<8 235 |/WHMMNDNNIIIL EPIL POE LALA AO ES peel A ‘lopographical Survey of the M. A.C, Campus W.M, BROWN §,W.McCLURE W, J. OARREL Nee er D WAGENVOORD 4 CO. BOOK BinOGRs and BLANK BOOK MAKERS, LANSING, - MICH. THESIS IsReaep Yi ceodL QS ag A M.A... ene a; i gt —— © as of tC eS Oe ee ge a i  -: THESIS :- A TOPOGRAPHICAL SURVEY of the Me Ae. Ce. CANPUS. BY Se 50 WP ate Clure bt aw . J ye - Gm Ww? x. Brown c Wi J. Carrel. nS CLASS 103 THESIS A TOPOGRAPHICAL SURVEY of the Me Ae Cw. CAMPU S. HRHEHEHE H This survey was made for the purpose of securing data for the completion of a man of the M. A. C. Camous and farm. On this man to a sccle of fifty feet to one inch was to be located accurately by means of a system of trianguletion all the numerous buildings, walks, and drives on Collese grounds, as ell as various toposrapnical features and contours. Mucn work had already been done. A system of six triangles, indicated (see man) by stations A, B, D, E, I, J, end K, con- nected to a base line alongs tre front of Faculty Row, had been establisned and plotted on the map, tne surveys having been nade by students jin their regular class work in Civil EFnrineeiz ine Tne lengtn of this vese, 936.27 feet, was established by taking the ean of many measurements, taken every vear since 1892 and the angles of te system were also well establisned by many repetitions. In the spring term of 1902 the old rough stone monuments, some of which had become covered wit: sod, vere replaced by cement blocks 6" x 6" x SO". This work was done by the classes of 'O2 and Civils of '0O38. All _ the stations were easily located from tre old field-notes of ne Civil Engineering Department. Large tripods (Fig. I) were set up over these triangulation stetions and tne point of a plumb-bob suspended over tne exact point as designated by a -l- 94273  cross mark on tie stone. Four stakes vere then driven end strings stretcreda intersecting at tre vlumb-line. The plumo- line was then taken up, tne old stone removed, and the new monument set in its place flush with the surface. The plucsb- line was then let down again, and a punch merk meade in the iron bolt in the center of the monument under tne point of the bob. Thus the exact point was preserved curins tne dissing ana transferred to tre new stone. Tne intersectirs strings were simply a check on the accuracy of the plurb, in case the tri- pod legs were moved sligntly. After these new monunents vere set the angles were agein read and thse wean of twelve repeti- tions recorded. Our first work was an examination of tre snap and old field notes in order to find ovt what work nac already been cone ana to deterz::ine uyvon a plan of procedure. In the transit hook belonying to C. E. Dept., merked "Base and References", we found reference to an old Base line as follows. “Runs nearly North and South along the West sice of tne far:: lane. ine North end marked: lst by the center of the bottom of a wine bottle set three feet under the surface of the ground; 2nd by a prickerunch mark in the end of a seven-eignt inch cast iron roa fourteen inches long set just atove tne bottle; Srd by a cross, cut ina stone set flusi with te surface, over tne iron rod. Located east of North-east of the sixth tree from the river, at a distance of eight end one-half feet from said tree, and six- teen end one half feet from tie wire fence on tne saine side of the road. We reedily found these old merks as recorded, -~2- except that the stone war covered witn sod, and replaced tnem by a monument, usin: the method described above. Tne The South end of the base was aiso referenced in the notes but in such an indefinite inanner that it could not be found. Tre ground for about nine hundred feet south from tre above located station was of an even slope and easily accessitle by a line of signt from any airection, so .re concluded to lay off tnere a pase line in th. true merician by an observation on Poleweris. This was found to be impracticable because the south end cane in the midale of tne road, the farm lane not being truly Nortn and South. We titerefore laid out the line parallel te tas road. Our vork was now, (1) to connect tris base by a sistem of triangulation with the old base above :rentioned, (2) to measure the base accurutely, (3) to observe the angles of all the triangles, and from the data thus obtzuined, (4) to co yute he Length of all the sides and plot the new system on the inape Tnén the details of topography were to be filled in vy a system of stadia traverses. By reference to tr.e accompanying map it will be seen that the earea to be covered ircludes the south-EKast portion of the Cazipus, treat part of the farm lying North of the Red Cedar River between tne Farm Lane and the P. M. Spur, and emoracing field “io. 6 South of said river and a portion of field “No. 8. A careful reconnaissance was made of this erea to obtain a familiarity with the renerel topopractni- cal features in order to proverly locate triansulation stations. This work took considerable tize for we realized that a Single station improperly located mignt occasion several -~3- days labor to clear a line of sirnt. We also visnea to obtain angles not less tnan trnirty caegrees or more than one hundred and tventy derrees so that the triangles ould be well proportioned; for triangles must be so formed that a small error in measurement will cause the least possible error ina calculated value. Tnis as proved by nicher Calculus is wren the triangles are as nearly equilateral as possible. The stations also had to be located where they would not be dise turbed, and at the same tive be accessible with en instrisent. Owing to tne many vuildings and trees we hud great difficulty in finding suitable locations, ana clear lines of sight, especially where the system crossed the river as the banks were thickly wooded. The instruments used in tne field were, an aneroid barometer, a prismatic pocketecompass, a field glass, and flags. We thus located stations, L, ™, N, 0, P, and Q, forming six triansles ( see man ), and set monuments at all the triangulation stations. All these stations were located in positions where they woulda not te disturbed if left flush with the surface except station M in field ‘'o. 6 Which was set one and one half feet below the surface to avoid the plow. After these menunents were firmly planted, they were referenced in the notes by tieing them to buildings, trees, or any permanent objects near at hand, so that they would not be lost if covered up. As this triangulation system forms the framnee- work of our map, each of its stations ::ust be accurately located, so thut a traverse could stert from any one of them and the notes taken for makings a plot of that particular ~4- vicinity, and many differe:t surveys made in aifierent parts of the system could be connected witn this sane skeleton framework and so form one united wiole. The angles of tne trian;les were easured by the method of repetition, taking three readings with the telescope direct and three witn the telescope reversed, as follows: We set the instrument over sone station, as O to measure tne ansle Pon (see map), with verniers at zero and sighted on station P. Clamped the lower :notion, loosened the upper motion and set telescope on station Q and clamped, read both verniers to eliminate errors of eccentricity, loosened lower motion, and set on station P, clanped and turned upper motion to Q and reed angle as before. We repeated the above operations until we had three additions on the limb and then reversed tre telescoue to eliminate error of adjustment in line of collimation and norizontal axis. Taree readings were now taken, adding: to those already on the limh. Tne sum of tne readings divided by the nunber of repetitions gave the :nean value or anyle. Wnen three angles of a triangle have thus been determined tneir sum would equal 180° if there were no error. Absolutely correct q ~5- results are however impossible and a limit of error of fifteen seconds was allowed. If tne observations were all considered equally correct eacn angle would be corrected by one third of the error, if not they are balanced according to the theory of probable errors, as i:ncicated by tne following specimen of notes. ota. ' I Index Ver Ae 65° 126° 190° 253° 317° 380° OO! 50! 00! 30! OO! 30! (Sample of “Totes) Anle go! 21 18 15 dl 7 Ver Be 26! 22 19 15 11 " “fean 63° 25-1/2! 126° 51<1/2' 190° 18-1/2! 253° 45! 317° 11° 380° 37! y, IK e Diff 65° 25-1/2! 63° 26! 63° 27! 63° 26-1/2! 635° 26!- 63° 26! ee tt ee Cee Cee Ye Ce eet Angle Direct 63° 26! Reverse 10" Computation of Probable Ervor in Arncles of the Triangulation. ? EE, =C ( = at ( n— 1 4ormulae ( E =z = 0 [za ( A n(ne-l1) n = nunber of observations. ad = difrerence between one observation and ariti: etic wean. E = provanle error of sinsle observation. KE = proha»vle error of mean. If tne ovservations are wei; ned M = any observation W = its weisht Weignt mean = =(W*) = ¥ E = C (wd* ) New E = © eB irae) (s w)(n--1) We considered all our observations of equal wei.ht. -8- Exarples of how those formulae are Ansle LIK Index Aritssetic to mean of all Observation Anzle Observations da 1 65° 2541/2! +40" 2 63 26! +10" 3 63 27! 65° 26' 10" -50" 4 63 26-1/2! =20" 5 63 26 +10 6 63 26 +10 O E, = C a* Neo BE 2 . 6745] /4800 = + 20.%83 E = CZ “= a* = 20.83 ™ n(n--1) Je 6 fetnod of annlvins the probable error ins example. aunliede d a +1,600" 100" 2,500. 400 100 100 4,800 = Zda* + 8."53 is shown by follow- Consider trian;le LIK. Mean of six Probable Anjrle readings error Balanced. KIL 63° 26' 10" 48.53" 63° 26' 16.86" IKL 50° 56' 55" 43.375 50 56 57.72 IIKK 65 36 40 46.74 65 36 45.42 Total 179° 59° 45" +18.645" 180° OO' 00.00" Sum 180° OO' OO" 179° 59! 45" 15" = error of triangle. Divide the error of the triangle by the sun of probable errors tnus,-= 15" = +.805 +18.645 Now multiply the probable error of eacn angle by the result just obtained and add or subtract the procuct to the anmsle according to wnether the error of the triangle is negative or positive. | Thus for Angle KIL 0-805 X 8.53 = 6.86 63° 26' 10" + 6.86 = 63° 26' 16.86" In the same manner apply corrections to angles IKL and ILK. The sum of the balanced angles must equal 180° -10- The base was .;casured with a 500' tape, wnich we tested with a K. & E. 100' tape standardized at Washinston. The testing was done as follows,-=- On as level a piece of cement walk as we could find we laid out 100 ft. with the standard tape at proper tension and supported trrouvgnout. supports consisting of a nail driven into the side of a stake were placed at the ends of this 100 foot length in order to support each end of each hundred feet of the 500 ft. tape on the same level, and leave it unsupported between the ends. Thus each 100 ft. was tested separately by hooking a spring balance to one end and applying tension until the hundred foot length agreed with that on the walk as shown by a plumb bob held beside the tape. These tensions for each hundred foot length were, commencing at the O end of the tape, 17, 16-1/2, 17, 16-3/4, and 18-3/4 pounds. The average tension, 17.2 pounds, was tnat required for the whole tape suspended at 100 ft. intervals. No correction for temperature was necessary in this test as the standardized tape and tape tested were of the same temperature. To prepare the base for measurement, stakes were set at intervals of 100 ft. along tne line and by aid of a level slats were tacked to them so as to support the tape on.the same level throughout its entire length. At each end of the tape we set up a board, firmly suyported by wires, (see sketch) with a threaded hook at the top by means of which tne required tension could be obtained and maintained while points were being transferred to the ground with a plumb bob. The ends of ~~] )- tne base were warked by plumb lines nung as follows: At the nortn end of the base, as the ground was about five feet vdelow the line, the plumb line was yun: from one of tne large tripods (used to mark the triangulation stations) and carefully centered over the punch mark in the monument. At the south end tne line passed about tvelve inches ahove the ground so tyne plunb line was hung froma transit. Five hundred feet was first measured alons the base nortne ward from tne south end. Four aoplications were isade by transferring tne five hundred foot point with a plumb bob toa board nailed to tvo stakes driven into tne ground. ine mean of these four apnolications was taken as tne measurement. The greatest difference between any tvo of these was aot over one=-sixteentn of an inch. Tne remaining part of tne line was measured from the north end of the line to tne point found by transferring the voint from the board up to the tase and tne tane reade Four readings of tynis were also taken and the mean usede The measurements were as follows. “easurement Temperature (F) Corrected “easurement. 867.880 50° 867.812 867.685 75° 867.791 867.736 75° 867.809 Mean = 867.804 Greatest variation fromm mean = .0O135 ft. = 1 66,754 -12- We computed tne sides of tiie triansles tnrouch the syste: fron the establisned base alons “aculty Row to our base in the Farm Lane. Two of us worked indevendently with seven place lorseritims and checkea. Tinie coOuputed length was 867.464 feet, a difference of 56. ft. The nearness of agree- ment Ltetween the measured and calculated lenstns deterinines tue degree of accuracy of all previous measurements and calculations. Calculating back froin the new to tne old base also served as a further checx on tne work. To deterniine the true azimuth of our buse line (OP) we worth O took an observation on Polaris from tae sewttn end, station P, using tne Buff and Berger transit. Tne reflector velonsin:; to the instrument was so neavy that it over-baianced tzne telescope, so we made a similar one out of White paper. It consisted of a cylinder mede of drawing paper inside of wi:ich was plaeged a card of »ristol board set at an anle of fortz- Tive desrees to tne axis of the cylinder. Throursn the center of the card an elliptical hole, threc-eignts incn minor axis, and concentric with the outer edse of the card, was cut, to persit sisiting trrougn tne telescope. A nole in tne side of the cylinuer permitted light to ne turown upon the card and reflected into the telescove to illuninate tne cross wires. Light was furnised by three bicycle linterns. South . The target at the ereth end was a box about 6" x 12" x 4", open on one side. On the opoosite side a slit oneecignth inc: wide and avout eignt inches lons was cut extending from one end tzroussh the center of the side. The slot in tne bvox ~13-  ; . north |. - + 4s was placed facins the sents. exactly over the center of the monuments and carefully plusbed. Within the box and behina the Slot one of tne lanterns was placed. Observations were made every five minutes by stendard time. With instrument carefully leveled, and verniers at zero, the telescope vas pointed at Polaris. Wito the lower motion clanped tne cross nairs were kept carefully on the star by the lower tangent screen until the time keeper announced ti.e tine to observe. This he did bsyy counting vacke wards the last fifteen seconds of the five minutes, thus: "15, 14, 15,-------5, 2, 1, and gol" The upper wotion was tien loosened and tne cross hairs set on the target at the South — . ; . ; . end of tne base, and tren cla.ped again, and angle read ana recorded. Tne telescope was tnen turned on tne lover motion and signted at tne star, and angle turned and rend as before. To eliminate instrumental errors six readings were taken with tne telescope direct and six reversed. Tne true azimuth correspondinzs to each observation was computed from tables given in tne U. 5S. "Manual of Instruction to Surveyors," and tne connection applied witn prover sign as shown in form of aotes below. Tne sean of tne coniected angles is the true aZimuth of tne base. Towing the azimutn of the buse tne azimuth of all the other lines of toe triangulation can Le aeternined by ,cuiputation. ~]14-~= Sune 18 199% Index Ver. Ooo° te) . Jo ° ’ Jo | Time -PM. 9:07' - 8:75 O DL fo BT VIS / PIL‘ . ° ; 00 x NLT ~ HOS & WSL o 9/0 F&F YS7 ~aIS 6S D4G ~IZO F , Sa ~ 930 4° Di57 OSS + LO%CE 240 4 /ClO7 ‘Q4as S00 Probable error of a Single obServation.-ccresveceee Probuble error of the ine // (4 1s 14 // zs SIM , Wea YY? A. Ver. B i/ / 4—- (Ss // 29 1S an = ' Mean Oo. 37 / / / 44 Zz 435 ze tt = I 3 PSR > sf 4 Ss ~¢ BB g s/ 37 Ss ‘ean..../../ /77sh Ver @ Brae Ver A Jngpent We Chua ye Netes Carrel Diff. AZinmutn oO. 37 sae Oo 34 tl oO TF3 TFSI Oo > 4 / o £9 4/ o 27 44 O Z4#AZ 46 o x34 AY Oo / S/ 0 "72 93 co Ik ss O J4- S57 oO! 50 ” Bearing Ni?’ 70' s0 W. ~15- Core 1 / S24 as 10 // AK JO Diff Traverse. A traverse of four sides Was run norta of the river for the purpose of locating yuildings, railroads, fencelines, etc., betvecn tne river end that pert of tne Ca:pus that nad been previcusly tied in. A nundred foot steel tape, and Lignt Mountain transit were used. pample of Notes. Cneck Sta. Line Dis Bearing AZimnutn Angle 1 le2 596.00 S 82° E 27° 31! 2 2-5 707.18 S 6° 25' W117? 11! 3 3-4 1187.15 N 60° W 231° 1! 4 4-5 552.07 N 68° 50' E 360° 5! 3042.40 Error of Closure = 1 set transit on station 1, siggznted on station 4 witn upper motion clamped on zero, (i.e.,- took tne first line as the true meridian). Clainped lower motion, inverted telescone, un- clamped upper motion, signted on station 2, read horizontal an«les and compass bearing. Lined in chainnen to measure line 1-2, and wake offsets from line to tie in buildings, etc. Repeated sane operation on all stations. -16- The Location of Contour by the Stadia ‘etnod. ee This work may be considered under tnree heads, viz.,- Observation or field work, Reduction of Notes taken in the field, and Plotting: said results on tne map. The field party consisted of an observer, a recorder, and a rodmwan. Tne instruments used were a lignt mountain transit and a rod graduated to feet and tenths. The wire interval of tne tran- sit was tested, and the svace subtended on tne rod found to he one onesehundredtn of tne horizontal distance from the telescope, tae horizontal distance being measured from a point f t+ c = -765 ft. from tne vertical axis of tne instrument, where f is the focal length, and c tne distance from tne center of tne instrument to tne objective. The ancsle subtended by tne crossewires was about tiirty-four ninutes. Te field work was to obtain tye tnree co-ordinates, as referred to sone known point of referénce, of a sufficient nunber of points in the territory gone over to enable contour lines to be plotted. Tne points of reference used wet. triangulation stations, wnose elevations were determined by running two lines of levels froin the bench mark on College Hall. The big Gurley Level was used for this work, after the bubble had been adjusted czure- fully to tne line of sight by tne peg adjustment metnod. These levels checked witnin .007 and .011 inches in about hal? a mile rune The stadia work was as follows,-=- Tne observer set up the transit over a triangulation station, with the vernier of the ~17- * horizontal limb at zero, and tne vertical circle at zero when tne line of sight was horizontal. With tne plates clamped in this position tne telescope was set to read on tne next triangulation station. The lower movenent was then clamned and an angle turned off on the horizontal limb to eny desired point. In order to set the proper cata to show tne cone ficuration of thre surface, points were taken close toretner wnere tnere was a sudden cnanse in slope and only a few where tne slope was comparatively uniform. The heilgent of the instrusment above the triangulation station was taken on the stadia rod, and in taking the elevation of points fron that station tne middle horizontal wire of the instrument is brougnt to this sane division of tre rod as it is neld on that point, and the vertical angle read. Tne upper, middle and lover intercents are also recorded in order to get the distance. Tre form of notes is as follows:= Ht. of Inst. = Object Hor. INTERCEPT S§S Ver. Ver. Cor. Dist. Elev. Upper Middle Lower A sketen was made on the opnosite page to aid in plotting tre work. Tne noints teken- were numbered corresponding to numbers in the column of objects, and approxi:mnate contours drawn ine ~18=  aoe oe See 7 “ e v WEY NG Seco. / 5: [S968 ie a Te GU A AN Wan: 1 ohh Secle of Feet ° Pats eto ene ea Pai y ie LA ' ¥ be | Fy | i : W ry a] x | : Ki | gt : = =~ } = | Sec /8 oo ee Poe | . Pr a F | Tas ui = ro aco “- us ae at . pe | Lay na A PE: ey 5 a* b se a) : a  a Adjusting screw’ v) No Fae Fanta ae ae FT > e-Teea7 e Monument fe Plurms line Oy Fak a CTR eal ia YJ Brace wes —_— ————— — —= —— eS ——— == =—_—_ eS — SS —= — — 145 3479 3.1293 03