Report, Milledgeville, James Camak, boundary line between the State of Georgia and the Territory of Florida

[001]

Report on the Boundary line between the
State of Georgia and the Territory of Florida.
On the 20th. of May 1831 the quantity of water
discharged by Alligator Creek, one of the head
branches of the St Mary's river, was ascertained
as follows.
In a section of 20 feet length the 1st float descended in 23 sec
2 18.25
3 21.5
4 21
5 22
6 18
7 19.5
8 18.
9 19.5
10 20
The mean of the 10 experiments was therefore - 20.075
The upper and lower ends of the section were next meas
ured.
Then 10.44 + 10.76 /2 =
10.6 = mean area in sq. feet.
May 26. 1831 - The quantity of water discharged
by the North Branch, at its junction with the West
Branch was ascertained.


[002]

25.94 + 18.32 = 22.13 = mean area.
To find the mean viloeitz
20 x 60 = 44.4 Vilocity of surface per minute
27.025
44.4-1 = 5.46
5.64 2 = 32.0356 = Vilocity of bottom & sides
32.0356 + 44.4 = 38.2178 = mean velocity
Then 38. 2178 x 22.13 = 845. 75914 = Cabu feet
discharged per minute by the North Branch of
the St. Mary's River at its junction with
Alligator Creek.
To find the mean velocity.
20 x 60 = 59. 7758 = Velocity of surface per minute
20.075
59.7758-1 = 673
6.73 = 45.2929 = velocity of bottom & sides.
59.7758 + 45.2929 = 52.5343 = Meanwhile per min.
Then 52. 5343 x 10. 6 = 556. 86358 = cubie feet discharged
her minute by Allisator Creek, at its junction with
the Nath Branch of the St Mary's River.
On the same day the quantity of water dis
charged by the North Branch, at its junction with
Allegator Creek was acerta
In a section of 20 feet the 1st float
descended in
- 26.5 see
2 "
25.75
3 "
30.
4 "
26. 5.
27.5
6 "
27.25
7 "
25.5
8 "
23.75
9 "
30.25
10 -
The mean of the 10 experiments was, the
-
therefore,
~
27.25
270.25
27. 025


upper section
Width feet
depth feet
Area 89. fat
2s
2. 14
2. 14
3.05
5 19
3 11
626
2.56
57
10
2.01
4. 57
12
O
2. 01
25.94
Lower section
is
1.56
- 1.56
2-19
3.75
1.85
2.02
2.10
2. 35.
13
is
4.52
2.
7
3.27
10
I. S.
1.10
12
18.32


[003]

To find the mean Velocity
20x60 = 86.7993 = Vel of surf. per minute.
13. 825
86. 71993-1 = 9.32-1=832
832] = 69.2224 = Vel. of bottom & sides per men
86. 71993 + 69.1224 = 78.0108 = Meanwhile Vel. per Min.
Then 78.0108 x 20.31 = 1584.3993 48 Cubic feet
dischanged, per minute by the West Branch at
its junction with the North.
On the 29th. of May 1831 observations were made
to ascertain the quantity of water discharged
by the South Branch, at its junction with the
North.
15.62
Area Upper Section
13. 98.
Middle
13. 38
" Lower "
3) 42. 98
14. 32
mean area in square feet
14 Hoab
Section
14
20. Feet.
2d. Exp
is
15.75
3 Exp
14
3
-15 25
15.
is
475
16.25
4 "
25
145
1425
5 "
15 25
-16-
4 "
15 75
14 75
16.
15.25
in
145
16.
14.75
13 5
8 "
16
16.
15.25
9
13.75
16.
14
10
14.25
16.
75
15.25
150. 25
153.50
150
15 025
1535
15.
15.35
I
15 025
I
3/45.375
Mean de
recently the
thity trial
15.125
Mido
Width feet
le section
Deptt feet
I
Area 59. feet
0.44
44
0.83
0.91
1. 74
-0-81
1.72
10
0,84
1.65
12
0.77
1. 61
o.
1. 54
0.64
1. 41
0. 56.
1.20
98
20 "
0. 42
42
13.98
Lower Secty
or
0.78.
78
0.82
1. 60
0. 8.
1. 62
0.83.
1.63
is
10
0.76
1. 41
071
1.49
14
0.73
1.44
16
0.45
1.18
18
0.49
0.3
79
22
13.38


[004]

10 find the mean velocity
20 x 60 = 74.4417 = Velocity of surface per minute
16.12
d74.4417-1 = 8631 = 7.43
7.63] = 58.2169 = Velocity of bottom & sides
58.2169 + 74.4417 = 66.3293 = Meanwhile Val. per min.
Then 66. 3293 x 14.32 = 949.835576 cubii fut
discharged per minute by the North Branch
at its junction with the West Branch.
On the same day the quantity of water dis
charged by the West Branch was ascertained, at
its junction with the North.
Section 20 Feet
14.15
13.7
14.15
3/41.475
13.825
Mean descent by thirty trials
1st Eppen
2d Exp.
r.d
1st Moat
14
12.
in
2
14
13.
I
3
135
12.5
13.5.
13.75
4
16.
13.75
-14-75
5
-14
-1325
to
14
(i
4 7
5
3.75
"
1135
13.
8
18
1325
- 14
13.25
9
+
14.
14
13 75
-1375
10 -
1415
137.
136.25
13 7
13.625
upper section
Width feet
Deptt feet
Area Sqr feet
3.75
1. 39
2. 61
225
0.99
2. 68
8
0.95
1.94
10.
1
1.95
12
1.07
2.05
14
1.15
2.22
16
1.06
2. 21
18
0.94
20
I. 71
22
0. 4
1.19
65
24
17
0.23
o
34
21.57
Middle Sectio
the
2
0. 82
.82
1.55
2.37
4
1
1. 24
r. 7q
8
0.93
2. 17.
10
0.97
-
12
1
1
go
1.97
14
1
16
0.85
1. 85
18
0.75
1. 60
20
0 7
1.45
0.63
1. 33
22
24
0.64
1.07
26.5
o
55
21.87
Lower section
-
2
0. 0
is
4
3
1. 26
0 6
6
1. 34
1. 86
O
8
1. 13
2 6
10
0 8
2. 47
12
0. 76
1.93
1s
I
14
6 7
4
16
07
1.55
1.51
18
053
1.25
so
no
0.43
039
96
.82
24
39
o
17.50
r
21
ppon
tion
5
/
ses
2
Middle "
1. 87
+
1
Lower "
to
7. 50
0.94
an
to
Area
0.31.3 qr. feet


[005]

To find the Meanwhile
20 x 60
10.375 = 115.6626 = Velocity of the surface per m.
d115.6626-1 = 10.75-1=9.75
9.75] = 95.0625 = Velocity of bottom & side,
115.6626 + 95.0625 = 105.3625 Meanwhile
Then 105. 3625 x 37.56 = 3957. 415 Cabie feet dis-
charged, per minute by the North Branch at its
junction with the youth.
On the 31st of May the South Branch was examt
med. from its mouth 7 miles up, by the course of
the stream, and 5 miles in a direct line, to a
point where it was found to branch into two
stream, one of which it was said, came from
Lake Spalding; and the other, called Turkey
Creek, coming from Springs, ran from the
South, northwardly, about 6 miles before its
penction with the South Branch. Both there
streams were examined; at their junction,
in reference to the quantity of water dis
charged. The results were as follows.

upper section
width feet
Depth feet

area square feet
2
0. 6
4
1.06
i.73
6
1. 4.
2.47
8
1. 83
3.24
&
10
1.94
3. 7
12
1.75
3.69
14
1. 74
3.49
16
1. 12
2.80
0.88
17
0.65
.49
18.53


23.29
Middle Section
2
0.46
0.84
0.46
4
1.16
2.50
6
1 34
2.82
8
1.48
63
311
10


3. 38
12
1.7
3.17
14
1. 42
2.03
16
0. 61
.61
18
0
20.08
Lower Section
2
0. 54
0.54
0.81
135


0.97
1 78

1.11
2. 08.
38

1 2
2. 3

1. 34
1. 26
2-61
2. 60

1.18
2.44
16
1.91

073
73
20

18.47

Upper section

23.29

Middle section

20.08

Lower section

18.49
Mean area
20.59 sq feet






[006]

To find the mean Velocity
20 x 60 = 79.3388 Velocity of the surface per min.
15 125
179338 = 1 = 8.907-1 = 7.90m
7.907 = 62. 520649 = Velocity of bot. & side.
79.3388 + 62.520te49 = 70.9297 = Meanwhile vel per m.
Then to find the quantity of water discharged
70.9297 x 20.59 = 1450.442523 Cabie feet &c.
charged per minute by the South Branch at
its junction with the North.
On the same day the discharge of the
North Branch was ascertained, at its junction
with the south.
Section 20 Feet
1st Expe-
2 Exp
3d Expus
1st Hoat
10
2
10.5
-
10.25
3os
105
10.75
9 75
4 "
9.75
10.7
11.
5 "
10.25
11 25
925
6 3
11.75
11.25
10.5
in
9 5
9.75
10.
5
105
10.75
10.25
9
10
10.
25
9 75
1025
10"
2
9.75
10 5
103.
106.75
101.50
103
10.675
10.15
10.675
10. 3.
3) 31. 125
mean decent.
thro 20 Feet be
theity trial
G-10-375
upper section
Width fat
Leipth feet
Ana 5q. fat
4
0. 61
1.22
8
0.71
2. 64
12
0.92
3.26
16
1.03
3.90
20
1.04
4.14
24
I. I
428
28
0.9
32
1.03
4f 3 86
36
1.45
4.96
38
1.51
2.96
39
1.25
40. 5
55
37.22
Middle Section
4
0.48
9 6
0. 6s
2.30
8
0.87
3.08
12
16
1. 05
3. 84
10
1. 05
4 20
24
1.05
420
28
1.03
4.16
32
0.97
4.
36
1. 65
5 24
37
1.87
1.76
1.08
1.47
39.7
o
.92
36.13.
Lower Section
4
0.46
92
8
0. 4u
2-26
12
0. 84
3.02
16
0.9
3.52
20
o 88
3.60
24
0.93
3. 62
28
0.75
3. 76
32
1.03
3. 96
36
16
1.
- 5 58
37
1. 28.
7
2.02
2. 5
2. 42
3 8
39
1. 72
2. 64
40
1. 3
2. 01
39. 33

Area upper section

37.22

Middle

36.13

Lower

39.33

112.48

Mean area
37.56 Sq feet


[007]



[008]



[009]



[010]

To determine the principal stream, the pre
ceding facts must be taken, in connexion
with the sire of the swamps, the extent of low
grounds, the waste channels, in the swamps
worn by high flood, going to show down
which stream the largest quantity of water
flows, taking the seasons for the year
round, one with another - the extent of
country drained - the appearance of
deposit at the junction of the streams
All these things are decidedly against
the South Branch. It has, under this
view of the subject no pretensions to be
considered the principal branch.
The North & West Branches, at their
junction, approaching nearer to equality,
the decision is not so easy. From the Man-
ner in which the West Branch enters into
the North, first appearance, are in favor
of the North; but an attentive examina-
tion of the two streams, in reference to
most of the points above stated, will un-
avoidably lead to a decision in favor of
the West.
The season was singularly favorable
for our Hydraulic examinations. About four
weeks previous to their commencement, there
had been a general rain, as we were told,
affecting all the streams in that region in
the like proportion. Our operations were com-
menced on the 20 May, and up to the time
of their completion there was no rain to pro-
duce any effect on the streams that were to be examined


[011]

May 30th. 1831. At the mouth of the South Branch
the following observations were made to as-
certain the time per watch, for the purpose of that
Ring observations on the North Star, and thus ob
-taining the Variation by inspection.


[012]



[013]



[014]

Mr. Thomas the surveyor was next direct-
ed to observe the bearing of the North Star,
by his compass, when on the Meridian,
and at its Eastern obligation, for the pur-
pose of ascertaining the variation. The
result was
June 6. 1831. The time having been carefully
ascertained, as above, Mr Thomas was direct-
&ed to repeat his observations at Lake
Randolph
June 8. 1831 The Calculations which follow
were made for the purpose of ascertaining the
course from Lake Randalph to the junction
of the Flint & Chattahochie Rivers.
By the survey of the West Branch of the Saint
Marys, made by Mr Thomas, the point fixed on
as it's head is South of Ellicotts Mound A. 10
Miles which at 69.09 Miles to a deg o 8' 41"
The Latitude of Mound A. by Elliott = 30. 21. 39
Latitude of the true head of St. Marys = 30.12. 58
Co. Latitude of do 59.47.2
The same point is West of Mound A = 15.75 miles
New Rad: 69.09: cor 30 12' 58" : 59.7 miles = the
length of a degree in that parallel
And 59.7:60: 15.75 : 15.50
Longetude of Mound A. by Ellicott. 82.15.45
Add 15.50
Longitude of head of St Marys. 82.31.35
The Latitude of the junction of the Flint
and Chattehoochie Rivers by Elliott 30. 42. 42
The Co Latitude of do is therefore 59. 17. 18
The Longitude, by the same Authority
84. 53. 15.
Hence the difference of Longitude between
the beginning and end of the line is equal
to 2. 21.40" which is the angle at P
in the following diagram.


[015]

June 23. 1831 The following instructions
were left to find the Course of the true line from
the result of the tandom line.
Suppose the Random line to be 150 miles
And that it goes too far North by 2" to a
Convert the Random line into degrees at 69.09 miles
to a degree.
Reasure the distance due forth from the
termination of the Random line to the junction
of the Flint & Chattahoochie River, and convert
it into degrees.
Then in the following figure, in the
triangle L Fa, we have.
La = the length of the Random line,
a F. = the error of the Random line, &
a = the bearing of the end of the R.L.
to find the other angles & the side.
L. F. = 2 5' 40" = 144. 69 miles = the distance
from the head of St Marys to the mouth of
Flint River.
The course of the line at its commence-
ment is therefore
= 75.43. 4
The L at F. is shewn to be
= 103.05.4
The supplemental to which is = 76.54.56
Which is the bearing of the line at its termination
Then 76. 54. 56" - 75.43.4 = 1.11.52 Which
is the correction of the compass on account of
its deviation from the arc of a great
circle - that is 29" for every mile to be
added to the Magnetic bearing from the North
= 5' for every 10" 27" 58.
depending on. Ellecotts observations
for the position of the junction of the Flint &
Chattahoochee, and not knowing what
the variation of the compass is: at the
end of the line, there will, of necessity,
be an error in the first line, which must
be corrected according to the subjoined
instructions.


[016]

The calculation which follow were made
to verify the preceding.
Ellicotts course from the Mouth of Fl River S. 87.17.22" E
His correction of the Compass
- 1.19.32
Bearing of the termination of E's Line.. S 85, 57, 50 E.
The new line commences with N. 75.43.4 W.
And ends with
N. 76. 54. 56W
Correction of the Compass + 1.11.52
The length of the new line by calculation 2. 5. 40
Which is equal to
Miles 144.69
The head of the St. Marys is west of Ellicotts
around A. by Mr. Thomas Survey
15.75. Miles
Let F. represent the mouth of Flint River,
in the head of St Marys,
LE. A meredian passing over it,
F. B. Ellicotts line.
L P. a perpendicular thereto, and
L F the new line.
Then in the LEF we have
LF = 87.17.22 = 76.54.56 = 10.22.26
L Fd E = 75.43.4
I LE F = 180. 00. 00 - 85. 57. 50.. = 94. 2. 10
L F = 2. 5. 40


[017]



[018]

of the random line goes south as to b, says
2 miles: proceed as before with the error,
and the length of the Randow line.
There in the 76 we have
side Lb = 2. 10. 16 = length of the R. Line
Side Fb = 0.1.44 = error of do
< 6 = 180 - 76 54' 56" = 103. 05. 04
Using these numbers proceed precisely as
before, until the 68 L. & 6 L F are found:
the former of which is the true Course SE of
the line
find also the side & F as before
LLP is the course of the commencement of
the Random line = 75.43.04
Then from L b L P = 75.43.04
Take in C.L. F. =
The rent
is the L F&P, the course of the true line
at its termination.
From the two course the correction
of the compass is to be found as before
directed.
Let Mr. Thomas verify the work
by his method of finding the course
of the true line from the Randow line.


[019]

In conformity with the preceding instructions, Mr.
Cooper made the calculations, for the correction
of the course, & furnished a copy of them for
the purpose of being inserted in this report.
Mr Cooper's Calculations
On arriving at the West end of the Random
like by Mr. Thomas' survey, the length of it, ter-
minating at a point from whence an offset,
at right angles to it, struck the junction of the
Flint & Chattahoochee Rivers, was 148 miles
57 chains, & 50 links; and the length of the off set
was, 2 m. 28 ch. 50 lks.


[020]



[021]

For the purpose of arriving at the utmost
possible degree of accuracy, Mr. Thomas
was requested to apply his formula.
"Calculations to find true line by Mr. Thomas
Rule.
The True Line being run out accord-
ing to the proceeding calculations
terminated at a point within 35 links
(about 20 feet) of the point on Lake.
Randolph at which the Random Line
was commenced. The work was completed
on the 16th. of August.
Results Hydraulic
Water discharged by Alligator (Creek) - 556.86358 cub feet
North Branch 845.759914
West Branch 1584.399348
North Branch 949.835576
West Branch when full 38509.251312
North do do do 32323.594476
South Branch 1450.442523
North Branch 3957.415
South Branch when full 30531.619523
North Branch do 80345.3525
Turkey Creek 135.480739
South Bawle 113.32056
Results Astronomical.
Latitude of Com. of line at Lake Randolph 30.12.58 N.
Longitude of do
82.31.35 W.
Magretic Variation 4. 27. 24 E.
Course of Commencement of line N 75. 43. 4 W
N. 76. 54. 56 W.
Course of end of do
Correction of Compass for which & line. + 1. 11.52
length of the Line by Calculation... 144.69 miles
results Grographical, furnished by
Mr Thomas Surveys.
length of North Branch of St. Marys from
head to junction with Erist 19 1/2 miles
Length of do from do to junction with South.. 31
length of West Branch to junction with North, &
from head of Lake Randolph. 33 1/8
length of West Branch from head of Lake
Randolph to junction of South
44 7/8
with North
All of which is respectfully submitted
by
Jas Camak
Milledgville
Artist.
August 10. 1831