&EPA
United States
Environmental Protection
Agency
Office of Radiation Programs
Nonionizing Radiation Branch
P.O. Box 18416
Las Vegas NV 89114-8416
SPA-520/6-85-020
June 1985
Radiation
A Low Frequency
Automated Magnetic
Field Calibration
System
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SO272-1O1
REPORT DOCUMENTATION
PAGE
1. REPORT NO.
EPA 520/6-85-020
3. Recipient's Acceiiion No.
5 2 27908715
4. Title and Subtitle
A Low Frequency Automated Magnetic Field Calibration System
5. Report Data
7. Authorts)
8. Performing Organization Rapt. No;
Arthur P. Ludwigsen
9. Performing Organization Nam* and Address
U.S. Environmental Protection Agency
Nonionizing Radiation Branch
Office of Radiation Programs
P.O. Box 18416
Las Vegas, N? 89114-8416
10, Project/Taik/Work Unit No.
11. Contract(O or Sr»nt(G) No.
CC>
(G)
12. Sponsoring Organization Name and Address
SAME
13. Type of Report & Period Covered
14.
15. Supplementary Notes
IS. Abmtract (Limit 200 words)
..--•This report describes the construction of an automated absolute magnetic field
generation system using a 0.5 meter radius Helmholtz coil. The system
operates over a frequency range of dc to 20 kHz and can generate field
strengths up to approximately 1 Gauss RMS. The theoretical fields in the
region surrounding the coil were calculated and compared with measurement.
The system is used for the evaluation of broadband survey meters and
calibrated antennas.
17. Document Analysis a. Descriptors
b. Idintlfiara/Opcn-Ended Tarms
c. COSAT1 Field/Group
18. Availability Statement
from NTIS
19. Security Class (This Report)
20. Security Class (Ttils Pago)
21. No. of Pages
22. Pri
(See AMSI-Z39.18)
Sat Inttructlon* an Revert*
OPTIONAL FORM 272 (4-77)
(Formerly NTIS-35)
Department of Commere*
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A Low Frequency Automated Magnetic Field Calibration System
by
Arthur P. Ludwigsen
December 1983
U.S. Environmental Protection Agency
Nonionizing Radiation Branch
Office of Radiation Programs
P.O. Box 18416
Las Vegas, NV 89114-8416
-7ZT
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DISCLAIMER
Although the work described in this document has been funded wholly by the
United States Environmental Protection Agency it has not been subjected to the
Agency's required peer and policy review and therefore does not necessarily
reflect the views of the Agency. No Official endorsement should be inferred.
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FOREWORD
The Environmental Protection Agency, Nom'onizing Radiation Branch 1s In
the process of developing guidance for acceptable environmental levels of
electromagnetic radiofrequency radiation. This guidance should recommend
which available instrumentation is to be used to measure field strengths.
Thus, it is necessary to develop systems for the evaluation of these hazard
meters. This report document one system, the EPA automated Helmholtz coil
system as used to evaluate broadband survey meters in the frequency range of 0
(DC) to 20 kHz.
Office of Radiation Programs
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ABSTRACT
This design project was initiated with the overall objective of creating
an automated Helmholtz coil magnetic field calibration system. This system is
to be used in the evaluation of broadband survey meters and calibrated
antennas which are employed for environmental measurements of low frequency
magnetic fields.
Expressions for the magnetic field in a Helmholtz coil are developed to
include calculation of the field in off-axis positions. Measurements were
made of the field at various points and compared with theoretical predictions.
The system layout, programming and operation are documented to show how
frequency, field strength, and evaluation of the tested object are controlled.
ii
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TABLE OF CONTENTS
Page
Foreword i
Abstract ii
Table of Contents in
Table of Figures iv
Table of Tables v
Acknowledgements vi
Executive Summary vii
Introduction 1
Magnetic Field Generation Device 4
Characterization of Helmholtz coil 9
Amplifier and Resistive Load 14
Other Equipment 16
Automation 18
Operating the System 21
Remaining Work 24
Conclusions 25
References 26
Appendix A; Computer Program Listings 27
Appendix B; Values from Characterization of 53
Helmholtz ceil
iii
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LIST OF FIGURES
Fi gure Description Page
1 Block diagram of Low Frequency Magnetic Field 3
Calibration System
2 Diagram uf Opposing Magnets and Magnetic Field 4
3 Helmholtz coil Wire Support 6
4 Helmholtz coil Support Stand 7
5 Polar Coordinate System used in Jackson's Formulas 9
6 Coordinate System used for Table 1 11
7 Area of Characterization of Helmholtz coil 12
8 Circuit Diagram for Resistive Load Characterization 15
iv
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LIST OF TABLES
Table Description
1 Comparison between Different Methods of Magnetic Field 11
Calculation
2 Comparison Between Theoretical and Measured Values 13
in Helholtz coil
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ACKNOWLEDGEMENT
I would like to thank Edwin D. Mantiply and Paul Galley for their many
useful suggestions during the development of this system and Michael Molony
for his progranming assistance.
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EXECUTIVE SUMMARY
The Noniofiizing Radiation Branch of the Office of Radiation Programs,
U.S. Environmental Protection Agency, is responsible for establishing guidance
levels for public exposure to electromagnetic radiofrequency radiation. It
also maintains a laboratory to develop and apply systems for the evaluation of
field strength measurement instruments. This project consisted of the design
of one system, the EPA Automated Helmholtz coil System, that is to be used to
evaluate broadband survey meters in the frequency range of 0 to 20 kHz,
The Helmholtz coil system had the following requirements:
1. Generation of stable magnetic fields with intensities up to 1.0 G
2. Frequency range between 0 and 20 kHz
3. Manual or computer control of the system
4. Ability to evaluate broadband measurement .instruments and calibrated
antennas.
Construction of the system and initial testing has been completed.
Initial testing revealed some areas which warrant further study. The
automation program has been written and tested. A theoretical
characterization of the Helmholtz coil has been completed but further
interpolation is needed to smooth out the data. A four-terminal shunt
resistor is being purchased and will need to be characterized over the power
and frequency range of the system so that accurate current measurements can be
made. Further study is needed of the system to determine its operating
characteristics over long periods.
vi i
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INTRODUCTION
The Nonionizing Radiation Branch of the Office of Radiation Programs,
U.S. Environmental Protection Agency, is responsible for establishing safe and
reasonable standards for public exposure to nonionizing radiation. As a
corollary to this responsibility, the Branch has the capability to make field
strength measurements to determine environraental exposure levels of the
public. The Branch also maintains a laboratory in Las Vegas, Nevada, to
develop techniques to evaluate the error associated with both measurement
instruments and measurement techniques.
The low frequency magnetic field calibration system discussed in this
report was designed to calibrate and evaluate instruments operating at
frequencies between zero (DC) and 20 kHz. This system is one part of a
project to expand the Branch's instrument evaluation capability into the low
frequency area. The magnetic field calibration system will:
1. generate stable magnetic fields from 0.5 milliGauss (mG) to 1.0 G
with a precision of *0.05 mG,
2. have a frequency range between zero and 20 kHz,
3. be capable of manual or automatic control, and
4. be able to evaluate broadband field strength measurement instruments
and calibrated antennas to determine overall bandwidth, resonant frequencies,
and other characteristics of the instruments or antennas.
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To accomplish these objectives, the system configuration illustrated in
Figure 1 was implemented. The magnetic field is generated by amplifying an
low level input signal (either discrete frequencies or a broadband signal) as
necessary and delivering it to a Helmholtz coil that generates magnetic
fields. The Instrument or antenna being tested is placed in the magnetic
field and it's output compared to the value of the established field. This
measurement can also be observed as a function of time or angular position
relative to the field orientation. The difference between the measured and
established values is the error and is used to correct readings from that
instrument or antenna when it is used for on-s1te field measurements
The process is automated by using a controller program specially written
as part of this project. This program computes the frequencies and voltage
levels needed ay the system, generates the magnetic field, and evaluates the
instrument or antenna being tested. This process is completely automated and,
once the operator starts the program, will free the operator for other work
activities.
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Bold lines are data transfer and computer command lines.
Thin lines are signal lines. Double line indicates extension from
rotator.
A. HP 3582A Spectrum Analyzer H.
B. HP 3490A Digital Multimeter I.
C. Helmholtz Coil J.
D. Crown M600 Amplifier K.
E. 0.1 n Current Shunt L.
F. 2.0 n Resistive Load M.
G. Instrument Being Tested
Rotator
HP 3314A Signal Generator
HP 59309A Relay Actuator
HP 59313A A/D Convertor
HP 9845B Computer
HP 2631G Graphics Printer
Figure 1. Block diagram of low frequency magnetic field calibration
system
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MAGNETIC FIELD GENERATION DEVICE
Various possibilities exist to generate stable magnetic fields for
laboratory use. Opposing magnets of opposite sign (see Figure 2) will
generate very strong fields but these fields cannot be quickly changed.
Alternating current (AC) magnetic fields can be generated by using
electro-magnets but the core of the magnet would remain magnetized after the
current was stopped due to the nature of materials used as cores for
electro-magnets. This Inherent tendency to remain magnetized also creates
difficulties In establishing magnetic fields of varying strength.
1
VSN
\
S
Figure 2. Diagram of opposing magnets and magnetic field
A Helmholtz coll is used In this project to generate the magnetic
fields. The Helmholti coil consists of two Identical loops of wire. This
device creates fields according to the Biot-Savart Law [1]:
dB = Mn I dl x r
o
(1)
where B is the magnetic field measured in Teslas, MO Is the magnetic
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permeability of free space (4irxlO~ Tesi a"meter/ampere), I is the current
through the coil is amperes, dl is the infinitesimal length of current in
meters, and r is the distance to the point where the magnetic field is being
calculated in meters. There are several advantages to using a Helmholtz
coil. Theoretical calculations discussed later show that the magnetic field
of interest varies less than 5 per cent within an imaginary cylinder centered
in the coil with a radius one-half that of the coil and capped by the rings of
the coil. Designing and building a Helmholtz coil is also a very simple
process.
The coil used in this project has an added feature of arbitrary
orientation in space, that is, it can be pointed in any desired direction.
This is done by using wheels at the base of the coil support stand to permit
rotation about a vertical axis. Pivots at opposite points on the
circumference of the coil permit rotation about a horizontal axis.
The coil has a diameter of one meter and, with the exception of the wire
coil and the wheels at the base, is made entirely from wood. The size was
dictated by a compromise between available laboratory space and the need to
have a sufficiently large volume magnetic field in which to place test
instruments and antennas. Wood was used for the ring support and stand
because it has virtually no magnetization, is easily worked, and was readily
available at low cost.
The wire support, illustrated in Figure 3, is made from two rings of
one-half inch plywood separated by one inch dowels and 2 x 4's at the pivot
areas. The plywood rings have a one meter outside diameter and are 10 cm
thick with a groove for the wire cut into the outside of the ring. The dowels
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Side
1.0m
End
If- 0.5
m
Top
k — . i « «, d
t
0.5m
1
Figure 3. Helmholtz coil wire support
and 2 x 4's are approximately 50 cm long and are trimmed so that the ring to
ring separation is 50 cm when assembled as measured from the centers of the
rings. The support stand, shown in Figure 4, is made from 2 x 4's also with a
4x4 main beam that has a mounting hole in the center and is braced for
rigidity. The pivots from the wire support ring are mounted through the top
of the support stand risers. All joints are either butt or tongue joints with
glue and 1/4 inch dowels for fastening.
Three turns of number 10 gauge solid wire are wound on each support
ring. The number of turns selected was based on the desired dynamic range in
field amplitude, the output capabilities of the amplifier, and the value of
the resistive load. The final selection of three turns per ring will generate
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Side
12.5'
End
46*
39"
Top
1* I
39.
46"
Figure 4. Helmholtz coll support stind
a 1.0 gauss RMS field with a coil current of 18.S amperes and results in only
17.8 microhenries Inductance. A low Inductance Is desired to reduce the
possibility of a resonant frequency within the test frequency range due to
stray capacitances within the system and to reduce inductive reactance that
would change the Impedance of the system, which Is approximately 2 ohns
resistive, thereby changing the current through the coll and the magnetic
field that is generated.
Measurement of the current through the coil will be made by measuring the
voltage across a 0.1 ohm * 0.1 percent 4-terminal shunt resistor In series
with the coil. The original concept was to use the amplifier's resistive load
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to measure the current but the results of a characterization of the load
showed that it would be unreliable for this purpose because of Instablity due
to thermal characteristics. Shunt resistors are designed for this application
and are more reliable in this context. In establishing a field within the
coil, the necessary current is calculated for the desired field strength at
the center of the coil and is based on the following formula from Reitz and
Hi!ford [2]
(2)
10
where B is the magnetic field in Gauss, N is the number of turns on each ring,
I is the current in amperes, and a is the radius of the coil in centimeters.
8
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CHARACTERIZATION OF THE HELHHOLTZ COIL
A theoretical characterization was made of the Helmholtz coil based on
the following series expansion from Jacfcson [3] of the Biot-Savart Law for a
loop of wire.
(-1)'
2n nl r>zn-
(3)
2n
where (2n+l)I! = (2nn)(2n-l)(2n-3) ...(5)(3)(1). In the first equation, r<
(r^ is the smaller (larger) of a and r. In the second equation, the upper
line holds for r < a and the lower line for r > a. These formulas are based
on the polar coordinate system shown in Figure 5. The Legendre polynomials
Figure 5. Coordinate system used in Jackson formulas
Pj-^fcos e) and Pg^fcos e) can be expanded
shown by NBS [4] and Gushing [5].
numerical analysis as
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Pn(x) =. C(2n-l)Pn_j(x) - (n-l)Pn.2(x)]/n (5)
where Pn(x) is the nth term of the Legendre polynomial of x and P_(x)
is the nth term of the first associated Legendre polynomial.
For a Helmholtz coil, the magnetic field through the coil and away from
the coil are summations of contributions from each ring as shown in the
following expressions:
BZ - B^cosoj + Br2cose2 * B^sinej + B^sinsg (7)
Br = Brlsinel * Br2sine2 - B^cose! - Be2cose2 (8)
where Br| and BQ^ are contributions from one ring and Br2 and Be2 are
contributions from the other ring. QI and e2 are the angles from the
central axis as seen by each ring. BZ constitutes the magnetic field
parallel to the axis of the Helmholtz coil and Bf is the field perpendicular
to the axis.
As can be seen from the equations, the Jackson formulas [3] are not
precise for r = a but do lend themselves to numerical methods and computer
analysis. The program FIELDS, listed in Appendix A, was written to compute
the magnetic field with the coil current normalized to one ampere. Since the
magnetic field is directly proportional to the current in the coil, other
field strengths at different currents can be easily interpolated. The program
IMTERP was written to account for values were r = a or where the FIELDS
program did not converge within the specified number of interations. This
program, which uses natural cubic spline interpolation is also listed in
10
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Appendix A. Examination of the data generated by this program shows apparent
Inconsistencies fn the radial component of the magnetic field (Br>. Further
work us1n§ spline interpolation will be necessary to smooth out the data.
This particular method of calculating the magnetic field 1n a Helmholtz
coll was compared with another method based on Reltz and Mil ford [6] where
elliptic Integrals were numerically integrated. Both methods compared well as
can be seen In Table 1 using the coordinate system in Figure 6 where the two
different methods are calculated using three different machines. These
different methods vary by less than 0.1 per cent from each other In
comparisons of the dominant field vector at a particular point and by less
than O.S per cent in comparisons of the less dominant field vector.
Figure 6. Coordinate system used 1n Tables 1 and 2
Table 1
R
Cm)
0.4
0.4
0.1
0.25
0.0
I
M
0.14
0.1
0.4
0.25
0.25
HP 15C *
B (mi) B (inG)
z r
60.1812
60.1812
54.0200
S2.1505
53.9505
-20.9562
20.9562
0.4441
0.0
0.0
HP 9845B *
B (mG) B (mG)
2 r
60.2183
60.2183
54.0183
52.1502
53.9506
-20.9562
20.9562
0.4441
0.0
0.0
HP 9845B **
B (mG) B (mG)
2 r
60.1760
60.1760
54.0197
52.1485
53.9545
-20.9556
20.9556
0.4467
0.0
0.0
* Numerical integration from Re1t2 and Milford [6]
** Legendre Polynomials from Jackson [3]
.U.
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Partial results of tills characterization are listed 1n Appendix B for an
irea from the center of the coll to a radius of 0.5 m and from the plane of
one ring to the center of the coil {see Figure 7). Neasurement of the
magnetic field 1n this quadrant adequately characterizes the field anywhere
• within the Helmholtz coll since the magnetic field is cyllndrlcally symmetric
about the z-axis and reflectively symmetric about a plane centered between the
two colls and parallel to the colls. That 1s, the magnetic field at a given
radius from the z-axis remains constant at any point on a ring of that radius
about the z-axis. Additionally, the field has the same magnitude at points at
a given distance above or below a central plane parallel to the coils.
Z=-.23m
Area studied
Area listed in Appendix B
Figure 7. Area of characterization of Helmholtz coil
Preliminary measurements at random points using a F. H. Bell Gaussmeter
show good agreement with the predicted values (see Table 2). These
measurements were conducted using a 200 Hz sinusoidal signal at 10 V rms. The
differences between the predicted values and the measured ones are attributed
to the inaccuracies in trying to measure a free points changes rapidly and so
even a 5 mm error in measurement of distance produces a much different
12
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predicted value. For example, if z = 0.1 m, the predicted magnetic field BZ
is reduced from B2 = 0.3672 S at r = 0.48 m and z = 0.10 ra to BZ a
0.1069 G at r s 0.52 m and z = 0.10 m. This is a 70 per cent change in the
magnetic field over a distance of 4 cm. The coordinate system used is shown
in Figure 6.
Table 2
R
(m)
0.0
0.0
0.23
0.4
0.4
0.5
z
(m)
0.0
0.25
0.125
0.1
0.25
0.1
Bz (Gauss)
Predicted Measured
0.5103
0.5395
0.5562
0.6018
0.3956
0.2323
0.500
0.530
0.470
0.505
0.335
0.155
Per Cent
Delivery
2.02
1.76
15.50
16.09
15.32
33.28
Br (Gauss)
Predicted Measured
0.0
0.0
0.0133
0.2095
0.0
0.4738
0.0
0.0
0.0
0.185
0.0
0.485
Per Cent
Delivery
11.69
2.36
0.5 0.25 0.2051 0.160 22.2 0.0 0.0
These calculations assume that the feed wires to the coil do not
contribute anything to the magnetic field. A study will need to be made to
determine how these feed wires affect the uniformity of the magnetic field
generated by the Helmholtz coil.
13
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AWLIFIER AND RESISTIVE LOAD
The driving source for this system is a Crown M600 laboratory amplifier.
It is a broadband amplifier with a frequency range of 0 to 50 kHz and a
specified output capability of 1300 W RMS into a 4- ohm load. The design
criterion for the resistive load called for a peak current output with minimal
power dissipation from the load and, originally, a load of 0.5 ohm was
selected on the premise that lower resistance means higher current at a given
power level. This design was found to be unreliable because the amplifier was
frequently tripped into standby by thermal safety cut-outs. After
consultation with the manufacturer it was learned that the amplifier reaches a
peak power output level for a resistive load between 2 and 3 ohm. Therefore,
a 2 ohm load was selected that did generally work satisfactorily. One problem
that did occur with the 2 ohm resistive load was that of heat dissipation.
Since the design of the resistive load called for it to be enclosed for safety
reasons, a heat buildup problem developed. A 20 ampere current through the
load dissipated 800 W that had to be removed to prevent heat buildup and a
possible fire hazard. This was corrected by ventilating the case of the load
and moving it to the top of the equipment rack above the other system
components. Additionally, two muffin fans were mounted to the bottom of the
load case to move about 150 cfm of air through the case for added cooling.
Preliminary designs for the calibration system called for measurement of
the current through the Helmholtz coil as a function of the voltage across the
resistive load. Therefore, a characterization of the load was needed to
determine its resistance at various frequencies and power levels. This was
14
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accomplished by using two digital multimeters and a 0.001 ohm current shunt as
shown 1n Figure 8. A 15 kHz sinusoidal signal was amplified and passed
through the load where simultaneous readings were made on both multimeters.
HP
3490
HP
3314
Crown
M600
Reiiltive
toad
(Current
(hunt
Fluke
8060
Figure 8. Circuit diagram for resistive load characterization
The results of this study showed that although there were no appreciable
effects due to frequency, drastic variations occured when different power
levels were applied. The resistance of the load varied from a low of slightly
less than 1.8 ohm to a high of about 2 ohm. This 10 percent variation in the
load resistance occured mainly when the voltage across the load was between 0
and 10 V, or at currents between 0 and 5 A. Since this is a current range
where the system will commonly be used, the variations in load resistance made
this design unsuitable for current measurements. As was mentioned earlier,
current measurements will be made using a 0.1 ohm current shunt. This will
allow accurate current measurements independent of the resistance value of the
load due to the design of the current shunt and the method in which it will be
used in the system.
15
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OTHER EQUIPMENT
Additional equipment needed for the system are a signal source, a digital
multimeter, a spectrum analyzer, and an analog to digital (A/D) converter, a
rotator, and a relay actuator. All of this equipment has to be interactively
programable by a Hewlett-Packard (HP) 9845B instrument controller for an
automated system and was available in the laboratory. A HP 3314A signal
generator was used as a signal source for the system. This generator has a
frequency range of 0.1 Hz to 20 Wz with 0 to 10 V RMS output. It is also
capable of arbitrary waveform generation when properly programmed. A HP 3490A
digital multimeter is used in conjunction with the 0.1 ohm current shunt to
measure the current through the Helmholtz coil.
The HP 3582A real-time spectrum analyzer is used when antennas are being
evaluated. It has a frequency range from 0 to 25 kHz and will display a
signal from an antenna on a cathode ray tube as magnitude plotted against
frequency. This analyzer can display magnitude on a linear or logarithmic
scale and can determine various characteristics about the input signal such as
the transfer function, differences between magnitudes or frequencies, bandwith
of a signal, and other characteristics. It is completely interactive with the
HP 9845B.
Analog signals from field strength measurement instruments with recorder
outputs may be converted to digital values for the computer by a HP 59313A A/D
converter. This A/D converter has four input channels, each of which is set
to a different full scale value. One channel is reserved for analog Inputs
with a maximum of one volt, another 1s used for maximum inputs of 3.5 volts,
and one channel samples an output from the rotator to determine position. The
16
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rotator is used to rotate the test instrument relative to the magnetic field
so that evaluations can be made on how the instrument operates in different
orientations. A HP 59306A relay actuator controls a commercial antenna
rotator by outputting a voltage to the porper direction line. When this
voltage is removed, the rotator stops. The position of the rotator is
indicated by varying voltage on a different line that is sampled by the A/D
converter.
17
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AUTOMATION
Two different options existed for developing an automation program for
the system. Either a controller program similar to other existing programs
could be used or an entirely new type of program could be written. The first
option was chosen in the interest of minimizing the training of operators for
use of a different type of system. A controller program named LOWGO was
written for the HP 9845B instrument controller to automate the system. This
program initially asks the operator a series of questions that describe the
type of evaluation needed, computes the necessary frequencies and voltages for
the equipment, and establishes the magnetic field desired. At this point, the
program will either pause for manual evaluations, make automatic evaluations
on instruments under test having a recorder output, or read the spectrum
analyzer when antennas or other appropriate equipment are being tested. It
then computes the error from the established field and displays the results in
graphs and tables. Manual evaluations are necessary when the instrument being
tested does not have a recorder output and the operator must read the meter
directly. The program merely sets the desired field in this case and no
printouts are generated.
The controller program was created by custom fitting various library
routines to the particular needs of the system and writing the necessary
calculation routines to fit into the customized program. Special routines had
to be written to control the signal generator, spectrum analyzer, and digital
multimeter as these particular instruments are not used In other similar
programs. Another routine was written to display and printout the information
from the spectrum analyzar. The final result is a controller program which is
one of a set of programs which are continually being revised and improved
18
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within the Branch to make the controller series programs faster, easier to
use, and more accurate. These programs are very user friendly, requiring very
little work by the operator.
When the program is initially started, it checks to see if all revel ant
equipment 1s on and in the proper operating mode. If this is not the case,
the operator is notified via a message displayed on the screen and the program
begins recursive operations until all equipment is set up correctly. This is
done in lines 1020 to 1810 for the printer, rotator and relay actuator, signal
generator, digital multimeter, and spectrum analyzer.
Beginning in line 1820 and extending to line 2620, questions are asked
concerning the evaluation procedure to be used and the desired field, such as
the operator's name, the title of the evaluation, whether the evaluation is
manual, automatic, or uses the spectrum analyzer, what units of measurement
does the instrument being tested use, what frequencies and field strength are
desired, whether or not the observation will be made based on time or
rotation, and what are the characteristics of the metering instrument.
The field is established in line 2630 to 3110 by transmitting commands to
the signal generator and reading the digital multimeter as feedback to check
for proper values. If the initial reading on the multimeter indicates that
the field is not correct, a binary search adjusts the output of the signal
generator until programmed tolerances are met. At this point, the program
checks to see if manual evaluations were requested and pauses if that
condition is true. The operator presses the CONTinue button of the HP 9845B
to set the desired field at a new frequency and this process is repeated until
the evaluation is complete.
19
-------
If either automatic or spectrum analyzer operations are selected, the
program receives data from the proper equipment in lines 3120 to 3960. For
automatic operation, data is received from the A/D converter in lines 3350 to
3650. The spectrum analyzer is sampled in lines 3690 to 3870. After the
sampling Is complete, the program checks to see what changes occurred in the
magnetic field during the sampling by reading the digital multimeter in lines
3880 to 3960.
The data received from the A/D converter Is converted to suitable values
for plotting in lines 3970 to 4300 and displayed on the screen in lines 4310
to 6390, dumping to the printer when the screen is filled. After all desired
frequencies have been evaluated, summary tables and plots computed in lines
6400 to 6800 are printed. The data from the evaluation can be saved
permanently if desired on disk or tape in lines 6810 to 7260.
20
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OPERATING THE SYSTEM
Using this system 1s relatively easy and does not require much equipment.
As can be seen in these instructions, the operator does not have very much to
do to obtain accurate evaluations of instruments. These instructions provide
all the necessary steps to complete an evaluation using the low frequency
magnetic field calibration system.
1. Place an HP-IB (Hewlett-Packard Interface Bus) extender in the
equipment rack containing the system components next to the HP 3314A signal
generator and connect HP-IB cables from the extender to the signal generator,
from the signal generator to the HP 3490A digital multimeter, and from the
digital multimeter to the HP 3582A spectrum analyzer.
2. Attach a suitably long cable with BNC connections on each end between
the extender located with the system components and an extender located near
the 9845B computer.
3. Connect this second extender to HP-IB Select Code 7 and make sure
that the printer, A/D converter, and relay actuator are connected to HP-IB
Select Code 10.
4. Turn on power to all equipment and adjust the output attenuator on
the Crown M600 amplifier so that it is about three quarters of the way toward
maximum. The system is now ready for operation.
5. Load the controller program LOWGO from the hard disk by typing
'LOAD "LOW60:X"' on the 9845B computer and pressing EXECute.
21
-------
6. Press RUN. The program will Initially check to see that all
equipment is on and in the proper operating mode and then ask for the
operator's name.
7. Enter the operator's name and press CONTinue.
8. Enter the title of the measurement and press CONTinue.
9. Select the type of evaluation desired and answer all of the questions
from the program.
10. If manual evaluations are selected, the program will establish the
desired field and pause. When all desired measurements have been taken, the
operator should press CONTinue to establish the desired field at the next
frequency.
11. If automatic evaluations are selected, the operator does not have
anything else to do until the program is finished sampling data. The program
will set the fields and receive data from the desired instrument, repeating
the process at all desired frequencies. All necessary calculations are
performed in the program and the results are printed in graphical form for
each frequency.
12. When the automatic sampling is finished the program asks for
comments. Here the operator should note any observation or special conditions
which may have revelance to the evaluation. The program will then print
summary tables and graphs and ask for the next set of frequencies.
22
-------
13. If no other evaluations are desired, the program can be stopped at
this time. For evaluations at different field strengths, the program should
be restarted by pressing RUN and repeating the procedure from step 7.
23
-------
REMAINING WORK
A few details need to be accomplished to complete the low frequency
magnetic field calibration system. Once the 0.1 ohm current shunt 1s
purchased, a complete study must be performed to determine Its Impedance at
all frequencies and power levels that may be used In the system. This is
necessary because this resistor will the standard on which currents are
measured in the Helmholtz coil and therefore the basis for the generation of
accurately known magnetic fields. Additionally, a study should be made of the
fields generated by this system to determine the variation in the fields over
a period of several hours. Lastly, a program needs to be written to compute
antenna factors in decibels with respect to mllligauss as this is the unit
used in the automation program used in this system.
To complete a general low frequency calibration system, an electric field
generation system needs to be built. This electric field system will
complement the magnetic field system designed in this project and will allow
complete characterization of antennas and field strength measurement
instruments at low frequencies. The automation program should then be
extended to allow either electric or magnetic field evaluations to be made.
Some of the necessary revisions have already been incorporated in the LOWGO
automation program in anticipation of this phase of the project.
24
-------
CONCLUSIONS
The low frequency magnetic field calibration system has been designed,
fabricated, and implemented for generating magnetic fields from 0.5 to 1000 mG
over a frequency range of 0 to 20 kHz. The computer program that controls the
system is flexible in that it allows the user to perform manual or automatic
evaluations with the results of automatic evaluations being printed out in
suitable format for documentation purposes. Additionally, this system is
flexible enough to incorporate future modifications that will be necessary
when an electric field calibration system is established.
This project is the beginning of an expansion by the Nonionizing
Radiation Branch into further studies of the low frequency area. This study
has particular relevance in that current power line frequency is 60 Hz and
there are recent developments in establishing high voltage DC power
transmission lines. Once research is completed establishing safe levels of
exposure in these areas, this project will allow instruments used to measure
the exposure to be evaluated quickly and accurately.
25
-------
REFERENCES
[1] Haliday, D. and Resnick, R. (1978). Physics, Vol 2, Sec. 34. John Wiley
and Sons, New York, NY, pp. 759
[2] Reitz, J. R. and Milford, F. J. (1967). Foundations of Electrpmagnetic
Theory. Addison-Wesley Publishing Co., Reading, MA, pp 156-158
[3] Jackson, J. D. (1962). Classical electrodynamics. John Wiley and Sons,
New York, NY, pp 141-145
[4] Abramowitz, M. and Stegun, I. A. (1964). Handbook of Hathmatical
Functions. Government Printing Office, Washington, D.C., pp 342-345
[5] Cushing, J. T. (1975). Applied Analytic Mathmatics for Physical Sciences,
John Wiley and Sons, New York, NY, pp 156-ib/
Reitz, J. R. and Milford, F. J. (1967). Foundations of Electromagnetic
Theory. Addison-Wesley Publishing Co., Reading, MAS pp 154-156
26
-------
APPENDIX A: PROGRAM LISTINGS
Projjram Description
LOWGO The controller program for the Low Frequency Magnetic Field
Calibration System
i /
FIELDS Program to compute the magnetic field in and around a Helmholtz
coil
INTERP Program to smooth out the data generated by FIELDS
27
-------
10
20
30
40
50
6?
70
80
9B
100
110
120
130
140
ISO
.160
170
180
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
34G
350
36G
370
380
390
400
410
420
430
440
450
460
470
480
490
SOO
SiO
520
*##*####*5Me#*###*#**###)^
*
* PROGRAM NAME: LOWGO REVISION: A 11/14/83
*
* COMPUTER: HP 9845B
*
* PROGRAMMERS: Arthur P. Ludwigsen and Micheal R. Mol.ony
* Non-Ionizing Radiation Branch
*
# DESCRIPTION:
# This program will direct equipment to generate accurately known
* electric and Magnetic field intensities for the purpose of
* evaluating the response of broadband, low frequency measurement
* devices. This system provides a convenient and accurate method
# to evaluate measurement device response to low frequency
* electric and magnetic fields and therefore establish uncertainty
# limits for instrument readings obtained in hazard survey
# measurements.
*
* WARRANTY:
# The Non-Ionizing Radiation Branch of EPA warrants only that
* testing has been applied to this code. No other warranty
* expressed or implied, is applicable.
*
*
*
*
*
*
#
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
#
*
###*######*####### ######*######*#*#*****###**##**##***##******#*#***#*##
0.0 HPIB DEVICE ADDRESSES Select Code #10 09/27/83
Model * Description . Address Code
2631G HP-IB Graphics Character Printer 01
59313A Analog to Digital Converter 06
59306A Relay Actuator 16
O.i HPIB DEVICE ADDRESSES Select Code t7 10/25/83
Model * Description Address Code
3314A Function Generator 07
3490A Digital Multimeter 22
3582.A Real-Time Spectrum Analyzer li
1.0 COMMON, DATA TYPE DEFINITIONS AND
PROGRAM INITIALIZATION
i.i STORAGE ALLO C A T I 0 N
530 COM INTEGER Generator ,Dmm
540 COM TitleftSO] ,Qper$l80]
550 SHORT Plotdb(9QQ>,Freqz<20fl),Pre err (200) , Post err (200 ) , Avqi<200)
560 SHORT Errdbi (200 >,Pmin.i (200 >,Pmaxi< 200), Status, Valx,Xl,Yi
570 SHORT Max f reqz ,Min_f reqz
580 INTEGER I ,Year ,B(900) ,Dir (900) ,Xorg(3) ,Yorg<3) ,Slen ,Samp_size,Sel , Equip
\590 INTEGER Card! ,Card2, Clock, Printer , Analyzer ,A_d_c on w, Rota tor ,Nf
''" x- ' -* A
-------
600
610
620
630
640
650
660
670
680
690
700
,49
710
720
730
740
750
760
770
780
INTEGER Pxi(i>3),Px2<2>3)>Pyi(i,3)>Py2<3,3)
DIM Units*(i!6,i)i:25],C*(iO)ti60],Sy=5teM$(l)Ii53,A<2SS),M*I1303
! i.;
ASSIGNHENT
0 F
VARIABLES
800
810
820
830
840
850
860
870
860
890
900
910
920
930
940
950
960
970
980
990
1000
1 0 .1 0
1020
1030
1040
1050
1060
1070
1080
1090
1100
iiiO
1120
1130
1140
1150
1,160
1170
1180
READ Xorg(*>,Yorg(*>
DATA 2.5,12.5,2.5,12,5, 10,10,3,3
READ PxiC*),Pyi<*>
DATA 15,75,15,75, 50,110,50,110, 55,55,10,10, 85,85,40,40
READ Px2(*>,Py2<*>
DATA 0,65,0,65, 61,126,61,126, 60,125,60,125, 45,45,0,0, 90,90,44,44, 49,5*
1,4,5,4.5, 84,84,38,38
j
Esc*=CHR$<27)
Quote*=CHR$(34)
i
Una ts$(l,0) =
Units* = "<
Units*(2,0)="V/M"
ASCII code 27 used for escape sequences
Unitsf <3,0) =
Units*<3,l>="r"
Units*<4,Q>="dBuV/M"
Units*(4,i>="dBuA/M"
Units*(5,0>="V"
Plates"
Syste«*Quote*&Storet*&Quote*
PRINT " HP Real Ti«e Clock Select Code: "jClock
PRINT " HP-IB Select Codes aret ">Card2>"and"jCardl
-------
1190
i?.oo
1210
1E20
1230
12SO
i;?.6o
:L27Q
1280
1290
1300
1310
1320
1330
1340
1350
1360
1370
1380
1390
14(10
1410
1430
1440
1450
1460
1470
1480
1490
1500
1510
1520
1530
1540
1S50
1560
1570
1580
1590
1600
1610
1620
1630
1640
•1650
1660
1670
.,16 BO
1690
1700
1710
1720
1730
1740
1750
1760
1770
4785
PRINT " HP-IB Generator is on Address: ">TAB<43)^Generator
PRINT " HP-IB Spectrum Analyzer is on Address: " >TAB<43)jAnalyzer
PRINT " HP-IB Multiweter is on Address: ">TAB(43)>D««
PRINT " HP-IB Printer is on Address^ ">TAB<42)^Printer
PRINT " HP-IB A/D converter is on Address: ";TA8<42>jA_d_conM
PRINT " HP-IB Actuator is on Address: "jTAB<42>jRotatortLIN(i)
PRINT "A/D Calibration Settings"
PRINT " Channel tl t i V" ;TAB<25) •> "Meter Recorder Output"
PRINT " Channel tal 3.5 M" ^TAB(25) •> "Meter Recorder Output"
PRINT " Channel *3= 3.5 V" jTAB(25) > "Rotator Reading " ji_IN< i )
! 2.1
CHECK STATUS
0 F
DEVICES
2.11 2&31G Line Printer
'turn printer on-line
lhard off-line, user Must turn on-line
SET TIMEOUT Cardi^i
ON INT #Cardl GOTO 1420
STATUS Printer>Cond
OUTPUT Printer. USING "#,K " jE
STATUS PrinterjCond
IF BIT(Cond,6) THEN 1440
DISP "TURN PRINTER ON-LINE."
GOTO 1380
DISP "NO POWER APPLIED TO 2631G PRINTER"
GOTO 1360
OFF INT tCardi
SET TIMEOUT Card1>10000
i
! 2.12 Probe Rotator and A/D converter
i
OUTPUT A_d._con«>"H4AJ"
N=SHIFT0 THEN 1570
DJSP "NO POWER APPLIED TO ROTATOR, OR OUT OF CALIBRATION."
GOTO 1490
i
! 2.13 Function Generator
i
SET TIMEOUT Card2>i
ON INT *Card2 GOTO 1610
STATUS Generator;Cond
GOTO 1660
DISP "Turn on h-p 3314A Function Generator"
GOTO 157»)
i
! 2.14 Digital Multimeter
SET TIMEOUT Card2jlOOO
ON INT #Card2 GOTO 1710
OUTPUT DM«;"R7F2TiMiE"
ENTER DMMjA$
GOTO 1760
DISP "Turn on h-p 3490A Digital Multimeter"
GOTO 1690
i
! 2.15 SpectruM Analyzer
i
SET TIMEOUT Card2jl
ON INT #Card2 GOTO i!300
STATUS Analyzer)Cond
!set MultiMeter to default state
-------
1790 GOTO 1850
1800 DISP "Turn on h~p 3582A Spectrum Analyzer"
1810 GOTO 1760
1820 !
1830 !2,2 DEFINE MEASUREMENT PARAMETERS
1840 !
18SO OFF INT *Hard2
i860 SET TIMEOUT Card2>1000u
1870 OUTPUT Dmm»"R7F2TiMiE" iset multimeter to default state
1880 OUTPUT Rotatorj"A4B56" !set actuator switches to default state;
1890 !
1900 ! 2,21 Identify the Measurement
1910 !
19;?.Q EDIT "Enter operator identification" >0per$
1930 EDIT "Enter a title for this measurement",Title*
1940 DISP "Is data collection <1) manual, (2) A/D converter, or (3) Spectrum An
alyter">
19SO INPUT Equip
.1960 IF (Equip=i) OR (Equip=2) OR (Equip=3) THEN 1990
1770 CALL DcoK "Only selections 1, 2, or 3 are allowed, try again.")
1930 GOTO 1940
1990 GOSUB Get_freq 'enter frequencies into array Freq(#)
2000 IF EquipO2 THEN 2100
2010 Rot$="Y"
2020 INPUT "Do you need rotation? (Y or N)",Rot*
2030 IF Rot*~"Y" THEN 2100
2040 INPUT "Enter measurement time span in seconds",Delay
20SO
2060 2.3 DEFINE THE FIELD TO -ESTABLISH
2070
2080
2090
2100 Sel=i
2110 INPUT "Do you want to enter Electric(O) or Magnetic(i) field units?",Sel
2120 IF CSel=0) OR (Sel=i) THEN 2180
2130 CALL DcoK"Only selections 0 or 1 are allowed, try again.")
2140 GOTO 2100
2150 >
2160 ! 2.32 Select the Units to use
2170 !
2180 N=2
2190 IF Sel=0 THEN DISP "Enter units: (1) kU/m, <2) M/m, <3) U/cm, or (4) dBu
y/m " >
2200 IF Sel = l THEN DISP "Enter units.- (1) A/m, (2) mGauss, <3) T, or <4) dBuA
2210 INPUT N
2220 IF 6) THFN 2190
2230 ! *
2240 ! 2.33 Enter the Field and Convert to mGauss (magnetic) or V/m (electric)
2250 «
2260 DISP "Enter Desired Field in "&Units$(N,SeD>
2270 INPUT Valx
2280 IF (NO4) AND <(Valx<0) OR l. OE8)) THEN 2190
2290 IF (N-4) AND 2SO) THEN 2190
2300 Inval=Valx
2310 !
232(1 IF N=4 THEN Valx~10A THEN Malx=Valx*100
2.31 Select Electric or Magnetic
3;
-------
2360 IF AND CSel=l) THEN Valx*Valx*iE7
2370 £F Sel=i THEN I_init=Valx*i*l. S/
2380 V_init=.001*1 init
2390 Setdb=20#LGT<0"alx>
2400 IF Equip<>2 THEN Start
2410 !
! 2.34 Enter Meter Parameters
2430
2440 INPUT "Enter Meter Full Scale Voltage",Fsvolts
24^0 IF FsMolts>5 THEN 2440
2460 DISP "Enter Meter Full Scale Field in "«,Units$(N,Sel> >
2470 INPUT Fsval
2430 IF N=4 THEN INPUT "Enter scale range in dB",Fsrange
2490 I
2500 ! 2,35 Computer Selects the proper A/D Channel
| 2510 !
I 2520 Cn=2
! 2530 Cnset=3.S SVolts
' 2540 IF ABS(Fyvolts)>i THEN 2S70
25SO
2560
Cnset = l IMo.lt
i 2570 Conv=Cnset/i022
! 2580 - Instr$=»H"&VAL*(2A(Cn-i))««"AJ" iconnand to sample channel 'Cn'
2590 PRINT LINVAL* ". Press CONTinue wh
en ready."
2620 PAUSE
2630
2640
2650
2660
2670
2680
2690
2700
27iO
2720
2730
2740
2750
2760
2770
2780
2790
2800
3.0 PROGRAM EXECUTION
3.1 INITIALIZE EQUIPMENT FOR EXECUTION
3.1.1A Position Probe
IF Rot*-"N" THEN 2800
Mdir=i
OUTPUT A_d_conv j"H4AJ"
Dig=SHIFT-8>+READBIN
2830 ON INT *Clock GOTO 3610
2840 !
3850 ! 3,12 Setup LOWGO Screen
2860 !
2870 Start: DISP
2880 Gp=0
2890 GOSUB Setu^_screen
2900 !
S910 FOR 1=0 TO Nf
2920 Try=i
2930 Cf=Freqz
-------
H9SO !
2960 ! 3.13 Update Screen with Current MeasureMent Paraneters
2970 I
2930 SWRITE 7,16,VAL$CF>&" "&F*&"
2990 SWRITE 8,26, VAL*(PROUND(Setdb ,-2) >V dB"MJnits$< S,Sel >
3000 SWRITE 9,2S,VAL*(PROUND
3040 !
3050 ! 3,14 Program Frequency and Anplitude on Generator
3060 !
3070 CALL Set_freq_3314
3080 CALL Set_3Mp 3314#10 00,-2>
3110 DISP
3.1.20 !
3130 !
3-140 !3.2 SAMPLE RESPONSE
3150 !
3160 Try—Try+i
3170 SWRITE iO,H8,VAL$ "«cVAL*( In val )&" "iUnit
s*(N,Sel)
3.1.90 IF EquipOi THEN 3240
3200 DISP "Press CONTinue for the next frequency"
3210 PAUSE
3220 NEXT I
3230 END
3S40 IF Equip<>3 THEN 3280
3250 DISP "Set Analyzer to desired configuration and press CONTinue"
3260 LOCAL Analyzer
3270 PAUSE
3,?BQ DISP " Sampling data."
3290 IF Equip=3 THEN 3690
3300 REDIH Dir(Slen),B(Slen),Plotdb(Slen)
3310 MAT Dir^ZER
3320 MAT B=ZER
3330 SUSPEND INTERACTIVE
3340 IF Rot*--"N" THEN 3570
3350 !
3360 ! 3.21A Safiple Data froM Instruwent and Rotator Box
3370 !
3380 IF Mdir>0 THEN OUTPUT Rotator}"B4A6" Iprobe clockwise
3390 IF Mdir<0 THEN OUTPUT Rotatorj"B6A4" Iprobe counter-clockwise
3400 FOR J=0 TO Slen
3410 OUTPUT A_d_convjInGtr* !A/D Channel for Probe
3420 ENTER A_d_conv BFHS 2 NQFORHATjBCJ)
3430 OUTPUT A_d_conw}"H4AJ" !A/D Channel for Rotator Position
3440 ENTER A d_conv BFHS 2 NOFQRMAT^Dir5 THEN 36?»0
3490 IF B<=0 THEN Err2i
3SOO NEXT J
3*310 Erri9s DISP "Systett Malfunction Check rotator connections,"
3S20 PAUSE
3530 GOTO 2980
-------
3540
355 0
3560
3570
3S80
\f^90
3600
3610
3620
3'630
3640
3650
3660
3670
3680
3690
3700
3710
3720
3730
3741)
3750
3760
3770
3780
3790
3SOO
3810
3020
3830
3640
3850
3860
3870
3880
3890
3900
3910
3920
3930
3940
3950
3960
3970
3980
3990
/*(] 00
4010
4020
4030
"4040
4050
4060
4070
4080
4090
4100
4110
4120
\4130
! 3.21B Sanple data frow instrunent while in delay
OUTPUT Clockj"UIG"
FOR J=0 TO Slen
ENTER A_d_conv)Instr$
NEXT J
RESUME INTERACTIVE
IF J "IMSNNiMi3 "&VAL$< Marker)
OUTPUT Analyzerj"LMK"
ENTER Analyzer}Tenp,Freq
IF ABS"MP"iVAL*"AAOAB1AXONU3AV2"
OUTPUT Analyzeri"LSTl"
IF NOT BIT(READBIN(Analyzer),6) THEN 3800
OUTPUT Analyzer>"LMK"
ENTER AnalyzerjAnax,Freq
OUTPUT Analyzer;"LAM"
ENTER Analyzer^MHi
OUTPUT Analyzer>"LDS"
ENTER AnalyzerjA(*)
! 3.22 Check for drift'
j
CALL Read_349Q
Post_erra>=PROUNIX*iOOO,-2>
SURITE 11,26
Power=0
Slen=J*1.15
\
! 3.23 Convert Values to Plotting Units and SUM up powers
IF Equip=3 THEN 4210
REDIM Dir
DISP " Converting value* for plotting. (Sample =";Sawp_size>")"
IF Rot$="N" THEN Mdir=-i
IF N04 THEN 3950
FOR J=0 TO SaMp_size
TMp-F«5val-Fsrange+B< J)*Conv/Fsvolt-3*Fsran»Tnp-Serdb
Power-Power+iO"
-------
4140
4150
4160
4.170
4180
4190
4200
4210
4220
4230
4240
4250
4260
4270
4280
4290
4300
431(1
4320
4330
4340
4350
4360
4370
4380
4390
4400
4410
4420
4430
4440
4450
4460
4470
4480
4490
4500
4S10
452.0
4530
4540
4550
4560
4S70
4S80
4590
4600
4610
4620
4630
4640
4650
4660
4670
4680
4690
4700
4710
4720
4730
N
i
i
i
Ii
E
i
i
j
H
H
0
D
G
I
i
t
}
!
j
i
j
j
0
0
I
i
j
j
D
D
I
!
i
IF Mdir=-l THEN Plotdb< J)=20*LGT-Setdb
IF Mdir=l THEN Plotdb ~Setdb
NEXT J
i
! 3,24 Cowpute Average
IF Equip=3 THEN 4290
Awgi < I)-Power/SaMp_size
Errdbi OR THEN AMtji( I)-Aygi (I )/12 . S
IF (N=i) AND (Sel=0) THEN Awgi ( I)*Avgi (I )/iOOO
IF THEN Avcji < I )=Avgi (D/1.00
IF (N=3) AND (8e3-i> THEN Avgi ( I >=Avgi( I)/1E7
IF N=4 THEN Avgi (I)=20*LGT(AMgi< I ) >
GOTO 4340
Errdbi >HIN jPwinK I)
HAT SEARCH Plotdb <*> ,MAX;Pfiaxi ( I)
OVERLAP
DISP
GRAPHICS
IF Gp>0 THEN 4650
4.i
INITIALIZE GRAPHICS
! 4.ii Plotting Titles
PLOTTER IS "GRAPHICS"
SCALE 0,15,0,15
DEG
LORG 5
CSIZE 5,7/15
HOVE 7.5,14.7
LABEL. USING "*,K "j Title*
CSIZE 3.5,8/15
MOVE 3,13.9
IF Equip=3 THEN MOVE 7.5,13.9
LABEL USING "=t,K "j "Applied Field; "&VAL*&" "&Unit«t«(N.Sel>
HOVE 12,13.9
IF Equip=3 THEN 4630
LABEL USING "*,K "> "Hsf er Full Scale; "&VAL$?«" "S,Units*(N,Se3 )
IF DO THEN 4650
! 4.12 Prograw Printer for Perforation Skip, and Dump Title
OUTPUT Printer USING "t,K " >CHR* (12)S,CHR$( 10 ^Esc*«,"&166p58f6diL"
DUMP GRAPHICS tCardi>13.5,15
IF Equip=3 THEN 5950
i
! 4.13 Setup Scales for Polar and Rectangular Plots
DbMin=PROUND(PMini(I)~.5>0)
DbMax=PROUND+.S,Q)
IF Rot$="N" THEN 5520
Iround to nearest dB
! 4.20
POLAR PLOTS
-------
4740
47SO
4760
4770
4780
4800
4810
4820
4*830
4840
4850
I860
4870
4880
4890
4900
4V 10
4920
4930
4940
4VSQ
4960
4970
4980
4990
SO 00
5040
5020
SO 30
5040
50SO
5060
S070
S080
SO 90
5100
5110
5120
Si 30
5140
S15Q
5160
5170
5180
5190
5200
5210
S220
5230
3240
5250
5260
5270
5280
5290
5300
5310
5320
5330
4,21 Setup Plotting Paratteters for Polar Plots on Rotation
SHOW 0,15,0,15
IF 1=8 THEN OUTPUT Printer USING "*,K">Esc**«"*,166p54f6diL"
Xorg=Xorg(Gp>
Yorg=Yorg(Gp)
RMin=.5
Rfiax=2.5
Rtic=2
CSIZE 2.25,7/15
4.22 Draw Plotting Area
MOVE Xorg,RMax#i,3+Yorg
LABEL USING "*,K">VAL**RMin+Xorg,SIN(Angle)*RMin-t-Yorg
DRAW Xi*l.05+Xorg,Yl*i.05+Yorg
MOVE Xi*l,2+Xorg,Yl*i.2+Yorg
IF (A=0) OR
-------
4,31 Setup Plotting Parameters for Rectangular Plots on Delay
S340 PLOT X,Y
S3SO NEXT J
5360 !
S370 PENUP
5380 R=M*Errdbi+Xorg
S410
5420 PLOT X,Y
5430 NEXT J
5440 !
54SO SERIAL
S460 GOTO 6,500
5470
5480 4.3 RECTANGULAR PLOTS
5490
5SOO
5510
5520 LOCATE Pxl < 0 ,Gp ) ,Pxi ( i ,Gp) ,Py,t ( 0,Gp ) ,Pyl < l,Gp)
5530 SCALE 0,Sa«p_size,DUttin,.0bMax
5540 FRAME
5S50 CSIZE 2.25,7/15
5S60 X_corr=Sa«p_size*. 13
5570 Y_corr=ABS<
5580 Grid_x=Delay/S
5590
5600 AXES Grici_x>Grid_y ,0,DbMin
5610 LORG 8
5620 FOR L=Db«in TO Dbwax
5630 MOVE 0,L
5640 LABEL USING "*,MPZ,X"jL
5650 NEXT L
5660 LORG 6
5670 FOR L=0 TO Delay
5680 MOVE L,-Y_corr
5690 LABEL USING "*,D1>»,X" jL
5700 NEXT L
5710 MOVE 0,Errdbi(.i:>
5720 DRAW Sa«p_size,Errdbi(I)
5730 MOVE 0,Db*in
5740 !
57SO ! 4.32 Plot Converted Data
5761) !
5770 FOR J=0 TO Sawp_size
5780 PLOT J,Plotdb(J)
5790 NEXT J
5800 !
5810 ! 4.33 Plot Labels
5820 !
5830 LBIR 90
5840 LORG 5
5850 MOVE ~X_corr,/2
5860 LABEL USING "*,K";"dB Error"
5870 LDIR 0
5880 MOVE Saiip size/2,-2*Y_corr
5890 LABEL USING "*,K"j"Ti«e <*>"
5900 GOTO 6300
5910 !
5920 ! 4.4 SPECTRUM ANALYZER DISPLAY
5930 !
•5 ••?
3 f
-------
5940 ! 4.41 Get parameters from Analyzer
5950 !
5960 IF 1=8 THEN OUTPUT Printer USING "*,K" >Esc$&"«bl66p54f6dlL "
5970 OUTPUT Analyzer|"LB3"
S980 ENTER AnalyzerjDbnax
5.9V 0 !
6^)00 ! 4.42 Calculate position and spacing and plot labels
6010 !
6020 Dbttin—Dbwax—8*10 !10 dB/div
6JJ30 Xtic=Span/500Q
6040 LOCATE Px2<0,Gp>,Px2Mf165,963
6140 MOVIE 0,0
6150 LABEL USING "*,K";M*[97,1283
6160 !
6170 ! 4.43 Plot display
6180 !
6190 LOCATE Px2(0,Gp),Px2<2,Gp),Py2<2,Gp),Py2<3,Gp)
6200 SCALE 0 ,255,Db«in ,I)brtax
6210 FRAME
6220 AXES Xtic,10,0,DbMin
6230 MOVE 0,Db«in
6240 FOR J=0 TO 255
6250 PLOT J,ACHR*(10)
6340 Gp=0
6350 EXIT GRAPHICS
6360 NEXT I
6370 GRAPHICS
6380 IF Gp=3 THEN DUMP GRAPHICS #r.ardi ^-110,115
6390 IF Gp<=2 THEN DUMP GRAPHICS fCardlj5,115
6400 !
!>41Q !4.6 PRINT REPORT SUMMARY
6420 I
6430 Print report: PRINT PAGE
^>440 EXIT GRAPHICS
6450 FOR C=0 TO 10
6460 C*(C) £i,«53 = " "
6470 LINPUT "Enter coMfients and terwinate with a blank line. " ,C$(C) £63
6480 IF C*0 THEN REDIM C$LIN<4>}TAB«8i-LEN
-------
6S40 PRINT 1)^$;" "iMonth*jH "iDate*ES>23 j ">"> Year ;TAB<54> , "Start Ti*e •. " ;Ti
*jl.IN
6550 PRINT "Operator: " ;Oper$;TAB(S9> jSysteM*(Sel ) > " System"
6560 !
6570 ! 4.6i Statistics
6580 !
6590 PRINT LIN<3)jTAB<35)>"Statistics"jLIN<2)
6600 PRINT " Freq. Awy . Reading Avg . Error Low Error High Error H
igh-Low Error"
6610 PRINT " ";LIN
6620 FOR 1=0 TO Nf
6630 PRINT USING 6660>Freqz >PROUND ,-3> >Errdbi( I) iP«ini iP«axi"AppUed Field = "jPROUNDC Inval ,-3) >Uni ts* "CoM«ents: " ;I..INC*<*>
6680 !
6690 ! 4.62 Setting Error SwMMary
6700 !
6710 PRINT PAGEjLINLIN (3>
6730 PRINT " Initial Final"
6740 PRINT " Frequency Setting Error Setting Error"
6750 PRINT " (kHz) («U> (MO)";L.IN(1)
6760 IMAGE 6X, 3D. 3D, 8X,MOZJ)»,12X,M!)Z. 1)0,10X^30. 3D
6770 FOR 1=0 TO Nf
6780 PRINT USING 6760 >Freqz ( I ) ,Pre err ( I ) ,Post err(I)
6790 NEXT .'C
6800 CALL Su«Mar^_j3lot2 THEN Write
7040 DISP "Enter the Protect Code for ";File*>
7050 INPUT Prot*
7060 ASSIGN ti TO File*, Status, Pr ot*
7070 GOTO 6910
7080 Write: !
-------
7090 PRINT tijTitle*,Date*,Time*,Oper$,Sel,N,Inval,Ualx,FsMolts,Fsval
7100 PRINT tijFsrantje,Version*,C$<*>
7110 FOR 1=0 TO Nf
7i?0 PRINT *ijFreqz(I),Pre err,ErrdbiFi:i ef&Storet*
7180 ON ERROR GQSUB Err20
7190 GOTO 7240
7200 Errors: !
7210 IF ERRNO59 THEN Err20
7220 PRINT "File ";File$;" is not large enough. "
7230 GOTO Save_file
7240 GQSUB Get_freq
7250 GOTO Start
7260 END
7270 !
7280 !5.0 IN-LINE SUBROUTINES
7290 !
7300 !
7'Z.iO Abort; ! %%% Abort
7320 STOP
7330 !
7340 Get_freq; ! Enter Frequencies from the Keyboard ### Get Free
7350 EXIT GRAPHICS
7360 Nf=200 (Maximum Number of Frequencies
7370 REDIM Freqz (Nf> ,Avgi (Nf > ,Errdbi (Nf) ,Pnini ~
7420 MAT SEARCH Freqz<*>,MIN;Min_freqz
7430 MAT SEARCH Freqz(*),MAX>Max freqz
7440 RETURN
7450 !
7460 Setup_screen: ! Setup the LOWGO Screen jjoK# Setup ncreer
7470 PRINTER IS 16
7480 EXIT GRAPHICS
7490 SCREATE 20,32
7500 Sub_setup: SWRITE 1,19,"Low Frequency Automatic Control System"
7510 SWRITE 4,i,Day$&" "\Mo
7520 SWRITE 4,55,"Start Time:
7530 SWRITE 6,1,"System ;
7540 SWRITE 6,50,"System: "&System$
-------
7680
7690
7700
7710
7720
7730
7740
7750
7760
7770
7780
7790
7800
7810
7820
7830
7840
7830
7860
7870
7880
7890
7900
7910
7920
7930
7940
7950
7960
7970
7980
7990
8000
80.10
8020
8030
8040
80 SO
8060
8070
8080
8090
8100
8110
8120
8130
8140
8150
8160
8170
8180
8190
8200
8210
8220
8230
8240
8250
8260
8270
l.,ow=I init-.S
X2=(High+Low)/2
CALL Read__3490
DISP " Setting Digital Voltmeter i " >PROUND(V2*1 000 , -2) >"
I_teMp-U2/,Q01
TeMp=I_init-I__teMp
IF < = .05) OR < . 01) THEN RFTURN
IF I_tenpI init THEN High-X2
X2=CHigh+Low)/2
CALL Set a«p 3314
GOTO 7700
i
! Miscellanous PrograM Errors
i
Erri7: DISP "Progra« Malfunction Error in setting frequency
PAUSE
STOP
Err2i= DISP "SystGM Malfunction Check mete?' connections."
PAUSE
RETURN
Err20 : DISP "PrograM Malfunction PrograM Error = ";ERRM*
ROTO 7890
!
SUB Dcol(Af) !
!
! SUB DcoKA*)
! A$ String to Display
j
Size=LEN
FOR 1=0 TO Size-i
DISP TAB < Si ze~I > 5 A$[ 1,1 + 1:!
WAIT SO
NEXT I
FOR 1=1 TO 3
WAIT 325
DISP A*C21
WAIT 325
DISP A$
BEEP
NEXT I
WAIT 40*Size
SUBEXIT
SUBEND
j
SUB Tiwe(Date*,TiMe*, Day*, Month*, INTEGER Year, Type)!
SUB TiMe
-------
8280 OUTPUT 9;"Recall
8290 ENTER 9>Month,Day ,Hour ,Minute,Se?c
8300 Month*=Honthf(Month)
8310 OUTPUT Date* USING Date^ormat jMonth ,Day ,Year-1900
8320 IF Type=2 THEN 8350
8330 OUTPUT TiMe* USING Ti«e forwatijHour,Minute,Sec
§340 GOTO 8390
8350 M$="AM"
8360 IF Hour>ii THEN M$="PM"
8,370 IF 12> OR
8380 OUTPUT Tine* USING Tiwe_f orinat2>Hour ,Minute,?•!$
8390 Year_=Year-
8400 Month=Month+12*
BA10 Year_=INT(i.25#Year_)-INT MOD 7
8430 Day$=Day»*(Weekday> ~"
8440 SUBEXIT
8450 !
8460 Date_fopMat: IMAGE *,iX,ZZ, 'V",ZZ,"/",ZZ,"."
8470 Ti.Me_forMatl: IMAGE t, ,IX,ZZ, " , %ZZ, " . ",ZZ, " . "
8480 TaMe_forMat2t IMAGE t,iX,DD,"«n,ZZ," ",AA
8490 SUBEND
8SOO !
8510 DEF FNC(V,F$,Pr)l **# FNC
8520
DEF FNC(M,F$,Pr)
8530
8540
85SO
8560
B570
8S80
8590
8600
8610 DIM NM*<-i:3>m
8620 READ NM$<*)
8630 DATA «Hz ,Hz , kHz ,MHz,GH7
8640 I=INT(LGT(V)/3)
8650
V NuMeric valus
F$ String equiualent
Pr Power Rounding Factwr
Description
Use internally to conMert Hz to kHz, Mhz, GHz, etc
8660 RETURN PROUND(M/iOA ( 1*3) ,-Pr )
8670 FNEND
' *** SuMMary Plot
8690 SUB SuMMary_plot ,Pmini (*) ,P«axi <*) .Er
(*) )
8700 !
8710 INTEGER Point(Nf)
8720 PLOTTER IS "GRAPHICS"
8730 GRAPHICS
«74Q DEG
87SO !
8760 ! Setup Scaling, and Plotting Lirtits
B770 !
8780 LOCATE 20,120,10,93
8790 MAT SORT FreqzC*) TO Point
8800 F«in=Freqz>
88.10 FMax=FreqzDbmin
8830 MAT SEARCH PwaxK*) ,MAX}l)bMax
8840 DhMln=PROUND
8850 DbMax=PROUND(Db«ax+.S,0)
8860 IF Nf>0 THEN Fc=/Nf
-------
8870
8830
8890
8900
8910
8920
8930
8940
8950
8960
8970
8980
8990
9000
9010
9020
9031)
9040
90SO
9U60
9070
9080
9090
9100
9110
9120
9130
9J.SO
9160
9170
9.180
9190
9200
9210
9220
9230
9240
92SO
9260
9270
9280
9290
9300
9310
9320
9330
9340
93SO
9360
9370
9380
9390
9400
94.10
9420
9430
9440
9450
9460
II
Fi
F(
SI
FI
Ci
Y
X
Xi
CI
A;
Ui
LI
Fi
Nl
Li
Li
FI
Nl
C!
II
^i
rl
I
1
!
I
i
i
Ni
X
L
C
L
M
L
IF Nf=Q THEN Fc=F«ax/2
Fttin=FMin-Fc
Dbwax
_corr#2>I
SCALE Ffiin,F«ax,DbMin,Db«ax
FRAME
CSIZE 2.75
Y_corr=(Dbnax-DbMin)#.01
corr=#. 02
Xc=X_corr
CLIP F«in~X__corr,FMin,Dbp»int
AXES Fc,i,FMin,Db«in
UNCLIP
L08G 8
I=Dbrtin TO
MOVE Frtin-X
LABEL USING
NEXT I
LORG 5
LDIR 0
1=0 TO Nf STEP :CNT,DbMin-Y corr
DRAW Freqz(I)
MOVE Freqzd) __
LABEL USING "*,K %Freqz CI)
NEXT I
CSIZE 2.50
Nf>15 THEN X corr-0
? J=0 TO Nf
I-Poin-KJ)
LINE TYPE 10
MOVE FreqzU) ,PMini< E)
BRAU Freqz(I),PMaxi(I)
! ** Label the Y axis **
DRAU
LINE
Freqz ,ErrdbiU>
LABEL USING "#,K">"0"
Label the Plot and DUMP it to the Graphics Printer
LORG 4
IF Nf>iS THEN LORG 2
IF NfMS THEN LDIR 90
MOVE Freqz-X_corr,PMaxi+Y_corr
LABEL USING Nt>HDZ.DDH;Pnaxi(I)
MOVE Freqz(I>-X_corr>PrtiniiS THEN LORG 8
LABEL USING "*,MDZ. DD1! jPrnini (I)
NEXT J
corr=Xc
LORG S
CSIZE 3.3
LDIR 90
MOVE FMin-X_corr*6,/2
LABEL USING "#,K">"dB Error"
-------
9470
9480
9490
9SOQ
9S10
9520
9530
9S40
9SSO
9560
9570
9580
9590
9600
9610
9620
9630
9640
9650
9660
9670
96BO
9690
9700
9710
9720
9730
9740
97SC
9760
9770
9780
9790
9800
9810
9820
9830
9840
98SO
9860
9870
9880
9890
9900
9910
9920
LDIR 0
9940
99SO
9960
9970
9980
9990
10000
10010
10020
10030
10040
10050
MOVE Xi,Db«in-Y corp*8
LABEL USING "t,K" t "Frequency (kHz)"
CSIZE 4
HOVE Xi,Dbnax+Y_corr*4
LABEL USING "*,K" ;Ti tie*
PRINT PAGE
DUMP GRAPHICS #10,1
PRINT PAGE
DUMP GRAPHICS *iO,l
SUBEND
i
SUB Enterf (INTEGER Nfreq^SHORT Freqx(#>>
*** E
SUB Enterf (INTEGER Nfreq,SHORT Freqx(*>>
Nfreq Number of Frequencies that were entered (Initially
indicates array size)
Freqx<#> The actual frequency value* in Glii
Description s
Subroutine to enter frequencies from the keyboard into the program
array Freqx(#)
External &-.
Dcol
Displays messages on DISP line of CRT (usally errors)
D:CH Z* 1 25 3, A* 1 160 3
SHORT Fr c?q, Inc, Ma x_f r eq , M in _freq, Start, Stop
INTEGER C , Con t , I , Nf ,Sep ,Sij;e,Stopx
PRINTER IS 16 .
Max_freq~P.O, 0
Min_freq=0
Cont=19 iCONTinue key code
Stopx=S2 !STOP key code
i
ntRr_freq: Nf=0
DISP "Do you want to enter separate frequencies or a range? (S or R)"
Z$=UPC*(CHR*Nf-«-i > Z
LINPUT A*
IF Size=0 THEN Exit
FOR 1=1 TO Size
Freqx(Nf)=UAL(A*m)
V
IF (Freqx(Nf )>=Min_freq) AND CFreqx (Nf ) <=Max_freq) THEN 10080
CALL DcoK "Specified Frequency is out of Range, Try Again...")
•H-
-------
10070
10080
10090
i'OiOO
iOliO
10120
10130
10140
10150
10160
10170
10180
10190
eq) THEN
10200 IF
10210
10220
10230
10240
10250
10260
10270
10 280
10290
10300
10310
10320
10330
10340
10350
10360
10370
10380
10390
10400
10410
10420
10430
10440
10450
10460
10470
10480
10490
10500
10510
10520
10530
10540
10550
10560
10570
10S80
10590
10600
10610
10620
10630
10640
10650
GOTO 9960
Nf=Nf+l
PRINT TAB<6Q>>"Frequency *
Z*="Pre«5« CONTAnue to Exit
IF C=0 THEN 9960
'
="}Freqx
NEXT I
j
! Enter frequencies as a range
i
Range: !
INPUT "Enter Start, Stop, and Increment Frequencies ",Start,Stop,Inc
IF Max_freq> OR (Start>Max_freq> OR 0 THEN 10300
CALL Dcol<"No Frequencies Defined! Try Again...")
GOTO Enter_freq
Nfreq=Nf-l
PRINT USING "#,K%""
SUBEXIT
Bad nuwber;!
IF ERRNO32 THEN 9960
CALL PcoH "Illegal NuMeric Response. Try Again
GOTO 9960
SUBEND
(Position cursor to first unfrozen line
')
j
Set_freq_3314= !
SUB Set_freq_3314CFJ
COH INTEGER Generator ,DMM
IF F_khz=20 THEN F_khz=i9
F khz=F_khz*1000
C«d$="FR"«,VAL*C«d*
SUBEXIT
SUBEND
i
*** Set_freq_3314
Set_anp_3314= !
SUB Set_aMp_3314=10 THEN 1059C
IF AMp<1.0 THEN 10560
CMd*="AP"&MAL*(A«p H"MO"
GOTO 10570
CMd$="AP"^MAL*(AMP*!000H"MM"
OUTPUT Generator>Cwd$
SUBEXIT
DTSP "AMPLITUDE OUT OF RANGE ON 3314'
PAUSE
SUBEND
i
Read_3490;I
SUB Read_3490
COM INTEGER Generator,Dn«
*** Set_aMp_3314
*** Read 3490
-------
10660 OUTPUT J>M«;"R7FgTiHi:
10670 ENTER
10680 Maluc?
10690 SUBEXIT
10700 SUBEND
-------
10 I PROGRAM FIELDS UPDATED: 11/10/83
20 !
30 ! PROGRAM DETERMINES MAGNETIC FIELDS BASED ON JACKSON
40 !
iSQ PRINTER IS 16
60 OPTION BASE 0
70 DIM Bx<10Q,200>,Bz<100,200>
80 REAL Rl,R2,Kri,Kr2
"90 INTEGER B,C
100 SHORT X45,Y4S
110 ASSIGN *1 TO "FLDATA:T14"
120 ASSIGN *2 TO "BZ'TIS"
130 DISP "Insert 'BX' tape in T14 and 'BZ' tape in T15 and press CONTinue"
140 PAUSE
ISO !
160 ! INITIALIZATION AND INPUT
170 !
180 COM A,Kth,PMiMUsi,P,Pplusl,Pplus2,Pi,Rp
190 1=1
200 A=.5
210 Kth=-3*PI*I*AA2
220 PRINT "PLEASE DO NOT DISTURB, REMOVE TAPE CARTRIDGE, OR TURN OFF THIS MAC
HINE"
230 PRINTER IS 0
240 PRINT "DISCONTINUITIES IN MAGNETIC FIELDS BASED ON JACKSON"
250 PRINT "SUDDEN ZEROS INDICATING JACKSON FORMULAS ARE NOT PRECISE"
260 PRINT "THE FORMULAS DID NOT CONVERGE AT THE FOLLOWING POINTS";LIN<1>
270 PRINT " Z B Rp C"jLIN(i>
280 B=0
290 FOR Z»-.2S TO .25 STEP .005
300 C=0
310 FOR Rp=0 TO i STEP .005
320 DISP Z,Rp
330 Zi=Z
340 Rl=SQR
350 IF Rl=0 THEN R1=1E-10
360 Z2=Z-A
370 R2=SQR
380 IF R2=0 THEN R2=1E-10
390 Krl=6*PI*I*A/Ri
400 Kr2«6*PI*I*A/R2
410 Thetai=ACS
420 Theta2=ACS
480 RMin=MIN(A>Rl)
" 490 CALL Bfieldr(Kri>RMax,RMin,Ri,Zi,Bri>Bthi)
500 !
510 ! CALCULATES MAGNETIC FIELDS DUE TO DISTANT COIL
520 !
530 Far_ring = !
540 RMax=MAX(A,R2>
550 R«in=MIN(A,R2)
560 CALL BfieldrRMax,R«in>R2»Z2>Br2,Bth2)
570 Printout s !
580 IF (Bri=0) OR
-------
590 Bzi=Bri*CQS
600 Bz2=Br2*COSCTheta2>
610 Bz3=Bthl*SIN
620 Bz4=Bth2*SIN
630 Bxi=Brl*SIN(Thetai>
640 Bx2=Br2*SINCTheta2>
650 Bx3=Bthi*COS(Thetai)
660 Bx4=Bth2*COS
670 Bz THEN PRINT USING 78QjZ,B,Rp,C
700 C=C+1
71,0 NEXT Rp
720 B=B+1
730 NEXT Z
740 PRINTER IS 16
750 MAT PRINT *i;Bx
760 HAT PRINT *2jBz
770 END
780 IMAGE D.DDD,SX,DDD,5X,D.DDD,5X,DDD
790
SUBROUTINE LEGENDRE POLYNOMIAL
GENERATES ODD LEGENDRE POLYNOMIAL TERMS FOR Z/R
800
810
820
830
840 SUB Leg_poly
850 COM A,Kth,PMinusi,P,Pplusl,Pplus2,Pi,Rp
860 X=Zp/R
870 Pl=0
880 IF (X=i> OR THEN X=SGN0 THEN 930
900 P=i
910 Pplusl=X
920 GOTO 960
930 Pninusi=P
940 P=Pplus2
9SO Pplusi=< <4*N-*-i)*X*P-2*N#PMinusl)/<2*N+l)
960 Pp1us2= < < 4*N+3)*X*Pp1usi-(2*N-H)*P)/<2*N*2)
970 IF RpOO THEN Pi = (2*N+2)/SQR ( i-X*X>*R THEN Ba=Kth*J*FNFactth/<2AN*<2*N+i)*AA3)
1170 IF A
-------
1190
1200
1210
1220
>1230
1240
1250
1260
-1270
1280
1290
1300
1310
1320
1330
1340
1350
1360
1370
1380
1390
1400
1410
1420
1430
1440
1450
1460
1470
1480
1490
1500
1510
1520
1530
1540
1S50
1560
1570
1580
1590
1600
1610
1620
1630
1640
1650
Bft=Bf t+Ba
IF ABS200 THEN 1240
GOTO 1110
Br=Bft=0
SUBEXIT
SUBEND
FUNCTION FACTORIAL R-VECTOR
CALCULATES RESULT OF FACTORIAL DIVISION FOR R-MECTOR OF JACKSON
DEF FNFactr(N)
K=N
F=2*K+i
L=2*K-i
IF K MOD 2 THEN K=K-i
Testr •. !
IF OR (L=0> THEN Endr
F=F*
L=L-2
K=K-2
GOTO Testth
Endth . !
RETURN F
FNEND
-------
.1.0
20
0
«,
PROGRAM INTERP
This prograM uses cubic spline interpolation to fill in values
where the Jackson formula* did not convercie.
40
50
6t DIM Bz(100,200),Index(50),X<2QO),Y(200>,Dona in(50>>Deriv(50).FunctSO)
70 ASSIGN #1 TO "FLDBZ=T14"
80 READ tijBzC*)
94) Eps=!E-6
100 !
110 ! Interpolating the rows is done here.
120 !
130 FOR 1=0 TO 100
140 D£SP "WORKING ON ROW " ; 1
150 V.Ux-0
160 Indexi-Index2~0
170 FOR J=0 TO 200
180 IF Bz(I,J)<>0 THEN 240
19.0 Indexl=Indexl+i
200 DoMain(Indexl)=Malx
2.1.0 Index(Indexi)=J
220 IF 50> OR ,Y<*), Domain <*> ,Func (*) ,Deri v <#) ,Int,E
ps)
310 FOR J=i TO Index!
320 Bz(I,Index(J»«Func(J>)
330 NEXT J
340 NEXT I
350 !
360 ! Interpolating the columns, and incidently all remaining unknown ua'Jues,
370 ! is done here.
380 !
390 FOR J=0 TO 200
400 OISP "WORKING ON COLUMN " ;./
410 Valx=-.25
420 Indexl-=.Tndexi^O
430 FOR 1=0 TO 100
440 IF Bz(I,J)<>0 THEN 490
450 Indexi=Indexi+i
460 DomaindndexD-Malx
470 JndexJ)
520 Valx=Valx-f.OOS
530 NEXT I
540 IF Indexi=0 THEN '590
550 CALL Spline,Y(*),Domain(*),Func<*),Deriw(*),Int»E
ps)
560 FOR 1=1 TO Index!
570
-------
S80 NEXT I
590 NEXT J
600 REWIND
611) PRINT
620 END
630 SUB SplineNarg,X<*),Y<*),Do«ain<*),Func<*),Deriv<*>,Int,Eps)
640 !
650 ! *#***#****#*****#^^
660 ! #** SPLINE FIT FOR FUNCTION VALUES, INTEGRATION AND DIFFERENTIATION.
670 ! f*************************^
680 !
690 !
700 ! *** BAD DATA CHECK.
710 Baddta=(N<=0) OR ,"ERROR IN SUBPROGRAM Spline."
760 PRINT "N<=">N,"Eps*"iEps,LIN<2>
770 PAUSE
780 GOTO 710
790 !
800 !
810 ! *** BEGIN SUBPROGRAM.
820 OPTION BASE 1
830 DIM S,Work
860 Xirtl=X(I--l)
870 Xn.pi=X(I-H)
880 Yi=m>
890 YiMl=Y(I-i)
900 Y.ip.1.=Y<.C + l)
910 X=Xi-Xi«4
920 H=Xipi-XiMi
930
950 3=SU THEN U~H
1060 S(I)»S=Eps THEN 1010
1090 FOR 1=1 TO N-l
1110 NEXT I
ilEO IF Narg=0 THEN 1440
1130 !
1140 !
1150 ! *** CALCULATE FUNCTION VALUES AND DERIVATIVES.
1160 FOR J=i TO Narg
1170 Correctors 1=1
-------
1180 T=DoMain=X<1> THEN 1270
1200 PRINT LT.N<2>, "ERROR IN SUBPROGRAM Spline.
1210 PRINT "ARGUMENT OUT OF BOUNDS."
1220 PSINT "X(l) = "5X(l>,'
1230 PAUSE
11340 GOTO 1170
1250 »
1260 !
1370 1=1+1
1280 IF I>N THEN 1200
1290 IF T>X(I) THEN 1270
1300 1=1-1
1310 H-DoMain
1320 T=DoMain-X
1330 X=H*T
1340 S=S-l/24*HA3#(S(
1480 NEXT I
1490 SUBEND
6~2-
-------
APPENDIX B
Table of Values for the
Magnetic Field
in a
Helmholtz coil
53
-------
Magnetic Fields perpendicular to the
.000
.005
.010
* of the Melnhnltz Coil
.015 ,(I2li .OPS
. 030
.040
.345
.050
.055
0 .000
0.005
0.010
0.015
0.020
0.02S
0.030
0.035
0.040
0.045
O.OSO
0.055
0.060
0.065
0.070
0.075
0.080
0.085
0.090
0.095
0.100
0.105
0.110
0.115
0.120 '
9.125
0.130
0.135
0.140
0.145
0.150
0.155
0.160
0.165
0.170
0.175
0. 180
0.185
0 . 190
0.195
0.200
0.205
0.210
0.215
0.220
0.225
0.230
0,235
0 240
0.245
0.250
0.0000
0.0000
0.0000
0. 0000
0.0000
0.0000
0. 0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0 .0000
0.0000
0.0000
0.0000
0. 0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0,0000
0.0000
0.0000
0.0000
0.0(100
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 '
0.0000
o. oooo
0.0000
0.0000
0.0000
0.0000
0 .0000
0.0000
0.0000
0.0000
0.0000
-.1113
-.1046
-.0974
-.0902
-.0835
-.0792
-.0758
-.0717
-.0678
-.0639
-.0603
-.0567
-.0532
-.0498
-.0464
-.0432
-.0401
-.0371
-.0342
-.0314
-.0288
-.0263
-.0239
-.0216
-.0195
-.0175
-.0156
-.0138
-.0122
-.0107
-.0093
-.0080
-.0069
-.0058
-.0049
-.0040
-.0033
-.0026
-.0021
-.0016
-.0012
-.0009
-.0006
-.0004
-.0003
-.0001
-.0001
-.0000
-.0000
-.0000
0.0000
-.1U32
-.1B07
-.1786
-.1752
-.1688
-.1601
-.1510
-. 1432
-.13SS
-.1251
-.1216
-.1138
-.1065
-.0995
-.0926
-.0862
-.0802
-.0741
-.0684
-.0628
- . 0575
-. 0524
-.0477
-.0432
-.0388
•S0349
-.0311
-.0276
-.0243
-.0213
-.0185
-.0159
-.0136
-.0115
-.0097
-.0080
-.0065
-.0052
-.0041
-.0032
-.0024
-.0017
-.0012
-.0008
-.0005
-.0003
-.0001
-.0000
-.0000
-.0000
0.0000
- . 2973
- . 2BS6
- . 2739
-.2619
-.2495
- . 2389
-.2281
-.2150
-.2030
-.1917
-.1806
-.1698
- . 1592
-.1444
-.13f>?
-!l305
-.1204
-.1105
-.1025
-.0938
-.0861
-.0784
-.0713
-.0644
-.0581
-.0520
-.0464
-.0411
-.0362
-.0316
-.0275
-.0237
-.0202
-.0171
-.0143
-.0118
-.0096
-.0077
-.0060
-.0046
-.0034
-.0025
-.0017
-. 0011
-.0006
-.0003
-.0001
-.0000
0.0000
0 0000
0.0000
-.3970
-.3B04
-.3643
-.3487
-.3330
-.3170
-.3014
-.2859
-.2689
-.2559
-.'2408
-.2260
-.2119
-.1982
-.1848
-.1719
-.1595
-. 1474
-.1325
-.124B
-.1143
-.1050
-.0950
-.0851
-.0767
-.0691
-.0615
-.0542
-.0488
-.0419
-.0362
-.0311
-.0267
-.0225
-.0186
-.0153
-.0125
-.0099
-.007?
-.0058
-.0044
-.0031
-.0021
-.0013
-.0007
-.0003
-.0001
0.0000
0.0001
0.0001
0.0000
- 4690
-.455B
-.4453
- 4338
-.4176
- . 3977
- . 3767
-.3566
-.3379
-.3187
-.S985
- . 2828
-.2641
-.2473
-.2305
-.2143
- . 1987
-.1836
'.1917
-.1553
-.1421
-.1295
-.1124
-.1062
-.0955
-.0854
- . 0773
-.0680
-.0596
-.0510
-.0443
-.0381
-.0329
-.0276
-.0229
-.018S
-.0149
-.0118
-. 0093
-.0070
-.0050
-.0034
-.0022
-.0013
-.0007
-.0002
0.0001
0.0003
0.0003
0.0002
0.0000
- . 60?9
- . 57B5
-.5534
-.5273
-.5006
-.4761
-.4524
- . 4278
-.4038
-.3816
- . 3595
- . 3378
-.3165
-.2949
-.2753
- . 2564
- . 2374
-.2193
-.2020
-.1854
- . 1695
-.1544
-.1400
-.1264
-.1136
-.1015
-.0902
-. 0797
-.0699
-.0609
- . 0526
-.0451
-.0395
-.0320
- . 0265
-.0216
-.0167
-.0132
-.0101
-.0075
-.0057
-.0038
-.0023
-.(1013
-.0002
0.0002
0.0004
0.0004
0.0004
0.0(01
0.0000
-.6968
-.6671
- . 6382
-.6105
-.5835
-.5551
-.5266
- . 4993
-.4716
-.4447
-.4190
-.3928
-.37S9
-.3440
-.3204
- . 2974
-.2753
- . 2549
-.2341
-.2150
-.1962
-.1795
-.1610
-.1460
-.1309
-.1169
-.0811
-.0916
-.0801
-.0696
-.0600
-.0512
-.0432
-.0360
-.0296
-.0241
-.0191
-.0148
-.0096
-.0081
-.0057
-.0035
-.C019
-.0015
-.0004
0.0007
0.0010
0.0007
0.0005
0.0005
0.0000
-.8084
- . 7733
-.7372
-.7011
-.6661
- . 632B
-.6021
-.5721
-.5367
-.5072
-.4749
- . 4478
-.4196
-.3914
- . 3577
-.3385
-.3134
-.2904
-.2660
-.2432
-.2222
-.2024
-.1829
-.1648
-.1478
-.1316
-.1167
-.1027
- . 0897
- . 0778
-.0668
- . 0573
-.0478
- . 0397
-.0324
-.0260
-.0204
-.0155
-.0109
-.0080
-.0052
-.0030
0.0018
-.0001
0.0001
0.0011
0.0013
0.0012
0.0009
-.0007
0.0000
-.9027
-.8633
-.8240
-.7852
- . 7475
-.7113
-.6752
-.6388
-.6037
- . 5679
-.5353
-.5021
-.4698
-.4390
-.4083
- . 3789
-.3503
-.3231
-.2969
-.2718
-.2487
-.2250
-.2030
-.1828
-.1639
-.1458
-.1287
-.1130
- . 0986
-.0852
-.0728
-.0617
-.0516
-.0425
-.0344
- , 0273
-.0211
-.0158
-.0113
-.0075
-.0045
-.0021
-.0004
0.0009
0.0016
0.0020
0.0020
0.0018
0.0013
0.0007
0.0000
-.9709
- . 9333
-.8990
-.8650
-.6287
- . 7882
-.7485
-.7114
-.6678
-.6304
-.5925
-.5559
-.5195
-.4864
-.4508
-.4177
-.3864
-.3562
- . 3332
-.2989
- . 2724
-.2470
-.2219
-.2002
-.1788
-.1591
-.1402
-.1224
-.1064
-.0916
-.0782
-.0658
-.0545
-.0446
-.0358
-.0280
-.0211
-.0154
-.0105
-.0065
-.0033
-.0008
0.0010
0,0022
0.0029
0.0031
0.0030
0.0025
o.ooia
0.0009
0.0000
-1.0757
-1.0329
-.9926
- . 9526
-.910?
-.8660
-.8214
-.7783
-.7309
-.6907
-.6489
-.6085
-.5684
-.B304
-.4929
- . 4578
-.4218
- . 3879
- . 3563
- . 3253
- . 295B
-.2680
-.2414
-.2165
-.1929
-.1709
-.1509
-.1315
-.1135
-.0970
-.0822
-.0688
-.0569
-.0459
-.0363
-.0277
-.0205
-.0144
-.0892
-.0049
-.0015
0.0011
0.0028
0.0039
0.0045
0.0045
0.0041
0.0034
0.0024
0.0012
0.0000
-------
Magnetic Fields perpendicular- to the 2-ax.iE ul the Helnholtz Coil
R .060 .065 .070 . O7'j OflO . OBS
.0911
. 095
. 100
. 105
.110
.115
Pi 0.000
Jj? 0.005
So .010
1 0.015
| 0 . 020
p| 0.025
1: 0 . 030
1 0.035
$ 0 040
fi 0.045
1 0 . 050
p 0.055
I] 0. 060
£J 0.065
a o . 070
| 0 . 075
M 0.080
| 0.085
!j 0.090
li 0 . 095
Jl 0. 100
0.105
0.110
0.115
0.120
0. 125
0.130
0.135
0. 140
0.145
0 150
0.155
0. 160
0. 165
0 .170
0.175
0. 180
0.185
0 . 190
0.195
0.200
0.205
0.210
0.215
0.220
0.225
0.230
0.235
0.240
0.245
0.250
-1 .1963
-1 . 145)
-1 .0940
-1.0431
-.9924
-.9419
-.8924
-.8443
-.7965
-.7511
-.7052
-.6607
-.6171
-.5753
-.5340
-.4941
-.4560
-.4194
-.3846
-.3507
-.3181
-.2879
-.2589
-.2315
-.2059
-.1818
-.1595
-.1386
-.1203
-.1010
-.0856
-.0710
-.0576
-.0460
-.0357
-.0270
-.0191
-.0125
-.0069
-.0025
0.0009
0.0034
0.0051
0.0061
0.0064
0.0063
0 0056
0.0045
0.9032
0.0016
n .noon
-1.2BB7
-1.2260
-1 .1665
-1. 1136
-1 .0709
- . 9832
-.9315
-.9516
-.8614
-.8093
-.7605
-.7117
-.6641
-.6171
-.5739
-.5310
-.4891
-.4494
-.4110
-.3744
-.3391
-.3062
-.2752
-.2455
-.2175
-.1917
-.1674
- 1448
-.1242
-.1051
-.0877
-.0730
-.0586
-.0455
-.0345
-.0249
-.0164
-.0096
-.0040
0.0005
0.0038
0.0063
0.0080
0.0089
0.0090
0.0084
0.0073
0.0057
0.0040
0.0021
0.0000
-1 .4100
-1 . 34B7
-1.2839
-1.2186
-1 .1550
-1 . 094-?
-1.0361
-.9802
-.9238
-.8687
-.8150
-.76i7
-.7106
-.4607
-.6128
-.5662
-.5209
- . 47B2
- . 4368
-.3971
-.3595
-.3231
-.2898
- . 2582
-.2282
-.1999
-.1812
-.1499
-. 1276
-.1071
-.1285
-.0699
-.0569
-.0436
-.0320
-.0219
-.0139
-.0065
-.0003
0.0043
0.0077
0.0103
0.0116
0.0121
0.0118
0.0107
0.0092
0.0073
0 .0050
0.0025
0.0000
-1 .40.15
-1.4201
-1.3598
-1 2993
-1 .2357
-1. 1730
-1 . 1099
-1.0456
-.9851
-.9260
-.8691
-.8078
- . 7557
-.7028
-.6505
-.5987
-.5518
-.5058
-.4611
-.4183
-.3780
-.3396
-.3024
-.2689
-.2369
-.2072
-.1792
-.1534
-.1295
-.1079
-.0882
-.0704
-.0545
-.0405
-.0283
-.0177
-.0088
-.0004
0.0045
0.0090
0.0123
0.0.145
0.0156
0.0155
0.0149
0.0137
0.0117
0.0093
0.0065
0.0033
0 . 0000
-1.5913
-1 .5206
-1.4506
-1.3810
-1.3121
-1 .2444
-1 .1772
-1.1110
-1 .0481
-.9819
- . 9?.fl 1
-.8602
-.7999
-.7422
-.6861
-.6331
-.5812
-.5312
-.4941
-.4382
-.3947
-.3539
-.3151
-.2784
-.2434
-.2118
-.1826
-.1552
-.1302
-. 1071
-.0862
-.0675
-.0508
-.0362
-.0234
-.0124
-.0031
0.0044
0.0102
0.0134
0.0179
0.0197
0.0204
0.0200
0.0190
0.0175
0.0144
0.0113
0.0079
0.0042
0.0000
-1 .6003
-1 .5411
-1 .4928
-1.4452
-1 .31102
-1 .3194
-1 .2472
-1.1779
-1 . 1(156
-1 .0375
-.9696
-.9058
-.8427
-.7814
-.7213
-.6646
-.6089
-.5554
-.5058
-.4561
-.4101
-.3661
-.3249
-.2863
-.2498
-.2159
-.1843
-.1554
-.1285
-.1044
-.0826
-.0632
-.0456
-.0305
-.0169
-.0057
0.0036
0.0112
0.0171
0.0217
0.0243
0 . 0258
0.0261
0 . 0253
0.0235
0.0209
0.0172
0.0137
0.0087
0.0047
0.0000
-1 .7077
-1.7004
-1.6150
-1 .5351
-1 .4647
-1.3918
-1 .3153
-1.2389
-1 .1652
-1.0922
-1.0236
-.9515
-.8857
-.8184
-.7544
-.6948
-.6346
-.5778
-.5239
-.4725
-.4241
-.3770
-.3329
-.2919
-.2537
-.2177
-.1844
-.1538
-.1265
-.1003
-.0774
-.0565
-.0385
-.022?
-.0091
0.0023
0.0118
0.0194
0.0253
0.0293
0.0318
0.0328
0.0325
0.0311
0 .0287
0.0253
0.0211
0.0163
0.0111
0.0056
n.nnon
-I .8697
-1.7773
-1 6944
-1.6171
-1 .5416
-1.4635
—1 .3828
-1.3015
-1.2229
-1.1433
-1.0691
-.9948
-.9243
-.8537
-.7863
-.7213
-.6589
-.5987
-.5411
-.4866
-.4349
-.3865
-.3399
-.2958
-.2550
-.2173
-.1824
-.1503
-.1195
-.0935
-.0703
-.0489
-.0305
-.0140
0.0003
0.0120
0.0217
0.0292
0.0347
0.0383
0.0403
0.0408
0.0399
0.0376
0.0355
0.0302
0.0251
0.0194
0.0132
0.0085
0.0000
-1 .9796
-1 .8852
-1.7931
-1 .7040
-1 .6185
-1.5335
-1 .4483
-1 .3633
-1 .2793
-1.1978
-1.1158
-1 . 0378
-.9619
- . 8875
-.8159
-.7474
-.6813
-.6173
-.5567
-.4986
-.4439
-.3906
-.3434
-.2974
-.2552
-.2152
-.1784
-.1444
-.1138
-.0879
-.0611
-.0389
-.0195
-.0028
0.0120
0 . 0234
0.0329
0.0401
0.0451
0.0485
0.0500
0.0499
0.0483
0.0453
0.0410
0.0358
0.0296
0 . 0228
0.0155
0.0078
0.0000
-2.6174
-3.3148
-3.7452
-3.3811
-1.6952
-1.2364
-1 .5138
-1.4228
-1.3339
-1 .2469
-1.1623
-1 .0783
-.9976
-.9183
-.8413
-.7714
-.7018
-.6343
-.5712
-.5088
-.4511
-.3962
-.3449
-.2969
-.2518
-.2102
-.1719
-.1366
-.1048
-.0758
-.0497
-.0269
-.0052
0.0101
0.0246
0.0365
0.0453
0 . 0528
0 . 0576
0.0603
0.0613
0.0603
0.0577
0.0537
0.0484
-.3906
0.0346
0.0266
0.0180
0.0092
0.0000
-2.1B36
-2.0808
-1.9773
-1 .8740
-1 .7717
-1.6737
-1 .5793
-1.4851
-1.3872
-1.2944
-1.2055
-1 .1161
-1.0306
-.9497
-.8700
-.7933
-.7191
-.6489
-.5807
-.5163
-.4564
-.3982
-.3441
-.2934
-.2465
-.2031
-.1630
-.1262
-.0926
-.0628
-.0362
-.0129
0 .0076
0.0251
0.0397
0.0515
0.0606
0.0672
0.0720
0.0735
0.0735
0.0716
0.0680
0.0627
0.0564
0.0489
0.0403
0.0310
0.0210
0.0106
0.0000
-2.2754
-2.1638
-2.0540
-1.9479
-1.8476
-1 . 7392
-1.6328
-1.S390
-1.4442
-1.3425
-1.2467
-1 . 1542
-1.0655
-.9775
-.8937
-.8120
-.7348
-.6599
-.5889
-.5217
-.4577
-.3971
-.3407
-.2881
-.2388
-.1929
-.1513
-.1133
-.0788
-.0482
-.0205
0.0038
0.0247
0.0424
0.0569
0.0685
0.0772
0.0833
0.0870
0.0882
0.0873
O.OB43
0.0796
0.0732
0.0656
0.0566
0.0468
0.0358
0.0242
0.0123
0.0000
-------
Magnetic Fields perpendicular to the z-axis of the Helnhnltz Coil
R
0 .000
0.005
0.010
0.015
0.020
0.025
0. 030
0.035
0.040
0.045
0.050
0.055
0.060
0.065
0.070
0.075
0.080
0.085
0 . 090
0.095
0 100
0.105
"0 110
'.0.115
0.120
1 0,125
0.130
0.135
0. 140
0.145
0.150
0.155
0. 160
0.165
0. 170
0.175
0 . 180
0.185
0. 190
0 . i 95
0.200
0.205
0.210
0.215
0.220
0.225
0.230
0.235
0.240
0.245
0.250
) .120
-2.5590
-2.7180
-2.7859
-2.5812
-1.9228
-1.6797
-1 .7011
-1.6108
-1.4905
• i .3865
-1.2730
-1.1896
-i.0949
-1.0031
-.9153
-.8292
-.7471
-.6694
-.5933
-.5235
-.4567
-.3937
-.3262
-.2785
-.2278
-.1804
-.1371
-.0976
-.0617i
-.0298
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1 .7949
1 . 7628
1.7188
1 . 6643
1.5994
1 . 5254
1.4426
1.3512
1 .2524
1 . 1 468
1.0351
0.9191
0.7866
0 . 6694
0.5392
0.4U72
0.2725
0 . 136S
0.0000
.245
-4.6513
-4 . 2656
-3 . 8827
-3.5033
-3.1274
-2.760S
-2.4025
-2.0522
-1 .7109
-1.3821
-1 .0603
-.7498
-.5001
-,1B2B
0.1895
0.3044
0.5407
0.7504
0.9469
1.1261
1 . 2084
1.4291
1 .5566
1 . 6665
1 .7611
1 . 8363
1 . B994
1.9443
1 . 9749
1 9903
1 .9915
1.9781
1 .9522
1.9151
1 . 8639
1.8025
1.7303
1 . 6487
1 . SS75
1 . 457B
1.3502
1 . 2355
1.1146
0 . 9B7B
0 . 8593
0.7192
0.5B02
0.4375
0.2930
0.1467
0.0000
.250
-4.7267
-4. 3181
-3.924R
-3.S265
-3.1338
-2.7482
-2.3705
-2.0826
-1.6456
-1.3004
-.9684
-.6458
-.3692
-.0515
0.3274
0 . 4569
0.7059
0.9165
1. 1261
1.3080
1 . 4738
1.6211
1.7504
1.861B
1 . 9556
2.0341
2.0921
2.1343
2. 1612
2.1726
2.1722
2.1518
2.1201
2.0743
2.0183
1.94B5
1 . 8696
1 7791
1 . 6794
1.57fi6
1 . 4535
1.3295
1.1983
1.0615
0.9196
0 . 7729
0.6230
0.4696
0.3144
0.1SB1
0.0000
. ?55
-4 . Bi 26
-A . 3078
-3 . 9624
-3.5456
-3.1328
-2 . 7267
-2.33U1
-1.9443
-1.5701
-1.2085
-.8611
- . 5276
- . 2253
0.0931
0 . 4699
0.6250
0.8B47
1.1111
1.3040
1 . 49B4
1.6764
1 . S2B6
1.95BS
2.0719
2.1656
2.2402
2.2985
2.3390
2.3619
2.3690
2.3603
2 . 3359
2.2981
2.2469
2.1815
2 . 1 053
2.0141
1.9170
1,8077
1.6B71
1 .5634
1.4280
1 .2B66
1.1395
0.9865
0.8292
0 . 667B
0.5041
0 . 3366
0.1690
0.0000
. 360
-4 . 8936
-4.4452
-3.9997
-3 . 5592
-3.1250
-2.6991
-2 . 2027
-1.8770
-1.4833
-i .1048
-.7406
-.3935
-.0685
0.2527
0.6217
0.8097
1 .0785
1.4483
1.5252
1 . 721 0
2.6540
2.0484
2.1818
2.2960
2 . 3B93
2.4620
2.5185
2.5554
2.5746
2. 5767
2.5617
2 . 5322
2. 4873
2.4274
2.3551
2.2690
2.1732
2.0629
1.9441
1.8154
1.6781
1.5340
1.3804
1.2212
1 . 0575
O.BBB3
0.7152
0.53BB
0.3617
0.1S09
0.0000
. :.»6S
-4.9728
-4.5010
-4. 031B
-3.5679
-3.1109
-2 . 6626
-2.2246
-1 7988
-1.3B63
-.9BBS
-.6069
-.2433
0.1013
0.4290
0.7874
1.0120
i . 2B86
1.8448
1 . 7657
1 . 9579
2.1317
2.2816
2.4215
2. 5354
2 . 6283
2.7013
2 . 7535
2. 7868
2.8013
2,7980
2 . 7755
2.7408
2 . 6875
2.6201
2 . 5384
2.4423
2.3361
2.2175
2.0875
1.9484
1 . 7994
1.642B
1.4791
1 .3080
1.1319
0.9509
0 . 7656
0 . 5768
0.3859
0.1948
0.0000
.270
-5.0506
-4.5529
— 1 . 05B1
-3 . 5703
-3 . OB94
-2.6177
-2.1^71
-1.7092
-1.2761
-.8586
-.454B
-.0778
0.2841
0 . 6238
0 . 9720
1 . 232B
1.5166
2. 1856
2. 0178
2.2016
2.3896
2.5448
2.67B3
2.7927
S.BB46
2.9516
3.0038
3.0329
3.0412
3.0335
3.0060
2.?611
2.9000
2.8238
2.7321
2.6278
2.5094
2.2038
2.2404
2.0878
1 . 9275
1.7596
1 .5821
1 . 3992
1 .2090
1.0170
0.8177
0.6160
0.4122
0.2062
0.0000
. 375
-S.126B
-4.6025
-4. OBJ 9
-3 . 5672
-3.0603
-2 . 5638
-2.07H6
-1.6079
-1.1578
-.7146
-.2946
0.1098
0.4818
0 . 8378
1 .1801
i . 4732
1.7640
2.4648
2.2841
2.4647
2,6656
2.8206
2.9543
3 . 0575
3.1590
3.2259
3.2715
3 . 3088
3.2948
3 . 2833
3.2478
3.1930
3.1292
3.0388
2.9374
2. 8210
2.6932
2.5514
2.3989
2.2361
2.0641
1.8805
1.6912
1.4949
1.2937
1.0830
0 . 8735
0 . 6573
0.4401
0.2203
0.0000
,2BO
-5.2046
-4.6522
-4.1000
-3.5569
-3.0224
-2.4971
-1.9887
-1.4988
-1.0129
-.5541
-.1149
0.3031
0 . 6982
1.0700
1.4165
1.7340
2.0322
2.7040
2.5671
2.7512
2.8955
3.1118
3.2436
3.3623
3.4207
3.5160
3 . 5556
3 . 5754
3.5721
3 . 5526
3.5044
3.4425
3.3634
3.2649
3.1543
3.0264
2.8863
2 . 7292
2.5666
2.3901
2.2037
2.0088
1.8053
1.5940
1.3784
1 .1567
0.9308
0 . 7026
0 . 46B3
0 . 2350
0.0000
.205
-5.2781
- 4 . 6926
-4.1127
-3.5380
-2 . 9759
-3 . 4S42
-1 .8856
-1.3640
-.8610
-.3773
0.0843
0 . S223
0 . 9352
1.3230
1 . 6835
2.0164
2 . 3226
2 . 9246
2.8697
3.0618
3.1717
3 . 4257
3 . 5654
3.6769
3.7633
3.8214
3 . 8589
3.8723
3.8615
3.B294
3.7769
3.7046
3.6147
3.5061
3.3809
3.2426
3,0891
2.9225
2.7429
2 . 5521
2 . 3525
2.1431
1.9226
1.7003
1.4694
1.2436
0.9909
0.7466
0.4990
0.2499
0.0000
.290
-S.3497
-4.7324
-4.1198
-3.5145
-2.9196
-2 . 3362
-1.7682
-1.2192
-.6892
-.1817
0.3025
0.7607
1.1937
1.5982
1.9747
2 . 321 0
2.6367
3.1481
3.1943
3.3975
3.4915
3 . 7628
3.9058
4.0098
4.0961
4.1519
4.1825
4.1866
4.1832
4.1278
4.0646
3.9810
3,8800
3.7595
3.6231
3.4700
3.3022
3.1217
2 . 9285
2.7238
2.5085
2.2897
2.0510
1.8089
1 . 5632
1.3105
1.0S41
0.7942
0.5306
0.2661
0,0000
.295
-5.4215
-4 . '/6B8
-4,1209
-3.4806
-2.8514
-2 . 2358
-1.6375
-1.0590
-.4999
0.0347
0.5426
1.0243
1,4764
1.8982
2.2B93
2.6489
2.9761
3.395B
3.5437
3.7589
3.8526
4.1244
4.2671
4 . 3692
4.4529
4. 5031
4.5222
4.5175
4.4933
4.4415
4 . 3693
4.2733
4.1595
4.0267
3.8763
3.7095
3.5274
3.3314
3.1239
2.9026
2 . 6769
2.4310
2.1824
1 . 9257
1.6605
1.3939
1.1205
0.8437
0.5648
0.2823
0.0000
-------
Magnetic Fields perpendicular to the 2-.ix.iR of the Helwhnltz Coil
I R (n)
1 Z
fi|
1 0.0(10
1 0.005
1 0.010
m o.ois
I 0,020
1 0.025
1 0.030
1 0.035
1 0.040
0.045
0.050'
10.055
0.060
0.06S
0.070
0.075
J 0.080
0.085
0.090
0.095
0.100
0.105
0.110
0.11S
o.iae
0,125
0 . J.30
0.135
I 0.140
! 0.145
0.150
0 . 1 55
-'- 0 . 160
? 0.165
ft 0 . 170
^ 0 . 175
t 0 . 180
| 0.1B5
!fl 0 . 170
t 0.195
f 0,200
W- 0.205
IL n.sio
1 0.2i5
s 0.220
I 0.225
I 0.33(1
'/ 0.235
f O.H40
V 0.24S
t (I . 250
.300
-S.4919
-4.8010
-4.1159
-3.4375
-2.7721
-2.1219
-1.4892
- . B779
-.2901
0 . 2778
0 .8016
1.3106
1 . 7B33
2.2239
2.6304
3.0041
3.3423
3.6894
3.9205
4.1470
4.2524
4.5121
4.6530
4 . 7598
4.8322
4,8729
4 . 8B68
4.8746
4.8315
4.7750
4.6891
4.5B29
4 . 4539
4.3063
4.1418
3.9596
3 . 7626
3,5516
3 . 3263
3,1026
2.8423
2,5842
2.31B9
2.0423
1 . 7654
1.4800
1.1899
0.8952
0 . 5984
(1.2993
0.0000
.305
-5.5620
-4.8298
-4. 10JB
-3.3844
-2.6798
-1.9915
-1.3232
- . 6778
- . 0578
0.5339
1.095D
1 . 6237
2.1.193
2.5786
3.0004
3.3876
3.7382
4.0503
4 . 3273
4.5625
4 . 68B5
4.9375
5.0650
5.1732
5 , 2329
5 . 2743
S.2736
5.249B
5.2019
5.1269
5 . 0275
4.9076
4.7790
4.6145
4.4213
4.2232
4.0(195
3.7813
- 3.5393
3.2855
3.0208
2.7466
2.4623
2.1711
1.8731
1.56B8
1 ,2615
0 . 9525
0.6343
0.3174
0.0000
.310
-S . 6289
-4.8SHB
-4. OB07
-3.3201
-2 . S734
-1.8444
-1 . 1373
~.45SB
0 . 19B6
0 . 8220
1.4115
•1 , 9660
2.4841
2.9638
3.4042
3.8049
4 . 1653
4 . 4856
4 . 7668
5.0063
5.1583
5 . 3723
5.5051
5.6091
5 . 6578
5.6866
S . 6824
S.6SOO
B . 5fl62
5.4996
5.3B6Q
5.3491
S.090B
4,9170
4.7145
4.4992
4 . 2679
4.0219
3.7619
3.4893
3.2059
2.8760
2. 6115
2.3010
1.9852
1.6629
1.3360
1. 0060
0.6709
0 , 3365
0 .flOOO
.315
-5.6951
-4.B700
-4.0513
-3.2430
-2,4513
-1.6790
-.9305
-.2091
0,4813
1.1382
1.75B5
2.3405
2 , BB24
3 . 3826
3.8403
4,2552
4 , 6269
4 . 957S
5.3416
5 . 4826
5,6595
5.8480
i.9748
6.0704'
6.1089
6.1237
6.1156
6 . 0684
5.9938
5.B907
5.7633
5.6065
5 . 4327
5.2383
5.0214
4 . 7875
4.5380
4.2726
3 . 9942
3.7043
3.4004
3 . OH76
2 . 7678
2.4349
2.1017
1.7603
1.4129
1 . 0633
0.7135
0 . 3554
0,0000
.330
-5.7600
-4 . 8826
-4. 01211
-3.1537
-2.3123
-1.493(1
-.6996
0.0639
0 . 7935
1.4 859
2.1385
2.7480
3.3163
3.8376
4,3135
4.7427
5.1249
S.4614
5.7519
5.9970
6.1895
6. 3563
6.4760
6 . 5599
6.5883
6.5915
6.5744
6.5412
6.4230
6.3026
6.16B6
5,9869
S.7926
5.5776
5.3430
5.0893
4.S19B
4.5346
4.2404
3.9246
3.6026
3.2709
2.9272
2.5780
2.2317
1 . B590
1.4941
1.1235
0.7505
0.3756
n .DODO
.325
-5 . 8233
-4.8090
-3.9622
-3.B490
-2. 1545
-1.2fl39
-.4421
0.3663
1 . 1375
1.86B1
2.5551
3.1959
3.7895
4.3326
4.8266
5.2701
5.6625
6,0060
6 . 2968
6 . 5337
6.7458
6 . 8987
7.0104
7.0B06
7,0978
7.0902
7 -0596
7.0351
6,8757
6.73B2
6.5733
6.3828
6.1670
5.9312
5,6778
5.4040
5,1128
4.8074
4.4878
4. 1539
3.8109
3.4542
3.0948
2 . 7226
2.3471
1.9633
1 , 6457
1.1059
0 7B73
0 . 3967
0,0000
.330
-5.8839
-4.BB9II
-3.9010
-2.9171
-1.9757
-1,0532
-.155B
0.7012
1.5172
2. 2884
3,0115
3.6842
4.3044
4.B708
5.3826
5.8387
6.2432
6.5924
6.889,1
7.1341
7.3298
7 . 4770
7.5798
7.6351
7 . 6397
7.6203
7 . 5722
7.1412
7 . 3522
7.1945
7.8034
6 . 798E
6.5621
6.3052
6,0275
5.7315
5.4190
5.0914
4,7449
4.3940
4.0270
3.6549
3 . 267<
2 , 8749
2.4770
2.0721
1 . 6628
1.2503
O.B34B
0.4179
0.0001)
.335
-5.9455
-4.8017
-3 . B26B
-2.7886
-1.7733
- . 7077
0.1626
1.0722
1.9362
2.7517
3.510B
4.2100
4 . 8663
5.4562
5.9063
6.4575
6,8703
7.2241
7,5178
7 . 7645
7.9544
8.0933
8.1B50
8 . 2265
8.2158
B.1B21
8 . I 129
B . 0629
7.B528
7 . 6737
7.4666
7.3433
6.9730
6.6920
6.3956
6.0727
5.7343
S.38S3
5.0186
4.6414
4.2522
3.B525
3.4459
3,0316
2.6093
2.1822
1.7510
1,3168
0 . B826
0 . 4399
o.ooon
.340
-6. (1037
-4 . 8660
-3.73B6
-2 . 629U
-1 .5452
-.4940
0.5171
1.4819
2 . 3986
3.2592
4.0652
4,8021
5.4794
6 . 0931
6.6'«13
7.?. 256
7 . 5462
7.9039
8.H015
8 . 4397
8,£>221
8.7508
8.B267
S . 8562
8.B281
B , 7768
8 . 6839
8.6036
8.3780
8.1?63
. 7.9467
7 . 6886
7.4018
7.0968
6.7702
6.4261
6 . 0673
5. 6855
5.2999
4.8971
4 . 4836
4 . 0582
3.6287
3.190B
2.7459
2 . 2964
1 .8468
1 . 3849
0.9250
0 , 4622
0.0000
.345
-6.0606
-4.8418
-3.6342
-2.4469
-1.2880
-.1662
0.9116
1.93B9
2.9100
3.8193
4 .6640
5.4421
6.1489
6,7860
7 . 3523
7.84B3
8.2747
8.6361
8.9307
9.1630
9.3351
9.4500
9.511H
9.5221
9 . 4788
9.4024
9.2829
9 . 1666
B , 9285
8.7022
B.4462
8.0433
7.9703
7.5164
7.1619
6 . 7935
6.4071
6.0047
5.58B1
5.1622
4 . 7229
4 . 2757
3.8196
3 , 3565
2.8871
a. 4093
1.9286
1 . 4545
0.9624
0.4B60
o. nnoo
.350
-6.1159
-4.8077
-3.5120
-2.2388
-.9981
0.2012
1.3511
2. 4445
3.4752
4 . 436S
5.3266
6.1412
6.8802
7. 5408
B.1244
8.6315
9.0645
9.4243
9.7141
9 . 9378
10.096S
10.1953
10.2376
10.2270
10.1672
10.0617
9.9140
9 . 75S5
9.5047
9.2514
8,9667
8.4784
8 . 5328
7.9528
7,5702
7.1759
6.7SB2
6.3300
5,8872
5.4337
4,9683
4.4999
4.0139
3 . 5264
3,0329
2.5407
2.0330
1.5280
1.0208
0.5103
0.0000
,355
-6.1693
-4 . 76SS
-3.3697
-2,0016
-.6715
0,6125
1.8414
3.0060
4 ! 0999
S.1.177
6.0552
6,9103
7.6791
8.3637
i.9636
9.4802
9.9156
10.2728
10,5549
10.7656
10.9085
10.9881
11.0083
10.9732
10.8872
10.7540
10.5770
10.3737
10.1071
9.8239
9.5081
B . 9798
9.0519
8.4449
7.9841
7.5649
7.1212
6,6561
6.1926
5.7039
5.2212
4.7201
4.2114
3,6971
3.1B16
2,6471
3. 1296
1 .5973
1 . 0675
o.sasa
0.0000
-------
*ftagnetic Fields perpendicular to the z-
R (n)
t Z (n)
•,0.000
0.005
0.010
0.015
0^020
0.025
0. 030
0.035
0 .040
0.045
.0.050
' O.OSS
0. 060
' t',065
0,070
,0.075
0.080
0.085
0.090
0.095
0.100
0.105
0.110
0.115
0.120
0.125
0. 130
5\ 0. 135
rv.0.140
0.145
0. ISO
0.155
a. 160
0. 165
0.170
0.175
0.180
0. 105
0,190
0.195
0.200
0.205
0.210
0.215
0.220
0,225
0.230
0.235
0.240
0,245
0 .250
.360
-6.2211
-4.7051
-3.2046
-1.7330
-.3029
1.0742
2.3886
3.631«
4,7931
S.B702
6 . 8576
7 . 7523
8 . 5536
9,2606
9.8754
10.3988
10 .8346
11.1859
1 1 . 4569
11.6515
11.7746
11.8310
11.8252
11.7619
11.6457
11.4805
1 1 . 2727
11.0245
10.7363
10.4196
10.0704
9.5335
9.5411
8 . 9364
8.4129
7.9715
7 . 4966
7 0070
6.5032
5,9941
5.4766
4.9519
4.4185
3.8774
3 . 3324
2.7797
2.2313
1 . 6748
1.1178
0.5591
0.0000
.365
-6.2711
-4.6334
-3.0136
~1 . 4268
0.1131
1 . 5927
3.0007
4 , 3270
5 . 5629
6.702B
7.7424
8.6788
9.5109
10.2393
10.8665
11.3944
11.8270
12.1687
12.4244
12.5986
12.6975
12.7263
12.6902
12.5945
12.4441
12.2455
12.0008
11,7114
11.3929
1 1 . 0385
10.6533
10,1256
10,0139
9.4163
8 . 8584
8 . 3895
7.B6B1
7 . 3569
6.8290
6.2950
5 . 7435
5.1866
4.6245
4.0569
3 . 4850
2.9102
2 . 3336
1.7517
1 . tA77
0 . 5B34
0.0000
.370
-6.3191
-4.54611
-2.7930
-1 .0777
0 . 5H37
2.1757
3.6864
5 1043
6,4189
7 . 6256
8,7192
9 , 6976
10.5600
11.3085
11,9433
12.4698
12.8918
13.2259
13.4615
13.6113
13.6798
13.6761
13.6048
13.4720
13.2845
13.0459
12.7617
12.4352
12.0760
11.6806
11.2568
1 0 . 7420
10.4838
9.8934
9.3185
8.8160
8.2500
7.7209
7.1592
6 . 5872
6.0091
5.4253
4.8348
4.2416
3 . 6422
3 . 0335
2 . 4365
1.8285
1.2115
0.6102
0.0000
-axis of the HfrTnhol1
.375
-6 . 3654
-4.44(13
-2 . 5382
-.6796
1.1167
2.8338
4 . 4568
5.9737
7.3767
B.6497
9 . 7994
10.8196
11.7110
12.4763
13.1184
13.6428
14.0554
14.3626
14.5716
14,6899
14.7244
14.6823
14.5710
14.3967
14. 1653
13.8832
13 . 5556
13.1879
12.7821
12.3456
11.8808
11. 36B9
10.9642
10.3761
9,7913
9.2503
8.6455
8.0909
7.4917
6 . 8BB4
6.2780
5.6677
5,0421
4.4246
3.7991
3.1713
2.5391
1.9041
1.2707
0.6355
0.0000
.3BO
-6.4097
-4.3135
-2.2440
- . 224B
1.7221
3.5771
5.3237
6.9473
8.4381
9 . 7888
10.9956
12.0571
12.9752
13.7531
14.3959
14.9103
15.3039
15.5848
15.7605
15.8408
15.8334
15.7473
15.5893
15.3671
15 0877
14.7524
14.3818
13.9649
13.5139
13.0319
12.5244
11.9922
1 1 . 4685
10,8732
10,2747
9.6915
9.0522
8.4632
7 . 8294
7.1971
6.5607
5.9131
5 . 2749
4. 6158
3.9588
3,3009
2.6568
1 . 9882
1 . 3237
0.6616
0.0000
17 Call
. 3BS
-6 . 4522
-4,1624
-1.9037
0,2963
2.4117
4.4201
6.3026
8.0427
9 . f-r. 4
11 . Oi,j3
12,3227
13.4236
14.3645
15.1473
15.7867
16.2841
16.6S10
16.8975
17.031B
17.0: i4
17.0B9S
16.8710
16.6606
16.3846
16.0512
15,6691
IS . 2379
14.7700
14.2697
13.7392
13.1840
12.6067
12.0102
11.3932
10.7668
10.1392
9 . 4676
B.B378
8.1716
7,4930
6.8451
6.1572
5.4B04
4.8010
4.1191
3.4341
2.7502
2 . 0662
1.3750
0 . 6067
0.0000
.3911
-6.4937
-3 . 9B2B
-1.5092
0.8950
3.1998
5.3791
7.4113
9.2778
1 0 . 9686
12.4735
13 . 7975
14.9344
15.8913
16.6785
17.3016
17 . 7727
18.1028
18.3045
18 . 3926
18.3748
18.2551
18.0560
17.7854
17.4487
17.DS43
16.6109
16.1244
15.6015
15.0460
14.4641
13.8581
13.2330
12.5912
11.9358
11.2656
10.5925
9.8892
9,2148
8.5167
7 , 7781
7.1269
6.4036
5.7168
4.9903
4 . 2B26
3.5651
2.8524
2.1417
1.4277
0.7137
0.01)00
.395
-6.5312
-3.76?3
-1 .0507
1 . 5656
4.1041
6 . 4728
8.6716
10.6799
12.4743
14.0630
1S.439S
16.6073
17.5732
18,3526
18.9513
19.3640
19.6685
19.8136
19.8371
19.7515
19.5704
19.3039
18.9632
18.5SB3
18.0985
17.5885
17.0391
16.4557
15.8414
15.2017
14.5458
13.8700
13.1795
12.4774
11,7692
11.0508
10.3147
9.5944
8 . 8632
8.0616
7.4061
6.651B
5.9460
5,1810
4.4402
3.6984
2.9598
2.2336
1.4806
0.7515
0.0000
.4011
-6.5678
-3.5159
-.5158
2.385B
5.1462
7.7314
10.1081
12.2601
14.1978
15.8435
17.2707
18.4629
17.4300
20.1860
20.7471
21.13C2
21.3528
21.4283
21.4016
21.2159
20.9545
20,6114
20.1927
19.7114
19.1768
18,5754
17.9804
17.3315
16.6563
1S.957B
15.2437
14.5194
13.7757
13.0272
12.2743
11.5120
10,7415
9.9765
9.2094
8.3524
7.6821
6.9000
i.1576
S.37B2
4.S798
3. 8289
3 . 0556
2 . 2994
1 .5286
0.7718
0,0000
.405
-6.6824
-3.2142
0.1114
3.3174
6 . 3533
9.1760
11.7550
14.0660
16.0974
17,8462
19.3168
20.5212
21.4744
22.1804
22.7013
23.0173
23 . 1597
23.1597
23.0147
22.7631
22.4126
21.9786
21.4735
20.9065
20.2904
19.6319
18,9435
18.2240
17.4824
16.7238
15.9506
15.1670
14.3743
13.5764
12.7760
11.9716
11.1671
10.3614
9.5537
8.6597
7.9549
7.1465
6.3580
5.5568
4 . 7294
3.9563
3.1535
2.3635
1.5810
0 . 7929
0.0000
,410
-6.6348
-2 . 8538
0 . B507
4.4088
7.7596
10.8516
13.6509
16.1310
18.2819
20.1041
21 . 6063
22.8087
23 . 7289
24 . 3924
24 . 8256
25.0517
25 . 0993
24.9903
24 . 7487
24.3915
23.9377
23.4017
22 . 7985
22.1436
21.4361
20 . 6952
19.9253
19.0259
13.3200
17.4953
16.6607
15.8161
14.9683
14,1263
13.2766
12.4301
11.5869
10.7438
^ . 8952
B.9924
8.2239
7.3894
6.5537
5.7395
4.8905
4.0809
3.2540
2.4279
1.6247
0.8068
0.0000
.415
-6.6653
-2.4212
1.7281
5.6960
9.4080
12.8094
15.8523
18,5022
20,7709
22.6558
24,1751
25.3515
26.2148
26 , 7973
27,1295
27.2454
27.1839
26 . 9438
26.5782
26. 1000
25 . 5276
24.8808
24.1672
23.4056
22.6066
21 . 7758
20.9196
20.0465
19.1617
13.2696
17,3731
16.4714
15.5692
14 . 6739
13.7753
12.8810
11.9933
11.1100
10.2303
9.3597
8.4891
7 . 6269
6.7510
5,9160
5.0543
4.2022
3.3550
2.490B
1 . 6295
0,8456
O.OODO
-------
jjfHaijnetic
I-
K
1
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n
R (n
Z (n)
000
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010
015
020
025
030
035
040
045
050
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060
065
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100
105
110
115
120
125
130
135
140
145
150
155
160
165
170
175
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190
195
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205
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215
220
225
230
235
240
a 45
250
Fields perpendicular to
-6
-1
2
7
11
15
18
21
23
25
27
28
28
29
29
29
29
29
28
27
27
26
25
24
23
22
21
20
20
19
IB
17
16
15
14
13
12
11
10
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6
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5
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n
420
6933
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4
9
13
17
21
24
26
28
30
31
31
32
32
32
31
31
30
29
28
27
27
26
24
23
22
21
20
19
IB
17
16
15
14
13
12
11
10
9
9
8
7
6
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7200
2616
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33
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29
28
27
26
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24
22
21
20
19
18
17
16
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14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
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the z-gxis of the HeJntio!
.430
.7441
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38
38
38
38
37
36
35
34
33
32
31
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28
27
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24
23
22
21
20
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
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1
9
17
23
29
34
37
39
41
42
42
42
42
41
40
39
38
36
35
34
32
31
29
28
27
25
24
33
22
20
19
18
17
16
14
13
12
11
10
9
8
7
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37
35
34
32
31
29
28
26
25
24
22
21
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17
16
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10
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-------
Magnetic Fields perpendicular to the z—iixi& of the Kelwholtz Co'ii
R («) .480 .483 .490 .495 .500
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0
0.
0
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0
0
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. 140
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, 160
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. 175
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137
121
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98
88
80
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47
47
44
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26
24
22
21
19
18
17
15
14
13
11
10
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. 0357
.6331
.3333
.4247
.6225
.5984
.4211
.9957
. 0544
.9563
.4903
.4993
.7447
.4315
.8422
.6574
.9049
.4676
.4106
.4895
.8022
.3567
.0385
.8983
.8801
.9797
.2039
.4676
.8474
.2963
.8202
.3901
.0134
.6926
.4098
.1689
.9611
.7846
.6340
.5116
.4012
.3125
.2384
.1770
.1237
.0725
. 038(1
.0000
-6
93
178
234
244
217
130
157
139
122
109
98
89
80
74
68
63
58
54
49
47
44
41
38
36
33
31
29
27
26
24
22
21
19
18
16
IS
14
13
11
10
9
8
7
6
S
A
3
2
1
0
.9190
. 4S12
.7!iSO
.0414
.1793
.3967
.7437
.HH 19
.1407
. 0659
.5838
.3094
.2534
.9042
.5985
.7434
.3957
.8107
.6010
. 6238
.3037
.2H09
.3861
.7070
.2531
.9486
.7998
.7846
.8835
. 0933
.3800
. 7637
,2153
.7416
.3150
.9503
.6268
, 3535
. 1168
.9150
.7417
.5957
.4729
.3700
.2901
.2169
. 1595
.0963
.0761
. 0352
.0000
-------
Magnetic Fields parallel to the z-axis of the HelMholtz Coil
R (n)
Z (M)
0.000
0.005
0. 010
0.015
0 . 020
0.025
0. 030
0.035
0.040
0.045
0. 050
0.055
0.060
. 0.065
0. 070
0.075
0.080
0.085
0. 090
0.095
(1.100
0.105
0.110
0.115
0.120
0.125
0.130
0. 135
0.140
0.145
0.1.50
0.155
0. 160
0.165
0. 170
0.175
0 . 180
0.185
0 . 190
0.195
0.200
0.205
0.210
0.215
0.220
0.225
0 . 230
0 . P35
0.240
0.245
0 . 250
.000
51 .0275
51.2233
51 .4109
51.5902
51.7614
51.9244
52.0794
52.2267
52.3661
52.4978
52.6222
52.7391
52.8489
52.9519
53.04131
53.1377
53.2209
53.2981
53.3694
53.4350
53 . 4952
53.5504
53.6005
5316460
53.6871
53.7241
53.7571
53.7B66
53.8126
53.8355
53.8554
53.8728
53.8876
53.9003
53.9110
53.9199
53.9272
53.9332
53.9379
53.9416
53.9444
53.9466
53.9481
53.9491
53.9498
53.9502
53.9504
53.9505
53.9506
53.9506
53.9506
,005
51 . 0293
51.2251
51.4127
51.5921
51.7634
51.9265
52.0814
52.2285
52.3679
52.4997
52.6239
52.7409
52.8507
52.9535
53.0496
53.1392
53.2225
53.2996
53.3708
53.4363
53.4965
53.5515
53.6017
53.6471
53.6881
53.7251
53.7580
53.7874
53.8134
53.8362
53.8561
53.8734
53.8882
53.9008
53.9114
53.9202
53.9275
53.9335
53.9381
53.9418
53.9446
S3. 9467
53.9482
53.9492
53.9498
53.9502
53.9505
53.9506
53.9506
53.9506
53.9506
.010
51 .0366
51 . 2322
51.4195
51.5986
51.7695
51 . 9324
52.0874
52.2345
52.37.16
52.5053
52.6294
52.7462
52.8559
52.9586
53.0546
53.1440
53.2270
53.3039
53.3750
53.4404
'53.5004
53.5553
53.6051
53.6504
53.6913
53.7279
53.7608
53.7899
53.8158
53.8383
53.8581
53.8752
53 . 8898
53.9023
53.9127
53.9214
53 . 9286
53.9344
53.9389
53.9425
53 . 9452
53.9471
53.9485
53 . 9494
53.9500
53.9504
53.9505
53.9506
53.9506
53.9506
53.9506
.015
51 . 0466
51.2423
51.4297
51.6088
51.7796
51.9425
52.0973
52.2441
52.3832
52.5147
52.6386
52 . 7552
52.8646
52.9671
53.0627
53.1519
53.2347
53.3113
53.3821
53.4472
53.5068
53.5614
53.6110
53.6559
53.6964
53.7329
53 . 7653
53.7942
53.8196
53.8420
53.8614
53.8782
53.8926
53.9048
53.9149
53.9234
53.9303
53.9358
53.9402
53.9436
53.9461
53.9479
53.9491
53.9499
53.9504
53.9506
53.9507
53.9506
53.9506
53.9506
53.9506
.020
51 061 1
51.2568
51.4441
51.6231
51.7938
51.9565
52.1111
52.2578
52.3965
52.5278
52.6514
52.7677
52.8769
52.9789
53.0743
53.1630
53.2454
53.3216
53.3919
53.4567
53.5159
53.5700
53.6191
53.6636
53.7037
53.7396
53.7717
53.8001
53.8251
53.8470
53.8661
53.B825
53.8964
53.9082
53.9181
53.9262
53.9327
53.9379
53.9420
53.9451
53.9473
53.9486
53.9499
53.9505
53.9508
53.9509
53.9508
53.9507
53.9506
53.9506
53.9505
.025
51 . 0829
51 . 2V7EI
51.4640
51.6420
51.8121
51.9746
52.12139
52.2753
52.4138
52.5447
52.6679
52.7CI3CI
52.8925
52.9942
53.0890
53.1773
53.2592
53.3350
53.4050
53.4689
53.5275
53.5810
53.6296
53.6736
53.7131
53.7484
53.7799
53.8078
53.8322
53 . 8536
53.8720
53.8879
53.9013
53.9126
53.9220
53 . 9297
53.9358
53.9406
53.9442.
53.9469
53.9488
53.9501
53.9509
53.9512
53.9513
53.9512
53.9510
53.9508
53.9506
53.9505
53.9504
. 030
51 .1027
51.2982
51.4854
51.6641
51.8345
51.9966
52.1507
52 . 2968
52.4349
52.5654
52.6882
52.8035
52.9117
53.0129
53.1071
53.1948
53.2761
53.3512
53.4203
53.4837
53.5418
53.5945
53.6424
53.6857
53.7244
53.7591
53.7899
53.8170
53.8408
53.8615
53.8793
53.8945
53.9074
53.91BO
53.9268
53.9339
53.9395
53.9437
53.9469
53.9492
53.9507
53.9516
53.9520
53.9521
53.9519
53.9516
53.9512
53.9508
53.9505
53.9503
"53.9503
.(•35
51. 1300
51.3254
51.5124
51.6909
51.8610
52. 0229
52.1766
52 . 3222
52.4599
52.5898
52.7121
52.8270
52.9346
53. 0350
53. 1286
53.2152
53.2960
53.3704
53.4387
53.5013
53.5S86
53. 6106
53.6576
53.6999
53.7380
53.7717
53.8010
53.8279
53.8510
53.8709
53.8879
53.9023
53.9144
53.9243
53.9325
53.9388
53.9438
53.9475
53.9500
53.9518
53.9528
53.9533
53.9533
53.9530
53.9526
53.9520
53.9514
53.9507
53.9503
53.9501
53.9500
.040
51. 1602
51.3557
51.5430
51.7217
51.8918
52.0532
52.2065
52.3517"
52.4889
52.6182
52.7398
52.8540
52.9609
53.0606
53.1533
53.2395
53.3192
53 . 3926
53.4600
53.5218
53.5780
53.6290
53.6751
53.7165
53.7535
53.7864
53.8153
53.8406
53.8627
53.8816
53 . 8977
53.9111
53.9224
53.9316
53.9389
53.9445
53.9487
53.9517
53 . 9538
53.9548
53.9552
53.9552
53.9545
53.9540
53.9530
53.9522
53.9514
53.9507
53.9501
53.9499
53.9496
.045
51.1967
51.3920
51.5788
51.7571
51.9267
52.0878
52.2406
52.3852
52.5217
52.6504
52.7/14
52.8847
52.9908
53.0896
53.1816
53.2667
53.3455
53.4178
53.4842
53.5449
53.6001
53.6500
53.6950
53.7352
53.7711
53.8028
53.8307
53.B549
53.8758
53.8937
53.9088
53.9213
53.9315
53.9397
53.9461
53.9508
53.9542
53.9564
53.9576
53.9580
S3. 9578
53.9572
53.9562
S3. 9550
53.9537
53 . 9525
53.9513
53.9504
53.9496
53.9492
53.9483
.050
51.2433
51.4371
51.6216
51.7977
51.9659
52.1266
52.2788
52.4229
52.5587
52.6866
52.8067
52.9193
53.0244
53.1223
53.2132
53.2973
53.3748
53.4461
53.5115
53.5708
53.6247
53.6735
53.7171
53.7562
53.7908
S3. 8213
53.8479
53.8709
53.8906
53.9072
53.9211
53.9325
53.9416
53.9487
53.9540
53.9578
53.9602
53.9615
53.9619
53.9615
53.9606
53.9593
53.9577
53.9560
53.9542
53.9526
53.9511
53.9499
53.9490
53.9484
53.9482
.055
51.2873
51.4810
51.6656
51.8416
52.0095
52. 1696
52.3212
52.4647
52.5996
52 . V2A8
52.8460
52 . 9576
53.0616
53.1584
53 . 2482
53.3312
53.4075
53.4775
53.5414
53.5995
53.6521
53.6994
53.7418
53.7793
53.8126
53.8416
53.8669
53.8885
53.9068
53.9221
53.9347
53.9448
53 . 9526
53 . V585
53.9627
53.9653
53.9667
53.9670
53.9665
53.V652
53.9635
53.9614
53.9591
S3 . 9568
53.9546
53 . 9525
53.9507
53 . 9492
53.9480
53.9473
53.9471
-------
^'Magnetic Fieldt parallel to the z~axi5 of th& Helhholt? Coil
^
R <«)
2 <«)
0.000
0.005
0.010
0.015
0 . 020
1). II 25
0.030
0.035
0.040
(1.045
n.oso
0.055
0.060
0.065
0 . (170
0.075
0.080
0.085
0 . 090
0.095
0.10Q
0.105
11.110
0.115
(J.120
0.125
0.130
0.135
0.140
0.145
0.150
0.155
0 . 160
0.165
0.170
0.175
0 . 180
0.185
0.190
0.155
0.200
0.205
0.210
0.215
0.220
0.225
0.230
0.235
0,240
0.24S
0.250
.060
51.3322
51 . 5267
51.7123
51.8892
S2.0574
52 ..2 170
52 . 3680
52.5105
52.6447
52.7709
52 . 8892
52 . 9997
53.1026
53.1982
53 . 2867
S3. 3683
53.4433
53.5119
53.5744
53.6310
53.6B21
S3 . 7278
53.7686 '
S3.B048
53 . 8364
53 . B639
53.887S
53.9077
53.9246
53.9383
S3 . 9495
53.9581
53.9646
53.9691
53.9720
53 . 9735
53.9737
53 , 9729
53.9713
53.9691
53.9664
53 . 9635
53.9605
53.9576
53.9547
53 . 9S22
53.9499
S3.94B1
53.9468
S3. 9459
53.9457
.065
51 . 3853
51.5797
51.7653
51.9420
52.1099
52.2687
52.4187
52.5610
52.6941
52.8192
52.9364
53.0457
53.1474
53.2416
53.3287
S3.40d9
53 . 4824
53.5494
53.6104
53 . 6653
53.7148
53.7588
53.7979
53.8323
53 . 8623
53.8880
53.9100
53.9285
53.9436
53 . 9559
S3 . 9654
S3. 7725
53 . 9776
S3.9B06
53.9820
53.9821
53.9810
53.9790
53.9763
53.9730
53.9694
53.9656
53.9618
53.9581
53.9546
53.9515
53.9480
53.9467
53.9451
53.9441
53.9438
. 070
51.4405
51.63S1
51.8214
51.9908
52.166B
52.3250
52.4744
52.6152
52.7476
52 8717
52 . 9U77
S3. 0956
S3. i960
53.2888
53.3743
53.452V
53.5248
53.5901
53.6493
53.7025
53.7501
53 . 7924
53 . 8297
53.8621
53.8902
53.9142
53.9346
53.9SOB
53 . 9642
53.9747
53 . 9652
53.9878
53.9912
53 . 9927
53.9926
53.9912
53 . 9B88
53.9855
53.9814
53.9770
53 . 9723
53.9675
S3 . 9628
53.9583
53 . 9542
S3. 95 OS
53.9474
53.9448
53.9430
S3. 9419
53.9415
.075
51.5116
51 7052
51.8887
52 . 0628
52.2284
52.3B58
52.5344
52 . 6742
52.8055
• 52.9283
53.0430
53.1495
53.2484
53.3397
53.4236
53.5004
53.5705
53.6340
53.6913
53.7426
53.7882
53 . 8285
53.8637
53.8943
53.9202
53.9421
53.9603
53.9749
53 . 9862
53.9947
54.0006
54. D 042
54. 0058
54.0055
54,0037
54.0008
53.9968
53.9919
53.9866
S3. 9810
53.9751
53.9693
53.9636
53.9583
53.9535
53.9491
53.9454
53.9424
53.9402
53.9389
53.9385
.OHO
51.5766
51.7701
51.9542
52.1291
52.2947
52.4513
52 . 5989
52.7377
52.8678
52 . 9893
53.1025
53.2076
53.3048
53.3943
53.4764
53.5514
53.6196
S3. 6811
53 . 7363
53.7855
S3. 8290
53.8671
53.9001
53.9285
53.9523
53.9720
53.9879
54.0004
54.0097
54.0161
54.0199
54,0214
54.0210
54.0189
54.0154
54.0107
54.0(150
53 . 9987
53.9919
S3. 9850
53.9778
53.9708
53.9640
53.9577
53.9520
S3. 9470
S3. 9428
53.9394
53.9370
53.9355
53.9350
.OBS
51.6801
Si . 0667
S2.04U5
52.2053
52.36S2
52.5215
S2.66B1
52.8057
52.9345
S3. 0546
53. 1663
53.2698
53.3652
53.4529
53.5331
53.6061
53.6721
53.7314
53.7844
53.8314
53.8725
53.9UB3
53.9390
53.9649
S3.9B64
S4.0038
54.0174
54.0275
54.0344
54.0385
54.0401
54.0396
54.0371
54.0328
54 . 0274
54.0208
54.0134
54.0054
53.9970
53 . 9BB6
53.9801
53.9719
53.9640
S3.9S67
53.9501
53.9444
53.9395
53 . 9357
53 . 9330
53.9313
53.9306
. II9II
Si .7266
51 9104
52.1008
52.2743
S2.437B.
SS.5967
52.7421
52.8784
53.0059
53.1244
53.2345
53.3361
53.4297
53.5154
53 . 5935
53.6643
53.7281
53.7851
53 . 8357
S3.B802
53.9190
53.9521
53 , 9B03
54. D 036
54.0225
54.0374
54.0484
54.0560
54.0606
54.0622
54.0614
54,0585
54.0537
54.0474
54.0398
54.0312
54.0219
54.0121
54.0021
53,9920
53.9820
53.9725
53.9634
53.9551
53 . 9476
S3. 9410
53.9355
53.9311
53 . 9279
53.9260
53.9254
OV5
51 .13163
52.0077
52 . 1B63
52 . 3S.55
52.51B9
52.6767
52.8309
52 . 9559
53.0818
53.1988
53.3070
53.4069
S3.49B4
53.5820
53 . 6570
53.7263
53.7876
53.8421
53.8901
53.9320
53.9680
53.9978
54.0240
54.0446
5". 0608
54 . 072B
54.0811
54.0860
54.0878
54.0873
54.0836
54 . 0782
54.0710
54.0624
S4.0S25
54.0418
54.0304
54.01B7
54.0060
53.9910
53.9035
53,9726
53 . 9622
53.9527
53.9445
53.9368
53.9306
53.9256
53.9221
53.9195
53.9192
.ill!)
51 .8999
52.0883
52.2666
52.4373
S2.6027
52.7618
52.9048
53.0384
53.1627
53 . 2778
53.3842
53.4819
53,5713
S3 . 6526
53.7260
53.7919
S3.BS07
53.9025
53.9478
53,9868
54.0200
54,0476
54.0701
54.0B7B
54.1010
54.1102
54.1156
54.1175
54.1165
54.1129
54.1067
54 . 0987
54.0889
54.0777
54.0654
54.0525
54.0389
54 . 0250
54.0112
S3 . 9977
53.9845
S3 . 9720
53.9602
53.9495
53 . 9399
S3. 9316
53.9246
53.9191
53.9151
53.9127
53.9119
.105
51. 9947
52. 1859
52.3661
52.5349
52.6916
52.8409
52.9938
S3. 1258
53.24B4
53.3616
53.4660
53.5616
53 . 6486
53.7274
53.7981
S3.i6i5
53.9173
53 . 9664
54.0087
54.04-4?
54.0748
54.0994
54.1187
54.1332
54.1433
54 . 1 493
54.1515
54.1505
54.1464
54 , 1397
54.1307
54,1197
54.1081
54.0934
54. U 785
54.0631
54.0472
54.0311
54.0152
53.9997
53.9847
53.9705
53.9574
53.9453
53.9346
53.7848
53,9176
53.9114
53.9070
53.9043
53.9034
.110
52.0893
52.2737
52.4491
52.6187
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52.9479
53,0880
53.2185
53.3391
53.4504
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53.6457
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54.1414
54.1259
54.1093
54.0917
54.0736
54.0552
54.0368
54.0186
54.0011
53.9842
53.9683
53.9536
53.9402
53.9283
53.9179
53.9092
53.9024
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53.8945
53.8935
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52.1958
52.3783
52.5511
52.7187
52.8858
53.0492
53.1876
53.3164
53.4351
53.5442
53.6440
53.7347
53.8166
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53.9551
54.0124
54.0621
54.1047
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54.1698
54.1932
54.2108
54.2232
54.2308
54.2340
54.2330
54.2283
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54.2096
54.1963
54.1809
54.1636
54.1450
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54.1048
54 . 0839
54.0628
54.0419
54.0215
54. 0017
53.9828
53.9650
53.9406
53 . 9337
53.9205
53.9090
53 . 8994
S3.H919
S3 . 8866
S3 . 8B33
53.8822
-------
1 Magnetic Fields parallel to the z-axis
1 R (n)
1 2
r
1 0.000
I 0.005
I 0 .010
1 0.015
| 0.020
| 0,025
f 0,030
§ 0.035
i 0.040
S 0.045
1 0.050
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t] 0 . 060
If 0.065
B 0.070
m 0.075
1"- Q . 080
5 O.OB5
S| 0.090
i 0.095
'•' 0.100
i 0.105
0.110
0.115
0 . 120
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0 .130
0.135
0 . 140
0.145
0.150
0.155
0.160
0.165
0.170
0,175
n . IBO
0.185
0.190
0.195
0 .200
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0.210
0.215
0 . H20
0.225
0 . 230
0.235
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0.245
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52.3077
52.4901
52.6624
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52.9917
53.1515
53.2930
53.4199
53.5364
53.6432
53.7402
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53.9075
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54,0399
54.0938
54.1402
54.1793
54.2114
54.2371
54.2567
54.2706
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54.2775
54.2691
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54.2259
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54.1177
54.0939
54.0700
54.0465
54 . 8235
54.0014
53.9803
53.9606
53.9424
53.9259
53,9111
53.8906
53.8881
53.8799
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53.87D4
53.8693
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52.4253
52.6080
52.7798
52.9440
53.1038
53.2601
53.4040
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53.6431
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53.9272
54.0032
54.0704
54.1290
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54.2093
54.1838
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54.1304
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of the Ho I who It ?. Cir
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54.2548
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54.1771
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54.0346
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55.0172
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55.1049
55.1321
55.1489
55.1559
55.1535
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55.1233
55.0967
55.0631
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54.8139
54.7520
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54,6213
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54.4850
54.4160
54.3474
54.2795
54.2127
54.1477
54.0846
54.0243
53.9656
53.9124
53.8617
53.8149
53,7723
53.7341
53.7006
53.6719
53.6481
53.6295
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53.6054
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54.0023
54.1839
54.3541
54.5044
54.6332
54,7519
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54.8914
55.0516
55.1241
55.1807
55.2248
55.2585
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55.2892
55,2895
55.2807
55.8625
55.2363
55.2026
55.1618
55.1147
55.0618
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54.9418
54.8759
54.8068
54.7354
54.6619
54.SB74
54.5121
54 . 4367
54.3618
54 . 28BO
54.3154
54.1449
54,0767
54.0114
53.9492
53,8906
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53.7857
53.7400
53.69BB
53.6631
53.6320
53.6065
53 . SB65
53.5722
53.5636
53.5608
-------
'Magnetic Fields parallel to the z-axis of the; Helnholtz Coil
R CM) .180 .185 ,191) .195 .2011
.210
.215
.220
.230
.235
0.000
0,005
0.010
0.015
0.020
0.025
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0.035
0.040
0.045
0.050
0.055 '
0. 060
0.065
0.070
0.075
0.080
fl.OBS
0.090
0,095
0.100
0.105
0. 110
0.115
0.120
0.125
0.130
0.135
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0.145
0. 150
0 . 1 55
fl.160
0.165
0.170
0.175
0.180
0.1B5
0.190
0.195
0.200
0.205
0.210
0.215
0.220
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0.230
0.235
0.240
0.245
0.250
54.2046
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54.5521
54.7026
54.B334
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55.0129
55.0603
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55.4165
55,4314
55.4353
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55.3124
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55.2089
55.1484
55.0827
55.0128
54.9390
54.8624
54.7833
54.7026
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54.4563
54.3749
54.2947
54.2161
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54.0662
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53.5884
53.5605
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53.5240
53.5147
53.5116
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54.5986
54.7631
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55.0435
55.1544
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54.1321
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55.2591
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55.4338
55.6153
55.6644
55.7166
55.7429
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55.7601
55.7466
55.7251
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55.6521
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53.8461
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53.6959
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56.07117
56,1479
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54.1811
54.0711
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53.3929
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53.2933
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55.6470
55.8218
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56.1123
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56.4513
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54.8062
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54.4124
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54.1645
54.0457
53.9341
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53.6304
53.5424
53.4616
53.3884
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53.2658
53.2171
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53.1454
53.1229
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55.9263
56,0996
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56.3Q60
56.5349
56.5931
56.6674
56.6497
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56.7377
56.7967
56.7702
56.7435
56.7018
56.6413
56 . 5776
56 . 4976
56 . 4067
56.3059
56.1968
56.0797
55.9557
55.8260
55.6911
55.5S20
55.4109
55.2672
55.1224
54.9771
54.8325
54 . 6897
54.5479
54.4094
54,2746
54.1440
54.0181
53 . 8976
53.7Q30
53.6751
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53.4800
53.3941
53.3161
53.2467
53.1858
53.1341
53.0914
53.0581
53.0340
53.0197
53.0153
56.2180
56 . 3943
56.5455
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56.7841
56.8717
56.9462
56.9542
57.0141
56 . 9985
57.0428
57.0030
56 . 9659
56.9154
56 . 8489
56 . 7692
56.6775
56.5749
56.4622
56.3405
56.2111
56.0748
55.9315
55.7855
55.6347
55.4811
55 . 3257
55.1691
55.0125
54 . 8569
54.7029
54.5514
54.4032
54.2587
54.1191
53.9847
53.8561
53.7340
53.6188
53.5114
53.4113
53.3201
53.2374
53,1629
53.0991
53.0441
52.9987
52.9632
52.937V
52 . 9225
52.9174
56.5331
56.7033
56.8520
56.9781
57.0819
57.1653
57.2290
57.2705
57.2885
57.2800
57.2992
57.2462
57.1975
57.1380
57.0602
56.9680
56.8643
56.7490
56.6236
56.4887
56.3465
56.1968
56.0417
55.8817
55.7180
55.5516
55.3835
55,2150
55.0464
54.8792
54.7140
54.5516
54,3930
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53,8092
53.6793
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53.4423
53,3366
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53.0730
53.0045
52.9463
52.8982
52.8607
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52.8176
52.8123
56 . 8578
57.0270
57.1729
57.2953
57 . 3956
57.4750
57 . 5289
57.5641
57 . 5762
57.5845
57.5658
57.5004
57.4398
57.3694
57 . 2787
57.1753
57.0SB2
56 . 9295
56.7903
56.6421
56.4856
56.3222
56.1532
55 . 9793
55.8019
55.6222
55.4409
55.2593
55.0783
54.8989
54.7218
54.5481
54.3802
54.2140
54.0550
53 . 9023
53 . 7565
53.6183
53.4880
53 . 3665
53.2540
53.1512
53,0577
52 . 9747
52.9022
52.8405
52.7896
52.7500
52.7215
52.7044
52 . 6987
57.2005
57.3687
57.5102
57.6293
57.7240
57 . 7957
57.7934
57.8715
57.8767
57.9062
57 . 8428
57 . 7663
57.6913
57.4102
57.5070
57.3901
57 . 2594
57.1164
56 . 9626
56.7998
56.6330
Sfc.4505
56 . 2666
56.0783
55 . 8866
55 . 6926
55.4974
55.3022
55.1084
S4.91SB
54 . 7263
54.5407
54.3598
54.1842
54.0149
53 . B523
53.6974
S3. 5505
53.4122
53 . 2832
53.1639
53.0548
52 . 9566
52.0682
52.7915
52 . 7262
52.6724
S3. 6304
52.6005
52.5821
52.5761
-------
Magnetic Fields parallel to the z~axis
S (n)
Z CM)
0.000
0.005
0.010
0.015
0,020
0.025
0.030
0.035
0.040
0.045
0.050
0.055
0.060
0.065
0 . 070
0.075
0 . 080
0.085
0. 090
0.095
0.100
0.105
0.110
0.115
0.120
0.125
0. 130
0.135
0.140
0.145
0.150
0.1S5
0 . 160
0.165
0.170
0.175
0.180
0.185
0.190
0.195
0.200
0.205
0.210
0.215
o . aao
0.225
0.230
0.235
0.240
0.245
0.250
.240
57.5588
57.7244
57.8647
57.9787
SB. 0641
58.1331
58.0725
58.1928
58 . 1886
58.2075
58.1302
58.0445
57.9552
57.8610
57.7451
57,6140
57,4681
57,3098
S7.140B
56.9621
56.77SS
56,5818
56.3824
56.1792
5S.971S
55.7627
55 . 5S28
55.3433
55.1352
54 . 9296
54 . 7372
54.5288
54 . 3359
54.1490
53 , 9688
53 . 7960
53.6308
53 , 4755
53.3291
53.1923
53.0659
52.9504
52.8460
52.7538
52.6739
52,6027
52,5460
53.5015
52.4696
53.4505
52 . 4442
,245
57,9347
58.0989
58.2357
58.3465
58.4336
58.4877
58.5223
58.5305
58.5173
58.4792
58.4281
58.3357
58.2314
58.1225
57.9934
57.8456
57.6844
57.5101
57.3245
57.1296
56.9261
56.7149
56.5001
56.2799
56.0568
55.8321
55.6069
55.3822
55.1594
54.9394
54.7234
54.5123
54.3066
54.1077
53.9163
53.7329
53.5581
53.3928
53.2376
53.0932
52.9591
52.8369
52.7266
52.6283
52.5419
52.4700
52.4097
52.3629
52 . 3294
52.3092
52.3022
.250
58.3407
58.5078
58 . 6273
58 . 7327
58.8107
58.8617
58.8863
5B.BB53
58.8596
58,8106
5B.73B9
58.6405
58.5207
58 . 3954
58.2520
5B.OB56
57.9090
57.7174
57.5144
57,3014
57.0808
56.8528
56.6195
56.3821
56.1420
55.9004
55.6592
55.4185
55.1803
54.9455
54.7149
54.4903
54.2716
54.0600
S3 . 8568
S3 , 4623
53 . 4770
53.3019
53 . 1377
52.9846
52.8432
52,7141
52 , 5976
52.4940
52.4035
52 . 3265
52 . 2634
52,2139
53.17H6
52.1571
52.1503
of the Helnhnltz Cull
.255
58.7495
SO . 9074
59.0410
59.1381
59.2(196
59 . 2525
59 . 2693
59.2571
59,2193
59.1571
59.0706
58 . 9596
58.8240
58.6B05
58.5213
58.3345
58.1419
57.9315
57.7104
57.4784
57.2390
56,9924
56.7406
56.4849
56 . 2269
55 . 9677
55.7090
55.4521
55.1974
54.9469
54.7016
54 . 4623
54.2300
54.0055
53 . 7898
53.5835
53 , 3879
53.2023
53,0286
52 . 8673
52.7175
52.5812
52 . 4583
52,3490
52.2538
52,1726
52.1059
52.0542
52.0168
51.9943
51.986B
.260
59.1858
59 . 3436
59.4703
59 . B653
59,6397
59.6641
59.6686
59.6460
59.5974
59.5201
59.4193
59.2936
59.1419
SB . 9785
SB. 8015
58.5932
58.3B34
58.1515
57.9119
57.6606
57 . 3775
57,1345
56.8631
56.5800
56.3111
56 . 0335
55.7564
55.4817
55.2103
54.9435
54.6824
54 . 4279
54.1814
53.9434
53.7147
53.4964
S3.2B87
53.0934
52.9096
52 . 7389
S2.5B16
S2.43B5
52,3083
52.1933
52.0927
52.0073
51.9373
51.8828
51.8436
51.8199
51.8119
.?65
59.6465
59. BO 15
S.9,9243
60.0139
60.0709
60.0964
60.0910
60.0SS.5
59.9917
59.9010
59.7B40
59.6417
59 . 4753
59.2900
59,0927
58 . 8622
58 . 63.16
58.3790
SB. 1200
57.8470
57.5654
57 . 2793
56.9867
56.6913
56.3941
56.0970
55.8008
55.5077
55.2184
54.9345
54.6570
54 . 3865
54.1251
53 . 8729
53.6309
53.3991
53.1807
52.9739
52.7804
52.6003
52.4345
52.2832
52.1467
52.0256
51.9201
51,8303
51.7564
51.6991
51.6579
51.6335
51.6249
.270
60.1321
60.28!j7
60.4054
60 4873
60.5358
60.S369
60.5339
6U.4B5B
60,4070
60.3002
60.1740
60.0057
59.1233
59.6157
59.3953
59.1424
58.8926
58.6154
58.3347
58.0386
57.7351
57.4256
57.1114
56.7943
56.4759
56.1584
55.8419
55.5292
' 55.2212
54.9191
54.6244
54 . 3378
54.0602
53.7935
53.5377
53.2936
53.0622
52 . 8728
52.6403
52.4505
52.2756
52.1164
51.9731
S1.B456
51.7342
51.6404
51.5629
51.5026
51.4594
51.4335
51.4247
.275
60.6446
60.7952
60,9085
60.9847
61.0247
61.0298
61.0003
60.9373
60.8321
60.7186
60.5673
60.3989
60.1816
59 . 9554
59,7095
59. 17*3
59.160'/
SB.B607
sa.sssa
58.2354
57.9072
57.5739
57 . 2364
56 . 8969
56.5557
56.2159
55.8791
55 . 5447
55.2184
54.8971
54.5842
54.2808
53.9867
53,7047
53.4342
53.1769
52.9325
52.7029
52 . 4879
52.2889
52.1044
51.9371
51 . 7867
51.6529
51,5360
51.4368
51.3565
51,2928
51.2476
51.2204
51.2113
.280
61.1800
61.3263
61.4403
61.5099
61.5409
61.5338
61.4904
61.4001
61.3046
61 . 1587
60.9843
60.7834
60.5562
60,3071
60.0355
59.7387
59.4380
59.1143
58.7829
58 . 4369
58.0849
57.7214
57.3618
56 . 9973
56 . 6254
56.2702
55.9109
55 . 5563
55.2081
54 . B672
54.5358
54.2143
53.9038
53.6048
53.3199
53.0483
52.7914
52.5469
52.3232
52.1134
51.9206
51.7447
51.5865
51,4467
51.3243
51.2205
51,1354
51.0694
51.0216
50,9931
50.9836
.285
61,7509
61.8990
62.0022
62 . 0672
62 . OB42
62.0640
62.0077
61.9126
61.7815
61.6191
61.4247
61.2005
60,9488
60 . 6738
60.3750
60 . 0563
59 . 7246
59 , 3?57
59.0158
58 . 6425
58.2652
57.8751
57.4866
57.0
-------
Magnetic Fields parallel to the i-axin of the HelnholTZ' Coil
R (M> .300 .305 .310 .315 .321) .325
. 330
.335
.340
.345
.350
.355
0.000
o.nns
0.010
0.015
0 . 020
0.025
0.030
0,035
0.040
0.045
0,050
0.055
0.060
0.065
0. 070
0.07S
0.080
0.085
0.090
0.095
0.100
0.105
0,110
0.115
0.120
0.125
0.130
0.135
0. 140
0.145
0.150
0.155
0, 160
0.165
0.170
0.175
0 . 180
0.185
0 . 1.90
0.195
0.200
0.205
0.210
0.215
0.220
0,225
0.230
0.235
0,240
0.245
0 .250
63.6653
63.0003
63.8828
63.9197
63.9042
63.8409
63.7319
63.5779
63.3819
63.1632
62,8622
62.570D
62 . 2328
61,8690
61 , 4785
61.0710
60.6423
60.2011
59 . 7456
59.2773
5B.B1S3
58.3399
57.8529
57 . 3778
56.9048
56.4376
55.9773
55.5262
55,0860
54.6572
54.2421
S3.B414
53.4567
S3. 0885
52.7376
52.4052
S2.0917
51.7976
51.5236
51.2685
51.0380
50.8264
50.6371
50,4701
50.3233
50,1998
50.0983
50.0193
49.9630
49.9289
49.9178
64 . 375S
64.5072
64.5877
64.6110
64.5816
64.5014
64.371B
64.1942
63 . 9735
63.7102
63.4075
63.0694
62,7022
62,3025
61.8729
61 , 4285
60,9681
60 . 4881
59 . 9983
59,4927
58 . 9993
58,4913
57 , 9695
57 . 4597
56.9408
56 . 4623
55,9740
55 , 4958
55.029S
54,5768
54,1383
53.7166
53.3217
52,9234
52,5560
52,2072
51.8793
51.5709
51.2844
51.0196
50.7769
SO , 5563
50 , 3S84
50.1835
SB . 0315
49.9026
49.7971
49.7160
49,6560
49.6208
49.6089
65.1335
65.262*
65.33?7
65.3437
65 . 2992
65.1999
65.04B5
64.8446
64 . 5963
64.3028
63,9663
63 . 5934
63 . 18BS
62 . 7527
62.2909
61.8070
61.3033
60.7045
60 . 2552
59.7090
59.1826
58.6393
58.0821
57.5330
56.9525
56.47Q5
55.9604
55.4540
54.9609
54.4831
S4.0213
53,5769
53.1509
52.7439
52 . 3582
51.9926
51.6484
51.3269
51.0275
50.7506
50.4977
50.25J9
50.0617
49,8794
49.7214
49.5872
49.4774
49 . 3920
49.3309
49.2942
49.2819
65 . 9363
66. 0605
66.1218
66,1205
66.0597
65.9391
65.7624
65.5326
65.2517
64.9244
64.5536
64.1435
63.6990
63.2224
62.7192
62,1935
61.6493
61, 0972
60.5185
59.9342
59 , 3643
58.7829
58.1899
57.5983
56.9466
56.4833
55.9353
55.3996
54.B7B9
54 . 3746
53.8882
53.4200
52.9737
52.5469
52.1422
51.7599
51,4004
51.0640
50.7519
50 . 4635
50.1997
49.9604
49.7461
49.6570
49.3921
49.2529
49.1389
49.0500
48.9B63
48.9484
48.9360
66 . 7889
66.9088
66.9609
66.9464
66.8666
66 . 7229
66.5189
66.2592
65.9447
65.SH03
65.1698
64.7177
64.2319
63.7107
63.1642
62 . 5940
62.0035
61.4004
60.7859
60.1627
59.5439
58.9213
58,2922
57 . 6561
56,9298
56.4752
55 . 8979
55.3302
34.7B16
54.2496
53.7477
53.2475
52.7785
52.3313
51.9078
51,5081
Si , 1338
SO . 7B22
50.4562
50 . 1565
49.8821
49.6329
49.4104
49.2138
49.0432
48.8989
48.7805
48.6Q82
48.6228
48.5B31
48,5701
67.6966
67. BUS
67.8539
67.B23B
67.7230
67.5570
67.3219
67,0272
66.6756
66.2708
65,8184
65.3220
64.7903
64.2202
63.6249
63.0069
62.3658
61.7162
61.0381
60.3218
59.72(15
59.0533
58.3882
57.7072
56,9087
56.4S32
55.8463
55.2410
54.667S
54.1082
53.5704
S3 . 0553
52.5614
52.0965
51.6534
51.2363
50.8446
50.4796
50.1410
49 . 8289
49.5436
49.2841
49,0541
48.8505
48,6736
48.5234
48,4236
48.3062
48.2368
48,1976
48 , 1837
68,6673
68,7730
68.8047
68.7992
68 . 6342
68.4383
68.1727
67.8407
67.4483
66.9990
66.4995
65.9543
65.3690
64.7493
64.1003
63.421&
62.7394
62.0362
61.3253
60.6086
59 .8932
59.1782
58.4771
57.7523
56.8901
56.4164
55.7783
55.1309
54.5356
53.9473
S3, 3816
52.8429
52.3281
51 . 8394
51.3775
SO , 9427
50.5352
50.1553
49.8037
49.4796
49.1837
48.9164
48.6769
48.4653
48.2026
48, 1280
48.0013
47.9031
47.8326
47.7906
47.7765
69 . 6930
69 . 79B6
69.8189
69 . 7527
69.6048
69.3778
69.0754
68.7027
68.2650
67.7704
67.2095
66.6162
65 . 9751
65.2995
64,5932
63 , 8657
63.1231
62.3615
61,5698
60 . 8272
60.0602
59 . 2967
58.5526
57.7919
56.8806
56.3638
55.6918
54 . 9997
54.3837
53.7651
53.1734
52,6039
52.0703
51.5605
51,0798
50.6263
50,2023
49.8084
49.4432
49.1075
48.8013
48.5241
48.2768
48.0588
47.8696
47.7100
47.5795
47 . 477B
47.4063
47.3617
47.3476
70.7975
70.8966
70.9017
70.8149
70.6393
70.3780
70 . 0353
69.6107
69.1286
68.5770
67 . 9786
67.3103
66.6066
,65.8711
65', 1017
64,3125
63,5062
62 . 6871
61.8661
61.0393
60.2206
59.4102
58.6014
57.8212
56.8870
56.2944
55.5845
54.8473
54.2095
53 . 5599
52.9409
52 . 3497
51.7886
51.2571
50.7S64
50 . 2855
49 . B462
49 . 4375
49.0590
48,7118
48.3951
48.1098
47.8535
47 . 6287
47.4341
47.2691
47.1349
47.0301
46 . 9554
46.9110
46.8955
71.9779
72. 071)5
72.0605
71.9503
71.7438
71.4438
71.0563
70 . 5876
70.0445
69.4324
68.7599
68.0413
67 . 2672
66,4610
65.6257
64 . 7688
63 . 8944
63.0148
62.1287
61.2462
60.3678
59.5023
58.6502
57,8208
56.9159
56.2072
55.4542
54.6736
54.0106
53 . 3294
52 . 6836
52 . 0697
51.4772
50 . 9285
50,4081
49.9199
49 . 4644
49.0410
48.6501
48.2914
47,9647
47 . 6697
47.4068
47.1750
46.9744
46.8036
46.6677
46.5594
46.4845
46.4367
46.4214
73.2432
73 . 32B6
73.3022
73.1666
72.9248
72,5818
72,1438
71.6187
71,0140
70.3330
69.5920
68.7928
67.9533
67 . 0724
66 . 1647
65.2308
64.2913
63.3391
62.3884
61.4491
60.5032
59.5824
58.6767
57.7934
56 . 9366
56.1013
55.2986
54 . 4787
53 . 784B
53,0717
52 . 3993
51.7593
51.1388
50.5723
50.0320
49 . 5269
49 , 0556
48,6183
48.2151
47.8450
47.5087
47.2067
46.9347
46 . 6964
46.4907
46.3171
46.1750
46.0645
45.9866
4S . 9389
45 . 9233
74.6031
74.6806
74.6357
74.4743
74.1893
73.7987
73.3038
72.7140
72.0379
71.3857
70.4660
69.5958
68.6653
67.7064
66.7166
65.7073
64.6868
63 . 6636
62.6401
61.6244
60.6242
59.6420
58.6812
57,7457
56 . 8397
55.9684
55.1157
54 . 2623
53.5296
52.7845
52 . 0853
51.4172
50.7729
50 . 1056
49.6285
49. 1055
48.6190
4B.1&B8
47.7527
47,3729
47 . 0265
46.7147
46.4373
46.1930
45,9818
45.8054
45 . 6585
45,5464
45.4650
45.4175
45.4008
-------
Hagnetic Fields parallel to the
R
Z ^t
0.000
o.nos
o.nio
0.015
0.020
0 . 025
0.030
0.035
0.040
0.045
0.05D
0.055
0.060
0.065
0.070
0.075
0 . 080
O.OB5
0.090
0.095
0 , 100
0.105
0.110
, 0.115
0, 120
0.125
0.130
0.135
0.140
0.145
fl.150
0 . 155
0. 160
0.165
0.170
0.175
0.180
0.185
0.190
0.195
0.200
0.205
0.210
. 0.215
i, 0.220
T, 9 . 225
;*'0;230
T. 0.235
•0.240
:: 0.245
. 0.250
(M)
1)
76
76
76
75
75
75
74
73
73
72
71
70
69
68
67
66
65
63
62
61
60
59
58
57
56
55
54
54
53
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51
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50
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47
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77.7055
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77.3786
77.0036
76.4967
75.8653
75.1227
74.2806
73.3524
72.3495
71.2871
70.1730
69.0251
67.8529
66.6641
65.4711
64.2811
63.1029
61.9399
60.8009
59.6880
58.6085
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56.5559
55.5848
54.6561
S3 . 7650
52.9221
52.1134
51.3582
50.6332
49.9492
49.3471
48.7353
48.1712
47.6568
47.1800
46,7424
46.3422
45.9792
45.6526
45.3622
45.1072
14,8871
44,7018
44.5511
44.4331
44,348?
44.2993
44.2834
79
79
79
79
78
77
77
76
75
74
73
72
70
69
68
67
65
64
63
62
60
59
58
57
56
55
54
53
52
51
50
50
49
48
48
47
47
46
46
45
45
45
44
44
44
44
43
43
43
43
43
z— axis
.370
.3545
.4032
.2860
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.2817
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.5059
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81
81
81
80
80
79
78
77
76
75
74
73
71
70
69
67
66
64
63
62
60
59
58
57
56
55
54
53
52
51
50
49
48
48
47
47
46
46
45
45
44
44
44
43
43
43
43
43
43
43
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the HelMhnltz Coil
.375
.2061
.2433
.0950
.7667
.2661
.6058
.8018
.8630
.8168
.6547
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83.2202
83.2437
83.0592
82.6733
82.0966
81.3428
80.4273
79 . 3682
78.1872
76.9002
75 . 5326
74.0990
72.6221
71,1147
69.5949
68.07B9
66.5682
65.0843
63.6274
62.2107
60 . 8372
59.5095
58.2349
57.0119
55.8431
54 . 7259
53.6719
52.6680
51.718(1
50.8244
49.9810
49.1896
48.4484
47.8157
47 . 1387
46.5183
45.9688
45.4607
44.9984
44.5727
44.1096
43.8453
43.5404
43 . 2737
43.0434
42.8500
42.6950
42.5697
42 . 4828
42.4307
42.4136
85
85
85
84
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83
82
80
79
78
76
75
73
71
70
68
66
65
63
62
60
59
58
56
55
54
53
52
51
50
49
48
47
47
46
45
45
44
44
43
43
43
42
42
42
42
42
41
41
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4170
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51
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48
48
47
46
45
45
44
44
43
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41
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82.8522
81.0427
79.1476
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75.2110
73.2274
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67.4154
65.5698
63.7911
62.0814
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51.1208
50.0832
49.1125
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45.1636
44.5334
43.9602
43.4320
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41.7730
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40.4700
40.3815
40,3298
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93.3169
92.9139
92.1803
91.1403
89.8248
88.2669
86.5125
84.6481
82.5583
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78.2689
76.0803
73.8991
71.7467
69.6411
67.5963
65.6184
63.5314
61.9036
60.1799
58.5424
56.9900
55.5263
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52.8386
51.6353
50.4956
49.4320
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45.1084
44.4156
43.7931
43.2142
42 . 6838
42.2145
41.7331
41.3668
41.0209
40.7078
40.4280
40.1973
40.0002
39.8409
39.7167
39.6286
39 . 5767
39.5582
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96.5990
96.5117
96.0267
95.1613
93.9443
92.4190
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88.6144
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84.1367
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79.3519
76.9276
74.5171
72.1859
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65.5936
63.5673
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58.1119
56.4980
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53.5514
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46.7618
45.8890
45.0812
44.3342
43.6447
43.0115
42.4281
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41.4225
40.9457
40.5808
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39.6431
39.4077
39.2168
39.0592
38 . 9366
38.8503
38.7982
38.7809
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100.1917
100.0690
99.4813
98.4522
97.0233
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93.1678
90.8585
88.3747
B5 . 7722
83.1017
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77.7390
75.1118
72.5555
70.0855
67.7187
65.4629
63.3204
61.2960
59 . 3876
57 . 5942
55.9131
54.3423
52.8702
51.4996
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48.9854
47.9283
46.9034
45.9516
45.0717
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43.5086
42.8211
42.1802
41.6016
41.0747
40.5915
40.1327
39 . 7622
39 . 4223
39.1170
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38 . 5846
38.4042
38.2544
38.1257
38.0466
37.9950
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104.2133
104. 0465
103.3319
102.1049
100.4162
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93.2486
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87.4524
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81.4516
78.4942
75.6124
72.8288
70.1632
67.6350
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62.9578
60.8291
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56.9700
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52.1000
50 . 6979
49.3977
48.1930
47.0731
46.0393
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43.3854
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41.9472
41.3178
40.7367
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39 . 7345
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38.9107
36 . 5748
38.2744
37.9906
37.7359
37 . 5639
37.4279
37 . 2BSS
37.2197
37.1671
37.1502
-------
'.Magnetic Fields parallel to The z-axis of the Helnholtz Coil
R
(n)
420
.425
.430
.435
.440
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455
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465
470
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0.195
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0.230
0.235
0.240
0.245
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108
108
107
106
104
101
98
95
92
89
85
82
79
76
72
70
67
64
62
60
58
56
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52
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49
48
47
46
45
44
43
42
41
41
40
39
39
38
38
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113.5917
112.5219
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105.4034
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87.0588
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76.2579
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69.9008
67,0125
64.3213
61.8175
59.4903
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55.3545
53.5208
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50.2617
48.8193
47.4866
46.2760
45.1467
44.1104
43.1577
42.2812
41.4780
40.7396
40.0644
39.4400
38.8833
38.3709
37.9058
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37.1167
36.7831
36.4920
36.2339
35.9915
35.8072
35.7084
35 . 5287
35 . 4945
35.4357
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119.7608
1 19.3808
118,0544
115.0673
112,9452
109.4301
105,4886
101.2721
96.9170
92.5457
88.2414
B4 . 0757
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76 . 3283
72.7942
69.4997
66.4401
63.6090
60.9941
58.5904
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52 . 4747
50.7571
49.1811
47.7358
46.4521
45.1869
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43.0408
42.0983
41.2346
40.4415
39.7165
39.0536
38.4480
37 . 8966
37.3978
37.0672
36 . 5375
36.1743
35.8471
35 . 5657
35.3169
35.1004
34.8942
34.8143
34.6181
34.5977
34.5358
34.5254
126.5454
126.0493
124.3869
121.6773
118.0964
113.8482
109.1435
104.1799
99. 13113
94.1257
89 . 2697
84 . 6296
80.2538
76.1779
72.3705
68 . 8625
65.6432
62.6881
59.9816
57.5053
55.2533
53.1744
51.2090
49.5625
47.9849
46.5426
45.2243
44.0370
42.9505
41.8994
40.9705
40.125D
39.3518
38.6429
37.9964
37,4066
36.8723
36.3876
35.9491
35.5540
35.1999
34 . 8878
34.6105
34.3690
34.16S6
33.9602
33.8968
33,6900
33.6794
33.6157
33.6071
134
133
131
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123
118
113
107
101
95
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80
75
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64
61
58
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53
51
49
48
46
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43
42
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40
39
38
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36
36
35
35
34
34
34
33
33
33
33
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32
32
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142.9461
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103.2149
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60.1039
57.2729
54 . 7226
52.4239
50,3467
48.4687
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45.2440
43.8311
42.5680
41.4075
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39.4004
38.5274
37.7325
37.0092
36.3490
35.7503
35.2029
34.7094
34.2729
33.8583
33.4940
33.1707
32.8836
32.5908
32.4078
32.2350
32.0364
31.9895
31.7929
31.7825
31.7239
31.7153
155.02H4
153.8552
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144.6066
137.4B87
129.4B88
121.1276
112.7919
104.0388
97.3712
90.5087
84.3049
78.6682
73 . 6296
69.1514
65.1401
61.5711
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55.5314
53.0292
50.7109
48.6636
46.8211
45.1602
43.6640
42.3115
41.0B31
39.9713
38.9617
38.0443
37.2100
36.4511
35.7606
35.1342
34.5547
34.0453
33,5734
33.1500
32.7685
32.4221
32.1290
31.8452
31.5565
31.3985
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31.0499
30.9988
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154.2131
141.3025
128.6594
116.8472
106.1564
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33.7314
33.1232
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29.9599
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-------
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------- |