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tions at the two stations whose difference in elevation is
required should be made as nearly simultaneous as possible,
as temperature and atmospheric conditions are constantly t
changing.

Let Z difference of elevation of the two stations in

feet;

h = the reading in inches of the barometer at the
lower station;



690 SURVEYING.

H= the reading in inches of the barometer at the

higher station ;
t and /' = temperature (Fahr. ) of the air at the two sta-

tions.
Then,



Z= (log // - log H) X 60,384.3 X l + 9 ~. (96.)

EXAMPLE. Reading at lower station, Si = 29.52 in.,. / = 70; at
higher station, H '= 27.15 in., /' = 62.

Log of/;, 29.52 = 1.47012
Logoff, 27.15 = 1.43377

Difference = .03635
/ + /'- 64 70 + 62 - 64

1 + ^00 =1 + - 900

Hence, Z= .03635 X 60,384.3 X 1.0755 = 2,360.4 feet, the difference
between the elevations of the two stations.

Tables are prepared giving values of (log.// log H} X 60,384.3 and

of 1 H - j^r - , which greatly simplifies the work of determining
"00

differences of elevations.



HYDROGRAPHIC SURVEYING.

1305. Hydrographic surveying is the process of
determining, by means of soundings, the location of the deep
and shallow places of harbors, sounds, rivers, etc., and
recording them in charts for the use of engineers and
navigators.

1306. Sounding. Sounding is measuring the depth
of water". The surface of the water forms the datum line,
and the various depths measure the undulations or changes
of elevation of the bottom of the body of water being
sounded. The extent of knowledge of the bottom gained
will depend upon the number and accuracy of the soundings.

For depths to 18 feet, a sounding rod graduated to feet
and tenths is used ; for greater depths, a lead line, marked
to fathoms and half fathoms, is employed. It will be found
necessary to keep the lead line well stretched and its length
frequently tested.



SURVEYING. 091

13O7. Conduct of Survey. The mode of conduct-
ing a hydrographic survey is as follows: Stations at con-
spicuous points on shore are first carefully located by
trigonometrical surveying. They form the base line by
which all irregularities of shore 1 line and the location of all
soundings are determined. A good station mark is a post
set firmly in the ground with about one foot of its length
exposed. A hole is bored in the center of the top of the
post and a flagpole set in it. The pole can be pulled out
and a transit set directly over the station. Each station
should be distinguished by the combination of colors on the
flag, and the number of the station should be distinctly
marked on the post. A permanent bench mark must be
established and the height of water at the time of the
soundings recorded.

Buoys are made of light wood, and painted in such colors
as will make them conspicuous.




The location of buoys and soundings is illustrated in Fig.
305. The stations A and B are located and their distance
apart known. A transit is set up at each station and back-
sighted to a rod at the other; the vernier plate is then un-
clamped and the leadsman in the boat is carefully followed
with the instrument. At a given signal, the leadsman takes
a sounding, and both instruments sight to him and read the
angles, which give a side and two adjacent angles of a
triangle from which to determine the location of the point D.
In the same manner C and any number of points can be
located. A man in the boat records the time and the sound-
ings as they are read by the leadsman.



692 SURVEYING.

13O8. Tide Gauges. By means of a tide gauge the
height of water at any time may be known. The datum or
zero line is mean low spring tide. A simple form of tide
gauge is a board nailed to the upright front of a dock. The
face should be painted white and graduated to half-feet or to
feet and tenths, and the zero line set at mean low spring tide.
The feet marks should be in heavy black figures, so that
they may be easily read.

The tide gauges used by the government are automatic,
and are provided with an indicator which registers on paper
the fluctuations of the tide.



LAND SURVEYING.



1 3O9. The United States System of Surveying
Public Lands. The public lands of the United States are
divided and laid out into approximately equal squares, the
sides of which are true north and south or east and west
lines. This is effected by means of meridian lines and
parallels of latitude established six miles apart. The squares
thus formed are called townships, and contain 36 square
miles or sections. Each section contains, as nearly as may
be, 640 acres, giving an approximate area of 23,040 acres for
each township.

1310. Principal Meridians. A principal merid-
ian running diie north and south and a base line running
due east and west are established astronomically, and the
half-mile, mile, and six-mile corners are permanently marked
on them. These two lines form the basis of all subsequent
divisions into townships and sections. All other lines, with
the exception of these two and the standard parallels, are
run with the compass and chain.

Fig. _306 represents a section of country thus laid out. The
scale is 10 miles to 1 inch = 633600 : 1. The diagram shows
the principal meridian running truly north and south, and
a base line which is a parallel of latitude running truly
east and west. Parallel to these are other lines 6 miles apart,
forming townships. All the townships situated north or
south of each other form a range, the ranges being named^
by their number east or west of the principal meridian.
The seven ranges east and seven west of the principal merid-
ian, shown in Fig. 306, are described as R. 1 E, R. 1 W, etc.
The townships in each range are designated by their num-
ber north or south of the base line. Thus, in the diagram,



694



LAND SURVEYING.



the township marked A is denoted by T. 3 N, R. 4 W; that
marked B, by T. 2 S, R. 3 E. These abbreviations should









1


*St


indi


ird .


Par*


llel\Noi


th










































A






S




























^C

j


























Ba


J


Lt


ne.
























I




























v

_s






B






















ft<






















12-


Sta


nda


rdP


ira(


ien


^out


h.





































N



FIG. 306.

be read township 3 north, range 4 west, and township 2
south, rangeS east.

1311. Township Divisions. Each township is divi-
ded into 36 sections, each one mile square and containing

640 acres as nearly as
may be. The sections in
each township are num
bered from 1 to 36, as
shown in Fig. 307. The
numbering of the sec-
tions begins at the north-
east corner of the town-
ship and goes west from
1 to 6, then east from 7
to 12, and so on alter-
nately until section 36 in
the southeast angle of
the township is reached.
The sections are sub-
divided into quarter-sections, each half a mile square and



W


6


5


4


3


2


1


7


8


9


10


11


12


18


17


16


15


14


13


19


20


21


22


23


24


30


29


28


27


26


25


31


32


33


34


35


36


S
FIG. 30T.



LAND SURVEYING. 695

containing 1GO acres, and sometimes into half quarter-sections
of 80 acres and quarter quarter-sections of 40 acres. By this
system the smallest subdivision of land can be accurately
located ; as, for example, the southeast quarter of section 36
in township one south in range two west of Willamette
meridian.

1312. Obstacles. The law requires that the lines of
the public surveys shall be governed by the true meridian,
and that the townships shall be six miles square, two condi-
tions involving a mathematical impossibility, for strictly
conforming to the meridian would necessarily throw the
township out of square, for the reason that a degree of longi-
tude, which, at the equator, is G9|- miles, constantly dimin-
ishes as one approaches the poles. As the meridian lines are
strictly adhered to, the requirements of the law respecting
areas are not fulfilled. The townships assume a trapezoidal
form which increases the higher the latitude of the surveys.
To meet these conditions the law provides that the sections
shall contain 040 acres, as nearly as may be, and further pro-
vides that " in all cases where the exterior lines of the town-
ship thus to be subdivided into sections and half-sections
shall exceed or shall not exceed six miles, the excess or
deficiency shall be specially noted and added or deducted
from the ivestern or northern ranges of sections or half-
sections in such township, according as the error may be in
running the lines from east to west or from south to north."
In order to throw the excesses or deficiencies, as the case
may be, on the nort/i and west sides of a township, according
to law, it is necessary to survey the section lines from south
to north on a true meridian, leaving the result in the northern
line of the township to be governed by the convexity of the
earth and the convergency of meridians.

Thus, suppose the land to be surveyed lies between
46 and 47 of north latitude. The length of a degree of
longitude in latitude 40 north is taken as 48.0705 statute
miles, and in latitude 47 north as 47.1944 miles. The dif-
ference, or convergency per square degree, = .8701 mile .=



696 LAND SURVEYING.

70.08 chains. The convergency per range (8 per degree of
longitude) equals one-eighth of this distance or 8. 7G chains,
and per township (11 per degree of latitude) will equal
8.76 chains divided by 11^=. 76 chain. Hence, we know
that the width of townships along their northern boundary is
76 links less than on their southern boundary. The town-
ships north of the base line, therefore, become narrower and
narrower than the six-mile width with which they start by
that amount.

1313. Standard Parallels. Standard parallels,
called correction lines, are established at intervals of
30 miles to provide for the correction of the error arising
from the convergency of the" meridians. They also serve to
limit errors resulting from inaccuracies in measurement.
Such correction lines when lying north of the principal base
line form new base lines for the surveys north of them.
The convergency or divergency is taken upon these correc-
tion lines, from which, as base lines, the townships start
again with their proper widths. On these correction lines,
therefore, double corners will be found, one set being the
closing corners of the surveys ending tJicre, and the other set
the standard corners of the surveys starting there.

1314. Running Township Lines. The principal
meridian, the base line, and the standard parallels having
been first astronomically run, measured, and marked accord-
ing to instructions on true meridians and true parallels of
latitude, the process of running, measuring, and marking
the exterior lines of townships is as follows:

For townships north of the base line and west of the
principal meridian, commence at Station No. 1 (Fig. 308),
the southwest corner of T. 1 N, R. 1 W, as established on
the base line, thence run north on a true meridian line
480 chains, establishing the half-mile and mile corners there-
upon, according to instructions, to No. 2, which is the north-
west corner of the same township. There establish the
corner of townships 1 and 2 N, ranges 1 and 2 W; thence
run east on a random or trial line, setting temporary stakes



LAND SURVEYING.



697



at the half-mile and mile points and noting the distance
where the line intersects the eastern boundary north or
south of the true or established corner. Run and measure
ivestward on the true line, establishing permanent half-mile
and mile corners, noting all water crossings and the charac-
ter of the land, as per instructions, to No. 4, which is iden-
tical with No. 2. The last half-mile will fall short of

Standard Parallel.





28


14


14


28




27


13


13


27




25 26


11 12


12 11


26 25




24


10


10


24




22 23


8 9


9 8


23 22




21


7


7


21




19 20


5 6


6 5


20 19




18


4


4


18




16 17


2 3


3 2


17 16


29


15


1


1


15




Base




Li


ne






1


K
e

M








g

{


c

V

fc





FIG. 808.

40 chains by about the amount of the calculated conver-
gency per township, which, in the above supposed case,
equals 76 links.

The terms random and true lines are explained in Fig.
309. The boundary from Station 1 to Station 2 is a true
meridian and 480 chains in length, with permanent corners
set at each half-mile and mile. From A run and measure



698



LAND SURVEYING.



towards B on a true east and west line, as shown by the dot-
ted line A B, which is called a random line, setting tem-
porary half-mile and mile posts. This random or trial line
being run on a parallel of latitude, must intersect the prin-
cipal meridian near the true corner C, previously established.
The return or true line always connects this true corner
with the one from which the random starts. Random lines



Random Line 479.25 chains = 47925 links.

10 4O 4O 4O to to 4O 39.',




Sta. 1.



T.l.N.R.l.W.



Base Line.



C\



are either true east and west or true north and south lines,
i. e., they are either parallels of latitude or true meridians.
Suppose the random line intersects the principal meridian
X Y at B, 75 links to the north of the true or established
corner at C, the length of A B is 479 chains and 25 links.
The triangle A B C is a right-angled triangle, right angled
at B; dividing B C=7o links by A .#=47925 links, we
have the tangent of the angle BA C= jrVrg- .00150 =



LAND SURVEYING. '699

tan 05'. The angle B C A is, therefore, 90 = 05' =
89 55', and the return course, or true line, C A is
N 89 55' W. Setting the instrument over the true or estab-
lished corner C, the compass is set for the true course C A,
N 89 55' W, and measuring 40 chains from C, a permanent
half-mile or quarter-section post is set, 40 chains further a
mile or section post is set, and so on, setting half-mile and
mile posts at regular intervals of 40 chains until the last
half-mile post is set; between it and the township corner A,
the distance is but 39 chains and 25 links, thus leaving
the deficiency in the western tier of sections as prescribed
by law.

In case the random line materially falls short, or overruns
in measurement, or intersects the eastern boundary at a con-
siderable distance from the established corner, it will be evi-
dent that there has been considerable error either in direction
or measurement of the lines, or both, and the lines must be
retraced even if it should be found necessary to rerun the
meridianal boundaries of the township (especially the west-
ern boundary) so as to discover and correct the error. The
true corners must be established, and the false ones destroyed
and obliterated, and all facts carefully set forth in the notes
so as to avoid future confusion.

Then proceed north from 4 to 5, establishing corners as
before; No. 5 is the N W corner of T. 2 N, R. 1 W; east
to No. 6 (the N E corner of the same township), west
to No. 7 (the same as No. o), north to No. 8 (the N W cor-
ner of T. 3 N, R. 1 W), east to No. 9 (the N E corner of
the same township), west to No. 10 (same as No. ), north
to No. 11 (the N W corner of T. 4 N, R. 1 W), east to
No. 12 (the N E corner of the same township), west to
No. 13 (same as No. 11], and thence north on a true merid-
ian to the standard parallel or correction line (which is here*
five townships, or 30 miles, north of the base line), throwing
the difference over or under four hundred and eighty
chains on the last half mile, according to law. At the inter-
section with the standard parallel establish the closing corner,
the distance of which from the standard corner must be



700 LAND SURVEYING.

measured and noted as required by the instructions. In
case any obstruction should have prevented the extension of
the standard parallel along the field of the present survey,
the surveyor will establish a corner for the township, subject
to correction, should the parallel be extended. The surveyor
then returns to the base line, and, from the southwest corner
of T. 1 N, R. 2 W, carries up another tier of townships,
closing as before.

For townships north of the base line and east of the prin-
cipal meridian the order of survey is as follows: Beginning
at the southeast corner of T. 1 N, R. 1 E, proceed as with
townships north and west, except that the trial or random
line is run and measured west and the true line east, throw-
ing the difference over or under 480 chains on the west end
of the line. Accordingly, the surveyor, having measured his
trial line west, will first determine the length of the last half-
section line, and commence the measurement of the true line
with such excess or deficiency, and, consequently, the re-
maining measurements will all be exact half miles and
miles.

1315. Running Section Lines. The interior or
sectional lines of all townships, however situated with refer-
ence to base and meridian lines, are laid off and surveyed,
as shown in Fig. 310.

In this figure the squares and large figures represent sec-
tions; the small figures are referred to in the following di-
rections. Commence at No. 1 (see small figure in the
diagram) which is a township boundary for sections 1, 2, 35,
and 36 ; thence run north on a true meridian; at 40 chains
establish a half-mile or quarter-section post, and at 80 chains
establish the corner of sections 25, 26, 35, and 36. Thence
east on a random line to No. 3, setting a temporary quarter-
section post at 40 chains, noting the measurement to No. 3
and the distance of the random's intersection north or south
of the true or established corner of sections 25, 36, 30, and
31. Thence correct west on a true line to No. 4, setting the
quarter-section post on this line equidistant from the two



LAND SURVEYING.



701



corners whose distance apart is now known. In like manner
proceed from 4 to 5, 5 to 6, 6 to 7, and so on to No. 16, the
corner of sections 1, 2, 11, and 12, thence north on a random
line to No. 17, setting a temporary quarter-section post at
40 chains and noting the length of the whole line and the
distance of the random's intersection east or west of the true
corner of sections 1, 2, 35, and 36 established on the town-
ship boundary, then southwardly from the latter on a true



31



32



33



34



35



36



1

12
13
24
25
36


6

99 98


97

5

96 72


71

4

70 54


53

3

52 36


35

2

34 18


17

1

16


6
7
18
19
30
31


/%/
i

92


94 95

8
91


68 69

9

67


50 51

10

49


32 33

11

31


14 15

12
13


93
18

87


89 90

17

86


65 66

16

64


47 48

15

46


29 30

14

28


11 12

13

10


88

19

82


84 85

20

81


62 63

21

61


44 45

22

43


26 27
23

25


8 9
24

7


83

30

77


79 80

29

76


59 60

28

58


41 42

2?

40


23 24

26

22


5 6

25
4


78

31


74 75

32

73


56 57

33
55


38 39
34

37


20 21

35

19


2 3

36
1



654321

FIG. 310.

line, noting the course and distance to No. 16, the established
corner to sections 1, 2, 11, and 12, care being taken to estab-
lish the quarter-section post at 40 chains from said sectiori
corner, thus throwing the excess or deficiency on the north-
ern half mile, according to law. Proceed in like manner
through all the intervening tiers of sections to No. 73, the
corner of sections 31, 32, 5, and 6. Thence north on a true
meridian 80 chains to 74, setting a quarter-section post at



702 LAND SURVEYING.

40 chains, and at 80 chains setting corner of sections 29, 30,
31, and 32; then east on a random to 75, setting temporary
quarter-section post at 40 chains, noting the entire measure-
ment to the eastern boundary and the distance of the ran-
dom's intersection north or south of the true corner of sec-
tions 28, 29, 82, and 33; thence west on a true line, setting
the quarter-section post on the true line and equidistant
from either end, to No. 76, which is identical with 74', thence
west on a random line to 77, setting temporary quarter-sec-
tion post at 40 chains, noting the full measurement of the
line and the distance of the random's intersection with the
township boundary nortli or south of the established corner
of sections 30, 31, 25, and 36; thence eastwardly on the true
line, giving its course and setting the quarter-section post
40 chains from the corner of sections 29, 30, 31, and 32, thus
throwing the excess or deficiency of measurement on the
western half mile of the section according to law. Proceed
north in like manner from No. 78 to 79, 79 to 80, 80 to 81,
and so on to No. 94, the southeast corner of section 6, where,
having established the corner of sections 5, 6, 7, and 8, run
thence successively the random line east to 95, north to 97,
and west to 99, and by reverse courses back on true lines to
the southeast corner of section 6, establishing the quarter-
section corners, and noting courses, measurements, and
distances as prescribed by law.

In townships contiguous to standard parallels the above
method is varied as follows : In every township south of the
principal base line which closes on a standard parallel, the
surveyor will begin at the southeast corner of the township
and measure westward, establishing the half-mile and mile
corners and noting their distance from the preestablished
corners. He will then proceed to subdivide as directed
under the above head.

In townships north of the principal base line which close
on the standard parallel, the section lines must be closed on
the standard parallel with true meridian lines instead of
course lines, as directed for townships otherwise situated;
and the connections of the closing corners with the



LAND SURVEYING. 703

preestablished standard corners are to be ascertained and
rioted.

In case the surveyor is unable to close the lines on account
of the standard not having been run for some reason, as be-
fore mentioned, he will then plant a temporary post or con-
struct a mound at the end of the sixtli mile, thus leaving
the lines and their connections to be finished when the
standard shall have been run.

1316. Water Frontage. Departures from the gen-
eral system of dividing land have been authorized by law,
especially in the case of water frontage.

In surveying the public lands of Louisiana, which border
on rivers, streams, lakes, and bayous, surveyors were author-
ized to divide the land with water frontages of fifty-eight
poles and running back four hundred and sixty-five poles in
depth, "and of such shape and bounded by such lines as the
nature of the country will render practicable and most con-
venient. " Later, authority was given to survey lands with
two acres water frontage and running back a depth of forty
acres, tracts so surveyed to be offered for sale entire in-
stead of in half quarter-sections. In localities where it
would best subserve the interests of the people to have
fronts on the navigable streams and running back into the
uplands for timber, surveyors were authorized to increase
the quantity of land so as to give four acres frontage and
forty acres in depth, giving tracts of 160 acres, but in so
doing they were only to survey the lines between every four
lots (or 640 acres), establishing the boundary posts or mounds
in front and in rear, at the distances requisite to secure the
quantity of 160 acres to each lot, either rectangularly where
practicable or at oblique angles where otherwise. The angle
is not important so long as the principle is adhered to of
making, as far as possible, the rear lines square with the
regular sectioning.

1317. Meandering. This name is applied to the
usual mode of traversing or surveying a navigable stream.
The instructions for this work are in part as follows: Both



704 LAND SURVEYING.

banks of navigable rivers are to be meandered by taking the
courses and distances of their sinuosities and the same are
to be entered in the meander field book. At those points
where either the township or section lines intersect the
banks of a navigable stream, posts, or, where necessary,
mounds of earth or stone are to be established at the time of
running these lines. These are called " meander corners,"
and, in meandering, the surveyor will commence at one of
these corners on the township line, coursing the banks and
measuring the distance of each course from the commencing



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