&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 Srnt(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

-------
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

-------
                                  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

-------
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

-------
                             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 Tie 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  TryTry+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-F5val-Fsrange+B< J)*Conv/Fsvolt-3*FsranTnp-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*&"  "&Unitt(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,Sap_size,DUttin,.0bMax
5540  FRAME
5S50  CSIZE 2.25,7/15
5S60  X_corr=Sap_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=Dbin 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 Sap_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"Tie <*>"
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$&"bl66p54f6dlL "
5970   OUTPUT Analyzer|"LB3"
S980   ENTER AnalyzerjDbnax
5.9V 0   !
6^)00   !  4.42  Calculate position and spacing and plot labels
6010   !
6020   DbttinDbwax8*10  !10 dB/div
6JJ30   Xtic=Span/500Q
6040   LOCATE Px2<0,Gp>,Px2Mf165,963
6140   MOVIE 0,0
6150   LABEL USING "*,K";M*[97,1283
6160   !
6170   ! 4.43  Plot display
6180   !
6190   LOCATE Px2(0,Gp),Px2<2,Gp),Py2<2,Gp),Py2<3,Gp)
6200   SCALE 0 ,255,Dbin ,I)brtax
6210   FRAME
6220   AXES Xtic,10,0,DbMin
6230   MOVE 0,Dbin
6240   FOR J=0 TO 255
6250     PLOT J,ACHR*(10)
6340     Gp=0
6350   EXIT GRAPHICS
6360   NEXT I
6370   GRAPHICS
6380   IF Gp=3 THEN DUMP GRAPHICS #r.ardi ^-110,115
6390   IF Gp<=2 THEN DUMP GRAPHICS fCardlj5,115
6400   !
!>41Q   !4.6             PRINT   REPORT   SUMMARY
6420   I
6430 Print report: PRINT PAGE
^>440   EXIT GRAPHICS
6450   FOR C=0 TO 10
6460     C*(C) i,53 = "     "
6470     LINPUT "Enter  coMfients and terwinate with a blank line. " ,C$(C) 63
6480     IF C*0 THEN REDIM C$LIN<4>}TAB8i-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) iPini iPaxi"AppUed Field = "jPROUNDC Inval ,-3) >Uni ts* "CoMents: " ;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 SuMar^_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 ap 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 Tie 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 (*) ,Paxi <*) .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  Fin=Freqz>
88.10  FMax=FreqzDbmin
8830  MAT SEARCH PwaxK*) ,MAX}l)bMax
8840  DhMln=PROUND
8850  DbMax=PROUND(Dbax+.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=Fax/2
Fttin=FMin-Fc
               Dbwax
              _corr#2>I
SCALE Ffiin,Fax,DbMin,Dbax
FRAME
CSIZE 2.75
Y_corr=(Dbnax-DbMin)#.01
  corr=#. 02
Xc=X_corr
CLIP Fin~X__corr,FMin,Dbpint
AXES Fc,i,FMin,Dbin
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,Dbin-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*="Pre5 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
Cd$="FR",VAL*Cd*
SUBEXIT
SUBEND
i
                                                         *** Set_freq_3314
Set_anp_3314= !
SUB Set_aMp_3314=10 THEN 1059C
IF AMp<1.0 THEN 10560
   CMd*="AP"&MAL*(Ap H"MO"
   GOTO 10570
CMd$="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         Kr26*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         Rin=MIN(A,R2)
 560         CALL BfieldrRMax,Rin>R2Z2>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      DSP "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(JFunc(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(*),IntE
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<*),Doain<*),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-Xi4
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
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0.0685
0.0772
0.0833
0.0870
0.0882
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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
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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
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-2.5812
-1.9228
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-i.0949
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-.0617i
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-.0011
0 . 0233
0.0498
1). 0618
0.0761
0.0874
0.0958
0.1015
0.1044
0.1047
0.1026
0.0985
0.0925
0.084B
0.0760
0.0648
0.0533
0.0408
0.0275
0.0136
0.0000
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-2.7931
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0.0979
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0.1228
0.1197
0.1141
0.1067
0.0975
0.0866
0.0743
0.0606
0.0464
0.0313
0.0158
o.ooon
.130

-2 . 9795
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-3 13:J"5
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-2.6325
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C.2126
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0.0254
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150

-2 9034
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-3.0705
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-3.1620
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0.0482
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0.2506
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-3.2518
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0.0331
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0.1525
0.2025
0.2464
0.2823
0.3139
0.3416
0.3579
0.3714
0 . 3792
0.3816
0.3795
0.3727
0.3614
0.34al
0 . 3272
0.3043 -
0.2785
0.2500
0.2190
0.1B56
0.1497
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0.0763
0.0386
0.0000
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-3.3226
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0.0846
0.1490
0.2070
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0.3018
0.3386
0.3694
0.3944
0.4119
0.4240
0.4303
3.4310
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0.4177
0.4101
0.3858
0.3637
0.3378
0.3087
0 . 2767
0.2419
0.2053
0.1665
0.1262
0.0848
0.0426
0.0000
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-3.4163
-3 . 2222
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-2.8311
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-2.3126
-2.1374
-1.8912
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0.0679
0 . ',414
0 .2079
0.2670
0 .3175
0.3625
0.3997
0.4303
0.4537
0.4704
0 .4806
0.4858
0 .4847
0 . 47B2
0.4666
0.4499
0 .4286
0.4032
0 . 3739
0.3408
0.3055
0.2679
0 . 2262
0.1834
0.1391
0.0935
0.0468
0.0000

-------
lagnetic Fields perpendicular  to  the  z-axis  of  the Hplnholtz  Coil
R (n)
Z (n)
.000
1.005
) . 010
1.015
1.030
1.025
1.030
0.035
H. 040
0.045
0.050
0.055
0.060
0.065
0. 070
1) , 075
0.080
0.085
0. 090
0.095
0.100
O.iOS
O.iiO
0.115
0.120
0.125
0.130
0.135
0.140
0.145
0.150
0.155
0. 160
;*?165
0.170
0.175
0. 180
0.185
0. 190
0. 195
0.200
0.205
0.210
0.215
0.220
0.22S
0.230
0 . 235
0.240
0.245
0.250
.180

-3.5103
-3.3043
-3. 098?
-2.B952
-2.6978
-2.5136
-2.3505
-2.1788
-1 .9115
-1.7194
-1.5603
-1.3876
-1.2212
-1 .0616
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- . 2546
-.1463
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0.0454
0.1291
0.2047
0.2730
0.3327
0.3846
0.4292
0 . 4663
0.4959
0.5184
0.5338
0.5430
0 . 5459
0.5458
0.5334
0.5188
0 .4991
0.4746
0.4456
0.4128
0 . 3762
0 . 3365
0.2938
0 . 2499
0 .2018
0. 1525
0.1025
0.0515
0 .1)000
.185

-3.6026
-3.3853
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-2.7458
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0.01S7
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0.3437
0.4042
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0.5894
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0.6101
0.61Q8
0.6049
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0.5242
0.4915
0 . 4546
0.4140
0.3698
0.3232
0.2726
0.2208
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0.1121
0.0563
0. DOOR
.190

-3.6936
-3.4668
-3.2405
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-2.7951
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-2. 4068
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-.8440
-.6856
-.1694
-.3946
-.2605
-.1370
-.0217
0.0851
0.1822
0.2712
0. 3506
0.4208
0 . 4029
0.5362
0.5804
0.6160
0.6444
0 . 6647
0 . 6778
0 . 6823
0.6804
0.6717
0 . 6566
0.6313
0.6091
0 . 5774
0 . 53B7
0.4995
0.2022
0.4052
0.3533
0.3065
0 .2412
0.1827
0 . 1326
0.0615
0. 0000
.195

-3.7B04
-3.5405
-3.30?6
-3.0742
-2.8526
-2.6175
-2 . 4237
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-.8025
-.6388
-.4826
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0.1609
0 .2620
0 . 3524
0 . 4334
0.5055
0.5682
0.6214
0.6653
0.7011
0.7281
0.7470
0 . 7572
0.7600
0.7552
0.7438
0.7256
0.7009
0.6704
0.6342
0.5930
0.5445
0.4970
0.4432
0 . 3859
0 . 3260
0 . 2639
0.1980
0.1338
0.0672
0.0000
.200

-3.8754
-3.6254
-3.3763
-3. 1301
-2,8866
-2.6337
-2.4328
-2.2785
-1.9563
-1.7175
-1.5186
-1.3189
-1.1232
~.934fl
-.7548
-.5835
-.4232
-.2678
-.0819
0.0085
0.1318
0.2458
0.3484
0.4412
0.5244
0.5975
0.6591
0.7139
0 .7582
0.7938
0.8182
0.8349
0,8432
0.8434
0.8362
0.820?
0.7993
0.7709
0.7371
0.6950
0.6491
0.5981
0.5391
0.4834
0.4213
0.3557
0.2876
0.2175
0.1451
0.0732
0.0000
.205

-3 . 9827
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-2 . 9290
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-2.43B5
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-1 .0837
- . 8876
-.6994
-.5204
-.3532
-.1950
-.0438
0.0984
0.2203
0.3372
0.4428
0.5390
0.6231
0.6966
0 . 7607
0.8142
0 . 8577
0.8911
0.9151
C.9291
0.9360
0 . 9335
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0.9042
0.8775
0,8451
0.8057
0.7601
0.708.9
0.6530
0.5921
0.5271
0 . 4588
0.3871
0.3128
0 . 2368
0.1586
0.0794
0.0000
.2.10

-4.0500
-3.7753
-3.5QSB
-3 . f!324
-2.9675
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-2.4460
-2.2714
-1.9495
-1.7082
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-1.2210
-1 .0520
-.8310
-.6347
-.4499
-.2534
-.1101
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0.1876
0 .3177
0.4369
0 . 5469
O.A439
0.7298
0.8052
0.8697
0.9224
0.9649
0.9963
1.0197
1 . 0323
1.0356
1 .0304
1.0152
0.9992
0.9624
0 . 9247
0.8806
0 . 8297
0.7732
0.7112
0.6445
0.5735
0.4984
0.4205
0.3397
0.2565
0.1719
0.11865
0.0(100
.215

-4.1403
-3.8S22
-3 . 5663
-3.2821
-2.9717
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-2.4556
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-i.i693
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-.1888
-.0178
0.1434
0.2883
0.4235
0.5475
0 . 6567
0 . 7583
0.8525
0 . 9220
0.9862
1 . 0375
1.0807
1.1115
1.1328
1. 1417
1.1418
1. 1324
1.1141
1 . OS74
1 052*
1.0101
0.9604
0.9042
0.8414
0.7732
0.7002
0.6225
0.5408
0.4561
0.3681
0.2781
0 . 1863
0 . 0934
O.ODOO
.220

-4.2310
-3 . 9252
-3 . 6P45
-3.3277
-3.0335
-2 . 7326
-2 . 4572
-2.2129
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-1.3870
-1.1152
-.9595
-.6966
-.4907
-.2836
-.0945
0.0815
0.2477
(I . 3994
0.5398
0 . 6659
0.7800
0 . 8826
0.9713
1 . 0475
1.1124
1.1647
1.2056
1.2340
1.251B
1.2589
1.2557
1 . 2427
1.2203
1.1888
1.1490
1.1009
1.0456
0 . 9829
0.9110
0 . 8393
0 . 7593
0 . 6773
0.5861
0.4936
0.3988
D.3011
0.2017
0.1013
0 .001)0
.225

-4.3133
-3 . 9966
-3.6B11
-3.3695
-3.0620
-2.7586
-2.4609
-2.1711
-1.8915
-1.6206
-1.3373
-1.0S70
-.8937
-.6088
-.4121
-.1723
0.0103
0.1943
U.3639
0.5217
0.6652
0.8001
0.9130
1.0162
1.1068
1.1842
1 . 2493
1.2996
1 .3383
1 . 3652
i.3807
1 . 3847
1.37BO
1.3606
1.3333
1.2972
1.2511
1.1973
1.1355
1 . 0666
0.9915
0.9092
0.8224
0.7304
0.6340
O.S342
0.4311
0 . 32SS
0.2178
(1,1095
0 .0000
.230

-4.3996
-4.0666
-3 . 7359
-3.40P7
-3.0BW
-2.7681
-2.4563 .
-2.1518
-1.8573
-1.5605
-1.2801
-.9931
-.8148
-.5137
-.2448
-.0809
0.1242
0.3147
0.4919
0.6542
0.8027
0.9360
1 . 0562
1.1618
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1.3302
1.3936
1.4444
1.4818
1.5064
1.5188
1.5193
1.5109
1.4861
1.4538
1.4115
1.3602
1 . 2998
1.2320
l.iSbl
1 . 0732
0.9848
0.8892
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0.6851
0 . 5766
0.4651
0.3513
0.2350
0.1178
O.ODOO
.235

-4 . 4835
-4.1336
-3.7875
-3.4437
-3.1049
-2 . 7992
-2.4B09
-2.1258
-1.8157
-1.4862
-1 .2151
-.9217
-.7229
-.4121
-.0919
0 . (1390
0.2500
0.4454
0.6331
0.7983
0 . 8399
1 . 0892
1.2106
1 .3175
1.4102
1.4878
1.5510
1.6002
1.6353
1 .6567
i . 6656
1.66*9
1 . 6466
1,6200
1.5816
1 . 5344
1 . 4765
1.4098
1.3342
1.2508
1.1605
1.0630
0.9610
0.8514
0.73B6
0.6217
0.5013
0 . 3781
0 . 2535
0.1269
0.0000

-------
(Magnetic  Fields  perpendicular  to the z-axis af the Helnhnltz Coil
R (n)
2 
0.000
o.ons
o.nio
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
O.OBO
0.0135
0.090
0.095
fl 100
0.1 OS
0.110
1). 115
0.120
0.125
0.130
0.135
0.140
CA 0.145
' 0.150
X. U.155
0.160
0.165
0 170
0.175
0. 180
0 185
0 .1.90
0.195
0,200
0.2D5
0.210
0.2t5
0.220
0.225
0.230
0.235
0.240
0.24S
0.250
.240

-4.5676
-4 2008
-3 . 8361
-3.475ft
-3.122B
-2.8244
-2 . 4966
-2.0932
-1.7682
-1.4242
-1.1420
-.8412
-.6100
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0.0513
0. 1665
0 . ,1882
0 . 5932
0 . 7B24
0.9597
1.1116
1.2529
1 . 3777
1.4754
1 .5802
1 . 6566
i .7187
1 . 7658
1 . 7985
1.B172
1 . 8222
1.B152
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
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-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
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-.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
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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
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-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

|o
?0
|o
N
0
0
0
0
0
10
I)
0
o
0
0
(]
0
fjfl 0
P o
0
0
0
0
0
0
tl
0
0
(1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
n
R (n
Z (n)

000
005
010
015
020
025
030
035
040
045
050
055
060
065
070
D75
0811
035
090
095
100
105
110
115
120
125
130
135
140
145
150
155
160
165
170
175
lao
IBS
190
195
aoo
205
?i(l
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
9
B
7
6
6
5
4
3
2
1
0
n
420


6933
89B4
7763
2256
3551
0920
3952
2370
6160
5456
0564
1789
9547
4248
6263
6023
3867
(1104
4961
8834
17BO
4026
5720
7002
7970
8676
9225
9684
0075
0426
0783
1181
1601
2100
2654
3350
396B
4765
5526
7178
7493
8571
9564
0877
2.121
3196
4551
5526
6426
8822
0000



-6
-1
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
5
4
3
S
1
0
0
425


7200
2616
0440
0595
6712
7926
3793
4052
87B4
8247
2927
3225
9707
2B63
3S32
1254
7334
1882
5136
7401
8816
9661
0075
0153
9980
9674
9070
8972
8456
806B
7781
7536
7409
7371
7422
7639
7879
8271
8766
9347
0007
0763
1579
2508
3552
432B
5527
6136
6747
9000
ooon



-6
-
5
11
16
21
24
28
30
32
33
34
35
35
35
34
34
33
32
31
30
29
28
27
26
25
24
22
21
20
19
18
17
16
IS
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
0
the z-gxis of the HeJntio!
.430


.7441
.4782
.5888
.aaoo
.4535
.0051
.891,3
.0919
.6302
.5572
.9283
.8141
.2810
.3979
.2245
.8168
.2183
.4692
. 6045
.6495
.6303
.5624
.4621
.3380
.2049
.0664
.0568
.7956
.6738
.5605
.4622
.3758
.3048
. 2534
.2070
.1812
.1690
.1681
.1341
.2067
.2413
.2821
.3410
.4071
.4803
.5413
.6466
. 6742
.7207
,9279
.0000



-6
0
7
13
19
24
29
32
34
36
3B
38
38
38
38
37
36
35
34
33
32
31
29
28
27
26
24
23
22
21
20
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
0
.43.5


.7661
.4972
.4964
.9996
.13263
.8567
.0505
.4004
.9596
.7997
.0103
. 6822
.9070
.7810
.3327
.6624
.8236
.8469
.7637
.6092
.4257
.1678
.9213
.6612
.4013
. 1526
.9173
.6644
.4825
.2991
.1252
.9804
.8532
.7448
.6575
.5847
.5311
.4961
.4771
.4660
.4730
.4911
.5132
.5625
.6013
.6446
.7351
.7348
.7758
.9418
.0000



-6
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
6
S
4
3
2
1
D
0
4411


7Bt,2
7293
8859
3735
9673
51B7
0075
4560
9496
6256
5842
9558
8730
3888
6318
6687
5414
2941
9787
6033
2019
7894
3778
9734
5856
2176
8538
5534
2676
0051
7690
5593
3756
2138
0003
966B
8762
Bill
7492
7169
69S8
6804
1049
7085
7206
7424
8171
7959
8349
9533
0000
I Coi 1.



-6
3
12
21
29
35
39
43
45
47
47
47
47
46
45
43
42
40
39
37
35
34
32
31
29
28
26
25
24
22
21
20
IB
17
16
15
14
13
12
10
9
8
6
6
5
4
3
a
i
0
o
445


8040
3134
9293
6214
o?&n
2021
9515
4125
7387
1064
6888
65 17
1352
2628
1241
7945
33B3
8003
2125
6030
9971
3913
B097
2586
78BO
252B
8283
3932
0194
6833
3771
1073
B701
6623
4818
3289
1997
2165
0007
9386
B715
8565
6181
8424
8339
8341
B909
8577
B
-------
Magnetic Fields perpendicular to the ziixi& of the Kelwholtz  Co'ii



     R ()  .480      .483       .490       .495       .500
0.
0
0.
0
0,
0
0
0
0
0
0
0
0
0
0,
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
n
0
0
0
0
0,
0
0
0
0
0
0
0
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0,
0
onn
.005
.010
.015
.020
.025
.030
.035
.040
,045
.050
,055
.060
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.075
.080
.085 .
.090
.095
.100
.105
.110
.115
.120
.125
. 130
.135
. 140
.145
, 150
.155
, 160
.165
.170
. 175
.180
, 1B5
. 190
.195
.200
.205
.210
.215
.220
.225
.230
.235
.240
. 24E
.250
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114.
139.
144.
141.
132.
122,
113.
103,
95.
SB.
81.
75.
69.
64.
60.
56
52.
4?
46
43.
40
38
35,
33,
31 ,
29
27
25
24,
22,
21 .
19
IB
16
15.
14,
13,
li,
10.
9.
8,
7
6.
5,
4
3,
2.
1.
0.
8693
8361
9336
0602
9131
0810
5414
.8129
,1086
,9802
6466
1157
.3576
2947
,8168
,9332
4384
.3361
.6380
.3377
.1052
.3319
,5598
,0284
6563
.4943
.4283
,5314
.5503
.9436
,2486
,6330
1520
,6728
3478
9058
.6361
.4197
1319
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7656
6167
5446
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3106
2688
1746
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0754
0381
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-6,
114.
179.
195.
186,
170.
153,
138
124,
112.
101.
92,
84.
77.
72
66.
61.
57
S3
46
46
43
41
38.
36,
33
31,
29.
27.
26,
24.
22,
21,
19
IB,
17.
15,
14
13.
11 .
10.
9,
8.
7
6.
5.
4
3.
2,
1,
0,
B690
.6356
8744
2112
,7317
,9026
.6412
.0037
,1297
,2399
.8641
,9132
9311
5084
.0654
,8152
9471
,5756
.6581
.5465
.8179
.9411
,0713
,4554
.0398
.8073
.7045
,7524
.6856
.1254
3987
7826
.2618
,7699
,3800
,0122
6862
.4245
.1861
9738
.7960
6462
.5220
.4051
.3202
,2481
.1776
.1292
. OQ28
.0378
.0000
-6.
81.
157.
207.
219.
199.
169.
149.
132.
118.
106.
96.
87.
79.
73.
68.
62.
58.
54.
46'.
47.
44.
41.
38.
36.
33.
31.
29.
27.
26.
24.
22.
21 .
19.
18.
17.
15.
14.
13.
11.
10.
9.
8.
7.
6,
5.
4.
3.
2.
1..
0.
9212
67911
4864
704S
5366
170B
434B
2357
507B
1615
3979
2628
489B
2994
6406
093B
9467
4207
3372
4741
2755
2990
3829
7158
2794
9901
8634
8684
8336
2146
4731
8568
3109
8215
4038
0260
7118
4S34
1911
9804
7668
6518
5242
4167
3249
2532
1848
1310
0846
0404
0000
-6
90
173
228
238
213
178
155
137
121
108
98
88
80
74
68
63
58
54
47
47
44
41
38
36
34
31
29
27
26
24
22
21
19
18
17
15
14
13
11
10
9
8
7
6
5
4
3
2
1
0
.9336
7373
. 89B6
. 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
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0.035
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n.oso
0.055
0.060
0.065
0 . (170
0.075
0.080
0.085
0 . 090
0.095
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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
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52 . 3680
52.5105
52.6447
52.7709
52 . 8892
52 . 9997
53.1026
53.1982
53 . 2867
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53.4433
53.5119
53.5744
53.6310
53.6B21
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53.7686 '
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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
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53.9468
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53.9457
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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
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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
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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
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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
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53 . 9542
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53.9474
53.9448
53.9430
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53.9415
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51.5116
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52 . 0628
52.2284
52.3B58
52.5344
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52.8055
 52.9283
53.0430
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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
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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
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53 . 7363
53.7855
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53.8671
53.9001
53.9285
53.9523
53.9720
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54.0004
54.0097
54.0161
54.0199
54,0214
54.0210
54.0189
54.0154
54.0107
54.0(150
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53.9919
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53.9778
53.9708
53.9640
53.9577
53.9520
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53.9394
53.9370
53.9355
53.9350
.OBS

51.6801
Si . 0667
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52.2053
52.36S2
52.5215
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52.8057
52.9345
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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
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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
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53.9501
53.9444
53.9395
53 . 9357
53 . 9330
53.9313
53.9306
. II9II

Si .7266
51 9104
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52.2743
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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
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53.9190
53.9521
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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
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53.9355
53.9311
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51 .13163
52.0077
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52.51B9
52.6767
52.8309
52 . 9559
53.0818
53.1988
53.3070
53.4069
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53.5820
53 . 6570
53.7263
53.7876
53.8421
53.8901
53.9320
53.9680
53.9978
54.0240
54.0446
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54.0811
54.0860
54.0878
54.0873
54.0836
54 . 0782
54.0710
54.0624
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53.9910
53.9035
53,9726
53 . 9622
53.9527
53.9445
53.9368
53.9306
53.9256
53.9221
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51 .8999
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53.0384
53.1627
53 . 2778
53.3842
53.4819
53,5713
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53.7260
53.7919
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53.9025
53.9478
53,9868
54.0200
54,0476
54.0701
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54.1156
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54.1165
54.1129
54.1067
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54.0525
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53 . 9399
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53.9151
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53.9119
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51. 9947
52. 1859
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52.5349
52.6916
52.8409
52.9938
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53.9997
53.9847
53.9705
53.9574
53.9453
53.9346
53.7848
53,9176
53.9114
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52.0893
52.2737
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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
53.897S
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
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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
54.8204
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
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B 0.070
m 0.075
1"- Q . 080
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0.110
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0.125
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0.150
0.155
0.160
0.165
0.170
0,175
n . IBO
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0.190
0.195
0 .200
0.205
0.210
0.215
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0.225
0 . 230
0.235
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. 120


52.3077
52.4901
52.6624
52 . B283
52.9917
53.1515
53.2930
53.4199
53.5364
53.6432
53.7402
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53.9075
53.977B
54,0399
54.0938
54.1402
54.1793
54.2114
54.2371
54.2567
54.2706
54 . 2787
54 . 2S29
54 . 2822
54.2775
54.2691
54 . 2574
54.2429
54.2259
54.2069
54.186S
54. 1636
54.1413
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
53 . 8739
53.87D4
53.8693
.125


52.4253
52.6080
52.7798
52.9440
53.1038
53.2601
53.4040
53.S2B7
53.6431
53.7475
53.8421
53.9272
54.0032
54.0704
54.1290
54.1794
54 . 2222
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54.3077
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54.3331
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54.2564
54 . 2336
54.2093
54.1838
54 . 1572
54.1304
54.1034
54.0765
54.0501
54.0245
53.9999
53,9767
53.9549
53.9348
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53 . 8066
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52.5505
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52.9043
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53.5214
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52.6781
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54.6092
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54.5967
54.5773
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54.5257
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54.3445
54.3036
54.2611
54.2187
54.1765
54,1350
54.0942
54.0547
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53.9827
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53.9154
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53.8608
53,8380
53.8184
53.8021
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53,7746
53 . 7729

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53.1183
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53.6319
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54.2653
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54.7021
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54,6678
54.6429
54.6136
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54.5040
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54.4193
54.3728
54.3265
54,2805
54.2329
54.1862
54.1404
54.0957
54.0524
54.0110
53.9717
53.9350
53.9006
53.6693
53.8412
53.8165
53 . 7952
53.7776
53 . 763B
53.7549
53.7480
53.7460

.155


53.2808
53.4ABO
53.6385
53 . 7869
53.9241
54 . OSBi
54.1771
54.2962
54.4088
54.4947
54 . 5693
54.6330
54.6861
54.7297
54.7625
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54.8022
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54.8091
54.8015
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54 . 7672
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54.5487
54.5012
54.4518
54.4011
54.3496
54 . 2977
54.2460
54.1949
54.1445
54.0957
54.0484
54.0033
53.9606
53.9205
53.8034
53.8495
53.8191
53.7922
53 . 7692
53 . 7502
53 . 7353
53.7247
53.7183
53.7161

.160


53.4474
53.6326
53.8043
53 . 9526
54.0882
54.2184
54.3258
54.4361
54.5593
54.6410
54.7118
54.7716
54.8195
54 . 8576
54.8857
54.9046
54.9145
54.9160
54.9097
54.8963
54.8760
54.8496
54,8177
54.7807
54.7394
54 , 6942
54 . 6456
54.5944
54.5409
54.4857
54.4274
54 . 3724
54.3153
54.2581
54.2022
54.1473
54.0939
54.0426
53 . 9936
53.9471
53.9038
53 . 8635
53 . 8268
53.7939
53.7650
53.7402
53.7196
53.7037
53.6921
S3 . 6B5H
53 . 6828

.165


53.6229
53.8075
53.9778
54.1258
54 . 2608
54 . 3872
54 . 4827
54.5008
54.7163
54 . 7952
54,8609
54.9156
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54.9918
55.0145
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55.0315
55.0270
55.0144
54.9946
54 . 9676
54.9350
54 . B965
54 . 8529
54.8050
54 . 7533
54,6983
54.6407
54.SB10
54.S197
54.4573
54 . 3942
54.3319
54.2695
54.2082
54.1483
54.0904
54.0346
53.9814
53.9311
53.8841
53.8408
53.B012
53 . 7657
53.7346
53 . 7079
53.6B61
53.6685
53 . 6559
53 . 6485
53.6460

.170


53 . 8084
53.9920
54.1604
54.3159
54.4424
54.5650
54.6488
S4.7321
54.BB02
54.9558
55.0172
55 . 0667
55.1049
55.1321
55.1489
55.1559
55.1535
55.1424
55.1233
55.0967
55.0631
55,0233
54.9778
54 , 927 4
54.8725
54.8139
54.7520
54 . 6877
54,6213
54 . 5536
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
53.6itl
S3. 6081
53.6054

.175


54.0023
54.1839
54.3541
54.5044
54.6332
54,7519
54 . 8252
54.8914
55.0516
55.1241
55.1807
55.2248
55.2585
55 . 2786
55.2892
55,2895
55.2807
55.8625
55.2363
55.2026
55.1618
55.1147
55.0618
55,0040
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
^3.8360
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
(1 . 030
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
fl.140
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
0.22S
0.230
0.235
0.240
0.245
0.250
54.2046
54 . 3862
54.5521
54.7026
54.B334
54.9483
55.0129
55.0603
55.2309
55.3000
55.3516
55.3900
55.4165
55,4314
55.4353
55 . 4289
55.4128
S5.3875
SS . 3538
55.3124
55.2639
55.2089
55.1484
55.0827
55.0128
54.9390
54.8624
54.7833
54.7026
54.6200
54 . 5385
54.4563
54.3749
54.2947
54.2161
54 . 1393
54.0662
53.9957
S3 . 9287
53 . 8657
53.8070
53.75E9
53.7036
53 . 6595
53 . 6209
53.5884
53.5605
53 . 5392
53.5240
53.5147
53.5116
54.4174
54.5986
54.7631
54.9114
55.0435
55.1544
55.2128
55.2406
55.4186
55.4799
55.5299
55.5625
55,5825
55.5908
55 . 5877
55.5740
55.5503
55.5174
55 . 4756
55 . 4258
55 . 3695
55.3064
55 . 2375
55 . 1636
55 . OB53
55.0035
54.9189
54.8318
54.7432
54 . 6539
54.5642
54.4755
54 . 3864
54.2995
54.2145
54.1321
54 . 0527
53.9769
53.9050
S3 . 8372
53.7741
53,7161
53 . 6633
53.6160
53.5744
53.5392
53.5101
53 , 4873
53.4709
53.4610
53.4579
54.640B
54,8197
54.9B28
55.1301
55.2591
55.3707
55.4261
55.4338
55.6153
55.6644
55.7166
55.7429
55.7S61
55.7601
55.7466
55.7251
55.6946
55.6521
55.6021
55.5439
55.4787
S5.4068
55.3292
55.2465
55.1595
55.0691
54 . 9760
54.BBOS
54 . 7837
54.6863
54.5888
54.4919
54.3961
54.3021
54.2105
54.1218
54.0364
53.9556
S3 . 8775
53.8049
53.7363
53.6750
53.4891
53.5680
53.5237
53.4838
53.4547
53.4303
53.4128
53.4022
53 , 3987
54.8782
55.0580
55.2131
S5.3577
55.4742
55.5957
55.6538
55.6415
55.8215
55.B560
55.9128
55.9317
55 . 9372
55.9306
55.9121
55.B824
55.8421
55.7920
55.7331
55.6661
55.5915
55.5104
55.4235
55.3315
55.2354
55.1358
55.0334
54.9294
54.8239
54.7179
54.6122
54.5072
54.4039
54.3025
54.2037
54.1084
54.0166
53.9290
53.8461
53.7682
53.6959
53.6280
53.5690
53.5151
53.4678
53.4275
53.3941
53.3681
53.3493
53.3380
53.3342
55 . 1 178
55,2952
55 . 4553
55.5966
55,7209
55 . B262
55.8958
55.8654
56.0378
56,0568
56.1189
56 . 1278
56,1262
56.1115
56.0846
56.0461
55.996B
55,9374
55.8670
55.7922
55,7076
55.6170
55.5203
55,4186
55.3127
55.2034
55.0917
54.9780
54.8637
54,7484
54.6341
54,5208
54.4093
54.3003
54. 1941
54.0914
53.9931
53 . B992
53.B103
53 . 7273
53.6499
53.5789
53.5124
53.4569
53.4064
53.3633
53.3278
53,3000
53 . 2798
53.2681
53.2641
55 . 355S
55.5510
55.7087
55.B477
55.9676
56.07117
56,1479
56.1069
56 . 2647
56 . 2692
56 . 3348
56.3331
56 , 3235
56.3003
56 . 2643
56.2163
56.1574
56.0882
56.0096
55.9224
55 . 8282
55.7268
55.6197
55.5075
55.3913
55.2719
55,1500
55.0266
54.9022
54.7780
, 54.6544
54 . 5325
54.4123
54.2950
54.1811
54.0711
53.9655
53 . 8653
53.7704
53.6815
53.5989
53.5230
53.4542
53.3929
53.3391
53.2933
53 . 2555
53 . 2259
53.2048
53.1921
53 . 1878
55.6470
55.8218
55.9731
56.1123
56 . 2267
56.3253
56.4050
56.3679
56.5027
56.4954
56.5607
56.5471
56 . 5295
56.4969
56.4513
56.3935
56 . 3237
56.2446
56.1553
56.0574
55.9520
55.8391
55.7215
55 . 5984
55.4714
55.3412
55,2086
55.0746
54.9403
54.8062
54 . 6729
54.5414
54.4124
54 . 2B65
54.1645
54.0457
53.9341
53.8268
53 . 7254
53.6304
53.5424
53.4616
53.3884
53 . 3229
53.2658
53.2171
53 . 1769
53.1454
53.1229
53.1095
53.1949
55.9263
56,0996
56 . 2526
56.3Q60
56.5349
56.5931
56.6674
56.6497
56 . 7S23
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
53 . 5739
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
56.6745
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
54 . 2387
54.0893
53,9461
53,8092
53.6793
53 . 5567
53.4423
53,3366
53 . 2393
53.1513
53.0730
53.0045
52.9463
52.8982
52.8607
52 . 8338
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
52
51
51
50
49
49
48
4B
47
47
46
46
46
45
45
' 45
. 45
45
* 45
' 44
44
44
.360

.0666
.1356
.0694
,8716
.5463
.0998
.5420
.6813
.1261
.2909
.3853
.4174
.4072
.3567
.2823
.1849
. 0820
. 9770
.8786
.7930
.7233
.6778
.6588
.6695
.7155
.7880
.9029
.0244
.2428
.4658
. 7392
.0422
.3772
.7786
.1971
.6542
.1534
.6893
.2627
.8719
.5162
.1976
.9137
.6633
.4476
.2659
,1172
.0021
.9202
.8702
.8547
.365

77 . 6455
77.7055
77.6158
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
S7.5629
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
.0069
, 5738
.9943
.2817
.4494
.5059
.4724
.3623
.1882
.9667
.7112
.4294
.1359
.8439
.5700
.3059
.0636
.8488
.6682
.5256
.4212
.3604
.3431
.3700
.4654
.5638
.7252
.9398
.1888
.4866
.8822
.2403
.6551
.1279
.6400
.1922
.7832
.4126
.0796
.7836
.5242
.2998
.1096
.9574
.8381
.7519
.7022
.6851
of


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
43
the HelMhnltz Coil
.375

.2061
.2433
.0950
.7667
.2661
.6058
.8018
.8630
.8168
.6547
.4223
,1267
.7831
.4095
.0148
.6145
.2200
.8396
.4860
.1534
.8622
.6104
.4023
.2389
.1249
.0593
.0457
.0770
. 1624
.2977
.4814
.7081
.9872
.3747
.7091
.1045
.5656
.0672
.6103
.1934
.8165
.4776
.1763
.9130
.6857
.4944
.3384
.2172
.1311
.0792
.0613
.380

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
84
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
41
41
3H5

4170
4246
1981
7457
0800
2165
1779
9B03
6508
2139
6904
1043
4766
8216
1688
5186
8897
2921
7336
2203
7647
3612
0174
7334
5111
3229
2467
2095
2262
3055
4380
6291
8680
1960
5263
8952
3364
8197
3552
9149
5315
1845
8757
6062
3739
1786
0201
8964
8085
7564
7388


87
B7
87
87
86
85
84
82
B<
79
77
76
74
72
70
68
67
65
63
62
60
59
57
56
55
53
52
51
50
49
48
48
47
46
45
45
44
44
43
43
42
42
42
41
41
41
41
41
41
41
41
.390

.8210
.81114
. 5352
.0042
. 2337
.2442
.0598
.7021
.2052
.7115
.8964
.1381
.3404
.5329
.7238
.9333
.1739
,4572
.7935
.1877
.6369
.1551
.7425
.3978
.1211
.9130
.7715
.6967
.6878
.7370
.8467
.0161
.2434
.5230
.8689
,2340
.6672
.1438
.6784
.2205
.8418
.4940
.IfliO
.9101
.6771
.4U01
.3202
.1964
.1084
.0556
.0379
.395

90.4659
90.4357
90.0960
89.472B
88.5796
87.4407
86.0871
84 . S552
82.8522
81.0427
79.1476
77,1940
75.2110
73.2274
71.2538
<,9 , 2825
67.4154
65.5698
63.7911
62.0814
60.4462
58.8859
57.4033
55.9997
54.6697
S3. 4 152
52.2358
51.1208
50.0832
49.1125
48.2053
47.3579
46.5715
45.8396
45.1636
44.5334
43.9602
43.4320
42 . 9656
42.4923
42.1203
41.7730
41.4585
41.1840
40.9504
40.7S37
40.5936
40.4700
40.3815
40,3298
40.3112
.400

93,3739
93.3169
92.9139
92.1803
91.1403
89.8248
88.2669
86.5125
84.6481
82.5583
80.4368
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
S4.148D
52.8386
51.6353
50.4956
49.4320
48.4407
47.5157
46.6504
45.8506
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
.405

96.5990
96.5117
96.0267
95.1613
93.9443
92.4190
90.6248
88.6144
86 . 4365
84.1367
81.7595
79.3519
76.9276
74.5171
72.1859
69.9055
67.7012
65.5936
63.5673
61.6506
59 . 8327
58.1119
56.4980
54 . 9762
53.5514
52 . 2276
50.9656
49 . 7992
46.7132
47 . 6972
46.7618
45.8890
45.0812
44.3342
43.6447
43.0115
42.4281
41 . 8986
41.4225
40.9457
40.5808
40.H375
39 . 9278
39.6431
39.4077
39.2168
39.0592
38 . 9366
38.8503
38.7982
38.7809
.410

100.1917
100.0690
99.4813
98.4522
97.0233
95 . 2455
93.1678
90.8585
88.3747
B5 . 7722
83.1017
BO. 4140
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
50.2214
48.9854
47.9283
46.9034
45.9516
45.0717
44 . 2568
43.5086
42.8211
42.1802
41.6016
41.0747
40.5915
40.1327
39 . 7622
39 . 4223
39.1170
3B.8303
38 . 5846
38.4042
38.2544
38.1257
38.0466
37.9950
37 . 9772
.415

104.2133
104. 0465
103.3319
102.1049
100.4162
98.3275
95 . 9346
93.2486
90.405B
87.4524
84 . 4529
81.4516
78.4942
75.6124
72.8288
70.1632
67.6350
65 . 2233
62.9578
60.8291
58.8322
56.9700
55 . 22B3
53 . 6 072
52.1000
50 . 6979
49.3977
48.1930
47.0731
46.0393
45.0B36
44.2007
43.3854
42 . 6323
41.9472
41.3178
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-------
'.Magnetic Fields parallel to The z-axis of the Helnholtz  Coil
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-------
Magnetic Fields parallel TO
R (n> .400 .485
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-------