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POLICIES AND GUIDELINES

IN THE CLASSROOMPrayer. Each class begins and ends with a prayer.Greeting. Students greet the teacher “Good morning, Sir/Ma’am/Sister. Praised be Jesus andMary!” before the beginning of the class.Attendance. Only for valid reasons can students be excused from class.Identification Card.A validated student identification card must always be worn by all students.Promptness. Students are expected to come to class on time. More than 3 minutes is consideredlate.Participation. Asmuch as possible, students are to participate in class discussions and activities.Intellectual Integrity. Cheating is strictly prohibited. Any form of dishonesty shall be dealt withaccordingly. Honesty is the best policy.Use of Cellular phones. All cellular phones are put in silent mode inside the classroom. Texting andanswering calls are to be done at designated areas in the campus. If caught, phone(s) will beconfiscated and will return after 3 hours from the end of the class.Energy Conservation. Lights and fans are put off by the one nearest the switch after every class.Submission of Requirements. Haste makes waste. Class requirements are to be submitted on time.Courtesy. Respect for others is practiced at all times and in all places.

GRADING SYSTEM

PERIODICAL EXAM – 30%

STUDENT’S DAILY PREPARATION – 70%

QUIZZES – 40%

CLASS PARTICIPATION/BOARDWORK – 15%PLATES/ASSIGNEMTS/SEATWORKS – 15%

TOTAL – 100%

GRADE: 75% LEC + 25% LAB

A. LECTURE:

B. LABORATORY:PRACTICAL EXAM – 30%PERFORMACE/EXERCISES – 70%

TOTAL – 100%

BASE 40

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TRAVERSE

ADJUSTMENT

WHAT IS A

TRAVERSE ADJUSTMENT?The procedure of computing the

linear error of closure and applying

corrections to the individual latitudes

and departures for the purpose of

providing a mathematically closed

figure.

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LINEAR ERROR

OF CLOSURE

MATHEMATICALLY

CLOSED FIGURE

There are different rules and methods

used in adjusting a traverse.

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COMPASS RULEThe Compass or Bowditch rule is a very

popular rule for adjusting a closed traverse.

The compass rule is based on the

assumption that all lengths were measured with

equal care and all angles taken with

approximately the same precision. It is also

assumed that the errors in the measurement are

accidental and that the total error in any side of

the traverse is directly proportional to the total

length of the traverse.

COMPASS RULEThe compass rule may be stated as

follows:

• The correction to be applied to the

latitude (or departure) of any course is

equal to the total closure in latitude (or

departure) multiplied by the ratio of the

length of the course to the total length or

perimeter of the traverse.

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COMPASS RULEThese corrections are given by the

following equations:

𝐜𝐥 = 𝐂𝐋𝐝

𝐃𝐜𝐝 = 𝐂𝐃

𝐝

𝐃Where:

cl = correction to be applied to the latitude of any course

cd = correction to be applied to the departure of any course

CL = total closure in latitude or the algebraic sum of the north

and south latitudes (ΣNL + ΣSL)

CD = total closure in departure or the algebraic sum of the east

and west departures (ΣED + ΣWD)

d = length of any course

D = total length or perimeter of the traverse

TAKE NOTE!All computed corrections should be

added to check whether their respective

sums equal the closures in latitude and

departure.

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How can we adjust the latitude

and departure of any course?

To determine the adjusted latitude

(departure) of any course, the latitude

(departure) correction is either added to or

subtracted from the computed latitude

(departure) of the course.

A simple rule to remember is:

If the sum of the north latitudes exceeds the

sum of the south latitudes, latitude corrections

are subtracted from north latitudes and added to

corresponding south latitudes. However, if the

sum of the south latitudes exceeds the sum of the

north latitudes, the corrections are applied in the

opposite manner. A similar procedure is used

when adjusting the departures.

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After the latitudes and departures of the courses of a

closed traverse have been so adjusted, the bearings (or

azimuths) of the courses and their lengths should also be

adjusted to correspond to the adjusted latitudes and

departures. The following are the equations used for this

purpose:

𝐋′ = (𝐋𝐚𝐭′)𝟐+(𝐃𝐞𝐩′)𝟐 𝐓𝐚𝐧 𝛂 =𝐃𝐞𝐩′

𝐋𝐚𝐭′Where:

L’ = adjusted length of a course

Lat’ = adjusted latitude of a course

Dep’ = adjusted departure of a course

α = adjusted horizontal angle between the reference

meridian and a course

SUMMARY1. Compute the latitude and departure of each course.

Latitude = (Distance)(cos θ)

Departure = (Distance)(sin θ)

Note:

• For Bearing and Azimuth from North, + for North and East; - for

South and West

• For Azimuth from South, - for North and East; + for South and West

2. Determine the total closure in latitude and departure.

CL = ΣNL + ΣSL

CD = ΣED + ΣWD

3. Determine the corrections for latitude and departure.

𝐜𝐥 = 𝐂𝐋𝐝

𝐃𝐜𝐝 = 𝐂𝐃

𝐝

𝐃

All computed corrections should be added to check whether their

respective sums equal the closures in latitude and departure

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SUMMARY

Solution check for adjusted latitudes and departures, the algebraic

sum of the adjusted latitudes or departures is equal to zero.

5. Adjust the length and bearing of each course.

𝐋′ = (𝐋𝐚𝐭′)𝟐+(𝐃𝐞𝐩′)𝟐 𝐓𝐚𝐧 𝛂 =𝐃𝐞𝐩′

𝐋𝐚𝐭′

4. Adjust the latitudes and departures. Note: if the sum of north

latitudes exceeds the sum of south latitudes, latitude corrections are

subtracted from the corresponding north latitudes and added to

corresponding south latitudes. Vice versa if the sum of south

latitudes exceeds the sum of the north latitudes. A similar procedure

is used when adjusting the departures.

Given in the accompanying tabulation are the observed data for

a traverse obtained from a transit-tape survey. Determine the

latitudes and departures of each course and balance these quantities

by employing compass rule. Also determine the linear error of

closure, bearing of the side of error, and the relative error of closure.

Tabulate tables accordingly.

COURSE DISTANCE BEARING

AB 495.85 m N 05º30’ E

BC 850.62 N 46º02’ E

CD 855.45 S 67º38’ E

DE 1020.87 S 12º25’ E

EF 1117.26 S 83º44’ W

FA 660.08 N 55º09’ W

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Given in the accompanying tabulation are the observed data for

a traverse obtained from a transit-tape survey. Determine the

latitudes and departures of each course and balance these quantities

by employing compass rule. Also determine the linear error of

closure, bearing of the side of error, and the relative error of closure.

Tabulate tables accordingly.

COURSE DISTANCE AZIMUTH FROM

NORTH

AB 229.70 m 82º12’

BC 130.55 131º48’

CD 161.46 228º20’

DE 180.49 267º43’

EA 171.83 352º01’

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TRANSIT RULEThe method of adjusting a traverse by the transit

rule is similar to the method using the compass rule.

The main difference is that with the transit rule the

latitude and departure corrections depend on the length

of the latitude and departure of the course respectively

instead of both depending on the length of the course.

It is not commonly used as the compass rule,

however, it is best suited for surveys where the sides of

the traverse are measured by the stadia or subtense bar

method.

TRANSIT RULEThe rule is based on the assumption that the

angular measurements are more precise than the linear

measurements and that the errors in traversing are

accidental. Since it is merely a rule of thumb it may not

be applicable in some instances.

The transit rule may be stated as follows:

The correction to be applied to the latitude (or

departure) of any course is equal to the latitude (or

departure) of the course multiplied by the ratio of the

total closure in latitude (or departure) to the

arithmetical sum of all the latitudes (or departures) of

the traverse.

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TRANSIT RULEThese corrections are given by the following equations:

𝐜𝐥 =𝐋𝐚𝐭(𝐂𝐋)

𝚺𝐍𝐋 − 𝚺𝐒𝐋𝐜𝐝 =

𝐃𝐞𝐩(𝐂𝐃)

𝚺𝐄𝐃 − 𝚺𝐖𝐃Where:

cl = correction to be applied to the latitude of any course

cd = correction to be applied to the departure of any course

CL = total closure in latitude or the algebraic sum of the north and

south latitudes (ΣNL + ΣSL)

CD = total closure in departure or the algebraic sum of the east and

west departures (ΣED + ΣWD)

ΣNL = summation of north latitudes

ΣSL = summation of south latitudes

ΣED = summation of east departures

ΣWD = summation of west departures

TRANSIT RULELatitude and departure corrections are applied in

a manner similar to that described for the compass rule.

However, before any corrections are applied it is

important to first check if the sum of the computed

corrections for the latitudes (or departures) equal the

closure in latitude (or departure). A perfect closure will

always be assured if this is done.

After the latitudes and departures of the courses of

a closed traverse have been so adjusted, the bearings

(or azimuths) of the courses and their lengths should

also be adjusted to correspond to the adjusted latitudes

and departures. The procedure is the same to the

compass rule.

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SUMMARY1. Compute the latitude and departure of each course.

Latitude = (Distance)(cos θ)

Departure = (Distance)(sin θ)

Note:

• For Bearing and Azimuth from North, + for North and East; - for

South and West

• For Azimuth from South, - for North and East; + for South and West

2. Determine the total closure in latitude and departure.

CL = ΣNL + ΣSL

CD = ΣED + ΣWD

3. Determine the corrections for latitude and departure.

All computed corrections should be added to check whether their

respective sums equal the closures in latitude and departure

𝐜𝐥 =𝐋𝐚𝐭(𝐂𝐋)

𝚺𝐍𝐋 − 𝚺𝐒𝐋𝐜𝐝 =

𝐃𝐞𝐩(𝐂𝐃)

𝚺𝐄𝐃 − 𝚺𝐖𝐃

SUMMARY

Solution check for adjusted latitudes and departures, the algebraic

sum of the adjusted latitudes or departures is equal to zero.

5. Adjust the length and bearing of each course.

𝐋′ = (𝐋𝐚𝐭′)𝟐+(𝐃𝐞𝐩′)𝟐 𝐓𝐚𝐧 𝛂 =𝐃𝐞𝐩′

𝐋𝐚𝐭′

4. Adjust the latitudes and departures. Note: if the sum of north

latitudes exceeds the sum of south latitudes, latitude corrections are

subtracted from the corresponding north latitudes and added to

corresponding south latitudes. Vice versa if the sum of south

latitudes exceeds the sum of the north latitudes. A similar procedure

is used when adjusting the departures.

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Given in the accompanying tabulation are the observed data for

a traverse obtained from a transit-tape survey. Determine the

latitudes and departures of each course and balance these quantities

by employing transit rule.Tabulate tables accordingly.

COURSE DISTANCE BEARING

AB 495.85 m N 05º30’ E

BC 850.62 N 46º02’ E

CD 855.45 S 67º38’ E

DE 1020.87 S 12º25’ E

EF 1117.26 S 83º44’ W

FA 660.08 N 55º09’ W

Given in the accompanying tabulation are the observed data for

a traverse obtained from a transit-tape survey. Determine the

latitudes and departures of each course and balance these quantities

by employing transit rule.Tabulate tables accordingly.

COURSE DISTANCE AZIMUTH FROM

NORTH

AB 229.70 m 82º12’

BC 130.55 131º48’

CD 161.46 228º20’

DE 180.49 267º43’

EA 171.83 352º01’

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GRAPHICAL METHODThe graphical method is essentially an

application of the compass rule. It provides a

simple graphical means of making traverse

adjustments. In this method each traverse point

is moved in a direction parallel to the error of

closure by an amount proportional to the

distance along the traverse from the initial point

to the given point.

RECTANGULAR COORDINATESThe two horizontal distances measured to a point from a

pair of mutually perpendicular axes are referred to as the

rectangular coordinates of a point. All coordinate values are

computed from an origin fixed by the intersection of an x-axis

and a y-axis. The x-axis is a reference line which runs along an

east-west direction and the y-axis runs along a north-south

direction.

Coordinate locations are given by two quantities, the X and

Y coordinates. The X coordinate of a point is the perpendicular

distance from the y-axis and its Y coordinate is the perpendicular

distance from the x-axis. Thus, when the rectangular coordinates

of a number of points are known, their relative positions are

explicitly defined.

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Given in the accompanying tabulation are the adjusted

latitudes and adjusted departures of a closed traverse. Calculate the

coordinates of each station along the traverse if the coordinates of

station A are X = 3,000.00 m and Y = 4,000.00 m. Tabulate tables

accordingly.

LINE ADJ. LATITUDES ADJ. DEPARTURES

+N -S +E -W

AB 405.50 202.25

BC 218.13 175.64

CD 71.08 415.36

DE 325.67 355.62

EF 389.70 58.51

FA 488.52 739.08

SUMS 949.30 949.30 973.23 973.23