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Thomas Jefferson’s Field Notes and Calculations of Altitude of the Peaks of Otter, [10–ca. 17 November 1815]

II. Field Notes and Calculations of Altitude of the Peaks of Otter

[10–ca. 17 Nov. 1815]

Field Notes. 1st operation.

1815. Nov. 10. went on the top of the sharp or South peak of Otter, & from thence made these observations.

°
   the meridian altitude of the sun by sextant  71–  8
− error of instrument  1– 30
 71–  6– 30
 35 33 151
  
   magnetic rhumb of North or flat peak N. 35.° 50′ E.
  (the varian2 of needle had been before observed to be 2° East of N. i.e. 2° to the right of the true rhumb in all points)3

∠ of elevation of N. peak from apex of S. peak 52.′

  

from the apex of the sharp peak

   the highest point of the main ridge of Willis’s mountains makes an ∠ with the course of4 the summit of N.5 peak of 43°–37′
magnetic rhumb of same point in Willis’s mount N. 80. E making the error of the needle 33′
∠ of depression of the same point in Willis’s ridge from the apex of the S. peak is 46′
 
 

1815. Nov. 11. 2d opern

this Fig. is entirely in the plane a.b.h.

at c. observe it’s position

   the vertical ∠ acg. + 7°–15′
  magn. rhumb c.g. N. 46. W
  height of instr. above water. ch 8.f
  verticals icd + 21′7
ch  l
measure c.d. to bank of Otter  25–52
to publick road  17–
at d. observe 42–52  = 2806.32 f

the vertical ∠ adf 8°–12′8

 

both vertical & horizontal angles refer to the horizon.9

the rhumb is magnetical. varian 2.° E. of North.

measures in chains of 4. po.10 & 100. links, except where otherwise mentioned11

 

Notes for corrections

   Fig. 2. in the vertical ∠ i.c.d. the elevn of 21.′ pointed 18 I. above the true parallel to the inclined plane. c.d.
note that in all the operns the plane of the theodolite was 3 f 8 I. above the ground.
Fig. 3. in the vertical ∠ t.n.m. the elevn of 27′ pointed 11.f. above the true parallel of the inclined plane n.m.
Fig. 2. where the measured line c.d. crossed the main Otter river the plane of the theodolite was 3 f–8 I + 4 f–4 I = 8. f above the surface of the water.
Fig. 3. at the close of the measured line n.m. of 399.33 po. the main Otter crossed it at 8. po. from m. and twice more in the 12. po. preceding the last crossing.12
 

1815. Nov. 11. 3d opern

at n. observe it’s position

the vertical ∠ l.n.p. 8°–20′
horizl t.n.p. 90°–1313
magn. rhumb. n.p. N. 56. W
vertl14 tnm 27′
rhumb nmS 32° 25′ W
   height of instrum. above the water NS. 3 f–8 I + 4 f–4 I = 8 f
the altitude of summit of N. peak L 8°–27′
     it horizl with n.p. 27°–11′15
with n.m 117°–24′16
   it’s magn. rhumb. N 29°–52½′ W

measure n.m. 399.33 po. = 6589.f

at m. observe

   the vertical ∠ lmo 8°–2′17
horizl ∠ omu 70°–41
rhumb of mo N. 37–45 W
alt. of summit of N18 peak L 7°–13′19
it’s horizl ∠ with mo 21°–53′
 mu 48°–48′20
it’s magnetic rhumb. N. 15°–45′ W21
 

Nov. 12. a repetition of the observns from the station m.

 
the ∠ between mn. & the N. peak. 48°–48′  u.m.L.
rhumb of the N. peak N. 15°–45′ W.  m.L.
verticl ∠ of altitude of N. peak 7°–13′
horizl ∠ between that & S. peak 21°–53′ o.m.L.
rhumb of S. peak. N. 37°–45′ W.  m.o.
verticl ∠ of altitude of S. peak 8°–2′

Fig.22 2.

in the vertical23 cdi. to reduce cd. to ci
R : cd :: d : ci
R. : 2806.32 :: S. 89°–39′ : ci  =  2806.261
Log. 2806.32 = 3.4481372
L.S. 89°–39′ 9.9999910
  Rad. 3.4481291.  = 2806.261
reqd d.i.
R  : cd   ::  c :  di
Rad : 2806.32 :: S. 21′ : di  = 17.1427
Log 2806.32 = 3.4481372
L.S. 21′  = 7.7859427
  Rad. 1.2340799  = 17.1427
but this is to be corrected by subtracting  1.5 see page 3.
gives the true length of di. = 15.6427

now to reduce the ∠ icd. to the corrected length of d.i.

in the △ cdi. given  ci = 2806.261
di = 15.6427

 reqd ∠ icd

ci : di :: Rad : T. dci
2806.261 : 15.6427 :: Rad : T. dci = 19′–9″
Log. 15.6427 =  1.1943118
+ Rad 10.
11.1943118
Log 2806.261  3.4481279
 7.7461839  = 19′–9″

then in the △ cdi as reduced & corrected

   the ∠ icd = 19′–9″
ci = 2806.261
di =   15.642724

 

in the vertical25 △ dik, to find i.k. in order to reduce ci. to ck.

 given di. and all the angles

S. k : di :: S d : ik
S. 8°–12′ : 15.6427 :: S. 81°–48′ : ik = 108.5521
 Log. 15.6427  1.1943118
 L.S. 81°–48′  9.9955370
11.1898488
− L.S. 8°–12′  9.1542076
 2.0356412  = 108.552

then ck = ci − ik = 2806.261 − 108.552 = 2697.709

 
in the vertical26  ack to find ak.
given ck = 2697.709
∠ c = 7°–15′
∠ k = 180° − 8°–12′ = 171°–48′
∠ a = 180° − c27 − k =  57′

 reqd ak.

S. a : ck :: S. c. : ak
S. 57′ : 2697.709 :: S. 7°–15′ : ak = 20533.8
 Log. 2697.709  3.4309952
 L.S. 7°–15′  9.1010558
12.5320510
− L.S. 57′  8.2195811
 4.3124699  = 20533.8
 
in the right ∠d vertical28 △ akg. given ak = 20533.8
∠ k =  –12′
∠ a = 81–48
reqd ag. and gk.
Rad : ak :: S. k : ag.
Rad : 20533.8 :: S. 8°–12′ : ag. = 2928.711
Log. 20533.8 4.3124699  +    4.333
L.S. 8°–12′ 9.1542076 2933.044 = ab
− Rad.  3.466677529 = 2928.711

Rad : ak :: S. a : gk.
Rad : 20533.8 :: S. 81°–48′ : gk.  =  20323.9
Log. 20533.8 4.3124699
L.S. 81°–48′ 9.9955370
− Rad. 4.308006930  = 20323.9
 +  2697.709  = ck
23021.609  = cg31
 

Fig. 3.

in the r. ∠d vertical32 △ mnt to reduce nm. to nt

 and to find mt.

  given nm = 6589. feet.
 ∠ n = 27′
 ∠ m = 89°–33′
reqd nt. and mt.
Rad. : nm ::  S. m  :  nt
Rad : 6589 :: S. 89°–33′  : nt.  =  6588.8
Log. 6589 3.8188195
L.S. 89°–33′ 9.9999866
− Rad. 3.818806133  = 6588.8

for mt. say Rad. : nm :: S. n. : mt
Rad  : 6589 :: S. 27′ : mt = 51.7493
   Log. 6589. 3.8188195
L.S.  27′ 7.8950854
  Rad. 1.713904934 =  51.7493
to be corrected by subtracting 11. see page 3.
true length of mt = 40.7493

next reduce the ∠ n. to the corrected length of mt.

in the r. ∠d △ mnt. given nt = 6588.8
mt = 40.7493
reqd ∠ n.
nt : mt :: Rad. : T. n
6588.8 : 40.7493 :: Rad. : T. n = 21′–11″
Log. 40.7493 + Rad. = 11.6101202
  Log. 6588.8  3.8188061
 7.7913141. = T. 21′–11″

in the horizontal △ npt. given nt. = 6588.8
 °   ′
∠ tnp = 90–13
∠ ptn = 70–41
∠ npt = 19– 6
reqd pt. and pn.  
for pt. say S. p. : nt :: S. n : pt
S. 19°–6′ : 6588.8 :: S. 90°–13′ : pt. = 20135.61
Log. 6588.8  3.8188061
L.S. 90°–13′ = 89°–47′  9.9999969
13.8188030
  L.S. 19°–6′  9.5148371
 4.3039659  = 20135.61 = pt35
 
for pn. say S. p : nt :: S. t. : pn.
S. 19°–6′ : 6588.8 :: S. 70°–41′ : pn. = 19002.2
Log. 6588.8  3.8188061
L.S. 70°–41′  9.9748361
13.7936422
  L.S. 19°–6′  9.5148371
 4.2788051 = 19002.2 = pn

in the r. ∠d verticl △ lmo given mo. = 20135.61
∠ m. = 8°–2′
∠ l  = 81–58
reqd lo.
S. l. : mo :: S. m. : lo.
S. 81°–58′ :  20135.61 :: S. 8°–2′ : lo.  =  2841.83
oq.  =   48.7493
Log. 20135.61  4.3039659 lq  = 2890.5793
L.S. 8°–2′  9.1453493 op  =  mt =  40.7493
13.4493152 pq  =  tr =   8.
  L.S. 81°–58′  9.9957172  oq. =  48.7493
 3.4535980 = 2841.8336

let LOPQ. be points in the axis of the North peak corresponding horizontally with l.o.p.q. in yt of the S. peak; and S. the summit of the North peak.

we have still to find  the horizontl distance of the two Axes
the height of S. by the observns at  l.
at  m.
at  n.

reduce the inclined37 trapezium lmnL. fig. 4. to it’s corresponding horisontal38 one p.t.n.P. in the horizontal plane of n

 
In the horisontal39Ptn.
given nt = 6588.8
°  °  
Pnt = 117. 24   or 62–36
Ptn =  48–48
∠ tPn =  13–48
reqd Pn.
Pt.
to find Pt. S. P. : nt :: S. Pnt : Pt
S. 13°–48′ : 6588.8 :: S. 62°–36′ : Pt. = 24523.3
Log. 6588.8  3.8188061
L.S. 62°–36′ 9.9483227
13.7671288
  L.S. 13°–48′ 9.3775493
4.3895795 = 24523.3

to find Pn. S. P : nt :: S. Ptn : Pn.
S. 13°–48′ : 6588.8 :: S. 48°–48′ : Pn = 20783.21
Log. 6588.8  3.8188061
L.S. 48°–48′ 9.8764574
13.6952635
  L.S. 13°–48′ 9.3775493
4.3177142 = 20783.21

In the horizl40Ptp. given Pt = 24523.3
pt = 20135.61
Ptp = 21°–53′
reqd pP.41
 
Pt + pt : Pt − pt :: T. tpP. + pPt2 :  T. tpP − pPt2
°  ′    ° ′   ″
44658.91 : 4387.69 :: T. 79–3–30  : T.  26–55–26
Log. 4387.69  3.6422278  79– 3–30
L.T. 79°–3′–30″ 10.7134430 105–58–56 = tpP.
14.3556708  52– 8– 4 = tPp.
  Log. 44658.91 4.6499081
9.7057627 = 26°–55′–26″ = T d/2

for pP. S. tPp : pt :: S. Ptp :  pP
S. 52°–8′–4″ : 20135.61 :: S. 21°–53′ :  pP. = 9506.451
 
Log. 20135.61  4.3039648
L.S. 21°–53′  9.5713802
13.8753450
  L.S. 52°–8′–4″  9.8973264
 3.9780186  = 9506.451

In the horizl42Pnp. given Pn = 20783.21
pn = 19002.2
Pnp = 27°–11′  reqd pP.
Pn + pn :  Pn − pn  ::  T. npP + nPp2 :  T. n.pP − nPp2
° ′   ″ ° ′   ″
39785.41 : 1781. :: T. 76–24–30 : T.  10–28–2343
Log. 1781.  3.2506639 76–24–30
L.T. 76°–24′–30″ 10.6165949 86–52–53 = npP.
13.8672588 65–56– 7 = nPp.
  Log. 39785.41 4.5997239
9.2675349 = T. d/2 = 10°–28′–23″

for pP. S. nPp : pn :: S. Pnp :  pP.
S. 65°–56′–7″ : 19002.2 :: S. 27°–11′ :  pP. 9507.27
Log. 19002.2  4.2788039
L.S. 27°–11′ 9.6597633
13.9385672
  L.S. 65°–56′–7″ 9.9605114
3.9780558  =   9507.27
 9506.451
19013.721
by mean of 2. operns pP. =   9506.86 f. = 1.8 mile
 9506.45
19013.31 
mean length of p.P.   9506.6544
 

By way of proof of these operations, we may at this stage collate the magnetic rhumb of m.n. or t.n.45 observed Nov. 11. and transferred by calculation to p.P. fig. 5. with the rhumb of l.S. or p.P. observed from l. Nov. 10.

from p. in the horizontal trapezium ptnP. Fig. 5. draw pv. parallel with tn. this parallelism makes the ∠ tpv the supplement to ptn.

°   ′ 
we found the ptn = 70–41   
then is tpv = 109–19   
but tpP = 105–58–56
and consequently P.pv = 3–20– 4
by observn Nov. 11. tn = pv is  N. 32–25– 0  E
add the Ppv 3–20– 4
gives by calculn pP N. 35–45– 4
by observn of Nov. 10 pP. N. 35–50– 0
  difference 0– 4–56

altho’ the needle is not to be relied on for exact precision, the magnetic rhumbs of the lines were taken as general checks on the other observations, and particularly to indicate whether the corresponding angles observed were to the right or left. the rhumbs now collated are so far a confirmation of the correctness of the intermediate work.


for the height S. above l. that is, the height of the North peak above the South, by the observns at l.

in the right ∠d vertical △ lLS. Fig. 1.
given ∠ SlL. = 52′
lL = pP. = 9506.86
reqd LS
  Rad : lL :: T. SlL : LS
Rad : 9506.86 :: T. 52′ : LS = 143.482
Log. 9506.86 3.9770371
L.T. 52′ 8.1797626
  Rad. 2.1567997 46 = 143.482

for lS Si. of lSL : lL :: Rad : lS
S. 89–8′ : 9506.65 :: Rad : lS  = 9507.73
Log. 9506.65 + Rad.  13.9780275
L.S. 89°–8′  9.9999503
3.9780772  = 9507.73 = lS.47

for the height of S. the summit of the N. peak by the observations

  from m.

in the horizontal △ Omu. Fig. 4.

  given mu = 6588.8
 
  ° 
∠ umO =  48–48
muO = 117–24 or 62°–36′
mOu =  13–48
reqd mO
uO.
   S. O : mu :: S. u : mO.
S. 13°–48′ : 6588.8 :: S. 62°–36′ : mO.  = 24523.3
Log. 6588.8  3.8188061
L.S. 62°–36′ 9.9483227
13.7671288
  L.S. 13°–48′ 9.3775493
4.3895795  = 24523.3

for uO, S. O : mu :: S. m : uO
S. 13°–48′ : 6588.8 :: S. 48°–48′ : uO  = 20783.21
Log. 6588.8  3.8188061
L.S. 48°–48′ 9.8764574
13.6952635
  L.S. 13°–48′ 9.3775493
4.3177142  = 20783.2148
 
In the right ∠d vertical △ SmO
given mO. = 24523.3
° 
∠ m =  7–13
S = 82–47
reqd SO
S. S : mO :: S. m : SO
S. 82°–47′ :  24523.3 :: S. 7°–13′ : SO.  =  3105.261
Log. 24523.3  4.3895795  + oq  = 48.749
L.S. 7°–13′ 9.0990651 SQ  = 3154.01 
13.4886446
  L.S. 82°–47′ 9.9965459
3.4920987  = 3105.261

In the right ∠d vertical △ SnP.
  given nP = uO = 20783.21
° 
∠ n =  8–27
S = 81–33
reqd SP
S. S : nP :: S n. : SP
S. 81°–33′ : 20783.21 :: S. 8°–27′ : SP.  =  3087.54
Log. 20783.21  4.3177142  + pq  = 8.  
L.S. 8°–27′ 9.1671586 SQ  = 3095.54
13.4848728
  L.S. 81–33 9.9952597
3.4896131  = 3087.5449
 

Proceeding to the result of the observations of altitude, they do not come out so fortunately correct as the horizontal angles did. for, taking a mean of the two altitudes of the S. peak, and of the two of the North peak, that of 143 f resulting from the observation at l. will not fill up the whole space of their difference. to bring them together we must distribute the whole error equally among the several vertical angles which enter into the operations.

3. of these are in Fig. 2. viz. acg. dci. & adf.

2. are in Fig. 3. mnt & lmo.

1. in Fig. 1. SlL.

2. in the altitudes of the N. peak, the one taken

8.   from m. the other from n.

the following equation gives the portion of error in altitude to be ascribed to each of these vertical angles.

2933 + 3x + 2890 + 2x2 + 143 + x = 3154 − 2x + 3095 − x2.
3054.5 + 3.5x = 3124.5 − 1.5x
5x = 70
x = 14

there must be a correction then of 14.f in altitude for every vertical angle entering into each result, as follows.

the height of S. peak
   from Fig. 2. is 2933. add 14 × 3. ye error for 3 ∠s gives 2975
from station m. 2890 + 14 × 2. for 2. ∠s 2918
5893
the mean may be considd the height of S. peak  2946.5
 
the height of N. peak
from station m. 3154. subtract 14 × 2. error for 2. ∠s 3126.
from station n. 3095. − 14 error of 1. ∠ 3081
6207
the mean height of the N. peak  3103.5
to the height of S. peak 2946.5 add 143 + 14 = 157 for 1. ∠  3103.5
from the height of N. peak 3103.5 subtract 157 2946.5

this error of 14.f. in altitude on every vertical observn amounts to about 2¼′ which with an instrument whose Nonius indicates to 3.′ only, is perhaps as near as we may generally count on coming; at least as near as eyes of 72. may come. add to ys too the diameter of the crosshair which, magnified as it is produces sensible uncertainty.50

 

To recapitulate

the mean height of the sharp or S. peak  f   
   above the surface of Otter river is  2946.5
of the North peak 3103.5
their difference of height 157. 

the distance of the 2 summits nearly 1.8. mile exactly 9507.73

the magnetic bearing of the summit of the North from that of the S. peak is N. 35–50. E from which 2.° must be subtracted for the present variation of the needle.

the base lines measured, the one of 2806.33 feet or .55 of a mile, the other of 6589 f. or 1¼ mile, were on the plains of Otter river51 belonging to Christopher Clarke esq. & to Donald’s heirs, near the mill of the latter; the former line in exact direction to the axis of the S. peak, the latter nearly parallel with the bearing of the one peak from the other.

the distance of the base lines measured, from the points in the bases of the mountains vertically under their summits was, the nearest 19002.2 f. the farthest 24523.3 f. or about 4. miles generally.

supposing the radius of the earth 3965. miles and the height of the52N. Peak 3103.5 feet = .5876893 mile then it may be seen over a level country to the distance of 68.2083 miles, which will include the whole or a part of the counties of Amherst, Nelson, Albem.Fluvanna, Buckingh. CumbldFranklin, BedfdCampbllPr. EdwdCharlottePatrick, Henry, Pittsylva, Halifax

  and over the tops of the intervening mountains in Rockbridge & Botetourt, the following is the proof.

in a right ∠d △ given the hypoth. b.c. = 3965.588 miles a leg. ac = 3965. required the other leg. ab.

   bc : Rad :: ac : S. b.
3965.588 : Rad. :: 3965 : S. b  = 89°–0′–52″
Rad. + Log. 3965  13.5982432
  Log. 3965.588 3.5983075 °   ′   ″ 
9.9999357  = 89– 0–52  = ∠ b
and 59– 8  = ∠ c53
Rad : bc :: S c : ab
Rad : 3965.588 :: S. 59′–8″ : ab 68.2083
Log. 3965.588  3.5983075
L.S. 59′–8″ 8.2355299
  Rad. 1.8338374 54 = 68.2083
vertical angles corresponding bases corresponding perpendiculars
° ′ 
SlL. 0–52 lL  9506.86 SL.  143.482
icd. 21 ci  2806.261 di   17.1427
akg 8–12 gk. 20323.9 ag. 2928.711
acg. 7–15 cg 23021.609 ag. 2928.711
tnm. 27 nt.  6588.8 mt.   51.7493
lmo 8– 2 mo. 20135.61 lo. 2841.83
S.mO 7–13 tP. 24523.3 SO. 3105.261
SnP. 8–27 nP. 20783.21 SP. 3087.54

to estimate loosely the average of error in the vertical observations the average of the perpendiculars is 1888. of which 14 f. is the 1135 part the average of the vertl angles is 5°–6′–7½″ = 18360.″ 135th part is 136″ = 2′–16″55

 

Map of the ground. scale 1000. f = ¼ inch

The56 form of the Peaks as seen from mr Clark’s

MS (MHi); filed with TJ’s Weather Memorandum Book, 1802–16; written entirely in TJ’s hand on rectos and versos of several long sheets, folded and stitched together; partially dated, with terminal date conjectured from TJ to Charles Clay, 18 Nov. 1815.

A nonius is “a device consisting of a series of concentric arcs engraved on a quadrant, used for the accurate measurement of angles, altitudes, and heights” (OED description begins James A. H. Murray, J. A. Simpson, E. S. C. Weiner, and others, eds., The Oxford English Dictionary, 2d ed., 1989, 20 vols. description ends ).

In addition to the sketched map of the ground that he included here, TJ created a similar sketch on a separate sheet that depicts the same points of reference, but shows the Peaks of Otter at two different sizes, with the smaller sketch superimposed on the larger (MS in MHi; filed with TJ’s Weather Memorandum Book, 1802–16; written entirely in TJ’s hand on one side of a single sheet; undated; endorsed by TJ on verso: “Mountains. Peaks of Otter. their heights measured. Nov. 10. 11. 12. 1815.”).

TJ summarized these calculations in a manuscript revision to the query on mountains in his Notes on the State of Virginia, stating that “In Nov. 1815. with a Ramsden’s theodolite of 3½ I. radius with Nonius divisions to 3′ and a base of 1¼ mile on the low grounds of Otter river, distant 4. miles from the summits of the two peaks of Otter I measured geometrically their heights above the <bed> water of the river at it’s base and found

f
that of the sharp or S. peak  2946¼
that of the flat or N. peak 3103½
as we may with confidence say that the base of the Peaks is at least as high above the tidewater at Richmd as that of the Blue ridge at Rockfish gap (being 40. miles farther Westward) and their highest summit of course 3203½ f above that tidewater, it <shews> follows that the summit of the highest peak is 343½ f. higher than <the top summit> that of the Alleganey as measured by Genl Williams” (Jefferson, Notes on the State of Virginia [London, 1787; Sowerby, description begins E. Millicent Sowerby, comp., Catalogue of the Library of Thomas Jefferson, 1952–59, 5 vols. description ends no. 4167; Poor, Jefferson’s Library description begins Nathaniel P. Poor, Catalogue. President Jefferson’s Library, 1829 description ends , 7 (no. 365); TJ’s copy in ViU, with revisions, including this one, tipped in between pp. 28 and 29]).

1Row of numbers interlined.

2Abbreviation for “variation,” here and below.

3Omitted closing parenthesis editorially supplied.

4Preceding three words interlined.

5Reworked from “S.”

6Page ends here.

7Reworked from “8°–12′.”

8Page ends here.

9TJ here canceled

“in vertical ∠s + or x >. means elevation
o means the horizon
− means depression
in horizontl + or [. . .] means inflection to ye right
− or [. . .] inflection to the left
and always refers to the last course unless otherwise mentioned.”

10Abbreviation for “poles,” here and below.

11TJ here canceled a drawing of a triangle and its explanation.

12Page ends here.

13Number added in place of “89–36,” with “117°–24′” canceled afterwards.

14Reworked from “horizl.”

15Number added in place of “26°–34′.”

16Number added in place of “118°.”

17Number added in place of “7°–57′.”

18Reworked from “S.”

19Number added in place of “7°–9′.”

20Number added in place of “70–42” with a question mark canceled.

21Figure added in place of “N 16. W.” Page ends here.

22New page begins with this word.

23Preceding three words interlined.

24Page ends after horizontal rule.

25Word interlined.

26Word interlined.

27Reworked from “i.”

28Word interlined.

29Reworked from “13.4666775.”

30Reworked from “14.3080069.”

31Page ends here.

32Word interlined.

33Reworked from “13.8188061.”

34Reworked from “11.7139049.”

35Page ends here.

36TJ here canceled a set of calculations by enclosing them in a box that struck through the first and last lines. The original reading was

“in the r. ∠d vertl △ lnp. given p.n = 19002.2
∠ n = 8°–20′
∠ l = 81–40
reqd lp 
 S. l. : pn. :: S. n. : lp. 
S. 81°–40′ : 19002.2 :: S. 8°–20′ : lp. = 2783.42
Log. 19002.2  4.2788051 pq =  8.
L.S. 8°–20′  9.1611639 lq = 2791.42
− L.S. 81°–40′ 13.4399690
 9.9953902
 3.4445788  = 2783.42.”
Beneath these calculations and the horizontal rule depicted here, the page ends with five heavily canceled and partly illegible lines.

37Word interlined.

38Word interlined.

39Word interlined.

40Word interlined.

41Page ends here.

42Word interlined.

43Reworked from “10–28–33.”

44Page ends here.

45Preceding two words interlined.

46Reworked from “12.1567997.”

47Page ends here.

48Page ends here.

49Page ends here.

50Page ends here.

51Word interlined.

52Preceding three words interlined.

53Page ends here.

54Reworked from “11.8338374.”

55Page ends here.

56New page begins with this word. Drawing and heading are oriented perpendicularly to preceding text.

Index Entries

  • Allegheny Mountains; altitude of search
  • altitude; calculations for Peaks of Otter search
  • Clark, Christopher Henderson; and height of Peaks of Otter search
  • Donald, Andrew; mill of search
  • Jefferson, Thomas; Writings; Field Notes and Calculations of Altitude of the Peaks of Otter search
  • Jefferson, Thomas; Writings; Notes on the State of Virginia search
  • mathematics; trigonometry search
  • Mount Prospect (Christopher Henderson Clark’s Bedford Co. estate); TJ visits search
  • nonius; and surveying search
  • Notes on the State of Virginia (Thomas Jefferson); TJ’s revisions to search
  • Peaks of Otter, Va.; altitude of search
  • Ramsden, Jesse; theodolite of search
  • scientific instruments; sextants search
  • scientific instruments; theodolites search
  • sextant; TJ uses search
  • surveying; nonius for search
  • theodolite search
  • Williams, Jonathan; and altitude calculations search
  • Willis’s Mountain; and altitude of Peaks of Otter search