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MAY BE RECALLED with earlier due date if requested. 0m1402909-- 6/07 p:ICIRC/DateDue.indd-p.1 THE MAKING, PLACIYG, AND PRECISE DETERMINATION OF THE ELEVATION OF BENCH MARKS IN THE VICINITY OF THE CITY OF EAST LANSING AND TEE COLLEGE CAMPUS. A Thesis Submitted to The Faculty of MICHIGAN STATE COLLEGE of AGRICULTURE and APPLIED SCIENCE By E. J. fitrom. C. F. Zimmerman Candidates for the Degree of Bachelor of Science June 1951. THFFHS IREFAGE This thesis is a problem.selected by us for the pur- pose of furthering our knowledge of Precise Leveling and Precise Leveling Methods The bench2marks are of our ovn design and yere built and placed by us previous to running the levels. .- _ we have attempted to conform strictly to the_nethod used by the United States Coast and Geodetic Survey both in our computations and adjustment of the level net, and in our observations in the field. Table of Contents. Section. Precise Leveling .............................. The Need and.Benerit or A Precise Level Net ----------------------------- The Bench Karine-nun»-~-----------,- ......... The Instrument ---------------------------------- The Adjustment of the Coast Survey Level -------- The Precise Leveling Reds ....................... The method ...................................... Thesis or June 1917. I. The Level Net ------ ------ ...... --.----.- 2.” Description of Bench Marks .......... a--- 3; Final Elevations------------------------ Thesis of June I929. I. The Level Net -------------- ------------- 2. Description of Bench Marks----- ........ 3. Final Elevat ions------'g;+--.§.------;---- The level Net ’- About the City or East Lansing-- Description otiBench.marks------------------..-- Selple Deternination or (c) -----------.-----.-- Sauple The. of'rield notes -----------.----..--- cmt‘t ion. -Q---‘-”-------------------------- 4V1”). EIOYI‘ionB -""-"-------.-----------------~ Page. I. 24. 25. 32. 33. 34. 37. 38; 39. 42. 43. 45d 49$ 1 Precise Leveling The purpose of Precise Leveling is to determine: with. greatest precision the elevation above sea level of points: on the earth's surface. even when these points are at great distances from the sea. The elevations are referred to mean sea level as a datum. The mean sea level is found at a number of places. by means of automatic tide guage records which extend.» over several years. In the work of the United States Coast _‘ and Geoditic Survey the elevation of mean sea level is. tak- en the some for the Atlantic and Pacific Oceans and for the Gulf of Mexico. _ - 4 . _ _ _ _ Precise leveling differs from ordinary leveling_in the refinements introduced into the construction of the instru- ments and into the method used. ’ In the United States and its Possessicns. the greater - part of the precise leveling has been done by the U.S._ Coast and Geoditic Survey and the U.S. Geological Survey. _Lines of precise levels have been run and bench marks established along these lines covering all the United States. Panama and Alaska. The elevations and discriptions of these bench marks may be found in the publishedreports of the Superintendent of the Coast and Geoditic Survey; 2 The Feed and Benefit of a Precise Level Net In all cities and towns there is considerable con- struction work going on, such as buildings, laying of water:nains and sewer systems. etc. In the laying out of this work it has to be tied in or referred to sane established datum. This means that a line of levels has to be run fro-.some known and fixed elevation. In some cities this line:lay be of considerable length and it will take time and probably cost considerable to run every thee as needed. 3 By having a Precise Level Net which covers the entire city, an accurate line of levels can be run in a.nuch short- er tine. A greater accuracy is obtained by making an adjust- ment of the Net according to the method of least squares ihich is very precise. Therefore, there is a saving of time and money; and also. a greater accuracy is obtained. The Bench Marks. In this work a matter of great importance is placed in the making and placing of the bench marks. They have be of a very permanent nature in order to give the acc- urate results desirable. The following design was decid- ed upon. The monument was to be of concrete, cylindrical in shape with the following dimensions:- 6" diameter by 4' 2" long. This length places the base of the monument well below the frost depth found in this locality. Into the top of this was set a brass plate (for detail. see Plate 1, fig. a which was securely riveted to a piece of %' water pipe extending lengthwise through the monument. Besides holding the cap in place. this pipe also acted as a reen- forcement for the monument. preventing any cracks. A pat- tern was mads for this brass cap, and the cap cast in the College foundry. These caps were later ground and smooth- ed on a buffer. Fig b of plate I shows the assembly of the monument. In placing these monuments wet cement was placed in the bottom of each hole and the monument set in this. Dirt ' was then firmly tampsd about the monument up to the ground surface. By placing these monuments in wet cement a wide firm base was formed which will prevent any possible heaving of the monuments due to frost action. All of the monuments were placed withthe top flush'with the surface of the ground. ‘ , a -, :6 f y r VET—1 ., Kg J .9 $1”; T\\\ " \"(\\\ .\\ ‘gé’a (3'; W, “ ~~-—.~.. I \ - ' ‘ ' awhkmxxasu _ HM: ' ; i r -915. I “fi'etél. :33, '5: '. ] ‘. If} -‘ . .7 _:.- r- - $2,!Q‘t‘- It:: I- A I!!!” b/ea’ anJ [mp /d(eo/ Mona/wen f dare/r Mark Free/3! Level ? We ' ' $14 Cap De fal/ FLA TE-I The Instrument. The dumpy level is the form of instrument now used by the united States Coast and Geodetic Survey and the United States Geological Survey. With it the most precise, most rapid and cheapest precise leveling is done at the present time, The distance between the level tube and the line of collimation is reduced by placing the tube in an opening cut in the telescope. This reduces to a.minimum the effect of temperature changes on the parallelism of the axis of the bubble tube and the line of collimation. The tele- scope with its inseted bubble tube is placed within a tube- shaped support toward one end of Wflich two pivot screws pro- vide a horizontal axis about which the telescope can be rotated a small amount and the line of collimation made horizontal by means of a micrometer screw mounted at the other end. The tubular form gives the strongest and light- est form of support of the telescope and also serves to pro- tect the level mounted in it. The level-reading device, consisting of a pair of prisms mounted in a tube at the side of the telescope and at binocular distance from it, enables the observer to stand with body and head erect Wflile observing the level with one eye and the rod with the other. A small mirror is attached at the top of the tubular.support and reflects the light from the level to the prisms of the levelereading device. The telescope, the tube incasing the level vial, the draw tube, the reticle ring and the tubular support are made of an alloy of nickel and cast iron. The point- ed screws pivoting the telescope, the screws holding in place the bubble tube, the screws holding in place the reticle ring and the micrometer screw are made of nickel- steel. The telescope, its tubular support and the bubble tube, are covered with a coating of cloth dust of bluish; gray color, giving a finish WHiCh has the appearance of a cloth of fine quality. By using these materials and fins ish the effect of temperature changes is reduced to a minimum. The main points in the construction of the level are: First. The telescope is not reversible, being support- ed on trunnions between the objective and the middle of the telescope and on the point of the micrometer screw near the eye end. The bubble tube is fixed with respect to the tele- scope, except the small change provided for adjustment. Second, The device for reading the position of the bubble enables the observer to stand erect and to see the bubble and rod alternately by merely changing the attention from the one to the other, Third, The design and materials used greatly reduces the effect of temperature changes in different parts of the instrument. WAGONS .5 E I G ,ms 8 ,1; '1 ll- ‘.'.l"£i y . 3.. Tia.-- _ . \ lggifiuuvbfl .r ,. unswsl: r -I V 'l m r J .‘5 . p- (‘5‘ cacti-J“ ‘1‘. -: s:- _, j V t 3! (x 1 ‘ . Audi-t " a "e e» (u:- 4,21%. 1 . N“. a:- i 93% IV a» 5d.- ‘-'5 , '11-” 1“ .-: '. . . ..: , . ‘ all ., ' ‘A‘54 “3 6 Adjustment of the Level. The only adjustment of this instrmment, whcih should be made daily, is as follows: TO.MAKE THE AXIS OF THE BUBBLE PARAIJEL To me. LINE or SIGHT. This ad- justment is made by the ordinary peg method, the bubble tube being raised or lowered at the adjusting end as may not be disturbed at any time because they have been permanently adjusted for collimation by the maker of the level. In testing the adjustment the rod reading is taken as the mean of the three crosshair readings, and the rod interval as the difference between the outside cross-hair readings, the bubble being kept exactly in the center while all of the three cross-hairs are being read. Two turning points are set about 100 meters apart. each rod being kept on its own point if two rods are used, or one rod being shifted as the case requires. The level is set up approximately in line with the tow points, forst about ten.meters beyond one point, and then about the same distance beyond the other point. The rod reading is taken for each point and for each point and for each position of the instrument, the terms 'distant rod' and "near rod" being used to in- dicate the relative position of the rods for each set “P. New having taken the four readings we have. C 2 Sum of near rod readin s - Sum.of distant rod readings mm of near rod intervals in which C is called the bubble error or constant for the day's work. If c does not exceed 0.010 (numerically) it is not advisable to change the adjustment. The tele-' scope looks up when G is negative and down when G is pos- itive. so that is an adjustment is necessary the line of sight ( here taken as the middle cross-hair) is raised or lowered on the distant rod by 0 times that distance. and the bubble tube adjusted to bring the bubble to the center. A correction equal to C time the excess interval be- tween the foresights and backsights are in excess the cor- rection has the same sign as C, and if the foresights are in excess the correction has the opposite sign. 8 The Precise Leveling Rods The rod used in precise leveling work is of the self- reading type. It is non-extensible and in section are -- shaped. It is made of high grade white pine and treated with paraffin to make them.impervious to moisture. The rod is 5.2 meters long and graduated in meters and centimeters. the meter graduations are marked with silver plugs. As the telescope of the level used in precise leveling is inverting, the figures are placed on the rod upside down, so that they appear erect when seen through the telescope of the level. Attached to the rod is a centigrade thermometer, reading from.-25° to 55°, and a circular level for plumbing the rod. the base of the rod is fitted with a brass shoe, the end of which is cylindrical in form and rounded on the very bottan to fit into the top of the foot pin. The foot pin which is used as a turning point is driven into the ground with a wooden mallet. } THE mmon. The following instructions are taken from.Special Publication No. 18 of the COAST AND GEODETIC SURVEY and comprise the method of precise leveling that is carried on at the present time. GBHBRAL INSTRUCTIOHS FOR PRECISE LEVELING 1. Except when specific instructions are given to proceed otherwise, all lines are to be leveled independ- ently in both the forward and backward directions. 2. The distance between successive permanent bench marks shall nowhere exceed 15 kilometers. There shall be no portion of the line 100 kilometers long in which there are not at least 20 permanent bench.marks. No permanent bench mark is to be counted in considering these limits unless it is adequately described, nor shall both of two bench marks be counted if they are placed so near to one an- other and in such manner of exposure as to be likely to be destroyed at the same time. The above-stated limits are to be regarded as extreme lower limits. It is desired that the number of bench.marks shall, in general, greatly exceed that just necessary to keep within the limits. It is desired, also, that the bench marks in each general locality shall belong, in part, to each of the several classes such as bolts or other marks on buildings, squares cut or bolts or discs set in railroad masony, such as bridge piers, water tanks, etc.. stone posts, and iron-pipe bench marks. lO 3, The line of levels is to be broken by temporary bench marks into sections from 1 to 2 kilometers long, except where special conditions make shorter sections advisable. 4. Temporary bench.marks should be established in places where they will be free from disturbance by the track hands working along the road or by materials un- loaded from cars. Inlb is espeCially important when the temporary bench mark is expected to hold the line for any densiderable time. 5. At each city along the line, the leveling should be connected with at least two stable bench.marks which are connected with the city datum. Connections should also be made with all stable bench marks of other organizations which may be found along the route.. 6. In general, the top of rail of the railroad track should be used as the rod support. However, footpins should be carried along during the progress of the work and they should be used whenever a train is known to be approaching or when there are special reasons for supposing the rail not to be in sufficiently stable conditions. ‘ 7. When elevations and descriptions of bench.marks est- ablished by railroad (over which a line is to be run) are furnished to this office with a reguest by officials of the road to have the precise leveling done by this sur- vey connected with them, as many of the railroad bench marks will be incorporated in our line of levels as can be done 11 without greatly delaying, its progress. The railroad . bench marks which are of permanent nature areto be. treat- ed in the same manner as new permanent.bench marks est-:- ablished by the precise leveling party. If the permanent bench marks of the railroad are chiefly of the same gen;- eral type, they must not be given full weight in deciding- whether there are enoughbench marks in any section of the - line. ( See paragraph 2. ) Bench marks of the, railroad which are not of permanent character may be determined by extra foresights, as in the manner provided for determining the height of rail in front of a railroad station ( See parse. graph 10). It will not be necessary to connect the precise leveling with the railroad bench marks which are in places not easily accessible, It will not be necessary to connect with each railroad bench mark where they are less than one kilometer apart. The benefits derived from. connecting a line of precise leveling with railroad. bench marks are. (a) that time is gainedby having some permanent bench marks already established; (b) the elevations of the railroad bench marks resulting from the connection with precise level- ing are of great value to the railroad concerned; and, (c) as the work progresses, a check is obtained on gross mistakes which might escape notice, by comparing the elevations fur- nished by the railroad with those by the precise leveling party.. . y . 8. All old bench marks are to be called by their old ' names or numbers and are to be described fully by quoting ' 12 . the old description, if one is available, and by making additions or corrections to it. 9. All new bench marks are to be designated by-cap-. ital letters with numerical subscripts after the alphabet has been exhausted in each state. 10. The elevation of the top of the railroad rail in front of each railroad station along the line of levels . is to be determined with a check. This may be done by us- ing the point on the rail as a rod support in either the_ forward or backward running of the line, or by taking extra foresight to it on both the backward and forward runnings or by taking extra foresight to it from two instrument stations near it in one of the runnings of the line. ll. When it is desirable to get the elevations by means of which to compare the line of levels with the profile of the railroad, such elevations.may be gotten by single read- ings on the rod held on top of the rail opposite water tanks. and over bridges and culverts. .Such structures are usually shown on therailroad profiles.“ 12. It is desirable that the backward measurement on ,each section should be made under different atmospheric conditions from those which occur on the forward measure- ment. It is especially desirable to make the backward measurement in the afternoon if the forward.measurement was:made in the forenoon, and vice versa. The observer is to secire as much difference of conditions between the forward and backward measurements as is possible without 13 . materially delaying the work for that purpose. 13. On all sections upon which the forward and back- ward measures differ in millimeters by more than 4t/"§T_? (in which K is the distance in kilometers leveled between adjacent bench marks) both the forward and backward measu- res are to be repeated until the difference between two _ such.measures fall within the limit. so one of the quest- ioned measures is to be used with a new'measure in order to get this agreement. . , 1 14. If any measure over a section gives a result differ- ing by more than.6 millhseters from the mean of all the -‘. measures over that section, this measure shall be rejected. no rejection shall be made on account of a residual smaller than 6 millimeters unless there is some other good reason; for suspecting an error in this particular measure, and in‘ such cases the reason for rejection.must be fully stated in the record. 15. Whenever a mistake, such as a misreading of 1 deci- meter or 1 meter, or an interchange of sights ( the backs sight being recorded as a foresight).is discovered in any measure after its completion and the necessary correction applied, such measure may be retained provided there are at least two other measures over the same section which are not subject to any such uncertainty. Provided, further, that when it is found that the mistake was made on the last instrument station of the second running of a section and it is corrected on the same day and before beginning work on 14 an adjacent section, such measure may be retained and no further measure of the section are to be required on ac- count of the mistake. 16, The program of observation at each station is to be as follows: Set up and level the instrument. Read the *_ three lines of the diaphragm as seen projected against the_ front ( or rear ) rod, each reading being taken to the_near- est millimeter (established), and the bubble being held con- tinuously in the middle of the tube ( i.e., both ends read- ing the same). As soon as possible thereafter read the" three lines of the diapgragm as seen proJected against the rear ( or front) rod, estimating to millimeters as before,‘ and holding the bubble continuously in the middle of the tube. 17. At each rod station the thermmmeter in the rod is to be read to the nearest degree centigrade and the tamp- .erature recorded. ’ _ . 18. At stations of odd numbers the backsight is to be taken before the foresight, and at even stations the fore- sight is to be taken before the backsight. As the same rod is held on a rod station for both the fore and back- sights, the effect of this is that the same rod is read first at each stt-up, it being the rod used for the back- sight at the first instrwment station. 19. The difference in length between a doresight and the corresponding backsight must not emceed_lo meters. The difference is to be made as small on each pair of sights 15 as is feasible by the use of good Judgment without any expenditure of time for this particular purpose.: 20. The recorder shall keep a record of rod inter- vals subtended by the extreme lines of the diaphragm on each backsight, together with their continuous_sum.between each two contiguous bench.marks (temporary or_permanent). A similar record shall be kept for the foresights. .The two continuous sums shall be kept as nearly_equal as is feasible without the expenditure of extra time for.that purpose, by setting the instrument beyond (or short of); the middle point between the back and front rods. The two continuous sums for a section shall not be allowed to liffer by more than a quantity corresponding to a distance' of 20 meters. 21. Once during each day of observation the error of the levelshould be determined in the regular course of the leveling and recorded in a separate opening of the ; record book as follows: The ordinary observations at an. instrument station being completed, transcribe the last for- sight reading as part of the error determination, call up_ the back rod and have it placed about ten.meters back from the instrument, read the rod, mews the instrument to a pose ition about ten meters behind the front rod, read thexfront rod and then the back rod. (The two instrument stations are between the two rod points.) The rod readings must be taken with the bubble in the meddleof its tube. The required constant C to be determined, namely, the ratio of the re: quired correction to any rod reading to the corresponding l6 subtended interval, is C 3 Sum.of near rod readings-Sum 9f digtant rod readings Sum.of distant intervals - Sum.of near intervals The total correction for curvature and refraction must be applied to the sum.cf the distant rod readings before using it in this formula. The level should not be adjusted if C is less than 0.005. lf.c is between 0.005 and 0.010 the observer is advised not to adjust the level, but if C exceeds 0.010 the adjustment must be made. If a new adjustment of the level is made, C should at once be redetermined. It is desirable to have the d9f. termination of level error made under the usual conditions as to length of sight, sharacter of ground, elevation of line sight above ground, etc. The adjustment of the ing. strument to reduce c must be made by moving the level vial not bylmoving the reticle. . . 22. Notes for future use in studying leveling errors shall be inserted in the record, indicating the time of.- beginning and ending the work of each section, the weather conditions, especially as to cloudiness and wind, and. whether each section of the line is run toward or away frmm the sun. Such other notes should be made as promise to be of value in studying errors. 23. The instrwment shall be shaded from the direct rays of the sun, both during the observations and when moving from station to station. 0 24. The maximum lenght of sight shall be 150 meters, 17 and the maximumis to be attained under the most favor- able conditions. 7’ 25. At the beginning and end of the season,‘ and’at least twice each month during the progress of the leveling, the _ 3-meter interval between metallic plugs on the face 9f: each} level rod shall be measured carefully with a steel tape which shall be kept continuously with the party during the sea- son for that purpose only. The temperature shown by the- thermometer inserted in the rod and by the thermometer. at- tached to the tape at the time of each of these measures . must be recorded. The purpose of these. measures is to_ det- ect changes in the length of the rods and not to determine the absolute lengths. The. absolutelengths are determined at the.office between field seasons.‘ . _ . ‘ . M 26, The tape furnished. by the office.for measurement of the rods is a piece of steel tape about 3.1 meters long,“ having near one end a fine line graduation and about three meters from it (at the other end of the tape), a series of fine_millimeter gradufiations on a steel rule riveted to the tape. With this special form of tape the measurement of. a rod should be made somewhat as follows: .The rod “#193141. be supported at about the 0.85 meter and 2.45 meter points only (approximately quarter points) to get the leastbend- ing of the rod for any two support system. In making the measurement the single line should be made to doincide with the fine line on the silver plug nearest the bottom of the rod and the reading should be made at the line on the sil- 18 ‘ ver plug at the top of the rod. It is possible to estimate; the half-tenths of millimeters on the rule which is attached to the tape, The tape should be placed on the face-of the rod in such a way that the edge of the tape from which the rule does not project, coincides with the edge of the face of the rod nearest the meter marks of the r9d9, Care must: be taken that the two edges coincide closely in order that the tape may always assume exactly the same position, The end of the tape at the foot of the rod should be clamped firmly to the rod after the line on the tape and that on_; the plug have‘beenmmade to coincide. The tape should then be smoothed down by the hand to make it lie pet-roomy flat on the face of the rod. _With the hand lifted and, coneegf uently, no tension on the tape, the reading should be:made from the rule attached to the tape near the upper or top end of the rod. \ 27, The field computations and abstracts are to be kept up as the work progresses. .As soon as each book of the_ original record is out of use it is to be sent to the 9": fice by registered.mail. The corresponding abstracts must be retained until an acknowledgment of the receipt of the original record at the office has been received, 28, No duplicates of the original records are to be made except of the descriptions of bench marks, of which duplicates in theform of carbon copies are to be made. At least once during each.month such carbon copies as have accumulated are to be sent to the inspector of Geodetic 19 work. . 29. At least once each.menth, during the progress of the leveling, a test must be made of the adjustment of the rod levels, and a statement should be inserted in th§.r9f. cord showin the manner in which the test was made, whether the error was found to be outside the limit stated below, . and whether an adjustment was made. 'With the bubble of the level rod held at the center, the deviation from.the vert-oo ical of the plane intersecting the center of the face offthe rod, must be determined. The deviation from the vertical of the plane coinciding with the face of the rod, must also be determined. If the deveation from the vertical 93°°9d3.7 10 millimeters on a Sdmeter length of the rod, the rod level must be adjusted. ‘ .. . . ,_' . 30, On the left-hand page of the record the_numbe of each instrument station at which the instrument_is not” st up in the railroad track is to beincludedinparenth-~ eses, Sheilarly, on the right-hand page of the record, the designating letter for the foresight rod (V,W,etc.) shall be inclosed in parentheses, if said rod is not supported on the railroad rail. If the length of any portion of the level line run off the railroad is 25 meters or mere greater than the railroad distance between the points_of depart- _ ure frmm and return to the railroad, the the distance along the track between these two points must be shown in the re- cord. The purpose of these requirements is to furnish the 20 ) office a means of detecting blunders in the leveling, by plotting the level line on the profile of the railroad. 31. When it is expected that the forward and backward runnings of the line are to be completed up to any one place, the elevation at that place should be held by twp; points, established at least one set-up of the instrument apart. When the leveling is continued frmm or to suchra pair of points, the instrument should be set up between them.readings of the rod taken on each point. The ‘~ same arrangement of points should be used at the completed end or ends of any detached portion of the line of levels._ Either one of the two points may be used for carrying along the elevation, withe the other used only as a check against mistakes in reading the rod, or a disturbance 9f;933 or_both of them. The records should show clearly whichone of the two points was used to carry the elevation, and it is P91? ieved that it is a good policy to use the same point (back? ward or forward) in each case as for as may be praeticable. It is believed that, by employing this method, ne mistake. of a.meter or a decimeter made in reading the rod, held on a'bench.mark, will escape detection. f _ 32. As far as possible, all the permanent bench.marks should be in the main line of levels and not on spur or ' branch lines. One of the exceptions to this rule is where the line runs several miles off the railroad to the.manh of a triangulation station. in such a case the sour, or branch line, is the more economical way of doing the work 21 and will be satisfactory. Whenever a permanent bench.mark is established by means of a spur or bench line, which has only one set-up, the forward and backward lines of; the spur or branch should be run at a different time of, the. day or on different days, if practicable. If it should be ”8998?? ary to have the two runnings made one immediately after the other, the height of the instrument should be materially changed to make the second measure.. This would help to prevent any mistake in the leveling. 33. Except in rare cases, the permanent bench marks should be established before or during the first running of the; line. It is believed to be inadvisable to delay the tying . in of the permanent bench marks until after the line has. been run, even in only one direction. 'When is is impract- icable to establish a permanent bench mark before: or' during the first measurement of the line, an acceptable manner. of tying in the permanent bench mark or including it in the . main line of levels is to establish a temporary bench mark on each side of the proposed location of the permanent bench mark and to leave the distance between them unleveled un- til the permanent bench mark has been set. The arrangement of the temporary bench marks established for this purpose should be similar to that described in the latter part of paragraph 31 of these instructions. This would provide for two points, the difference in elevation between which are known, on each side of the permanent bench marks and the distance between the two pairs of points makes a section 22 in the main line of level. A diagram showin the arrang- ment of the stakes and the permanent bench mark is shown below: ----0----X----O----X----B----X----0----X----O---- The position of the instrument are shown by X, the position of the temporary bench marks by O, and the pos- ition of the permanent bench mark by B. 54. Chiefs of party should keep the length of sight great enough to make it necessary to do a moderate amount of rerunning. If an observer is extremely cautious and confines all his observations to sights sufficiently short to insure easy reading of the rod, it is posssble to work month after month with almost no rerunning, but the pro- gress will be slow. On the other hand, it is certain that an attempt to take sights of the limiting length, 156 met- ers, at all times would lead to a very large amount of re- running and the progress would not be rapid. It is believed that the maximum speed consistent with the required degree of accuracy will be secured by continually keeping the len- gth of sight such that the amount of rerunning will be fran 5 to 15 per cent. An extremely small percentage of rerunning would indicate an excess of caution on the part of the observer. The occurrence of apmoderate amount of rerunning is due largely to an attempt on the part of the observer to obtain maximum progress consistent with the required de- gree of aeeuracy and not to inability to secure such observations 23 that little or no rerunning would be necessary. Obser- vers have found a convenient rule in fixing the length of sight to be shortened the sights whenever the upper and lower thread intervals subtend on the rod are found to differ frequently by more than a selected limit. Each observer should fix.the limit from his own esper- ience by noting the relation between such a provisional limit and the amount of rerunning found to be necessary while using it. Such a rule is based upon the idea that the additional errors which are encountered when the len- gth of sight is increased are, in the main, those due to the increasing accidental errors in reading the rods. 35 35. It is not thought advisable to state definitely in these instructions the allowable lhnit on the rate of di- vergence between the forward and backward lines, but this should be kept small. 36. The record and the prelhminary or field computat- ions of precise levels must conform to the examples fol- lowing, except that in the computation in the field, the five corrections for curvature and refraction, level, index, length of rod, and temperature are not to be applied. 37. Should the experience of the chied of party indicate to him.that a change or changes in these instructions would facilitate the work in the field, he is urged to communic- ate with this office regarding such changes. When cases arise which are not provided for by these gen- eral instructions or by specific instructions, the chief of party will use his own Judgement in the matter. 24 THE LEVEL NET 2/ \__ 20 §\ c \\\\<\ [7.5 D, ¢ 14/ Bu. cat/1. Gov. 5M. \ ' 4 2 5 // "' 9 / // 5' 0 //, / .— 3 . I, r 05. O / 7 / /9 2 ' '\ l7 0 J 0 l6 \. pa 1 /6 24 \\\ - i 2460/? \_\ 0 F0 f. > NE 4» 5.5: 25 DESCRIPTION AND LOCATION OF BENCH HARKS. Note I. This station mark consists of a copper plate 3- in diameter set flush with the surface in cement and having a horizantal bar across the face. Note 2. This station mark consists of a cross made with a hamer and cold chisel. Note 3. This station mark consists of an iron Pipe. Note 4. This station consists of a 6'16'x4' concrete post set flush with the surface of the ground and having in the center of the top an iron or copper bolt with a punch mark in the center. BO“. #1. In front of Dean Shaw's Old House 50' south of S. E. cornerof Shaw's House and 6' W. of S. E. corner of Said House. liarked as in Note 4. B.H. #2. 147' N. E. of the N. E. corner of the new Gymnasium and 136' S. W. of the S. VI. corner of the Armory and 6' N. E. of tree stmp. Marked as in Note 4. 26 3.11. #3. In front of Pres. Shaw's new House. 45' 8.1:}. of Evergreen Tree and 68' S.W. of the S.W. corner of Shaw's House and 33' NJ. of iron hitch-L post on drive in front of House. Marked as in Note 4. IBM. #4. In front of Old Taft House. 13.5' South of the Iain Drive, 26.4' East of shrubbery. An elm 30" diam. on North side of road bears N37°W distant 38' . Other references are: a maple bearing S70°E distance 55'. 24- diam; and a basswood 24- diam., bearing 34o°n e distance 64.6' . Marked as in Note 4. B.M. #5. Fast and North of College Hall Just N. E. of fountain. . ‘ , References:- N. W. Corner College Hall to E. 66.5'; n. a. comma Sink or fountain 7.2'. Marked as in Note 4. 3.1!. #6. Directly in front of library and near top of slope up to College Hall. _ References;- I. 33.3. Corner College Hall 376° so'w. distance 80.1'; 2. Oak Tree ns9°w distance 28.I'; 3. Fire Hydrant 83303 distance 78.0'; 4. Evergreen ROE distance 28.7'. Marked as in Note 4. 27 B.Mo #3. In lawn Forth and‘west of the Greenhouse, 12' N, of 3. line of Greenhouse and '75' I. of same, References:- ’ "Iater plug to N, 30,8' (1' pipe); Iron clothes post to I;- 35.0'; N,E. corner Hot-bed Wall ; 23,5v. Marked as in Note 4. B.M, #8 In front of WOman's Building. 70' N,W. of end of walk in front of building and 3-5' S.W. side of main Drive. Marked as in Note 4. B.M. #9 In front of Bacteriology Building. 7.5' N. from.the center line of walk leading from building and 3- West of walk leading to Horticultural Building. References:- Fire Hydrant to E. - 10.5' Marked as in Note 4 Bone #11. On Soth side of road passing Agricultural Building, at N.W. corner of pasture lot, 2.6' N.W. of corner post at South side of large boulder 3" beneath the surface. Referenceszo N.E. Corner Farm Mech. Bldg. 18.2' Bearing W. S.W. Corner Ag. Bldg. bearing N,E. app. Marked as in Note 4. 28 B.M. #13. On farm lane situated 32.5' 8.3. of concrete gate post at South Entrance to Campus and 17’ W. of East fence. References:- Corner fence post - N.E. 37' W. Marked as in Note 4. M.M. #16 On East side of Main Drive 55' North of old culvert wall at road to athletic field. References:- 1. Iron elec- tric light pole 36,9' N.; 2 Oak tree on edge of bank to west -blazed- 54.5' . Marked as in Note 4. 3.1.21. #17 At intersection of Main Drive and Hospital Drive. References:- S.W. Corner of Hospital 129' N.E.; Fence 30' S. Marked as in Note 4. s.M. #18 On athletic field just next to curb on south side of running track. Heferences:- S.E. Corner of Grand Stand 146' S.E.; Curve in Curb 25' S.E. Marked as in Note 4. B.M. # 19 About 450' West of B.M. #17 and North of the ‘Main.Drive. Referencesz- Shrubbery 28' North; Main Drive 20' 8.; Pine Tree 50' S.W. 'Marked as in Note 4. 29 B.M. #20 In Elm Row across street from 216 Michigan Avenue. References:- 8' S. of South Rail of M.U.T Co. Marked as in Note fi. B.H. #21. In Elm Row on South side of M.U.T. Tracks and West of Stone Walk. Referencesz- S. Rail M.U.T. 7' N.W.; Stone Walk 15' N.E. Marked as in Note 4. B.M. #24. Sothwest of Greenhouse on South side of River Drive, 5' from South edge of Road. References:- A on South trunk of double oak tree distant 16.6' to Eastward; A on main trunk of a clump of maples to South distant 17.5'; An Oak to S.W. distant 17.7'. Marked as in Note 4. 3.11. #D.B. On S.E. corner steps of Dairy Building. References:- 3.5' S. of Dairy Bldg.; 15' E. of Center Line of Dairy Bldg. Marked as in Note 2. B.M. #ABUT. On S.W. abutment of Farm Lane Bridge. References:- 10' W. of W. side of Bridge. Marked as in Note 2. 30 B.M. #NtB. On West side Farm Lane about 400' South of Bridge over Red Cedar. References;% 18' S. of N.E. Cor- ner post of Field 8; 15.5' E. of E. Fence Field 8. Marked as in Note 4. B.M. #S.B. On West side of Farm Lane about 900' South of North Base. References:- 313' S. of N.E. corner post of Field #10; 12.5' E. of E. Fence Field #10. Marked as in Note 4. B.M. #GOV. B.M. HAR. AME. Across the road from and nearly in front of the'White Elephant' 33' N. of the center line of street car track; 61' W. of sidewalk crossin Michigan Avq/ U.S.G.S Iron pipe 10' above surface. Marked as in Note 5. mi. #F. Cross cut on curb on west side of Pennsylbania Ave. ( Lansing, Mich.). Reference:- 1' N. of Telephone pole #2326 on curb. Marked as in Note 2. BOM. #WOB. 7.5' W. of S.W. Corner of porch on weather Bureau. Copper disc cemented on top of step. Marked as in Note 1. 31 B.M. # FOR. 2" Gaspipe 6' East of East Fence Forestry Plant and 63' S. of center line of P. M. Spur. ‘Marked as in Note 3. B.M. [£818 . Situated 34' south of the Northeast cor- ner of the D. M. C. Depot and 14.5 North of the Nbrth side of the smoking room door and 2.16' above the pavement. Copper disc set in cement in East Wall of M. C. Depot at Lansing, Michigan. E: ‘L L TILT?” r. '3 ’L:TAEIL ’ é‘c::; B’VTATIT (* at) 5,5 252. 943C; 847. 63/ w. 50. 26/. 2745 957/77 F.‘ 263.54/3 364.634 5 257.327? 857- 006 0 258-593/ 34.9 40/ C 256’- 3022 347.446 0 253.0453 832/67 A 253. 956/ 9331/27 60V.5.M 255.2633 837.475 20 258. 8544 847. 257 2/ 258. 2764 244329 ? 257- 77// 345‘. 404 // 258.6272 24 9. 5/7— 0.0. 25?. 4560 857-232 /3 256. 0/l7 83?. 730 Abe”? 254.7044- 835- 833 Ma. 26/.0479 856.452 5. a. 26/. 665/ 858.479 For. 250°. 2500 847.275 24 252.6234 823-8/4 "3 253.//05‘ 5730,4/4 “5 258.4273 847. 5756 ’7 2626/44 86/.5‘73 /7 262.7002 86/- 875‘ 3 260.7376 5755244/ / 260.23/? 853. 934 4 257. 0/87 343-233 8 256. 3844 J’4/-/5‘3 6 259.322/ 952.433 5 253. 0477 846.é09 T 7 257.2290 844.//? 2 2 56. 9035‘ 24 2 .945 ‘ 33 THE LEVEL NET Sec/3 b 8 [K 8 .V) g a h . ‘ 3:53: : ‘o t t Sec. /9 ' Q 520.20 \ g 8‘ k e"? ' /<=1U H ”f Hope Food 2} - ' ' a“ K o i .. "e 't 3 E’ Sec. 27 . if: a: 4a N Sec. 25' sec. 30 f 34 DESCRIPTIONS OF BENCH MARKS. B. M. s-F.L.B. A sduare cut in the corner on the N.E. corner of a manhole in the East wing of the South abutment of the Farm Lane Bridge. B.M.-'A“. .A concrete monument at the S.W. corner of Pinetum. 4.2' N. and 2.5' W. of fence corner. 25.8' E. of center line of Hagardorn road. B. M.-'B". .A concrete monument at the intersection of Hagardcrn road and the Grand Trunk Railroad. On theNorth.side of tracks. 3.5' E. and 2.0' N. of fence corner and 19.9' W. of center line of Hagardorn Road. B.M.-JG" . .A concrete monument at the intersection of’Mbunt Hope Rd. and.Hagardcrn Rd. 24.5' N. of center line of Mbunt Hope Rd. and 21.52 W. of center line of Hagardcrn Rd. 85.7' S.E. cf S.E. ccr. of red n brick farm house. B.M.-'D'. .A concrete monument on the South side of mount Hape Rd. one- half mile WEst of the intersection of Hagardorn Rd. anddnt..Hcpe Rd. 29.4'~S.icf center line of Mt. Hcpe Rd. and 29.4' W. of center line of side road. 2.6' N. of con- crete corner post of fence lines. C 35 B.M. -':'.E". .A concrete monument, one-half mile South of B.M. EE'. 52.6' W.and 4.0' S.cf concrete corner post of fence lines. 44.0' W. and 2.0' S. of 24' Elm in the N. W. corner of the intersection. B. M. 9 'F". A concrete monument at the Town Line on the East and West road, one- half mile South of MT. Hope Rd. 19.5' N. and 40.0' E. of Quarter Corner. 40.0' E. and 3.0' S. of fence corner. B. M; - ”G". .A concrete monument , one - half mile South of the intersection of Mi. Hepe Rd. and Harrison Rd. 14.0' N. and 5.4"W. of the N.E. fence corner. 22.0' E. ofthe center line of Harrison Rd. and 37.8' N. of center line of the cross road. B. M. - "H”. A concrete.monunent at the N.W. corner of School Lot at the intersection of Harrison Rd and Mt. Hepe Rd. 30.0' E. of center line of Harrison Rd. and I.4' S. of North Boundary of School LOT. r... 36 B.M.-"I". -A concrete monument on theanst side of Harrison Rd. about mid-way between the Grand Trunk Tracks and the P. M. tracks. 21.5' E. of center lin e of Harrison Rd. 2I.5' I.W. of 50" maple and 10.2' S. of 12" maple. B.M.-"J". .A concrete monument, one mile North of intersection ofiM . Hope Rd. and Harrison RD. Across the road from the Michigan State College Police Barracks. 45.0' S. and 5.7' W. of fence corner, 29.0' E. of center line of Harrison Rd. B.M.-DQH. .A square cut in the concrete coping on the N.W. corner of the East wing of the Front Steps Of Demenstration Hall. 37 FINAL ELEVATI ON M'S. ELEVATION {figte::) ELEVATICT {Fret} ___.—._;; ;”"i::f__;o-~z:_ A 2 57. 27.43?— 44 4. /2 52 0’ 257 fee 3 .452. 6 2 / 3 c 2623/35" 460.4506 0 21/345/ .454 4042 -E .Z ”6:5775__ __ - 677272323 34' .c Eggs... 3»... 24;; 6 2 53—72519" 5’45 5‘. 2434'- H_ 2 a 44/24 557 a 4.2 4 Z ,2 60.__5_'_305‘ 554. 4’0 0 6 Z 275; 54 a .44 4. 4.: 5‘4 .0 4 _ 25'6/64/ 54 0. 4744 38 THE LEVEL NET .30 3‘? 38 37 a. :L 36‘ 39 DISCRIPTIONS OF BENCH MARKS Concrete monument in N. W. cor. of intersection of Grand River Ave. and Charles St. 57.1' N. N. W. to S.E. cor. of Standard Oil Station. 5.5' N. to walk. 2.3' E. to walk. 2.8' S. to inside edge of curb. B. M. #26 Concrete monument in N.W. cor. of intersection of Grand River Ave. and Gunson St. 3.0' E.N.E. to S.W. cor. of concrete base for lamp post. 51.5' E.N.E. to S.W. cor. cf Hausr's Grocery Store. 4.0' N. to walk. 3.8' S. to inside edge of curb. B. M. #27 Concrete monumentin S. W. cor. of intersection of Gunson and Ann Sts. 1.8' W. to walk. 2.5' E. to inside edge of curb. 82.8' W. to N.E. cor. of House #289. 58.9' S.S.W. to N.E. cor. House #285. B. M. #28 Concrete monument in S.E. cor. of intersection of Linden and Bailey Ste. 59.6' W.N.W. to center of Fire Hydrant. 33.4' N.W. to center of manhole cover. 30.6' W. to water shut off valve.' 1.9' W. to inside edge of curb. B. M. #29 Concrete monument in S.W. cor. of intersection of Division and Beech Sts. 54.7' N.N.E. to center of Fire Hydrant. 3.6' W. to walk. 55.1' W.S.W. to N.E. cor. House #549. 61.8' S.S.W. to N.E. cor. House #545. 40 B. M. #30 Concrete monument in N.W. cor. of intersection of Abbott Road and Fern St. 58.3' N.W. to S.E. cor. of Heuse #531. 5.4' W. to walk. 3.9' E. to inside edge of curb. B. M. #32 Concrete monument in N.E. cor. of intersection of Abbott Road and Linden St. 46.4' E.N.E. to S.W. cor. of Fire Station. 7.8' E. to walk. 2.4' W. to inside edge of curb. 5.9' E.S.E. to center of Fire Hydrant. B. M. #53 Concrete monument in between the entrance and exit to College. S. of Abbott Road And Grand River Ave. 63.5' N. to base of signal post. 2.1' N. to inside edge of curb. 78.8' W.N.W. to N.E. cor. of Music Building. B. M. #UeseGeSe Government B.M. on N. side of Michigan Ave. near Harrison Road. 1.3' S. to walk. 86.4' N.N.E. to S.W. cor. of Chevcrlet Garage. 41.1! N.W. to S.E. cor. of House. B. M. #35 Concrete monument in N.E. cor. of intersection of Michigan and Crowley Aves. 56.0' W.N.W. to center of Fire Hydrant. 1.1' W. to walk. 0.9' S. to walk. 10.1' S. to center of Bell System manhole cover. 41 Concrete monument in S.E. cor. of intersection of Grand River and Crowley Aves. 3.8' E. to walk. 8.4' N. to walk. 59.5' N.N.W. to center of Fire Hydrant. 75.5' W.S.W. to N.E. cor. of Porch of House. B. M. #37 Concrete monument in NoE. cor. of intersection of E. Oakwcod and Grand River Ave. 1.4' N. to walk. 100.7' E.S.E. to center of Fire Hydrant. 111.9' S.E. to N.W. cor. of House #919. B. M. #38 Concrete monument in S.W. cor. of intersection of Wildwood Drive and Harrison Ave. l.l'_E. to inside edge of curb. 9.8' W. to walk. 43.9' N. to center of manhole 0 cover. B. M. #39 Concrete monument in N.W. cor. of intersection of Center Lawn and Sunset Lane. 1.8' N. to walk. 41.4' '.N.W. to S.E. cor. of House #901. 69.4' E.N.E. to S.W. cor. of House #904. 42 DETERMlNATION OF C. May 5, 1931. 3:00 P.M. 1.4-“ __4>—————<..'4_ y. ____4 A uuewesrveo‘hwa _ t \ NM. . n . s \ SN. _ l i Inna mNqummWL a mmnxemwx ovum. new J i mmm N _ hm we . set? R.\ a. ”MEN a WexN . k as - as}? net? Q m MMQN h M .1 Mac? 2 _ . - i _. new. a hex when u \N o\ . mtnx emx mauve Run 3 t w. exnmx mnm\ E News. s~n\ Mo xxthN as}... QN inmate...) axe; \ux ex . 3: KA... RN , Matthew toasts x o betxau sot? lactose... bot. .6 necks , the? 3...th \ 0 80m, _ _ ‘00 NKAKK _ 50m. . RNKRN 0\< __ 43 FORM or FIELD NOTES @4th n \\\\. muss sit %.\IOQWI $.Nxhh... .w e e \ m “.an mew yam msz NM swath mess on\ an VSnVN «meN . \ewo \oVN now ®N\ FWD he.“ NN\ i=3 eN\ S.\.\MQ , owns om! $1 Wreck i sci \NNQ . N$0\ Pom .2 on Gem Go I. mass M at newsman a Been a 32 w me wish NGQ _ seam . «.03 w . . l . “ mt a we moms. . SON ms\ a _. Nut . oo\ SNMNN W amaN L .QN _. +3 2 Nikki . emfi _ 2 i and a i Mai n\tx.\b\.QN _ \0\.\N\ RN 2 ($080“... .wkettk n\b\.\thN ,, \WXKNX RN 2 l*%o{o£_ cortex” K0 bbNKVk teuxi msxuoumx _ .0 20 \0 .QWGKXN . _ QBME mkxboom Sen _ E Batik _ boa—x Eon i i _ .ooekfi k .w .03} bkexxkok .0 .. can u 1. {W ox mm... xx W Rxoklk .RN\ he, met .85“ COMPUTATION OF PRECISE LEVELS 44 D MEAN ROD Hilda/”65 MEAN 5 M15. ’02:” 2’: 53:17::vzo OIJTA/VCE INS-3:94“ A PFROX‘ 775”” sac/(mm 07/17/00.: za—zF 2‘5 2;: D’F": "- 5“ 0‘ RODS x9. = . mm. Km: x7702 __ M. M. M. 6—25 F 3 /03/ .20 ~05 26700 51337? ~26??? 2? 5 4 “2'75? -Z.'é -04 7.6074 4.70?3 fzéfop/u 27 Z5~Zé F 6 30/4 .60 0 M7406 74683 423223 25‘ B 6 3006 60 +06 3/430 .04623—23/73 26 2627 F 3 /443 27 40/ 425.727 3.3073 #2756 23 13 3 04-46 24 770 3.4302 4.7042 4.2740 23 27.250 F 4 20/4 .40 403 7. 3—757 .4. 7703’ ——/. 375/ /2 5 4 2036 .4/ 4/2 8606 7. 2370 75/. 3726 23 28-24 F 2 /3.S‘5‘ .27 «09‘ 3'77 2.24744 40.7753 // 5 3 /4~/’7 .23 7/." 3.72/7— 4474’7 07774 /S‘ 2?- 30 F ’3 /6 £0 .34 7‘02 4 2.7/7 33’83’3 70.32954 7 B /602 .32 7‘06 6.4/4.9 6.20/4 03.470 /6 30—34 F '3 -/4/57 .24 “—04 4.5420 5.7536 ”7/676 24 £3 3 #432. .29 402 57552343970 27/653 24 37—300 F .6‘ 2/00 .42. —-04 /0.4’/// 8.7557 +/65.S‘4 20 5 0‘ 2707 .42 40/. Mfg/7 054%? 4652/ 22 34—37 F 2 /0/6“ .20 ~41 3. 8733 2/7/3 // 7020 /7 5 2 /007 .20 —27 2.0427 3.7453 -/ 7026 20 37- 36 F 2 7/7 24 05“ 3/423 2.0570 #/373 /J’ 5 2 422 44 436 /.67/6 24277 “/4341- /7 1+5 COMPUTATION OF PRECISE LEVELS 60/?th 7/0”: DIFFERA‘NCE 0F £15m 770/v CORY/I TURE L E/VG I'h‘ TEMA DIVER - mm ””5" ”w" a; a; EACH L/NE MEAN saves REFBOCD'OV [RPOR ERROR R00 R00 6 -' F 177/77. ”7. ”7. mm. m. m. mm. M M mm 0 0 .2 ~2.700/ -2aé7¢2 7/“? p 0 .-2 7‘2. 6 ¢X 3 0 0 .2 +2.3225‘ 2232/0 -3.0 0 fl .2 --2. 3/?6‘ A: 0 0 Q {L ./ +/. 2757 7‘ /. 2750 —/.4 "3/ ‘fl/ Q\ -/ -/. Z 740 fl :7 J a -'/, 375/ -/. 373:? “2.6 .1/ _.,/ § ‘3 ./ 7"/. 372 5' . 7‘./ r./ x \Q 7 740. 77.515" 7‘ 0. 776 6 +22 . g 0 0 2 “4 0 20.3384 +0387? —-/.2 —./ 0 It ./ ~0. 3 ?72 N ‘3‘. 0 0 § § / --/. /6 77 —-/./éés‘ -2.3 fl 0 3’ \l ./ 7'/. /0 5‘4 0 0 ‘ 1‘; / 006551? 2065738 fz.7 0 0 g E ./ “A 6 532 \ \0 f-/ 7‘./ < +/.7023 207023 0 7&2 7‘.2 —-/- 70 2 3 0 0 ./ 1‘/./374 20/3 7/ 20.6 7.3 —.‘:3 ./ -—/./3é§ COMPUTATION OF PRECISE LEVELS 46 MIA/V R00 Rae/N65 ”MN FORM” ”0 SUM OF R00 ”00 APP/am. rt”)? B. M '5. 0"? 0” ”erRvALs OHM/ms ’N’E’MLS 01/7: or- a. or mww arAT/avs I'd-2F to 2'; R005 *3/2= mm. xms. mm. M. /V. M, 36— 35‘ F 6 2/04 .42 ~06 42.973 5.67% —73723 24 13 6 207.? .42. +02 /3.37/2 3. 72/3 773599 2/ 35—0365 F 2 /5‘?7 .23 70/ 4.2456 34223 20.8233 zé ,. 8 3 .0400 271.0; 45677 573587 072/0 27 0503-33 F 6 2926 .60 0 #7724 6.7759 745.0965 23 5 '6 2950 .60 M4 6 3-787 ”.4725 1510738 25‘ 33-6 F 4 /’335" .27 7403 5.572? 6.0578 0532?? g 5 5 /369 .27 0 77.734 7.7554 76.53000 30 30‘ ’52 F 3 //€ 7 .24 7’73 56767 47/20 20.?f47 5" B 3 /20/ .24 «05- 76320 56/37 4.7/60 /7 32-33 F 1 - 684- ./3 0 0.7700 2025-4 #7375 n? a / 6?? ./3 ~02 2.0207 0M/7 #7350 /$’ fro/3" F 3 x36? .27 7‘// 5/334 54707 «0.3033 33 5’ 3 /378’ .2? —-02 5356747736 r0343/ 27 1+7 COMPUTATION OF PRECISE LEVELS CORREC r/oxvs DIFFEREME 0F 52 EVA 770w cmrm: ,1va was): t [NGTH TEMP. DIVIR - AND gnaw? ERA”)? OF OF EACH L/Nf MEAN iii/:5 Erratum R00 R00 A . . mm mm mm. mm. mm. 11/. M mm 0 0 .7 -9. 3732. ~7-3‘7/7 ~25“ 0 0 .5? 7‘ 7. 3707 , ./ 7‘fli234 +0527” -252 t/ +./ K ./ 08207 Q 7 0 \h‘ is + 5- 0770 #370756 —2.7 fl 0 ‘0 g 6' ~5'. (7743 N ‘K‘ s V . - 0 0 g ./ ~fl. $370 ~05386 -0.9 0 a v) 19 ./ f§- 538/ V: “\‘ . h g\ ‘0 u A -./ -—./ 9:) “in 0 7‘ 0.70046“ + 0.7753 7% 6 p 0 ./ 'fl' 7? 6/ a . E .‘l . 0 0 g “X ./ */. /37? —-/. / 350 +03 7‘ ./ 0 § ./ f/ / 3 5 2. I \l 5‘.) x 3‘ $3 .. .. < \ ./ ../ ./ «7.3636 -0.3634 -04 5 . 0 ./ 7‘0. 39 32 48 ADJUSTMENT OF CIRCUIT L/NE DASH/WE MEAN DIFfE/PE/VCE C 0"? R[- COPPfofD D/fFfRfA/(E ms. c770/v + - + -— 0~25 .30 2. 6772 -.2 2.6774 25-26 .70 2. 3 2/0 -.5- 2. 3205- 26-27 .43 /. 2750 -.3 /- 2747 27—27 .60 A3737 -,4 63742. 2 i -z 7 .4/ 0. 776 6 -.2 0. 776 4 29- 30 .77 0- 3375’ -.3 0- 3875‘ 30-37 .42 /./665' —.3 /./667 37-— 38 -6 3 / 656 S" —.4 /. 6564 37—37 .30 /, 702 3 --.2 /.70 2/ 37-36 .27 /«/37/ —.2 /./367 36—35 .63 7 37/7 —.4 7. 3723 35-0565 .42 0. 5’2 2/ -.2 0. 72/7 4565-33 .70 570756 v.37 5‘. 075/ 33- 6 .40 0.5376 -—. 2 0.533;? 7/0 /.5“. /7 4 3 5. /70 0 4.3 /5. /7/5‘ 577/5 /5‘./ 700 C/nzc/v Error 4 3 30-33 . 6 0 0.0767 30—32 .4/ 0.7753 72. / 0. 7574 32 -33 ./7 /./33-0 70.7; ___ /./34/ .60 0. 7753 7/350 30 0. 7X74 /. /34 / 0. 7753 0.75774 0. 07 77 0660/? 0/467 0/467 Err0r' 3.0 6 — 03 .42 0. 3 634 49 FINAL ELEVATION B. M'S. ELEVATION (Meters) ELEVATION (Feet) 6 257.822] 852.433 25’ 257/227 5’43. 577 26 257-4432 75/757 27 260.7/77 5551372 27 257.3437 850 763 27 260/20/ £53.4H 30 260.5076 5754.662 37 257. 3407 5750. 5’54 3.? 260.7772 756. 2.9.9 37 2626773 86/. 973 36 263. 73 62 765‘. 603 35 254.4437 834. 7760 0565 255. 2657 737.774 3’5 260. .3607 354. 20/ 6 257.9221 352.433 7 30 2605076 854.662 32 26/4750 0057. 72/ 33 26 0360‘? 754.20/ 22.0. 2574587 605/.24/ mm. Calputations for the Adjustment or Lam cumin by the Method. of Least Squares . Oondit ion Equation ’- Y W +1 .1 7.1 + I O -I + I Noml Equutionn T'- A B + 2.0 F’-I From equation II, sot B 225 B +7235 ----‘o B: “42054 Substituting 3 in equation I, set. A 2 A+42054+£+£3 o a= 1-4317? carnation for Line 6 4- 25 .30 _ -. 7:“ (“40177) 7- T-_ 002“. ‘.‘b 1‘ ‘- J, 57”," - . . ‘ :.. v. . D is», .I' . y. . CHI CAN 8T TEAT EUNIVERSITY LIBRARIES "III IIII III ”am 031 2 IIIIII“IIIIIIIIIIIIIIIll