D-136AC OMRRS O OFETOSOLESSQASADUTNTF 1/TRRYERSES(U) NAVAL POSTGRADUATE SCHOOL MONTEREY CA

u NCASFE F/O 12/1 L

mmmhmmmhlmhmmhhhhEohhEEIEhhmhhmhhmhlom1mohmhhhohmhEEI

11.1111L028 112.0

11111!.25 .4

1.6

MICROCOPY RESOLUTION TEST CHART

NATIONAL BUREAUI OF STANDAROS-63.A

NAVAL POSTGRADUATE SCHOOLMonterey, California

f-7- LECTEMAY 10 Q85Jf

InB

THESISA Comparison of Methods

of

Least Squares Adjustment of Traverses

byLJ. Saman Aumchantr

December 1984

Thesis Advisor: Rolland L. Hardy

Approved for public release; distribution unlimited.

85 04 15 13

SECURITY CLASSIFICATION '-)F THIS PAGE (When Date Entered)READ INSTRUCTIONS

REPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM

I. REPORT NUMBER 2. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG 'UMBER

4. TITLE (and Subtitle) S. TYPE OF REPORT & PERIOD COVERED

Master's ThesisA Comparison of Methods of Least Squares December 1984Adjustment of Traverses S. PERFORMING ORG. REPORT NUMBER

7. AUTNOR(s) 8. CONTRACT OR GRANT NUMBER(&) 2Saman Aumchantr

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELFMENT, DROJECT. TASK

uNaval Postgraduate School AREA & WORK UNIT NUMBERS

Monterey, California 93943

11. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

Naval Postgraduate School December 1984_ _ _ _o~_ _ _ _ __ 13. NUMBER OF PAGES

Monterey, California 93943 15114. MONITORING AGENCY NAME & ADDRESS(If different from Controling Office) IS. SECURITY CLASS. (of this report)

UNCLASSIFIED

I5a. DECL ASSIF$I CATION DOWNGRADINGSCHEDULE

16. DISTRIBUTION STATEMENT (of this Report)

Approved for public release; distribution unlimited

"'* 17. DISTRIBUTION STATEMENT (of the abetrect entered in Block 20, if d' .rent from Report)

IS. SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on reverse side If necessary id Identify by block number)

Adjustment, Approximate Method, Comparison, Condition Equation Method,

Least Squares Method, Traverse, UTM grid coordinates.

20. ABSTRACT (Continue on reverse aide If necessary and Identify by block number)

Traverse is a method of surveyinq in which a sequence of lenqths anddirections of lines between points on the Earth are measured and used in

determininq positions of the points. This method is one of several used tofind the accurate geodetic positions which various agencies use. Tr&Versingis a convenient, rapid method for establishina horizontal control.

The theoretical background is provided here to explain the method oftraverse station position computations and adjustments in the Universal

D JAR 1473 EDITION OF I NOV 65 IS OBSOLETF

S. N 0102- LF 014- 6601 1 SECURITY CLASSIFICATION OF THIS PAGE (When Dete Entered)

.............................................................. .% . . . .

SECURITY CLASSIFICATION OF THIS PAGE (Whm D-0 EIteO,-

Block 20 (continued)

Transverse Mercator grid coordinates. Closed traverse station positionswere computed and adjusted using the Approximate Method and by the LeastSquares Method. The adjusted coordinates of both methods were transformedfrom the Universal Transverse Mercator grid coordinates to geoqraphiccoordinates and compared with the coordinates which were adjusted by the U.S.National Ocean Service.

S N 0102- LF.014- 6601

2 SECURITY CLASSIFICATION OF THIS PAGEWPIof Data Ent.,d)

Approved for public release; distribution unlimited.

A Comparison of Methodsof

Least Squares Adjustment of Traverses

by

Saman Aumchantr0Lieutenant,' Royal Thai Navy

B.S., Royal Thai Naval Academy, 1976

Submitted in partial fulfillment of the

recquirements for the degree of

MASTER OF SCIENCE IN HYDEOGRAPHIC SCIENCES

from the

NAVAL POSTGRADUATE SCHOOL 0

December 1984

Author: c"' ------------------

Approved by: ...... _----

r en 7-5cefer;73 on 9--

0

CBYITU?1 9 ;.K. Z53r iir ma n,Department of Oceanography

-- ---------4 -----------Dean of Science an Engineering

3

ABSTRACT

Traverse is a method of surveying in which a sequence of

lengths and directions of lines between points on the Earth

are measured and used in determining positions of the

points. This method is one of several used to find the

accurate geodetic positions which various agencies use.

Traversing is a convenient, rapid method for establishing

horizontal control.

The theoretical background is provided here to explain

the method of traverse station position computations and

adjustments in the Universal Transverse Mercator grid coor-

dinates. Closed traverse station positions were computel

and adjusted usingthe Approximate Method and by the Least

S/uares Method/, The 'adjusted coordinates of both methods

were transformed from the Universal Transverse Mercator grid

coardinates to geographic coordinates and compared with the

coordinates which were adjusted by the U.S. National Ocean

Service. . .

4 -

.p , . * ,j -

-, -'..J A, . -,

..................................

:.... . -....... .... ........... ..... ............ :{:i

TABLE OF CONTENTS

I. INTRODUCTION...................10

II. TRAVERSE.............................12

A . GENERAL..........................12.-

B. ANGLE AND DIFECTION MEASURE:IENT........13

C. DISTANCE MEASUREMENTS................15

D . ACCURACY........................16F

E. DATA ACQUISITION........................16

III. TRAVEFSE COMPUTATIONS AND ADJUSTMENTS ......... 21

A. INITIAL TRAVERSE COMPUTATIONS..........21

B. COMPUTATION OF DISCREPANCIES...........23

C. ADJUSTMENT OF A TRAVERSE BY AN APROXII ATE

METHOD..........................26

D. ADJUSTMENT OF A TRAVERSE BY LEAST SQUARES

METHODS.........................28.

1. The Principle of Leist Squares........28

2. Least Squares Adjustment of Indirect

observations.................31

3. Least Squares Adjustment by the

Condition Equation Methad...........47

IV. DISCUSSIONS AND ANALYSIS OF RESULTS.........59

V. CONCLUSIONS AND RECOMMENDATION............66

A. CONCLUSIONS......................66

B. FECOMLIENDATION.......................67

APPENDIX A: PROGRAM 1..................68

APPENDIX E: PROGRAM 2..................89

5

APPENDIX C: PROGRAM 3......................121

LIST OF REFERENCES....... ................ 8

- BIBLIOGRAPHY............................149

IVITIAL DISTRIBUTION LIST....................150

6

LIST OF TABLES

I. Classification, Standards of Accuracy, and

pGeneral Specifications for Horizontal Contr~l . . . 17

II. Coordinates of'Known Stations and Azimuths . . . . 19

III. Grid Distances and Standard Deviations........20

iv. The observed Angles and Standard1 Deviations . . . . 20

V. rata --"r Initial Traverse computations.......23

VI. The Azimuth Calculation ............... 24

V1I. Initial Traverse Computations............25

VIII. Initial Traverse Computations (Approximate

Method with Adjusted Azimuth) ............ 27

IX. Adjusted Coordinates (Approximate Method).......29

X. The Comparisons Between the ::omputer Storage

Area and CPU Time of Programs 1, 2, and 3.......60

Xi. Geographic Coordinates.................64XII. The Comparisons Between the Standard Deviations

of Least Squares..................65

U' 1 or 2 7ro

Do

7 ~ ~ n

tAijPV TEI p

LIST OF FIGaRES

2.1 Closed Traverse...................12

2.2 Closed-loop Traverse .. .. .. .. .. .. .. .. 13--

2.3 Horizontal Angle..................15

3.1 A Closed Traverse..................22

8

AC KNOWNLEDGEMNEN TS

I express sincere gratitude to my Thesis Advisor, Dr.

Rolland L. Hardy, and Second Reader, Cdr. Glen R. Schaefer,

foc their suggestions and assistance. Finally, I thank Ms.

Tamiara M. Hayling, Lt. Nicholas E. Perigini, and Messrs.

Mark L. Faye, Peter J. Rakowsky, and James R. :herry who

made this thesis possible.

9

I. INTRODUCTION

Hydrographic surveying includes many branches of science

for the purpose of the production of nautical charts

specially designed for use by the mariner. The determina-

tion of position in hydrographic surveying is as important

as the measurement of depth. Before determining an accurate

hydrographic position, accurate geodetic positions' for

shore control must be established. There are many methods

available to establish geodetic control in the survey area.

These methods are:

1. Triangulation

2. Trilateration

3. Traverse

4. Intersection

5. Resection

The process of making a proper nautical chart consists, p

first of all, in setting up a framework of marks on the

ground. Before 1950 the main framework of a geodetic survey

almost always consisted of triangulation, which was replaced

by traverse if the topography made triangulation impracti-

cable. During the last decade, the introduction of elec-

tronic distance measuring (EDM) equipaent has made both

trilateration and traverse economical, and an acceptable

substitute for triangulation. In fact, it appears probable

that these new methods will replace triangulation as the

main framework for new geodetic surveys [Ref. 1]. It is

evident that triangulation and traverse are the main methods

used for establishing control. There seems to be no

'A position of a point on the surface of the Earthexpressed in terms of qeodetic latitude, geodetic longitudea r geodetic height. A geodetic position implies an adoptel - ]geodetic datum. p

10

I

.. .. .. -• . 2.. . . .. --~k.' . . 2. . . . 2 . . .'.' .. i. i . .i , ii . .. . - -i . .. ..- ,A.-- --.... A..t-. . ... .-..

agreement among the various agencies as to which of these

two methods is mostly used. The U.S. National Ocean Service

(NOS) does the majority of its horizontal control surveys

for hydrography with traverse (about 90%) [Ref. 2]. The

main factor for the selection of one or the other method

depends on the geographical configuration of the survey

project area and the availability of good EDM equipment.

Traversing is a convenient, rapid method for establishing

horizontal control. It is particularly useful in densely

built areas, when the coastline tends to be even, along a

railroad track, and in heavily forested areas whcre lengths

of sight are short so that neither triangulation nor

trilateration is suitable.

The objectives of this thesis are to show methods of

traverse station position computation and a comparison of

methods of least squares adjustment. Closed traverse

station positions were computed and adjusted using the

Approximate Method and by the Least Squares [lethod in the

Universal Transverse Mercator (UTM) grid coordinates. The

computer programs were written to calculate the adjusted

traverse station positions. Test data included those data

obtained during the Geodetic Survey Field Experience course

at the Naval Postgraduate School (NPS) in October 1983.

The results of comparative computations are shown to

more significant figures, in this thesis, than are normally

considered desirable in production work. The same observed

data are used with each of three computational methods. It

is important to recognize that what is being compared is not

observational precision but computational precision. ience,

it is considered necessary for a rigorous comparison of

computational precision, including round off error, to show

results to several more decimal places than is justifiable

based on observational precision alone.

~11

II. TRAVERSE

A. GENERAL

Traverse is a method of surveying in which a series of

straight lines connect successive established points along

the route of a survey. An angular measurement is taken

using a theodolite at each point where the traverse changes

direction. Distances along the line between successive

traverse points are determined by EDM equipment. The points

defining the ends of the traverse lines are called turning

points, traverse points, or traverse stations. Each

straight section of a traverse is called a leg or a traverse

line.

A closed traverse originates at a point of known posi-

tion and is closed on another point of known horizontal

position. Traverse 1-1-2-3-F originates at point I with a

hacksight along line IA of known azimuth and closes on point

F, with a foresight along line FB also of known azimuth

(Figure 2. 1). This type of traverse is preferable to all

A BI "--__________________-__-

12

.................................1ldTae..............

• . ..-. .

7t

others since computational checks are possible which allow

detection of systematic errors2 in both distanze and

direction.

A closed-loop (closed polygon) traverse is a special

case of a closed traverse in which the originating and

terminating points are the same point with a known hori-

zontal position. Traverse 1-1-2-3-4-I, originates and

terminates on point I (Figure 2.2). This type of traverse

permits an internal check on the angles, but there is no

check on the linear measurements. Therefore, there is a

possibility that an error proportional to distance may occur

and not be detected.

4

3t 2

Figure 2.2 Closed-loop Traverse.

B. ANGLE AND DIRECTION MEASUREMENT

Angles and directions may be defined by means of bear-

ings, azimuths, deflection angles, angles to the right, or

interior angles. These *juantities are said to be observed

2 Systematic errors may be caused by faulty instrumentsor factors such as temperature or humility changes whichaffect the performance of measuring instruments.

13

........................... -*-*.- ... 2-.

I

when obtained directly in the field and calculated when

obtainel indirectly by computation.

A theodolite is an instrument designed to observe hori- 0

zontal directions and measure vertical angles. It consists

of a telescope mounted to rotate vertically on a horizontal

axis supportel by a pair of vertical standards attached to a

revolvable circular plate containing a graduated circle for p

observing horizontal directions. Another graduated arc is

attached to one standard so that vertical angles can be

measured.

Repeating and direction theodolites have features that

are common to both types of instruments. Repeating theodol-

ites are read directly to 20" or 01' and by estimation to

one-tenth the corresponding direct reading. Direction theo-

dolites are usually read directly to 01" and can be esti- p

mated to tenths of seconds (Ref. 3, p. 215]. In general,

direction theadolites are more precise than are repeating

theodolites.

The direction theodolite observes directions only and

angles are computed by subtracting one direction from

another. Assume that the horizontal angle AIB (Figure 2.3)

is to be measured with a direction theodolite. The theo-

dolite is set over point I, leveled and centered, and a

sight is taken on poirt A. The horizontal cirzle is then

viewed through the optical-viewing system and the circle

reading is observed and recorded. Assume the reading is

450 02' 40". The telescope is then sighted on point B. The p

hocizontal circle is then viewed through the optical-viewing

system and the circle reading is observed and recorde:.

Assume the reading is 1240 11' 59". These two observations

constitute directions which have a common reference direc-

tion that is completely arbitrary. The clockwise horizontal

angle is

i = (1240 11' 59") - (450 02' 40") = 790 09' 19"

14

-. - . .'..- '~..-.-. -... -.. - .... ... *.. . • .-. . . .- - . .i . .i. - :. . .

II IA1

IBI

Figure 2.3 Horizontal Angle.

C. DISTANCE nEASUREMENTS

There are several methods of determining listance, the

choice of which depends on the accuracy required and the

cost. For example, tacheometry, taping, and EDI equipment

can be used. The general availability of EDM egauipment has

practically eliminated the use of taping for the measurement

of traverse lengths. Accuracies are comparable, or

superior, to those obtained with invar tapes.

Distances measured using EDM ejuipment are subject to

errors arising from the instrumental components, calibration

of the equipment, inaccuracies in the meteorological lata,

elevation discrepancies, and centering of the instruments or

reflectors. The reduction of measured distances involves

converting the slope distance to a horizontal distance,

converting the chord distance to an equivalent arc distance,

and reducing the arc distance to the ellipsoid. The reduc-

tion of slope distance to horizontal distance is necessary

to compensate for the difference in elevation of the end

points of the measured line. The horizontal distance is

15

1. 5.. . . - . .. . . . . ' < '- ['

reduced to the geodetic distance Ly applying a sea level

corrector and a chord-arc corrector to the horizontal

distance [Ref. 4, pp. 124-125].

D. ACCURACY

In general, the accuracy of a traverse is judged on the

basis of the resultant error of closure of the traverse.

This resultant closing error is a function of the accuracies

in the measurement of directions and distances. The classi-

fication, standards of accuracy, and general specifications

for horizontal control have been prepared by the Federal

Geodetic Control Committee (FGCC) 'Ref. 5] and have been

reviewed by the American Society of Civil Engineers, The

American Conqress on Surveying and Mapping, and the American

Geophysical Union (Table I). The third-order traverse class

I and class II are of particular interest because these are

the orders of accuracy the hydrographer is usually required

to accomplish.

E. DATA ACQUISITION

The data for this thesis were acquired at Moss Landing,

California, by NPS Hydrographic students during the Geodetic

Survey Field Experience course in October 1983. All of the

known station positions and azimuths (Table II) were

adjusted by the Coast and Geodetic Survey by third-order

methods [Ref. 6].

The distances were observed by using a Kern DM102 and a

Tellurometer MRk5. The Kern DM102 is an electro-optical

distance meter. The measuring accuracy was ±(5 mm + 5 ppm)

The Tellurometer MRA5 is a microwave instrument. Precision

in terms of probable error, in the temperature range of

-320C to +440C, is ± (5 cm + 100 ppm) for a single

16

.........

C6 B

a' E0 0

0

440 1J" 10

o= E Uj3.E p- - SCM I

o 0 6

N c5I ~ . -

44) f 2

p.2 4a tag zzZ Z

-aa

. I!17

C I

;5- W- 1

gt.± 1 . - 0 I j--

351i 5 '' 3 K; z

E 3c

.> ij SwE.~ 4Z

4)~ ~ IE' ~ ~ ~ uevfh tm -~z18

.- X~f1 j

.4.) I*~c"

-018

TABLE II

Coordinates of Known Stations and Azimuths

( T grid coordinates ,Station Grid Nort ing Gril Easting .

Moss 2 4,072,555.85206 608,279.04404

Holm 4,079,258.31754 612,238.85256 i

Grid azimuth clockwise .from North Azimuth I0

From Moss 2 to Pipher stations 100 16 23.772 I

From Holm to Moran stations 136 33 26.334

determination. The distances were observed in the field,

cocrected by temperature and pressure for propagation error.

Unfortunately, meteorological data are generally acquired

only at the end points of a measured line. Using the mean

of these meteorological values only approximates the actual

conditions of the entire measured line anJ does not

completely correct for errors in the propagat-ion velocity of

electromagnetic radiation. By applying the elevation, sea

level, and scale factor corrections they were reduced to UTM

grid distances [Ref. 4, pp. 124-125]. The UTIM grid

distances and standard deviations of the distances were

determined in meters (Table III). -

The angles were observed by using a Wild T-2 theodolite.

To ensure the correctness of the beginnin and ending

azimuths, a check azimuth to a second station of known posi-

tion was observed. The angles were observed at stations

Moss 2, Mossback, Dune Temp, and Holm (Table IV). All

observations were made by NPS students and conform to

specification for a third-order class I traverse.

19

..................................S*.** . . . . . . . . . . . . . . . ..

. . . . ..'-.-. . . .... ..-,-.-'-..-. ....,...'. ...'. ...... ... ,.. ......... ..-.-...,..-.... :-...-.: ..-.. _ . ....... . ., ,..: . .:. '. ' ? .-

3

TABLE III

Grid Distances and Standard Deviations

StandardGrid distances betwees i Distances deviationI

stations(i.(n)

M1oss 2 and Mossback 1,424.004 0.001

Mossback and Dune Temp 365.744 0.001

Dune Temp and Holm 6,476.271 0.003

TABLE IV

The Observed Angles and Standard Deviations 0

Backsight Center Foresight Observed Standard

station station station angles deviation10 3

Pipher Moss 2 Mossback 246 05 43.200 01. 984

Koss 2 Mossback Dune Temp 222 51 08.600 01.405

Mossback Dune Temp Holm 190 15 02.600 01.203

Dune Temp Holmn Moran 277 05 17.000 01.614

I

L' --- -----

S-7

IIIll. TRAVERSE COMPUTATIONS AND ADJUSTMENTS

A. INITIAL TRAVERSE COMPUTATIONS

A traverse (Figure 3.1) originates at station 1 (known

position) and terminates at station 4 (also know. position)

(Table V). To compute the forward azimuth (Table VI) of an

unknown leg, the angle is added to the back azimuth of the

previous leg (Equation 3. 1)

Az i = Az F + - (i-i) 1800 (3.1):Z1

Where: i = the number of legs,

Azi = the forward azimuth of an unknown leg, and

Az = the fixed initial azimuth.

For the computation of UTM grid coordinates, let LE 1

and / N be designated as the departure and latitude for leg

i (Figure 3.1) so that the general formulas to compute theIJdeparture and latitude are

/! i = d i sin Az i (3.2)

IN = di cos Az (3.3)

where i = 1 , 2 , 3 , . . . n,

n = the number of the observed angles.

The algebraic signs of the departure and latitude for atraverse leg depend on the signs of the sine and cosine of

the azimuth of that leg. The algebraic sign of the depar-

ture and latitude is determined by the following rules:

1. UTM grid azimuths are refered to grid north.

2. For azimuths between 00 and 1800, the departure is

plus; for all other azimuths, the departure is minus.

3. For azimuths between 900 and 2700, the latitude is

minus; for all other azimuths, the latitude is plus.

21

2 1 -1

p .

.. . ... ... ... ... . . . . .... . .. ... .. . .. . .. ... . . .. .- .. . :. .. . . .- ... . . . . . . . . - -..- . . ... ... . .. . .. . . . .- . , . . .-. . ..

I 4

4-3

LN 3 d 3

E 3

LN 2 \d2

Az1

Figure 3.1 A Closed Traverse.

The calculators and computers with internal routines for

trigonometric functions yield the proper sign automatically

given the azimuth. The major portion of traverse computa-

tions consists of calculating departures and latitudes for

successive legs and cumulating the values to determine the

coordinates for consecutive traverse stations.

22..]

TABLE V

Data for Initial Traverse Computations

Leg Distance Angle

0 I-

1 - 2 d i = 1,424.004 01 = 246 05 43.200

2 - 3 d2 = 365.744 C2 = 222 51 08.600

3 - 4 d 3 = 6,476.271 c03 = 190 15 02.603

The initial UTM grid azimuth AzF = 100 16 23.778

UTM grid Northing NI = 4,072,555.85206 m.Station 1-TM grid Easting E = 608,279.04404 m.

The coordinates of station j (j = i + 1) are Ej and

Nj, the coordinates of station j are

E. = + LE (3.4)

N. = Ni + LN (3.5)

where i = 1 , 2 , 3 , . . . n.

The values of departures, latitudes, and coordinates are

shown in Table VII and were computed from the data in Tables

V and VI by application of Equations (3.2) through (3.5).

B. COBPUTATION OF DISCREPANCIES

A closed traverse at Moss Landing (Figure 3. 1) origi-

nated at station 1 (Moss 2) and closed at station 4 (Holm).

The closing errors for a traverse are caused by observation

errors in the observed angles and the measured distances.

The closing errors may be computed by applying Equations

(3.1) through (3.6).

23

. .... "...

I

TABLE VI

The Azimuth Calculation

Forward Back ObservedAzimuth Azimuth Angle 0 ! ,

Az 100 16 23.778AF

246 05 43.200

Azi 346 22 06. 978

180 00 00.000

Az2 -1 166 22 06.978

2 222 51 08.600

Az2 389 13 15.578

- 180 00 00.000

Az3_2 209 13 15.5784 0 3 190 15 02.600

Az 399 28 18.178-180 00 00.000

A Z 219 28 18. 1784-3

The angular error of closure may be computed by applying

Eruation (3.1) becomes

nAzF + i(i- (n-1)180 0 - Az = (3.6)

F : L

where AzL is the fixed closing azimuth and W, is the

angular error of closure. AzL is the grid azimuth from

stations Holm to Moran (AzL = 1360 33' 26.334") (Table II).

The computed closing azimuth is egial to Az4 3 plus the

observed angle at station Holm = (2190 28' 18.178") +

(2770 05' 17") = 4960 33' 35.178" = 1360 33' 35.178". From

Equation (3.6), the angular error of closure is

(1360 33' 35.178") - (1360 33' 26.334") = + 08.844".

24

... -. _ _ _ _._

TABLE VII

Initial Traverse Computations

~1

Values in meters Values in meters

N1 4,072,555.85206 E 608,279.04404

1,383.89267 £E 1 - 335. 60166

N2 4,073,939.74473 E2 607,943.44238

eN 2 319.20061 E 2 178.54871

N3 4,074,258.94534i E 3 608,121.99109

4N3 4,999.28284 nE 3 4,116.94755

N 4 ,079,258.22818 E4 612,23S. 9386 4

To compute the errors in closure in position for a

closed traverse. Equations (3.2) to (3.5) are applied to

obtain:

n-1

W = >/2E. - ( E T - El ) (3.7)i:1 I

n-1

w = Ni - ( NT - NJ ) (3.8)i:1

or

w2 = E n - ET (3.7a) -

w = N n - N (3.8a)

Where: n = the number of observed angles,

W2 W3 = precalculated discrepancies,

E, NJ = the fixed initial coordinates,

E T T NT = the fixed closing coordinates, and

E n Nn = the computed closing coordinates.

The result of the errors in closure in position of a

traverse is

25

* .. . .. . . . . . . . . . . .

d W22 + W2 )1/2 (3.9)

The computed closing coordinates of this traverse are

E4 612,238.93864 m and N 4,079,258.22818 m. The fixed

closing coordinates are ET 612,238.85256 m and NT

4,079,258.31754 m. The precalculated discrepancies can be

computed by using Equations (3.7a) and (3.8a). The results

are W 0.08608 m and W -0.08936 m. By applying

Equation (3.9), L5d is 0.12408 m. From Table III, the total

measured distance is 8,266.019 m. The ratio of the distance

error of closure to the total distance is 0.12408/8,266.019

or 1 part in 66,618. The ratio is an indication of the

goodness of this traverse.

C. ADJUSTMENT OF A TRAVERSE BY AN APPROXIMATE MlETHOD

The angular error of closure of traverse may be distrib-

utel equally among the observed angles. The angular error

of closure of this traverse is +8.844#1, which corresponds to

a correction for each angle of -2.2 11". The observed angles

were correctei by this value. The adjusted azimuth was then

computed. The departures, latitudes, and coordinates were

recomputed hy using the adjusted azimuth (Table VIII). The

closure corrections in E and N coordinates are +0.09635 m

and -0.04326 m, respectively. The resultant closure is

0. 10562 m. The ratio of the distance error of closure to

the total distance is 0.10562/8,266.019 or 1 part in 78,262.

The adjustments of a closed traverse by the Approximate

?1e~hod are completed by the compass rule which proportions

the errors in E and N coordinates according to the distance

of the course [Ref. 4, p. 354]. The corrections are applied

to the departures and latitudes prior to computation of

coordinates.

26

TABLE VIII

Initial Traverse Computations. (A roximate Method withAdjusted Azi ut-)

Observed angle Correction Adjusted azimuth0

AZF 100 16 23.778

2460 05' 43.2" - 2.211" 246 05 40.989

Az1 346 22 04.767

- 180 00 00.000

z2-1 166 22 04.767

C(2 2220 51' 08.6" - 2.211" 222 51 06.389

Az 2 389 13 11.156

- 180 00 00.000

Az3 _2 209 13 11.156

C( 3 1900 15' 02.6" -2.211" 190 15 00.389

Az 3 399 28 11.545

- 180 00 00.000 .-

Az4 - 3 219 28 11.545

(k 2770 05' 17.0" - 2.211" 277 05 14.789

AZ4 L 136 33 26.334

Values in meters Values in meters

N1 4 ,072, 555. 85206 E 608, 279. 04404

N, 1,383.88907 nE E - 335.61649

N2 4,073,939.74113 E2 607,943.42755

/nN2 319.20444 /2E 2 178.54187

N3 4,074,258.94557 E3 608,121.96942

n N3 4,999.41523 n E3 4,116.78679

N4 4,079,258.36080 E 612,238.75621

NT 4,079,258.31754 ET 612,238.85256

dN 0.04326 dE - 0.09635

27

-... • . . , i-, -i -i -..., - .... i,-.i -,, - ,.'. .•............................................-V-.........,.........-.......V. , ..

-t . - . . - - -.. • • - --"* -- -

SE. = ( dE / D ) . d i (3.10)

8N, = ( dN / D ) . d. (3.11)

Where: SE. = correction to nEi,

8Ni = correction to LN 1 ,

dE = total closure correction in the E coordinate,

dN = total closure correction in the N coordinate,

and

D = total distance.

The adjusted E and N coordinates (Table IX) were

different from the fixed E and N coordinates (Table II) by

0.00001 m due to round off error. The calculations and

adjustments were illustrated in sections A, B, and C by

using the hand calculator (TI-59) and rounded off at 5

decimal places. The computer program was written to calcu-

late the adjusted traverse station positions by the

Approximate Method by using 16 decimal places (Appendix A).

The approximate traverse adjustment is based on an assumed

condition that the angular precision equals the precision in

linear distance.

D. ADJUSTMENT DF A TRAVERSE BY LEAST SQUARES METHODS

The method of least squares provides a rigorous

adjustment and best estimates for positions of all traverse

stations. The Least Squares Method is used to

simultaneously eliminate closing errors in azimuths and

coordinates of traverses.

1. The Principle of Least S&uares-

The fundamental condition of the least squares tech-

nique in surveying requires that the sum of the squares of

the residuals be minimized. A residual is defined as the

difference between the true and observed values. In making

28

TABLE IXAdjusted Coordinates (Approximate Method)

Departure Correction Grid Values in meters

E 608,279.04404

6E 1 -335.61649 + 0.01659 - 335.59990

E 607,943.44414

nE 2 178.54187 + 0.00426 178.54613E 3 608,121.•99027

LE 3 4,116.78679 + 0.07549 34,116.86228

E4 612,238.85255

Latitude Correction Grid Values in meters

NI 4,072,555.85206

IN I 1,383.88907 - 0.00745 1,383.88162

N2 4,073,939.73368

INN 2 319.20444 - 0.00191 319.20253 -

N3 4,074,258.93621

IN 3 4,999.41523 - 0.03389 4,999.38134

4 4,079,258. 31755

physical measurements, the true values can never be deter-

mined. The least squares principle establishes a criterion

for obtaining the best estimates of the true values.

If the best estimates of the true values are stated

by x, and observed values by i, the residuals are expressed

asV. = I. - X.

V. i iThe fundamental condition of least squares, for

uncorrelated observations with equal precision are expressed

as

29

nS

( v 1 )2 = (v 1 ) 2 + (v 2 ) 2 + (v 3 ) + . . (Vn) 2 Minimum1:1

or in matrix form 0

VTV = inimum (3. 12)

In general, the observed values are of unequal

precision. The observed value of high precision has a small

variance. Conversely, a low precision of the observed value

has a large variance. Since the value of the variance goes Ain opposite directio to that of the precision, the observa-tion is assigned a value called weight corresponding to a

quality that is inversely proportional to the observation'svariance.

For uncorrelated measurements xI , x 2 , x 3 , .S 2 2 1-'S, with variances 2 n"respectively, the

weights of these uncorrelated measurements are,

62 2 2

Pnl~~ 113 13) P3 6.(322

2 2

P~~~ o-0 / (5 3 3

where Or. is the proportionally constant of an observation

of unit weight [Ref. 7, p. 67]. These weights may be

collected into a corresponding diagonal P matrix, called the

weight matrix:

p 0 p0 •. 0

0 22

00 p. 033

p = .. ..

P!

. . . .• . . . . . , . . • . . . . . . . .. . .. . ,. . . . ,. .,•. . . . . .. . • -p /,

n n

30

The weight matrix consists of weighted observations

of a traverse with mixed kinds of measurements. They are

distances and angles. The variance of a measured distance

is expressed in meters and an angle in radians. For

uncorrelated observations of unequal precision, the funda-

mental condition of least squares is expressed as

nj pvV = 2

2v + p V2 . . . . . . p v 2

1 i111 Vl P22 2 :333 nn n

- Minimum

or in matrix form

VTpV = Minimum (3.14)

In the problems involving the adjustment of observed

values, all observed quantities are expressed by functions

of the quantities to be determined. In simple cases these

relations are linear, but when this is not the case, the

relations must be converted into the linear form by

expanding them into Taylor's series. The terms of higher

order are neglected, so as to obtain linear relations,

solving the resulting linear equations, then iterating until

the effect of the neglected higher order terms are

minimized.2. Least Squares Adjustment of Indirect Observations

The observed values are related to the desired

unknown values through formulas or functions which are

called observation equations. One observation equation is

written for each measurement. To solve for the best value

of each unknown parameter, at least one redundant observa-

tion equation must be written. That is, the number observa-tions must be greater than the number of unknowns. Thelinear ohservation equations can be written in the general

form as follows:

31

- i

. ., -.

",?-...'-- b :?b '-b :.. .' -/ .'..-.'... .i ... ' .-- i-. .% ..'. - -... -. & . -.-"-xL L :." .' ." . ..-" i . . .. -. - - ..

* -,.. -

I

alO a 1 1 x + a 1 2 x 2 +- + aim xm =G 1 + V 1

a 2 0 + a 2 1 x 1 + a 2 2 x 2 +.. + 4a 2 m Xm= G 2 + v 2

* . , . . .

ano+ a nlX1 a n2. 2 + a nmx m G n + V n

where n is the number of observations; m is the number of

the unknowns; aO, a2 0 , . . . ano are constants; a, , a, 2 ,

• . . anm are coefficients of the unknowns xI , x 21

X m ; and v1 , v2 , . . . vn are the residuals.

Because the observations G i (i = 1, 2, . . . n) areI

not free from random errors, each G. must be corrected by a

residual value, v. . let b; = G; - a.o. Thus

all zl + a 1 2 x 2 + . m x m b1 = v 1

21 a2 2 x 2 * " " " 2m m- b 2 =v 2

*- . .-.

a nlX 1 + a n2X2 + + anrnxm bn n V"-

or in the matrix form

V = AX - B (3.15)

This equation is called the observation equation or

the observation equation matrix.

For uncorrelated observations of unequal precision,

substitute the value for the V matrix from the observation

Equation (3.15) into Equation (3.1 )

32

.,... .,..,j._o...','.- ,........'...... .... . ....,,. ... . .•... .. ,.,...•- .. -.:...

V TPV =(AX B) TP (AX -B)

= (AX) T BT)p(AX - B)

=(XT T -BT)P(AX - B)

=(X TATP p BTp) (AX - B)

= XT AT PA X -XT ATPB - BT P&X + BT PB

= XT AT PAX -XTATPB - XTA TPB + BTPB

= XT ATPA 2XTATPB + BTPB (3. 16)

T =_[fLrom matrix algebra, (AX) X TAT and BTPAX X TAT PB]

The minimum of this function can be found by taking

the partial derivatives of the function with respect to each

unknown variable (i.e., with respect to the x1 , x2 *

Xm) must egual zero. Hence,

S(VTpJ) -ApA - 2ATPB =0 (3.17)

axDividing Eguation (j.17) by 2, the following result -

is obtained:

A TPAX A AT PB

This represents the normal equations, and by multi-

plying this equation by (AT PA)-'1, the solution is obtained:

X = (ATPA)1IATPB (3.18)

For uncorrelated observations with equal precision,

the weight matrix is an identity matrix, and eguation (3.18)

becomes

X = (A TA) IATB (3. 19)

This equation can be derived similarly to the

unequal precision case. Eguations (3.18) and (3.19) are the

basic least squares matrix equations.

33

I-

If the relations are nonlinear, the relations must

be converted into the linear form by using Taylor's series

expansion [Ref. 3, p. 919]. Let F = f (x, x •. x M)

be the general observation equation that is a nonlinear

function. The Taylor's series expansion is

= f(x 1 , x 2, . . x,) +_f X, +_f X . + fX2 X**X*m

1~ ,2

+ Higher order termso0

where x i, X0, . x* are the approximate values of the

variables at which the function is evaluated. For the

traverse problems, an approximate value can be the

precalculated value, and 8x I , 8x 2 , . . . Sxm can be the

corrections. The higher order terms in the series are

neglected and only the zero and first order terms are

maintained, the approximate value must be improved by

successive iterations until the effect of the neglected

higher order terms is minimized. After linearization, the

observation equations become:p

=, f 1 (X x . *10m X.ix+~8 2 + + 1 xm- G,

2~ mm X

v= f (x, x , . .. x%) +- f 2 1 + _f 2 Sx 2 + . • +._sxm- G2

2 m

o f -+

n n1 2 ) n8 xl+. a I+fnSXm -- Gvo, = fn(xi, x"2, . . x0.' a,} _lo~ 2+ a.fx-G

1 "p

or in the matrix form

V = AX -B (3.20)

I

34

.. ., .. .

.. . . . .. . . . . . . . . . . . . .. .

where

Zfl '3f 1 . . -fl vi2 f . ..... 2 V

1 0 2A = . . V = .

A .

a -f-n - n Vn

a@ %

Dx* )e2 m

G- f, (X0, 1 , .... m) 5 x 1

G f ('Ic x 2 . . 0 * 0 mG2 f2 C 16#

B = . . o . . I =

* S * . .•

Gn - fn (XI t2 X 6 M

The remainder of the least squares procedure is the

same as indicated by Equations (3.16) to (3.19).

There are two types of observation equations for the

adjustment of the traverse. They are the angle and distance

observation eguations. Both of them are nonlinear, and they

must be linearized using the Taylor's series.

To derive the observation equation for the angle & .

(Figure 3.1), first write the two azimath observation

equations for the azimuth AZlk and Azij , where AZik is the

back azimuth and Az.. is the forward azimuth.IJ

Ek - EAzIk = arc tan N

E- E;Azij = arc tan N.-N.

35S]

....................-.--"....... -• .... . .• ... . .•/ i < : . •il -

Then, the angle observation equation for the angle d&. is

v. = Az.. - Az.k - ..I ij •

Etan - arc tan t- d. (3.21arc NN. N -- (.)

II k

Equation (3.21) is nonlinear in the parameters.

Write this equation in function form:

v. = f. (E., N., E. N., E , N ) -I I I , E! Ni k k

Thus, the linearized form of the angle observation

equation is S

fN , E , N . °, ° N.

of 8EI +3fibN. +6f.SEk + 3f. 8 N k

J J k k

The observation equation for the distance di between

two points i and j is

v = [(E - E I)2 + (N, - N;) 2]/ 2 - d;

J' " " -

or i- the functional form

V = fi(E;. N i, Ei, N; ) -d,

Thus, the linearized form of the distance

observation eguation is

V, = f i(EO , N, E0 , N 01 )+ ~f SE, + Zf if1

* ~ ~ ~ E afS. f.N+~~ Z)f S i °N

For the adjustment of the traverse which was

conducted at Moss Landing with the technique of adjustment

of indirect observations, four angle and three distance

36

observation equations need to be written. The seven equa-

tions would include as unknown parameters the four coordi-

nates of stations 2 (Mossback) and 3 (3une Temp). Four

normal equations are formed and solved for corrections to

the approximate values (precalculated values) of the parame-

ters. The corrections are added to the approximations to

update their values, and the solution is repeated until the

last set of corrections is insignificantly small.

The linearized equations of this problems are

v, = a11 E2 + a 12 8N 2 + a1 3 6 E3 + a14 N 3 - bI

V2 = a21 E2 + a22 N2 + a23 5E3 + a24 5N3 - b 2

v 7 a7 &E + a SN + a SE + a 5N -b

7 71E2 72 2 73 3 74 3 7

The zero order terms of the angle and distance

functions are0

lE= arc tan E a nN 3 - N 1 -N£

f- E) arc tan N' Nzf2~ ~~ = 1r an N

f = arc tan E4 E3 - arc tan El- E"22N -N N 2 - No3 _.:

3 -f4 = AZL arc tan 3 -_ c--N4 2

= [N(E - E2 )2 + (N - No )]I/2

S= ((E4 - )2 * - 33 )2]1/2

4= [(E - E4 ) N2 (N - N4 )2]1/2

By using the data of the known coordinates (Table II) and.

the approximate values (Table VII) " .,

a = 0 = r N2 - N1 = O. 682'96 x 1O- 3 .,.%al1 -E 1 LN_N 1 )2 + (E2_E 1 )j

37

- '- .. . - . ) + ( " - . .. ....

- . - -r r . • . -, - -- l 7r .,

a E- E, : 0.16550 x 10-3

12 = - E,-)2

a 1 3 = - 03 f

al 4 'af =0-6 N0

3

a3, =3f;- N o3 -N ° ] - N, -Nh

21) 2 21

E* N;- N; 2 4- No o2

J 1 ( 1 - 2 (E 0-E2)

= - 3.06868 x 10-3

f 1-E,-*a22 -2 (N- N2 )2 + (E- E 2 ) N N0 )2 i-(E1-E' 2

-3 3 20 2 12

= 1.16926 x 10- 3

a2 3 3 f 2 = ~ -N ]=2.38621 r 10-3DE3 LN- N 2 )2 -4- (E 0 -E

a 2 4 2 = -o - E 2o]= - 1.331476 x 10 - 3

[NNN3-N2 + (E 3 - E 2 )2

0

a3 -13f 3 = - j = - 1.33476 x 10-3

a3 3 ='--f = -FN 4 - ti3 1 ' 2 -N S1-2 _ 2

+- (E 2E) 2=

E% - )2 (-E- E )2 N2 N032 (E;-2 3

: - 2.50541 X 10-3

a 34 N'-3 (N4_-No 2 [i (7NE)2 No )2 + (E E o )2,3 2 - 3

= 1.43291 x 10-3

38

.- .

E 02a 1 B&4 f 0

42-4No

a =4 3 'f 4a = -N 4 = 0.11920 x 10-sa43 1: LNo- N4)2+ (E - 4 )2"

a4 = =- E ]=-0.09816 x 0

N3 N3_ .N )2 4)

=5 af = - El E2]= - 235.67466 x 10- 3

a 1 -(2El- E°2 ) (NI N 2)2 /- -f5 Ni 2 = 971.83201 x 10 -

5 2 ]iN5 E.1/ 2J2

a =af = 0

a 5 3 5 =0

a 5 4 Bf =0

3

a6 1 f 1=- 488.17948 x 10-

a [-6 )2 -t-( o N 3 )2 ]1/2

2 f= - NN ]= - 872.74326 x 10- 3

a~--0 )2 (N -N 21/2J2 (E )2 E; C~~N

3

a 3 =af6 =Ea- 488.17948 x 10-3

G6 =- - 2 8E~ ~ 3 -~ 2 NJ Q212

* ~~(2-E3 2

a0

3 2. 3

71 -f 0 ., , - . ... : -

. . . .~~~~~~~~~ E-2 " "I I

"iI_. .I

• - " II II 1 II " "I' 1"! i I i

a 3 ~f 7 E; E___________ , 635.68254 X 10-3

3 L(E; E 4 (N - N4 )]l2

a 74 Bf N 3 N4 -771.95059 x 10-3

3 (E- (N-N 4 )

or in the matrix form

0.68246 0.16550 0.00000 0.00000

-3.06868 1.16926 2.38621 -1.33476

2.38621 -1.33476 -2.50541 1.43291

A =10-3 0.00000 0.00000 0.11920 -0.09816

-235.67466 971.83201 0.00000 0.00000

-448.17948 -872.74326 488.17948 872.74326

0.00000 0.00000 -635.68254 -771.95059

The computation of B matrix, by using the datafrom Tables II, III, IV, and VII

= - f1 0.00000 radians

b2 Ot 2- f2 =0.00000 radians

b 3 = C(3 - f 3 = 0.00002 radians

b = c&4 - f4 = 0.00002 radiansb4= -f .000mtr

b5= d, - f5= 0.00000 meters

b7 d 3 f 7 =-0.01426 meters

or in the matrix form

B T [0 0 0.00002 0.00002 0 0 -0.0 142 6)

The weight matrix can be computed by using the vari-

ance of the observed angles and distances from Tables III

*and IV by applying to Equation, (3.13). For uncorrelated

observations of unequal precision, the weight matrix is

defined as the diagonal P matrix.

40

p11 = 1 / sin2(1.9841) = 10,808,537,426.79957

P2 = 1 / sin2(1.40511) = 21,552,498,219.02474

p3 3 = 1 / sin2(1.20311) = 29,398,082,997.43487

p = 1 / sin2(1.61411) = 16,332,144,194.08730

P = 1 / (0.001)2 = 1,000,000.00000

p66 = 1 / (0.001)2 = 1,000,000.00000

P77 = 1 / (0.003)2 = 111,111.11111

For uncorrelated observations of unequal precision,

the values of A, B, and P matrices are applied to Eguation

(3.18). The correction vector is found to be

SE = 0.01284

X = SN2 = 0.00336

SE = 0.01079

6N = 0.004953

The approximation values were improved by adding the

corrections to the first approximation values. The improved

approximation values after the first iteration are

E2 = 607,943.44238 + 0.01284 = 607,943.45522 m.

N2 = 4,073,939.74473 + 0.00336 = 4,073,939.74809 a.

E3 = 608,121.99110 + 0.01079 = 608,122.00189 m.

N3 = 4,074,258.94534 + 0.00495 = 4,074,258.95029 m,.

Using these values, the solution is iterated. After the

second iteration, the correction vector is zero to six

decimal places, so the improved approximation values are

the final estimates of the coordinates.

For uncorrelated observations of equal precision,

the correction vector is found by solving Equation (3.19).

The correction vector after the first iteration is

2 = 0.01756

[ = 5b 2 = 0.00426

B 3 = 0.016603b 3 = 0.004793

.. . . ..-......--.. ~' - . .41

The imprcved approximation values after the first iteration

are

Z = 607,943.44238 + 0.01756 = 607,943.459914 a.

N2 = 4,073,939.74473 + 0.00426 = 4,073,939.74899 a.

E3 = 608,121.99110 + 0.01660 = 608,122.00770 a.

N3 = 4,074,258.94534 + 0.00479 = 4,074,258.95013 a.

The solution is iterated by using these adjusted

values. The correction vector is zero to six decimal places

after the second iteration. These values are the final

estimates of the coordinates.

The standard deviation of an observation which has

unit weight can be found by the following equations, for

uncorrelated observations of unequal precision,

=5. VT Py ' (3.22)n~rn

for uncorrelated observations of equal precision,

CO= [vTV ] 1/2 (3.23)

where n is the number of observation equations and m is the

number of unknowns (Ref. 7, p. 249]. After calculating the

best estimate values of the unknowns, the V matrix can be

computed from Equation (3.20).

The standard deviations of the best estimate values

for the unknowns are then given by the following equations:

.5= o Si ' 1/2 (3.24)

where 6. is the standard deviation of the ith aijusted

quantity. The quantity in the ith row of the X matrix, Sii

is an element of the (AT PA) -1 matrix for uncorrelated

observations of unequal precision. For uncorrelated

observations of equal precision, S,; is an element of the

(ATA) - 1 matrix [Ref. 7, p. 250].

42

.. . . . . .. . ... *'. .-- *********:***.:-*** ..... . ... . . . .2 ~ * p .. % j, 5..AJ .r..J .. a. t '.. ,,L -

11 S12 . 5 1M

S2 1 S2 2 - - - - -*2

(A PA).. or (TA)1 . . .*

SM1 Sm2 .M

The standard deviations of adjusted angles and

distances can be computed by the following equation:

6=6[.] 1/2 (3.25)

where 6. is the standard deviations of the ith adjusted

guantity. The quantity in the ith row of the V matrix, jis an element of A(AT PA)-1AT matrix for uncorrelated

observations of unequal precision. For uncorrelated

observations of equal precision, Q0 is an element of the -

A(ATA)-1AT matrix [Ref. 3, p. 912].

Q21 Q2 2nA (AT PA) -1AT. .. 0

or- . . . . .

A (AT A)-lAT.

QnI n2 Q nn)

A closed traverse was conducted at Moss Landing.

After the second iteration, the V matrix can be found by

applying the values of A, B, and X matrices to E~uation

(3.20).

43

L

For uncorrelated observations of unequal precision,

the V matrix is found to be

'al = 0.93149 x 10-5 radians or 1.92134"

= -1.63120 x 10-5 radians or -3.36459,-

Va3 = -1.28363 x 10-5 radians or -2.64768"V Va4 = -2.30436 z 10-5 radians or -4.75308"

Vdl = 0.00024 meters

Vd2 = 0.00039 meters

Vd3 = 0.00358 meters

The standard deviation of unit weight is found by solving

Equation (3.22), the result is

6 = + 2.69685

The values of (ATpA) - are

1.25178 0.22019 1.25575 0.10788

10-s 0.22019 0.13819 0.21810 0.11127

1.25575 0.21810 1.46408 0.03815

0.10788 0.11127 0.03815 0.22515

The standard deviations of the best estimate values for

positions can be found by solving Equation (3.24), the

results are

6E2 = ± 0.00954 meters6 N2 ± 0.00317 meters6 E3 = ± 0.01032 meters6 N3 = ± 0.00405 meters

4

i i::44

.

The values of A(ATPA)- *AT are

0.064 -0.052 -0.021 0.010 -4.165 -6.963 -63.88

-0.052 0.225 -0.175 0.002 3.415 4.690 41.59

-0.021 -0. 175 0.211 -0.014 2.563 3.574 31.79

10-10 0.010 0.002 -0.014 0.002 -1.813 -1.301 -9.501

-4.165 3.415 2.563 -1.813 9917 -117.4 -1047

-6.963 4.690 3.574 -1.301 -117.4 9830 -1525

-63.88 41.59 31.79 -9.501 -1047 -1525 76323

The standard leviations of adjuste! angles and iistances are

found by solving Equation (3.25), the results are

al = ± 1.40346 seconds

da2 = ± 2.64103 seconds

a3 - ± 2.55260 seconds

a4= ± 0.26137 seconds

d1 = ± 0.00269 meters

6 d2 : ± 0.00267 meters6 d3 = ± 0.00745 meters

For uncorrelated observations of equal precision,

the V matrix is found to be

va I= 1.26896 x 10-5 radians or 2.61742"

Va2 = -1.56893 x 10-5 radians or -3.23615"

Va3 = -1.75414 x 10-S radians or -3.61817"V = Va4 = -2.23358 z 10-5 radians or -4.60710"

vd = 0.14037 x 10-7 metersvdl

= 0.23844 x 10-7 metersVd 2" -

Td = 0.24365 x 10-7 meters

The standard deviation of unit weight is found by

solving Equation (3. 23) , the result is

± 2.01144 x 10-5

45

. - ~ La a~j• ..

The values of (ATA)-I1 are

10-4 0.06827 0.01664 -0.20731 0.170751

-0.854~49 -0. 20731 2.59561 -2.13724L0.70380 0.17075 -2.13724 1.75999lo

The standard deviations of the best estimate values for

positions can be found by solving Eguation (3.24), the

results are

E2 = * 0.00 107 meters6 N2 = ± 0.00026 meters6 E3 = ± 0.00324 meters

0 3= ± 0.00267 meters

The values of A (AT A) -'AT are

r1.1472 -27. 197 26.960 -1.235 -0.518 -0.343 -0.856

-27.197 5 03 .1 -498. 7 22. 855 J.348 0.480 0.473

26.960 -498.7 494.4 -22.66 0.370 0.523 0.518

10-3 -1.235 22.855 -22.66 1.038 -0.201 -3.159 -0.134

-0.518 0.348 0.370 -0.201 10000 -0.001 -0.001

-0.843 0.480 0.523 -0. 159 -0.00 1 10000 -0.001

-0.856 0.473 3.518 -0.134 -3.001 -0.001 10000

*The standard deviations of adjusted angles and distances are

found by solving Eguation (3.25) , the results are

d'ai= ±0.15917 seconds

a2 = ± 2.94270 seconds

da3 = ± 2.91732 seconds

a4 = ± 0.13370 secondsOd= ± 0.00002 meters

d2 0.00 mtr6d 3 0.00002 meters

46

The computations in this subsection were performed

by the NPS IBM 3033 computer using 16 decimal places and

were rounded off to 5 decimal places prior to output.

3. Least Squares Adjustment b __the Condition Equation

Method

The general principle of least squares adjustment by

the condition equation method in surveying is

to minimize a function consisting of the sum of thesquares of the corrections to the observations plus thenecessary mathematical conditions involving some or allthe corrections; each condition by itself is made eaualto zero by adding the corrections to the discrepancydeterminea from a preadjusted calculation (i.e. calculatedfrom the observed values rather than from adjustedvalues); thus, the magnitude of the sum of the squares isnot changed by adding conditions [Ref. 8].

For uncorrelated observations of unequal precision,

the principle condition of least squares function may be

expressed in matrix form as follows:

U = V - 2K[BV U!

= VTpv - 2[BV + W]TK

= VTPV- 2 (BV)T + VT ] K

= _ 2[vTBT+ WT]K

= pV - 2VTBTK + 2TK

= minimum

where U is the least squares function matrix, K is a matrix

of Lagrange multipliers, P is the weight matrix, V is the

correction vector, B is the constant coefficients of the

corrections, and W is the precalculated discrepancy

[Ref. 9]. It is numerically more convenient for later

development to multiply by 2. Taking the partial

derivatives of the U matrix with respect to each of the

corrections and equating to zero leads to

47

. .... ,. .

7I

__ = 2PV - 2BTK = 0VI

or

V = P-1BTK (3.26)

This equation is called a correlate eluation or correlate

equation matrix. The solution of the Lagrange multipliers p

matrix can be derived by multiplying Equation (3.26) by the

B matrix then adding the V matrix

BV + W = BP-*BTK + W SI

(BV + W) is the condition equation matrix which must equalI

zero. The solution of the Lagrange multiplier vector is

BP-BTK = -W

K = (BP-1BT) -1 (-W) (3. 27)

The correction vector is derived by substituting

E~iuation (3.27) into Equation (3.26)

V = P-1BT(BP - * BT)1- ( -V) (3.28)

For uncorrelated observations of equal precision,

the correction vector can be derived similarly to the .

unequal precision case or by using the inverse of the weight

matrix which is the identity matrix. Equation (3.28)

becomes

V = BT (BBT)-1 (-W) (3.29) i

Closed traverse station positions may be adjusted by

using the technique of least squares adjustment by the

Condition Equation Method. There are two condition equa-

tions. They are the azimuth and coordinate condition equa-

tions. The coordinate condition eluations are divided into

two parts, which are E and N coordinate condition equations.

p

48

................. . .. .. ..

The azimuth condition equation is the sum of the

corrections to the angles in a traverse plus a precalculated

discrepancy W, (Equation 3.6) which must equal zero. Where

Va, equals the corrections to the angles, the general equa-

tion can be written:

or :n n-1

,a + I0.v +d; = 0 (3.30)(:1 :1

where vdi is the correction to the distances. However,

this term equals zero and does not effect the ejuation, but

it does reserve space in matrix notation for distance

corrections. A closed traverse which was conducted at Moss

Landing can be written with an azimuth condition of

1.V + 1.v + 1.v + 1.V v + 0 O.v

al a2 a3 a4 "dl d2 Vd3

+ W1 = 0 (3.31)

where the precalculated discrepancy (W1) is +8.844" or

+0.00004288 radians.

The simp±e linearized form of an E coordinate condi-

tion equation is the sum of the adjusted departures and must

equal zero. By applying Equations (3.2) and (3.7), the

general formula for E coordinate candition equation isn-1

>(d' V ) sin AZa - (ET -E 1) = 0 (3.32)

where 1

Az = AZF + >(c~. 4 Va) - (i - 1) 1800 (3.33)j:l

AZa is the adjusted azimuth. By using Equations (3.32) and

(3.33) with the data conducted at Moss Landing, these

equations become

(dI * Vdl).sin AZal + (d2 + vd2 ).sin AZa 2

+ (d 3 + Vd3).sin AZa3 - (ET - El) = 0 (3.34)

49

IJ

where

Az = AzF + 1 + Val

= zi + va.1>

a 2 F 1 al 2 + Va2

= Az2 + Val + Va2

AZa3 = AZF + 4LI + Val * 'L2 + Va2 + L 3 - 3608

= Az3 + Va + va2 + Va3

Azi is the precalculated azimuth or unadjusted

azimuth (Equation 3.1).

From trigonometry P

sin ( A +/LA ) = sin A.cosnA + cos A.sin5A

in which 5A is a very small angle in radians, letI

cosLA 1 and sinnA -/\A

therefore,

sin ( A +LA ) = sin A +/nA.cas Afrom the first term of Equation (3.34)

(d1 + Vdl )sin AZal

= (dI + Vdl )sin (Az 1 + Val)

= (di + Vdl)[sin Az 1 + ValCOS Az I )

= d sin Az1 + a dlCos Az1 + Vdl sin Az1 + Vdl+a1 COS AZ1

(3.35)

(vdl .Val) is very small, by letting this term egual zero,

Equation (3.35) becomes

(dl + vd1)sin AZa"

a dIsin Az, + Val dlcos AzI + "dl sin AzI (3.36)

50

SI-

* %•.•A"t.|

II

The second and third terms of Egquation (3.34) can be derived

similar to Equation (3.36), so

(12 + vd2)sin AZa 2

= sin Az2 + (Va1 + V 2 )d 2 cos AZ2 • vd2 sin Az2 (3.37)

(d 3 + vd 3 )sin AZa3

= d3 sin Az3 + (Val +Va2 +Va3 ) d3 Cos Az3 + Vd3 sin Az3 (3.38)

Substituting Equations (3.36), (3.37), and (3.39)

into Equation (3.34) and rearranging terms

val (d 1 cos Az1 + d2cos Az2 + d3cos Az3)

+ Va2 (d2 cos A Z 2 + d 3 cos AZ 3) + Va3 d 3 cos Az 3

+ Vdl sin Az + Vd2 sin Az2 + sd3in Az3

+ d sin Az1 + d2 sin Az2 + d3 sin Az3 - (ET - Ej) = 0

This equation can be written in the general formula asn-1 n-1 n-I n-1,

l('a 2dkCos AZk) + 2vdi sin Az. + d sin Az.9 :1 k:i i 9,.: 1iI:

- (E T - E1 ) = 0 (3.39)

substituting Equations (3.2), (3.3) , and (3.7) into Equation

(3.39)

n-1 n-1 n-1•(v, Nk + v d sin Az; + = 0 (3.40)

i:1 k:I 1:1

For example, if the number of the observed angles (n) at

Moss Landing is four, this equation can be expanded to

Val (,INN 1 +INN 2 +L8 3) a 2 (N 2 N 3) a3 V5 3

+ vd sin Az + Vd 2sin Az 2 vd 3sin Az 3 W = 0

51

I

Substituting the numerical values from the precalculated of

this traverse into this equation, the result is

+(4999.28284I)v + 0.v(6 7 0 2 . 3 7 6 1 2 )vai +(5318.48345)vi 2 a3 a4

-(0. 2 3 56 7)vd +(0. 4 8 8 1 8 )Vd2 + (0.63570) Vd3 + W2 = 0 (3.41)

where the precalculated discrepancy (P 2) is 0.08608 m and

O.Va4 is equal to zero, which does not effect this equation,

but space is reserved in matrix notation for the last angle

correction.

The N coordinate condition equation is the sum of

the adjusted latitudes and must equal zero. By applying

Equations (3.3) and (3.7), the general condition equation isn-1__(d. + Vdi) cos AZa- (NT N) 0

i:1

This equation can be derived similarly to the E coordinate

condition equation case, resulting inn-1 n-1 n-1

2(v;2 nEk) 4 2vdi Cos Az + W3 0 (3.42)i:1 kzl i:1

From the data acquired at Moss Laniing, this equation can

be expanded to

-Val (LEI +nE 2 +E3) - Va 2 (nE 2 +6E 3 + Va3!ZE 3

v 1 Cos Az, Cos Az2 + Vcos Az3 + W3 0+l 1 d 2 2 d3 Co

Substituting the numerical values from the calculation of

this traverse into this equation, the result is

-(3959.89460)Vi -(4295.49626) va2 -(4116. 94755) Va3 + 0.va4

+(0.97183)vd1 +(0. 8 7 274) Vd2 +(0. 77194)Vd3 + W 3 = 0 (3.43)

where the precalculated discrepancy (W3) is -0.08936 m.

-7't

52 '

.......... ,

.. . . . . . . . .. . . . .

c.'" "''" I 'L ;" <'" .. ... .. . , _ . _ _ _ , ,..-..' ".'.i..". '.. -[[i . ". i.'..'',i _ L-1 _,L" "._ . , .? ..L 3.'- .- ' '. - L. .-'.' L [ . ' i-[ ...".".."... .-.. . . ...... . . . . ....-. .... . .... . .. ..... .<. .

Equations (3.30), (3.40), and (3.42) can be written

in the matrix form as (BV + W), where B is the constant

coefficients of the corrections, V is the correction vector

which is composed of the angle and distance corrections, W

is the precalculated discrepancy. Equations (3.31), (3.4 1),

and (3.43) are written in matrix form as

1 6702.37612 -3959.89460 Va 1

1 5318.48345 -4295.49626 Va21 4999.28284 -4116.94755 Va3

B r 1 0.00000 o.oooo V 4

0 -0.23567 0.97183 Vdl

0 0.48818 0.87274 Vd2

0 0.63570 0.77194 Vd3

-W1 = -0.00004"

S -W = -0.08608 1--W 3 = 0. 08936

For uncorrelated observations of unequal precision,

the inverse of the weight matrix is the diagonal matrix,

which is equal to the observation's variance. The diagonal

elements of the inverse of the weight matrix is

p-I = sin2(1.984 " ) = 0.92519 x 10-10

p-1 = sin2 (1.405") = 0.46398 x 10-1022

P31 = sin2(1.20311) = 0.34016 x 10-10

P-1 = sin2(l.614 ' ' ) = 0.61229 x 10-1044

p-I = (0.001)2 = 0.10000 x 10-55

p-I (0.001)2 = 0.10000 x 10-s66 ?,

p = (0.003)2 = 0.90000 x 10-s77

53

For uncorrelated observations of unequal precision,

the correction vector is found by solving Eguation (3.28)

Val = 0.93141 x 10-5 radians or 1.92117"

= -1.63114 x 10-5 radians or -3.36446"

Va3 = -1.28358 x 10-5 radians or -2.64758"V = 4= -2.30438 x 10-s radians or -4.75312"

V = 0.00024 meters

Vd 2 = 0.00039 meters

Vd3 = 0.00357 meters

The corrected angles are

0(1 = 2460 05' 45. 12117"

0( 2 = 2220 51' 05.23554"

cI 3 = 1900 14' 59.95242"

0[ 4 = 2770 05' 12.24688"

The corrected distances are

PIP= 1424.00424 m.

d 2 = 365.74439 a.

d3 = 6476.27457 a.

Using the corrected data to recompute the coordinates is

similar to the initial traverse computations. The adjusted

coordinates are

E2 = 607,943.45521 m.

12 = 4,073,939.74809 m.

E3 = 608,122.00189 m.

N3 = 4,074,258.95029 m.

E4 = 612,238.85256 m.

14 = 4,079,258.31754 m.

The last adjusted coordinates are the same values as the

fixed coordinates. Hence, it is not necessary to iterate.

For uncorrelated observations with equal precision, the

correction vector is found by solving Eguation (3.29)

54

Val = 1.26884 x 10-5 radians or 2.61717"-

V 2 = -1.56886 x 10-s radians or -3.23601,

V 3 = -1.75408 x 10-5 radians or -3.61804"V = 2.23360 x 10-s radians or -4.60713"1 'a 4

V.d = 0.14034 x 10- 7 meters

vd2 = 0.23842 x 10-7 metersVd3 0.24362 x 10 - 7 meters

The corrected angles are

OI = 2460 05' 45.81717"

C(2 = 2220 51' 05.36399"

03 = 1900 14' 58.98196"

= 2770 05W 12.39287"

The corrected distances are

d1 = 1424.00400 m.

d = 365.74400 m.

d3 = 6476.27100 a.

By using the corrected data to recompute the coordinates,

the adjusted coordinates are

E2 = 607,943.45994 m.

1 2 = 4,073,939.74899 m.

E 3 = 608,122.00770 m.

M3 = 4,074,258.95013 m.

E4 = 612,238.85256 m.

N4 = 4,079,258.31754 a.

The last adjusted coordinates are the same values as the

fixed coordinates. Hence, it is not necessary to iterate.

55

'.- ~ A . ... -o -

The standard deviation of an observation which has

unit weight can be found by the following equations. For

uncorrelated observations of unequal precision, P

[VT [T 1/2 (3.44)

and, for uncorrelated observations of equal precision, S -

= [v / 2 (3.45)

where r is the number of condition equations. There are Ithree condition equations for a closed traverse (r=3). The

standard deviations of adjusted angles and distances can be

found by the following equation:

=~ 60Q ' 12 (3.46)

6, 6. -i,

where is the standard deviation of the ith adjusted

quantity. The quantity in the ith row of the V matrix, Q Pis an element of the P-1 - P-1BT(BP-1BT)-*BP - 1 matrix for

unzorrelated observations of unequal precision

[Ref. 3, p. 918]. For uncorrelated observations of equal

precision, Q;i is the element of the I - BT (BBT)-1B matrix. V7

The matrix P-1 - P-1BT(BP-IBT) -BP - 1 or the matrix

I - BT (BBT)-B is equal to

S

Q11 Q 1 2 * . * Q n

Q 2 1 Q 2 2 . . . . Q2n.•."

* . * * o . . . . P

Qnl Q n2 Qnn

56 • "

.............................................5.. .. .. . .. _______________________

For uncorrelated observations of unequal precision,

the standard deviation of unit weight is found by solving

Equation (3.44), the result is

o = + 2.69679

The results of P-1 - P-*BT(BP-*BT)-1BP - 1 are

0.064 -0. 052 -0.021 0.310 -4.165 -6.963 -63.88

-0.052 0.225 -0.175 0.302 3.415 4.689 41.59

-0.321 -0.175 0.211 -0.014 2.563 3.574 31.7910-10 0.010 0.002 -0.014 0.002 -1.813 -1.301 -9.500

-4.165 3.415 2.563 -1.813 9917 -117.4 -1047

-6.963 4.689 3.574 -1.301 -117.4 9830 -1525

-63.88 41.59 31.79 -9.500 -1047 -1525 76323

The standard deviations of adjusted angles and distances are

found by solving Equation (3.46); the results are

d'al = ± 1.40340 seconds6 a2 = ± 2.64096 seconds

(a3 = ± 2.55253 seconds

6a 4 0.26136 seconds

d1 = ± 0.00269 meters6 d2 = ± 0.00267 meters

6 d3 = ± 0.00745 meters

For uncorrelated observations of equal precision, the

standard deviation of unit weight is found by solving

Equation (3.45), the result is

= ± 2.01139 x 10-S

57

r

°

The results of I - BT (BBT)--B areS

1.472 -27. 199 26.962 -1.235 -0.518 -0.843 -0.856

-27.199 503.1 -498.7 22.855 0.348 0.480 0.473

26.962 -498.7 494.4 -22.66 0.370 0.523 0.518 -

10-3 -1.235 22.855 -22.66 1.038 -3.201 -0.159 -0.134

-0.518 0.348 0.370 -0.231 10000 -0.001 -0.001

-0.843 0.480 0.523 -0.159 -0.001 10000 -0.001

-0.856 0.473 0.518 -0.134 -0.001 -0.001 10000

The standard deviations of adjusted angles and distances arefound by solving Equation (3.46); the results are

6a, = ± 0.15918 seconds

(5a2 = ± 2.94262 seconds

da3 = ± 2.91722 seconds

.(a4 = ± 0.13369 seconds

"d1 = ± 0.00002 meters6d2 = ± 0.00002 meters

6 d 3 = ± 0.00002 meters

The computations in this subsection were also Pperformed on the NPS IBM 3033 computer; they used 16 decimal

places, and were rounded off to 5 decimal places in the

final solutions. These are more decimal places than are

normally used in practice because such precisions are not

generally attainable by corresponding observations.

However, in comparing two computational methods that are

theoretically equal, one method may be more sensitive to

round off error than the other. This will be commented on Pin the next chapter.

58

~~~~~~~~~~~~~~~~............. ... .-. . . .. . -... . . . . . . . •. •....... ,.,•.... ,- ..-..

IV. DISCUSSIONS AND ANALYSIS OF RESULTS

Three programs were used to compute the initial traverse

and adjust the closed traverse station positions. Programs

1, 2, and 3 were used to compute and adjust the traverse

station positions by the Approximate Method, the Indirect

Observations Method, and the Condition Equation 4ethod,

respectively. The programs were written in WATFIV language

for implementation on the NPS IBM 3033 computer. The

computer output and listings of Programs 1, 2, and 3 are

provided in Appendices A, B, and C, respectively. The

maximum number of intermediate traverse station positions

that can be computed and adjusted by these programs is 30.

The programs were tested using several fictitious data sets

to ensure their performance in handling the various

intermediate traverse station positions.

The computer storage area and CPU time of Programs 1, 2,

and 3 has been compared (Table X). The adjustment of a

closed traverse by the Approximate Method did not use a

weight matrix in the matrix computations. The computer

program for this method was written by using the variables

in only one dimension for storage of both data and results.

This method did not require any iterations. The least

squares adjustment of a closed traverse characteristically

is used to simultaneously eliminate closing errors in

azimuths and distances, and Programs 2 and 3 toth utilized

such an adjustment. The computation by either Least Squares

Method used matrices'in two dimensions to compute the

correction vector. Likewise the computer programs were

written using variables in two dimensions. Included are all

subroutines from Program 1 and extra subroutines for each

individual program. Therefore, both Programs 2 and 3 used

more computer storage area and CPU time than Program 1.

59

. "..

L'...- " ? .- '.-'".-'.--'.'. " - -. "-, - . " "."- . " - . . . -. .. . .. . . . .- .

I w) In

U).)UM ps

0) CC) *.N

V.. %

I"R Ln

0 Id.4 N~ U.

~ U)~ InU4a a

09 0a40 I (1n ) a) En Uf)IE-4 W I 4 a -W S h

Li 0 0 al Li IiI- w~ w~ U) a) 0 ~M M

010 CIO a.. it 0 0

4104 4-4 '44 UD w w 04. 0I0 0 U)0 0 r

I) In 4J 4.) W n4 4j41 U ) 4) 0 w . Cfl w 1

d) a 41Ii '- laC U)I)6 I a ) (L) (n a) a) r- = S 2

Q) 0) a5 S a 4)' 1 4) rn4-) (U) W) = 0 ~4.) 4-

00 4J Q) ) 0..4 tv C4-) w~4 -

aU 41 4-) :3 0 N 0O('4 0 0. 0.o U) (n 0..U *.U .44 U u I112 Io- 11

.1- 0 44- 4-4 0 4- In 4 In 44 4-I U 0 m- 0 -0 MI 0 ii) 4)0 0

n - m fif 0 : 0 e) 0m.L-a n .,j 4v -~ 4 w -i 4 w H4 -1

11 0.. rd 4) 41 4) M 4JIn4J M -

(o 9 v 0 v 0 mm 0I4(d;

60 a

CN w W w rc

The Indirect Observations Method requires that the

number of otservation equations be eqjual to the sum of

observation equations of both observed angles and distances.

The number of observation equations is not constant. it

changes depending on the number of the traverse stations--

this means that the row dimension 'of each matrix will change

depending on the number of observation equations.

Therefore, the subroutines affected by the number of trav-

erse stations are difficult to write in the general program.

The coefficients in the A matrix are computed by taking the

partial derivatives of the functions with respect to each

unknown variable, where the number of unknown variables is

not constant. The number of unknown variables changes

depending on the number of the traverse stations.

Therefore, the subroutine for the computed A matrix is also

difficult to write in the general program. The Condition

Equations Method has only three equations which makes it

K easier to derive the general form and write the computer* program. The adjustment using the Indirect Observations

Method does not apply the corrections to the observed valuesdirectly; therefore, it requires the approximate values of

the unknown coordinates be computed for the correction

vector of the unknown coordinates. This method requires at

least two iterations to check the insignificance of the

correction vector when it is compared with an arbitrarily

selected small number. The adjusted coordinates from the

Condition Equations Method can be checked at the first iter-

ation. Thus, Program 3 is more economical as it uses lesscomputer storage area and CPU time than Program 2 (Table X).

The closed traverse at Moss Landing originated and

dtermined by thitrorde mentwths Thew azsithosuric wase

dtermined at conrdode ponteths know poimtonsuhic were

.2.211"1 per station and the position closure was 1:66,617.The classification, standards of accuracy, and general

61

77.

7 - 7

specifications for a third-order class I traverse (Table I)

indicate the azimuth closure is not to exceed 3"1 per station

and position closure must be better than 1:10,000. This

traverse met the specifications and standards of accuracy

for a third-order class I traverse.

Using Programs 1, 2, and 3, the traverse was computed

and adjusted in UTH grid coordinates. The final adjusted

coordinates were transformed from UTM grid coordinates to

geographic coordinates [Ref. 4, pp. 319-3211. The differ-

ence between the coordinates for each method and NOS

(Ref. 10] have been computed (Table XI). The technique ofS

Least Sguares for both methods yields identical computa-

tional results to at least five decimal places (Table XI,

Methods 3. 1 and 4.~1; 3.2 and 4.2) . Least Squares provides

the test estimates for positions of all traverse stations.S

Program 2 performs a statistical test, yielding the standard

deviations of both adjusted positions and observed values.

Conversely, Program 3 only yields the standard deviation of

adjusted observed values. Comparisons of the standard devi-

ations of adjusted observed angles and distances were madebetween these computed by the Indirect Observations Method

and the Condition Equations Method (Table XII) . The

computed standard deviations of the adjusted angles differed

significantly in the fourth decimal place in several cases,

which is a slight indication that the Indirect Observations -

Method is more sensitive to round off error. The standard

deviation estimates are larger for the Indirect ObservationsS

Method in every case of a significant difference in the

fourth decimal place. However, a significant difference in

the f~ourth decimal place is insignificant in terms of the -

observational precision. The standard deviations of the

adjusted distances for both methods yield identical results

(Table XII). Both Methods differ from the NOS positions in

the fourth decimal place in seconds of arc for both latitude

62

and longitude. The horizontal control for third-order stan-

dards recjuires accuracy to three decimal places in seconds

of arc for both latitude and longitude--thus, these methods

* can be used for computing third-order positions.

63

D C) 0 r 0 (n 0 0) 0 00 C) CD

04 C C " 0 0 0 0 44) 0-1 0 0 0 04- C) C) n C*- l C) C) <D

0 ~ C 0; 00 0 0 00 :I + + + + I + + + +.

m r") m' CN m' a - 0 0 (NN Il 1n M 110 ' .o CO n C.04 V) r-4 c L

In Ln U, U U,) U, Ul m' a' ) all a' m' a'

I- r-) r= rn ry- r) 10 %Z

0 cl C14 (N C N ( N ~ ( N (N (N N -( I_ -r- r- r- r -----

0 0 0 0 0

r-4 0M -N~4- 0: C00M nary 9..4 0 V- 00 > 0 00 0

41 n~d 0 0: c 0 ) 0 0 CD C3 0

H w + I U2 + I I I I

a n M C N Ui (N a'0 .. CL C r- '- N - Nwz u- -%d- U,) y ') U) %.n Ln 6.- r- 1 (N (Ni (Nj r4

0. 1 - r- r- r- r- Ir- a) 0 - C> - I .

co u It 71 a) m~ a m' M' m E-z Z co c Ic a 0aCd *-4 l.Q- 00 00 0 0 C C rn) pf n rv I

F- =.- -1 = ~ 0 1. 0c . I

(.d Or Nd N'. '.0 N. C14 N. =110 Md m'. '.0 M. '0 '. e0

0r 0 0m I I -4j - o cc o co co- co 6-1 0 0 w CO C) c

r. 0 U 0 r-*HCU 0 0)0. a H -4 0 F; -4 r4i* . -HCdi U) r- 0r U) -.) C U) . 0 U)

> 4. ) 4 -J -1 .) > -~4 (1) .6.) H4 C.)w- 0 w- (d C. w- w- U. W- md U W-

U) ul w U) w1--) Q .-- I W r'4 Q3. a). Qi Cd -4

4J.- 0 cdrd 41~ 0 0dCCd -4 !V 0 -4 W d -4 r -4 I4I M) V - d 0 Cd tr M) 4J Ma' Cd 0 Cd0

., U) =1 *-Q 3- ) U) :jH 1) ) -1 W. v (1C: 4- Cx r ' + - rl: z x W) tl r. 4) al

00 -r~ -4 Wz :D 0 01- P rx- .-r- M

0. C14 r..' '- N ~ ' N En' Q4 0..'C C14 "N (Nr. 9 0 q .0 ia. . 0 . I .0. .

3E: ~ ~ H m) u' ::r zr X: cc H m' m' U. -- -

64

___________ - - -

LA) L) (N4 (N

* U) C)0 C

a) 0 0 1 00 -

4.3 c' a'N C14

a) 004 D

w C4 (N 1= 0 0IC)' 00 I 1.-I 19 0 0 1

00 CI) 00

tr 0 w-

to .14 4J 0 OW -W

*eW 4- U)'4 -4 44 '-0

I > n .o fu r, CD 'd .0 W 3-. 004 N 0- U) 0 I 0

(n 0- CD 0 C)

0) I ~ ~ 0) L> C)0 .0. ~ 0 N r~

0 ~~ _ ~~d4 (N (NO H - -

M 0 CD >- a'm CLO H ..J ~ ' ~H H 0 0 LA LAO M )~ ' 0 I

0~ 3-D ., mJ M 0

H 0) (N ( I V( (

W (d a) I'dhJ S I ~ 0) U-0 ( Q . )(N

H 4) m' 0 ) '.Ln0 rq 41 M ICH~ M3 I= U) 0 n 0 U) a) ( nO

b4 ) I oc 0 . . * . . .

r4 HN I H3 I

ca d N n 541- (n I

ag 41a C)ul (N N 6Z

V. CONCLUSIONS AND RECOMHiENDATION 0

A. CONCLUSIONS

The computer programs developed by the author and

contained in this thesis have a variety of useful and prac-

tical hydrographic applications. In hydrography, geodetic

field work plHys a key role. :orizontal control is neces-

sdry in determining positions and, even in areas which

appear to initially have adeouate control, additional

control stations often need to 1e established aZtcr a iv,.i

in t-e .ield. These field-generated zontrol pgints nist .,eadj'2rtea to fit .jithin the xzistijij surcvt net ir! t i

miz. er s r-;. i-. tr.e " .a.:.,nt. The errors can be

minimized by these computer programs. Direct applic.ution of

these programs would be enormously beneficial, since no

equivalent software exist at NPS to perform such adjustments

at the present time.

In the Approximate Method, a traverse is adjusted by

computations using a hand calculator. This method is suit-

able for field computation and the adjusted coordinates meet

the specifications and standards of accuracy for a third-

order class I traverse. Although the accuracy from this

method is less than the Least Squares letnod, it does not

require a computer and it furnishes coordinates which can be

checked in the field by the field party.

The Least Squares Method provides the best estimates for

positions of all traverse stations. Least Squares does

require more of a computational effort than the Approximate

Method. However, the accuracy of Least Squares is better

than the Approximate Method, and the Least Squares Method

should he used for the final office computations. Both

66

0

......................... . ,* ,.

Least Squares Methods vield identizal. results, but the

Condition Equations Method is more economical aad easier to

derive than the Indirect Observatians Method. Therefore,

the Condition E~iuations Method should be applied at NPS.

B. RECONMENDATION

Stuiies should be continued at NPS to compare the

economy of adjustment methods used in this thesis with other

methods of least squares adjustment.

67

. .. . . . . . . .

00M

LD 0 0

'-A- A 0 Z0

.- z5 -'- m It*

0 0z0 000

VI OI c 0 04 Ia. LAU I- 0 C

rLv M: <(NJ r-- m C) )

m 0 I a 0

I- 1-4 'S.: N

I- I-- tflV) 0 'Dd /M nO 0I * L!I -W -4

0 F-< 0- 0*O~ 0 0 0 01(/*2- Z*% 20 0 N N .LA (

0. 00 " -* 0-4- r ( 0 * n C 0 0

CL L 4ui -4* 0-m V* -4 -4 -4 -

.4 CL 2o *y 00000. -. ~i 00 .c') 0- 1, 0* 0 0 00i0.. r, W< 4* !x2! (I) Ln U) U* 0 0 0 0 V

<4 P.LA -* 1-- 1: >C * L100 0 0 00L Zw In 0I (/ ) L ' '..JO. 0* P0 P- LA L* UJ *

CO. d* C') N: 0' 0*4

0 2

-J 0*L)LA LI)

e.0 0 uu

0I. LI) LA m w V) z -0:Z 0 m

0~ C)0' 0 Ui oc 04 -

S7 C) '0 a.0 LA LA 0

=>~ I- - r-

"t 0 e 0 .n N Vc

"- i w. M, N N -4 - (NJ M iCC ULL

C., * 0 " C0S 07% a, 0%. '0

Z* 0 00 N 4 r N'i (cn Ln

A A A A AA A

f^* F-4J Ce 0 N N m'f m t '

c.D .4. a LA 0 0

0* 0% 0 0f -I

V) w- . ' 0 ci' 0 ---

uJ .4 W 0 0 0 't. W -

tf I- i-a' 0*-4 m .c IS 4% WU P- N cC) N N

2j z0 N 0' -4 N 0 .0 cc0* 1-4 c P- N co N O0 U' I-

0 CC 0 0 o 0 1-7%1--4 .....U1* 0 0 '0 '0 '.0 -4 ui '.0

'4* 0 11u 0 tD0 ( '4. o10 0

z 0 r-. (n 0O'.10 0* 0 ~4N It. U) coN 'r

0M* " ) LA It. 't N cUj I I-- w c . 0' N0 *U) w .0

0* r) I LA 0'. 0-* 1 Z LA LA\ LA i0

0-* f- rL ' N -

0* it)

-J*~

'4* V)

0* CL) V)Z 0 L)

'4* 0j 0.-0L* -)c

I- a w

Cd) V) V) u<. V) -0 C

0 0 W U~00 4 1 -

W 2 a uJ69

o 000000~~Wf r-- '.0 L0A ~

Z* U 4 e 0 - L -- r -t N

0* F-43 2' V) N -Nr

U* CC) 0.

Uj~ * 11 %0 0 0% 0% %00l - '0 N0 (n

m* -4 N N-

=0 00 N-4flN UX* I-I.- ;r0* M A A A A A A AW* xx

c Pj cc.j 0 -t N ,t~4* LL Z

z U, N '0l*I Z 004 N UI- It C % U)

-* W4 w **-* I.-W I.-0%

0A* zo NC.* "6. 0o 0- 0

* Oc(') 10 '0 10 102F* 0

z 0 10 N U, -o* .- N m 10S

0 - U, Go 0-(7oc* L- 0% N

J* M0 LN 0 0; 0(A* 0u 0n 0n 0n

U-%-* w~ f

0* n 0 0

0

0L* I- 00* 1.-.

I- U.

1-*0 W 2LN 4 1--

w Zn 0

0* V4 In In- Z4* Z 0 0 D 0 0 beD<

0

0) L 0.

L) u 0. WL

uZ C- W L- 3c 0 "-ZU)I.. u0 CL >L) 0 cic~z0) ". CL 4< z z Qc-4S.4c

1-0 - 0. cc e tn he4 4 IC U'0 ). 0. -uj LUJ 3-I We U

L)1 CL I- .... V. ) aC0Ucnsq cu 0U L a. 03~ 0 . C406/I 0.

0 ) 0 L LU"- 4 U) _j S u..0 LUu .1 C- 4/) z (D c.D 0. 0 0

L) L)V) C. O w 1-0 ZO u n=9-4u L.) cc 0. -.3O 4US 0=) "* 4 Z WWLLCZ Z I'-0 u IlU CL L >ZU) VIM I-UI .4 1-4-"-0 - 4u C0 > CL LUJ 0Z z'-' P-4U 01- 0~--*0 u < 0. W- )-P-0 ON. Ifl-I LU 00U 0.C-4- . U)0) 0 cc CL o" I-" "-4 00 > "M0 =X1-< 00L) 0 t- am LL Z.-.- o-- O..Z Ix owt cool- Z=~ w

0 L) 0- z :301-0,40 4 LU I--0 Uf- ) <. Il0 0LI.). 0. Wol OC)U2iz-e-" Z *us CW .J w "-s LIJ

0) L) 0 0- 0.- a00 :~307-I LWJwUwtL inU L) 0. 0-4 U J 0..." CD 0W4c0 o: L~r ce ) .dU.L WQ 0 o- 0 =z 1-LU 2>- ZZ-I -11wZ w -1 C

CL.2 0 U.. l-3-Z4U)UJ Newcw 0"<- >W LLI 00 0 0L 0) 03l-Qc W<X < 1-- 11 <I>QCZZ cc-

Q z UJ 0. co . it ZDU)LUi,- U..U)w- WJUIU) W040p.4 W) l'- 0 0 - z lz ez > Oco MP--l-Qca

j w u .4 0.. 04cu) lez<4 D Z ZONN -Wc-j IllQ -J 9 M. U) "-.-4uj :3c CCs LL< MM~'LL WO< ...

u cc 0) MCI 0. Z -CW U-111. 01--C DL. eel- 0-u I- 0 o m00 0 -4omml-X It MOLJN * U)Lu-- C1)Ulc0 OZu Z U ..jm 0. "- _j )-0 I-NU..- x 0J~a )U)0 0wl-04)

-4 0 4 0 41I- 0. 1-- =)CW -U.. 0U) ma ZLUDNJNZOZ zx u 0 mW 0-4 0UwexmuLL.U U zWz-0~co U)4-'sZp4UJUIlj0~~~ m4 Z a -4I- .4 DDWU a4)Z4W--.J

> u~ mm u w m- <Z.ixo MIX uJ Lww01IU)IL-. 0 O'0 OW m -LI. W4ZDW<" M~oZU)ZWY..-oU~- V)

LL e 0 <-4 0 LLI-- m. LU zc,-ZxzCJ lo-zLU =5 -- D 4 iI itI- U U 0 -4 M 0 Wce06 .4.a - > .011WU)LLNNzWl 0< U 0 Z - U 7.2 0. ODOxD-l1-ZLU-U)uwc-zm<Oc~ .j..jUn~)2

x 0 < U <"- C- LU U-U-W.-4wU Mtz LUon<U<4-4.4Nu 0 X*4 u wx 0m ... N441--1U~' I~~-U4--

m. 0 0 <-4 0 00 m. m ZZI-fZwx E-"* M 11111 IOC~4L'm. Z 0U) 0 u O m. < c0 0 I-0- l- It0-1- U)r-Jr00l-- WUI--LL< U :0- u W0.. 0. P"i ""Xu -00 Ws"N Mmom 44,

0 > U4 00 w C .D. C- w 1-ON" 11 -sC-U.4WZ1-IF-WLL CI 11 ILUW -Z

4 U -1) Q 4 M- > Dou..1C30-. OCI -If )I- - -- 1I4Nu-IU U). x )-C- -U vN): -'-NN 'J4 N

W) 0) L. 0 )~ CD I 0. fil = I iI 1 V m D -0 11 U- 11 NCr4)nm 11 1I 4 <) U 0 L - . 0-t -I '-N N en(In LU LUJ

-.1 0- CC 0 U) CL '-.4 t-4 NM Q-0)0 0 '-.0 C-z m -00II0 -41 IU)-Cc J

x 0 m<0 0 -0 0. U- T-CCXXU4 1-- 1-00N0" r-40 n

0 0 u u " 0.i MM 0. 010- -Z O"CU-MZWaW'- <0 0) u U) C- DO OZLUUi,-0 OU04 U0I-oOOOWOWQ Lu

u 0 DC-0C-

0 0

71

4/) > 0-4Z 0 )WU > -x< L)- > wl-

U)4 > (DOV))--4 -'0 :Dtn U! z > Wi .- eC)X> 0n r.J V(A X > 4-)1orOO (J-4V) I.- M > -- W1: UJLLw) c > Uc~rWC)0 wou 0w) w 0 0 > Nmo0%.)U) b-'2 o 0

I.1- Z 0 > rI0O- -. 041: 0~ 4.) > 4 -fncn-- 0 ..-

1:> wm7-4CN -4-r-J0W 01* -Z0> .. t40-m MNC\JU1 %*

0 : -~J..> ON~ 641o 0cmllI- X<0 0 MMI > -4<a0j-'- 0 o" 00 z 2 : 0. > F14-%O.oC>. .j-o,. m

< W. "m0 > <0Cfl3o< . 0N Z1: J1:> UJ-41 -w1- WONN-J U0~ J 44'-> ftz:)- ._ "'-4m~ .

0 0 > -=ZNW0W *%U.. M w 0-4 > NO~~ Z.. X- 0

" qWX> tX-C-)N::

x o0 1.- > - :C-. W -f-4<~14 > ~rjwmi~l W.-44U- 0

c- U..2L- > 1-4 -<O WUWYJ %.out 000 > 4 I,-Oz V )

l'-OWU 4< > CD.t!DL) wx) 0-104 -MU "ZI-Z > )U: '-4 -ui-n 0

O.Uj(3 0 0"'0 > V) *4)4W.-- Z -4-40 0ZW)U 4 "-et4 > Z M-t< I---

0 a1-o.- > 0 rsJ040Uw o-w.0 40o.4 > m ob * .'0L) L)WJ wx %

WZW w -J I - > I.- N 14-W - -X:0.1 00<0 0 m3m>4---" -,w- <I--w aWl2 M, z wWO. > w vpU)L-pJ I.Z-lN 0 (AC4w4c < -JWM > < NJ41-40M =I-= - e ccMI-. 4 30 > -1.4 49c :D()00 0 wj4-)MLZL UlI-U. > U- I.L-4 -0-- 0fu 01 >O

2 -a U. > w UN U.LtN1 U 64M mY <W"W84w a:MC > 0 NiN o-rna '..AI QCa01:000 0 0 > - 4<rTf-t I- "--- . 0 1--U-.. LL. LLU.. > WU >1 -#J V N ft '0

ft cr 0 U- > _-j 1-4-4U)A o--~ M zIL w wowzuJ > w 1:NI-.O3- Z4<('I x < UZWZOZZZ<Z > 4 =)4lh-ZN =I---= I--L

.- U'1t..*..> P" 0"i04m 00)-- Z 4 c

=):L=P: > 4 Z U) 4.% -. I -0W020U)000 > > 0-.-<0 Is'N<0wowoQe w w > .-ONN..J'-0 0... 0000000 *M M4L)Momwm > WMMVNAIU)- 0-4 4- 0 0.

> e qp-o) &+-- - o Z lr4l1dim4-? V)

)IUV))V)-)> wo)-- .4w) )wl-.. - 0 4W..4 2

If 11 11 11 11 > woZ "Wo 0U)4cf 0 X1: -- 1000001O000> O..a<:40L.)- .2 x: X - .

>3 0 -LL - W1l- ) I- --- -- 0.> WZN.-.UJ UJ~-n Z 1-0 0

cr U/) .4 > -JU))-.J(3 0- o-4i cc I WWWWWWWLUJULLUIWWCA V) 17 Z 4) > co .1: *-MC W:Zd 40 0 z in---+x: 0 4 >- > ~:-u * -0- 1-0 LD 1 ..... ui-'* 4 9

0 a I- ) > ON~r*40,4 ZWZU 40 .-J cc L> OI040> Pocm-c 40. 3m333333x W0

72

w

.1

U -a>

LLI-

-j I0

I- z- z ;I

a CID co z0 Vw 0w :

.4'- .44

z am>

0 ZZ " 0 ----

Ud CL) I.- CH a 0LJ -WO w ,~

.44 0. 0 - 0- 0- t.44r-H z J-N4. f43U 0 1111 WW 01111 -

z LMoM V) n oo~ oo0 .1 - MLor- or-.oO W o0O

W W Hi s.4O4f "Mw -1xwx3r'OCxw

4..) 0. Z I-~ ~ 0.0 NO OW O-'OOW

l' 04DIMO z O - -

NJLWL 0000 "-4 "PM WW 0 W WW OWo% LA V)r(1 Id) 0 z* -N H1-ZIC--a4-l4j 1w.4 w. w4 -4.4 Zu LL. OC'0 C , 0 *-. 1144-~~-glCc~ 3:3:33 cc op UII- Lim .w~~L

-4 0~ 9. .-4 C.D JII -73

IAI*M

w L.A oxx 0

x -4 -44 z S>- 4-

XU) -x x -xU

l.AMM- .. 'o-4 u

24 2:a .. 4 .ox : : 1-- : 00 0 1-a xc

0 0o4 - - > ~ l40* OM- L-, 0 0-->

-4 -44 -4 -4 4 -4

N t 02:2: Z 04 ft 02:2 ft0A01 t A (nM

o -00 o n i: a -t a4 o -- 0 2:in a-- - - - -- -- ) - Z2 >- a -4

uj 22:- 2:L~ I-4N 2: 2: 1-4 2:20 :-- 2: UQQ -4N

I.- zC.Ii-n ..4 CA.- t 0-LUO-r--- CI

- = -4Ircxl42:0 q 2: 2:@44xt " C us x -4,,.-. ,

a 2:- v)u 1

0 . aa -a -

- - 1-0-4AL 402:c

02:~~~~.-L w .4 10 0 0 - 20~ 0'zI Z= x1 ~ 0~ 00 OP00OlIu

~~OL O'erL oz11 I--~C H 0 4 (l .4~i

.-. ~~~~~ ~~ ~~~ - w: 4 ~ *,4.4*S- 4~ a*~~~~~~~~~~~~ .4l N N2 4/ U U ./ 4) W

02:--2:0 0 0 0 00 0 2- 2:0- - 0 -'.0---------------- - '0 - - 0 0r-

-I-2:UqJII - - - . -I-0:U74I

00 >--4-4 =

Doc D-. 0

0-4~ >- 0 -r

x~o z 0-4

I- w 0 N 0- ams-0-4 0-4 00 -4 000= - 4 0 0II-V -- MW m- ON

U.; 0 U ->(7%.Z,. 'a 0 I '0 %D'O0 > L,~4 - w4 p-~ -4 _4 0 -4 -4

U .1 0 0 -(A4~ 0 F- ~-1, (I

-4w 0 1--0- -4- '0-' V- 0111IU~4I 0 oil0 '0-LI0n4 V 0" L w* aa 0 M 0" -() 9"* -4 _L

4 9~- Cm to-W MUD) -=-) cc" --- W a4 L-jt M D D

"Zo* W Z LU _ 0 U94 go- -30 " Z U-

oil0 Uj III It~ 0-' -~C II i -

= a 00.0=0.~-40lI OI-~I-- ou. ONW0cW'W<zzzzwwi,--z F- O00Z4rU- 0c4,UWkCuJ"

LU .- ZO- 4p -- 4" L)t 49Ul'-Z CIt F_ Z

~WOw0 0 11. OLL CCMau0 Le 00 00Uu

0 00 00) 0 0 -Co -4 - 4 -

75

U:. 0Z

11 Z

-45

- -

3r -44 c

-4 -- 4 c

X:s =) 0X~02: 0- 0- 0 <:

M- >- f- Y W Z<

7: 0 - OW C -4 -VI )+.5 0= LD- -- )C

PIn 1 0 0,-4 4 '- -

0- z* , - 1-- 0., _j I0 ,- .4 .4 Z 00000 -OLL ) -4 0000-

-1-. ;1 4,LJ" V 0< Owlo N - Uz

11- 0)J -4-4 U .- -j -- 1 U 4

V4iZ "j 1 2 - ,, -.0 4 00-. " - 0,,,,,0 -A

00-<0 0.ma 4 0- 0 P3 - -i) L- -

Ow0-ZZO0 -Z 0Z OL -w 4-z

F- - o- - I- 7, .-Z = 0 Z- w 0- -0 ".1 P1/).

O4'..- I 0 0 '0 Z -j cc: WW ---. crc 0 -' w - -

0 ) I- wo ) 4u < 00000 XX M -xOwO .- 0000

0 0 0 4 a .. .. 0 0 '~W I 0---4 .4

-- C. *U - I 4 ) a0 -4 rZ a aaa

'fw W 1- Z - 0~OO.'00a~ u:a '00'~OO76Q '

Uz

zz

z

zl z

-4 .4%

m -. - z0 -n

oui N UI 0 rw M C

X lw -J a ~ -0 D /-J 4 m>x 0 -L

0 crA < -: ZII .4 cc = In*z NI. N-L N0d.x 7' zw-

cc 0- -J< a -

-zma Mcc 4

e0 - - wu t. z0 L L0% z -I 1- - - I. 10 00c~

-4 = ' - -4 .4 a Lu 0-4= ) (0- C 4- -4 0- -w I I-- MM

L .L N 4- -- >=U) .4 -44 11 1 "OW -- N Li - a 0 C z CON

0 - rOZ -;st 'r 0 0-N + .4 -4- 0. z 00 0-I--q D

1 ~-0Z -<- a z 0 4u X.~- -I-- Z I- NI 0-W 0- nI-i it N 0 4 ~

W.4Z I-- U L O I .1N 0 0 P- -0 <L--

D"a I1 1-- 0 g-04/)" .4 0 0J z X a-LU-4-- 0.W-.t S I II IIII0W D b-C.O LfL 0 C.1 0J-:) U

* N.e l:c PCu-ju in w4 UO' a4 "O -

ZO z-~ .oo "Zo 0v 0 0 Il -JL OO z-~-Lt 0N -4L '0-0co Z Ni '-I-L 0002* II-..-J-4

0w 0.- 0......U

WUW -I 'Z ' I ~~ ) ~0 ANU. O~U77L.

~#4 III- 4-WIi~- W W 2~ U Z IWW.4II I ~.4'- UUU7U

- >_

Ca-

ujW

on 000 LN4 0. ** c

X2E~ '-4 n

- -- 00

a -> III jCi -- LZ -,44 _ - -w4 0A I- 00 ~ j

MI on.440 c o

LK 11 11 11I I %-- m

>.. --. < 0 -3x--0 0 oz--- .

o aII w-l - -- 1 O I_ ,I 11 -l z o L U111 ZUX- 0 4uW -0 NUI-I- -_,I-f_

'0 0U- 0 -

--- "4C.

2p I

~00~I aP4~ (..) - - 00NN ''O0aco 0I~~00 ...I ..D ..OO

0~ ~I 14~ J-04 w 0~ cc- C%4(Dull~ ~~~~~ NlI' '-N Clf 4 ((

>~ >>- I IIII * 0 -- Z -78-

-r.

LD0-

N Qz

W L N4

- . 4 . 04/ .- d4<-

N ~ ~ L)11 -

z P-4- I -4 -4 IA

4 .0W -J CC) 0 2: oft m X 110U_ am: "1%4 ' .'u I-) M 0 Wj

tin u rn<" -. 4 Z - M0 X: 4 0 0_

-4 - Z X:- tI) C r_4 0 x W - Z-- X_ E

-4Uf -I- MT4 +Z. ~ ~ E ~ s~.

0 0~ W0I.)l- L I-~ C wow UO-- = 4-4 a:ciP- LJ(DU) I- Z00~ 0 rx -:x oxx~ 00L*4t .- 4 Ile 0-0 =) '0 ft W<4 -CZ=) .) LUZ-

-I U.. I-- _r. ' .l C-cn 0 1 -

_G -400 00c NL ) - I Ln<. C~ . ) u -' P.- : -4 -

- 00 - 0Ce 0 I- -% 0 W< X-.LN <= 4-- x___ 0N L%-4-OuI) C.D u t.*-!Z 00-0 =5 4-.4 I I WL

!l z Zt- cinz'. I 00 - .cn-j OflAA0III 1

abe 0 l0 0:--Ztn0-J(~444.0.4 U) s-- P- - I- I-- 1-.4 4<<<00~

z - .0 -Ou _Z -J..Jac.-- I .u.. M w~ (0 )-1- ~*0 Z'-4 0 M 04+ 9*l4 P-4 - 00-- u)VA

(f1 -4W-" =)- .. 000 0- 4_< -- 00~0c U -1-Z 0 Z Q 0IO- rf-U W NM~4r1 I- -- iii

SN 9 *WC.,W U) .4 -0- *" ell -t-l-NN-.J<-ZZI/ -ZZ(/A a-0 NO I-U3l - .- do LL. zz4-4LL p-4- ""=-

00C' '-4 - :-9- Wl-.t LD~ 4.4 00'0. 0-.0-0e..-. Nr

ON + I- ZW *.-.(D uJ-UIZ 0 11 rJ-'.r-4 :)ii i i I I-411 -OLL 0= WLJ= Z L) ) Wu <<Z-u~lI U) IA

-~~~~~~ - 3' 0-4 )Zi4CUZ o -0 *4.l -Wr.4=- I10 0 ?IA00'-

-- 0 Z ZMO1W OMM1U.

-z z

00a 00 0 0

79

"-i -

-- X C ~

..L I < -

Z* -* z ":-

c-'* C )< C0* mw- z N

tJNJ NJ f* i-C C

r-04 4 0Z* Z N 0(A==) -4* - - -U- C 0 - o* X-'

P-q-mv)"< 0 * -- < z )<r

I .- *- inU 0-

"C40" .4 MOM I-* a.- -

4fl~ a a Id r-4"""+).) i-* OlA -a) >Czzt4 CI W. * <w Z *

<(-DON LLJ C*Wz (A -jLn0. 0... a L/)JZ r-.J*I/

"-oru40o-w a zc O 0*w M---ZZNN c 4110 )*4 9- ~- 4

CC t - m 0000 Liii .~~i .LL -.aL 01"0 0 0 - )(I) ~*a. X 7'>

0 NNN- 00 0 -4gI0'" C4 0*0 -u- < 0mQau 0 ii-j M a- X * LI Z --> >U

Z----- 2 M 1i 1i CIL. 0* P-.0 - -,r L^.-*4 0oZ 0 -c 4l CLA4a.

Z wWWww -ozI-i>. 000 IC x = )< 0U- -- *- -1- 0 m4 -C0 -4NOCI0 I.- -. 0 M~ Wa -

"owwwa. > 0 0=== 4-0w~ - XX-W- 4X< 7:c393 7.x I 0 LiIA/V)Z a4-COO-4

m =) 0 Z: -W1u .ooWiZ - 0 0 -NrN Z - N -nV) 1- - * 1110 0 4< ' ~-c oZWU 0--9Iil 0 ;I I. X- a -> 1 .

W. U 0 0Dw flV) -4 WL -- 4w > N)X N-Li" Z O*Ww>)>-*- - M ~N

0 " -- 000W 10~W -..-. Ii- 0. ----- --

WU Lit- 3w P- 4444 Q-4-

Ou.. ow z F- OOCCj0'..0jQCC-C-Lir Li*- Li3 W- L/) L .U..LL '.L CLU.. - Lu

00000 0D 00 C00) 000 0 0-NM-r Un z * -10 rQ% 0m0 00000 0 00 0(n ("MM~W I i

80

-~~~~F P-4- - * --

Z 0( V* 0 LU C>4 G-IC *. -, - .- >

9-.~~~~- 9-.* * - ' I Z c

V) WA ~ ()**~ C 9-ocz a (A ~ - uJ C * ( * 9

- a ~ ~ .. q * * -9- 0.* LL. 9 -* - * - LW~ On < V 0 L)

-Z4 * *EL) 7 * t--o~c 0 Lm ~ C~ t ZO) V) L i

- -9- * *-.- 9- w* Z 9- c* W * - LtLL <49 LL ( - A U.. c

0 >< 9-)* -- (A x - *U -~r >.- V OO * C) 'D V.) *ic -j < ..JC -

-- W> *L *. <. - i- W * -*F- C'*.(l ()< * *) _j - ccA* T* i~:

r.- * w-~r -* <cz* F- C cgco W U'% WI- * * 1 11 0-WL * Cd c..

-- - > * Co - 4- > * r-~ V) C- W 00 40 * *-L6 - C.) U..N< * NW * 01-)(WJ C0 >L" X UL ~W * * - )( 2 * b-49- M CL _*0~ j

- -9-A * *OX co 0 - -9- * .L * L-) -ce

z 2 _C2.j * *4. - 9. i. 0 * 4XZ.L U- L U..4-4 - Wu- *LIN CC < -** * We. * ce1 C) Z

-.. -4 U) 0. * * - 0 -*40A * wn - * Q)".. ON-U I~ w *) *)X CA 0 * W Ln' * O9-Z Z P-

0 Cl w WN rn wm .J * - * C mo C 9-cem U. U..0 - 4 UJW U J.49L *1 U. LL 0 * 0C/'- CL0.

* C0- C * L * - Ui Z- * .CL.-4 * Ccr'- 9- C* -J - ' W * * M 0. <4- -. 0-U..-c a- 40L 4 -4*- A -I 2- * t *4i- I -e-C) *- -a*C j. . cc

*-Z )< - 0.4 * *.g cc ,i)C)< n.- * vZcem) Ma* a 0 N "- *U.)< 1: C -. CO-- Z .- 00-)u OWJ

*O%.- tn 9-= 0 -- 4 " e CC -4z *-=II *1 -1 1-4-.J .j >q9--a I4CL) * *)< aJ L W -W * 0 * Cl- -< < r

- c _< j J.4 ('()N 4 W 0 -M 0:.c * .4<L) Q V)WF.*- 0

64LL 0. * * <% "-W)-9-*%. W 19i

O C ) - - L)L. *_ *...J 1 L)C/ * . 4 ) -- I-- N WLaC9) _c . JW It*4 -< 9- .D<40.*- U9-z * .- - 9i

>U- b.-4 <~ * *LCA.9- 4we)0** W04 * X~*- - 4*WC '%- -J. * *-I *nC 7- ... j-000**I92- * -XX>-) X < X 1W.w I.) C 2: *~ *> q+- "- <CAL)< M*L)-tn/ * , (7-r-'r r* :r J

*4AWL -.t-4 a - 4 - N.F- -"--4j 9. - a-4 W X- > - CL 0<011 9< -,t -XX - -- 4 - < 00< .U -W -<0 * - -0-

-40< 0 U-.-4t~ * L * -N I)< - - X)CI* X- - N * *** * *a> -

M. Z - -<U-<4-4 - -- 4"-NN -- , 0 '* N -- -4- Cox*

- )-.?~ %.. ~ ~ .C a'. *NN-.- * '.NN 0'.?) )0<) -)<- )* -NQ3)(-.'0 a)<N)(.%% Ln r-XF-X%%- ft- - - -'-, * ' - --

4NCN40 000-0* -%-

C -, 4NI n-4 *%-N

-C - -- - - - - - - - )< .- en--

cO0>xccO0COOvcAC-.COCCM~cDCOO O*00000000* CO.*Ozc.j--cOU.-L~n.ULLLLLU.ZLUU..Z Lu..LLU..u..>LL-u..* LL-LL-CLLL.* LU.. -ZILCL- -Uu..-

000 0000000 0 00000 0 0000 0 00000000 00 0 0 000%O-.4 N n~Lltf-C 0. 0-Ncq4-r VN lor-coa 0 -4M' 0nor-c CO - N rn-s-0.-4' --- ~4 - N N N NNNN M' Mn M*M M.4. 4 41

* U) A -4 Q.. LU L) * -4 0 -4 V) ~ - (AI0 ~w= P-.- a- w VN( C LULL (A 04<

cc 0 X 31 W11%~ CC %0 M.49- 0 (L. I- Z .0O< C4 0M > w a 0. QoZ CL. O(A 0 C'- 1,-

co- u. - =LW lm- z Z L w . - C- cCI < I-- C W.-J WU V- Z~ C Ma, Z 0a -L - Z -

> 4- - 4 0 VAo. x . 3X 0- X "-NZ-0-4 CZaw N-" CIO x N) LeN 0 W- X 0 tmI- (A Ct0

Ne ~-Wa 4l0 Z U'% o< -4 a Lu r 24 <' p 4. 0 F-.--al" -- .J "C 0 )0 OW .. I eF- N be F-zoo- 1-u' <-

U- lmI. - - * iuWi - i. Ln (A l I- (A WOl V)lu t-4 u I-- U' 4 1u!-Z im- Fr. - vbu0o~ C'(Ax -

4Z- LU V) "A - ' 0 2: 4 i, Ul vN LU w N0 0CN 7I-.-ZZ 9 0 (A Un 0 *: -~ 0: (A 7.- W: 'AZ9,-U,% 0-- cc

.4 MCFi- C. L ' zou. U- ": W - " awouit- (A -lO a-. : .. N 0- fl- "0> LL. LU UJ a LL W'P-OC1 o< LLA-. u

.w4- I ' N 00a1 > ov) ->1- ()Nt- nW: 3-O-P-.0 L (A t- 0 2)< z Z-411 Ill < _... w <4~wQ( F-.- I0%WlU'. OL4LL W: Vi - N 0 Q.4Ln = W Q-. =- a:(AE-3 9-Y I-N- "M 0 0 " < '4 -.- 4 0 .4ow I-- tm- -4 l- -oz Lu lm- 0 =) c2-, Oa.0 Lu U. -I I- -Q '0- .0 LI 1 '-4 04.:A<i-a X-UL aZZ1 V) ( J W. <"-. 40 - I- 1-4 z z a- lA.. P- 0

wu-02 UL V) 4 Q.-4 Lu~kUJ=Ln9-WL C.D f-JO'C1 ;Oi>= Z >WCO 2 w W0.-4Z> .O 4aln

- Lu 0 i')Il'- =LAC'- -WW>- LUJ US 4 a xZm.0uL "=I-- -

(A .- 0le4 m (A (A W: V) V) rc L 0 LPW.-U -1,- lmi-M "e241-L X 0 c 4c ow"- z Z LN -W--~ c(-aLLI

zL ZWZ W 044 >M~ V)W (Aa-.o 0<'J O-'-.4N02 C 2 Z _<0 4. wow O~W.NO Zw< z,-MCL P-o0-c 0 c-0 0a0V 0w.QOE-.)w - X1WLM. waw.-. i, -- '- 2W-'- zv~ LUJ US (A0 ZO..ZVWNW-~ =00 im-

0)-I--OWo--. )-.9- a:4( C 4 > > m < C~"1-tnZ - (A -'-.Oe-- -. O-t,-w.j-. W: a:C CC% lm-29-Wi-- -< aWaWa

0 '-"-4Z(A 0) WA0() 6 0(AZ (A-I WUL '0 fA0:)f> -2 000~C34 00..oWioO..,o "a.- Lu... (A LOA *-4 V'4-.* *(-l--u'. 0.>0.W ow 0 oWI(A) w cg.-o0 LnAw "x W

4<cLJ z a: >wN=Zow0 0-0 0 LU( 4 I9-Wc 9--I--wo -Il-Z 3 ZWZwLA1m-00'..J0I-40. .j 09-0 _..WI- -0. <Z X 0-- McAXWO.CO 04 , -4 .1. Liw 0.- "-.AI-00.-- r4ac-w0v~ z 00oo(A1 O*(A-mx~ovA)NX= w a: azw( X AVV.)(A < N

W< "Z e ZCZaM<un-< <4" OZcV- tm- <X( OLUJO4<M -41I WI-OW e Y- 0)<cxu -x- Ita4 4o -4 (A U A

a:Z (A- V) V) Wu'n-AWWO-9sIaMOW WLUN W C W -aLNI M--IWLUW-<4<A V-4 (V(A( N< F- O< 9-LU LU awww>4 U< 444 L4= LW=" = F4~-AaaI. - u- === I>-~0 1 00%1-4-.J3c F- Z 03-W0304 0- <24-4O .39 333g LL-

*- 20. - -1.-w0- L.'?- = LLN- I-lOUW LU LL.. Wa:W -tLO-- --* aja . a -4Jam LL: - co U- F - I- *9--.% 'a

4OSNxo X> N '<Z)'CX><NI-- O>C'N )(W)( >C- >C > O .(- N NN'o N-4- -4--4N -4 N<NZNI--4<(AN -4WUNl-N 0 .0"- N)CN ON .-- 4 -4-4-4 -a'

0.- .4 a - -4<-4Z .. 0,4Wc -J-4Z.-4 -4- -4(A0.-4N'-4- -..4x. - .* . a

N ) a - a aI- ) a Z <... -Lu 0 a WO4 a '%, -N %)

=c6:WwW 4W aa %W 24W -4%umN LU W oww- c N.-= aINIWr: -OCCO- a0-. - - 0-4 0.-) -0 ~- .U.. -ZO=l--voOc - z - -

-. 4 a. 1-4 M) 4 .4 4 -4 -4 4 --- -

4444~44-<N a -'4c~:..j44~I-4Z~4A4 82~.

a~a~~a~~a:.~ o: .a: 0. O.W~a:N:L~:- : *~za:- *: aZa:a:Naa~a-4-:N1

a. CL >>>>>>> -

L) L0 >. V>U oZ 0.>

U L U 0.>U Q~i 0- >

U U 0. >U 0 0. >

U 0U >U U 4 >. >

U )0. > Z nU U e. > . 0 t

U U WL CL > 0 * +.

U U Z- M > 0 0 -U U " m a > Q 2 10

U U M C.. z > z c

U U . 0. 0 > ~u U a. zu > zo w'Q U0L . 0) > -u 1: zU i..) -u a. > ~U U 0 C WJC > o.Q L-) 0. V > u LJ a

U U U L#1 0. =)c > z l'- C 0

LUJ U u 0in) 0- PI > - 0 oUI L)I. C) 0 'W I > 0 Z u. a

U.. Q .' 0n CL > -0(_) U Z(A 0. C > - .~ 0

Z U U P4qdl 0. *0> CU4C. Z U I-LI) 0.L9 > IIS 0

Q I- U m a. LwUJwW0ln= > 0 0 X T-4 U U a-2: 0. 110-.1.--Z.. > V) - O -. 4 ruj

-4 UT, 0 CL n WM=Z > -ZNO C)4>Z>.C)~ U 0 U 00 0- = QZOZU) > 0 >- 'n ix >~

> wU U I- U Ulm 0. 0 W'-WW > x 0 xr l0 U z U 0 -~ 0. -* 0a01/)w > X- -4 MM =_.

LI. U <M U w U n. X > 4D '.0 no-a-

I-- -U =WU or w0- z2zzz- > w0 PI 04 >- U UCUU. w LI w0. z'se- >4 <~ x C --

3 U -U 0 L u- > - .SU 7) U wu- 0 m u- <44440 > U- z 9-I-.

0 U 4. U- Z 2 a. III I-I-I > LUJ 2: W 4 11)0m- 0 U "-W 4 Ia. 0 44 4 Z 0 > 0 X M" Ps-i ...-

UZNU- u. 00o00C. 0 > ~0 < <010-U 4 U b -L 00>L0000

u Xw U 0 Z0 .949-I)0>.J 0 -

OWULI~ U (r. 0 4 ..0.00.u.o00 > 4 0 0 E 40U0U D J 0- 4 ZZZZZ=00O > 14 00 CL-~-

(- U * - U )4 12 W. .. -44 > CL V) Z >4:<4<_jU 1.-(_ U C-) <. > 4 2..0 LU

LU U .JO U a4-- . > u1191114 > > Q 0 2-..1 _J-imz U U cm 0z . > LU 0 wU Mu--LL

U .... Q(/ L W. -N 0> CL aO

9U Us.-'-000. a . 0 > 0~1SU wLU U > M.Z444 U- -11 tll

W 0- U 44)a..... 0. Z WQEXM > LUJ Z Lu N" ~Z 0. w~W-m > -. D if >.

U 10 U Ze 1,I- 0. nnox::nC/zzz > -4 2 -4Z-4

~= m -- 1~0 > cozz 4 -cLU Ld U )0. 0- > 0 < X -u~- W Z

w Q 010 > 0 0 U vicoxti m~wU U W-=) 0.>

Q 0 U LLP40.Lu U U 0

LU UU0. >.-

83

Li L.) 0. >

ui L) -0. >

Li ) 0- > 0u w L) t m >

L) ui W 0. > -

Li i LU a- > z

u U Li . 0. >0L) Li )0 >Li LO0 >0

L) Li0 0. >0

i Li Ix0 > 0M c0

Li Li00 > 0

Li L >.

Li 0iW 0 > 04 0Li ui- 0 > z 0n

126 Li (D 0 > 0~~Li I- L i 0. c:D > Zui L C.. WLuO > Q a .

Li ui (L W-4L > 0n im ~ '

Li Li 0. cx0a-' > 0 0.Li Li 0. I.DC > '0 0Li U LD 1- 0 W > 0Li Li ZC 04"0-4" > 10 -0 -

Li Li <S CL > z

U Li Li( CL _rZZZ > 04 0 0Li LiZ 0. 000 > 1'0 zOLi * Q W 0. V) 2zz >. 0L ie oz Li <<4x<UL > 0

-L Li 4-) Li Li 0. LL iL > cc 04 - Li <m 0 o-f . 1- > ~

U mm Li Z<O m-i Z > 0

-. xA i U cli -a 0. WLW > V) 00

.: Li X4~ Li L-4 C m - U . .ZL > z0 u. Li Q Li z Cmf 0-- 00000l > C -4 co 4u 2: Li Li4- ui 0 .2 C >

eni u:-L cc 0. '' U.U.ULU. > 2 - 0 -

Li 0 Li uL 01-4 m. =)D: > z2Li c) Li 0 0. 0 w L~~ > 1- - 0 .

-) L) Z j Li u- 0. > >> > 4i .4 L47

x L im u Li L M)2 0- aUj.j. > u 0 '0

0 i 0 Li V)-,-4 M. "- WWU.WW 00 > LU -" -4 -

Li Li *- i ) 0cl 06 CC Zz=:om'o > 0 V) It~

Lu Li .JO Li Z.. a. > > Lui

Z Li Li V)< CL II111111 I111111l > .J LU -

Ui ".. LiCL > 0

0Lui01-L w:):D- CL -4 oc)olo> wLu 0. -

a Li M4 Li 20.1- 0. 6 > < _jm Li -0 Li .- 2m LA. 0- :flez= > > w .40 I:D i ) Li o 2:0 > M -0 1-V) i ui <0.C > 0 40 -4~ Z

Qi Li0 > 0 . LUiF- Li L 0- >*

Lu Li Li>ui L 0.>

84

L) L) 0L-

ui L 0- ac >L) L) 0. WL >Li L) CL 0Li u Z m U >L) L 4 CL 1>

L) u 0. Z>L) Liu 0.>

ui ui 0- 0> %....ui U 0. z> ML-) L 7 0- < > l-lLi u) 0 m > .-oL) ui W- 0. .. i> U.ui Li U- m. > "oL) ui 0L LULLWJ > coui Li () (L W -w >Li L U 0. W= >Li Li -. 1 0. Lozz > WoLi ui ( 0. W.-.W > oQi QiZ a- c~W > I--4 -Li Li < 0. WW0iZ 3 >Li Q (I. wi-Z4zzI-- > 0.4Li L i CL W=C . . ..W > C1Li Li m 0L OZLiO (3 > -O0Li Li 1-- 0- W~i-4WJ.LWW > =0Li Li 0. 0rv)w-j..jw > -oLi Li U 0. UK=D > a.Li Q Q 0. zzzzzz..j > cc0

U LiZ 0. - -<< > ZlouL Li4 0. > >

wi Li Z 0. WJLUWUILIWIL > -. 0N L) Li Li CL 0. .. J.J.J.J > 'o

u~L L 0 >. (3CI-r-Li * Li~z 0cl ZZZZ I->

N Li oc Li 00 0 Z ~~.L > N~ZLi I-- Li LLUi 0. 0 COLL > ()0 O-Li Z Li Lu 0. '-4 ULUWJ c > -

N Li M. LUCAV 0- 1-- "-=ZWW > N rt '3 z0 Li Liz N M.~' -- f~ > rc3%-4W

Li LO Li "-0Cd 0.. -J..jw > (A) f-I"-u Li Z- L -z C. " LLL LIL.U > Z NQ'0.1,-

c~ Li u Li 4 0 0m U.. 00000>W > 0 0 m> Li UL 0 Z 0. LU W > 1'.f%

Li m Li ~w < 0. 0 W~wWW-~iJW > 1-mLL Li ZN Li wl- CL D=M=<L > W CL-I- I

Li .4 Li == N4 CL LU ..J-J..J.J..-I,-U. > O WO Z Z(Al Li Xc Li 4/)z 2 . -1 0 .- > < N1-40-4 -

3 ~Li.~ L 0.~ >-I-0> -.1 ZO'OW0N ON0 i I~ i 1 0.4> Li C~m -M

ar Q 0 Li -4 0. wwwwL1JWUiW > wU,'~Li Li Li - Li 4/-W N 0- ======= > 0 W0- 1 -- 10

LI-Li Li 1-4 M0 0. -L1----400 z zIll Qi JO Qi LUJ 0. > U LiQ (3IZZ Li Li tuW.. 0. 11111 11 t11 1111 > Ji We'lZ.<LU.4L".

Q i.. L) CL0 > w 0% c0-.0o.-

1Li Li u D-0 > U- LC)Li LWoi >-1- 0. > UC U. c t10It1

~ Li~ L 0.- CL - LUU > < .i -a Li OZ= 0L -NNNWOX"'- > > W4'3 it z 11

ML Li 1-"c0 (LZ1Cx-- > =I-W. L LLU l'-0(1 L 4 Li 0. > 040N"X~NI.-N LUwLi L) 0. > 01I-001-10(1) Ix LU

Li Li L 0.>LU Li Li a.. >

L"U Q Li Q

85

- - >r ~ -- .--

0 L) >

L) L) V) 0. > tL) UW 0 CLZ > WU

0) L) CL 0W > x

0 ) 0 = m > 00) CC I-- > 0

L0 C' a.o > .40) 0.0 0.Z d' >

0) 0U Z4 >'~. x0) ) 0 0 ~ ZC'l I-X > U..

0) 0 " a- ZOe-z clz44 > Zu u cl 0. Z0-1-O 0 >

0 0 C. -C . Zo I >0) 0L 0. " e-i- > L/

Q~ 0 x o- 0. I-"Cnc" W)<> > U- WQ 0) 1-- 0- "oAc . = > - u

NO Q = C o. tl01--ZZ > 02z

>. (0 0 0. 0. 20. x* > 4

x 4) ) L 30z~c wu.Z> z0

Ne 0 0 CL 0 ~ ld U*4-t > .4-'4 00 m- 0.dz ll ujl#) > 4d z

cmD 0) u aa . W wa -4- > N-z~ u Q1-N 0. W=wzZ Mo00> -4W 0

401 Q M-t 0. CL-I > f 0 0.-4~ ~ C u 0. . I-I wLu > 0/ Z2

<4 N 0. 0 xz 0- (A U.. LL Z O== > z 0 w -- ZL) W 0 0. O<.OLO m z w-I- > 0 IX :c..

.~) 0 -I-t 0) 0 CL 0 0 0 LU > . N W WWZ 0u ZOO 0 0 CL (.D Jo 39 Z Z > I -U- N N Z

U.. 0 <04% 0 w~ 0. CL oDzozZ -- > 4 L. -4-4 e..,-.I-. 0 4 0 < 04 0.m-2-W1 > Ix N1 "- 00 z

u 0 LI. 0. 2 - C.-4 L'ILUJ > < )( 0 223 > 0 0 N 0. i---i-i 1-oo > -J 0 <<

U 0 0W-4 0.U. owow"Zz > 0 - w W0.- 0440 2 - C. Wj <0400V)?-JW > W >- M - - =

0 Q~ 0 "V 44) m. 0 wzwzzo<Wm~ > 0 1 -0 Z 0) M-- 4m .o Ww > 1-4 Zu)

< > 0 0 0- WU 00001- O0U. > W )X U. "-0 LL0 w CLe 0 0 i ".-f""kA-.fZ"LUU > _j 0 u)0 0

0044 0 -4~ M. m www -mw-i4 > w Z 00 Xu V)m 0 > - m. < 000000000 > < 0 2 2 L UU

x( Q wU -4 CL " z 20 0 0 w 0 f>O 0. w wuWWWWzwww -b " "/ o-n* ~0

0j 1-WU 0- Z m~ -c -L=XZXM -- < NN F- - -

WO .JL04 0..Q<- >I -- I---- > >04-4-44<+4+Z O 0- Q C > w .j /)V) -j

P1 0 *' 0 £fl-4N CL Illi4-41111

m 0 ww C > 0. 00i)

00 Of.- L)V) 0. We > u 4 111 4 1111 ZLiZ4 0. N N > .J 0

co 0 I.-I 0u I- m. -4 -4x>. > c >D 0L V) 0 -In a.vp.U > m w U-u. w I

M/ 4 0 fo. M. -4NN"- Z"""*- > C = 1 NN w Z00 a-i- C. ).O-)>-o 400 > 0 F- 00 1- )(- Cc

0= 0. Z>

u 0 0) >.WQ 0- 0) 0-)

U) u N > WjL) Q 0 CL > 0 14. l'-u uZ z L - > 0o a

U 4 0. .4> -4 0 ZU U0. 0 > 7- 0

U M O.. > TU) U I, CL -4 > 0

4.) L3 m. 2 > N U

43) U NJ m- "*'4 > 0 UL) t-) <. L > CL

) U) CL =(A > C4 NL) U O N CL (Al'-* z x > x L wU) U) 1-4 0L n2'00 <der > 0 M 0

u W wt a. zoo" > - 2U. L)( 0 I. 0-4Zi- I > M

(- Uu 0 CL 0- - 4 > 4- %(3 Q WLJZ C. I-s-Wo X. > m o

N U U X-4 o- "M > >- 0 U--4 u I-- a. VnO-0 z z> U- 0I-- u u 1-4 0L 00.. 0.4" > - ()2

U) (3 UU 0.mzz > 0 0 w4<U. a: CL)0 ~ 0 Z03 Wu. > - o -J

In U U 0. Z39wo (3( > x on0-U U Z4) 0m 3OLL-Z z 7 > U- z- <.

W L) u 0 z - 02L Oz .<<> i 0 .4w.J u " .C ~ 0L Z b4LL -I > 0 o(D U U t '- 0. 4 V) V()/)> * -4 WO 00Z Q u -41- 0. WI-W "-4 > cc I- W r-.<4 Q32 U -.- 4 0. W=3= n> .1 M 0- -4N

0 U 1- U) Mtn 0. I-I- > C) Z in c%):

Q- .-Jo. 15- 4) U-cZ Z > Z <4N 0.(0 2'-> .U c U M4 0 z2 U..C.JUJI > 0 ft-4 0 Zu -00~4N U) I-- u UZ CL000 UW > P- NI- 0 ul 07*2

U- )( U z'r U 3m 0- s-4 0. 3 zz > l'- >-) a =V) m: D MI- <W U WOU N M-I (3zx11-- - >' < f.4 0 U MZZ4 -4 U 4 O% U 02'- 0-M *i- > W~ NO4 0 0n Z.-

> )-u U-4 uL -~ 0- z ;:Xm WW > <4 x( - C Oz -00:u xZ U ON o. " - (-UQ > .-j -W %%* l-<4 0X

- U ~u WWLZ-4 m-U- V)Q"IllWZZ > (3-40 0 -,u x U 4 UZ-0-WC4Ill'-UWWJLI>UJ)-r- aW

U U m4.V 00 W2"4Z WWc > 0 WN x 4/)Z 2-- u I N"- 0- <(PUW > -4 X : -00

U' 4 L) Z)C00. w Oaoi-Wu.UL >WLu z z' 0 o.4 U- X>- u ) MW 0- . .. VIL-,-AULLL > -J ) 0% UON.*".Z U '4W L U j W-O0- M M -1-.i- > M ZC W "S2

4 u V).4 U M3 Z C- < (3(3(3UJo0 > < 00 0 WU M=Q- U QU =--4< M -x > " -4C0 0 Z z

U U 9Z U v)WU>- 0- m wuiwwU WW > w (/)-4 0U I-occ m. W 0- <4 = XZXM -, < "D4 I ----

WU U -J) w3 14 ...1 a.>-4- > > UZ 0 M2' U U W(3 0-C > WU 0 :w9-4 U '. U ')U-4Z CL [1111 III > W:o 0 W ))VI- U #UZ(40. > M-0 X: CO :2M uUJ W 4 L 0-. > 0% M M 000n0 U cl1- U CAI.-4. 0- > WUM Z (A UUUw U =qxU~f 0- C > jo U 1,-0 U M41-0 N > Co <4 -

SU M u M-I~0 NNW-4 > =0 --V1) W <'4 U o ~0. X>-->l- X>- > or- <4 . '..

U) U W0.I,- 0- - "34/ LLCL. > ON a U U(U(UI- U U =zM0 C 44z"-4i- > *U U U t.--i 0- )X>.4o 00 >

87

I,))wz

00

4 U.1

I.J0

U x - z

z -. 1

U.

p-i 0-- U 0 (n

LU j 0 =00 W ..ZZM - 3

l'-- * NW

w 0 00 Ix U.

WL LL x l-a 0 x- U- U- 0U- 0 :4 0 0 -)- 11I-c D

U- ~ z Z 0 I--Zo0~04

0 0 *Z *.J- 00 0O- 0 04

X>- I.A. a 1--( I-a U--0. 1L 0Z u 11 0) _ 4 11-

-. 1 ~z -.1 -c " o wo M .u LL 0 . *-.JI ZO *ZL W W L)

>c, W0W)=U-(3 01c - 00l -ior lol 4 0* 0zn u<O4(.OZ z 4 %

I..IJ ...J z0 z-~ ZO 0U Wi

xJ M:) LL U OfDWU 7 oU~u.- oU

t. I. In U- OL 0- 00 1

88

V ~~~)W r- m ______

000

Z ~00

00 00. 00

z 00. -t U-J 000'A AA *z a I*

X70L 000J

z . * ~z 0 * 0 0C %

00- 000z 0 f

o-VU 0 I-I--? L)L 0ICL -iL mA0Z 0~ CD0

LLJ pU, M I 0 0- )I- '-. ao. x4 NA N 0

C13 L03 NJc0 0 -4 C.W ) C% N Z0W WOL '-E *- C' 0 ..0. 0 -4l -4 '

z w 0- zLLI0 W- 0* 0" r *0.- .- Zn 0n Ln 4A *

<1Z 0o * ow- U, LLMi- ui * 0.W tA 00 LU

xW 0* N4 U* WOwA . - - Q 0 w 0 0~=o- *n 44 WM u- 00

LAZl 0* -- 0 0 X: n 0 0

aZIO 3 Z* Q0I-A O0- N -0~l-4 4* 0 0%- r4 I ~ -

-. ~ 4z l* 00 4~~> u>0 LA* LD* 0

Zz 0 L*0 0

0. 0) 4* 4 , L W0 0 0 0

a.~ ~ i* i 0> 0 0 0 0C*U wU N* 0 N- A ~ W u

.. I-')~.* ZLU LA z wA .. ui co~Nx =* V)-x LANX:*mWC.DV)4 -

0'0 0 0 0 Z - 0 0

.- .... 0* . .-. N

0000Coco000 c

Lu w - - - I,- r- fl p'- r-51 te. ot 0% U-.% If-

S N n en CO N rN

cc L LL* '0 .0 0% G' 0% a, '.00 r '.4 .N O 0

m P-4 N N

A A A A A A A

V*

0* Z M 1~'0 Vf E) I

I"- (I' ' r m' 0 0 Wj

Vfl* I-W 1- 7 .4 4< .4 W - r .4 N fn co N

L* z 0 x N 0' -4 N * 0 cc4fl* I. co r- co N 0 N W P,-I .-.

0e cc 0 0 0 1-4Uj c 0 10 10 '.0 '0 W '.

>4 * '000 '.0 co co

z 0 M -4 00 a'.0N U'% cN N4 U'

V* '.4- .- N ~NLU a I-- w o 1- 0' N * * -

0* C) I--Ln% 0

N1 en ~ ON 0 0 -. ....0L* P- r' N0* cr. a if4 0'11 1

LL*

0*z 0 0n 0 i I II0 0.4 L.) .4 ' wwz

uj * m iCC* 'A 0-. 1* cc:

CL* 0 0 r

ui ccz .i I w24 (A 0WJ 2 0 u

z. 0. C- 00%

0~ f-W4~0Nj N m W

90 =

U- m

LI)* V) s

0 0 r.- co

Z*

'4* L- i ) U0 0CA LI)L t

1;* < w St>I) V) i- '-iS

4* w~ 0o0 0 .4Wwc0* ~ ~ ~ ~ " '.0 V)-.A 4 L L

0.-* 0o 0 c 0- a 0l-.W 4 00 0 u ) u uLZ.. Ill - 0 n L ) ( )

tn* u. 0 0 M V

U* ty 04 * NCA* M 0 0o 0 04 0 0

cl: I- z0 4 = r Q0U* LI U). NA 10 N 0 L>* U. M W<-* U- I- 0 0 0CAC* >- 0 M aa

I- co N 0'- m- V'cD L) L) L) L) ) 0d aI aI

Z* Ill -i 1O It0 0

*g. 0 . . 0 0wW

Z* C Q' Lu w W W w:<A .4 -d -4N N LI) ') t M

*o In 0 *C

a- ) r- -4:c 7* . 0 ) - 4

~~* 00t'4 z 4z zOO 4 0

mC cn m) u'j U. U.1 0 0 0

-J* >- Il Il V) 0 0 0Lo4x* N r- z CA 0

* Z La St - ~ Z 9 *

V; IL: I-

44 N N -

0 m 0 OC

O 0r-' U U- 0 00

V) z.) L 0z. 0 '0L

-4 '*

00 w .4 00

W. 0- Ln * N *0 0 00

0-4 (1

1.W 0* w WL 0 -A Nw Ma* UJ 0 00 0* (

oz40* No N N

W> =) 0 00 Z 0

-Croz 0 0WP- -J 0 - z

04A-- * " = ) l 4 U* a a2

M W .1r rl- P- F- - r- ~X vi cr *n -4 -4 -4.

< 4- -- 4 -4 (V

n C 0 m CYj w\ w4 m

CI uLL0 10 10 a, 0% 91 a, 10

7* ~ -40 N N N M-L

L)~?%* ZOO N-' 0 "c'* <- U- z

I0 I IT CA a I I

* I)r- - N m ~ CO V V) LLJ* z Q0 - 0 0 0 c

V* co I, co N4 NO N a N LLW* ZO 0N 0 -4 N c.Lu* 0cl: C0 0z 0 10 -4 U. 20w* M 0 -o~ 04 2 10>* o o 0W. * U ' 0 '. 10 co

l'* z 0 m -4 00 10 .0* -N U- % co N r 4.

0* - ) - -r. N 00 0Wj* cc 0I-c r- 0~ N S 5

urf (z ix W 0 0 CS 0 00* r) I. n 0% 0o c

* L N 4. V)

-L P- rl- l0*0 0C 0 0 I f 11 11ii I

0j*

w * z ) L

L))

Z r~ V) Of

F- cU- !l l w

0~ W 00

Z~ 0P 04

93

LU* ' 0o0* * 0 -4

4* I- V) r 0V) I) * *

L0 0

zN CV)* c N -

-4* 0-U A0 )) .40

=I~ r-- W l No

LIo* - N

VJ*x 0 0 10

0 04 0 LnA L

CA* =) zC* I-0 .

* >L 0) * -. 1 0Z*-' *J 00 '0 0 0 ."

en 00 0 0 -

0* V) (.D N)* *

-)* Zx 00 aLit 0r-CC* 0l C. 4 w o mL-J* Z4 It N a U% oU ->fl I'- in LI) Z-m L 0 '

.* > 'rD C' a L n) 01* ccO - ) M (tU N) -4 V) U) L)

Z* J 00 ZO t 00 'o

a- 0) 0 10 *n N ~ 0 U 4 w L

L* W -s

LU* V) - - - I- )3 ' 000 01 '0rn4t) 0 ' ~ '

Z* 0 0 L4.) Z 40' Nx w0r) 4L

0* LI. 0' <A N 0' N0j C10 L N 0 0

x) V) -N -4 w) 000* z Z .4-A . Z Z Z

0) I.- Ill4 N Il w l )I- -i -i -jI-

LL* LI) 0 0 0 w V iV0* z- -4 N

* U. 0 O~ ii i I94

L) L3 .

ui u 0- wUui U 0. LLL) Li 0. WWLLL) 0. C. > LU :

ui LZ La- WI- :3 0l"L) iC 0 > u 0 o0-4Z

Li) ~- 0. -. U-V u v c

ui Li Q. cZ z 03 0 W C<C)V) C)

Li Li 0m I" -g U- CCC) L 0. 0LLi LV) 0. C0 a-' IC U cc=0

ui Li w 0. ...i0 <.#1 zf U.. E U-.ZuL u L W L 0. L >ZV) VnY I-Vn < I-I--C -Wi ui> 0. Wj OZ Z.- "W 0 F-' --

u Li < 0. W-J )-"C 0C.i )-j W OAC/ 0.0.41.-Li Li w 0m 0" 1- "<' 0C) > '-ia YX..-< O.:

QiLI 0. LL. X:"i- 9F- M. zwow cCntn- =ccLi Li *L 0. Z Vl-V4)<C < WU F- UiL) V/) < =

ui L LL 0.C L CT~ 00'AzI-.- Z .1) LO *j iiiui CC) 00 0. o 0-.C0 0 O 30CZC WLL.1'ULLaL,'ftU Mui =i L 0. < W M"'- C) CW4C< al LihIc-l'A <xu

Li Li I-m0 0 ZZ I-UL Z>- =ZZ---UjC:: MfLi Li ZU1 0.. U. F-Z=<nui Y-.w ./)(-< >WL * CLi) 0 Li m in. 0>. 03I-Wm WU<= < I-I 1 4>(Xz=Lid Z LiI 0. 03 - 11 COWF- U- V nO?- UIn Q <Cp-Li ) iII 0. Z0 YZ > c0n XU ~---I- C at

Qi L .Jo 0 (L P.'I4.4 MW 0. U-< MMLL Wo-:rLi~ ~ C L .. 0.71-<Cxmu.oC-- WU.. LL clI-c CU-eI

Li I- LiLi- M0. C 40MF-=Z t M ~0W LL 040 I-- OCZCuLi u Li < CL.J ". i-. >0 I- beLL - x J-rc)C uuiI-

-4 Li < L4> 0L F- =)L -LL C0n mo ZWC0%JP-ZC)Li L) LCr 0. i-q UuW ,el:O.LL. L 7.,u JZ -CC (n4 <-< u L M

Li Li Li W 0. Z ..JI- .- 4 OcWW =<LnUMO<4U- -FI-J=> Lix- Z'4 WLi QIn 0. <Z..IIC) XW WZ WWWi1.-I

U. Y- u <91 ui U.C 0.m W Z0.zxZ0 H-ZW< D -- 0<< 11Q-L Li -4 Li 0. 0 WLI'-~ -- < - 0 > ..0C/LLuNNZWJ

4L W Li u Li - 0L CC2r0I-I-ZW-'Al IWLJZ=<O~ .J..jn

X u Li< - Li <Li 0.. WL U-U-W-4Cm4A =tZ =WN<I-U. M<<L i) L ~ 0. -1 ~ 4u- -n"~Z-.-I-

00 Li <-4 Li OWQ M. M Z=.-MZLLI -.'1 = WI' rCrw <Z z ui (A-4 Li 0'- m. Cc 0 I-IIUiI--IIC"--- Wtnr -C)0I -4-U-" . Q Li cc = CL. - C '-nin 00 W"N XMO0 <<

C)> N Li 0C) Li 0.L 0. CL W--C~- 1 -WV)-<W)DZ--wuL.c 11 11 UJLLj --q x. wL t- = i m- 0. MQW4W LnU<.L4-IZ~-z IL)~ .L 7W- < U -iJ< Ui < 0.. > W0U-MQQ- -C(LI-ZF--<X=) 11H -- H-I.- I- In mi Li >-0nN - 'AZ . C -- Nc'J r-.J

In L.) .. 0. Li In) 0 CL i 11 :D 111 -n -0 11 - (Li 11 Ncl o 11 11 <

w Li I Li -1 V .CL- -,r -iNm Nm r'

Li QI L I 0. .-4.--WW0 -I -M Z -- Cc0-Qi "4L -C 0- Li )-CCM1I:( -'- - F -44100"" -40J

U Li -C Li M"- 0. -. -""4<tW 1-Z-0 m ~ ~ <.

Liu Li -I 0. a.= 0~Z <Z -- 0 C /)0<4CoCZ: L:

co Li ui 0L0 Li CL

95

-A153 612 A COMPARISON OF METHODS OF LEAST SQUARES ADJUSTMENT OF 2/2TRAVERSES(U) NAVAL POSTGRADUATE SCHOOL MONTEREY CAS AUMCHRNTR DEC 84

UNCLASSIFIED F/G 12/1 NL

II. IIIIIIIIIIIIIIIIIII

,MENIIIII

11111 1. UJL1 32

1111 -!.25

MICROCOPY RESOLUTION TEST CHARTNA11ONAI. BIRLAU OF STANDARDS-1963 A

U', 77 9

>>>>>>>>>>>>>> )Uuuu

>n - 4.0- 7 in .-

W) I.- 00 > UqlI-cwc4oN wJ-0

15 LUI 0 V) > "0-u.I-.. -. 4 0 M0 1-- 2 Co > MO 34#AX: 02U..C 0 C

=.4 U..i > N- - .- o- <L)9- 0" = 0 > ~ ~ ~ ?~ 0.--Z:".

0M 2: 1-N.U. > wO--. NNCC.0 0 Mz*=00 > MCZ)O- 0 CfTh1-4O. -4zO z4 - 2-0 6/5 > -44 -t. -- 4 ftW Ix

"M w PJZxWI- > NJ4C. -0-0. uL. CLz11-w LU a 4-- > <-40 .WJN--t "-Zow w-40 I-- LD =)d >4 fE -z, 0.4NO.I-U. = w1 a- Z > .0(~nr- C3 = &f,4~i 0AId) z 0 " W-"." > -Xr > 1.JC.J4. UN< a

<4 WV&Oz > NXD-4-<- *!eUJ 0 04Wo. I- in - > -omz>-.o- 0: o +0.00 * U.ZLLOI- > V) .ovaW-- L * .-

2Wz00O0L.4 > r4%X4C.CX-t - "rI%4-) i~t0 4 > > < M= Z -. O 0-.- -. .oma Z9-7ww > cos4Z-4 . -CU'W- 0 . ICCLUKO 03 v,-4D 0 =n u4 >- 4A Z ftN 0 u

WZVnW -4 .- oin-Oi > 2 '1*. - M.tam 2 .LU" 0 w m-2 > 0 CtZ-.'- -4-

a qt0L400 > - Nrfl: .inX-W QwN.J4: . 9--WULZUI LU .J 1-LW > - )-4l 0 .24'-.i 0

Oz z 2 owu..u > w in04ca J2..... -2 -u- 0*.4w< <4 -jwxmw > .4 P4 ft -0-Uwin-t Z * i-Q

Zumuzu Ui-Uo- > U U..-4'-q o.~ 0 .Zx '.0 (00OwL Z <4 w .40i > U iJN.LLN.J---X L).T (n Z

WM 2 > 0 .. Nd4NO. -.tw * LUJWg-0000 o 00- > 9 . 4( *- -a,-- 0 VU) LL U- -U. U..WU-I-- > LU >-- Q- .- 1 0 zz --

OC Q * ) ) > ..J MN-Ui00-4, i-i-is.o m <0 U U UwzWWm > tm Xr-iN -030-0 Z<IcX x L.4 NZU)ZWJZOZZZ.4ZZ > .4 =45M-'Z9-M: - =)I- -W. :D V)2 0

4N~s-C..I-.-m..w > -4 0 .-- J<i3'J Ov)..tI- 2%- ZI'IgcI-9----n > ce .- 1-< ft 40 L) e .oc) -S> .4 ZNWLLZ-Z- %a W-' F- -I-~wzv'oocw> > OCA""eONOX I-. o 00 z

2 .. ~ ~ > in .ilin. -'f C3 00o -zemmmcwm > -~ -)f -<l'.'~% C-4 -'J 0. -a

U)~~v~~It C1 L)2u.*: ld)r'r% CLN.> LUNCM.JLI-LUL'.s) LW-4 %.0 ..411 if 11 11 1111 > cjm f4cQ 0LALUo ax .- 40 0LU~~~ CL.-40- 0.'4'- r -

O Z - 0 '0-t .4~n H*~ ,I. U,-.WO3W-- LU'-Z- 2 - c

0 qx u> j.e D-4_),)-JZ -~ O.-0N 3 tiNOn in x 2 u > CJOONCC .403-i Uz~i-rim .0 aO..NX 0x >qI- > Z-QI- i-- 9- 0

40 0 X0~ > cuZx0(30z M.Wzo 140 ULL..

96

z

I.-

-i zUJI-4

U.4

I- 1- 1-40 .

4Z -<

(nw~

00n 40 C' 1

WiWX 0 0

0. -1 zz zo 0ou~ I-- W 0

0 lii nil C-.) -of

-- .-4 ft00 "0. 10.N %cV o1 41 Q1 01 04000

-: -- - --- - 0. - N

I.- WWwWWWWWuIW WWWWW IIUU

C. -~ @~-@ ~ 4 - -- 4 F - 4/) z 0

0*)qWjJ * Q*

97

-4d

ItI

-4e

-4 -4

.4 ad 400 -4

22

0-4( -4 - -4

In 2: 10

0 0a l' C oo ai o -4a

* 4- P4 4 -4 4 -4-4-- -( 2:02:2: -0 q V

0.~ ~ ~ ~ 0 0 .1OW - N4 OW001"Ow00- W N 02:2:-X 0 mw

.4 w wa w aw w U L -4N UJ WW40002: W4-4 -

Z0 002- L2: LU- Z >is- I- 2 2 4 2::-2 .- 2

0> 0>ZA OZ3aa 0 - 0> 0)

I.- .- .: ..a 0 2..z 0 ~ 0 0 2 N4 ~ 0 0

or00o'o O'. .i IID00'O 0.

N oo M Nri -11

~~'-U~- .~~-4 '0 - a..a ~ A.4~98 .OA

Ult Lu

-4

a,:7-. 4

z0U, xx

-- wz . 0 0T Y

0 M04 a n

-4 C4 -44 P4xx "m

lmi OX,: X~ 0 a a34c M

0, a- -11 1 )41t-4 0 4 4

I-A. z0- ) U.1 Qu aq -4-4. c t-UJ V CC-.l-CLi) 0 ~ -t,. 0ZZ- aON) 0L -4 400 'O*,) '

- Ln 4- 0) I .- Ill O

M a4 - C1 1 CO- :- ,)p

-. lO C 1 0411 U)cDz Z -1--u N11Ut.-4116 aa'V.-) CDa>I.4-Z ,

-44 .4a. : . U Il 0l Zj .4 a a _

'OW'O0 'U) tflI(4 LL 0 'CU 0C- 0- 0

0 ,:-- 00 0 - 0 0 -)- - 0 0 -- W 0 -0Go C% -

-...- 0:L tJI 0 > J' 4 4 . I 4

W Il ILJL -N J U~I ~ .1WO * ai)~99a

z0

0

LU4

o~. 0 .C3-42: 0 - 42: 4 Z

OaJcr be 2>= >- ' I.- I- II- 01 -.) 4 0

04 x4 oeO-~ x 0 Z- m ZLLm M- +N >)Dcl . x

I z aZ00 a00010 z or- I-

'4 0 03' O 4 0 1 I..4 11 0 0,0-4 I U-O -IL) .J -4 -0.-' 0-'4u L)- 1-- 0

I a--Luc - QCAO.4fQ)- I-- .nd .4 Z 0a Zoil 10~BI OOW I'ow Z Oil -4,OLW P" V ) 0

-icy 0" Ij LU C0.- C-" DO Li 419X (x -jcc CDWOJ it QCCJ=) n i QWUZ 11- u~ CL 7C. UJ 01 z,-.,.4 Z -- -- Q-

Z - - LUP-OWJ uow Z "-LLI x- 2: -IL LUJ I1.-=L - I- if 11 I--IOO UI--=W I-OwDU m LU

z I- Co0ZU.. il 20CUZOWWZ z

0m 2- I-- 1- - I-- I- 7 -< m z Z=) z Z in 0.

0 LU OLLO 0O0O oC 00 c Z -jcr. U".- L)0 QUO)' L)c u LU L0 3

o% m N 1)'0-4 -4- 4 -4 -

UQ(UU

100

Iz

4. LL1 0

Z- -

on: z N 0

-e u -z-

- 410-4.6.1 te - l

rn le - Il

: 4 ?% Ne xA

N-- -4LL -. -4 .

x- ccs: .- 4 0

-AW4x 1- 0- Ii'.fne- Z.4 a Ncz

--- LA Z II-

- H -- 4-

ON .- M4A -t -M -

_j 0 -4 - 0) LA.d -4-000004 OC-- 00000 O-4O: - -00 ove o-d fnr ., 41Z 0. oIIs NM4 -AZ 0 10 I- rI ) 00010 00 9 LLJ ?- 0 044444 -- N +N "-4 a z-4

It MU -V -0C - - - -4.-4P"Mo -p. ft . i0 .c UO --. . I.

0, .-4,0 -4 "uj 0-,-,, , 0 I-, LJ/U Z -4 l'

W---- Z"-= --- -- - .- 2 - -*ou OI--4 N 0 o~a.4 4crm 0

. r .- .4 0I-. ... "0.-.ww -0 LcmWc~a Om)1- cc) -U 0. -u - a- z-

0. r0- 000' ZON0 -ON ~ ~ '"I-4 -4 st LA - 4 0

0 - - . 0 ~ -001

VS

0.'

z x0 m -4

0 xA

>C

No 0 c

0i.

cc( W X- f-1..4 0 m. - 0 - U- -

V) .4 ONO ul2 to Cz cM -- 4 o " N-4-

P"O L a -Z~ Ox < - 0 .I N 0 qcI:: - -- D4

>- < W O nI12: 4 '

Li 00 0: 2

LU I <<x X z - 00 1-~-O z

13. LU z 00 IA + 'P'O 002:aO -GO -402: 0Z9 Z 1- <P -4--- 0 + +~-.- N:.I-4 OL D

I 1.1 20 :)- 4 4~: 011 1-210 W o0

IL 0 n- 0- *f'0iti 0-- -. 4N44- I 1 1 O.-f-4- .0 (3cIM- - 404

z/ 2 N 2:41-+ XZ M-2 2: ::-1-- U LL

~z 0.xx Z 0 10:>)0)l: .0-20 F0 - 4 *r."J ~0 ~ -CO oO2UOCu 04 ZO X- 4rJ-.-1-. 4+ ccJ-4.4 LU .J

I Zl.L >0 CCOJ 4d C.UII ,ii

0 - - -1 moo M -4 0 I-- .- CO - -. N?-p- L LJ 0-8-4Li ON 11 ~ -~- ap" lii 1-MllO PI .

P" Cfl4 L) ItIL 02:<.n4 44"-4WW== ' 2:IMaMiIII 1- -1-ad C-) 1 It 1- 1- -0<- 4N o- W -.--

0 U.1 0- -<00p,4D~-0 0 W LL 0

4 - L)O-40 Qi 0L

102

. .

-1 "C

o* U 4

1Z. - 04

U .

-<- pq -u 41j0 2: -iAo i) M-

LU loi C) -LL P. - m I

7: CC .. -

0<X UQ -4 7--4 ocn< rr % .fl x ~ - iflbe - ec -< 4W -LJ -411 OinQc-

<C 49. .4 / -C -4:=Zc m l'U -40i

-~ 4e- 00. - 0

U I- -- InZ 0 V.- ~-u ; om iflL'-4 0m )

-4 W0- Cj- 00 0f < u- <C =

1-a I-0 . 0-4 () 0+ 1 r4 I*.-04 l - 4uLt'4 'r 000 l'- < < - ( "o

o0~Na OZ I-Oa:N- OW <-4-4/

LLC\J- -. - -0 N -u -U - 4= u-(' )z-Z4- -00"W--u s e~ 14' -L) U ZI~ -40"p" - -,< (A C-

00 co -~~ . o0e 0P" Clu 0 <<< ~ t'.) 4-..

rn 0 - - -: -0 -04 o~eu' OZZ) in44NJ4

1 4 4r0 ,0 I-j 4-44 fl U 0

0 ~ 0- Ql4I .

'0 000 0 -4' 00 W* 'U 4 4 ZOs' 0pI-.4t"0 4- fl0c (7%0.' - 40 .J..W +O-si i-- O OO t s-s' - cl '.j-J c -NN i II

~-44~ I -U- J :- Z 4Zs-s-U103I

ClIo *o X

L 942J V)V) Ix .cc 003I0 Z-

-

CD4D w--

-- U) 4c

110 0I - -00C% -O C

mma -d

w P.41-- i

"v-4/X -

oxx ocaN~ 2i N0== -.-- 4P..J 0- p..

-4 0 0 N" .t s-eU

:34 1 *I--4"a 0 Z0 LOtzmn In .D* P14114 -s- UJ 0r\J0

N<XC-WFO WZ-u-4 g- 0z.-000ZX (\,.WL OU ) ZU. -

C - -0 if1 ~ - -U) -- 0zZ--' 0000- 000Z4OcO~4 c- 0 :-

4004zZ 0Z -- 0 -- - -- Z-ta---- ....X"ON 0 "--O- 0%0-4U) 0z m*w 0>-%o,00- 0,0u0- 1)U 0 C" 411 II cL0LZ- U - L

>0= ow V<I-j.V 00 0 - -- - - -0-00000 1- 000--

-- Nt 4WWLLW .. Or .. . U) co N W Q0O--( _j #Az

0~~ 11 Ws Wr Cf.UN-0 -I~~ (n -z zzox3:x x L---- -) - IJ0)0.1U)-

0 U) OZUJZ ~ ~104 J)0 UZ

=3 (N. z ocU- 41"

Mu en CL

V) C LL C N-i *

M C* ow*-I * - .i-

-- -- I.- *

-4~mm -.. 4 2 -. U I-*-n -) -U >.~

0* =0- z' VIC ) ~ V.-A*<Xo4 CL- X: *- I- LY 0 0 *

z .o- F- - 0 >

w/) V*I -t - -4 . > *

P" V Oj*0 V) " - ./ - O.)4 *

L/)' * Z - - oc LL *00z*.j )<o CC -- I- ( . 0 *

CO 0* 0 UO ) UJ'% 1,- w w 0-C J "-*oZ (~Qs LL LUUJ *3 *z 0c

B-* .c4 ... 0* a, i.-'= *-41 M 4*)I- - -0 *i C *

P-4/ )N -- < a:* 16J 0 m<

00 .. o Z/* LL4 V) cc*- > LL 44 UJL * *

Z.04oz - Y*-W 0 WISL 0* w - LI 0. *0 61 a/ M...i*4/) - . CX. *C-4 0o F-*I-- 44 +,a) V)0 *x ax .L *VL 't4

-0il XX1*-O U 1-4 XX4*-IA O< -,t - *11C 10 in (I =)* a. w-* 0* - - C- *0*

L-~ 10~ C C) -NN -~ Z N-i. * *1-Lu' -*O -U.- 0* ". -0. -01 Q Z*0- ;W -- W*--; -nz xL

"- 2U *L) 00 x ) >* q-<,, >XNXJ..J *

>00 ~ ~ C 0M* ~ -* I V -. L- 0>-0"'C '4j /L* ------ - -

c-1- wo r- - x*~ 0 *l -- C

Oi" 0 0 IQi~ - IFQW4 )CWWC *4-'4>O<qCW * -*IIm z .04 t')OO O-0 m *-o-c4 0Lroo *r-u- , *

u --W -j ) u0 u- u-- .u- - 0 -u t- LLL L* LL . L L . LL - Z u-%,u

0.JZ-. I - W,% .4 (mm .. ~r- . - mNJ--4% . N.QQU4 -

o o~o o- ~ 105

LLI

< * 0- 0 c C I,~ - L

- * X ac Z U o ~ ~- * * 1>. 0.. 4L L^ F-

U-0 F- F- .- m *r 0 Z CC

-e (f A P- ON * 7-C 'n u < - U '. 4 ICN (N LL C -*3 LA z *L -.- V^ - - i

* - 1. -- -1^ U..0. L- W z ' 0 V-* nu < WI X l' Ln LA C CC <'A -l * 4- c

eX., 0* LU = N < I.-a. > -V J%. L .. 0- -

0l 01 .0Uw u- I---U 0 A . - U. LU -

04nA I 'A > -. U 'X IT, 04 <O I - -- ' ' LUO <W* W7i '-'0 -Cl.-.'- 0--~L 4(LL, r'j =0LU OW* -I LU -I-r& J0

X.-4 W* Le- LA *L LL~ 0 ozc V- ' tr 'A 1-JL V LL-No * a- W * * 1-.) - -PO-. >-CL L ..

-- -) I * Z F- Nn LL -jW- F-- C ''

OX CO II 0> *. - uL I QW. WL W V VWC U L

-4 111 U.1 V4 <Z U- LL *L < U 3c .23AC W.CvU.. N ix 0LN * 0% Wo 1 0I> C z C-. LL~~

L- cc Z U M.- L) *4 F- N * Cr- q . .. o C 1-I-C JCU" -

-- uiC Q -4 *1 < N * Ln~o " 0. 0 0.) aZ' U) 0 XLn.- - is Z 0 * *L x - LA * F'A - F C' m-C0 4O 'A"

m4 W I- - LL * A * * 4-L .t4-.. 3 3 ps.U ~ x 0 .' "cm * 0 0 *- "01C- C 0 < Ui=-

- W I *.-..eC * Z- C L U_. _* -- ZN4~.C ZWZx .PQ A )<..1* 'A- - * C -.4Z-1C 000Z-T:r Cvm

ao> -f( *. I,- < m = m-FC -NtW.. "Z Z - -'-_j =UU- =(/ *Z4 * -V 0-'4 N- 0-C >-CFI I-c be -- I-

U)^<)-- D < -- * e. - * C- - V) (4 0 CLvlJOI4 U') X 'A >2- L ..tXX * XA0 =W=I--~~. 0 0>.

> - <..u- 00< u Ul . -*cc- IU %* 'A--4 4 Za 2f'(N4 I--LUL 0 -4F** N *- -. '4XL X . . .-'A 0 .- 1'

ft4% '->.4.I-4*I- 4 IN) *-- I I- I M 4 .-.Zx Z zC2x.J = 0~)~A* * xI'-- (Nf LUW - N N<N-4 I (.N%%t)~~* - 4 - - NI'~ A-'

LAA41.I- ~ 4a.%Q Z * c x -N <:)~ 00 0- 0 *a X4W~<~' A

- -~.-* * Z - -I X- M-27).0) -M-4Z<lX ~ )<c to: *W W W* cc -ww wx (NO-'-'- .- 4.ww cg~-4( *('. WN4N

0NN N NN I *l n m m m m r I -r -rll-rrtr- 4nUAu

a' 4- *4 -)<-4 -4- -4 -. ---

44 4 4 4444114* 444 44 *4 . 4.4' 44 44410 -'6

) z N 0% -0- - ") - - - - -a < N -4 " V) I. ( - - * .- W

1- c- LA: .. uw (C OW <A C u4 -II W(A V) M 0 Ia. < - 0 0- - z -C -oW 4M> u. -- C Z CL V i) C '1 U.. w

cc.. LL, - - Z Z- . c . < V)'0 WLIJ L N '6- Z C X- Z C: .. W I- Z - -OD Vi. 2: a '- C_ 3 -N=-- CZ- V: LN mT (A ()A C w. X~ 0 V) 1-t ,-C.1 7UC% c< 'r M. W Z 4 L .4, z 4- -C "<-' 6 (A -i 4CC x. 0 Wu .- j Y_ N 1-. ZOO- -1-Lr' <- LD I

*Ww 't I 0 VA Wj . (A Ulm2 ZA-L9 z U Z w- (A I. OZ OA> < -4

Lfl F-W a 2: 4 U.1 "-.. V. wL 3N0c a. CN 2: : NCU) C o W. I) 3 r M A l-u.- L 0.-4 CC 0 C 0

LL u. a 0% w Z 0Ii - . .- s-i c: C' U 1-0 (A - 0. 0 " -J C L/NNI 0. r- P-40> u.. w L) a LL. W'- cc *4 *-.-r LL 0 I- fAW LUCt

.N a cc > 0 V) ->-- as I- -* I In M(A 01- LLjo Zx - Z-4Ui LL < .. j W <"- La'( Os I V0' Zn F

C ONI CO 0.-4(n Z 0 0-4 X-. =Lo OM' - INI 0=) .S0 "amO .4 I- '- - .0-C Z Wj 0- C =)o 0- C ), 77

Q--. I-.0 Wu 6 -4 (1 Mt 0.<.(A M40 -4 z < w 00 <_ 40 -- -j- z z l-.W = -4LL " s V)<Z '- - 4) < 0- W~jqLLZ t/) I-WL 1-c P-4a' U_.

> - Z >W.0 Z LUUJO' -Z> WJZ0ID <M U-C U- 0I F- -. W) M w_ 4. 313 Cw .. I "M C V

0.: V) (, z m 0 0 C W,-.U.2< 0-1-- VAlI- M' 0.-Z 'Z O(A Z0C CC n4 cw'- Z Z wN~ ".gcn.. '- Z0.'V.- 0.UINC C -'Z -4

w 0. WM 0. < < >n - (Ao'Ou- CCO4r-J 01- -a " .0 u..-40 <.. w. W(AWLL LDNCO "-ZW< Z. FI- t-o-

COOu0 V CC (A C W, o W XWI c.( IWA 441--o-- 1w-- Ztl)Z WU W (AC ZC.ZVA WNW <0CC0- W"- " .L40.04(A W. 4.0 > > m < 40x w =NE >""o_4 =)..1-> > - I001- - W--w- W. Ca' I- ZI-W F- -< 0.0.0.0 <Lw W >o(AZ (I1 LU WU '0 (AC(A> -Z W000 *.ZC C w -'.,0 '-..- ua-i (A (A . -4 in--a.. 0.* ( /)-OWL Cn OwI(A) coc 01-00. Idw~ mZM w Con C N

WNI'4ZZOWCO= C-C C UV)( < 1- W0I 01-1-1- .-JMC0.0 W. M... U~.-C'.-11--e0 _J"- Cl-C .JW1- _ 0. o 04 < < 0

O-.O 0-t LLJ -w u 0- "(A-OCL 0.1-m I- ("j< -M o(A-M0(AO)-NIC Z 7 - M. W Z MEW(A L k0(A(A(A <NL Z "-iC<ULn-< <,r-4 *ZM1- F- <X OWO< 41<Xi LaU-- x <~ < z 24X~ I-0.>r < x -t (A X 0 F.C- - -<LA-(AWWO1- 11100. 0M LUN IX0M. W_ WLNI- P-1-1-I- 2:.( (A) t/) WN< P- o< l-WU WU *uJwLL()< Un< 0<<< 0 0l GOA 1.)

0r-:vzwZ0.a' *@3 1- 1-0. ->I-N cr0m Z=== oCO'w ul I z0O3M-WLCP'-30c-Z Z 0 - Z<Z-4 C -. P-333X LL 4 I ww 4LL~t. = LLN I-lOL Lu U_-L WW - U..- -7 -I -.. II

>(WJNI- *x'ON )<W)< )<- )0 )< *. x- N - NNO N -x x< )< 0NI-.-4<VAN -4WLNF--N 0 90"-'- NX<N v N '- --4 -4() - -4 . >X-4Z I- 0-4W. *-I-4Z- -4- -f(A0-4N-q _4x - )< x.. -'4

4"NN -Z *WUNO. -jw u -. Jc '-4 - - ('O nN N"NN% N. )< ft

U N Z -4 U. a. 0-4 N V-(

,0 (An * 41-NI- 1- .- 1WF--1- 1-0-41-01-- I- - I- o1-I-- 1- -1-1-- I-I--

4 ~~M< M.4 -0X724.4.7.1 4X4IN4Z4 4(A4 2:4-44 X7 4CC ww UM0.N0.u-0W .Oc ciz0.I- ow. =z1 W. o.NMWM. ',tWN0. M. w0-0. Cn0- C-i C0- 0 -CZO0CIczCC-0v~r0~ccoc0 -OC-C-oc'-CD ZLL ou.0 11 .. NU.. -U..) CLL"U..0.-u..CU., u- LL U. - u-f u. LLNLLU. LL U_ -u- W

0 0 0 c0 0 0 0 0o 0 0 a 0 0000 0 00 0 00 0*** UL 0 rl O a'% 0 -4 N n It '.j 1011.O-00c 0 _4(N rn I 'n 10uI LA~ Un Un U. LO 0Q '0 10 '.0 Q. 4. ' ONO'O0Q-Z ~ r-

-4-4 -44--44 4 4- - - -- 4.4-4 -4 -414 -4 -4-4 -4

107

. .2

1- 0 0 . > Z

0 ft 0 CL > zCD- u 0 L a > 4

<X ii U. CL >-Z u U. M. 0 cz x > Sd)

0- L0 0> 1) .CL Z>"-g4 u L) CI 0. -0>

lxt- Q 0 CL LL U U>

u.. U ce a- "- > 0WW U 0 L 4' L a. 4' 0 w >

0 u u 0 w . -aui0 > 5u~ 0> 0. z AL u 2- I>

z - 0 0U a. L > V) Z Q 4>.D- u u 0 . Q< Il < $ Tz > 0

Zr . 0 0 O a.)Z t I.- w> >

c('m u uw aj . 014141- V)a-= >uJ 0) V)o0. LW.*jl- Z -4 e -1>

u4i 0 (La L0U)L 40 X-4<= > cu~ _j 0 .i La zz"III- -. JXCL >L) 0t 00- C404 00a W a - >

F-4d 0 ) LLMa CL -000 Wcc 40>.4m 0) 0 a. <4uLJUw V) cc m ul > 0

u~ 0n 0- >>W a.J Ill V) mzwj >uZU 0-- oz La (W)W 0 > W

-0 f- U 0 ll w - a. )41-- Z 0 X: WUJS,, > Z wN. 0 Z u I-- a. COC3LIZ P4- 1-t-aCL- > 0Mm~ ) L) 0 -4< a. 00m" = 0 L L.. M UIZ > - -Zu. u Ix u U> a. It-= 0 a Moa.>"- > I

L) 0 mw m A. U ULLLL U Mt-0 xx a > 4 -aLou cc 0 -wa. zoCoco mo zU)z 00"m > se 0ZO 0 u l- u 04/) a. 0 "ZU~ OWUO 004L > < --f- 0 z 0 <m a. "- waQ NPJ-4 "0.b-4 w w > .1 wO0V) u .4 L) 0 ak. g-wwww Coco~-Z1 00 > u 0Z 0 M z. 0n an a.o 4WW444-dd 1--1-LLu.. > W Z

m~0 o -- a z xiix: ..i X -~t--' X~ > 0 . .-x 431 u UQ m " a. D <Cl"Q0-~>V#> " wJILww > -

4 U- M -4 U Ww a. U. Z~ZZ "-4LZw~w W~ ZZZZ > Ll >--x 0 At 0 zx a. w 1--U) 4000 I-)( 0-4.... > _j M

Z -0 41 Z-4 0) I-m0a. 4444 7Z-.i 0000) xar-=mm > <u. aoZ 0 <.4~ 0 Z a. w o-aW -00J > -0

4 7 X 41 00- M~ a. 0000-"0-~~c > Z3c W"V', 0 fll U M a. 4< -wwoWrUZ40 Zm= > > c

Cc- U .D- WW J V)(-.d44u U)OVI) >V) U)01 U .0 0 V) a. U. x OIW-W ) > 4/)

0- q) j .41 <~ a.> w I 0-1

Z)-Uw L) L.. 0) a. CL >. \ cc-iUv)4) u 0) P"i 0.~- -. > a.

I-4 W 0 C. .- <00 7ZQl- 01- 0 4/) a. -4<ZZ- --- u-u. > wi

0411 0 u =<a 0 "---C--1-.- U.Nx > -W.-' u I,-M X a. ~<l,--I ZZZl,-X..>u > M

M-.4 0 < u 0. 1-<00. 0Z-gEZ~'4 > 0V. 0) 0 a zzzz 444)UU3n1>.J> 0

W0 LL >0 00

108

-2Z

-pJ-4.

I-- j

i.- -N

-mm:

Z 0 %a0

-LZ aA X -

0n- (A CA

> -Z M0-=1) z : 7 )

0. - 0 XVA 0 1(Na u LUJ =0 wU 0

(AM<. IIIO 0 >0 CIO

a- UL 0 W 0- * - V).

71-I-- 0 00 0 z 0 a

0. -w 0 00 X0 01- 6.4 Z 0 00 11 10- -n. I . f,-LfI-z " 0 0 0 Z 4 -4z.,

OZ- Cc 0 1, - LL 4z LL 0 u.0 0. 0 0 0 40-11 0 0 off I ---

1-N-I - 0 21.- Z 10- Z 4 U.IZmld c~ 0 It- 11 (0 z .4fla z Pe-40- -11 X=).Z~c WLJ Z( - 0 '- nC 0 -- d P 7

I- 4 4 U5 - " II 1-4 + II -n 17 -21.a t- I -4 Z2- to- 11 11I I

-X(NO-4LI 0 Z LW .4-4 -. 4u) .4 4X-4 77Zx 0.Z Z, w < -It MD P"' o-s. W -2> W".-OLL o'-

z -Z-N - p- x 4 9u-~ > X-o= MOD r*-"- -N ~ *+W -7 W1 -LJ0Z 0U lIU0 7:i~z t 1

aI-NV ft If 10 M- I- j 0 0~I'- 0 0 -- '0C

ZWUZ- "'POXU-0S'4w 0 2 0 ZW -4 -r0 -D MIX-. wI-, 0 0 0 0 00

F- -"Z W Zm 0 U~ 4% 0V).x- LD is 11 00 O0op 0 0

. 14 W .4 11 (M . ul,-'- 2 70tf'- F-- I-- -4L z- <

W.(-M Z 4 U0..-4 W 0 Cu. 1,- l'-0~> ZZZCA V)4C CAV

000 0 0 0-4(-4m P.. A

L) VQ U)U~

109

V) UP a:LL

6- 4 4x

z z

0 -- 0 xL c.o a: z:VL LI. LU P* 1 U 1 . P*

z u- m4 Ni L N w

2: ". a . a

4 U) 4 .- JL 4 .aZ - V ^ - )

-~I- U- C:)- - I- - IZ(a z Z 03-

x i-a &< CL V)

cc I- - Lw 14 W <L N <.X 4D0 CL w- Z CL w

C) 0.- 40 4 -L

- 2: 0z . (A W .

I -Z 0 a. z 0.1 a. -

r- 0 .0 ce LU ZI Za: -z 0. < N) - Z N

40 - 0 .4 OZ 0. -.L .Z~

1-0L ZZ 7. Z4---

= I- c x 0 LL : a: cc <:- a

0 - 0 U. 4 - .N,4 -3 U-t U-L-. 0 -4 0. 0 - 3

j (.y UL U- .4 Z LU ZZ U. U ...

:) NJ~ U- z L --- z C 4 4

U.. 00. *. X~ LU ZjPt4X"L

Z 9-u *--4 -41 - LI..--- xLU Q) _- YZ. L f- Z> 4

I.- Zjw ujli 0 0I- m.. C".J

11(- w-UU W CJ m0 .- ~0 t- 1- M-

,w ""-4.4..J. LU _j m.J -i uJ U Z L 0. CL. 0 0.on I-a: W<Z -4x <LU)=4 -j0 0 X4 < 4 X:<uz C 0333 Z~m zf U4le o U ) 4- 4 0 Q 0 u 0 Q C

Z "z z -.i LU wi LU Lu

0 L C 0 00C

00 0~ .

-..

Go -% -4 -4QQW QU Q UUUU WUU UUUUU UQUU W4UU

110

a U.

- - UJ

LU 0 N U - Lrf -

.. - 0. N N 0a 0 CLu z.. Z nU z U') 0. z 11.

N Lu m* - 0 0 Ln' Z0- > 4n u. I- z 0Z C. L.4z Ul% 0. z Z - z N Z

Z m3 0. Z - 04 NL ft .T 0 -Wj -4-4 ~ z z N 0m -4 N

F- P-0 c I I N 4 Q. Z Z * 0F- W ft NL Z - N 2

I- U WN Z z 0..L N N Q.Lz wL P --Laft 2 N M. 0.L Z N

- e -Z F' - 0- z z CL. -N cr oa -- z z N 2m. 0 .4N a . - N N 0z. L.) )4(L I- - z x 0 0. = 4 Z

-4 LU .. IJ - a 1 - l

z ,-zz 00 U.- g- Zz on '0 L ca ao cc z F a a

Zia u.. (..) L). u Q L)

2 ce NN Lt .i 4 - - a '-

MT < zz . --. U U U U

a- NX .. Al ~3 I.- Z. Lu 41Mv 0NM Olt O4.r 010 O r0- 000 00' 00 0-dF- _1 o" << 0 0 0 0 0 0 0 -0~-0 4-.-x. LU xx .4 * -.d.4 -4-4 -4-1 -.4-4 -.4"4 - 4 -4-4 -.4-.4 --

co o zz X L£ I Z 0-il &a~Z aa a~ -. ~ a~.a -1 a Z--

- LL -- X * 3 3 3 3 3 3 3 3 -.- IW0 0 -4- Q - - A - - / . . - Z 0

LA. ULI LL w -1 0: m 0D D D m 0 0 zU.. Z NU.. a. 11 I.-UlW wUJ LWw Lww LWw ww WUI WjI" WWIU~0-1 0 >-i 0. -- -- J---F -- -F - --- F jFF i-- 2-00 . - La

> .4 .. J> LU O Z U 3U 3 3 U 3 3 33 3 J 3 .JzZ .t4)4fl44 p-4

-j 4x< P-C U'-. c

U 4

LU= 0.

F--

U) UUQU UUUUL)

lit

Wl N -a- a 0.

z CC Wa-

o 0. - CLI-- z 16-z z co0.

o nZ Z w . o

-4 N - z M I. C)

z

-I-. z I- Z -4)-0 z x -6-z I- 0- a

-P-4 0 - a- - ,-- :)- -4 - Z< 0

-- Li- 0 4n) > I-- -4z(0 Li--4 0 x N 0 - 4 Z-- N...i -

I-4. .I z( 0 u 1-2 u 0 ZO1-W - - -0 Z Z > Z 0 Z Z

WUI- 0 1 - - - * -- I . -

6 4* . * Z0 *IlZ% .0-9-4 0 4 --.X 0 u U - .- 40 .. ..2" -1 .M I.- - .I j * 1 OZ .. ) - /

=)4/ el -. 1 > 00 -~ w cc > 0--. cr ~a= W 000.01I 0 00 co< N 11

x( ..4N~e U.0 Li U. I- CO0N r) am IJ. LU.004U'% * 0L-- 401--u 0 0 -0 tnh/) 0-4-0-4- 0 - - 0--a- P-al) Z-

cc )UJW~ 0-4-4 -4-4 X:X 0-4 .4 -4-- N -4I- 11IW *u= Z Go Z 11 11 C7- - -2 3->0~r- -- Z-0.-4n4 -(-Z WU 0 a0 t 20, W..u.'-ouL 0 W',O.'O Z 0

2: ""r4J a-.Z P-4 ft~ a1 P - - - -4 aI-- t-= 0 1-- I 4-4)-) I /

.4 04/) ZZ <U. 4L < 4 LUU ..j LL- CyI- LWLL 0,-d -J Ui. ..J 11 - LU U-WW WW Li-U-WUJ WIUl LL..I 11

00 0x -J x J0~~~- 4z~I NZ0 oL) > < 00 zQ6)Cu3LJ < 0.33L'33Z> 0

0UII - i ... -dn>- z- J..J -.LL u 0 ou- 0 41u.-Q-

00 0 0C0

-4- N N

112

1. a S.7. oc a

3=

0. - Za<

43 V4) %x* a au *UI

-z Nd C4 -r.C.L *-

z CL- -L aa 4 (

* ~ Z3~ ~ - I - . . 4 0 .. *9. Va 0. -X. S.S. x

N aWO 3 006-4 )(0 * 0..0

-. s-N" LLJ Lf'n N P-W U-xI ~) cc~ C! ce <

0-. 0.L Z-0 0 9...4aa -Za)C>C4 L

> X1*-IV- ai rWx~fl ~ )L~c cox z z - c0O4o.W-I>.(DZ P" .0a ZQ.l 1 *1b~4*a

- -Z(D U 41-TQL

-l * C -- 0, C... . . ...... 04 *.-

4 CO 9.. -M 4/)- -i r--j-U) 0 aJ0' 0- Z n -u.- -- - -- L

*: " 0 W.'.u ZM . . .

P".W 4 LLO C3 m ) -u- ~ ~ S N- m- _j U--WUW 11 - *~*ZZ m _jz9.---. 0 zz

U0 &.W Q~JW~-~U 0-W - -'- - - -- -- -- --

zz < >0.33Uz0 zz z -9- - -

UP- .J- I-No UtI- mz j .-i z z F- 00 xU 00LL c 0 Lu 0OOCOCCOOOOOOOOOOC zU Up- Uu = L.LLL LL.U- LL- U L L L-u..U..U- u

000 0 coo ~ 0~~ Qr

N NN NNNN -4 -- 4 -4 4 .- 4 -4 4 4- -44

113

A-) uI 0.>-C 4) >I

z LI Q 0. > oV. L) UI Ca.

0 0I LI CL.

- I LI a. > 0

U LI LI a.LL4 L) LI a. W efJ

Q LI L 0. WL > _u LI LI a. > 0.

Ix W L. " CL 0 > Z.

C LI u 1- a. Zp" I > -C00 LI LI < a. 00 .4 > 0

u LI LIx a. "cc: Zfl > -C LI LI a. 1-C) P-Wu > 0)

0 I L . WLI=) WC > _<I- LI L U. a. L0 0.4 > w~

z Li LI 0 a. v)ZWWLL C).. > It4u L LI) a. U1.4 I- mnLI > ZO.u L L.) 2 a. .. n-z< w < > xw LI L 0 a. ovcm:C' -&.> > -LUl

Z LI 0Ia Z-" <-- > uz LI Q II- 40$-1< Z<> > Zf

0 LI) u LI4 a. -d0 *"x: > zox LI1- LI .Ja oo>W C-x > oa

SLI ac LI CL a. www(L wx > -Z LI LI uI 0. 0 I.- >wwm 00o > WL

0 LI W~.i. _jM =- wm4 ow > r4.1 a-t LI I- LI < a. 0 x~ WOWla U0.IIl > C-

0l LI0LIL. m- 0<-t4C a > 0a.SLI) X LI 0 a. - 4"J C1XLL1- W a. > XI

-4 um 0I L i-L 2 .41- 0 1<Wx >4/0 -Wu X~L Q% LI Ia. - . w LU.. LL -=w > Z -1U LI 4 0 LI CL a. u. 0M 0 W0 u..i--- > C) -t

> NJ 4 LIUZ a. W "W"- UJ > " 4< LI -L - .0 ~wi - > I--oi.

U.. LZ,4LIa CL "O<WWxWz r> <CD Oz0 LI 44 LI M W 2..) "Mw~w<--CO. > W >-W

< LI T LIr*xzx_ 0v.im 4L0JZZ > < I-33 X LI 4I-- u LI M a. W-== :)Cr- 11 0U., > _J Z -- r 0

IL. L IO umf LI (L a. < 404ZZ.izi- ZI- > LI 0-M~ 0: LI: Q D U M M w w 4 <_ > w "01-

U. 60 LI 0L CL r. XXW1<ULUJ -W1.4.)< -. > a oa10 N 0uI 1-m LI a. < "'-ULI X -OfN > "_4 . -.

WL LI -1< LI < a. > 1----~4.> WU.L--'q M

Z LI L 0. 0 x > .. JUIvC\ .-4 %.. .I

V) LI LI a. CCO-4-- 1- 4 004 .0

W LL LI < LI . -4d1z - > < LIa 0 .

MO) LI $.-a LI & Z--M0 > > MZZ W .4Z-4 LI UL 1- a. NrM1L401-_'1ZW)-X > =)Z - I-

nLI4 LI Ia. r r4lP4ZZC>-0OW > OZ- zLI I aL .4<<<4ZZu.1<1- > 0-u M

W L LI 0.6

114

N. -4 -4 LL r4 14C -4

P- NJ -- < -

U- Ia C.L U. CL L U

M4 f-4 (I x X414 -

4l 0 0 0-4 -4.04C- N- P-C . . .0 .

0--2 0- - C-

, 0 1.-'a. LU Ln-w U - w 0. -

M lIax- o I- 0 I-7o 0-Z ~ ~ 1--4 1-4-4 x X>- x )-i 04 C C-4

C)NN~~ ~ ~ ~ N"JO I-'- Itw <1 t LM, z zi2: (D- C)--- -

ON >N~~- a.' 0 N<IA -z> a .1 aZ- 0 a a.< Z CIoz N 4 < U-4w 4 <- <XX <"L--4 4 4 1 J .- 4

vn 1 1< 1 11-, o- a c F 0-4) - o 11 It 11 .-. ~ 11 11 11 ZlAIM - f4 -=) - il1<1 0 CZ ow. -- <N I--4- L1 )<)-I- ZU-< 0u 00 1)<L

a N,-N 1-u'-'W0 C" cI z.NNW 4-1 004I ii Z.DN if fnZwr4CL. .G-J)-1, OCOW - 449.- -- J) OoO CL--o -

Zaw o-4U- ZLL. LU 0M4jjuj<LLU ZI- -<U- 00. C -4LUr-LJU L 0

ii z .--NL -4WNWWOU 00O4WU4LU.00L0 0dWJWL

0- I-- I-.

00 Z z

NU.. OL 115

M .4

co 0 L F- - - ac

-a NJ +. -

P-4 .4 m I 10 cc. 4. P1441 x x 4 P- 0 0* I

LL '4. 0 0- -L 10m.. 0. 0. 1. 20 X N4 CV

9-. a-. UJ UJ 4

00 0. x x. 0 U '0. 0.. IL B l ~

Qo 0 0-0--4 9

aI 1 0- - W c C)-

0 W1 W D - - I'- C-z 0 N. 9-Z- -'U

-4 11111111 It1 -- -4 .4 = .4

NNNN U r. UU.' Li. .>X -> -

*MMaOa.Mt J tn-W .4I aI -'.-.b-- Z 0- aD " -DZX XJxi Z. -4- <.- <-f--w aa a

0L au - U UI-U 111. .ro0 0C)-)> o"4~ M-.j- 00-4 -4-4 41

'-.44Z(-- 0 I- I cc =a) .4-q =4-U-9] ~ -9

0 -4 (4WWW1W4L 00 0-4i III llI ll J -4

Z~~~~c W IJ J - j

0 0NU-OO WWW4W .4O. 0 C)

z z0 0- -c4coC

11G' L

ui L 0- >Li Li X 0. >0 9-4 0L V) >

0 00 4j >

L. 02:0 Zf> D0) 0) 0. - > cm

L) Ci C) -0 i >u CL CK cc > N

L) L. OZ . 04> 0.0 ) 0 3 W 0L 0 ->

L) Ui 0. Li 0 >X 0 Li Q0 m> < ." -1)0 L 00- 41 Z > > z

L0 LL CL0 W X > -U0 LU- 0- -0 >- >

L) u OW 0M .4 Z :L >14 ) L- o - 4n Ne >

U 0- 00 m 0 > CLx W L) m0"-I > Z

Z L jA C40 1-o LL 11> -

Y- 0) 9- 0L 414 0 > x- 0 0 U.M0- W0 .0 > V1) -

>- 0 u00 c.' Id >> 4Z 0) Li CL 4)ZWUD ui X: > - ZYi U u Z0 CL W< - 0 X > -

- i0 0- ..i-Z< -j = > 0N0 -0- owor < 0 > Z0- 01 CL0 Z'-'-.-V)> . > -

L) 0 U -J 0- <COW >. > 4n> )

0- L) CC Li U 0L w00> -* x > X2: -Z i 0. CA >WWm0-- : > -:.

w 0 <I m- 41 >W0-42 > '~-

0 0) I-- u U4 0 7 rwf4eA, 0 >U Z I L) 0. 0 4A o xi - > - -

40 4 0 w CLI--UJ wwm >> 7I--4 u 0 t 0 0 m- - 02:u..-Zm m 2:> Ix 10

U 0 C Qi L. 0-7 0 30.2: x 41) .= " Ncs.jI02:X0 u L "LLU. LO U 4> Z - .

>Z0 M4 0U 0 W MW) U-oa - > 0 -0L

U. u - 0 "- 0- 0 wwm =P-M > C-)-4 -0

(.jo Z-4 u I. - WW2:wwI-C~)- > < Z>- . i++Z< U: < N Ui M 0- MM W -2 > W Y-: X3 4C 0 2 0 0.-1 xx.J 2::2 11 d: > 4 2: - 4 tt-

LLw04.1 0 w a- w mm.JI 0 X > 0m m0 zm 0 l~n M M <- - J 4 1 - > U cc "-

0 0 *~ In- WW1-W-.Z N >0 (Am N .~

0 I-~ 0. ~J..~4.II>. > "->. " *W~~~~~ ~~ 0j ..i. - > II--1-x 2 J 0 1

z 0 -xw1-2 > ..j W2: -4L)V 0L ... 0s 41) 0- I IZ<Nm > cc cr -U- CL V- - 0-0.0 > .4 0.0 0- -l

D 0 ~w Q 0. -Z - > - - W Z-4 11 11 11 11 11

S-0 0 2:- 0-uZ2 > W 2 W N w z 0 -

411 0 4 0 0- 40 -- 12 > > -~D 0)M 0. >->.-I: > 0 0

0 L) CL0-z-< > cc* Y0C 0> 0

UIUU

117

>.UlS

>-X N C"JM- 7- (n

MM*0.

>S

N0 MxZ 10%. . ...-N-0- N I >-- 0-Z0

00 Z-M >- 0 0N

0t - <<> 0' 4 0 0r\ -

N- -> 10-- 1 1 co -- 1 11 Clif- fill X: N 0x C.

0 * 0 > -X o *>Xy-o t-O0ZZ* 1 if- Zz-',I *CNC'J I- I-i )

oz 0- GMT n- till5- o"D0 0 11~~ It 11(~- 0 >.1 11 XXIL-- 111 -1. Jl

00-u Mc" L~j0-~n" 11.1-4N~ 0 0- N

*t 11 0-4 oxxx - Z 6x -- 0, sm === -44 4-- - ' 2

tili.-4@ T4- N2):Dwnoam.t<Z Wno000Z WU~~4L0000-4< Z-)<Z 0e

*-C.J 1-0 s- F-0 G- I,- - 1**ZtnLw ZLuj Z ZU'wU

0.:-4LL C.4)-L CCU- 0-4Z-4.LL

z zXX-COLL C3LL CLL.

00 00 0r I0 00 c

118

2::2>

-- ' 4- >. >---

+o>- -1 1 Mx -xIxxlxm

* =) X-.. *z> vlT, O-oxm )VN-0 N--uj NOM --x<C=)XN- 4

* -4A 0 0 02:>- 0 In 0>Nll C0 0>2-:I1 Cf~*-*- Nl =M2: m II I I M:> ~I I M=

-4 0 - 4. 02 '-4 + +2:2+:X: L+)-I I ..-- 1--I It M-= - --

2:2:2: 0 N-0 0N No=) 0 NO-

0-4N04 0404 0 -4 0 -4 0

II--O otlxlxxl~x-- 2 :

=X-4-4=*4--= * MMX-

04Znooom0044Z W4~-iW-4Nm-~UnOe- WU-NM"-i 0

z zunw 2:2:2 ttw xxx2:22:2 UlC uj X:: J -1

ci.-. M ~ M0 9 M0MXM-4 M I-D

z z z zz z-"COLA- c0u. 00ul 0~w-

Ou- ou" ou" 1- =) 11 11-za

zcc

00

V I" 5--

N N c -Xm a-Z~

-- r4 N ->-=Zr * * % . 44cxx - C

>-* Z x Nr C

0% 0- 00Zm

Q-41 4 1 .4.

0l I I4IZ NrC0X x, >X N-4 ~ 0--=))= Ln >

I 0 OZZ- - --- ' -1 1>ZZ X=:

co O N ZZZx N moo

(D, cc- 0 000 0 0--O >.,<O-- - >-O-- i-mm I-m

00 .eO-4N1 CQc<0-4N 0 0onc-4~i n ct n !--I-- if If

N 00 0. 111111 ItIt11 -* * NN S NN >)~a -. ~.

C.. it it -4 aZ Z- X:2:X z 4:2x-- n) nI +Z ZZZ 27 XZZ wIJ iizx iiJ 11 - - 111111 -

1-4ZZ M~ Z M *:7- N N N N(vm r -4 Wln000.4)< z Wjn~000n-cc WLJ-NM-i,- W.-dNm'~-"

I-*0 6- ox0 *ZZ--0) 027Z----i ZMILmw zmw zxm rw LU M wX :LL

'4NN.-U. ON=-4LL p+ +---- Q- z'-'e- U X,4crj<< Z- 00 <

-7 05" Os-sP"U

0-"Dz z z zzmNZZx:LL OLL OLL. COLL 0s-.w

z~z

120-

00 I

C0 0 C

C)N 0 - 0coo0 10e 000)

Q4 CD 109

) D 0 C

-- 11 L) (A 0 DV)( A A oz = 0D N N

(A P-0r 0 OV I ..?L '

I . (A* 0 -'

o ... O* CD0< t-* z 0 Lrn

<CO V* 'r Nc<I -U i-. WV wA CD c

(AWj 0* Uj< wx CL Q. V V 0'C 0 0 0D 0

WV < LL C) C 000a(A(A" Z* Zo X N N r Ln M~ -.

u CCZ3 0* ,.--- c N 00 * ) 0 .'fl) wjo OW4 C) 0 4 V )( 0, 't j ~0

x>"ul( I-* L 1~ 0 ID V* (AS 0

" X <Z 4* 0 -4 -0 < Wc F-* 0 4

*Z m V-4 A* 00 '0 r C.)WL 0 C71- * aZ 0 a' * 00 00- 0 OWI< -. i* 0k- " ~ Ir 0 0) 0 0

0-c. u * -"= V) -4 WJ 0 0 0 0o C.41~ ~ ~ 0-cz: - o- x 0 >* 0 0 0 0 0)

00wlZ* o0 wl I w o* Wi N '0 00C.. J-(A 0 * 0 V n co Wu >LJU 0 0 1S0Va I- o PJ* XIz Lu LM U', (* ce _j L M 0 N I-

94 4 I ( N M1* ui QlU..0 W* 0 N 0% 0D* UlZflZO 0* -1-* ( .- 4 it' it

CW 1 cg: 00 0 X: LC)-

0 < Z* 1 0 NO C)r4>...j 3: -T N PI-

j-clUJ 0* N N -~N

M0

40 0 0

0.WLL 0 4= LL V

0 0.

c:0 0 Q wl CC N w N <VI-

=- W n x < w w x <CL 0 -j (A V) -j A (A w

Z 0 00 Z 00 0 00 0.L x 1011

00

z

121

0o0000 o o00 c

z V, Q 10 Ln LA m m4 '

0 0 . .

P-4 - 4 e

0LL

IdZ*

=l - 00 ti M~N tn u0*

0* 0 M- N 4 N0 r4) V) V)0* -4 cuw .

St 0j LA .0* m -4 00 -r -

-u* - 2: N -4

L* w W 0 10 z 0 0 4'- L I

I'L fl- m -4 a'0 "4 LU- t UN co N

P" = iZN It -t N co0-j Ix I--- NC co N O ]

0:) C) .0 Z

.4* Le a '

z 0: r- en -00 .* 0 .N ..L N S

0U* 0L I.- <A

0 L)ULA e LA LA0

LL*LJ

0* 0 0 0 0 CI i i i

* c.DSt St -t 40* LI,

122

. . . . . .. . . . . . . .

V) ~ ~ .4. 10 -

>D Lfl N '0 C

o -4 '0

4j* r- QL '0n

'o N

40 0

* Ll L LJ cc*

w*V wc. x4 t

N ) N -

z/

12

I.* =-4- - . - 0

Z* i- 0 0'. LA UA 4. .4%rZLIX: ) cc W% U'l a' a, a% o'. M

(7 ~ % C% '41 '.t m m '.0

c 0 0 NN 9" -j cc 2: N N -. NN M

* '0 a.0% % 0'. 0 '0-r) 0 4'0 NO a -Ct') N N w

'4* =C 0 N - 9)N 4. r9LMU

CY* A A A A A At'A

V1*1-* Nie 0 N N m '' .. '4

'4* 0'.UiJ*-.J* 0 4 0 '0-

C,0 z o 0% r"- Ln -4=4 0% f- N 0

CO I- I- L) '4. Ln 0 W)

*r WLIW Uj 0 '.?

Z* -UjI I.- C% (9) N 0o0* Z' < WF'r- It4 N 0 '4

C-'* Zo 3:N 0% -4 N~ 9 Wco -5- N 0 w

MW*~-0i 0 0 0 -4 4LI)* <4 W- LD0 a. '.0 '.00* =)0 LI -

M* O 0 WU <* WL QOt 10 0'a. I ..n It £L.1LI

Z* z 0 0% - L ,- ti CAI)~l w/ cr.W.C-0* Z 0 CV 0 0 P-0000O U-LJWWU

4*C c 4/)L% -t4 LA < I-z m4Z~ II-

w4 LL- 0 0 1.)UJL(. 0 XX7c) w- LA "" 0L W WWUIWJ W

LI0 mm ul LA% (n LA LA 0 WU vmtntmLI 1z ZU-ZL 0 N N1 0 3L1 0 ) a0(% Cy0'

WL* C0 :0 N ('' It. a% 0* 0 )ccrLI* P-4 f% r'.- ?I4/ O ) I-- '* .-. m'.OLA n ,

ce c 0 0 0m 0 4O W " 0 Mf'ON(N 0 .-4--4-4Wj* >- 0- -4 t '4r C)4 '4. OW < '4 %Lc L Q. 4 000

>I.'- =) 0tf'-'.4. N'N N<4 WU LL -~44.e' ur 000f o

W. ex:Z U- 0 CONNa' 0 00-.1: 0 -4'.ON'. 0 0 0.

a 0 (Ai 0% N) n ) 000

4/* ) 0 0 0 0 -a''- 0 000V) z c 0 " . 0 0 0 -

0* 0 CC .00I ONNO I-

LJ* I- " P* 4U-0 > >>

* ~0.-N'Z*U- e X 01111 0 0 11 11 1111 0

0* 0 Q) Wj Z 0

wL Z 0 wOC 0'4 L) V/) WI dc '4mu z ZUALLu.

'4 V) 4/) -j ..J I-Z '4 u'4 1 4 LQ..

2 0 a 0 0 d'4 -- 1I- -Z=Z7-* 0 X: uxQZI- LI) 4/') ULWWLIV) 4'4

0) - N m .4. LA Q<40 m ZZZZ I<-<-<<4'' I- 000

124

T L) X.

~ 3 ZLI) ~ '00 0

0 9 0000

LA L z 0 0A 0 o

LI) -4. 0 0 0 f D ( u4 10o 0004L zfn'

I- - A * 2 Z0 r

1-4) W ) -A0 c -- * uo ~0..D 0. 4 LL J 0 6

z j .4z*maW04C * z (NN.nm -

0Z 0* Zo 0 m-40

I--- z a)l

LI 0J* Wl 41 w *IU 0* LMW P4 0000

0wz Z*0w LJ *4 uw 000 0LI)L)I- 2 * 0 a; uNN > .u

P14 I* r.Z '0 U 0 LA(* w j ) n co N -4"-in 04* 0 cc* -4 -

LZ4 I-* 0 40-0 mA Q: 0 0 ~ 0*%

o w- .- *0 -c'jZ * 0 0 0 0P">.4 4* - I U 4 111 0 01LI)2> 0- -4 N-Z>

00 * *L J'

001 0000L)

C I--*

0 00 u N 4

LJO U)) LI) u

2125

co G o co c o c

_j W 7: N- N- -4 r- N- N- (f-

000 N 0 Nm

*- C C ' ' 0' 0Z*xa0 -4 mO Nm .r L

A A A A N

Zn* F-4 m- C s L0* I- - Z

Z-* LD 0o 0 L

0* 4 m~ Z4 1 ) )

N -4 c4*V 0fU 0 0 4 0' 0 0 k

w- < 4 U; 0 Nt * '.U)* L-W I- ' ON rq co ' 2:

* < LW r- -r N co NWj* 20 : N 0'% -4 N . 0 wV)* 0- o r- N m N O 0 w .W* 0 ac 0 a 0) -4 0' % -'

>* 0x (D 10 00 2: C0- L0*Z 2: 10

CC* u cD a -r Cz 102 0 PI- m - 0 0 CO

C 0'.N Ln co N -0* 4U Ln -t t4 N CON

0U* cc ccL 0o 0l O

t..)* C- UM co*' N* z Nm Cl ( ) LM 0

LL*

0U* 0 I II I I I

m:zj0.

4A l

CL* 0 0 w

V) V) z

U))

12G00

uQ t=

us 'r CO40 4N 1 r'

-*0Z ~ 0

cc -4 Lm0

4U* L 0 \J Ln -0

0j* LU% * -4 O

0 u LU(A9

:r V4 V) LA 2LW* w) LA) -

0 0.O n -0* N QCL

127 N

zS

2*J Lof w' a' a

in* co co It -t 4

c0 C:" 0j Ix . '. o

0j* f. : n N -4 N N -4

CO 04 N N

0* ~ A A A A A A A

?j* CC 0 -~N N mOC - ~4* '0

a' 0

in -4 CN uI- LI 4 U.) 0 Ul c

*Wi V) ) cc 0 co 0-(fl*2 LU < LU a 9 1 0 U!Z* I-- CO . (% f N c;'C

~"*0 ZO0 M:N a 4 CN .Luco.- fl- co N N )i

CL* 0C 0 0 1-4 4wLf*4 %. 0 10 10 '0

0:*~ 0 I20.* 0? CU 4

*u L 0 %0 a' a' -1 . n .. nv)Z* 0 0 N -0 c/c w =-Q

0*= 0 N 00 0 p* ona 0 "0 !UWW 5a' 00 (n 0000 WWW~u

*1-- 0ccD uj aU 0 0 UUL~u 0 X::C I- ul% a0o LU WJIWUJ LU

f*0 7-, 2 L m CO Ln 0 il i. IV ,(/)a' L N N) 0) O34/

LU*O m 0 N (n) '-t 0 :D: M-,

w0 0 0 0 " 0 PgLncn 0 Xir-m 5

U*)>- ow 't <W2 -4=OO < 4>* cc I- = -ONa'%0 C -

A4* Wi U.. U-4w LL-Lx* ox Li. 0 Qa'oN U- 0 NNr'-

X1 0 rcC'LACO 000O*0 4/) OON- L4n 000

a* woo 7 z o'lU)'0 Z 000.-.in* 0 0 0 0 'roQUN 0 0002) z 0 ". " a0

0* 0 ~ 0-I -O4NNO I--

* 4 LLOr 41

LL* I-L LUJ LUJ w 11 11 11

U- LL: 01111 0 0 Iil~0* 0 0 LUJ Z Ix 0

LUJ ZO O 0V*2 L) L) LU < M: oz z Z LLL: U

V L) V) Z ..J ,1-= -C 4 %f~tkf 4 L0z 0 0 : 0 0 4- - zzz

0*2: X: 0n Wx 2:1- LI) 4) WUJW V)44

4* I-E LU J 00Co~u u VI(A/)LI0*0 4 N (n 't A00 ZZZZ

Z 1 I- 444 F- C"

128

>> > >>>>>> >> >>

U L.) 0.U U 0.

U U C(I XU U CL . u w 9-

U U 0. (A c P4U U CL CL - iid7.V

w U Z 0- wI- 3 0 "n-ZVIo ) U CL >~ uU U " 0 .44 Z 2 ~ -

jU U. 1-- 0. cif Ix V) 4 -r LU.U U < CL i.-ULL Lu XNC"9- uU U I-- CL l'- _j LL( U))-U U V) 0- cz co * WU ~CcV, cU LU 0. W.-" < _j -J CO-V' LL -U OW 111 . U) Z Q) Cu . Lm LU UU) c- w~~ F- Z62 COz-U U w a. .. JC <V1 *:) ' 0 4 . LLUJQZJ 0 z I-U UU w . U >ZO)) w -U 4 I-t--'-. <U U > C. Lui C = Z.- . '-W C I,- * D--

3U U .4 0. _.j >" )-- NJ 0-i. Wu U)U) O.C4I- c. U)U U a C. "- X1- . -<4 OL > "cc 7- X *-- CgU U 06 LL X. P"#--.- & Z =W0U)-C ILJOti' a

U Q CL Z <U.v4 u J W- U IA <IX U,UU IL. 0. w4< mcfV)ZI,- Z *U O W u u I .- LI 0-

U 0i C. 0. 9- O.OcC)aw 310Zc uLIJjufL1'vU- 0U U *0. 0.4 Lu M"'- 0. 01UJ4o w Qmma <wi c-U U 0 C. 0 =Z i.-u. 2>- :ZZ -- LIW W._j C,

U U) 20 CL U. 9-3Z4UOW dWMU' 0)-< >W (.u L,U *U C= C. > C~xl-O: W4J< < 1- 1u4 >C.ZZ IX

j. U " 1- 0. in 0 1IZCVflW9-- u.L)I.9 WU.U)~ C.<C"<~ wuU L-U )L C. Z 0 e2 > Cc UO.I-CU c U dx C. 0<0.U) Ncz<it Oz It ZCC'C i-CC-J ILL.U U _j C. U) '-.9-4--W 3CM c. - L U.4 m)~u. WC4- _.jU Oc U. =Z C. Z L-0:IC- u. LL 01-0 cu_. W.i-U -. U 00 C. n <awt-=Z *r wu\5 * (IcA-- oujwc.0 OZ-U 2 U .. J"'C m n- " ._j -O) I~.- T 0C.'-.C.ou))o uulII-n<

-4 U < U <F- C. I- MCLLI -U- CO) =0z 0 ZWC0)NNPZ(DZ.~ U U L) C.) (L " Uwi . X0 LL U. U Zu17,-Ca) U)<.".-IZU2LI'ctU

U U* U = C3. Z -. it- 1-4 OCww ~UU0U(lI.> U mZ U c (Or C. " Z-JX(.D C WJI LLJW .LWW.U Q-I--)LD-W-

U =)ON U OW: CL .U. UW4CL)7D44- =r)CZU)ZCrX - -CC~Un-Z: Uf)L. x u <_4 U U. C. UI ZOO-.ZXZC i,-ZW 'u-c -- 040411 11I- U U U z C. C ceac.-. -="<4- > 0twU)U.NNZW m< LU U Z - U MO C (LO--W~W4~( ....i(JU)ZEA

3< U 4'- C. Lu U.U.C..4C) =,Z =WN<F-W cc<<.-4<NU XU 4 U .i - C.m. W249-Cj-)' X_-"-9--N N

Z C U <-4 U 0"'- C. M ZZI-=ZWM "Z W.' W It nmCC4<0 Z u U) U cc C. < 0C c -IUI-- 11C-1,-- LWU)Nr(-4i--,_LF_ LIU U >- U C.2 C. ""M -.- 00 Lu'-4"N mmaI <4

S (.0 > U *..J U 0.0 C. W. 11-O 11CUI-4 C~I-9W .I 11w LLJz 4 x U I_ m U U C. < Ln.">CC.uO<I-L,-.z muf IZ-mxEx

w. 4 U U U < . OCU.M-l3U'. 11IZI4f II-II- ) 0 U 20 : Nf CJ-)m f -C --. tN P1.1 N

U U4 C. 0 -'' - UN N~ mm u Lu_jU cc u U U) C. .t-- r- -* j fni OM

U Cli- U U)Z C. .--. MJu Z.~ -- CCi-

U ~ ~ ~ _ xwa4z U=0 r.0C 4-01U~I I0OIN

0 U U U) C. CU CZW)I-OC LU04 UO9-QU~uMOw wuIx U U CC.

m U U C.CU U- C.

129

>>> > >>>>>QL Ut.) S

Vnb- > O.-Oz '0 .o m ezWiz > '-44 -'-- - 4

I.-W > W I/I4- sVMM -N-W~ z 0cmVS.4m > Ccv0I 4-4 ftm. -Moo- 0 x

uA U!Z1- > LU .4-m 0wm L-) 1-= P_4 > urcm-o00 U-4f-O V)

O= 1 0 > .-. 4 -ZL)200 WLLJX u- W

qi) L 0 00 !,N NMO-0.tfl-a "-Z *4- 04/) I-- 2 0< > 1%10,0M ft -'t- o.4 " CL 0

x .4 U > .4 .(n--'0 -N- . 1 0

*; - = OW > -S40-m-.0 0.N<Z u40x 1 -CNbJ.c > V)- 0j ft -, NeU -,C

0 0 c~r > -44--I~ 0 -') -0 Z - 7 OM~ > _ .. a--

< 4 LU a > <cM~o<0 --ON- lLU .zxv) > W_1.iWi-- LI-.Nw W < a~4 I > wz1)0. -_j -LO I-Z~cn <4

O I- Mt. - > -=Z -- Lu-c 0.4WL mU. =LU 0 -4 4/) > 0*.-tcO. I.- 0_

z " w<LU > N -r- ,O- WNXX U_.4 _ ccftuI > Mrxoc0 -r .1-4.4 cx- 0 0. I*-..j > '('z JN-%0 ~--44.4*n- U > -)" rLycn4 . Cj:-.4 <LL 1/)000- LLZu..U- > N-Oo. 1.1 WjWuj .. j

ZIJ4 Z 0000 > .4 -4-WZ-CCO V)-I-Oj -4 > .. i-> -><O- 0-0-C4 $_ -..

M.L(. a 0C.-.0 > V) -''.n*-Q z .rJ0 > C)XU

'- 10--> 0 0.40I~w>-- 0-LU- la0 40c.44 > -. N - -O0L00m UWJ -: 1--I--

UWZWL Ul -i > - r~lliw .ac - -1-I: <Z 00<0C. o. mzm > . -4i-'-O-t <441-LU M"- 0zW z 4 Z JWT.-S > 4 IJLL'-J4Orf - I-z- i-oX-2.1 <X0< > .j44 - . =Mf00 0U=UJZU U1-Uu > U LL.-4 -C-)(I- 0 ..um 0.0 10

Z -I LUJ > LU u(N'.UNOOI L)_ -W -'2zwp £c"Cc WMW > 0 -N.N -rtIcco . 'i I.- Lu01000 0 00 > .. 4(n"- I-c' & ""/) Y0:tL.. LL 4uLLLUU..LL. > Lu >. - PJ-LftnQ) N ZZ 10

- w > ..J Z:_444A . ftI---4,< nLU U U(JWWWU > co X FU~_ ' z4XC(n LUI I. xzwz0zzz4zz > < nww".-ZNN'0 tnx a II0

'-W0-I---- > '- .04mr ')-- 2 ZN <I-l- *4lI-> ce 00 - m u -U41 1- 0 W-) 0

cWOZ0n000 > > 0-.404amxr I--tN< x z 00 I-wc o cca > "NN""M-'rJW4. O. c 0- a- 0 D

> - 041J- --- u 00~ 0. LW_._/).I -'1 I--N . NL NO%

II II II II IIII > Z-0~ o - V).4m 140 0 O1> UJOLDV UIO .,O NA M 1 0 .

>-. -0 %..~ 77M 1> WZN"-WcO0-4 W-4-l-0 ' 0. Z .

w V) AC >.U.J~~~ _j>O-o w 0_ W. s IVI 4) x 2 UCY > CID.2T, Ca04c:) W124 0.0. 4d 40 0,x 0<4>-V)> =-XL)O-1 I-UI-033 I- -0 0

0 0 w - X" ~> CN~-.C-3 J., ZwLJuc. LU .4 <0 -IU U u fuU > OM'0<0''-'4'0 0.4

UUQQUUQUUUUUU UQ uuuuuu uu QWUL

130

U3

4

LU

LLI z

P-4-

LL

4 u Z

UJI-

V)) Lcoc

4LiizI-I- oc 10

LUC 0'-.

4 44 - 0

1- 11 0 fi

w 40

0=00 No m- aii LiA I.- Cn (3 -

) - -4(N -r 0r -- r V)o

-. 1 -4 oft~? L/. . 0 .0 . .0iI.- P4 44- 4 ~ 4'.

- - a - - a a - - - - 0: -=U= a1 - a- 0 O( I

0 -0 l'I- LOZ o-JZI- LUWUILUWLwwwUlUW LULULUWL = I -

Z------- 0 ,-F-- I-- 0 C0 - -0.- F-.. .- . .-~- .I~gI- . . <Q- P4". < < F- (A Z 0 Z

SLU W. C c ac ce 0 LUI U U LULL. COLL cCL 333XX33333 w c 333Cg3 --X 0m-c t4J-)

131

- -

1-4

M-44

-4 LU 0c x

-M4

-4 -4Z- n . -4

07 = - j 0 0

-4 n-41 -n 4 1-n- - r- - - .L l -4 F 4 -4 0

C% 0

0 -t 0

U NL LU L

0-4W .40 0 2

CC - 0u cu>0.L) 0Z 40- 0> c- OL -r- I *3. Q"- r oU'I

-~ -~ -I> 0 C~-. - -CI- 0 I- 00 0 0 r.J4 I 0 0 00 1-

or-. r-ooo 000 0 ~ o~u132 0o-o~o o~ r

-41

-4- -ox

l- -4-

(A I Z -4 on r

a N'i fi I 11 l- L

r- P - C.. A-4 zz

-4 -4 -4 zr x X

IOLV V)MMO U-za~a "c* 0-..4 0 0 =-- o0 I

- -0 0 - (1 ' o 4 - 1 11

> )-- -4 -4P--I

Z- cc 0OM 111ZF1- 40 OJ))-4-0 m0i-~ a1 .. c D On

-4/11L c~- "7oz 0 .- 4 U

- Lu oi j1 00 E-o<

r-cr Q - Z.

CIO C)4 a 0 0-~'p to) Co~ .) ~ -.- a ~0 0 0 0

-I-0 ~ ~ QQQIL) II0 Q . 4 4 tI -

Lu u JQ) -N u LA~~ 1-J0 4.) -133'A

-44 0-x 0A

uI IZm

0 0 nx - -0 -L

0 ; -4 -40 11 " -4 11 A 04- -- --

C. 4u 0 '4-4 -0.-4 . 0-. t-- 0- Z-1--U'O -4 - - -- F -)z0 0 0

56 4"1 L-' I 00+U~ 00 et- I1 0 Iq CY. OU 0oI-. Z 1 Z X = -=00 01 0.0 00Z Z11- Z 0.--4-4 -

Q -4L 9 1.- P- 0-' - 0-L) -' - I- 0

I- -1W -4 - -4- -4t ---4 Z0 0 0

Z- *- z~ F- F- La- 0 .CY0F .. (.uj OWO cc 00 -0- 0- z~~ u-- CL WW. .C

cc Ii'-4 u 3( Z'"- uu U- -- u.. *- -4 CL 333 -9:3::c

ooo 0 -Z-40' C a - C . -I- OLJZ~.. L~0~WcZW..-Z0L~Z.0~W Z

I- -4*- ~ 1L~~1-a~V-- 4-3c~ 1134~nw

0 Z- I- IZ- I I- 0 z t--Mks-

4 IA -

I- - (d*

oz z N

-4 C-

-) zn - -

-4 _4" N4 z 1

C) -L) -0 -44 - -0U O) OLCIW -44 0

0-. -A~z 4 Y- N 0

-11 - 4 14z V

I-wu - - - - .-4'--4 V) 0% 7: x u4 r L

0ZJ Z4 II Z <. .'

I- o ZL - -4 ( - II u I

-'~ - 0- 7: z izfl -cc 0 0 <Z Z (A

WON --z I- O '4 W -S. ~~~~-- (A4 ' - ~ L

o.i z-- "o - 0z a a o - - -- L1l-- N 1 4 -t znL

-0 (0-W - -. Z 4-4 1 --. U-

oj -N 0~ J 0- L-04CJ4 - : (A Z0 auZ--0 00 0 0C -4 0 . 0 I- loo o~c aW LC

0- ~ 0< aC(A_4rf- tn(A 0 -0 * N -r -M C C- 45 " (A .- 4 0 - - 00 +AL <- 4UN ---

0. .000 -- 0 FLU 0.0 OZOO I0 -- jIW- Z,,00,,00 Z.- WV) '1Ul4 z

-0 -I4 0 -- - - -- -4 0- - IWM F-COLL 4N OW . L) -4:OZ N -4cz o L-4 z W- <

o ~ ~ .W . 00 00 0 .IZ0 -- - z * 00 O" 0 (Z 0. i'0-W1I-- '0L00 MW'NW4LtWZ@ N -1 '0.0 N czr a -- 0j 0..

o0 *.- W I-<_.U 00.444-- <4 N + 4 WN 44 0

- ~ ------- (JI' 0 t-. WOU-I--- *

'0S W '00''00.'00 0 ~ - WIW -I .Z' 135-

vI

z0

0.

V) XI-4 '-4

00

00 0 -x UNO Cox wo -4x

z 00- oxx 0X- >=='io4 -- F4)= '- mo o

'C ~D'O 00 X0 -~02:

(D 4- :D I- -- :0(LUz m0 U)II U-0 1-- r.-4-4.-

o3 - .-. Le 4 U co2: 'C- - 01111 11 110<4- 00Z- N

0 W--- ~ I 0 - 1 t 111I 1- > . 11111 0. 0 -ZU tn Z -: .. 2-4--I-I 04 ujjl

o0 oN X -2= 0=2 -- L)4> LL -M: 0-2: 0- 04 .W0*002:0 ~'OC

z CO f-.J= W - - .XI 11 11 904c - - -- "011 ~ 0'F4"-'< u1 II i I X- >- ac i 4Iiia 0-

0 -400 X- OLL M I) U0.'- 9x UW

-N -4 4iIl-4J 0 II>--- --- 40 Z) -i=CJ W43OZ

Z: --ULL.I 2: 0l. 4N '- L QLM I ..- 4 MWH~- Z4.J4 .JJ::z~4410Z00-

U 'O"ZOOOU. 0 b4U.0 .

_Jiw z<).-.'- 00 A

A

NN N

136

o04-

NV --

- -<

N -c W U 7

P- Ui-

Il N4 !I,= In" 4.

a- U- 44/) lionN U) -4cr 1 P1~4

- eu -4< Ln

r n- L) 0 l V) -- -.-. - S. - P4 11

z ' 4 rc !e o -4

- LL 0%z< I- u 'r

In U NoAL) L'f" Z0 - )-4. -n T- Q -4 0 'L-

0!2L--.t l MCC 0 P4 0 -4 W fr 1-1 1. LA 4 -Z u <~ =3

0 ~- io U lu I--Cci w cOw u2Ce. z.o( XAI' - zoo 0 MY

- .0 -ld C-- < -t = 0 o LLZ.4-4 L *- 1- 0 z~l 0-(') a) 1-

U C0- LnP-4 W Uz - ..- -oar-"- C4< 01 -LA 0 CE: < -L~7 .

- e Z--40~ -u in . -t. 101 C x- CIj. ..-ILJ -cm - - - LA- Cn 4 -tIP -4 LL.

.4 tieU0 0~ I-I- I.-.4.

1-c - u Z-4Ln C) :3 0 + oN000 (A- .-4uW - 0 - Co0n 0 I-<4 .- 0(00r-Z 0 Z16-- C'C -D r-L) Nrn (%Jf iN~f' N 9 *.-n--eW U 0 -" 0l -I--<-.N.-J..

-4-4-4 - - - -C N Oc g- = -P" -40 U.z.44rju- ft L -4fLLI.--41Z a - "- -JuX/-4P ~ . .. Cr " ..

4,,0 00 00000.- -4 - 0 @' OWC .Own .4.44 -a'O. .m r-a Min.4'A0--4 'o - I.-LUI--- 0 01 - 0 -J.JU. +40~4-" 11

--- N -4N 0CON +~ I- ZWj .- ~WJ WU-WZ CYIfi-4-4JD CL -. i-- -44 ~4II -0.1. OD WO Z UM WU <<.Z-4QII 11

UIUJWLo op ---- uj ow - -8 ' LI93 Z 9 0 o4/ (j) U.s4NI---1 0,0 00-0,,0 - Ili -4 W -' - 1--Li 4 - 11I11.J0l-.4W.4~

4 LU LL 1I 11 1---h Ig-W tiiI-j Zz Z(ACLL wWVc=-lQ.C)

3X3CO Z Z N'4.NLLU CU-. OZC3ZP-JZo<"4L~)1--3

ow=WWWWOwn3- )- L)' O4-

0 0 00 00D 0 0r- No Nn -404 (n Ir

137

00

-~-0

00c~.j (.4.4

2: 10 2:2 0 0= 1128 a00- 1Qij rJ-

x: - 00+ WWCC 00 to0--4~~-4~ cU.1 ci. 000 O.-() -4 0 a.-

'.400~~~411 00 x'4... *o Z wZ*-- 0 .'. z.x----.- 0Z 0w1 0jU O-. LO ~ 0T

=am mo 00CA -- 0+ L) 4u4- M-4-4 .V WM*OO"j-.-- ZO ZCLJ)""- 0 .. *

-400 02 : 0O N NNN- qL 0- 0--z *-*--,-,-, -1,x- 0-- I.-E JL-aCaI-~ . OLI.. 0000 0 0z -'-.-70 I->20 -z. - I- "'OO'07~ Oi 0 Z C- :D0

0oc x- v 00 (0u - $O -4g...4 Z c.-

U. ow =fl43 330 JO JZ.t02: -02(fOO-1 .w 1--- OL 0 0 = 1Ma -jNN.W 1- 0.11-10Ofl-Z C(D... J?%JItIrJ...JPJe%.J NJ4NM U.. c-Z Z O Z Z W Z - - x x - -:D X X X D -J0

" "CC0 aIM 13 c Z Z 11COCO O~ u -0 0

L) w <-Z 3 30uQ ~ utc L

-J~~~~~' f-4 r- 0'JN - N MI LWcq q -q -4: q - CL " M U .

cl:-

138

be z

Zn Nn UN- ft 14 .

- 4 6 - 4

0 0 4 0

(Amm + Y. zeY eIm ,

=)C4 - 4 ; ~ 4n)) . .

At --~4- -C )>

1.. -u -- I- .- wFJ UT x 4 -M -d M

44 I- <Z< II II01 p.-4 -z l'-4

l'oC o 0 a -4- ** - -

Li0--c P-4 W CC0

0 -t f i =d -- -- . - = Nbm -- -LLU-

00 <- o0N - N -40 - 10

11 --- 04 +4- :" F

0- >4 I-- Z4

ZZ4-oo I- --- - -01)- 0

0+11ZOIO - 0 "-" Z 000 )*(a

0l-~ CC)-. 0 wwwwwww4.~-ac o .c4-'0 .-m. I

Li-.-~~Z 11 -~ If ~ 0w 4) 1

0. .1 >j~ O'''O-U V. .. '.z O .- -... J0I(AU.-4(..) W ce tW W

OZ4ZZOI(A (AC,0 *'4~ d ,0 cc0.~L44'"4 -4- WWWWZN~'W ~ .- N0eC0O

0 2 ~Z l~~- .s- . L- eO A- ~-0 0 0 C~e~~ee~ee-e0 ~e~eZZ 4 -- (C,0-

Ce~~ 000 00-11NLInir I

0Z3ql)A03

1-139

... ......- - - - -

- 0 )( Z * *

1- LL " -C

IX) I I- I I x

-10 C a - I < *

&n '** 1.- 0 C*'> *

mo CL a U - - w t- -..

no * - a x -- * >V) 0 a<(D 0 ON *L co *t *

- -- , * -.". I ~ I U)* .* I 5-x:4 -* a a a aI I -'d *0 *

V*0 a N Z~ X -4 I-0 0* -. )( ItA, * a U * L.

-* -u - 0 -u 0. 1. .Or -* *V O-IL d) *X

-4a +f a- U.1 ** *L0 I- IX 0x c

-X0 >-~ 1 4 N a OC ) LL U-) * I

Mar 0 O.*ILL w* 1,.-, * *-LIo MF -9 "l I- o -cc II *n *4 7-

00 "*0- U- at.- -t * *Z X O

a.C)"d 0* 4th L . n * P 0 *c I1* z 0"a CVu 0I I .LJ -4.. 1 W e *uX

0. 0 ux X XL X ~ ** a< X -/ *0 *.t.- Q * ).- wt ao m 13 * I*N :.

CQ~ M-* au4- 2d ~ x 4 w ...% a*W I LL * .IC O *.WC 0 NIL -4 0 M LJI Iu :w Ln I. * *

X0 W - V) .2"t 1 - a AL -ta a I Iu. *<oi - m 4*UI0 1- 11-4 XXD -< C- * *X

,4 L-.0 10 Q- N*0 I L *Z ( a- 0q * LL<-4e-e ~ 1--a a 1*~ 0 1 )0 0' N *i..

a -Z. -4 - 04c 0*0 NU. 0*0 % ~-4L - *n t* a

390 zm =*0.z W aW-1 a L

1.4* I-.- I' 2*ICC- 4W(O)-*a0 - 9 -4U.. 4* *a

oE..) -4 04-'00000 ) U a0 a00 000000 * a

0.4 'C~-2co E) a £m an Of-- a00. a mttzlW .4.- 0%a* *-4

-F cII o 00000 0 a 0-4-4 N1-L *

'C i- ' Q 0 -N -. 2 N E~9~- -a4L140.

N . - F- - V Z

-4- l- V) 0 u. /z -~ * * -I.0 " 4n M ) =-u I- C 0

x 4 W 0 m Clf- WL 3 1 wt L-* I- >Ln .. 04 z4 < q< (- *- * 4Z 0 C - c C W~ c

NN 0 * -- C- -) - 40 CD VP- b-4 U. Ia. * IA "V z- . ~ w i - N CL

a 4- ** u-0. I- I -- e-o 1) 0 Z LCn CW * 0l Z*- * 004<(1) .. " 4 "-.C mXI1)0 l'-* - -J LL% -J 0. I- -

00 Wi * *. * 3 4) Z4 - W WL 0/ - FA --. 4 oo " 1-- W w~ Zl- "-,Z= = c 0/ L

-- ll( W I- * L F~ V* I-I Cn< MCCI.- F- M . LLX <W wi4)* - * 4 > 1.40 w 64 0N c

--- 4-O W 4. -O-0 o /,) 0 z%. * LL-L) * -* 4.V, w". CO)LL LL QL V) *

t; - W* * 4*- 0 a-M .0-00L

* I II 0 > * -Id) *CM a.W U- -.iCO1~ .'X = &Z .2 V) C wju-0Zv V,, LL W~ z ~-.

U.. * ) LLNw * NW * l -Xw 0 -- O-i >mm m >.X Z ~ P-41- * I,- . en0. ..1 i--'w C I"-I-l...'C 0 -- I ir C .40 u - W L>W211) In r:1

Wo .4 . * w- 7- * 7) - No0v) <-0~ 4 A V. ln11 -- W * 0 * 4Z-U- L.. LLZ4-*.L- M X C, C.

L4~4 .i * w. * o ~C. 0 0 1,-U t- L = w-0 i---40 *=0- * (.~-. ONa-.4Ncz Z Z Z -<4

W~f x -j* WL *n of--OZ Z -4 -0 0 00-COOC cc W~n Q.. - 0 * * c,:-. 0 )-CWM lm*w.-. z - .-

U 4.-l * U... *a CLVn4,< 0.00>--Ox- I-- I-.-- cw04Z LI 2 U.. U..rA.4 owl- - 0 CO <P- P- I- O

flO4-0*.O.L * 40. .44 -40 "-4inV)IOcf)O 04/)o' - I.~ * . *0-i -.1 w 34 0 0 ouaCon...Z

w VI)0CZ. *.0.- m M'2~~~l4)~I.0 >0WU ow'C X 0 P-co0I-** * -. 004. UJ ow <MfWI W >WUNM

-4 c - owC-d,-z**I * m 11 11 .J )-l-u.O 1--Z 2M-LFw . -- 4g.Q * 4/l. -4 4 z 2fq z7 x m MCn3L-IMM

N04 W 0 - <=**W * -4CL .)uj<aQj-WJ4/^ 0 0aa0vI *1/) ..- .

I-. "W > '4W)--4-* W *P".-4 1- W< "-Z Z 2zczmLA-.* .4 U in*V L* * I-CA -- 4 N4 WWI-0Wu 4 e eN XLM

I- - Q.Z<L)=**WF-Z * .- - l-VntZ VAl- IA WUnI-Ad4F- M 4<..J-* *Wu:) * ( .. 0* 1 1 i4WUcko4Xv) 4 i I<L/) N<

I U)0 X .Jl4:-Z4 * * X7-- * r-'CC-) 'C X w wWI- LL= - .- a-

-- 4 -4 00-4 ..* 4 * - .0 - -. ~W -..- uIN -X - 4--.- CW)*'C X- N -4* *-X 'C)< )< ft . -J .>P6.4N . - - .CJN* N -. -4 -- - X'O-tN'Co'C 'C 'C2'(xuiN

-q-'C '' 1-4 * -'C'- *- -%% 0- -- NO-4-4. -4-4N N N<NZNI,--.IXC *'' N 4 NNN..4 * ",NN O'4.) >('C' -X" '* -N4 -0* -- -, -4 4-4 -Z

*-X-. . * ., a% - -4rN q 0 000- 0*0- . - X 'C -% - -U.,-.

- - - -* - --C - -- -

ft1x<< * -cc< . -'C '.

444 ~ ~ Mwwww .4V*V)0www~c~ $Lt-w4 4<444444 w4 L4V4444444.44'.4

000m0w0000>0*0c00(.j0*00.-C.Z0.-C00c.C.)0-0 00%.0 .. 0LLLLL-LLLLU-LU..MU.* LU LU..LUU..* LLU.. -I ~-I LLL-U. - L UL.= -- u- L.. -LL. 'U-

000 0 0000 0 00000000 00 0 a00OOOQOOO 0 0 0 0 0NMt)'. U) or--#"M0NrU)'Ql,-M C0 .-4 N M-4 '.no?'.MC?' -4 N "f) '.r U)NNN N mNN mm mm m M- -r.4 '4 . .4'r'4...7 L A Ul% Ln ul

-4--44--44--4 0-4-4-4-444- -4-44-4-4- -44-1 -4 4 4 -4-44 -

141

V'*) 0.i Ou i 0/ C 4 zUJ) o%. 0. 0 V) -

LU - .0) C. i.. C-C. I- U-41 L/)

-J wu C'- V- Z C X . Z C ft Lu Z-2 I- - iJC.1 * or 0. 3 b-N =--I OZ" 1 Z

LA V/) 0 W- X 0 I.- - n LL-4 <a .. uZ4 -4.j -C LU I--r z .4 C)-

W 4 It c 41) LU V) UWO z V)" Z~- 4/It- W-.Z 1- )% V& LLIOZ < 04/))( - I. ix

w 0 x < w/ "% w-~ 4)L 3N0 I 0CN M Z 1/) LUC- 0 w1 tn ZI - Iz-Lt'" 4/) n..C0.ooC) I-

U_ Oc' -Ovl '-4 W~ Y_ - cc WI. - () wcv L.wU2 u.LP. - '> LLU. LU eJ U- WU" W 9< 0 ,.4/%.UOW- C-- x

-N ogx > 04/) ->1- 0')- I -. Z'-' *

N C 0-44/) w U4..- M.V) UMC6 % - -1-4)-40-"amI- - 1.- zw -4 .- ~'-0

-0 - so U . -4 M- <WV -4XI -Z< 4 0<a 4 -1-J-4 22 I-.z t4U-J ;-4* ";L- -4.D "- =l 4 4 03-4 WjvkWZ 61)-ul - r.4J'U-..

-Z >0 0 z L WO "Z> WLJ oZ(.! 4C41UCO .0C%- - LUW>- WJ WU < e 3C2:Rp CLL'4 ..J =iZ1- -0 -4 -4

O-0g- _.j _J X i-Cl--I-- .~ *CL)%. 1-~ 0 41)04/) U-#A) V) ZO 0. CD 0 W.*-.W4 0 .- - - wli-- 1-Iczzr-Z -c 4 OW-' z Z WcN "X~I .<_ ~ -4 1/). wCo-CZ wU a 0 < 4 >M) s- 4A ) 'x0U LL - V) Ltn C (I',-S.4L,0 cc.. cc W41)WL O3NO -% w ..a * ZJ 22-- - 4- 11u 0 0 4/7 0 0 Wo L.)OWU QX)W W 0 Xuw4- <W-". Z41) W LU 41)0 20.2) W*%W "Mi.-4~- U- '-00CO-O -**w.1 w <Wc > > M .4 <we =-x <*W -tu. - ,-.- . u

. L-1-Uj- c CCCC 1-21l--LU -- I- *. x )( occ~aw ULLw WL NZ 411-- W W 0 4)04/)> Z < * IA- -4 (.(.DO. * .0- 0 -

'-C0..- Wa-i 41V) 0 .. _ -. e4 *. 0 * Z 0 (OF0 OWM01 m 01--ar V1)L' I *s, OX N usZX LU (MONO-

Z0WO= 0-0 0 WV.) < I- WM= 0a *4- 54 --I-i-CO%-JOI--i. -it'- 01-0 ...JWI- W*XI--4 2)== CL .44 0-4

94 0.4. -4 - W CL "W" M-4A -- I-*0< >X C X(7'Co (n1-i)Z4flL- Zr a4 Z XLW41, U* 1- - -qf/41)4) <NZZ Z wj

-4 4.9-" Zcn)- I-X C) DD < <X LU*- V) X- 1-< -. > ct4C.. )-Q(4l 4 )(- 4r ) - cc* 0 V-~ eni W'i- IOdWW0I-- 11 MOMOW WN Q WW UNI-- CC* U- X.011-- 4)Wt1) 4

I-- I-L LU W UIJW Ln< 0* >0 %,.-Z <1 cc -j 1

"W0-42- <r- * 0S Lr-4UU3 C u-4=Z -X ULN- 1.-MoW ul U,. WW - U-C0- . 4/)x: 4 0 - -1---C

I-. 0 .4A).- -*1 - C% . XXD 9 ---------------

I- eXc.ON XW)< X<- XO -X X -)~ )N 0N04-- XtAU- NN' N XXXX~) X<44flN -4WN1lQ-N 0 .0.P. N>(N * N . 4. - ft -Itw - "-4.4-.4 -4-44-4 -4

- 0-4c _.4z124 -4. .44/)0.N-4- .- 4x a x Xxx) )~(..a4)*ftZ OJJ%%O. W 0 ft. *AWO _.4 '~ .C0.~%~. %%%

N- Z < LUw - 0-.4 % --~~~ -u -- -a -~ - ------------------ - -

a41) - WW CC oc~- ea: iX Ot 0

..I 0 0~ a 00 00 00040 OO00000000004 (aC000 0

Q0 ?I- m C% 0 (7. ~ 4.U 0- -N L)O-~ 04-N rnUn U) Ui Un 10 10 10 '0 '0 Q0 m0000PP~

-4-4 -4 4 -4 4 -4 -4 --- 1----------- 1-4 1-4-4-0-4 -4

142

U) L) M. >I~- Li Li C.>

Li a.>U L) (4C. ~) > a

Q Ll Ii >. MAML . .. > -<X~~~~ Li Li 0.(.- Li L C. 7 >

~ Li Li 0 .4 >~ i Li ) C >

X: L) L.) WL 0- 0 > ,-rco L) L) cc M. w. >

U U.. -a CL > > MCLCJL.) Ui M C. > Z=

cr L L Li U 06. ILL > Z-X- (L) Ln M. I/ > e-,

co Ui L I CL co >-X L1,- 0. C >

-4j- Ui L V) CL Wj > CC->Oc> Li Ui < 0. )'C x L(LL > W-.

,- Li) L. WL 0. -0 ZC) > V)roC Ui Li . CL cr. Xr-"W. > 1,<I-Z ULi 0. 1-- 16- 1- w.e. > 7->.

X: 4 L) U U. LL -We <<Qv.D)w > Y- *- -

91 - UA U 0 CL 1- 0 7Liz-m > -v-Wd L) Li - . z COi- "<Cz > -.

oC- L) L) Z CL :rut LLWA).d'... > > (0x: L) U Cc 0.. "W" Moo= >

1#'L) L) "-C 0. -Li >ceL.L"UlW > M: .7,UnC Li L -= CL. a- . g-->e.J > IdA MMN UQ.AL * L) -41-- C.. >(>txI-z< -J > Z .- d)- 0

4% O Li z Qi -Av L0 LiIL-Q--OXZ=W)I-. > 0 7-C - -0 - Ui I-- Qi 5x M ZWcxceW-." 071/AO > -- -X ml~I-= L1 we Li) Li a- M41--I-4 WI,- > X- -Z-0"i- Ui L -J7 CL tfl mU<<XQ7L V.#X<0 W > mmr00. Ui cr L) -40 0. -7 U, iXr IAJ-aW- W.LA > IX Z -.-

O1 LU I-- U~ U-~ a. 0 WZI- Ufcew.cu-u..r > <4 -M4 wZ - Li Z Li I m. '- L7A .. c->-0I > .. j .... >i u I.

<40 Li = LiCM C.M LC7cUV > W X1-7- -7 - Li )' Lit U L. CL z mucncw WWC).- > C Mm=-4

-4 _0QU zooL) WC.M'" owww C.~e e0 > -Coc-- z.4 =-I- Li wO 0i LW C.U.ocwZ.4C)00 > wl -- am

XZ Qi <-~ U ZZ C.m w 0~-..U..U.==00 > ..J n4-.-= 0> D" U Qi '-0 . 0 - 0" ZZ'.-l > W -1-Z I-'ZCC Ui Z a Ui 1-" CL <..Cifl--LAjUtI P-CL > x4 Z ~

LA. CL U < =t--.UJ -JV) W ZZZ-i...1.4> -i3fM=M

I- - a Li X.*. Li 0'- a. -i :)tZW)X P. . . 4x7IAr > c 7.-<4 3 Li .4 Ui Wo m. M i-4....----I-- > <4 AI- .2:C.

3c 0. Li Id) Li w7 C. <4 -jx~~==o > > 0 cn - P-O . 0V) . Li >- Ui =0 C. P- 4-'-I-IO-P > "W-ra. X 0Li) .17 Qi *.J Li I/u C. cr U<. <<4CeCW > V)-) C)VLi L> Qi t-m Ui M. CLWWW7AW > "4-z .

a LiJ- i - . > XX Z D=XLMLZ > WiM-- a-

Z-4 Li .... gLi V) C > tx-Xx -0U. Li Li 1i- C. 11 11 If g11 gog > CXCL.) 7-,

I- Liu tW Li C. > D -Z Otcf L 0- Qi /Ww C. LL U.. > UJZ - WL Z

ow 0. x .4 Li-7C AJ. > .. J-01,- 0co. CL U - Li l'- C. U..>... x > mx-E t .

3- Qi U4 =i 0. XxxxxxV)-X7.o= > C'moz <V)" UL) Li CL =wMO-.e>=->ZZZ > 0l-0- ~40

* i L) DCl. >U.1L Li 40.>

ULi Ci C.

1 43

* .* . .

>I

LLI

0S

00

0 ccOX-OpLL D* -=C V) :

W -I 00 00z-)xx) - 0 uj 0i

0j CI co c zcc- 0 C- - D-

141pX * -)Z .Z acom ii -4 if: 4- 0 -W[

oil "Q 0~ .CD -duP 0o I

0 ~ ~ ~ ~ ~ If -ON 11 1 -Z0 '

;.w 44 - cc cc

0 il -- l' .cc P U C ) Ulm -X:-~- .4a 4i z z UJI i- -. z I.- H0

4 )4(o c cO Z 0 > .. 0C. O J> >-.40-) "mZ rzooo UO c U20 z 0

C -40 0 0 0 00 0C).

144

4- z1uj

a:I CS uj L: U#A z I-

0. F- a-* - --

4/) 3 F- UJ WZZ Z F- Z M

4 0. 0a: -, ' :-LUI Z 0 42 - -

-- F: X z z I-W c>4 -0. (Of

- z I- . - 2~. I * ft -0 4.- - u. co- (1

z- Z - c 2- C m .* .

D fn (n a: w-4 z w -

Z Cl * z Y- z t-.* F- Lno P" . fn w F- "X W

a 0.z zzz 0.. >04' 1-.: " * ;

z co x z - 1- z - .

0 x z ca -z 14 4Zx LnI-0- I- X c Z CC

Ln WI M4 " . (n- fA LL: 7 O

w z z w/ m- x z x -4Z

w I Z -I- :3 ft -w ~ 0. Z z -

- > F! x =- -a a: .I -ZV -- 0.

CC C13 Z < -4 2: Z > mCt W. >- >I w- LL- .> 0. LL. - .

wl LL.~ U. co c~ 0. - - 01 -M) 0 m CI = > - Xn ux- x c

cz L c .3 cz a- 0ZI- C > Z z w 2-LU z co. LL. LL C= 0- c C 0

L-M0 0 - 0 t- - - - - -IzU -P- -to. I- PI-

OP-4W L- LL .- U..0U ZU- zU- <w- LLLI. 4LL. < LL 4ti-M 4 LL 4 LL N C LL 0 LL -.43 1.-. LL LL .4 U- .4 LI. -j

ZZ z Q - U4Z > _-.Jj M _j4=-0,-4u~~ 1-- -3 01.. - m I -- W 4.UI~ . 1 . I " 4 X 4 X J1 4I.

0- 0. > >.) V)1- > I- > ZL.)> >

2 z. 4 . > m~ j x 1 i .4 ) .4.j Wi . w .J WL

0~L 4-U w44 4 0444

UU.-UU UUjU UU UU J U QQQU U UUQ UQ

145

xS

LU a

Ln -

0 Ln --0~~t LA- '0Lo10 "Ao LA 0 :

-= 0 4ZL 0 Ln co-Z Z ala. ao

1- - 0 a z LI)x M z : -- 4 _a W -..M z z x.- W

z z 9( Z~ -nz Zn zI-~~~~ Z~I (~a-

Z x z x = . M Z I- '-

- - m - Zc) Z (In Z ftZm z zz Z~ 9-9rn

9- a4 LA cm co a. 0. co*cc ea- CL 0. cc a.e > (1 ' 3-

.4 z - - z z Z Z - z - -. 1 *Zl0. ~ ~ r ~ ~ (~ ..

Ze w. e a- W ax a aL a) aF-aa -L 4a- a- 00 0- 0* - 00 a a- cc 00 00 CC) CI

,-=00-a ~fn 't OLA 'o r- Oo~ a. 0 0-4 ON Omn rN\ L < DCI - 6O 000 0 00 0 0. 4 C 01--Z

0L WO' ZL-.~

0 w s-W3 3 333 33 3 a-3-l 5i

LA- w4 W ? w. W LUW LU L LU Lu WLl LUJW LUWLL Wul -J V) 1g-J IJF Z 3=)j-I 0 0

X 0 Wwo0 =) -1 11 -4> 0.L330m 0U U 3 J U 3 J3L3 Q 3 3z.3 < 0

.., a- 7W 0

Ix0 0 -CLA

146r

U') I-- I-. *

-,0 x c* (Da a P4 Il:

z - a.-s..*U

~~~~-~C >~> *-

xS' -XQ 41.. Z

*-~ 0 ( 0 -I-- -.- 4ZI-

0 Z X Z- LUJX-Z- Wc"<P-q-4 0 b- 0X~ O)<XI- -X-

0 0 W 4.-G*j~ii Q x Wj4Z* *Lw44I"WUC0

-, 00 - 1 *P- a...~ e 0

II - 00LXXX.XX - -~ --

-7 O*CW W..O.O10LL 0 .- )<((m.4-4NN-4 W1LnU't U' L

":"<=) -o /: 0 -N ............ f

I-- m

zZl.3Q = -- i---t

OLL 0:Lu 0000000000000000

C40tL 0000 00-C00 nI

147

*-- _ . _ _ - w . - , 4 - - - - . . - - - -- / -, . . . " - - " - , - . - - - -

LIST OF REFERENCES

1. Bomford Brigadier G., Geodesy, Second Edition, p. 1,Oxford 6niversity Press, T7TZ.

2. Palikaris, Athanasios E., Methods of HydroqrahicSurveying used by Differen -5tr s, !7S.-Tns, •

I--TPst gE dua e-H;E , I-M5HETE77-'cali fornia, p.139, 1963.

3. Davis, Raymond E., 7oote, Francis S., Anderson, JaMesN., and 'ikhai!, Edward M., Surveina :heor_ andPractice, Sixth Edition, 1cGraw--Ti , 779.-

4. Department of the Army Technical anual (TH1 5-237),Surveving Computer's Manual, 1964.

5. U.S. Department of Commerce, Federal Geodetic ControlCommittee, Classification, Standards of Accurac.Z, amdGeneral Spe5Y_ ica'3ff9 5 G-rU7offr51-7UVe ,s.

6. U.S. Department of Commerce, Environmental ScienceServices Administration, Coast and GeodeticSurvey Horizontal Control Data uad 361214, Stations1037, U5U-B70g1, -NEU-TU6 -70, 6 3.

7. Mikhail, Edward M., and Gracie, Gordon, Analysis andAdjustment of Survey Measurements, Van N3s--aF ---

8. Hardy, Rolland L., A Brief Outline and Demonstration -

of the Theorv and 2~a'P ie op-.eT~t-ures,

9. Hardy, Rolland I. Least Suares Adjustment ofTraverse, p. 4, 6npurSllhJ-

10. Pacific Marine Center, NOS, Horizontal Control Renortfor Moss Landing - aval PosEqiaie-SoI-E u_,

M 37---.:.-

=

148

. . .. . . |

BIBLIOGRAPHIY

rurgin Casper .4. and Sutcliffe, Walter D. Manual ofFirst-order Traverse, Coast a n 3eodet4c Survey1 Seciai

tT~U~ ~~377U.S. Department a! Commer :e, 1927.

Ewing, Clair F. and Mitchell, lichael 'i., introduction to3eodEsy, Zlsevier North Hoiland Publishi 75f~VV-179.

Graham and :lei;., introduction to Computer Science A1structure Ap nr -7I -P g3p7'r2

Hodgson, C.17., Manual of Second and Third Order:r ianguation -H.3'ra-verse- EHa~ e3er Survey

~ U.S. Department of Commerce,1 35.

14~9

INITIAL DISTRIBUTION LIST

No. Copies

1. Defense Technical Information Center 2 -

Cameron StationAlexandria, VA 2231'4

2. Lirr2

Naval Postgraduate SchoolMonterey, CA93943

3. Chairman, Department of Oceanography 1Code 68MrNaval Postgraduate SchoolMonterey, C A 93943

4. NOAA Liaison Officer 1Post Office Box 8688Monterey, CA 93943

5. Office of the Director 1Naval Oceanogra phy Division (OP-952)Department of tne ayWashington, D.C. 20350

6. Ccmmander1Naval Oceanography comm andNSTL, M!S 39529

7. Commanding Officer1Naval Oceanographic-officeBai St. LouisNST1L, MS 39522

8. Ccmmanding Officer 1Naval Ocean Research and Development ActivityBa" St. LouisNS'tL, M!S 39522

9. Chief of Naval Research1800 North Quinc yStreetArlington , VA 22217

10. Chairman, Oceanography Departmnent 1U. S. Naval AcademyAnnapolis, ID 21402

11. Chief, Hy drographi c Programs Division 1Defense .agping Agency iCode PPH)Building 5bU.S. Naval ObservatoryWashington, D. C. 20305-3000

12. Lt. Sanian Aumchantr 2Hydrographic DepartmentRoyal Thai NavyBankok 10600THA ILAND

150

p.

13. Personnel DepartmentRoyal Thai. NavyBangkok 1060THAILAND -

14. Library 2Hydrographic DepartmentRoyal Thai NavyBangkok 10600THAILAND -"

15. Chief Hydrographic Surveys Branch 1N/CG24 , Room 404, WSC-1National Oceanic and Atmospheric AdministrationRockville, MD 20852

16. Program Planninq, Liaison, and Training Division 1NC2 4 Room 105, Eockwall Buii ingNational Oceanic and Atmospheric AdministrationRockville, MD 20852

17. Director, Pacific Marine Center 1N/:IOPNational Ocean Service, NOAA1801 Fairview Avenue, EastSeattle, WA 98102

18. Director, Atlantic Marine Center 1N/M OANational Ocean Service, NOAA439 West York StreetNorfolk, VA 23510

19. Dr. Rolland L. Hardy 2Department of Oceanography, Code 68 XzNaval Post qraduate SchoolMonterey, CA 93943

20. Associate Deputy Director for Hydrography 1Defense Mapping Agency (Code DH "Building 5bU.S. Naval ObservatoryWashington, D.C. 20305-3000

151

.............................................. . .,

FILMED

6-85

DTIC