Map of the Northern Boundary of Iowa Astronomic Stations. Jackson, Monroe, Madison, Jefferson, Adams, Washington, Lee

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1 Map of the Northern Boundary of Iowa Astronomic Stations Jackson, Monroe, Madison, Jefferson, Adams, Washington, Lee

2 Lee s Letter to Colonel Abert

3 Deflections from a Given course

4 Offsets from a Given Course

5 Instruments Required

6 42 inch Zenith Telescope & 30 inch Astronomical Transit

7 Polaris Tables

8 Laying off the Line

9 Chaining the Guide Line

10 Table of Errors in Direction of the Guide Line

11 Table to Reduce Measurements on the Guide Line

12 Offsets and Angles to the Parallel first 6 miles

13 Offsets and Angles to Parallel from 44 to 50 miles

14 Astronomical Observations

16 R A N G E L I Offsets Guide Line Procedure from Guide Line to State Line MERIDIANS STATION WASHINGTON STATION 2 LEE S MONUMENT Second Guide First Guide PARALLEL 43* 30 INITIAL POINT Range Line 4 th /5 th

17 Guide Line Offset Table

18 Dubuque, Sept 20 th 1852 Smith s Report to Talcott Capt. Andrew Talcott Chief Engineer Iowa Minnesota Boundary Survey Sir, I have the honor to present herewith the observations, calculations, Etc for determining the azimuth of guide lines No s 1 & 2 from the Mississippi River to Station Washington, with the offsets from the same to the parallel of 43* 30 N. Lat. It will be seen by reference to the report that the whole of guide lines 1 & 2 with the exception of the last six miles was checked by setting up the zenith and azimuth instrument at three points, and corrections made for any deflections which were found to exist. The running of the guide line was assigned to Mr. G. A. Stuntz and the running and marking on the parallel to Mr. J. S. Sheller. The work previous to your arrival was much retarded by the unseasonal rains and scarcity of grass, making the transportation of supplies slow and difficult. In accordance with instructions left by you mounds have been erected at the intersection with the parallel of the meridians of Stations Jefferson, Adams and Washington. The mound at Station Adams fell upon the soft and marshy ground to the South of the guide line, but at Stations Jefferson and Washington the position of the mounds and the large size of the stones, which formed their bases was such to serve them against removal or injury. At Station Washington the post used for transit observations was removed and a large stone substituted in its place.

19 Smith s Report to Talcott The whole of the field work including that between the monument and the Mississippi River (which was left unfinished in the spring, on account of the height of the water ) was finished by the ninth of September, and the field notes returned to the office of the Surveyor General by Mr Sheller, under whose superintendence the whole of the parallel was chained and marked. The difference between the latitude of the established by Captain Talcott and that by Capt. Lee (according to offsets from the guide line No. 2) being 64.4 links, the latter being to the North, it is provided for by lessening the offsets on the guide line No. 3, 52.2 links. Thus throwing the curve further to the North, (the offsets being South) and diminishing the offsets, ( which are South) on guide line No. 2, throwing that portion of the curve further South. The corrections in the offsets for guide line No. 3 commenced at No. 52, where the correction is one link, and increased to No. 1 where the correction is 52.2 links, the intermediate corrections increasing in arithmetical progression the difference being one link. I remain, Sir Very respectfully Your obedient servant. Signed, Isaac W. Smith Asst. Engr. I. M. B. Survey Note: The remaining 12.2 links of the difference of latitude by direct observation at Station Washington and that given by the guide line from the iron monument was corrected by deducting progressively from 1 to 12 links from the southern offsets measured from stations 39 to 50 in chains on Guide Line No. 2.

20 Records of Observations Etc. made by Isaac W. Smith Principal Assistant I. & M. Bd. Survey B D C M A The zenith and azimuth instrument was mounted on a stump at the point represented by A in the figure above 5.76 chs South of the parallel. M representing the Iron Monument erected by Capt. T. J. Lee Top. Engr s and M. D. the parallel. The meridian A B through the point A was then determined by the following observations. Station 1 near Monument Mean of Verniers for Elongation Date Star h z a E W Meridian Apr 14 Polaris * * * * * * * * * * * * * * * * Apr 15 Polari s * * * * Mean of results 66* h = Sid interval from meridian transit to elongation z = zenith distance a = azimuth

21 The reading from the eastern and western elongations of Polaris differing 5 from the mean by elongation was adopted. Reading of Meridian 66* B D C M A A signal was then placed on a stump at the point C the initial point of the Guide Line No. 1 which is 3 chs 59 links North of the parallel and 76 links west of the Monument. The distance A. C. is chs. The azimuth of the line A C was determined as follows: Reading of signal on meridian 66* at C 140* Azimuth of A C corrected from A to C at A 73* C 253* The instrument was then taken to C and the following readings taken, Reading for C A from C 206* Azimuth of C A C 253* Reading of Meridian at C 312* Guide Line C B 142* 29 40

22 Smith establishes the Guide Line Meridian B Guide Line 270* C D Parallel 43* 30 North M A

23 Map Captain Lee s Monument to Initial Point

24 Azimuth of Guide Line from N to E 270* E D C M B A Previous to marking the parallel the guide line was tested as follows. A B M C E represents the guide line as run A initial point of guide line B ch W of A M ch west of B ch. W of A C ch M ch W of A E ch C ch W of A D a signal 18 links N of C visible from M & E By putting up the zenith instrument at B. M. & D. the following deflections were found in the line. At B 2 20 South front sight on M M 1 55 South D D 7 05 South E The deflection at D was caused by mistaking the point of the forward signal in setting up the smaller instrument with which the line was run and the line from D to E being visible in several points was found to be straight.

25 The portion of the line from A to B about 4.5 miles was assumed to be correct, a great portion ot it being laid off with the zenith instrument from A and the remainder ( one or two miles) being run with great care. The azimuth of D M from D being 89* and B. M. deflecting 1 South at M. the azimuths of A. B. B. M. and M. C. are as follows. Azimuth is from Azimuth of Prime Error to the Of line N. to E. verticel starting at A South A.B. at A 270* * B.M. B 269* * M.C. M 269* * C.E. C 269* * The corrections for the above deflections were calculated by plane trigonometry.

26 Smith s Instrument Stations Houston /Allamakee County Smith pt. D S Sec 31 R 6 Smith pt. B Initial Point Smith pt. M SE Sec 33, R 5 Smith pt. A Lee s Mon

27 Smith s Instrument Stations Houston /Allamakee County 12½ miles 8 ½ miles 3 miles 4 ½ miles Smith pt. D S Sec 31 R 6 Smith pt. M SE Sec 33, R 5 Smith pt. B Initial Point Smith pt. A Lee s Mon

28 Smith s Instrument Stations Fillmore/Winneshiek Counties Inst Sta. SE Sec 31 R 10 Astronomic Station 2 Near SE Sec 36 R 9

29 Smith s Instrument Stations Fillmore/Winneshiek Counties Inst Sta. SE Sec 31 R miles Astronomic Station 2 Near SE Sec 36 R 9 12 ½ miles

30 Station 2. Station 2 is chs. West of the iron monument erected by Capt. Lee, Top. Engrs, and 4.82 chains north of the parallel. The following are the observations by which the azimuth of guide line No. 2 was determined. Name Station 2 Mean of the reading of verniers Signal Of Elongation on Guide Stars h z a E W Meridian Line h.m.s * * * * * Ursa min maj , B cephei Polaris Reading of meridian by the mean of the above 233* Signal on Guide Line West 143* Azimuth of Guide Line No. 2 counted from N to E 269* In the above table; a = Azimuth of Star at elongation Z = Zenuth dist H = Sid interval from meridian transit to elongation

31 Station 2 Guide Line N0. 2 Azimuth 269* State Line Boundary as marked Meridian Second Azimuth Station ft SW Sec 31 R ft ft Guide Line N0. 1 Azimuth 89*

32 Guide Line No. 2 The azimuth of Guide Line No. 2 by elongations 269* mean of results by transits of high & low stars 269* Difference 11 The Azimuth adopted was 269* The signal on the Guide Line used in determining the azimuth was 11 miles distant from Station 2 at the point at which the signal was placed the zenith instrument was mounted, and a back sight being taken to Station 2 the line was tested to a point 8 miles west, or 19 miles from Station 2, and thence extended to Station Washington with the smaller transit. This latter instrument had from some cause been much injured, rendering it necessary to run the line with great care to avoid injury, and to test nearby the whole of it with the zenith instrument. No deflections however were found in Guide Line No. 2.

33 Smith s Instrument Stations Fillmore/Howard Counties Station Washington Inst Sta SE Sec 35 R 12 Inst Sta. SE Sec 31 R 10

34 Smith s Instrument Stations Fillmore/Howard Counties 6 miles 8 miles Station Washington Inst Sta SE Sec 35 R 12 Inst Sta. SE Sec 31 R 10

Station Washington Guide Line N0. 3 Azimuth 270* 20 11 Meridian 10.8ft 65.

35 Station Washington Guide Line N0. 3 Azimuth 270* Meridian 10.8ft 65.1ft 343.2ft 93.3ft SW Sec 36 R 12 Guide Line N0. 2 State Line Boundary as marked

36 Guide Line East of Lee s Monument to the River B Guide Line No. 1 C E 3.60 chs 3.60 chs D M F In the spring of the year the water was so high on the Mississippi River as to render it extremely difficult to produce the guide line east through the river bottom. It was therefore deferred until the return of the party in the fall. The line was then run and the parallel marked as follows. C. is the initial point of Guide Line No. 1, 3.59 chs. N of the parallel and 76 links west of the monument. M represents the monument. The instrument was put up at C and a signal placed at E (on the extension of the guide line) on the bluffs east of the Mississippi. A signal was then placed 36o links South of E. at F. The line D. F. is therefore parallel to C. E. and is consequently a prime vertical running 1 link South of the monument. A deflection of 1 30 was then made to the North and the guide line run to the west bank of the river. This section of the guide line runs 1 30 N. of the prime vertical. The Azimuth from N. to E. = 80* Commencing one link South of the parallel, the distance to the first mound east is 1 ch 90 lks. The offsets are calling the first mound east of the monument (1 ch 90 lks) No. 0. The distance from Monument to W bank of river ½ Breadth of the river at intersection of line 8.08

37 Straight Line Guide Line to Station 2 All offsets and distances computed directly from northings and eastings Straight Line Talcotts Talcott's Monuments Computed Actual Offset Distance Actual Talcott's Smith's Straight Lee's Description Miles Distance Station No. Offsets(Lks) Feet NORTH EAST Guide Line Offsets Difference Difference Distance Distance Offset ' Chains Correction Offsets Offsets Lee's Mon Lee's Mon SE S SE S SE S SE S SE 36 R S SE S SE S SE33 R S SE S SE S SE 36 R S SE S SE S SE S SE S SE S SE 36 R S SE S SE S SE S SE S SE S SE 36 R

38 Straight Line Guide Line to SW corner of County Straight Line 0.5 Talcotts Talcott's Offsets Monuments Computed Actual Offset Talcott's Smith's Straight Lee's DescriptionMiles Station No. Links Feet NORTH Guide Line Offsets Difference Distance Offset ' Chains Correction Offsets Offsets Lee's Mon Lee's Mon A SE S SE S * 49' 35" SE S SE S SE 36 R B 2' 20" S ' 08" SE S * 48" 27" SE S SE33 R M 4' 10" S ' 10" SE S SE S SE 36 R S SE * 46" 25" S SE S SE S SE S SE S C 11' 20" SE 36 R ' 14" S SE S SE S SE * 45' 19" S SE S SE S SE 36 R

39 Houston County Holding Instrument Stations to Station 2 Smiths Talcott's Talcott's Offsets Houston Co. Coordinates Computed Actual Offset Distance Actual Points Description Miles Distance Map No. Links Feet NORTH EAST Guide Line Offsets Difference Difference Distance A Lee's Mon A SE ### ### S SE S * 49' 35" SE S SE ### ### S ### ### B SE 36 R B 2' 20" S ' 08" SE S * 48" 27" SE S M SE33 R ### ### M 4' 10" S ### ' 10" SE ### S SE S SE 36 R ' S SE * 46" 25" S SE S SE S SE S ### SE ### C S ### ### C 11' 20" SE 36 R ' 35 S ### SE ### S ### SE ### S SE * 44' 00 S ### SE ### S ### SE S SE 36 R

40 Calculation of Offsets from Station 2 to Washington M*2 x Compted Talcott's DRB Jan 2011 Distance Lee's 40 Az Initial Lee's Offset Offset Lat Offset Offsets Miles feet Offsets Correct Offset Formula feet Links error Links Links Error Station 2 SE 36 R S South SE S SE S SE S SE S SE S SE 36 R S SE S SE S SE S SE S Inst Station SE S SE 36 R S SE S SE S SE S SE S SE S SE S Inst Station SE S SE S SE S SE North 8.2 S SE S SE 36 R Station S Washington SE

41 Straight Guide Line Station 2 to Station Washington Cumulative Township DRB Jan Talcotts Talcott's Offsets Monuments Computed Actual Offset Distance Actual Distance Description Miles Distance Sta No. Links Feet NORTH EAST Guide Line Offsets Variance Variance Distance Variance SE Fill Co SE 36 R S SE S SE S SE * 14' 01 S SE S SE * 27' 01.2 Talcott S Station 2 SE 36 R S SE S SE S SE S SE S SE S SE 36 R S SE S SE S SE S SE S Inst Station SE S SE 36 R S SE S SE S * 47' 44

42 S SE S Inst Station SE S SE 36 R S SE S SE S * 47' 44 SE S SE S SE S SE S Inst Station SE S SE S SE S SE S SE S SE 36 R S SE * 20' 11 Talcott Washington S SE S SE S * 29' 59 SE S SE S SW Fill Co SE 36 R

43 Guide Line Holding Existing Corners at Smith's Instrument Stations Cumulative Township DRB Jan Talcott's Talcott's Offsets Monuments Computed Actual Offset Distance Actual Distance Description Miles Distance Sta No. Links Feet NORTH EAST Guide Line Offsets Variance Variance Distance Variance SE Fill Co. SE 36 R S SE S SE S SE * 14' 01 S SE S SE * 27' 01.2 Talcott S Station 2 SE 36 R S SE * 59' 20 Talcott S SE S SE S SE S SE * 49' 00 S SE 36 R S SE S SE S SE S SE S Inst Station SE DEF 02' 23" S SE 36 R S

44 SE S Inst Station SE DEF 02' 23" S SE 36 R S SE S SE S SE S * 46' 37 SE S SE S SE 36 R S Inst Station SE DEF + 01' 21 S SE S SE S * 47' 58 SE S SE S SE 36 R S SE * 20' 11 Talcott Washington S SE S SE S * 29' 59 SE S SE S SE 36 R

45 Variations R 6& R 5 S 31 S 33 S 35 S 32 S 34 S 36 Smith pt. D S Sec 31 R Smith pt. M SE Sec 33, R 5 Smith pt. B Initial Point

46 Variations R 8& R 7 Fillmore / Houston Station 2s

47 Variations R 10& R Instrument Station Station 2

48 Variations R 12& R 11 S 32 S 34 S 36 S 34 S 32 S Station Washington Inst Sta SE Sec 35 R Inst Sta. SE Sec 31 R 10

Early Trigonometry. Calculations. used to. Determine Distances Across Impassable Obstacles. during the early. Government Land Surveys

Early Trigonometry. Calculations. used to. Determine Distances Across Impassable Obstacles. during the early. Government Land Surveys Early Trigonometry Calculations used to Determine Distances Across Impassable Obstacles during the early Government Land Surveys 1858 Jerold F. Penry, LS During the early government land surveys in Nebraska,