed in the pro-
cess of adjustment, different weights
being assigned to different runs, accord-
ing to their probable accuracy," may be
reduced so as to be practically imper-
ceptible.

OCCURRENCE OF MEANDER STATIONS.

No general rule can be given for the

97

frequency of meander stations, but in
ordinary country they will average per-
haps one to the kilometre. In this all
will depend upon local circumstances
and exigencies. In the survey of a long
and hidden valley, affording no opportu-
nity for checks, especial care must be
taken to preserve the integrity of the
meander, and the stations must be espe-
cially frequent; but in a survey by a
direct line across the plain two or three
stations a day may be sufficient. In a
winding path up a mountain side a
dozen stations may be necessary if there
are no chances for checks; but if the
ends of the trail, at the top and bottom
of the mountain, can be located by the
three-point problem, the intermediate
route can be neglected, being, at most,
sketched in by the eye.

There are two considerations to govern
the occurrence of stations; first, to pre-
serve the continued accuracy of the sur-
vey, and second, to note the local
geographical features which may be
encountered. Fory the latter purpose

98

stations will be made at the center of
every village, at every country-house of
importance, at the crossing and diverg-
ence of streams, roads and trails, at the
opening of a valley, at the foot and
summit of a mountain, and at the
many other geographical vantage-
grounds which the practical engineer
will know how to select. But in this, as
in the other departments of the survey,
too punctilious zeal may defeat its own
interests by causing delay, and the sur-
veyor who is too scrupulously exact in
the forenoon may have to virtually
abandon his task in the afternoon, in
order to reach a suitable camping-ground
by night.

SCOPE OF THE MEANDER SURVEY.

The zone of country considered from
a meander line may extend to the
farthest visible point, as a series of sights
upon a mountain even twenty-five kilo-
metres away will give its position to a
close approximation; but its principal in-
tent is the preparation of a narrow route

map, the areas encompassed by whose
windings will be filled in from the topo-
graphical stations. Since, from its nature
and narrow scope, it is fuller and takes
cognizance of objects more minute than
can be noticed in the other systems, in
this the engineer is liable to a charge of
partiality, reproved in the early part of
this article. But this is not partiality in
one field at the cost of neglect in
another, and the greater excellence of
this work is so much clear gain. More-
over, since the meander is usually by
way of roads of frequent travel, and
since a map is useful, and should be ex-
cellent, exactly in proportion to the num-
ber of people who are guided by it, it is
well that the meander plot should excel
in completeness those almost inaccessible
parts which will never be seen except by
the hunter or bandit.

MAKESHIFTS IN THE SURVEY.

In a forced march of forty kilometres
or more, the meteorologist and odometer
recorder, the safe carriage of whose im-

100

plements requires a slow and steady gait,
may proceed at a walk after taking their
readings at a meander station, which task
will occupy them but a few minutes,
while the surveyor lingers behind to make
the necessary sketches and observations,
and then, riding at gallop, overtakes his
comrades before the next station is
reached. Many such shifts as this are
known to the practical and energetic
geographer, who learns to emancipate
himself from too close dependence on the
text-books of surveying, some of whose
rules are very common-place and pedan-
tic, and brings into play his powers of
ingenuity and invention, to adapt himself
to the peculiar circumstances by which
he may be surrounded. If he finds him-
self alone, out on some trip of hasty
reconnoissance, or on some hunting ex-
cursion on which he could not carry both
rifle and transit, he draws from his watch
pocket an aneroid, and from his saddle-
bags a pocket compass or an altazimuth,
and his equipment for survey is com-
plete; as for distances, he can estimate

101

them, or determine them by the time
they take, calculating at the rate of five
kilometres an hour, or, better still, by
counting the steps of his horse and allow-
ing six hundred double paces for a kilo-
metre.

In a geological survey of Brazil very
much of the travel and exploration is
necessarily done by water, as the outcrop
of the various formations is most favora-
bly shown upon the banks of the rivers,
along which there is frequently no passa-
ble route by land. Here the stadia may
be used, provided there are two or more
boats in the party, or, in the less import-
ant instances, the methods of obtaining
distances by estimation or by time would
have to suffice. In either case the sur-
veyor should lose no opportunity to
emerge from the trough of the stream,
or to ascend some eminence, and insure
his position by observations upon three
or more known points. Should these be
wanting, he should resort to the sextant
and to its use in astronomical determina-
tions.

102

Since the attention of the geologist is
in great- part absorbed in the duties pe-
culiar to his profession, he cannot usually
carry any but the lightest and most con-
venient implements of survey, and since
these are amply sufficient for his geologi-
cal notes of dip, strike, trend, etc., it is a
matter of expediency to make them an-
swer for his geographical work as well.
With the engineer, however, there rarely
comes a necessity for being separated
from his portable transit, which admits
of being firmly set on its tripod, and from
which angles, either horizontal or verti-
cal, may be accurately read to the near-
est minute. And in the general geo-
graphical plan it is wise to deprecate as
far as possible the employment of unreli-
able pocket instruments, or of the devices
for learning distances that have been de-
tailed above. Since nothing is to be
gained in time by their use, and very
much may be lost in accuracy, the engi-
neer should teach himself to consider that
any method less complete than that of
the portable transit and odometer is but

103

a temporary expedient and makeshift,
serving an excellent purpose when all
other means fail, but not to be relied
upon as a permanent constituent of the
survey.

CO-OPERATION OF THE TRIANGULATION
AND MEANDER.

While the meander survey is an ex-
cellent apprenticeship for the young en-
gineer, it should not be despised, as an
occupation, by even the director of the
triangulation. Humble as it is, it per-
forms a task in the geographical plan
which no system of triangulation can be
relied upon to perform in a rapid work
of this nature. It enables the survey to
reach any point, however remote and se-
cluded, and to determine its positions; it
makes the map complete in all of the
details which are so useful to the trav-
eler; and as an agent in what we may
call the practical or economical branch
of geography it is without an equal.

It is dependent upon the triangulation,
it is true, but then the dependence is

104

mutual. The full benefit of either can
only be secured through the co-opera-
tion of the two. As without the trian-
gulation the map is unreliable, so with-
out the meander it is incomplete. To
use a homely illustration, the triangula-
tion may be compared to the framework
of the dwelling, and the meander to the
intermediate filling of wall or other sub-
stance which makes the house habitable,
and is a shelter to the inmates. This
frame, if its lines are true and its angles
correct, is a beautiful thing for the arti-
san to contemplate, but without its com-
pletion of walls and furniture, it is of no
real benefit to the world. In the same
manner a bare triangulation scheme may
be an interesting study to the geographer
himself, but to the traveling public and
the people at large, it possesses neither
interest nor value. On the other hand,
as the frame of the house is an absolute
necessity to it, securing and sustaining it
in its proper proportions, so is the trian-
gulation the rigid frame work of the
map and the skeleton to which the use-
ful data of the meander are attached.

105

CHECKS BY THE THREE-POINT PROBLEM.

Since the meander is from its very
nature so hasty and loose, the system of
frequent checks can alone make it relia-
ble, and at intervals of every few kilo-
metres, and especially at the crossing* of
divides and other eminences from which
there is a broad scope of country visible,
connection should be made with the
triangulation. Each of these stations
then becomes a new initial point, at
which the survey begins afresh and the
error again begins to accumulate.

This rectification is accomplished by
the use of the three-point problem, a
geodetic determination which, as a
means of locating topographical stations,
and as a connecting link between the
meander and the triangulation, is of the
highest importance in geographical sur-
veying. Having three triangulation sta-
tions in sight, and favorably situated, it
is possible for the observer to determine
his position in a few minutes of time
and by the simple operation of reading
the two angles included by those three

106

stations. From these and the data per-
tinent to the triangulation stations he
can compute his distance from them, and
hence his present latitude and longitude.
Or, plotting these angles from any cen-
ter on a piece of tracing cloth, he can
lay this upon the projected map and
swing it around until each of the three
plotted rays covers its proper triangula-
tion point, when this center will indicate
the position of the three-point station, as
it is called. For this graphic determina-
tion not only three points, but four, and
even more, if they are visible, should be
observed, as a greater number facilitate
the operation and insure the accuracy
of the result.

This method of trilinear determinations
cannot be introduced too often. A
three- point station in the streets of a
settlement, at the forks of a road, or at
the end of a mountain range, will locate
these important places, and in camp,
even in the center of a broad and vacant
plain, there is no more profitable man-
ner in which the engineer can spend his

107

leisure time, before or after dinner, than
by making a three-point station there
and determining his position. Every
camp thus fixed is a new and reliable
origin at which the meander of the next
morning will begin.

A SURVEY BY THREE-POINT STATIONS
ALONE.

In some cases a successful meander
may be carried on by three-point sta-
tions alone, when all other means would
fail. Take, for instance, the rugged
shores of a lake or bay, which are inac-
cessible except to a man on foot or in a
boat. In the mountains on the other
side of the water a series of triangula-
tion stations stand up in full view. By
means of these the engineer, working
his way, transit in hand, from bay to
bay, and from point to point, along the
water's edge, makes three-point stations
at all prominent changes of curvature,
and, sketching in the intermediate shore,
he determines its line by tangents and
intersections, and thus secures a good

108

survey of the coast. If there are islands
out in the water they may be surveyed
in the same way.

If the engineer was confronted with a
piece of geography like the bay and
islands of Rio de Janeiro, and if there
were no roads along the beach to make
direct linear measurements feasible, he
could extend his triangulation to include
all of the prominent peaks in the vicinity,
and then, by means of three-point sta-
tions, he could rapidly trace in the shore-
line. As the surroundings of Rio are so
broken and irregular, the triangulation
points could be made so numerous that
it would be difficult to find a spot on the
beach of mainland or island so secluded
that some three of these stations would
not be visible from there.

THE MEANDER PLOT.

Every three-point station, as well as
every other meander station, should par-
take more or less of the nature of a regu-
lar topographical station; that is, contour
sketches should be kept constantly on

109

the plotted page as it progresses, and a
continuous panorama of profile views,
drawn in a separate portion of the book,
should accompany the survey, so that,
as some geographical features are left in
the rear, others may be introduced in
advance.

As from one topographical station to
its neighbor, so every distance from one
meander station to the next should be
considered a base to be used in the loca-
tion of points useful in the structure of
the map. The longer this base, the more
distant may be the range of these views.
In case several meander stations inter-
vene between one observation and the
following, this total intermediate dis-
tance becomes what is called a broken
base, but it is none the less useful for all
of that. The above considerations will
influence the engineer in his choice of
stations, which will always be situated in
such positions as may offer the best ad-
vantages for the accumulation of what-
ever information he most needs.

110

THE DECLINATION OF THE COMPASS
NEEDLE.

The variation of the compass needle,
or, more properly, its declination, will be
carefully watched throughout the sur-
vey, and determinations of its angle will
be made from time to time; these will be
more than usually frequent wherever
there is suspicion of some attraction im-
mediately local, arising from the presence
of magnetite or other ore of iron, basaltic
rock, or other disturbing influence. These
determinations are important, not only
in the reduction of the meander notes
taken in this vicinity, but also for the
practical use, both present and future,
of the country at large. In addition, their
results will aid the general cause of sci-
ence in its investigation of the laws of
terrestrial magnetism, and in tracing the
course of isogonic lines around the world.

At every triangulation, topographical,
and three-point station, the observer
will note the direction of magnetic
north, as indicated by the pointing of
the compass needle. If his instrument

Ill

has a double movement in azimuth, as
all should have, it is well, for the sake of
convenience, to first set the zero of the
graduated limb upon the same point of
the vernier plate, by the upper motion,
and then, by means of the lower move-
ment, bring the north end of the needle
to the zero of its circle. His initial
entry in his note-book will then be
" Magnetic North, 0° 00' 00"." This
direction of the telescope being referred
to some line proceeding from here,
whose true azimuth will be found by
subsequent computation, the magnetic
azimuth or declination of the needle at
that place will be determined; it will
simply be the difference between the true
azimuth of the line, reckoned from the
north point of the horizon, and its ap-
parent azimuth, or the vernier reading
which he enters in his notes.

BY DIRECT ASTRONOMICAL OBSERVATION.

The declination of the needle will also
be determined directly by astronomical
observation in the evening at camp. For

112

this purpose the engineer will select such
nights, clear and still, as may appear to
him most favorable, and such camping
places as may most urgently require this
information. A star as near as possible
to the pole will be chosen, as, from its
greater declination, an error in the lati-
tude of the observer's place, and, from
its slower motion, an error in the time
of the observation, will result in less
serious errors in the azimuth; and the
smaller the polar distance of the star, the
more convenient will be the observation
and the computations which follow, and
the more exact is the result likely to be.
In the northern hemisphere a Ursce Mi-
noris, or Polaris, is almost always used,
as it is at present only about 1° 20' from
the pole, and it possesses the additional
advantage of a brilliancy of the second
order. But south of the equator there
are no available stars so favorably situ-
ated as this. The most southern one of
any considerable size is ft Hydri, of the
third magnitude, whose polar distance is
a little more than twelve degrees.

113

This would have to be accepted in a
survey of this nature in preference to
any of the less brilliant stars of greater
declination, as the observations would
have to be made frequently by engineers
of little astronomical experience, and
with instruments not especially adapted
to this kind of work. Indeed, it might
be necessary at times to use the small
meander transit for that purpose; arid it
is seldom that the telescopes of even the
theodolites for triangulation, as now con-
structed, are provided with the hollow
rotation axis requisite for a proper illu-
mination of the diaphragm, without
which it is difficult to see both cross-
hair and star, unless the latter is of con-
spicuous magnitude.

Knowing, at least approximately, the
latitude of the place, and also the decli-
nation of the star and its hour angle at
the time of observation, its azimuth
angle from the south point can be com-
puted. But as the hour angle depends
upon the local time at that place, and
there is great room for error there, the

114

observer, unless he has full confidence in
his ability to make an accurate time-de-
termination, should find the approximate
minute of the star's greatest elongation,
and follow it with the transit thread
until it reaches the dead point in its
azimuth motion, where it seems to stop
a few moments between its advance and
retrogression. Then, being at its
greatest elongation, the sine of its azi.
muth angle is equal to the cosine of its
declination divided by the cosine of the
latitude of the place.

Should the star 0 Hydri not arrive at
its east or west point at a convenient
hour, as at certain seasons of the year it
will not, the star Canopus, differing in
right ascension about six hours, or a
Trianguli Australis, of about sixteen
hours greater right ascension, may be
employed. These are respectively of the
first and second magnitude, and hence
are very well adapted to this purpose,
but, owing to their greater polar dis-
tances, it would be necessary, in their use,
for the observer to be especially sure of
the correctness of his latitude.

115

The sun is not usually available for
determinations of azimuth or time, as
the engineer is generally upon the march
throughout the day. The use of a star,
however, admits of greater precision in
the observations, while the resulting
computations are less complicated, and,
in the case of an azimuth determination,
a south star is doubly convenient from
the fact that its two daily elongations
always come above the horizon, and
whichever one occurs most opportunely
may be used; or it may be possible at
times to observe both, in which case it
becomes unnecessary for the engineer to
know his latitude. The same difficulty
of latitude, may also be avoided by the
method of equal altitudes of a star, taken
at several hours before and after its
meridian passage; the middle point be-
tween the two corresponding azimuths
will be upon the meridian.

THE METEOROLOGIST AND HIS INSTRU-
MENTS.

In all of his travels the meteorologist
will be the constant companion of the

116

engineer, so as to be prepared to take
observations at any point that the latter
may designate. At the beginning of the
field season he will be furnished with, at
least, two complete sets of meteorological
instruments, to be carried by himself and
by others who may be appointed to as-
sist him. Each set will be composed of
a cistern barometer, an aneroid, maxi-
mum and minimum thermometers, pocket
thermometers, and a psychrometer, con-
sisting of two similar thermometers, one
with its bulb capable of being moistened
by the capillary attraction of a loose cord
of cotton filaments leading to it from a
cup of water, and the other dry, as in the
ordinary instrument.

Prior to taking the field he will com-
pare these barometers by a series of
readings extending through several days,
with some standard barometer whose er-
ror is known, in order to obtain the in-
strumental errors of the instruments at
hand. Throughout the season, also, he
will lose no opportunity for comparisons
with any reliable barometers that may

117

be encountered, as well as for frequent
comparisons between these two. In this
manner the time of any possible disloca-
tion of the scale, or other source of error,
will be determined.

As in the rough and rapid travel of a
geographical survey, there is great lia-
bility to break the fragile glass tube
which contains the heavy mercurial col-
umn, an extra supply of barometer tubes
and mercury should be transported with
the party, and also an assortment of
tools and material for the filling, boiling,
and fitting of a fresh tube. This is a
delicate and difficult task, but it is one
in which every meteorologist should be
proficient. As full instructions for the
use and repair of meteorological instru-
ments have already been prepared by
the Commission, it is needless to repeat
them here.

METEOROLOGICAL OBSERVATIONS.

At every station of the survey, the
meteorologist will read from his instru-
ments the data from which the elevation

118

of that point may be subsequently com-
puted. Nothing more is then needed
for the precise determination of that
station's position. The engineer has fixed
it in latitude and longitude; the mete-
orologist, in its altitude above sea-level.
The meteorological data will be more or
less comprehensive and will be read from
instruments more or less reliable, accord-
ing to the geographical importance of
the place at which they are taken. The
more frequent the readings, and the
more prolonged the series, the more
trustworthy will the resulting mean be,
and the less liable to be materially
affected by errors of observation, and
by those erratic fluctuations to which the
barometer is subject, owing to the con-
stantly varying atmospheric currents and
other disturbing physical conditions to
which it is exposed, and whose effect
cannot be entirely eliminated by any
formulas that it is possible to devise.

Beginning at the point of outfit,
which, on account of the work of pre-
paration and the measurement of the

119

base-line, may be occupied some weeks
or a month, hourly readings will be taken
throughout the day and night for as
long a time as possible. The cistern
barometers will be read, as the height of
the mercurial column is the basis upon
which all barometrical determinations
rest. The attached thermometer will
be read, to learn the temperature of the
mercury, and hence what correction
must be applied to reduce it to the
freezing point, at which all barometrical
heights are compared. The isolated
thermometer will give the temperature
of the surrounding atmosphere, to be
used in determining the mean tempera-
ture of the stratum of air intermediate
between this and the reference station.
And the psychrometer will reveal the
amount of aqueous vapor in the atmos-
phere, and the influence of its pressure
upon the height of the column of mercu-
ry. In addition to these, note will also
be taken of the direction and force of the
wind, the condition of the sky, the proxi-
mity of storms, and other atmospherical

120

phenomena, as this information may
give the key to some abnormal baro-
metric oscillation which would otherwise
have to remain unexplained.

HORARY AND ABNORMAL OSCILLATIONS.

The hourly observations will be con-
tinued throughout the day and night for
the purpose of determining the amount
of the horary oscillation at that place.
This horary oscillation is a somewhat
regular rise and fall of the barometer,
occupying a period of twenty-four hours.
The range of this fluctuation in some
parts of the world is so great, that its
effect upon the mercurial column may
equal that which would be produced by
a change of fifty meters in altitude. It
is such that, if the successive heights of
the column be represented graphically
by a curve, this curve will show two
daily maxima and minima, occurring at
intervals of about six hours, the morning
maximum being attained at about ten
o'clock A. M. This horary curve, as it
is called, varies with the latitude, alti-

121

tade, and climate of a place, as well as
with the different portions of the year.
The value of the horary variation for
any hour of the day is revealed by a
study of the prolonged series of observa-
tions at that place, and may be assumed
to be the same for all observations taken
in the vicinity of that station and in the
same season of the year.

The barometer is also influenced by
the abnormal oscillation, apparently re-
sulting from the progress of great atmos-
pheric waves across the country, affect-
ing the mercurial column by a gradual
rise of several days, followed by a period
of subsidence of about an equal duration.
The effect of this disturbance can be
eliminated, approximately, by taking the
difference of the barometric readings at
the beginning and ending of any one day
of its rise or fall, and considering this as
its amount for that twenty four hours, a
proportional part of which will be its
value for one hour.

122

DETERMINATION OF HEIGHTS.

To obtain the altitude of the first
station of the survey, a mean of the cor-
rected heights of the mercurial column
is compared with a corresponding mean
of the same hours of the same days at
some permanent station, whose elevation
above the sea is definitely known, as, for
instance, the Imperial Observatory at
Rio de Janeiro. This, by a process of
computation, gives their difference of
altitude, and hence the total elevation of
the point in question.

Now, making this point of outfit a
reference station, at which an observer is
left with meteorological instruments to
be read at stated intervals throughout the
day, the party takes the field, and the
traveling meteorologist reads a series of
barometrical and other observations at
the first camp and at all others to which
they may come during the season.
These will be compared, as before, with
synchronous* observations at the refer-

* It is well to distinguish between the meanings, as now
understood, of the two words " synchronous " and " sim-

123

ence station, and the differences of alti-
tude will be calculated. At every topo-
graphical station, and station of import-
ance along the meander survey, such as
villages, f azendas, mines, mountain passes,
divides, etc., and at all other points that
may be designated by the engineer, the
meteorologist will read the cistern baro-
meter, the watch, the thermometer, and
the psychrometer, and, for the purposes
of comparison, the aneroid barometer as
well. These isolated observations will
also be referred to the main barometrical
station at a distance.

But, on the occasion of the ascent of
a mountain peak from a fixed camp, bet-
ter results will be obtained by consider-

ultaneous." The term " simultaneous " is applied to ob-
servations which are made at the same absolute instant
of time, as, for instance, upon the occultations and
eclipses of the heavenly bodies. Synchronous observa-
tions are taken at the same hour of the day, local time,
irrespective of the difference of longitude between the
two stations. Therefore, observations can be both sim-
ultaneous and synchronous only when the observers are
upon the same meridian. The word " simultaneous "
belongs especially to the province of astronomy, whilst
" synchronous " is most frequently used in connection
with the phenomena of physical geography.

124

ing the camp a reference station in the
determination of the altitude of the
mountain. This ascent will necessitate
the occupancy of the neighboring camp
for two nights and a day at least, and
perhaps longer, while the peak may be
occupied only a portion of a day, during
which time, however, there will be cor-
responding hourly observations at camp
and mountain-top. Hence the altitude
of the mountain will be most truthfully
ascertained by referring it, by these syn-
chronous observations, to the camp, and
then the camp, in a similar manner, to
the distant reference station.

HORARY CURVES AND REFERENCE STA-
TIONS.

Whenever the party, or a portion of
it, remains stationary in camp for a few
days at a time, hourly observations day
and night will be taken to determine the
horary curve at that place; the longer
the series, the better will be the result.
Since the horary variations are constantly
changing with altitude, country and cli-

125

mate, it is important to have as frequent
determinations of them as can practicably
be made, so that no very great distance
may intervene between the place where
a table of horary corrections is construct-
ed and the place where it is used.

For a similar reason it may be deemed
necessary to establish and sustain a sec-
ond meteorological reference station, if
the field of the season's survey should be
a wide one, or if it should vary greatly
in the atmospherical condition of differ-
ent portions of its area. No comprehen-
sive rule can be given to govern the num-
ber of these reference stations; all must
depend upon the judgment of the direc-
tor of the survey, and the resources at
his command. In general, the farther
the place of an observation from its
reference station, the less reliable will be
its result. But, as an exception, let us
take the example of a broad inland plain,
separated from the sea and its influences
by a wall of mountains, within which,
upon the plain, the reference station is
situated. In this case it may be more

326

justifiable to refer to this station a point
on the plain, five hundred kilometres dis-
tant, than one just over the mountains,
only one hundred kilometres away. This
is owing to the widely different climatic
circumstances of inland and sea-coast,
resulting in meteorological conditions so
dissimilar that equal amounts of pressure
cannot be relied upon as an indication of
equal thickness of the atmospheric enve-
lope.

THE ANEROID BAROMETER.

At the many stations of the meander
survey that are comparatively unimport-
ant, and that are occupied for a few min-
utes only, it will suffice for the meteoro-
logist to read only his aneroid, watch,
and thermometer. Although the aneroid
is not a reliable instrument, yet it serves
an excellent purpose where rapid and ap-
proximate work is sufficient. Since its
principal use is in obtaining profiles of
the meander routes, which will enable
the engineer to properly distribute the
contour lines upon his map, and since,

127

farther, the error of an aneroid will rare-
ly exceed the vertical distance between
two of these contours, the resulting inac-
curacy upon the plot will be quite inap-
preciable.

The aneroid is to the cistern barometer
what the meander is to the triangulation,
that is, a means of filling in, which,
while costing but little extra effort,
is productive of very valuable results.
The engineer who rejects the meander
and the aneroid, because they are not
rigidly exact in their functions, will find
himself reduced to the necessity of
tracing in the roads and streams of his
map, locating many of the villages, cross-
roads, etc., and drawing in the contours
from his judgment and memory alone;
and it is safe to say that the conjectures
of the most able and trained topographi-
cal intellect are by far less reliable than
the figures of those humble instruments,
the aneroid and odometer, when judi-
ciously used.

At every camp the aneroids are com-
pared with the cistern barometer, their

128

scales are adjusted in compensation for
any error that may have crept in, and
the vertical element of the survey starts
from a new and true datum plane when
the march is resumed. At the end of
the day's journey, also, they are imme-
diately compared again, and the error
accumulated throughout the day is
noted, and, by a process of distribution
along the day's profile, may be reduced
to a minimum. Before and after every
side trip, reconnoissance, or ascent of
mountain, the aneroid is compared with
the mercurial barometer, and thus, by a
continual and careful watch over it, it
may be relied upon to give results not
seriously in error. But if left to itself
and unchecked for any great length of
time, or for any great distance of journey,
or great change in altitude, this fickle in-
strument may continue to go astray, by
a shifting of its scale, exhaustion of its
spring, or from other causes, until its
readings are hundreds of metres too
high or too low. Even then, however,
it may be of use to the geographer in

129

drawing in the relief of the country, as
the discrepancy is usually of gradual
growth, and the relative altitudes during
the progress of the survey, as, for in-
stance, the height of a bluff above the
neighboring valley, are sufficiently exact
to be of much assistance to him in his
plotting.

BAROMETRICAL RESULTS.

As to the reliability of altitudes de-
termined by the cistern barometer, evi-
dences and opinions differ, but those per-
sons who are most thoroughly informed
are generally the most lenient in their
acceptation of results. Colonel Wil-
liamson, of the United States Army, who
has probably given more intelligent
study to the barometer than any other
man, has compiled a table of the maxi-
mum errors which occur in numerous
series of observations taken both in North
America and Europe. Among these are
many that exceed fifty meters in amount,
and he assumes that the barometer under
similar circumstances will be liable to

130

equal errors elsewhere. These, however,
are not to be considered as representing
the probable error of barometrical re-
sults; they are rather the extreme limits
of probable error, and may be taken as
the error to which the barometer is liable
under certain rare and very unfavorable
conditions. While exact truth concern-
ing altitudes is something which no
barometer can be expected to tell, and
while it is never safe to guarantee the
accuracy of such a determination, even
within many meters, yet when baro-
metrical work is prosecuted judiciously
and systematically, as it would be in this
survey, and based upon formulas which
represent the latest and most complete
knowledge of meteorology, its tendency
is to give results that are seldom more
than a few meters wrong.

It is often difficult for the popular
mind to comprehend how an error of
meters may be inevitable in some of the
processes of barometric hypsometry.
Since the scale of a barometer may be
read to a thousandth of an inch, and that

131

amount of variation is supposed to cor-
respond to a change of one foot in alti-
tude, it would naturally be thought
possible to determine the elevation of a
place to the nearest foot. But this diffi-
culty will be better understood when it
is remembered that the barometrical
measurement of the difference of altitude
between two places depends upon the
determination of the weights of a column
of atmosphere at each of these stations;
that this atmosphere is in a state of con-
stant change and perturbation, its press-
ure being modified by variations of heat
and cold, storm and calm, and the
absence and presence of moisture through-
out different portions of its extent; and
that, while some of these conditions are
quite unknown to the observer, those
that are apparent to him can be but in-
completely compensated for. There-
fore, since barometric hypsometry is not
one of the exact sciences, but is affected
by every change in the wind and
weather, any determination of altitude
that is true within a meter is as much

132

a source of surprise as of gratification to
the meteorologist, who will be obliged
to confess that this closeness could
scarcely be possible without some coin-
cidence and accidental equilibrium in
the disturbing influences to which the
barometer is subject.

DIFFICULTIES IN BAROMETRIC
HYPSOMETRY.

At times men of little experience may
have to be accepted as meteorologists.
They work, perhaps, under the embar-
rassments of exposure, fatigue, and a
lack of appreciation of the responsibilities
that rest upon them. It may be long
before they can be taught to regard
those niceties of barometrical work with-
out which it cannot be truly successful;
although there is but little hope of
determining an altitude to the single
foot, yet they have to learn that this is
no reason for neglecting that thousandth
of an inch which corresponds to a foot.
Their instruments may be out of order,
owing to the hardships of travel to which

133

they are exposed; the readings may have
to be referred to a distant station of very
dissimilar physical surroundings; or they
may have been taken upon the top of a
lofty mountain, in a belt of the atmos-
phere with meteorological phenomena
quite different from those properties of
the lower strata of the air, for which
our formulas were framed.

These are some of the sources of error
which may have conspired to vitiate
those results which are fifty meters or
more at fault. In Brazil, however, it is
hardly necessary to anticipate discrepan-
cies so great as this, since it is a country
in which no very great change of alti-
tude is possible, violent and phenomenal
storms are not frequent, and the atmos-
phere is of comparatively steady tem-
perature, and not liable to sudden transi-
tions from one extreme to the other.

BAROMETRIC FORMULAS.

Even if the observations have been
made under the most favorable condi-
tions of atmosphere, elevation and loca-

134

tion, and are perfect as far as human in-
telligence can make them so, that is, free
from all personal and instrumental er-
rors, there yet remains a consideration
which may materially affect the com-
pleted altitude. The same observations,
reduced by different formulas, will give
results in some cases widely different,
the discrepancy between the returns of
two well-authorized methods of compu-
tation frequently amounting to the sum
of the real errors of both; this is ex-
emplified in the following determination
of the height of Corcovado, in which one
system of reduction gives an altitude
above the true one, and the other places
it too low.

The barometric formula is composed
of several terms, each of which is a com-
bination of some physical constants, such
as the relative weight of air and mercury,
or the variation of gravity with latitude,
and some of the barometrical data, as
the temperature or moisture of the at-
mosphere. Of these formulas, there are
two general classes, based upon the equa-

135

tions of Laplace and Bessel. Not only
do they differ in those constant quanti-
ties upon which all barometrical determ-
inations must depend, but also in the
presence or absence of an entire term, as
the formula of Bessel has a separate fac-
tor as a correction for the humidity of
,the air, while Laplace includes the in-
fluence of the aqueous vapor with that
of temperature.

Thus it will be seen that the formula
of Laplace is more convenient, while that
of Bessel is more complete. The scien-
tific world has found it difficult to choose
between them, and while Delcros, Guyot>
and others have accepted the formula of
Laplace, that of Bessel has been adopted
by Plantamour, Williamson, and others.
But it is admitted, even by those who
are in favor of the former method, that
the constants in use in Bessel's formula,
as modified by the more recent arrange-
ment of Plantamour, are later and more
reliable than those accepted by Laplace,
and there is also a prevalent opinion
among scientists that some accuracy has

136

been sacrificed to convenience in La-
place's method, a concession which it may
sometimes be justifiable to make in the
application of a formula, but never in
its construction.

The advocates of each system have
published examples showing the close
accordance of their results with altitudes
determined trigonometrically or by spirit-
level. But as the number of these re-
markable coincidences is about equal on
each side, and as in each instance the
observations would have given results
considerably wrong by the application of
the other formula, they prove simply two
things; first, that they are coincidences,
and that to certain cases the method of La-
place is more applicable, while to others
that of Plantamour will yield better re-
turns; and second3 that it is quite impos-
sible to devise any formula that will
yield an accurate solution of all problems
in the barometrical measurement of
heights.

Since there seems to be a preponder-
ance of evidence and a growing disposi-

137

tion in favor of Plantamour's formula, it
has already been adopted by the Geo-
logical Commission as a basis for its
barometrical work, and its several terms
have been developed into tables for the
convenient computation of altitudes.
After the preparation of those tables and
as a test example with which to prove
their efficacy, the height of Corcovado
Peak was determined barometrically
with the following results:

Metres.

Altitude of Corcovado, by tables of the
commission, based upon Planta-
mour's formula 705 .84

By Laplace's formula 702.15

Determined by triangulation 704.74

Metres.

Error by Plantamour's formula +1.10

" Laplace's " —2.59

Discrepancy between the two 3.69

The foregoing is a very creditable and
satisfactory barometrical result, and is
one more argument in favor of the use
of Plantamour's complete formula.

ALTITUDES BY VERTICAL ANGLES.

As a supplement to the barometric

138

hypsometry, every theodolite, whether
for meanders or triangulation, is fitted
with a vertical circle, from which to read
the angles of elevation and depression of
those points which are located by inter-
sections, in order to compute the heights
of the same. From this angle and the
horizontal distance between any two
peaks, their apparent difference of alti-
tude is obtained by a trigonometrical
calculation, and then a correction is ap-
plied for earth's curvature and refrac-
tion. In the field these angles are
recorded as plus or minus, according as
the objective point is above or below the
observer's station, whose altitude is in-
variably determined by barometric read-
ings.

In this manner the heights of hund-
reds of points throughout the field of
survey are found with an accuracy
nearly equal to that of the peak from
which the angle is taken. Indeed, a
mean altitude derived from the three
angles of elevation, read from three
different triangulation stations, will give

139

the altitude of the point of intersection
with less probable error than that of
either of the mountains from which it
was derived.

METEOROLOGY IN THE SOUTHERN HEMI-
SPHERE.

Brazil stands almost alone as a great
civilized country lying in the Southern
hemisphere. It is comprehensive in its
latitude, reaching from north of the
equator far into the south temperate
zone. From this unique and favorable
position upon the earth's surface, as well
as from the liberal patronage bestowed
by its government upon the de-
velopment of science, it needs no
prophetic eye to see that this em-
pire is destined to become one of the
busiest and most fruitful fields of scien-
tific research. Especially is this the case
in the investigation of those great ques-
tions concerning the terrestial shape and
dimensions, and those others, still more
numerous, which from the form of the
earth, or from other and unknown

140

causes, vary with geographical position.
Important among the latter is the science
of meteorology, whose general laws are
not the same all the world over, but
which are largely influenced by latitude
and by proximity to either pole.

The following extract from Colonel
Williamson's valuable treatise on the
barometer and its uses, will illustrate
the absence and the need of meteorologi-
cal observations south of the equator:

" It has been determined by actual ob-
servations, and confirmed by theory, that
the sea-level pressure varies in different
latitudes by a definite law, modified in
practice by local peculiarities of climate.
It has been found that the mean baro-
metric pressure is less in the immediate
vicinity of the equator, and it increases
towards the north to -between latitude
30° and 35° where it is greatest. It then
gradually decreases to about latitude 60 °,
and from there towards the north pole
there is a slight increase. In the south-
ern hemisphere, where the observations
have been less numerous, the mean

141

pressure seems to increase to between
20° and 30° of south latitude, when it
gradually decreases to about 42°, and
then commences a remarkable fall, so
that towards the south pole, the mean
pressure is said to be less than 29
inches."*

In the table of mean heights of the
barometer at the sea-level, given in
various works on meteorology, there are
but two stations south of the equator;
these are Rio de Janeiro and the Cape of
Good Hope. In north latitude, however,
the list comprises more than thirty
places at which this determination has
been satisfactorily accomplished, by
years of observations, and these are
favorably situated at intervals between
the equator and the pole.

Again, while the horary oscillation in
the atmospheric pressure is greatest
near the equator, and diminishes thence
each way to the poles, the abnormal
oscillation is least in regions of small

* T36.6 millimetres.

142

latitude, and increases with the distance
from the equator. As the latter is
the more incomprehensible and less
regular of the two, and consequently the
greater source of error, it would appear
that, in general, barometrical work would
be most reliable in tropical regions, and
hence this system of hypsometry would
be especially applicable to Brazil. And,
in addition to their immediate and prac-
tical use in the construction of maps, the
meteorological results of a survey of the
proposed nature, taken at low and high
altitudes, at the sea-coast and in the
remote inland, with permanent stations
at intervals where long series of obser-
vations would be accumulated, would
form a basis upon which to establish the
general laws of barometric fluctuation
throughout this vast portion of the
Southern hemisphere.

CONTINGENCIES IN THE SURVEY.

The foregoing are the general divi-
sions and some of the novel features of
the geographer's work in the field.

143

While these are sufficient to carry the
survey across any ordinary country, cer-
tain districts may be encountered in
which these methods may not be easily
applicable. It is impossible, in a paper
of this nature and length, to foresee and
provide for all of the emergencies that
may arise; it is necessary for the geog-
rapher to first see his territory, and then,
if he is a true engineer, he will be able
to devise some means of survey which
will be competent to meet the difficulties,
however great they may be.

For instance, it may be asked how a
survey based upon triangulation can be
carried across the smooth and unbroken
table-lands of a country. The answer
will be that the plains are not usually so
broad that they cannot be spanned by
the length of a triangle-side ; and,
furthermore, if there are no eminences
that can be used for triangulation points,
so much less is there need for this system
of survey. Over the smooth plain it is
possible to travel in straight lines, such
being the usual character of roads in a

144

level country, and since a meander by
direct routes is reliable, the survey can
proceed from one known point to the
next with comparative accuracy, tracing
in the rivers, lakes, and. other geographi-
cal features as it goes. As a rough,
mountainous country is*its own remedy,
furnishing a great number of advantage-
ous stations for the survey, so, with the
absence of these mountains, vanishes in
great part the labors and difficulties of
this work.

THE STADIA, OK TELEMETER.

Although the stadia, or telemeter pro-
cess, is too slow for the general prosecu-
tion of a geographical survey, there may
be occasional areas in which the previous
methods will fail, and this will suffice.
The direct linear survey of a river, by
this means, has already been mentioned.
As another illustration, take the case of
a valley — as, for instance, the valley of
the Amazon — which is so broken with
lakes, swamps, and the many channels
and arms of the river, that its islands

145

and shores cannot be reached and located
by any means of direct measurement;
and where, farther, the vegetation is so
abundant and dense, that ordinarily no
three fixed points are visible from the
water's edge. Here the telemeter may
be the only instrument by which the re-
quired distances may be obtained. The
observer, establishing his instrument in
open ground, from which triangulation
stations can be seen, sends his assistant,
in a boat or otherwise, to such points
along the water as may be in sight.
These he locates by single observations,
reading the distances from the rod held
by the assistant. Thus the telemeter
station is referred to the observer's posi-
tion, which, in its turn, can be fixed by
means of three- point observations upon
the triangulation stations of the border-
ing cliffs.

In this simple and ingenious way of
determining distances by single observa-
tions, it is necessary that the diaphragm
of the telescope of the observer's instru-
ment should be fitted with two horizon-

146

tal cross-wires, and that his assistant
should be furnished with a graduated
rod, or telemeter. Then looking through
the telescope, the projection of the cross-
wires upon the rod includes a certain
amount of the graduation. This is a
chord subtending a certain constant
angle in the line of collimation, and, by
a principle in geometry, this chord in-
creases directly with its distance from
the angle which it subtends.

THE PLANE TABLE.

With the use of the plane table, there
comes so great a temptation to go into
the details of the work, to linger over a
small area, and to finish the sheets with
a topographical completeness, that its too
general adoption will be found to retard
the progress of a geographical survey.
In addition, it is cumbersome in its
shape, offering a broad surface of ex-
posure, and for that reason is not well
fitted for service upon high mountain
stations, where the wind is strong and
storms are frequent. In its favor, how-

147

ever, it must be said that this instru-
ment has been successfully employed
upon the extensive geological and geo-
graphical surveys under Major J. W.
Powell, of the United States, and that
very favorable reports have been made
concerning its usefulness. The incon-
venience of its shape has been modified
in this service, the table being composed
of slats hinged together, so that it may
be folded into a small compass for the
purpose of transportation.

When, in the course of a work of this
nature, there is encountered a district
where the importance of the field will
justify a minute and laborious survey,
the plane-table will serve an excellent
purpose there. It is very useful in the
mapping of a populous district, the
suburbs of a city, a mining region, or in
the representation on large scale of a
piece of topography which is interesting
as a type of geological structure. It is
always an easy matter for the geogra-
pher to accommodate himself and his
methods to detailed surveys like the

148

above, and it is a mistaken idea to sup-
pose that the exploration of a province,
unfits an engineer for the topographical
delineation of a parish. In all work of
engineering there is a constant tendency
towards greater accuracy, refinement,
and detail, and it is not freedom which
the geographer enjoys, in neglecting the
minor features of the earth's surface,
but rather a necessary restraint that is
imposed upon him, to keep him from
sacrificing the important to the unim.
portant.

THE OFFICE WORK.

As for the computations and other
reductions of notes which follow a field
season of the survey, there is not space
to discuss them here, nor is there any
special need of such a discussion, as they
do not differ materially from those
which apply to geodetic work in general.
Nor are the duties of the draughting-
room greatly distinguished above the
customary routine of such office work.
This thing only, may be noticed, that

149

the hand-to-hand struggle which the
field engineer constantly sustains with
the forces and obstacles of nature blunts
the delicacy of his touch, and makes his
hand too heavy for the fine drawing
necessary in a map finished for publica-
tion, and there should be in every office
a superior draughtsman who is accus-
tomed to the use of no heavier imple-
ment than the artist's pen.

This artistic finish is bought by some
sacrifice of accuracy, however, and be-
tween the field engineer and the final
draughtsman there should be few, if any,
middlemen to compile and replot the
work, because only the man who has
seen the country can reproduce its physi-
cal characteristics with truthfulness.
In every copy that is subsequently made
the face of the land grows more artifi-
cial and ideal; each mountain loses its
individuality of shape, and assumes a
symmetrical regularity which it does
not possess in nature; some of the nice-
ties of truthful representation are mag-
nified into exaggeration, and others are

150

overlooked and obliterated; the bed of
every canon grows broader in each suc-
cessive transcript; and the large hills
grow larger as the smaller ones dwindle
away. As in a popular parlor game, a
whispered story, passing current from
mouth to mouth throughout the round
of a circle, grows strange and distorted
beyond recognition, so in the successive
reproductions of a map by strange
hands, it loses its photographic truth of
execution as the idiosyncracies of the
various draughtsmen are wrought into
the plan. Finally it comes to represent
a country that is unnatural in its regu-
larity, made not so much by the acci-
dents of nature as by the design of
man, and moulded by the rules of a uni-
form and rigid geometry.

PLOTTING THE NOTES.

It is necessary that each engineer
shall plot his own notes, as he alone is
familiar with their arrangement through-
out his books, and only he is able to de-
rive the full benefit from them. There-

151

fore during the office season he will be
engaged upon a contour plot of the area
which he has surveyed during the pre-
ceding half of the year. Here he will
collect and compile in graphic shape all
of x the information which lies scattered
throughout the dozen note and sketch-
books which represent his labors in the
field. Upon this map fine drawing will
not be so essential as truthful representa-
tion and the utmost accuracy of position
that can be attained from the material
at hand; an inaccuracy that is barely
apparent upon the paper will correspond
to a very large error in the field, and so
a moment's oversight in the office may
invalidate the scrupulous care of a day's
or week's work upon the survey.

These sheets will be the basis of all
the maps of the survey, no matter in
what shape they may be published, and
hence the urgency of having them correct
in all of their positions, statements and
figures, and so complete as to include
every detail upon the pages of the
sketch-books, down to the shape of a

152

mountain-spur or village, or the presence
of a spring of water or dwelling place.
As the expense of sustaining an engineer
in the field is at least double the cost of
his office-work, he should confine himself
to what is absolutely necessary in the
collection of his notes, and then utilize
even the least of these in his subsequent
plotting and development of them.

CONTOUR PLOTS.

The plots will be constructed in con-
tour lines, as that is the only method in
which the engineer can give precise ex-
pression to his information and impress-
ions concerning the heights, slopes, and
forms of the country that he has sur-
veyed. While a map executed in
hachures would be more artistic and
more pleasing to the eye, it cannot be
made so mathematically invariable in its
conveyance of ideas, that is, it cannot be
made to convey the same ideas to all
persons; the bluff that would seem high
to one observer would seem low to
another, and the depth of shade that

153

would represent a steep gradient to one
draughtsman would stand for a moderate
declivity to another, according to their
peculiarities of judgment, or to the
different schools of drawing in which
they had been educated. The most
skilled cartographer, with one of the
best of hachure maps before him, would
find it difficult to estimate the angle of
any mountain slope, or to tell which of
two neighboring peaks was the highest,
unless their heights were given in figures.
In a glance at a contour plot, however,
he could count the excess of lines in one
of these mountains, and so compute its
superior altitude; or note the number of
lines in a centimeter of space, and so
determine the gradient of the earth's
surface there. For this reason the con-
tour plot is the only true basis from
which subsequent maps can be made;
then, no matter how many field engi-
neers may contribute to this work, their
reports will all come to the compiler and
final draughtsman, written in the uniform
language of lines at regular vertical in-

154

tervals. Otherwise, if the plots were in
hachures, this draughtsman would find
it well-nigh impossible to so assimilate
them that his finished map would not
reveal traces of the many different hands
from which it originated.

FINAL MAPS.

Unless the contour lines are so numer-
ous and close together as to produce
striking contrasts of light and shade as
the slope varies, this map has no mean-
ing to the popular eye. The ordinary
observer sees in it only a maze and con-
•f vision of lines, of whose design and
importance he is ignorant, and so it is of
no assistance to him. Therefore, since
maps are usually published for the in-
formation and guidance of the people at
large, it is wise that they should be
drawn with hachure shading, which
gives a more intelligible but less precise
picture of the country. In the construc-
tion of this, the contours of the engineer's
plot are so many guide-lines to the
draughtsman, who graduates the light

155

and darkness of the shade to accord with
the divergence or approach of these
wavering lines.

In addition to these a map in contours
may also be issued for the use of engi-
neers, the projectors of railways, and,
more especially, as a basis of the geo-
logical and resource charts, to which
this system is peculiarly adapted, as its
lines of equal level are of great assist-
ance in determining the extent of the
various formations, and for depicting
those areas of vegetable growth which
are bounded by fixed limits of altitude.
The dip and strike of a bed of uniform
slope being given at any one point of its
outcrop, it is an easy matter to trace
upon this map its line of reappearance
upon the farther side of a mountain-
range, or at any other point at which it
may be exposed again. Or, by counting
the lines of vertical equi-distance, the
geologist learns the thickness of the vari-
ous strata, the extent of a fault, or any
other fact in geological dimensions.

156

REVIEW OF THIS METHOD OF SURVEY.

In this paper the writer is at a disad-
vantage in appearing to advocate inac-
curate methods, and perhaps, at times,
actuated by a desire to give a perfectly
frank and honest expose of the subject
under discussion, he has magnified the
amount of inaccuracy to which the
operations described in these pages
would be liable; at all events he has
been very liberal in his allowance for
probable error. Indeed, to those who
have been in the habit of reading, and
believing, barometrical altitudes that are
given down to the tenth of a foot, or
sextant determinations to the hundredth
of a second, it may appear unpardomibly
liberal to allow for an error of meters or
seconds in these classes of work, and
perhaps to some it may seem indicative
of professional unfitness in the engineer
who would acknowledge the liability of
such. But while results like the above
are frequently published, their authors
would be either sciolists or charlatans if
they were to claim that they were abso-

157

lately reliable down to those small
fractions; it is often the custom among
the most conscientious and intelligent
engineers to make their reports in that
elaborated form, since those are the
figures at which their computations
finally arrived, and hence there are cer-
tain weights of probability in their
favor.

In like manner, in the computations of
a survey of the proposed nature, it would
never be allowable to neglect or throw
away any odd figure or fraction, on the
plea that it was probably exceeded by
the error of the whole. By following
this system, not only are habits of accu-
racy inculcated and sustained among the
assistants of a survey, but the closest
possible approximation to the truth is at-
tained.

In the ordinary branches of his profes-
sion, habits of rigid precision, at what-
ever cost of time and money, are the
best recommendations for an engineer.
In a geographical survey, however, to
enforce this rule beyond .the triangula-

158

tion, upon which the integrity of the
whole depends, and to continue it in full
force throughout all of the subordinate
branches of the work, would be to make
such a survey impossible in Brazil, owing
to the enormous expense that would at-
tend it. Viewed theoretically, the best
of maps, even those produced by the
tedious processes of the European topo-
graphical surveys, are but approxima-
tions to the truth; the question now
arises as to how close it is profitable to
bring this approximation. Viewed prac-
tically, the maps that would result from
the proposed system of survey would be
seldom, if ever, in error to a perceptible
degree, and it would seem that this is
the limit of accuracy bayond which this
country cannot well afford to go.

To condemn a method of surveying
because it is not absolutely accurate
would be to condemn all of the survey
of the world, and especially all of the
systems of ordinary land surveying,
which are so faulty that it is very sel-
dom that a purchaser of land does not

159

get either considerably more or less than
he pays for. Still, that has not been
deemed sufficient reason why all buying
and selling of real estate should cease
until its boundaries could be determined
by the instrumentality of such rods, com-
pensated for temperature or packed in
ice, as are used in the measurement of
geodetic base-lines. In one respect the
proposed system is far superior to the
land survey, as it is founded upon the
principle of triangulation, which, secur-
ing it in its true proportions, prevents
any great accumulation of error. In the
United States of North America, where
surveys of this nature are in active and
successful operation, it has been earnestly
advocated that the triangulation of the
geographical survey should be made the
basis of the land survey, the different
triangulation stations serving as initial
points from which to run the land bound-
aries, and it is very probable that, with-
in a year or two, this plan will be
adopted there.
There are different degrees of accu-

160

racy, each adapted to the end which it is
intended to serve; this degree, explained
here, is sufficient for the rapid prepara-
tion of a very useful and complete
geographical map. It would not suffice
for the measurement of an arc of the
meridianr such as has been proposed for
this empire. That is a work in which
no error, however small, that is not be-
yond the cognizance of the human
senses and judgment, can be excused or
overlooked. To publish a wrong result
here would be not only a national dis-
grace, but a misfortune to the whole
world, as it is upon the shape and dimen-
sions of the earth that many of our
geodetic and other scientific formulas
rest, while it is from the same source
that the world derives its standard unit
of length, by which the interests of all
civilized people are affected. Or, if
Brazil were prepared to enter into that
honorable rivalry in geodetic work, in
which some of the older nations are en-
gaged, each seeking to produce instru-
ments, methods, results, discoveries, and

161

developments that may be in advance of
everything hitherto achieved, this sys-
tem of survey would not be recom-
mended. It is not impossible, however,
that, from this as a beginning, there
might grow, keeping pace with the gen-
eral progress of the country, a geodetic
institution that would be equal to the
best.

ORIGIN OF THIS SYSTEM.

The writer by no means pretends to be
the inventor of the combination of
methods described in these pages, al-
though hitherto there has been but little
description of them in print. An effi-
cient system of survey cannot be the in-
vention of any one man; it must be the
outgrowth of years of practical expe-
rience, resulting in the gradual accumu-
lation of ideas and improvements con-
tributed by those who have been en-
gaged upon it. This one is the result of
a growth of at least a quarter of a cen-
tury, and therefore is not open to the
serious objection of being new and un-

162

tried. During that length of time, the
enterprise of geographical surveying
has been receiving more and more en-
couragement from the government of
the United States, which has wisely
adopted that plan, in connection with
geological and other scientific research,
as a means of opening and illustrating
its vast public territory.

At the present day there are actively
engaged upon this duty in that country
three important commissions of survey.
That of Dr. F. V. Hayden, geologist in
charge, is known throughout the world
by its extensive and important work, not
only in geology and geography, but in
all their kindred sciences as well. A
second is under Major J. W. Powell, the
intelligent geologist and intrepid ex-
plorer who was the first to descend the
great canon of the Colorado River. An-
other, more strictly geographical in its
nature, is under the auspices of the War
Department, and is conducted by Lieut.
George M. Wheeler, an officer of envia-
ble reputation in the United States Corps

163

of Engineers. While the general plan
is much the same throughout these
three commissions, it is especially to his
former associates, the geographers and
officers of the last-named organization,
that the writer wishes to acknowledge
his indebtedness for whatsoever of value
there may be in this paper.

BRAZIL AND THE UNITED STATES.

Although, as has been stated hereto-
fore, it is not wise for any nation to copy,
blindly, and without adaptation to its
own peculiar needs, the system of sur-
vey employed by any other country, yet
it would seem that the processes that are
fitted to the United States would require
but little modification to be adapted to
use in Brazil, so analogous are the two
countries in many respects. They have
equal amounts of territory as near as
may be, but, peopling this territory,
there are four times as many inhabitants
in the United States as there are in
Brazil; thus it would seem that the me-
thods that are deemed sufficient for the

164

former would certainly suffice for the
latter. In each country the population
diminishes from a thickly-settled sea-
coast back into an uncivilized and almost
unknown interior. In each of these
there is a great amount of wild land
which the government is anxious to open
to colonization and cultivation. To ex-
pose and popularize the natural wealth
of this public domain, the U. S. Govern-
ment resorted to the plan of scientific
surveys, to which the Geological Com-
mission of Brazil is very similar in all
respects, and so efficiently have they
accomplished their purpose that it has
become a noticeable fact in the cartog-
raphy of the United States that its maps
of some of the remote and unsettled dis-
tricts of the Rocky Mountains are
superior to those of its oldest and richest
States, and, therefore, there are now
plans on foot looking to the extension of
these geographical surveys over the en-
tire surface of the country.

As the American manner of railway-
building, more expeditious and involving

165

less first cost than the European methods,
has been found practicable in Brazil, in
some instances, in which all other plans
would fail, so with this question of geo-
graphical surveys, it may prove to be the
American system or none.

RESULTS OF THIS SYSTEM.

Considering now the results that could
be expected from such a geographical
survey of Brazil, this question can be
best answered by referring to areas sur-
veyed in the same manner in the United
States. From Lieut. Wheeler's annual
report, which the writer has before him,
it appears that in six years' continuance
of his commission an approximate extent
of 800,000 square kilometres has been
surveyed. Allowing an average of five
parties in the field during that time, the
season's work of one engineer reduces
itself to about 25,000 square kilometres.
Allowing proportional returns from the
various other geographical surveys at
present in commission, or that have been
in existence during the last ten years in

166

the western portion of the United States,
it appears that one-third of the area of
that great country has been thus sur-
veyed in that period.

This is at a total expenditure which,
while including the cost of all other
concomitant scientific labors, to which
the geographical work has been in large
part incidental and tributary, has never
exceeded four hundred contos ($ 200,000)
per year. There is probably no other
department of public enterprise which
has yielded so extensive and valuable re-
turns for an equal amount of money.

AN ESTIMATE FOR ONE SEASON.

In general, an area of from 10,000 to
30,000 square kilometres, varying ac-
cording to the geographical nature of
the country, is assigned to each party
for a season of four, five, or six months,
and its ability to satisfactorily cover
that district in that time is conceded.
To illustrate the possibility of such rapid
progress, let us take a typical area of
20,000 square kilometres and see what

167

can be done with it by one party and
one geographer in one season's work of
six months in duration. Of this time
the first month will be consumed in the
measurement and development of the
base, and in other preparation. Of the
remaining period one month more will
perhaps be lost in unavoidable delays
resulting from storms or other causes.
There will then remain four months,
which, at twenty-five available days in
each, will afford one hundred days for
active service in the field.

Allow one half of these days for the
meander survey, and the other half for
the occupation of mountain stations.
Fifty mountain stations will thus result,
and, in addition to these, there will be a
topographical station either upon or
adjacent to each day's meander. So
there are one hundred triangulation and
topographical stations distributed at
judicious intervals over this territory.
That is, there is one for every two
hundred square kilometres of ground, or,
typically, they are but about fourteen

168

kilometres apart, and the piece of coun-
try to be sketched in contours need not
extend more than seven kilometres in
each direction; this estimate ignores the
meander surveys, to which fifty days of
the season will be devoted, and by which
these stations will be separated and sur-
rounded.

At twenty-five kilometres a day, a very
reasonable allowance, the total distance
of meander route will be 1250 kilometres.
This distance would reach across our
area nine times, cutting it into strips of
sixteen kilometres in width. Hence, in
order to include the entire country from
this survey, the typical zone of each
meander would not reach more than
eight kilometres on either side of its
path; but, since it would be superfluous
to sketch from this base the country in
the immediate vicinity of the mountain
stations, these plots en route need never
extend more than four kilometres from
the central line. Of course, in practice,
these surveys will not be thus distributed
in straight lines at equal distances apart,

169

but will communicate, intersect, and
duplicate in every possible way. Still
the meander will serve its original pur-
pose of penetrating those regions and
traversing those border-lands that are
remote from the mountain stations, and
will trace out the roads, trails, and im-
portant streams, whose entire length in
this area will not be likely to exceed
1250 kilometres.

Returning to the office at the end of the
season, the engineer will have material
enough to make a plot of the country on
a scale of one centimetre to the kilo-
metre (100*000)? or one-half a centimetre
to the kilometre (^-oSror)' Or, to put
this statement with more precision, he
will have so much and so detailed mate-
terial,that he will not be able to portray
it conveniently and intelligibly on a scale
of less than 3-^-^0 o- But when the
final draughtsman comes to copy these
plots, he may condense them, if it be
thought expedient, to proportions of
TToVsr* or even smaller. On the other
hand, portions of this area may be plot-

170

ted upon a much larger plan than any
here noticed, should such be found nec-
essary for the clear and complete geo-
graphical and geological representation
of the same.

EUROPEAN SURVEYS.

Now, in contradistinction to the above
showing, let us take up the reports of
some European surveys. In Prussia,
12,000 square kilometres, a little more or
less, are surveyed annually, at a cost of
800,000 marks, or, as near as may be,
four hundred contos of Brazilian money,*
exclusive of the salaries of military as-
sistants; notice that in the United States,
with a total annual appropriation not
greater than this, at least 300,000 square
kilometres are geographically surveyed
each year, this territory being studied at
the same time by the geologist, the
chemist and the naturalist.

Upon the Ordnance Survey of Great
Britain there were over 1800 assistants

* A conto of reis, in Brazil, is equal to about five hun-
dred American dollars, or a hundred pounds sterling.

171

and employes engaged during the year
of 1874; the total area surveyed by them
was not more than 8,000 square kilome-
tres. With the methods in use in Austria
an experienced topographer can survey
in one field season of six months five
hundred square kilometres at the farthest.
In Switzerland the topography is in large
part done by contract, and it alone, ex-
clusive of triangulation and publication,
costs 700 or 800 francs per square stunde,
or about twenty-two mil reis* per square
kilometre. So with the surveys of Italy,
Spain, Sweden, and the other European
countries of comparatively small extent;
they are so slow, detailed, and withal so
expensive as to be inapplicable to the
great empire of Brazil.

AX ADVANTAGEOUS DEVELOPMENT.

So vast is the extent of this empire
that the idea of a geographical survey
of its territory, as a whole, is an astound-
ing one, and is liable, in itself, to forbid
all further consideration of the subject.

* Eleven American dollars.

172

But this plan does not necessarily imply
the regular extension of this survey over
the whole country, irrespective of popu-
lation and wealth. On the contrary it
would devote itself at first to such areas
as, from geological or other economical
reasons, might most urgently require it,
and a region of especial interest to the
geologist would be surveyed first and
with especial care, to the neglect or even
exclusion of those great stretches of
country whose structure is unvaried and
monotonous. In a few conditions of its
plan, as, for instance, in the system
adopted in the projection of its maps, it
might provide for any possible ultimate
extension, but in other respects it could
operate with equal facility, in whatever
districts might be assigned to it.

Nor does this plan imply the necessity
of any great outlay at the beginning, but
would ask to start upon a small scale at
first, with a view to gradual growth as it
proved itself worthy of encouragement.
As the aim of this project would be not
only the production of much-needed

173

maps, but also the introduction of these
methods of survey from abroad, and the
training of Brazilian engineers in the use
of the same, any very extensive initial
basis would prove not only embarrassing
at first but also probably disastrous in
the end. A survey inaugurated upon a
grandiose scale is too liable to exhaust
the patience and liberality of its official
patrons before it can exhibit results ap-
parently equivalent to the expenditure
that it has caused, and the frequent fate
of such enterprises is that they are dis-
continued at about the time when, their
organization being successfully com-
pleted, they are prepared to enter upon
an area of efficient and fruitful labor;
hence, all of the expense of organization
and other preliminaries becomes a total
loss to the government.

On the other hand, some of the rm>st
important surveys of the world have
arisen from humble beginnings. Such an
enterprise educates its own members, the
assistant engineer of one season becom-
ing the engineer of the next, and so on.

174

It develops gradually and with a healthy
growth, perfecting its own methods, and
always experimenting upon a small scale,
so that it is never liable to serious disas-
ter. And, above all, by its early pro-
duction and exhibition of results com-
mensurate with its size, and with its
cost, which is insignificant at first, it
buys the right to be continued, en-
couraged and increased from year to
year.

A GEOLOGICAL AND GEOGRAPHICAL SUR-
VEY.

There are two very good arguments
for such a geographical survey in connec-
tion with the Geological Commission of
Brazil ; first, its necessity to the geologi-
cal survey, as explained in the early part
of this paper; and second, because in
sudh a connection it can work most
economically and profitably. With a
combination of these elements comes
much valuable co-operation between the
representatives of the various branches
of science, and this is constantly acting

175

to lessen the expense and increase the re-
turns of such a survey. For instance, as
the meteorologist of the engineering
corps, an assistant with some acquaint-
ance with geology, could be chosen. As
his meteorological duties upon the march
would be but light, he could devote
much of his time to a geological study
of the road, leaving the regular geologist
at liberty to go from camp to camp by
any other route that he might select.
Again, the meteorologist, or even the en-
gineer himself, may make strati graphical
sketches upon every mountain, and bring
specimens of rock from the same, while
the geologist is away upon some detour
to regions of interest in another direc-
tion.

Or, reversing this illustration, the
geologist, whose profession is so closely
allied to that of the geographer, is con-
stantly making notes of direction, dis-
tance, slope, and altitude, which are of
the highest importance and use in the
construction of a map. These are lost
to the world if there is not an accom-

176

panying geographical survey into whose
plots they may be assimilated.

In witness of the sympathy with
which the present members of the Geo-
logical Commission regard geographical
work, and of their skill in the prosecu-
tion of the same, the writer would men-
tion their intelligent and extensive sur-
veys of the valley of the Amazon, from
Monte Alegre westwards, and of its
tributary, the Trombetas; of the island
of Fernando de Noronha; and of many
localities along the Atlantic coast and
elsewhere in the empire. These are evi-
dences of a willingness and an ability to
collect geographical information, which,
in themselves, assure the success of a
system of geographical surveying in
connection with the Geological Commis-
sion of Brazil.

*¥* Any book in this Catalogue sent free by mail, on
receipt of price.

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WEISBACH. MECHANICS OF ENGINEERING, APPLIED
MECHANICS; containing Arches, Bridges, Foun
dations, Hydraulics, Steam Engine, and other
Prime Movers, &c., &c. Translated from tlu
latest German Edition 2 vols., 8vo.

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Van Nostrand's Science Series.

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I. CHIMNEYS FOR FURNACES, FIRE-PLACES, AND
STEAM BOILERS. By R. Armstrong, C. E.

II. STEAM BOILER EXPLOSIONS. By Zerah Colburn.

III. PRACTICAL DESIGNING OF RETAINING WALLS.
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IV. PROPORTIONS OF PINS USED IN BRIDGES. By
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V. VENTILATION OF BUILDINGS. By W. F. Butler.
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XL THEORY OF ARCHES. By Prof. W. Allan, of the
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XII. A PRACTICAL THEORY OF Voussom ARCHES.
By William Cain, C.E. Illustrated.

XIII. A PRACTICAL TREATISE ON THE GASES MET
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XIV. FRICTION OF AIR IN MINES. By J. J. Atkinson*
author of "A Practical Treatise on the Gases met
with in Coal Mines."

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lustrated with numerous engravings, and three
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XXVIII. ON TRANSMISSION OF POWER BY WIRE ROPE.
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XXIX. INJECTORS ; their Theory and Use. Trans-
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XXX. TERRESTRIAL MAGNETISM AND THE MAGNETISM
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W. Rafter, Civil Engineer.

XXXIV. FOUNDATIONS. By Prof. Jules Gaudard, C.
E. Translated from the French, by L. F. Vernon
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