Nadal dl lt hl tld tie Ae Le
&
c : ; ye
t
r
f

Seto) ae

PRECISE LEVELING :

Oar an eee ae
a
Seca eT nec ea eee ae
yea UL :
rae ANDERSON Rs Cc. Ea :

 

 

ee as
THESIS
THESIS

 

 
PRSACIOSS LAVELING.
TO OBTURMINE THE ACCURATE ULOIVATION
OF BANCH MATISS

ON TH MICHIGAN AGRICULTURAL COLLiGs CAMPUS AND PARI.

A THSSIS
submitted to the Faculty of

Michigan Agricultural College

by

H. F. ANDSRSON . R. C. “HITH..

Candidzetes
for the

Degree of Bachelor of Science.

June 1917...
THESIS
PRuFACH.

The reason for underteliin. this work
was, first, to ascertain the accurate elev2tion of the
Bench liarxks on the Michigan Agricultural College Camnus
and Ferm; second, to attest to the correctness of the
results.

The elevation of these Bench Marks had
never been determined by Precise Leveling. Some of

tne elevations were knovwn to bs in error by as much

In performins this work we have con-
formed with the methods used oy the United States
Coast and Geodetic Survey, which are later describea
in aetsil under the section entitled "Instructions
for Ficld ork".

As en aid to our work ve have referred
to the U.'..C. & G.S. Revorts of 1909, also to Ingram's

——_

"Geodetic Surveying".

93774.
INDEX.

Pace.
2ection 1. Datum vlane for elevations above sea level. Ke
section «. The leveling instruments Oe

Adjustments of the level C.

Rode and turning yvoints 8.
cection &. Instructions for field work 10.
Section 4. The field work 14.
section 5. The record 1é.
section 6. Errors in precise leveling 18.
~ection 7. Description and location oz: bench marks wO
section &. Commnutations OD e

INSUSRTS.

Views of instrument Oe
View of rod and party in action Sa.
oample pase of notss 17a.
Com utation of "C" L7b.

1 tech of level net 4a.

tm
section 1. DATUM PLAN= FOR ELEVATIONS ABOVE SiA LEVAL.

opirit leveling is the name applied
to the determining differences of elevation by use
of the leveling instrument.

The grade of leveling used in carry-_._
ing accurate elevations from the sea coast to the
interior of the country is called vrecise leveling.

The datum plane to which all elevations
are referred is mean sea level as determined at points
on the sea coast by continuous automatic tide cauge
records extendin*s over a period of several years.

The mean of the hourly elevation of
the surface of the sea as scaled off the graphical
record is taten as mean sea level and is assumed as
being the same for ell vnoints on the surface of the
several other oceans.

This hes been proven by running a
line of precise levels across the United States and

also across the Isthmus of Panama.
%—

section <. TH LEVELING INSTRUMENTS.

Previous to the year 1900 the precise
leveling of the U.S.C. & G.S. was done with the
suropean Type of instrument. Commencing with the
summer of 1900 this work has been done with a type
of instrument designed by the U.S.C. & G.S. and is
<xnown as the Coast Survey Level. A vie. of the level
is shown on page Ja.

The instrument is essentially a dumpy
level, as the telescope does not rest in wyes, cannot
be removed from its supvorts, and cen meither be
revereed or inverted.

The base of the instrument is of the
usual three leveling screv type excent that the center
socket ic unusually lons and extends downward through
the trinod head. An outer vrotectins tube, through
which the telescope passes, is rigidly att=ched to
the vertical axis,

The telescove is pivoted at one end of
this outer tube and has its inclination controlled

by a micfometer screw at the other end.

The collimation adjustment is »erman-

ently fixec by the maker.
 

 

-—3a—

VIEWS OF INSTRUMENT.

 

 

 
—4—

The level tube is attached to the tele-—
scope, but has provision for adjustment. The strong
point of the instrument is the proximity of the bubble
to the line ot sight, the level tube beins let part
way into a slot cut in the top of the telescope tube,
the top of the level tube comming approximately flush
with a slot in the outer tube. The level vial is
chambered for adjusting therlength of the bubble.

The level reading device deserves
esvecial attention, as with it rests the credit for
much of the superiority of this instrument over
ordinary tynes.

Attac*’.ed to the left sice of the
instrument is « light auxillar; tube throuch which
an imase of the bubble may be seen with the left
eye while the right eye is observing the rod. The
tube is adjustable sideways to suit the eyes of
different observers. Besides the icns in the eyepiece
the tube contains two prisms, adjustable for len:th
of bubble, and placed opposite a slot running abreast
of the level viel.

The bubble is brought within the view

of the left eye through the eye lens, the two prisms,
and a mirror 2ttachead to the telcscone.

The vial is of the chambered type; it
rests within the level tube upon the ends of four
smali screws, two at each end, and is hela in place
by a flat snring at each end. Tow cork rings hold
it in place longitucinally. The method of setting

@llows the vial to exnana and contract independently

of the meval narts of thse tude.

(

The reticle has one vertical ana three
horizontal cross—hairs cemented to the reticle ring
which is hela in place by four screws which screw
into the ring. These screvs are covered by 2 cap,
screwed on, to ovrevent injurv, anc give a smooth
finish to the level.

The telescone tuve and outer casing
ere made of a nickle-iron alloy that has @ cosfricient
of exoconsion which is only one-fourth that or brags,
while the micrometer ecrew and other important ccrevs
are made of nickle etsel hevin=s a coefficient of
exnansion as low as 0.000001 oer decree centigrade.

This level has two constants and one

adjustment.
J

oection « cont. ADJUSTLIINTS OF TH: LEVEE

vhe only adjustment of this instrument,
which should be made daily, is es follows: TO MAKE
THs AATIO OF THe BUBBL: PARALLEL TO TES LIN= OF SIGHT.
This aciustment is made by the ordinary pes method,
the butBle tube bein: reised or lowered at the
acjusting end as mey be required. The cross-heirs
must not be disturbed at any time beceuse they huve
been permanently adjustec for collimation by the
macer cf the level. In testing the acjustment the
rod readins is taxen ac the mean of the three cross-—
hair readiness, and the rod intervel as the aifference
between the outside cross—hair readings, the bubble
bein: kent exactly in the center while all of the
three cross-hairs are being read.

Two turning voints ere cot about 100
meters enert, each rod bein: kept on its own point
if tro rode ere used, or one roc bein: shifted ar
the case recuires.

The level is set upd avproximately in
line with tha two points, first about ten meters
beyond one point, and ther. about the same distance

beyond the other point.
The rod readin, is taken for each
point and for each position or the instrument, the
terms “distant rod" and "neer rod" beins used to
indicate the relative vosition of the rods for each
set uv.
Now having taizen the four reacings
ve have
(sun of near rod readings) — (sum of distant
Cc rod readings)
(sum of aistant roc int:rvals) -— (sum 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 chens: the
adjustment. The telescone looks uv when C is
ressavive and down when C is vositive, so that is
an adjustment is necessary the line of sicht (here
aken es the middle crogss—hair) is raised or lovered
on the distant rod by C times that distence, anc the
bubble tube adjusted to bring the bubble to the center.
A corr:ction ecusal to C times the excess
interval between the foresishts and backcizhts is

annlied to the final elevation; if the bacsichts are

in excess the correction hes the same sign ag C, and
if the foresights are in excess the correction has

the onposite sisn.
oO

~ection & cont. RODS AL TURNING POINTS.

The rods used in precise wor are
vecod meters longs and are craduated in the metric
system by the U.S.C. & G.S. The subdivisions on
this rod are to centimeters. No targets are used
but the mean of the three cross—hair reacings is
taken out to tentns of millimeters. The wood of
which the rods are constructed is treated with
varafine to prevent absorption of moisture. A
“wateh slass* bubble is fastened to the back of the

rod and also a thermometer readinz to dersrees cent-—

igrede is set in the rod with a wooden slide neer
the handle used for carrying anc also to afford a
sriv for holdin: the rod plumb while a reading is
beings teken.

The foot of the rod is = small bronze
eylinder «ith a besrinzs face the segment of ea snhere.
The center of this face is directly in line with the
face of the rod. ‘The face of the rod is tvo centi-
meters wide, and has a line running covm the micdle,
the centimeter scuares of the rod ere painted
alternately blac:: end white. The meter and decimeter

sraduations are on the body of the rod to centimeters
-8a—

IN. ACTION.

PARTY

 

 

 

Rov.

VIEW OF

 

ae

if * I te ta

ra Sv

      

 

‘ie ous

n

 

 
back of the face. Tivo silver plucs are set into the
face of the rod ror comparative mezscurements with a
steel teps. As shown in the illustration, the fissures
on the rod are so formed as to read with an inverting
inetrument.

The turning points are cast iron foot-
olates about six inches in diameter with a socket
about an inch and a helf in diameter for the bronze

.in ebout two

ia

cylinder oi the rod to sst in. aA ch
feet lons is attached to the foot-plate thus enabling
it to be carried very easily. On the bottom of the
plate are three steel snurs about a half ineh in
lenzth which hold the plate in position after it has

been firmly placed.
-~10-

eection 5. INSTRUCTIONS FOR FIELD VORK.

1. All lines are to be leveled ind-
evendently in both the forward and backward directions.

ee The line of levels is to te broken
by temporary bench marks into sections.

Se The vrogram of observations at

each station i¢ to be as follows:-

set up enc level the instrument.

Reau the three lines of the diaphragm as seen
projected against the front (or rear) rod, each read-
ing being taken to the nearest milimeter (estimated),
and bubble bein’; held continuously in the middle of
the tube.

4. At each rod station the thermometer
is to be read to the nezrest degree centicrade and the
temperature recorded.

So. <At stations of odd numbers the
backsicht is to be ta:en before the foresight, and
at even stations the foresisht is to be taken before.
the becksight. As the same rod is held on a rod
stction for both the fore—- and backsights, the effect
of this is that the same rod is read first at each
-1ll-

setup, it being the rod used For ths becksight at
the first instrument station.

6. The cifference in length between
a2 foresight and the corresponding backsight should
not exceed ten meters. The difference is to be made
as small on each pair of si;nts as ic feasible by the
use of soca judgement.

7. The recorder shall keev a record
of the rod intervels subtended by the extreme lines
cf the ciavhrascm on each backsisht, together with
their continuous sum between bench marks. A similar
record shall be kept for the foresights. The two
continuous cums shall be kept as nearly equal as is
feasible, by setting the instrument beyond (or short
of) the middle point between the back and front rod.

8. Every morning before starting
worx the error of the level should be determined.
Take a readings on the rod about 100 meters dist«nt.
Then take a reading on the back rod about 10 meters
distant. Move the instrument to a position ebout
10 meters behind the front rod, read the front rod
and then the back rod.

The rod readinzs must be tceken with

the bubble in the middle of its tube. The required
-~1e-

constant © to be determined, namely, the ratio of
the reguired correction to any rod reading to the
corresponding subtended interval, is

(sum of near rod readings)=—(sum of distant rod

 

 

readings)
C Csun of distant rod intervals)-(sum of near rod
intervals)

The level should not be adjusted if C is less than
0.005. If C is between 0.005 and 0.010 the observer
is advised not to adjust the level, but if © exceeds

be made. Ir 2 nev adjust-

cr

0.010 the adjustment mus
ment of the level is made, C should at once be redet-—
ermined.

9, Notes for future uce in studying
leveling errors shall be inserted in the note book,
incicating the time of beginnings and ending the work
of each section, indicating the weather conditions,
especially as to cloudiness anc wind, indiczting
whether each section of the line is run toward or
awey From the sun and such other notes as mey be
of value in studying errors.

10. The instrument shall be shzuded
rrom the direct rezys of the cun, both during the
Observations ana the movement from station to

station.
-135-

ll. The izaximum lensth of sight shell
pve 150 meters, and the meximum is to be obtained only
under the most favorable conditions.

lz. The field computations cre to
be kent uv es ths work prorresses.

1Z. The allowable error is to be
ara Xn.

14. Rods should never be laid on

the fsround or taxen off foot-—pletes between readings.
—]4-

Section 4. THE FILD VORK.

The precise level as used at present,
weighs with the tripod 27: pounds. The increzsed
weight of the tripod to enable the observer to stand
erect is more then offset by the advantages of being
able to worx in this position.

In leveling uv, after the instrument
has been set and the legs of the tripod clamped, the
level is unclamped from the tripod, the wetch glass
bubble is brousht to the center of its run, then the
micrometer screw is set at its reversins point,
(determined by reversing the instrument 180 degrees
and brinsing the bubble helf way beck to the center)
and the leveling up completed by placing the telescope
over two screws and bringinz the bubble to the middle

of the run, then over the third screw. It is
nececser, in levelin:; un to loox at the images of
the bubble in the mirrors.

It is necessary to keep the level at
all times protected from the direct rays of the sun.
A large wagon umbrella is usec for this purpose. It
also serves the double purpose of protectins the

instrument rrom vibrations caused by the wina.
~15-—

when reacings are bein: taxen, the
rodman shoulc hold the rod on the voint marked, one
nena grecoing the handle ane the other raissd 2vove
his heed to steaay the roc as hich un ae nossiole.

In hich winas, the knee cen he uced to steady the rod.

cr
oO
ra
©
$
ry
cr
‘7
>
@)
©
r3
ct
©
Fy
Oo
Hh
ct
x
wm

The bubble should be kep
watch -~lase asc possible. The face of the rods should

be kent cleéen.

~

After the readings have been taken
and befors the instrument has been movec, the recorcer
iicures the wire intervals. If they do not ciffer
by more than two mm. he eeye "check".

The sights ere kent nearly equal by
pnecin;. When the adiscrezancy of the continuous
sum of intervals reaches eny considerable amount,
the recorcer notifies the observer by callin: the
foresizshts long or short, as the case may be, telling
him also the number of intervals discrepancy. At
the next cet up the observer ecualizes the sishts

by setting ahead or back of the middle point.
 

~16-—

Section 5. THE RSCORD.

The record has opposit3 pases for
back- and foresicshts. These pazes are identical
with the exception of the first column of each. On
the bacxsigsht pace this column is used for the
recordings of the number of the instrument station,
On the foresight pase it is used for the cesicnating
letter of the foresicht rod and the temperature of
tne backsicht rod. The second column ccntains the

ings of the three cross—-hsirs 2: siven to the

ow

Qn.

ree
recorcer vy tne observer. The third contcine the
moan Of the readings, the fourth the differences
betveen the first and sccond and the second and thira
and their sum. The fifth column contains the
continuous sum.

The mean is tazxen out by the following
chort method: the gquentities in the fourth column
ave conputead at once, then if the aifference between
readings of ths first and eecond wire is equal to
the difference betveen the second and third wire,
the mésan is the reading of the middle wire. If the
latter is one more then the former, add 0.5 to the
recding of the middle wire; if t.o more 24d 0.7; if

less, subtract instead of adding.
-17-

5

A aifierence of more than tvo ise

seldom vermiss2ble in »reciss work enc indicates a
toc hesty resacins:. The recore choule be maae in

v

isecsble. Footinss and

3
©

ai

rs

K, anc no erarures 2re

®
I+
waite 9

commutations of difference in elevation are mecde in

sancil.

a
 

-17a-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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LIdlaS

 
section 6. SARCH IN PAnOIoU Lav LIne.

urrore are of two clagses: comcoen-

all errore in @sti:.ete

3
oy
@
on

+:
a

(9

seating ana cumulative. T
ing millineterse, in holding the roc on th: turnings
mnoint, ena in the -osition of the bubble beleng to
the former class. If @ ressonavle exnount of care
is tazen in the execution of the work thes2 errors
tenc to cencel out.
arrors due to ricin. of the roc

suynoerte, to eettlins of the inetrument betvecn
~ointin.s on fore anc bee: recs, snc errors duc to
UnscUual refraction on croades belongs to the latter

XN
a

cloes,.

instrument between cointi.gs is eliminatoa oy reaaing
the eai.e rod firet at each sst-un, thus waking the
orocess a2 evmrmetricel one.

If a too hesty recscin: is ta-en, the
bubble msvr not be in the exact center or the tube.
A few seconds should always be civen it to come to
rest. when & reasonable eaemount of car: is tahen,
any error due to small cisvlecs.ents or the bubdbdle,

is coOnvensating.
-~19-

The accurate check, so-called, is made

9

by divicinz the sum of the thread readings in the

ww

first column of each vage by three. The result equals

the footins of the backsight (or foresirht) column
or agrees with it within the number of residuel tenths

vnich have been eddec or discarded at each reading.
Section 7. DESCRIPTION AND LOCATICN OF BUNCH LMIARKS.

Note l. This station mark consists of a copper
plate 5" in diameter set flush with the surface in
cement and having 2 horizontal bar across the face.
Note &. This station mark consists of a cross

mede with a hammer end cold chisel.

Note 3&3. This station mark consists of an iron
pipe.
Note 4. This station consists of a 6"x6"x4!

concrete vost set flush with the surface of the ground
and having in the center of the top an iron or copper

bolt with a punch marx in the center.
 

B e hi e 1 °

oe In front of Dean
rio

Shaw's House 50! south of S. i.

 

 

§

corner of Shaw'ts House and 6! VV.
of S. #. corner of Said House.

Liarxed as in Note 4.

147! N. 2. of the ARMORY.
I. be corner of the new Cymnesium
and 136' S. %. of the &. “. corner .
of the Armory and 6! N

Nw H. of Everrcreen Tree.' 7"!

Marked cs in Note 4. nas
My

 

  
Boi. 3:3.

— f In front of
 -Bref..Vedderts House. 45!
S. 5. of Evergreen Tree and
68' S. V. of the S. W.
corner of Yedderte House
and 33' N. .. of iron
hitching vost on drive in
front of House.

Marked as in Note 4.

B e kl e 54 e

In front of — :

Taft House. 15.5' South

of the Main Drive, <6.4' ast

of shrubbery. An elm 6" diam.

on North side of road beers NS7

 

 

 

 

 

 

 

 

FROF VEDUER.
HOUSE
ie
x

= ~~~ “nay /OST.
< MAIN DRIVE.
DRIVE. a
4 N
4

2) 24“/APLE.

24 "Bass woOon.

 

Or
wd

distant 3S'. Other references are;

a maple bearing S70°E distant 55', 24" diam; and a

bacswood 24" diam., bearing S40°E distant 64.6!

Marked as in Note @.

 
7 43° fle
~/ @3.-6 rr?) e

~@st and North
of Collese Hall just N. &. of
fountain.
neferences:-—

Newe Corner Collecse Mall
to i. 66.5'3 M.0). Corner Sint:
of fountain 7.<c'.

Niarked asc in Note 4.

“”
'

Directizx in front

of library anc near ton of
Slope up to Collese Hall.
References;-—-

lL. U.E. Corner Cclleze

reali 276° Scots, adistence

SOel!';

€ ee Je Man "Ce
we CE! aaou LEUS, Oe

. *
“ee a OW

ct

fn . re
a2

ae 0
tw A! @ WL 3 A

disc-

bd

rire Hydrant 533
tence 78.0'; 4. Svergreen N9°%
distance <3.%7!,

wearked as in Note 4.

 

 

 

 

 

COLLEGE
HALL.

 

 

  

 

 

  

a...

—jp-~

 

 
 

 

 

 

24
wn
J
350, }

Behl. 527. User jh te groomer

Y

In lavm North Z

Hor BEov. Uy, GREEN
nda. e Gree: . iy
an est of th reenhouse i HOUSE
le' N. of 2. line of Greenhouse Z

Lil

 

and 75' “'. of same.
References:-—

Water plus to N. = 50.8! (1" vine); Iron clothes vost to
em 2D.0's NE. Corner Hot-bed Vall - £8.6'.

liarized as in Note 4.

B.M. :8.

In front of Woman's Buildins.
70' NV. of end of walk in front of
buildings and S05! S.W. of S.17. side

of Main Drive.

 

Marized as in Note 4. N >

— 4

 

 
 

B.M. #9.
In front of Bacteriology

 

Building. 7.5! NW. from the center

 

 

line of walk leading from building

 

and 8" West of walk leading to

 

Horticultural Building.
References:-=
Fire Hycrant to HE. - 10.5'.

lwerked es in Note 4.

B el. e a1 e
On South side of poad

passing Agricultural Building, at

 

 

N.W. corner of pasture lot. ¢——s_o 2 AT
Be ‘ . &Srows. -
2e6' Nw. of corner post e _

 

 

at South side of large

  
 

boulder 3" beneath the AGRICULTURAL

surface. BLDG.

 

References:—

N

r

Noa. Corner Farm Mech. Bld=. 18.e' Bearings ‘i.
3.0. Corner Agricultural Blds. bearing I'.i1. and.

Varked as in Note 4.
 

3 okt e +7LO e

 

 

Qn farm

er

Situated 35.5! 3.5. of N ~<

 

lane
concrete fate post at South

sntrance to Campus and 17' “. of East fence.

References:-

Corner fence vost -—- 'N.4. 37!

rerxead as in Note 4.

Cn East side of

iain Drive 55! North of old

  
 

culvert wall at road to athletic

field. ——
s << To ATHLETIC Fiend

Referencss:-

 

1. Iron electric licht vole
56.9' N.3 2. Cax tree on eage of

bank to west -—blazed—- 54.5!

NMartzed ac in Note 4.

Wen\ Ce AR Fiver
- 2

Bolt. 3717.
At intersection of ‘sin

 

SENIOR

\ . . i
Drive and Sentor House Drive.
HOUSE

Vea. 8
References:- 3... Corner of Senior
Heuse 1lcO' N.e.; Fence 30! South.

Oy
4. e

warized ac in Note 4
MAIN DRIVE.

On athletic field just next to

curb on couth sice of running track.

neferences;—- 35.. Corner of Grand Stand 146!

=,

5.8.3 Curve in Curb 2d! 2.5.
Warizea «Ss in Note 4.

 

 

ATHLETIC FIELD.
> 2,

 

 

 

 

 

B.M. +419.
About 450! West of B.i. 3517 and
North of the Main Drive.
References:=
shrubbery ¢3' North; lain Drive <0O' South; Pine
Tree 50! S.iv.

Marked as in Note 4.

—~ 2

7

- . if
BM. 720.

In Elm Row across street from 216 Michigan

 

Avanue.
References:i-—
8' Ss. of South Rail of

1eU.T. Co.

 

 

Varked as in Note 4.

 
> 2,

B ele ole

 

In culm Row
on South side of 1°.U.T. Track
and .est of Stone Valk.

References:-

 

. Rail M.U.T. 7' N.W.; Stone Walk V
15' N..

Marked as in Note 4.

B.M. Bae | N
Southwest of Greenhouse

on South siae of River Drive, 5' from

 

g
J
“South edge of Road.

References:—

  
 
  

A & on South trunk of double

o2k tree distsnt 16.86! to

Bo JIOUBLE OAK
wy 25 SLA,
bastvard; A A on main Ta CULVERT é a LAE E
OAK Crump SIAPLES.
trunk of a clump of maples to & I

  
 

South distant 17.5'; An Oak to S.%. RivVeRR
distant 17.7'. =", A

Marked as in Note 4. BE
1° i .
B.kie Nh D.3. DA Ry
On S.E. corner stevs BUuI/oinc.

 

of Dairy Building. ¢

References:-=-

 

3.5' S. of Dairy Bldg.; 15° &.
of Center Line of Dairy 3ldg.

Marzed as in Note é.

B.M. -“-ABUT. \

On S.%. abutment of Farm

Lane Bridge.

 

LANE.

 

 

Reference: —

 

10' wi. of . side of Bridge.

Mervzed as in Note <c.

w ‘eZ
AeuT.”

FARIN

 

 
: hte.

On Vest side of Farm Lane

about 400' South of Bridge over
Red Cedar.
References:-—

18' S. of N.E. Corner post of

Field 8; 15.5' BE. of EH. Fence Field 8.

Marked as in Note 4.

On West side of Farm Lane

about 900* South of North Base.
References: —

513* S. of N.E. corner post
of Field 10; 12.5' E. of E.
Fence Field 3/10.

Marked as in Note 4.

%
0
<=
4
w
hs
©
S
ae
a
eo
———4____4____4__4__f

Fietp No./0

 

3/3"

 

FARN LANE

“

 

 

C

;

FARM LANE.

 

 

{

2
~32_

Belle (GOV. 3.0. HiR. AVG.
MicnH. AVE.

Across the MUS

 

  

 

vv F¥-UMEUCOUMTTC‘“W

 

road from and nearly in front
of the "Vhite “lephant" 33! N. of
the center line or ilichican Ave.,

61l' N. of center line oi street cay
track; 61' |. of sidewalk crossin;

-—

Miichican Ave. U.:=.G.S. Iron pipe 10" above surface.

Merked as in Note &.

Cross cut on curb on
.@st side of Pennsylvania Ave. (Lansing,
Mich.).

References:- l1' N. of Televhone pole

AVENUE.

 

 

 

 

eoee on curb.

 

 

Merked as in Mote &. { MICHIGAN AVENUE.

 

te |

 

 

VAN/A

nh J

#2326

 

 

 

( Pennsn
B e he e woe e 8B e

7.5' West of S.:¥. corner

 

of porch on weather Bureau, Copper

 

 

 

 

 

 

dise cemented on top of step.

 

 

Marked as in Note l.

B.kt. <-FCR.
2" Gaspipne 6! Kast

of sast fence Forestry Plat

 

 

    
   

WEATHER
BuUREAu.

 

and 63' S. of center line (
of P, lh’. spur.

Merked as in Note 3. N

 

 
 

 

Cpe

PM. SPUR.

 

 

For. DRIVE.

’ FOR. PLAT.

 
 

Bolt. oS 18°

Situated o4' south of the Northeast
correr of the it. C. Depot and 14.5! Worth of the North
Side of the smoxin=s Boom door and £.16!' above the
Davemcilt.

Conper dise set in cement in “ast wall

of Li. ©. Denvot at Lansing, lich.
—$J49—

NET.

SKETCH OF LEVEL

 

 

48

 

 

For

 

 

 

15

Abu7

N&

 

(5.8
~35—

Section 8. COMPUTATIONS.

The corrections used in these computations
were taken from tables given on pages 2.7 urd 2c of the
J.5.C. & GS. Special Publication #18 titled "Fourth
General Adjustment of the Precise Level Net in the
United States and the Resulting Standard Elevations".

The Level Error was obtained by multi-
plying the difference in the continuous sums (B-F) by
the level constant 7C". The former quantity is given
in column 6 of the left hand nage of comoutation sheet
and the correction is »nlaced in column & of the right
hand page. The sign of the correction is fixed by

the signs of the ahove two quantities.
=36=

COMPUTATION OF PRECISE LEVELS

MEAN Rop READINGS.

st. Sum oF Roe
A-
INTERVALS.

xB-EF; ze ZF

27247 4.3/7
b635G0 --3oF

 
COMPUTATION OF PRECISE LEVELS

CORRECTIONS.

LEvEeEWU
Reerac- | ERROR.
TION.

INDEX |LENGTH TEMP.

ERROR ROD. ROO.

ry ry. mrn.

t.4| 0
; —,/

——

t. O

Aa
x

a
x

DIFFERENCE OF ELEV. oN

EACH LINE MEAN

Zz 2,3)06S5
~2. 3|25/
-%, Jo
#2, 3\0

SYS ITO
— ¢ qo

-—GFlwt
+4: /

 
-
-oOs-

COMPUTATION OF PRECISE LEVELS

‘ E ROD MATE.
pacx-| STAr/SUT DISTANCE || TEMP.

WARD INTERVALS. $B-5F = B SF Dire. oF
, . yn 77M. mt. c~1.

F 2/3 - 3 I¢C&ko c SAL Z04N 132°

27> , 44 -/0 , 266, 3|-43096| 42-

oF
ROO0S.

0,7| S16%/
FS, SF /,

+ 47)\ 3070, o ¥ 4%.
FEY |2G S10 02.7\|-.02/ Sa

IDF | 2ASo00, ¥|42.4
FS. 3\| #7932, 0\—2.397

 
"S ¢

COMPUTATION OF PRECISE LEVELS

 

CORRECTIONS.

DIFFERENCE OF BLEVATION

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

converte LEVEL INDEX Langrt Teme EACH LINE. MEAM™. Gence.
RErRac- ERROR. | © RROR. Roo. ROD. B-F-
77. 1 PT. re wa. mrn. m EN ers. mM Ets. my.
-3| o| SS x 0 | ¢thaAck#t | rh3loze | 45/7
%F7| -/ mK | Ss O | —A3\075"
\G N\
<TR
#+.4\ oO Ss d ft | AB. STEPS Ff S\IOF | ABST
KIL FS |S Xe —f | -25/726
XN LS
1) IN
~,/ O RN N O FO 0\|226 FO,0\224 |-oOS
—_ oO Rm iy O -O,GQ22/
> | &
WY NX
SS
t#4| o | SIN | 4235977 _ | 42397F | 4OS
¥+,2| —/ ty .f -2,3/977
> K
STR

 

9

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
~40-

COMPUTATION OF PRECISE LEVELS

MEAN Kop READINGS

DIFF, OF

EB-ZF =B oe

=f;

—

 
COMPUTATION OF PRECISE LEVELS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a”
CORRECTIONS. DIFFERENCE OF ELEVATION.
DivE R-
“GEES eicta [ets MEE EET | even ee [ean ire
ae m™m rr. wry. mr. rr. METERS METERS. mm,
O O _2/ —SZACIST 3 te fo S-h- 2
—2| -/ » 2 | £25045
. N
Se Tt
—-/| io QR) YW | 7” | 4adls3th | ra38es7 | tb
fF. 2| —/ o / —-O,8\S5S37 :
R S
yy XK
—y7| ~/!) © |... 1.7 | 40 426 | #o,glasb |e
o |S
XN 9
4.5 | —. S| AS 2 |—-ZfY297 | -Z2 AVS | FF/
4#2| -7| ~ [NN | .2/1|43.4%6e0
~ \
wWvd 7
Aw N
x2) —-y |. SS ~1 | C2ZSSS | 4 2/47F | KZ
—/| 4#7\| 5% 3 af | ALUUGIF
NX N
~)
=~ N
+/\ —S | , 23 | ¢O.2n5SY0_| 462% 34 | +3
—4Y) +,7 \y 3 ~3 | -6.nH$27
- iS
x ™~
O| oO ‘ ~/ | 40,047 FOG SDK | FOr3
#+.7 | = 3 _/ | -0.647F .

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
eh

COMPUTATION OF PRECISE LEVELS

Rop MEAN ROO

SB-=F =B

2
m™.
/

 
—45—

COMPUTATION OF PRECISE LEVELS

ORRECTIONS. DIFFERENCE

vee | INDEX ACH LINE
ERROR. | ERROR. | OF, EACH

 
Ahn

COMPUTATION OF PRECISE LEVELS

NO.9O MEAN ROD READINGS.
e GUM OF
B.'s. Bac k- STA ' DISTANCE mare
DIFe. OF

WARD = B-5F $B SF

F . -9E|\|S9¥260| /23a97 0o|F¢/
4/2 Yotb ol -¥F/,

-—3SF|/I97 J65b.7>\+ 0.086
-¢6 AG J730. 0 |\-0.0

46213566./| 552743|-4 76>
—-3/\b65S540 A LNALIGSI

-/0 | 3/627| 9€625.7|-0. 4530
_ FWS,7| 29 $0 | 40, ¥5;

—-2o 2, 9 “Is. oO
4 ES|YCIF t/,

,2/| #44/6|$552, 3) 297
o2/ — SIH; of OQ.

 
—~45- .

COMPUTATION OF PRECISE LEVELS

CORRECTIONS. DIFFERANCE OF EL ION.

TURe
VE TEMe. Lo
e _& L INDE x LENGTH e EACH LINE . MEAN.

AN
REFRAC~| EKROR. | ERROR. or OF
TION. Ron R Roo. ROO.

ey | | | to
_ 4-/ a

 
 

 

 
~46-

COMPUTATION OF PRECISE LEVELS.

Fon | MEAN Ron REAavines. | peepar mare A
NP

FE OF or

B-Y F ¥B SF PPODs.
”

ymn9m9) ah
1|\ 707990, S473, Sef
SOS 2,

aS PCY¥,7| 536 6.3 42.79
—4 / IAS

 
—47—

COMPUTATION OF PRECISE LEVELS

CORRECTIONS. DIFFERENCE OF & VA

RVAT UR B
LeveL. INCEX< | LENGTH | TEMP
AND e or EACH LINE MEAN

Re ~ or, | ERROR. or
EFRac-| ERROR R.| Roo. | Rod.

= FS = Tt FSE2ZI
= 3

 
om .. Qo

ome 8

ADJUSTMENT OF CIRCUIT

MEAN DIFFERENCE CORRECTED DIFFERENCE
LINE DISTANCE RRECT-
+ — LON + __

 
-~43-

FINAL ELEVATION

 

ELEVATION (fes«r)

B.M’s.

ELEVATION (mMeETERS)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sg 258.768 S49. 63/
WEB 2G AD4YS. §57./97
S72 258.968 5479. 63/
E 263,54/3 Bl4¢ b63¢
EZ 2IF, 38 79 §BStCo0G
w/ 258,593/ 543. Hof
C 2598, 3028 S47, HC
££ 259, 6YS3 $532,767
At 253, IFSEC/ JS 33.787
Gor. BA 295, 20633 SIT SVS
LO 258. STHS SHI2ST
xt 258, 8769 549,329
MB 2OAATES SSZ/IT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 

 

 

a et a _—
ADJUSTMENT OF CIRCUIT

MEAN DIFFERENCE CORRECTED PIFFERENCE
LINE DISTANCE RRECT-

re _ | BON L _

rey.

22299
JZ,

 
—-5l-

FINAL ELEVATION

a

 

ee

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

B.M's. ELEVATION (METERS) ELEVATION (€eerT)
Wy, By, 261.290 4S BS2AI97
q 25 2IAI S4+5.704
J/ 258. 62I> ee
LB. 259, 45 bo SBSLABE
43. 256,.0//7 SBBIIG3C
ABUT. 254 764 YH S35.538
_ VE AGL OY IF 856. 45>
S. LB 264, 66S/ B53 479
FOF 22.53.2500 SF7.AVS
A F¢- 252, 6234 S28. 8/4
138 253,05 830, 412
AG 253.4273 SAT, 656
47 262, 6/44 SELSID
SF 262.7007 S61 87S—
J 260,7396 SSS 44 /—
/ 260.2818 353,939
ia 257, O187 E&Y3 233
Wh Bu RGN ATES 3S7 S79 7__ CHect.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
cfc

vo

ADJUSTMENT OF CIRCUIT

MEAN DIFFERENCE CORRECTED DIFFERENCE

LINE DISTANCE RRECT-—
iom

+ — + ~

7-/ WHS | 417393

7- 4K 2¢ . | 0.35
-/C| ., 2/ C
<4ES | 14497C| ©. 6 | A¥ICE| 0.3575
-0.356 -0.38 7S
+1 1409 tf. IBD 3| CHECK,
+4. 4/39
—/,

 
-95-

FINAL ELEVATION

 

ELEVATION (FEET)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

B.M’s. ELEVATION (merers)
7 257221 EYS,. 704
S 256, 3£ 44 SHI, 153
G 259,822) E52. 433
S 25%. O97 846. b09
7 257.2860 SH4 1/9
AF 252.6234 F285. Es
7 257, 28 Se SYAI9F
Ke 256. S305 SBF2.GFS5-
SG o258. ¥273 BY ZESC

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 

 
co

   

TU NMIMINi A
3 1293 I 1986