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[[Pages 190 - 206 appear to be Hall's log showing calculations, positions, weather and events occuring on the voyage back to the United States.  Many are nearly impossible to read let alone transcribe, especially this page 191 nearly undecipherable.]]
My obs Monday August 18th 1861 on board G.H. & the working up:
[[note in blue ink right corner]]
encircled 1
page encircled 2
se
preceeding p
FH [[/note in blue ink]]
"Lunar Obs.  = {h1-m54-s33 {Distance circumpunct & D N.L. 77°-19'-30"
"George H" Chro{           {Alt. circumpunct . . . . L.L. 45-11-00
               {           {Alt. D . . . . . . . . . M L. 39-58-00
Preparation:-
astronomical Time Aug 17th    h22-m10-s24  M.T. Ship
W.Long. by [[?afect]] in Time   3- 37- 54
Reduced Time Aug 18th           1- 48- 18 = G.T.
[[from this point on down the page there are four columns of figures: left margin; center left; center right; and right margin. Starting with the left margin colomn first]]
[[left margin column]]
[[?For]] time =(M.T. Ship)
              [[?L]]45°-11'-00 = [[circumpunct]]'s ^[[Obs]]Alt.
[[circumpunct]]S.D.     15- 51
Px . . . . . . . . . . . . . 7
                    45- 26- 58
Ref  . . . . . . . . . . . -56
                    45- 26- 02
Dip  . . . . . . . . .   3- 25
                    45- 22- 37]
                       45-22.6]
                       57.26      ,20522
                       76-54.3    ,01144
                    2)173-42.9
                       86-21.4   8,73905
                       45-28.8
                       41-28.8   9,82109
                              2)18,77680
h10-6-45                         9,38840
    3-39 Eq   [Aug 18th ship]
 10-10-24 AM [[?Mean ?time]]
 22-10-24 of 17 Aug A. [[?time]]
Line across left margin column]
[[/left margin column]]
[[Header over left center column, right center column and right margin column]]
[[underlined]]Preparation:-[[/underlined]]
[[strikethrough]]Aug. 17th[[/strikethrough]]
Astronomical Time Aug 17  - h22-m10-s24  M.T. Ship
W. Long. by afect in Time =   3- 37- 54
  Reduced time Aug 18th       1- 48- 18 = G.T.
[[/Header]]
[[left center column]]
[[?DSD]] Aug 18 Noon 14'-48.3"
         Midnight    14- 48.1
Difference                 .2
Table XI                    0
D's S.D. =           14- 48.3
[[?Avg. TXV             +10
D's Con S.D.         14'-58"
[[/left center column]]
[[right center column]]
D's [?Hour]] Px Aug 18 Noon 54'-14.3"
                   Midnight 54 -13.6
                 Difference       .7
                 Table XI          0
D's [[?Hon.]] Px =          54'-14.3"
[[/right center column]]
[[right margin column]]
[[circumpunct]]'s Obs Alt. ^L.L. 45°-11"
                  Add- - - - - - -  +12
[[circumpunct]]'s [[?A/c ?bft]]  45 -23
                   D's Ap. Alt = 39°-38'
[[/right margin column]]
[[text below the three columns above]]
Observed Dist. [[circumpunct]] & D N.L ......77°-19'-30"
Add D's S Diameter...........................   +14- 58
 " [[circumpunct]]'s S Diameter.................+15- 51
Ap. Dist [[circumpunct]] & D - - - - - - - - 77°-50'-19"
[[/right margin column]]
[[below here are two columns, left and right with some inter-relationships indicated by connecting lines]]
[[left column]]
D Hov. Px.                    0°-54'-14"....Prop Log 0.5210
[[circumpunct]]Ap. Alt       45°-23- 00 [[?Corcant]] 10.7476
D & [[circumpunct]]Ap. Dist. 77°-50'-14"[[Sine]]..... 9.9901
1st [[?Corr]]                 4- 20- 30 Table XLVII?  0.6587
2d  [[?Cor.]]                 5- 07- 28
3d  [[Cor.]]                      1- 32
                             87- 19- 49
[[?soft]] -                  10- 00- 00
                             77- 19- 49
[[circumpunct]] Px Tab. [[?]]        -4
 True Dist. [circumpunct]] & D 77°-19'-45
[[/left column]]
[[right column]]
[[?same - - - - - - - - - - - - 0.5210
D's Ap. Alt. 39'-38" [[Cosec]] 10.1953
[[dotted line connects the nest line to item in left column "Sine ..9.9901]]
.........................Tang. 10.6663
2d [[?Cor. or ?Con. or ?Cov.]]
                    Tab. XLVII  1.7386
[[/right column]]
[[line across two columns]]
[[underlined]]To find the Longitude[[/underlined]]
[[?True]] Dist. [[circummpunct] & D - - - - 77°-19'-45"
Dist. by N.A. at 0h - - - - - - - - - - - - 78- 07- 45 . . . .Prop. Log. .3452
Difference  - - - - - - - - - - - - - - - -     48- 00 . . . .Prop. Log. .5740
                                             1h 46m-17s  Prop Log Dif  . .2288
                                 Add - - - + 0h-00- 00
              Mean Time Greenwich Aug. 18th  1h-46m-17s
               "    " at the Ship  "   17th  22-10- 24
         Difference in Long in time . . . . . 3h-35m-53s = 53°-58'-15" W. from Greenwich
[[partially concealed in the fold crease]] (continued on page predeeding this)
[[end of page]]

Transcription Notes:
[[Pages 190 - 206 appear to be Hall's log showing positions, weather and events occuring on the voyage back to the United States. Many are nearly impossible to read let alone transcribe, especially this page 190 nearly undecipherable.]] I have taken some liberty with the underlining and strikethrough rules to make the transcription more readable. I have transcribed in journal window over transcription window so that numbers in the calculations are aligned on my end so that the mathematics can be more closely followed. The numbers are not guaranteed but best guess by checking the math. "G.T." may mean Greenwich Time, the basis for calculating Longitude. References to tables probably mean astronomical tables for figuring longitude and latitude based on known times.