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Distortion of amplitude and phase of alternating electromagnetic fields by presence of electrical conductors Mungall, Allan George 1950

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DISTORTION OF  OF  AMPLITUDE  AND  PHASE  ALTERNATING ELECTROMAGNETIC  BY  PRESENCE  OF  ELECTRICAL  FIELDS  CONDUCTORS  by ALLAN  GEORGE  MUNGALL  oOo  A  THESIS THE  SUBMITTED  REQUIREMENTS MASTER IN  OF  IN  PARTIAL FULFILMENT  FOR  THE. D E G R E E  APPLIED  THE  OF  SCIENCE  DEPARTMENT O F  -PHYSICS;.  0O0  |  w I THE  U N I V E R S I T Y OF APRIL,  BRITISH 1950  COLUMBIA  OF  Abstract  T h i s t h e s i s d i s c u s s e s both q u a l i t a t i v e q u a n t i t a t i v e c h a r a c t e r i s t i c s of the h o r i z o n t a l  and  electromag-  n e t i c f i e l d produced by the f l o w of eddy c u r r e n t s i n a conductor. The e x c i t i n g f i e l d  i s s u p p l i e d by a l a r g e h o r i z o n t a l  l o o p c a r r y i n g an a l t e r n a t i n g c u r r e n t , and the  secondary  h o r i z o n t a l f i e l d i s measured by d e t e c t i n g the v o l t a g e induced i n a s m a l l v e r t i c a l search c o i l  i n the plane of the l o o p .  Determinations of both the r a t i o of the h o r i z o n t a l f i e l d t o the v e r t i c a l , and the phase angle between them are made a t v a r i o u s p o i n t s a l o n g a diameter d i r e c t l y above the c e n t r e l i n e of each conductor. C o r r e c t i o n s t o e l i m i n a t e v o l t a g e s induced i n a l l p a r t s of the measuring  extraneous  apparatus are  a p p l i e d t o these measurements. The c o r r e c t e d values are then p l o t t e d as p r o f i l e s of r e l a t i v e amplitude and phase f o r s e v e r a l p o s i t i o n s of each conductor. The shapes of t h e s e curves and p o s s i b l e mathematical e x p r e s s i o n s r e l a t i n g them t o 'the p h y s i c a l dimensions and p o s i t i o n of the conductor are d i s c u s s e d , and some approximations of the c o n f i g u r a t i o n of s u r f a c e c u r r e n t f l o w are suggested. The present r e s u l t s are compared with those obtained by p r e v i o u s experimenters c e r t a i n changes o f fundamental  concepts are suggested.  and  Possible application interpretation  of these r e s u l t s t o q u a l i t a t i v e  of measurements taken over a c t u a l ore-bodies,  and methods of a c c u r a t e d e t e r m i n a t i o n of s i z e and depth of the bodies are proposed.  000O000  Acknowledgements  The  author wishes t o express h i s thanks t o the  members of the Department of P h y s i c s of the U n i v e r s i t y of B r i t i s h Columbia, e s p e c i a l l y Br. A. Van  C l a r k and  der Z i e l , f o r t h e i r a s s i s t a n c e and  i n connection which was  t o Dr. A. R.  to  suggestions  w i t h t h i s r e s e a r c h , the accomplishment  of  made p o s s i b l e by f i n a n c i a l a s s i s t a n c e from the  N a t i o n a l Research C o u n c i l of Canada.  00O00  T A B L E  O F  C O N T E N T S  P a g e  I  I N T R O D U C T I O N  I I  T H E O R Y  I I I  O U T L I N E  O F  M E T H O D  I V  D E T A I L S  O F  C O N S T R U C T I O N  S i g n a l  B  P h a s e  C  1  . %  A  1 .  '  .'  8  G e n e r a t o r  8  T r a n s f o r m e r  9  P r o o f  o f  q u a d r a t u r e  f i e l d  c o i l s  D i s c u s s i o n  o f  3 . '  C o n s t r u c t i o n  P h a s e  c u r r e n t  i  v a r i a b l e  o f  a n d  p h a s e  p h a s e  e . m . f .  1 1  t r a n s f o r m e r . . . . . . . . . . . 1 3  A m p l i t u d e  M e a s u r i n g  1 3  1 .  V a c u u m  2 .  V e r t i c a l  3  M e t h o d  t u b e  v o l t m e t e r  s e a r c h  o f  1 3  Ik  c o i l  m e a s u r e m e n t  1 5  R E S U L T S . . . .  1 8  A  C o n d u c t o r s  B  D e t a i l e d  F o r  n  . . . . . . 1 0  2 .  R e l a t i v e  o f  A p p a r a t u s  V  ,...6  U s e d  L i s t  o f  C o n d u c t o r s  C  P r o c e d u r e  D  C o r r e c t i o n s  1 8  1  E x p e r i m e n t a l  t o  C u r v e s  3  1 9  2 1  A p p l i e d  t o  M e a s u r e m e n t s  2 1  T a b l e of Contents  continued: Page 22  E  Sources  of E r r o r  F  D i s c u s s i o n of E x p e r i m e n t a l R e s u l t s  27 27  1^ C y l i n d r i c a l conductors w i t h i n the l o o p  ...27  (a) Phase curves (b) Mathematical  treatment of phase  r e l a t i o n s between the h o r i z o n t a l and vertical field (c)  27  components  R e l a t i v e amplitude  ..29  curves..  (d) I n f e r e n c e s from r e l a t i v e  amplitude 29  and phase curves (e) E f f e c t  of r e s i s t a n c e on phase and  r e l a t i v e amplitude c u r v e s . .  ..30  2.. R e c t a n g u l a r conductors w i t h i n the l o o p (a) Phase curves  3& .....38  (b) R e l a t i v e amplitude curves (c)  38"  I n f e r e n c e s from phase and r e l a t i v e amplitude  curves......  (d) Mathematical of  i  40  treatment of and d i s c u s s i o n  surface current flow  41  ( i ) C a l c u l a t i o n of h o r i z o n t a l  field  i n t e n s i t y assuming a c u r r e n t f l o w i n g o n l y i n the edge of the  conductor...41  ( i i ) C o m p a r i s o n w i t h experimental data.42 3. R e c t a n g u l a r conductors o u t s i d e the loop....43 (a) Phase c u r v e s . .  .43  Table of Contents continued: Page 43  (b) R e l a t i v e amplitude curves..  -..45  (c) D i s c u s s i o n of s u r f a c e c u r r e n t flow VI  SUMMARY  •  45 .47  Acknowledgements.  4$  Bibliography  LIST OF PLATES Page Plate 1  23  Plate 2  24  Plate 3  25  Plate 4  26  Plate 5  35  Plate 6  36  Plate 7  •  44  Plate 8  37  Plate 9  31  P l a t e 10  .  For a d e t a i l e d l i s t  of p l a t e s , see page 1 9 .  39  L I S T  O F  F I G U R E S  P a g e  F i g u r e  1 .  S i g n a l  G e n e r a t o r  ( a )  F i g u r e  2.  S i g n a l  G e n e r a t o r  (b)  F i g u r e  3 .  V o l t a g e  F i g u r e  4.  P h a s e  F i g u r e  5.  E x p e r i m e n t a l  M e a s u r i n g  £ > ( a )  8(b)  A p p a r a t u s  . . . . . 1 3 ( a )  .9(a)  T r a n s f o r m e r  L a y o u t  •  6 ( a )  DISTORTION OF AMPLITUDE AND  PHASE  OF ALTERNATING ELECTROMAGNETIC FIELDS BY PRESENCE OF ELECTRICAL CONDUCTORS  I  INTRODUCTION The p r i n c i p l e upon which e l e c t r o m a g n e t i c i n d u c t i v e  methods of, g e o p h y s i c a l i n v e s t i g a t i o n are based i s t h a t the t r a n s f e r of power from an e x c i t i n g l o o p t o a conductor beneath the s u r f a c e r e s u l t s i n a deformation of the phase and amplitude of the f i e l d w i t h i n the l o o p . A s m a l l , n e a r l y h o r i z o n t a l secondary f i e l d whose phase and amplitude are f u n c t i o n s of the d i s t a n c e from the conductor i s produced i n the plane of the l o o p . T h i s combines w i t h the v e r t i c a l or primary f i e l d  component t o form a r o t a t i n g , v a r i a b l e  amplitude  f i e l d v e c t o r , d e s c r i b i n g an e l l i p s e of p o l a r i z a t i o n . The depth t o which a conductor may  (1)  be d e t e c t e d by  o b s e r v a t i o n of the c h a r a c t e r i s t i c s of t h i s e l l i p s e of p o l a r i z a t i o n v a r i e s w i t h the frequency of the e x c i t i n g magnetic  field.  electro-  I t has been found i n p r a c t i c e t h a t the optimum  frequency f o r maximum depth p e n e t r a t i o n i s about The e x c i t i n g f i e l d may  500 c.p.s.  be produced by e i t h e r  h o r i z o n t a l or v e r t i c a l l o o p s , the former being p r e f e r a b l e f o r (1) H e i l a n d , C. A.,  G e o p h y s i c a l E x p l o r a t i o n , pp. 773-6*09,  P r e n t i c e - H a l l , New  York,  1946.  -2s h a l l o w  e a s i l y  T h e  d i p p i n g  h a n d l e d  l o o p s  o r  a n d  m a y  e x t e n d e d  b o d i e s .  a l l o w s  t a k e  t h e  t h e  f  f i e l d .  e  l  d  o  f  o n  o  c o i l s  f i x e d  a  a b o u t  twici3  t h a t  o  f i e l d ,  c o i l  t  i  l e a d s  s  i s  t h e n  i s  a  t o  t h i s  n  a  s  t h a t  s  m o r e  c i r c l e s ,  d u e  t  o  i  a  e  t  t h a t  h  e  n  t  e  t  o  a  o p p o s i t i o n  o  f  t h e  p r i m a r y  f  s  o f  e  l  d  i  n  t h e  i  s  a p p e a r s  h  i  n  e  a r e a  t u r n s .  t h e  o f  e  t h e  v e r t i c a l  v e r t i c a l  a c r o s s  t h e  e . m . f .  v e r t i c a l  c o i l  d e t e c t o r  c h i e f  n o t  h  a n  t h e  T h e  T h e  t  i n c o r r e c t l y  a x i s  t  n  p r i m a r y  o t h e r  a t t a i n e d .  p h o n e s .  s  b y  b y  t h e  r  I  m o r e  r  c o i l  c o n d e n s e r  e l l i p s e  i  i  o  m i n o r  o  o  r  r e c t a n g u l a r  m a n y  a n d  e  t w o  o  h a v i n g  i n d u c e d  t  F  t w o  v e r t i c a l  t u r n s  i  w i t h  f  o f  h  t h e s e  u s e d .  h o r i z o n t a l  b y  t  h o r i z o n t a l  o f  w i t h  t h e  e . m . f .  b a l a n c e  i  h  o f  o f  o n e  v e r t i c a l  t h e  n u m b e r  s  h o r i z o n t a l ,  p h a s e  n  a n d  p  s t a t i o n s .  c o n s i s t s  v e r t i c a l  t h e  T h e  a m p l i f i e r  r  t h e  n  i  i n t o  T h e  u n t i l  a  t  w i t h  i  a x i s .  c o n n e c t e d  m e t h o d  i  i  t h e  v e r t i c a l  d i f f e r e n t  i  d i s t o r t i o n  a b o u t  d  p h a s e  a p p a r a t u s  a s s u m e d  i n d u c e d  b a c k  s t a g e  t  p r o p o r t i o n a l '  m a j o r  v a r i e d  v o l t a g e  s  a n d  i n t e n s i t i e s  h o r i z o n t a l ,  i n d u c e d  d e t e c t o r .  t h r e e  t h e  i  i  b r o u g h t  i  f  s t r i k e  s u c c e s s i v e  a  m e t h o d  t h e  d e s i r e d  r e l a t i v e  m e a s u r e d  q u a d r a t u r e  f i e l d  t h e  a n d  a c r o s s  i  e . m . f .  a n d  o  s  t r i a n g l e s ,  d e t e r m i n i n g  b e t w e e n  a n g l e s ,  f i e l d  b e  T h e  o  r  t h e  r e c e i v i n g  r i g h t  s e c o n d a r y  h o r i z o n t a l  a  t  o  r e l a t i v e  B i e l e r - W a t s o n  e l l i p s e ,  i  r e c o n n a i s s a n c e .  r e c t a n g l e s ,  b e  r a t i o  t h e  d i f f e r e n t  f i e l d .  f o r m e r  o f  m a y  r  e a c h  t  s p e e d  i n f o r m a t i o n  c o m p o n e n t s ,  c o m p o n e n t s  c a s e ,  f  f i e l d  h o r i z o n t a l  a s s u m e d  o f  t h e  t h e  p o l a r i z a t i o n ,  c o m p o n e n t s ,  T h e  f o r m  i n f o r m a t i o n  v e r t i c a l  s o - c a l l e d  g r e a t e r  e q u i p m e n t  d e p e n d s  T h i s  e l l i p s e  a n d  i  p r a c t i c e ,  l i n e s .  R e c e p t i o n  o f  I n  d i s a d v a n t a g e s  v e r t i c a l ,  t h e  v e r t i c a l  -3c o i l and a quadrature v o l t a g e i n the  t i e horizontal  coil;  and the v e r t i c a l and h o r i z o n t a l f i e l d components are a c t u a l l y seldom  i n quadrature. Bruckshaw  due t o the assumption  of a 90  (2)  has e l i m i n a t e d the e r r o r s  degree phase d i f f e r e n c e between  h o r i z o n t a l and v e r t i c a l f i e l d s by i n t r o d u c i n g an  apparatus  to measure t h i s phase s h i f t and t o r e s t o r e the phase of the h o r i z o n t a l f i e l d . In e i t h e r case, the r e s u l t a n t d i r e c t i o n of the h o r i z o n t a l f i e l d  i s found and p l o t t e d as a v e c t o r which  p o i n t s towards the conductor and i n c r e a s e s i n magnitude t o a maximum over the edge of the conductor. T h i s p l o t t i n g of v e c t o r s does not l e a d t o a c c u r a t e q u a n t i t a t i v e r e s u l t s determining the p h y s i c a l dimensions and depth of the conductor. Any  c a l c u l a t i o n of the amplitude and phase d i s t o r t i o n  encounters severe mathematical  difficulties,  s i n c e the  boundary c o n d i t i o n s of s u r f a c e c u r r e n t f l o w i n g e o m e t r i c a l l y shaped  conductors i n a c y l i n d r i c a l e l e c t r o m a g n e t i c f i e l f l are  extremely d i f f i c u l t  t o a p p l y . Consequently, the o b j e c t i n  attempting the r e s e a r c h d i s c u s s e d i n t h i s t h e s i s was  to arrive  at more exact d e t e r m i n a t i o n s of the r e l a t i v e amplitude and phase v a r i a t i o n s of the h o r i z o n t a l e l e c t r o m a g n e t i c f i e l d as a f u n c t i o n of the c o n d u c t i v i t y , shape, d i p , depth, and  depth  extent of conductors; and t o attempt t o s e t up e m p i r i c a l  relations  between the experimental measurements and these v a r i a b l e s .  (2)  Bruckshaw, J . McG.,  Phys. Soc. P r o c , 46,  350,  1934.  -4II  THEORY S i n c e i n the l a b o r a t o r y , o n l y models can be used, a  j u s t i f i c a t i o n of t h e i r use, and a method of i n t e r p r e t a t i o n of the r e s u l t s i s n e c e s s a r y . C o n s i d e r a t i o n of Maxwell's Equations shows t h a t model methods of experimentation are v a l i d under certain conditions.  (3)  F o r a homogeneous i s o t r o p i c conductor, the f o l l o w i n g equations expressed i n M.K.S. u n i t s , d e s c r i b e the magnetic and e l e c t r i c f i e l d i n t e n s i t i e s and d i r e c t i o n s . -  where £  =o  G~E  i s the e l e c t r i c  field,  // i s the magnetic  field,  ytU. i s the p e r m e a b i l i t y of the conductor, <f~ i s t h e d i e l e c t r i c constant o f the conductor, (7 i s the d i f f e r e n t i a l o p e r a t o r , f'£r  /> %  ^ = <r(T  Let  l e n g t h =#ol. , time where(f  **Jj)  jtytf^/r^  7~ 7~  /Z»>  a  r  e  t  n  e  dimensionless  measure numbers o f . t h e f i e l d v a r i a b l e s i n a system the u n i t q u a n t i t i e s are , ^ o J/ &  e  }  0j  £  0j  67^ t~  f o r which  a  The measure numbers s a t i s f y the equations  V*? + ^/^0 where  <=^- -^sJo£  toe  =  o  G  1  M  cf- ^  &  n  are dimensionless c o n s t a n t s .  (3)  S t r a t t o n , J . A . , E l e c t r o m a g n e t i c Theory,pp. McGraw-Hill, 1931.  4#8-490,  A f t e r e l i m i n a t i o n of the common r a t i o ^ the f o l l o w i n g r e s u l t s U/o  €  f^?) =  constant , jt/  2  a  •=  0  /  constant  O  I f t h i s r e s u l t i s applied to a varying period^-  and  t o one  of a f a m i l y of-bodies  only i n s c a l e , of c h a r a c t e r i s t i c l e n g t h - ^ , that  Thus, t o preserve the work, t h a t i s , the  of  which d i f f e r  i t can be  seen  ^<T/Vo* = C  W  J/eC-fSoj^^O,  field  z  c o n d i t i o n s met  i n t e n s i t i e s and  i n practice i n f i e l d phase changes of  the  e l e c t r i c and magnetic f i e l d s , changes i n s c a l e f a c t o r must be and  compensated by the  changes i n frequency of the  exciting f i e l d ,  conductivity. In c o n s t r u c t i o n  a s c a l e f a c t o r of 1:100 a f r e q u e n c y and Therefore,  of the model used i n t h i s was  most a p p l i c a b l e , r e s u l t i n g i n  c o n d u c t i v i t y m u l t i p l i c a t i o n of  the experimental r e s u l t s d e r i v e d  of brass and  100.  from the  from surveys oyer ore-bodies whose  c o n d u c t i v i t y i s about 10 times t h a t of C o v e l l i t e , those from carbon, t o g r a p h i t e . G e n e r a l l y ,  the  of the model conductors isl from 10 t o 100 times than t h a t corresponding t o most s u l p h i d e  outermost p o r t i o n s considerably  induced c u r r e n t  greater  b o d i e s . However slight  flows o n l y i n the  of the conductor, which w i l l  weathered, and  CuS;  conductivity  c o n d u c t i v i t y of the massive m i n e r a l i s of o n l y  importance, s i n c e the  be  use  aluminum conductors would be comparable t o  f i e l d r e s u l t s derived  the  research  probably  w i l l thus have a d i f f e r e n t  c o n d u c t i v i t y . I t w i l l a l s o be a f f e c t e d by presence of m i n e r a l waters.  ' The  -6- .  above model t h e o r y has been a p p l i e d and j u s t i f i e d  by L . B. S l i c h t e r i n experiments performed by him i n 1 9 3 2 . ( 4 )  III  OUTLINE OF METHOD To p r o v i d e the necessary  field,  a 1:100 scale  model l o o p was b u i l t , 1 0 f e e t i n diameter of 5 t u r n s , t o c a r r y a c u r r e n t o f . 7 5 amperes, a t 50 k i l o c y c l e s . T h i s gave e x c i t i n g f i e l d i n t e n s i t i e s and l o o p c u r r e n t equal t o those found i n a 1 0 0 0 f e e t diameter l o o p used i n p r a c t i c e . The conductors were made of brass, aluminum, i r o n , and carbon to  g i v e a s u f f i c i e n t range o f c o n d u c t i v i t i e s , and were  constructed t o represent  o r e - b o d i e s . Power t o d r i v e the  e x c i t i n g f i e l d was s u p p l i e d by a s i g n a l generator c o n s i s t i n g of an R-C o s c i l l a t o r with v o l t a g e and power a m p l i f i c a t i o n stages. Phase and amplitude measurements were made by d e t e c t i n g the e.m.f. induced  i n a 2 cm. diameter v e r t i c a l  coil  o f 65 t u r n s which c o u l d be p l a c e d a t any p o i n t on a diameter of the l o o p . Because o f c i r c u l a r symmetry, i t was p e r m i s s i b l e to  c e n t e r the conductor d i r e c t l y beneath t h i s diameter and  at  any convenient  p o i n t along i t . However, s i n c e the v e r t i c a l  f i e l d was most uniform  i n t h e c e n t r a l p o r t i o n of the l o o p ,  most of t h e conductors were placed d i r e c t l y beneath t h e c e n t r e .  (4)  S l i c h t e r , L . B., Observed and T h e o r e t i c a l E l e c t r o m a g n e t i c  Model Response o f Conducting Spheres, A.I.M.E., Geophysical  Prospecting, pp.443-459, 1 9 3 2 .  F/GURE  S  EXPERIMENTAL  LAYOUT Woacftri -frame 3zfiruttSYoor  Tuneet  Sxc/fiof  £oo/* -  Stums,  MrrfSca/Hoi/-Zi*tQ  S/GA/AL  /O  'O.  65 ferns  ^  GeMBXAToK  TOSS ^  Box  -7The amplitude of the h o r i z o n t a l f i e l d was by a vacuum tube v o l t m e t e r measuring the v e r t i c a l c o i l ,  given  the e.m.f. induced i n  and c a l i b r a t e d t o read the r a t i o between  the h o r i z o n t a l f i e l d a t any p o i n t and the u n d i s t o r t e d ^ f i e l d at  the centre- of the l o o p . The VTVM a l s o served as' a n u l l  device t o i n d i c a t e the r e s u l t a n t amplitude of the sum  of  t h i s e.m.f. and another of equal amplitude but v a r i a b l e phase, s u p p l i e d by a phase t r a n s f o r m e r . The l a t t e r was  driven  by p a r t of the output of the s i g n a l g e n e r a t o r . The experimental v a l u e s of r e l a t i v e amplitude  and  phase were p l o t t e d ^ as f u n c t i o n s of the h o r i z o n t a l d i s t a n c e from the conductor. V a r i a t i o n s i n these curves which seemed c h a r a c t e r i s t i c of the p r o p e r t i e s of the conductor examined were noted .and approximate  formulae t o e x p l a i n them were  p o s t u l a t e d . Some e f f o r t was made t o f i n d the d i s t r i b u t i o n of  s u r f a c e c u r r e n t d e n s i t y n e c e s s a r y t o produce  these v a r i a t i o n s .  A c o n s i s t e n t d e p a r t u r e from the expected form of the phase curves was  found i n a l l of the experiments, and a p a r t i a l  e x p l a n a t i o n of t h i s i r r e g u l a r i t y was-attempted. Mefehods of d i f f e r e n t i a t i n g between bodies of d i f f e r e n t depth extent and dip  were o u t l i n e d  also.  IV  DETAILS OF CONSTRUCTION  A S i g n a l Generator The s i g n a l g e n e r a t o r c o n s i s t e d o f an R-C  oscillator  w i t h v o l t a g e and power a m p l i f i c a t i o n s t a g e s and gave an output o f 150 v o l t s R. M. S. a c r o s s 7000 ohms impedance. T h i s output s u p p l i e d a s e r i e s combination o f the e x c i t i n g l o o p w i t h a t u n e d impedance o f 3600 ohms, and t h e f i e l d  coils  of t h e phase t r a n s f o r m e r w i t h an impedance o f 3400 ohms. Thus t h e c u r r e n t g e n e r a t e d i n t h e l o o p was .75 amperes and t h a t i n each o f t h e f i e l d c o i l s o f t h e phase t r a n s f o r m e r was 15 m i l l i a m p e r e s . Since t h e s e l e c t i v i t y o f the tuned e x c i t i n g l o o p was l a r g e , Q=65 a t 50 k c , and s i n c e t h e o s c i l l a t o r f r e q u e n c y v a r i e s s l i g h t l y w i t h t h e t e m p e r a t u r e o f t h e carbon r e s i s t o r s used i n t h e t a n k c i r c u i t , some s o r t o f f r e q u e n c y adjustment and c a l i b r a t i o n was n e c e s s a r y . T h i s was a c c o m p l i s h e d by t h e i n s t a l l a t i o n o f an ammeter i n t h e l o o p c i r c u i t , and a v a r i a b l e ' r e s i s t o r i n the tank of the o s c i l l a t o r ,  controlling  t h e f r e q u e n c y and hence t h e l o o p c u r r e n t . S i n c e any v a r i a t i o n o f f r e q u e n c y i s i m m e d i a t e l y r e f l e c t e d by a c o n s i d e r a b l e d r i f t o f t h e a r b i t r a r y phase base o f t h e phase t r a n s f o r m e r , and as t h i s would o f course i n v a l i d a t e t h e r e s u l t s , f r e q u e n c y s t a b i l i z a t i o n was most i m p o r t a n t . A v o l t a g e r e g u l a t e d power s u p p l y f o r t h e s i g n a l g e n e r a t o r was b u i l t t o reduce f l u c t u a t i o n s  i n the amplitude  of -the e x c i t i n g f i e l d due t o changes i n l i n e v o l t a g e . S i n c e harmonics o f h i g h e r f r e q u e n c y p r e s e n t i n t h e  (vmgttoit\ ra  i  I  oa i  I  0  i N  N  5  8 I  x  k  A  $  «• ^ 4 *i  a & ^ * £I* 1  s ft  S  < S >S  < P £  * * £^ ^  & ^ -N  \5 • <* fl.Ji  ^  V,  "4 & $ ^ ^ $> s  i t U*  -8b-  <5 Q \ ii  \  Vn »  Q  n  \  ii  ^  «  8* s s>  *  k  <0 i.  |,  VS VS  ii  ,;  s> ^ NJ> ^jr  ^  1  Si  * V: * i|  u  i'  Il  n  'i N  N  -9exciting  current could possibly result  secondary as  field,  i t was n e c e s s a r y t o e l i m i n a t e t h e s e  c o m p l e t e l y a s p o s s i b l e . T h i s was a c c o m p l i s h e d  large negative and of  feedback  by u t i l i z i n g  t o t h e f i r s t tube  the voltage a m p l i f i e r tube. F i n a l l y ,  and  still  Phase  of the o s c i l l a t o r ,  t h e l o o p was t u n e d t o  farther the f r a c t i o n  that  phase, c o n s t a n t a m p l i t u d e  of the-exciting  v o l t a g e was r e q u i r e d . A D r y s d a l e two s e t s o f H e l m h o l t z  angles  c u r r e n t s 90 d e g r e e s  carrying  supplied  on 3 i  equal  by the s i g n a l  These c o i l s  inches diameter  lucite  v o l t a g e was i n d u c e d  extraneous The  induced  i n the r e s i s t i v e capacitative,  branch,  phase  o u t o f phase  copper  in a 1  specifications. wire  cm.  wound  phase diameter  with leads twisted  e.m.f. s. !  90 d e g r e e p h a s e d i f f e r e n c e  t h e two s e t s o f f i e l d  pair  with  at right  d i s c s . The v a r i a b l e  o f 10 t u r n s , mounted as i n f i g . 4,  reduce  coils  g e n e r a t o r , s a t i s f i e d these  c o n s i s t e d o f 40 t u r n s o f f i n e  constant amplitude coil  voltage  impedance a n d c o n s t a n t p h a s e b a s e r e l a t i v e t o  transformer,utilizing  the  o f harmonics  Transformer  low generator  in  by t h e use o f  to increase the loop current.  A variable  to  harmonics  only the l i n e a r portions of the c h a r a c t e r i s t i c s  50 k c . t o r e d u c e  B  i n c h a n g e s i n the-  between t h e c u r r e n t s  c o i l s was o b t a i n e d b y p u t t i n g one  branch  of a c i r c u i t ,  and t h e o t h e r i n  t h e same v o l t a g e b e i n g a p p l i e d a c r o s s  each  and a p p r o p r i a t e v a l u e s o f r e s i s t a n c e and c a p a c i t y  b e i n g used  t o supply  currents of equal  intensity.  Si  -10-  1.  Proof of quadrature of c u r r e n t  the t o t a l  coils.  C o n s i d e r the f o l l o w i n g c i r c u i t , where L  represents  inductance of the w i r i n g and two  coils,  the t o t a l  r  in field  a.c.  of the  r e s i s t a n c e of the w i r i n g and  the  coils,  which i s approximately equal t o the d.c. r e s i s t a n c e , C and R the l a r g e c a p a c i t y and c u r r e n t and  phase. The  and  r e s i s t a n c e used to "regulate  c a p a c i t y of? the w i r i n g i s n e g l i g i b l e . - ' W W -  t I f c#  c  and  Z.  r  z  r  represent  G  the c u r r e n t s i n the r e s i s t i v e  c a p a c i t a t i v e branches r e s p e c t i v e l y , and E the v o l t a g e a c r o s s the c i r c u i t at a f r e q u e n c y aJ  00  4 =  /E  Jtul  and  y-A y  are small compared w i t h R /?=  cue  and  capacitative currents  Ifrt-zfr  »  t  are equal and  n  e  n  '*~l/'*c  rom  (1)  and  t h a t the  (2),  and  resistive  found t h a t the magnitudes . of *~  s m a l l , were about jfo of R.  treatment.ewasmcarried F  coL  other by 9 0 degrees.  However, i t was and cul"while  and  and  T h i s s t a t e s t h a t the magnitudes of the r e s i s t i v e  c u r r e n t l e a d s the  applied  , then,  As a f i r s t approximation, i t can be assumed t h a t r  Then,  and  out.  Thus a more d e t a i l e d  -11-  Put —""/S , ou^^c=e^ assume much l e s s than 1 Then, s i n c e  ~  w c 3  For ^ t o equal c £  >  *  ~°<  , the t o t a l impedance of each branch must -«<ivz/  that of the other. Given L and r , C and R can be a d j u s t e d t o satisfy this condition. The phase angle between ^ Tan 6  =  'M+'X*-')  c  and  - /'+  =  i s g i v e n by £S-S3)  F o r t a n <fi t o be i n f i n i t e l y l a r g e , t h a t i s , 0 = 9 0 " and /?? should be v e r y s m a l l . For the c i r c u i t s a c t u a l l y used, the f o l l o w i n g v a l u e s were found f o r the c o n s t a n t s . giving and  °s - • OJ 2  0 = tan  ^r<S3~  Thus an e r r o r of about 1 degree i s i n t r o d u c e d i n t o the r e l a t i v e phase of the c u r r e n t s i n the f i e l d c o i l s . Since the maximum p o s s i b l e phase s h i f t s are 1&0 degrees,  the r e s u l t i n g  percent  error i s n e g l i g i b l e .  2 . D i s c u s s i o n o f . v a r i a b l e phase e.m.f. That the e.m.f. induced i n the s m a l l c o i l i s of constant amplitude,  r e g a r d l e s s of the angular p o s i t i o n of the  c o i l , and t h a t i t s phase i s g i v e n by the angle through which  - 1 2 -  t h e  c o i l  i  p a r a l l e l  t  f o l l o w i n g  s  o  r o t a t e d  t  h  Tcosu>f  a r e  t  h  p l a n e s  t  a  e  n  h  d  e  t  c u r r e n t  t h a t  out  f  a  n  a x i s  h  e  e q u i d i s t a n t  f i e l d  c o i l s ,  i  n  i  t  h  n  e  o n e  o  Moon out  d  s  e  s e c o n d  c o m p o n e n t s  f r o m  a  r e q u i r e s  n  t  d  h  e  (5)  t r e a t m e n t .  r e c t a n g u l a r  X- / / J V ^  a n  o  m a t h e m a t i c a l  L e t  T h e n  e  a b o u t  f  t o  f  s  e  t b  t  h  e  a  t  +Cos Luf=  n  d  c o i l s  b e  g i v e n  T c o t  y  r e s u l t a n t  t  h  e  b  y  .  a  t  r e s u l t a n t  t  h  e  c e n t r e  f i e l d  R ,  2  i  T h u s ,  t  h  v o l t a g e  e  X  a m p l i t u d e  i n d u c e d  p o s i t i o n  o  f  A t  t  h  a  c o n s t a n t .  i  e  n  o  n  t  f  h  t  e  h  e  f i e l d  c o i l  i  s  a  n  d  c o n s e q u e n t l y  i n d e p e n d e n t  o  f  t  h  t h a t  e  o  f t  h  e  a n g u l a r  c o i l .  y  i n s t a n t  t  h  e  t a n g e n t  o  f  t  h  e  i n c l i n a t i o n  o  f  x t h i s  r e s u l t a n t  t  o  t  h  T a n ^ -  T h u s  c o n s t a n t  c o i l  t  i n d u c e d  o  L a w s ,  i  e  f r o m  F .  i  i  A . ,  M c G r a w - H i l l ,  v e r t i c a l  ^ - =  s  s  t  a x i s  r e s u l t a n t  f i e l d  T h e  p r o p o r t i o n a l  ) ,  s  e q u a l  s  z e r o  o  t  t  o  s  y  .  h  e  T h e r e f o r e ,  h  e  t  a  f l u x  t  o  t  t  t h r e a d i n g  c o s ( ^ ^ - ^ )  t i m e - p h a s e  h  e  c e n t r e  a n g u l a r  a  t  n  r o t a t e s  h  d  e  t  h  e  Y o r k ,  1 9 3 8 .  i n d u c e d  d i s p l a c e m e n t  d i s p l a c e m e n t  M e a s u r e m e n t s ,  p p .  w i t h  s m a l l  p o s i t i o n .  E l e c t r i c a l  N e w  i  out.  T a n  v e l o c i t y .  s i n ( ^ ^ - &  e . m . f .  s e c o n d a r y  (5)  h  a n g u l a r  s e c o n d a r y  e . m . f .  t  e  2 9 8 - 9 ,  o  o  f t  f t  h  h  e  e  - 1 3 -  3.  C o n s t r u c t i o n o f the phase t r a n s f o r m e r . That any f i e l d d i s t o r t i o n r e s u l t i n g ' f r o m eddy  c u r r e n t s w i t h i n t h e instruments might be e l i m i n a t e d , o n l y l u c i t e and f i b r e board were used i n i t s c o n s t r u c t i o n . I s o l a t i o n from the f i e l d s generated by the l a r g e loop was accomplished by p l a c i n g i t w i t h the d e t e c t i n g  apparatus  on a t a b l e 2 0 f e e t from the l o o p and s h i e l d i n g i t with a 1 2 i n c h square aluminum box open a t the t o p . T h i s s h i e l d i n g e f f e c t i v e l y i s o l a t e d the d e t e c t i n g apparatus from.the  also  magnetic  f i e l d s generated by the t r a n s f o r m e r i t s e l f . I t was found t h a t the phase base v a r i e d c o n s i d e r a b l y w i t h any s l i g h t change i n the frequency o f t h e s u p p l i e d v o l t a g e . However, s i n c e t h e frequency remained  constant once the s i g n a l  generator had been o p e r a t i n g f o r a few minutes, t h i s l e d t o n e g l i g i b l e e r r o r s i n measurements o f r e l a t i v e phase. C  R e l a t i v e Phase and Amplitude Measuring  Apparatus  1 . Vacuum tube v o l t m e t e r . A s e n s i t i v e l i n e a r vacuum tube v o l t m e t e r tuned t o 5 0 kc. was designed and b u i l t t o measure the v o l t a g e induced i n the v e r t i c a l c o i l  by the h o r i z o n t a l f i e l d  component o f t h e  loop, and t o i n d i c a t e a n u l l when t h i s v o l t a g e and one o f equal amplitude and o p p o s i t e phase superimposed  were measured.  The vacuum tube v o l t m e t e r c o n s i s t e d of t h r e e stages of  voltage a m p l i f i c a t i o n g i v i n g a gain of  4 0 , 0 0 0  coupled t o  the i n p u t of a diode d e t e c t o r . A microammater, 0 - 5 0 m i c r o amps f u l l s c a l e d e f l e c t i o n , i n d i c a t e d the magnitude of t h e r e c t i f i e d c u r r e n t . Shunting o f t h e l o a d r e s i s t o r of t h e diode  IB ^  w*^ (finwramrmn s\ 1  I  4^4  -vr  1 fi?> $ (i»  in  I P iP  ^ ? §v2r I i 11 i 11 'i  , . , 1 1 1 1  «; *s ^ ^ ^  .  ^  \.  N  0  0  ft  N  ri  ^ Ml  M  ^1  S  i  '  i  "  .  «  «  •  .  f ?* &#?£ n II  'i «i •  " ' i"*\ X 3 ft it -i N N « • II •) § 4  8  .Co  5  I to  -14-  by a lower r e s i s t a n c e which c o u l d be switched  on or o f f  gave i n c r e a s e d s e n s i t i v i t y . Since a l a r g e v o l t a g e was to  the d e t e c t o r and  s i n c e the microammeter was  small r e s i s t a n c e , the d e t e c t o r was  supplied  shunted  made e f f e c t i v e l y  by a  linear  down t o a d e f l e c t i o n on the meter of l e s s than I microamp. T h i s ensured  a c c u r a t e d e t e r m i n a t i o n of the n u l l p o i n t sought  i n the measurement of phase. F o r d e f l e c t i o n s past 40 microamps, d e t e c t i o n was of  no l o n g e r l i n e a r because of curvature  the tube c h a r a c t e r i s t i c s f o r l a r g e g r i d v o l t a g e . An e x c e s s i v e l y h i g h n o i s e l e v e l r e s u l t i n g from  extraneous  e.m.f.'s induced i n the c i r c u i t s and  lead-in  wires n e c e s s i t a t e d e l e c t r o s t a t i c s h i e l d i n g of the vacuum tube voltmeter, use of s h i e l d e d cable f o r a l l l e a d - i n w i r e s , i n s t a l l a t i o n of s h i e l d e d tubes, and removal of the  entire  measuring d e v i c e a d i s t a n c e ' of 20 f e e t from the e x c i t i n g l o o p . S h i e l d e d g r i d i n p u t t o the f i r s t tube was The to  a l s o necessary.  second stage o f v o l t a g e a m p l i f i c a t i o n was  tuned t o 50 kc.  e l i m i n a t e 60 c y c l e n o i s e V o l t a g e .  2 . V e r t i c a l search The  coil.  i n t e n s i t y of the h o r i z o n t a l f i e l d was  determined  by measuring the e.m.f. induced i n a v e r t i c a l c o i l 2 cm. diameter,of  65 t u r n s , wound on a l u c i t e c o r e . The  f i x e d t o a s m a l l l u c i t e c h a s s i s , which t r a v e l l e d along a diameter  was  horizontally  of the l o o p , and c a r r i e d the c o i l o r i e n t e d  p e r p e n d i c u l a r t o the diameter. was  coil  in  Since the h o r i z o n t a l f i e l d  sometimes of the order of 1% of the v e r t i c a l f i e l d ,  the  planes of a l l t u r n s had t o c o i n c i d e w i t h i n a f r a c t i o n of a  -15degree, and the c o i l  i t s e l f had t o be o r i e n t e d w i t h the same  p r e c i s i o n . The w i r e s l e a d i n g from the c o i l were t w i s t e d t o minimize any extraneous induced e.m.f., and were l e d i n t o a s h i e l d e d cable w i t h i n an i n c h of the c o i l . The other end of t h i s cable was l e d i n t o the s h i e l d e d j u n c t i o n box. I t was found t h a t the p r o x i m i t y t o the search  o f the m e t a l , s h i e l d  o f t h e cable  c o i l had n e g l i g i b l e e f f e c t on the magnitude  or phase of the h o r i z o n t a l  field.  3. Method of measurement. The r a t i o o f the h o r i z o n t a l f i e l d component u n d i s t o r t e d v e r t i c a l component  a t the c e n t r e  t o the .  o f the l o o p was  measured by c a l i b r a t i o n o f a r o t a t i n g v o l t a g e d i v i d e r t a p p i n g the f r a c t i o n o f t h e e.m.f. induced i n the v e r t i c a l  coil  r e q u i r e d t o g i v e a h a l f s c a l e d e f l e c t i o n on the microammeter. The phase of t h i s e.m.f. was then given by a d d i t i o n t o another of equal amplitude from t h e phase transformer, of t h i s sum t o the vacuum tube v o l t m e t e r .  and a p p l i c a t i o n  The phase o f the  second e.m.f. was v a r i e d u n t i l a n u l l or minimum was i n d i c a t e d on the meter. The phase angle of the f i r s t  e.m.f. was thus  18*0 degrees p l u s t h a t i n d i c a t e d by the phase  transformer,  The f o l l o w i n g c i r c m i t was found s a t i s f a c t o r y i n the making of these  •franr-foz-mer Co//  measurements.  -16-  I n  t h e  v o l t a g e  a n d  P  t h a t  o f  w h e n  t h e  a b o v e  S,  i  t h e  s  o p e n  r e q u i r e d ,  S,  i  s  t h e  n e e d e d  a p p r o p r i a t e l y  t h e  t h e  c l o s e d ,  w i l l  b e  o n  t o  p h a s e  a s  s o o n  s h o u l d  b e  a s  R  b o t h  ,R -  V  p  ,R^  6  l a r g e .  a n d V p  y i e l d i n g  f o l l o w i n g  R^  w o u l d  b e  o f  a  R^=600-n_ R  l  b y  6 +  R=250-0.  R =40J2. 4  l  t h e s e  t h e  B y  a n d  o f  t h e  c l o s e d .  i  n  c o i l .  T h i s ,  a c r o s s  i n p u t  i n c r e a s e  o f  c o n s i d e r a b l e  0-25,000 P , = 0-500 J X  R  6  i  a n d  t o  t h e  a r e  n o i s e  7  R=0  f  "R^  s h o u l d  o n  t h e  R +-  a n d  ,  5  R;=0,  o r  r e s p e c t i v e l y ,  t u b e  l i m i t e d  l e v e l  v a l u e s  R  2  v a c u u m  e x p e r i m e n t ,  -Q.  m i n i m u m  a c c u r a c y  R r  R  c h o s e n .  n u l l  c o i l s  d e p e n d s  s i n c e  r e s i s t a n c e s  a  i m p e d a n c e  t h a t  s  ,  t h i s  a n d  i n p u t  s  t w o  S i n c e  e a s e  s  S ^ a r e  i n s t e a d  o f  i  z  f i e l d .  m i n i m u m  n e c e s s a r y  v o l t a g e  S,  s  b e t w e e n  i  f o r  P  r a t i o  m i n i m u m  a s s u m p t i o n  d e v e l o p e d  r e s i s t a n c e .  w e r e  e a c h  a r e  z e r o  i m p o s e d  v a l u e s  7  t h e  i  o f  a t t a i n s  d e f l e c t i o n .  a  a r e  c h a n g e  t h e  R  a n d  H o w e v e r ,  r e s t r i c t i o n s  t h e  o n  e f f e c t i v e l y  v o l t m e t e r .  i n c r e a s e  ,  A  R,  u n t i l  b o t h  s o  d e f l e c t i o n  v e r t i c a l  u n t i l  p o s s i b l e  f o r  s c a l e  t r a n s f o r m e r ,  m e a s u r e m e n t  v a r i e d  2  i m p e d a n c e s  a s  e q u a l  s c a l e  d i r e c t l y  v a r i e d  p  P  r e q u i r e d ,  z e r o  o f  v e r y  s  n e a r  a p p r o x i m a t e l y  a r e  i  i n p u t  m e a s u r e m e n t s ,  p e r m a n e n t l y  u n d i s t o r t e d  s w i t c h e s  b e  ,?R,  r e a d  b o t h  t a k i n g  s e t  s  h a l f  a n d  h a l f  a s  i n  4  a  m i c r o a m m e t e r .  t h e  i  a m p l i t u d e  t h e  V  p h a s e  W h e n  a n  r e g u l a t e s  t h e  a  t o  o f  E  P,  o f  c l o s e d ,  m e a s u r e m e n t  s i n c e  c h a n g e  c o i l .  S ^ o p e n e d ,  a n d  p o t e n t i o m e t e r  s e c o n d a r y  p r o d u c e  f i e l d  t h e  f o u n d  2  r e s u l t s .  t h e  r e g i s t e r e d  S  a n d  c a l i b r a t e d  p h a s e  a n d  t h e  t h e  s e a r c h  c l o s e d ,  h o r i z o n t a l  W h e n  b y  f i e l d  m i c r o a m m e t e r  v a l u e  c i r c u i t ,  d e l i v e r e d  t h a t  a  t h e  b y  w i t h  t h e  re  - 1 7 -  A  s e a r c h  c o i l  w a s  t h e n  a  d e f l e c t i o n  w a s  F  p o s i t i o n  o n l y  r e q u i r e d  f  T h a t  i  s  ,  i n d u c e d  T h i s  i  o  n  c o i l .  t o  p o i n t  w a s  t h e  s c a l e  l i n e a r  . 0 0 3 ,  w e r e  0  t o  p h a s e  w a s  l o o p  5 0  e n t i r e  n o t e d  c a b l e  0  o f  t o  o  a  n  r  o f  e . m . f .  . 0 1 ,  B e l o w  t e n d e d  t h e  s i n c e  a n  b e  f  o  r  i n p u t  a n d  n  a  t h e  c o i l  l e s s  f r a c t i o n  o f  m e t e r  t o  r a t i o  f o u n d  s e p a r a t e  o f  a n d  i  n  t h e  n e g l i g i b l e  l a r g e .  i n d u c e d  t h e  w a s  i n a c c u r a t e  r e a d i n g s  o u t p u t  A t  t h e  a m p l i t u d e  R ^ + R ^ w a s  i  n  r a t i o s  R a t i o s  t h e  t h a t  w a s  i  i  n  e r r o r s  S i n c e  t h e  s h i e l d e d  l e a d s .  t h e  c h a n g e d  f i e l d  i n d u c e d  o f  t o  a m p l i t u d e  b u i l t  t h r e a d i n g  t h e n  v o l t m e t e r .  ras::^' nrr  1 ,  p o t e n t i o m e t e r .  a s s u m p t i o n  w a s  d e f l e c t i o n .  b y  r e p r e s e n t i n g  v o l t a g e  e . m . f .  w a s  w a s  l e a d i n g  t  r a t i o  s c a l e  f i e l d  t h u s  i  l o o p - p l a n e  t h e  h a l f  . 2 ,  n o i s e  p l a c e d  t h e  t h e  a b o v e  t h e  a n d  w h e n  d e s i g n a t e d  t u b e  m i c r o a m p s .  k c .  f i e l d ,  s h i e l d e d  o n  i  Vfo  m u l t i p l i c a t i o n  r a n g e  t h e  r  w a s  p o i n t s  v a c u u m  b y  f r o m  f r o m  c o n s i d e r a b l e  w i t h  t h e  f  v e r t i c a l  m e a s u r e m e n t s  T h e  o  r e s i s t a n c e s  t h e  2 5  t h e  a n d  d e f l e c t i o n  e x p e r i m e n t s  t h e  t o  l o o p  o b s e r v e d  m a r k e d  a n d  g i v e n  u n d e p e n d a b l e .  r e s u l t i n g  t h e  t h e n  ^ = 0 ,  f r o m  t h e  t o  i n c r e m e n t s  w e r e  t h e  p o t e n t i o m e t e r  o f  t r a n s m i t t e d  h a l f  w a s  r a t i o  . 0 1 ,  . 0 1  b y  c o i l  e q u a l  . 0 1  t h a n  t h i s  f i e l d  s u i t a b l e  d o w n  a t  z  o n  a  T h e  r  t h e  p o i n t  m e a n i n g  i n  f  o f  t h a t  a t  s c a l e  c e n t e r  s u c h  h o r i z o n t a l l y  h a l f  t h e  d e s i g n e d  c i r c u i t  c h a s s i s  -18-  V  RESULTS  A  Conductors Used-  #1.  Brass c y l i n d e r , 2\  #2.  Brass c y l i n d e r , 3 i n c h e s l o n g , 1 f o o t diameter. •  #3•  Brass d i s c , 3 / 1 6 o f an i n c h t h i c k , 1 f o o t  #4*  B r a s s r i n g , 3 / l 6 o f an i n c h t h i c k , \ o f an i n c h wide, 1  #4(a), 1 #5»  foot  feet long, 1 foot  diameter.  diameter.  diameter.  ( b ) , ( c ) , ( d ) , Brass r i n g s 3 / 1 6 o f an i n c h t h i c k , f o o t diameter, \\\ 1 ,  %  f  \"j i n c h wide r e s p e c t i v e l y .  Brass r e c t a n g u l a r p l a t e ^ 2 4 by . 1 2 by 1/8 i n c h e s .  #6. B r a s s r e c t a n g u l a r box^' 2 4 by 1 2 by 3 inches,' f i t t e d w i t h angled end p i e c e s t o g i v e h o r i z o n t a l t o p s u r f a c e s f o r d i p s o f 0 , 2 2 i , 4 5 ^ 6 7 i , 9 0 degrees. # 7 ( a ) . R e c t a n g u l a r b r a s s p l a t e 1\  by l l g by l / S i n c h e s .  (b) . R e c t a n g u l a r aluminum p l a t e of same dimensions. (c) . R e c t a n g u l a r s t e e l p l a t e , 7h by llh, b y l 3 / 8 i i n c t e e s . # 8 ( a ) . S o l i d b r a s s b a r , l i i n c h e s square, 1 1 inches l o n g . (b) . S o l i d carbon bar, 2 i n c h e s square, same l e n g t h . (c) . Hollow b r a s s bar, o f same dimensions as ( a ) , o f 1/8 inch  plate.  The j o i n t s o f a l l composite s o l d e r e d t o ensure good e l e c t r i c a l  conductors were  connections and thus t o  preserve the c o n f i g u r a t i o n . o f eddy c u r r e n t s f l o w i n g on the s u r f a c e s of the conductor. The conductors were h e l d i n p o s i t i o n by wooden frameworks.  -19-  B  D e t a i l e d L i s t of Experimental Curves F o r Conductors 1 t o 8  Plate  Conductor Number  Distance Inside Circumference of Loop i n F e e t of Centre L i n e •5 5  1(a)  1  Kb)  1  1(c)  D i s t a n c e Below Loop i n Inches  Dip i n Degrees  12  90  5'  9  90  1  5  6  90  Kd)  1  5  4  90  2(a)  2  7  4  90  2(b)  2  7  6  90  2(c)  1  7  4  90  2(d)  1  7  6  90  3(a)  3  5  12  90  3(b)  3  5 .  6  90  3(c)  3  5  4  90  3(d)  2  5  12  90  3(e)  2  5  6  90  3(f)  2  " 5  4  90  4  . 0  5 .  4(a) 4(b)  3  Normalized d i s t r i b u t i o n of s u r f a c e c u r r e n t d e n s i t y .  4(c)  5  5  4  90  4(d)  5  5  4  45  4(e)  5  5  4  0  5(a)  6  5  4  90  5(b)  6  5  4  67i  5(c)  6  5  4  45  5(d)  6  5  4  22i  -20-  Table o f curves Plate  continued:  Conductor Number  Distance Inside Circumference of Loop i n F e e t , o f Centre L i n e  D i s t a n c e Below Loop i n inches  Dip i n Degrees  6(a)  6  5  4  0  6(b)  6  5  6  45.  6(c)  6  5  9  45  6(d)  6  5  9  22|  6  14  6(e)  8(b)  0  4  22|  4  22|  2* o u t s i d e  4  0  8(a)  6  4  0  8(b)  7(c)  %  4  0  d(c)  7(a)  5  4  0  8(d)  7(b)  5  4  0  7(a)  .6  7(b)  6  7(c)  7(b)  8(a)  9  "2»- 2 " o u t s i d e 1'  4 " outside  •  Graphs showing r e l a t i v e amplitude  response, and  v a r i a t i o n o f phase angle w i t h r e s i s t a n c e , c o n d u c t o r 3. 10(a)  V a r i a t i o n o f r e l a t i v e amplitude maxima w i t h d i p f o r conductor 6 , 4 inches below l o o p .  10(b)  V a r i a t i o n of r e l a t i v e amplitude maxima with f o r conductor  1.  depth  - 2 1 -  C  P r o c e d u r e  A  t a k e n  l i n e  a l o n g  o f  c u r v e  f o r  l  r e a d i n g s  o f  r e l a t i v e  a m p l i t u d e  a  d i a m e t e r  o f  t h e  d i r e c t l y  c o n d u c t o r  a t  i n t e r v a l s  e a c h  p l o t t i n g .  v a r y i n g  p l o t t e d  D  l  a s  d i p s ,  C o r r e c t i o n s  m e a s u r i n g  d e g r e e s  n o t  T h i s  e r r o r  i  c o i l  a  w a s  t h e  w a s  t o  s a m e  b o t h .  f  o  r  b y  E,  a n d  v o l t a g e s  d i a g r a m  t h e  t o  T h e  b o t h  r e p r e s e n t e d  a  b y  t o  n  a  l  l  1 8 0  d e g r e e s  o b v i o u s .  t h e  t o  a b o v e  t h e  c e n t r e  o f  f  o  r  a c c u r a t e  p h a s e  t h e  a n d  a m p l i t u d e  c o n d u c t o r s  w e r e  1 0 .  t w o  v a r i a b l e  p a r t s  t w o  ,  o f  p h a s e  t h e  t h e  v o l t a g e  H,  a n d  t h e  w a s  T h u s ,  p h a s e , '  H  ISO  d e g r e e s . "  a m p l i t u d e  t h e  t o  i  s u m  t h e n  s  o f  a s s u m e d  t h e  z  i  e l l i p s e  f  i n d u c e d  a n d  c i r c u i t  i n d u c e d  o r i e n t a t i o n  c o i l .  b y r  b y  m e a s u r i n g  o f  ISO  r e a d i n g s  a n d  v o l t a g e  v o l t a g e s  o f  t h r o u g h  d i f f e r  t h e  o u t  c o i l  a m p l i t u d e  i n c l i n a t i o n  o f  c o i l  t u r n e d  a n g l e s  i n c o r r e c t  V  v e r t i c a l  w a s  e x t r a n e o u s  t h e s e  v e c t o r  n  o f  s m a l l  t h e  a  T h e  t h e  i  t h e  p h a s e  c o n s t a n t  o f  f  a x i s ,  t h e  i  1  c o m p o n e n t  o r i e n t a t i o n s  ,  s  d  i  v a r i a b l e  s u m  i n d u c e d  i  i  i t s e l f .  t o  p o l a r i z a t i o n ,  o r  d  i n d u c e d  c o i l  d u e  f i e l d  a t t r i b u t e d  v o l t a g e  n  n o r  w e r e  M e a s u r e m e n t s  t h a t  v e r t i c a l  e q u a l ,  p o s i t i o n s  P l a t e s  t o  f o u n d  h o r i z o n t a l  w e r e  a n d  w a s  o n  p h a s e  a p p r o p r i a t e  m e a s u r e m e n t s  a n d  s h o w n  A p p l i e d  a b o u t  k c .  c o r r e c t e d  d e p t h s  g r a p h s  I t  5 0  T h e  l o o p  a n d  t h i s  i  n  t h e  n  t h e  o f  c o i l ,  b e  t h e  b e  c o i l v  t o t a l  t h e  f o l l o w i n g  -22-  A d e v i c e f o r the g r a p h i c a l c a l c u l a t i o n o f H, was e a s i l y c o n s t r u c t e d from two graduated c e l l u l o i d arms r e p r e s e n t i n g H, and E  Z  , centrally fixed to a protractor.  F i r s t H, and HJ. were l a i d  o f f from the r e a d i n g s taken f o r  both o r i e n t a t i o n s o f the c o i l . H, was then g i v e n by the d i r e c t i o n of, and one-half the l e n g t h o f AB. I t was found t h a t even when no conductor was near the l o o p , a measurable  h o r i z o n t a l f i e l d was p r e s e n t . The value o f  t h i s f i e l d was v e c t o r i a l l y s u b t r a c t e d from the t o t a l f i e l d , H, measured i n the presence o f each conductor. The remaining f i e l d was c o n s i d e r e d t o be due e s s e n t i a l l y t o the conductor alone, and the curves o f P l a t e s 1 t o 10 were o b t a i n e d . E  Sources o f E r r o r In  for  some o f t h e graphs, d i s c o n t i n u i t i e s o f phase  s m a l l and i n d e f i n i t e . a m p l i t u d e values can be n o t i c e d .  T h i s r e s u l t s from t h e a p p l i c a t i o n o f c o r r e c t i o n v e c t o r s o f almost the same magnitude and d i r e c t i o n as those r e p r e s e n t i n g .the measured f i e l d . Any s h i f t o f the phase base o f t h e phase t r a n s f o r m e r d u r i n g t h e i n t e r v a l .between the measurements o f o  normal and d i s t o r t e d l o o p f i e l d s would s e r i o u s l y a f f e c t the phase and amplitude o f the r e s u l t a n t o f t h i s In  subtraction.  cases where such a phase s h i f t seems probable, the phase  curves a r e not c o n t i n u e d . The assumption  t h a t the v e c t o r V i s constant f o r  both o r i e n t a t i o n s o f t h e c o i l may n o t be c o r r e c t as the p o s i t i o n o f the c a b l e l e a d i n g from^ the c o i l changes w i t h the p o s i t i o n o f the c o i l . T h i s change i n V, however, would be s m a l l .  -23-  P L A T E I.  A&scissa - £>/star}ce //-> Feet From Grvcmfeneice oF/oofr A/orxj ,A £>/amefa> Onfimtm -  Phase /r, Decrees  -  Re/atve  ^X/^-S^  -24-  PLATE2 Conductor 'Renter <»/ 7 , ^2 &<?/av Lt  Ca)  Z70 T  •is  '/  (6)  A  .// ./o  '$o  •Of  •og • OT  • oC  I  of.  •of  • as  9-  9o'  0  ~>  I  t I  I I  •03 r od  I  vi,  Cd)  62)  /So  /So •09  oa  •06 •os  96  •04  03 r  •03  '.0/  •0/  8  /)liscissa - O'Sfonce /n  /r-<?/  OrJ'vate -/?e/*/,,  /n Defers  e  frorry Circumference of Lao/> y^/ony a £)lat&efar fo/ /, a  A»/>A *^™'* /  ue  Oil**  PLATE 3 Cor>c/ttc/o/- 3 at Centre J>  Conett/c/or S  ^ofCentre  CoietocTor  Cr/i/re  /2 6v/oW t.Oo/3 Z70'  (a)  27t>  ./o •  i8o'\  I  So • ot •OS  • 07 <to°  Oi.  •04 •e>3 •0£  \  0/ '  Concfueisr **j? «/ Centre Conc/cie toy t  X?  Conductor- J£  a/ Cfottv  //? &e/ow Zoo/> £vo-\  Igo  9>o  Cer7f '-e L  •4$ "3e/ow Aoo/> Z7d'  7Zrr6*  /So  /So  80-  f  \  <9o  .oz 8  /P/staice /r> f*<rf /ror*> Grc^f^ice  o*/ao/> ct/or>y a £>,*r*e/erMonze/jJaS C/e/</  /feAttiire  AmfJ/tuc/e.  '  r-.——  j r-  ,y  Vet-ft cat rue/a  ~~  \  \  -26-  PLATE 4Conductor tf-  A"(Se/ow Loop afGrafre.  Mor-mat/zect Distribution of Surface Correct'. Oertsity  Conductor  & at  Centre  ^"se/oi* Loojo  P/'/o  9o'  for Conductor **3  \  ISO  IS  >P  10  J. J9 tO/iranee P/wrrectae of /  Conductor*?  Loop  27o  r  'at***- Cena'octor 3  at Cent*? 4- 8e'oW  D//°4S'  /eft Conelat**** J  Af Centre 8* tow  4  loop  Asse/sia-fi/itb/xc /» tee/ F/ont C/rev/»ferr/>fe of £oo/o afo/ig a Diameter Ordinate. - fiefa-i/Cre Phase Anytc A* O&jrres  nfo/^e/d rt'e/a^iz-e A/rp//y oa t Vertieo/ ^/etd l  y  - 2 7 -  F  D i s c u s s i o n  o f  1 .  C y l i n d r i c a l  c o n d u c t o r s  T h e  Amplitude ( a )  P h a s e  ( i )  A  1 8 0  E x p e r i m e n t a l  f o l l o w i n g  c u r v e s  w e r e  R e s u l t s  w i t h i n  t h e  l o o p  c h a r a c t e r i s t i c s  n o t e d  f r o m  P l a t e s  o f  t h e  1 ,  2 ,  p h a s e  3 ,  a n d  4 ( a )  ,  a n d ( b ) .  c u r v e s  d e g r e e  d i s c o n t i n u i t y  e x i s t s  o v e r  t h e  c e n t r e  o f  c o n d u c t o r  ( i i )  C u r v e s  d i s p l a c e d  c e n t r e  ( i i i )  S h a p e  d e p t h  ( i v )  l i n e  P h a s e  o f  o f  1 3 0  t h e  c u r v e s  e x t e n t  o f  m a x i m a  d e g r e e s  a r e  s y m m e t r i c  a b o u t  t h e  c o n d u c t o r .  s e e m s  t h e  i n d e p e n d e n t  o f  t h e  d e p t h  o r  t h e  c o n d u c t o r .  c o r r e s p o n d . r o u g h l y  t o  t h o s e  o f  r e l a t i v e  a m p l i t u d e  ( v )  S h a p e  t h e  ( v i )  o f  p h a s e  c o n d u c t o r  A c c u r a c y  c u r v e s  w i t h  i  s  i n d e p e n d e n t  r e f e r e n c e  o f  p h a s e  d e p e n d s  H o r i z o n t a l  f i e l d  c o m p o n e n t  t o  o n  o f  t h e  t h e  t h e  p o s i t i o n  o f  l o o p .  m a g n i t u d e  o f  r e l a t i v e  a m p l i t u d e .  ( v i i )  p h a s e  o r  e x c i t i n g  ( b )  1 8 0  f i e l d  M a t h e m a t i c a l  h o r i z o n t a l  I n  i n d u c t i v e  a n d  i n  d e g r e e s  a  o f  f i e l d  q u a d r a t u r e .  e x p e r i m e n t ,  T h e  o f  v e r t i c a l  p r e v i o u s  m e t h o d s  v e r t i c a l  t h i s  l  o f  s  a p p r o x i m a t e l y  p h a s e  w i t h  t h e  e i t h e r  i  n  v e r t i c a l  c o m p o n e n t .  t r e a t m e n t  a n d  l  o u t  i  f i e l d  w o r k  r e l a t i v e  t h e  t w o  r e l a t i o n s  b e t w e e n  t h e  c o m p o n e n t s .  d o n e  g e o p h y s i c a l  c o m p o n e n t s  a n d  p h a s e  i  n  e l e c t r o m a g n e t i c  i n v e s t i g a t i o n ,  w e r e  p h a s e s  f i e l d s  i n c o r r e c t l y  w e r e  w e r e  t h e  a s s u m e d  a c t u a l l y  f o u n d ,  h o r i z o n t a l  t o  m e a s u r e d  o v e r  o r  b e  i  n  n e a r  -28-  the conductor , t o be approximately i n phase or 180  degrees  out of phase/ the 180 degree d i s c o n t i n u i t y o c c u r r i n g over the c e n t r e of the conductor. The f o l l o w i n g  mathematical  treatment s u b s t a n t i a t e s these r e s u l t s . Let  the c u r r e n t i n the e x c i t i n g loop be denoted  by  Then, i f the c o e f f i c i e n t of mutual inductance between the l o o p and the conductor i s M, ,  where E  s  i s the v o l t a g e induced i n the conductor.  The secondary c u r r e n t , I  where I and/? denote  s  , i s then g i v e n by  r e a l and imaginary p a r t s of the e f f e c t i v e  secondary impedance, Z. The amplitude of I  5  Zg = A cos (ujt-&)  -^A - -?o  But,  I f  '  can be r e p l a c e d by A, =  giving  -/j  sys> u> ?  Z i s an i n d u c t i v e impedance, then 0= & or  and  -  22  S/Js/ritaf As a f i r s t approximation, t h e r e f o r e , the  c u r r e n t , and hence the secondary f i e l d , or 1#0  secondary  i s e i t h e r i n phase  degrees out of phase w i t h the primary c u r r e n t and  i n agreement w i t h the experimental r e s u l t s .  1  field'!  1  - 2 9 -  ( c )  R e l a t i v e  ( i )  C u r v e s  a p p r o a c h  o f  d e g r e e  ( i i )  1 8 0  a m p l i t u d e  M a x i m a  ( i i i )  T h e  s h o r t  ( i v )  .  t h e  m a x i m a  a n d  ( d )  F  a n d  h  o  e a c h  f  d e p t h  o  r  f  ' d e d u c e d  r  s u r f a c e ,  a s  f  t  w a s  4 ( b ) )  u n t i l  t  h  e  h  e  h  e  t  t  o n '  h  e  h  f r a c t i o n  e  f  w e r e  t  h  e  a r e a  o  f  t  h  e  r  c o n d u c t o r  a  o  f  t  h  e  c o n d u c t o r  e  r  o n e s .  h  e  t  t  h  e  c o n d u c t o r  e q u a l  o  l o n g  f  p o i n t  t  f  h  e  o  a n d  i n c r e a s e s .  r l o n g  a n d  l o o p . ( P l a t e  c o n d u c t o r s  T h e  t  o n  o u t e r  1,3)  p l a c e d o  m a x i m u m  i  f  f  -  s  h  m a x i m a  p o s i t i o n  a  h  e  l e n g t h ,  e  u p p e r  c o n d u c t o r  b y  o  d e p t h ,  a n d  o n l y  h  t  a r i s e s  f  t  h  h  e  e  h  e  o n e  o  e  f  m a x i m u m  o  w h i c h  t  h  e  c o n d u c t o r  v a r i a t i o n s  o  f  o  w a s  i n c h .  l o p p .  T h e s e  c e n t r e  m a x i m u m  e  f r o m  e d g e  v a r i a t i o n s  t  h  e q u a l ,  c u r v e s  e x t e n t .  n e a r  t  p h a s e  s l i g h t  f  s e c t i o n  a m p l i t u d e  o  o  a p p r o a c h e d  e a c h  t  o  d e p t h  t  e s s e n t i a l l y  s u r f a c e  f r o m  f  e  f i e l d  n o t i n g  r e m o v e d  r  r e l a t i v e  a m p l i t u d e  c h a n g e  f  t  c o n d u c t o r .  h o r i z o n t a l  r i n g  o  e  t  c o n c e n t r a t e d  N e g l i g i b l e  o  a  o c c u r r e n c e  w i t h  r i n g s  t  h  d e t e r m i n e d  w i d t h  p l o t t e d ,  f  a p p a r e n t l y  c o n c e n t r i c  ( P l a t e  f r o m  f  d e p e n d s  h o r i z o n t a l  m a x i m a  e  o  c o n d u c t o r s ,  c u r r e n t s  f  2 )  o  e d d y  o  c e n t r e  f  m a x i m a  o  e  s h o r t  m o s t  f  h  u n e q u a l  f  o  c u r v e  t  r e l a t i v e  o  f  e  f r o m  a m p l i t u d e  t  t  I n f e r e n c e s  a  o f  a s  e  c e n t r e  b o u n d a r i e s  o  b e  w a s  o  s h e e t - l i k e  c u r r e n t s  a s  e  ( P l a t e  v a r i a t i o n  r  h  r e g a r d l e s s  f l o w  o f  r  e c c e n t r i c i t y  o  t  b e n e a t h  e q u a l  T h a t  c a n  a  g r e a t e r .  T h i s  ( v i )  m a x i m a  c o n d u c t o r s  T h e s e  o v e r  d i s c o n t i n u i t y .  n e a r  r a p i d l y  t w o  c e n t r e  ( v )  z e r o  p h a s e  o c c u r  d e c r e a s e  c u r v e s  f  t  a  f  e d d y  h  e  t  o  m a x i m u m  a  d i s c .  r e c o r d e d  A  w a s  h i s t o g r a m  a  c o n t r i b u t e d  m e a s u r e  b  y  e a c h  p  -30-  o f  t  h  e  a n n u l a r  s u r f a c e  a  c u r r e n t  s m o o t h  a n d  i  s  t  h  e  o b s e r v i n g  a  i  c o n d u c t o r  a n d  b e t w e e n  w a s  t  h  e  a s s u m p t i o n  d i r e c t l y  4  (  w a s  b  )  a s  . P r o o f  r e l a t i v e  t  h  t h a t  e  t h a t  b y  t  e  t  h  f r o m  e  t o t a l  m a x i m u m ,  t h i s  h i s t o g r a m ,  c u r r e n t  c u t t i n g  a m p l i t u d e  h  a m p l i t u d e  c o n s t r u c t e d  d e m o n s t r a t e d  T h e  a p p r o x i m a t e  m a y  b e  (  i  v  s h o r t  )  / s i n c e  a n d  t  h  m a x i m u m  i  a m p l i t u d e  m i n i m u m  o  f r o m  e  f l o w e d  r i n g ,  a n d  d r o p p e d  t  o  t  o  a n d  o  f  h  e  r e s u l t s  o  f  t  h  e  a  c y l i n d r i c a l  i  n  l o o p  s e c t i o n s  F , l , e ,  d i f f e r e n t i a t e d  c o n d u c t o r s .  f  a  d e t e r m i n e d  f  e x t e n t  s h i f t i n g  l o n g  c e n t r e  s  d e p t h  d e d u c e d  c o n d u c t o r  E f f e c t  h  v a l u e .  T h e  ( e )  e  t  c u r v e  P l a t e  r i n g  n e g l i g i b l e  ( i i i j  n  t h a t  O n  v a r i e d  n o r m a l i z e d  s h o w n  a r o u n d  r i n g s .  t  c y l i n d r i c a l , ' '  b y  t  e  1 8 0  h  r e s i s t a n c e  o n  h  e  9 0  p o s i t i o n  d e g r e e  p h a s e  o  d e g r e e  f  t  p h a s e  a n d  h  d i p p i n g  e  r e l a t i v e  d i s c o n t i n u i t y .  r e l a t i v e  a m p l i t u d e  c u r v e s  T h e  w i t h  r e s i s t a n c e  v a r i a b l e  f r o m  P h a s e  a n d  t a n c e  w e r e  c e n t r e ,  a t  v a r i a t i o n  o n e  0  f  d i f f e r e n c e  t a k e n  t  o  t  h  a  e  1  o h m  t  t w o  e  r e l a t i v e  o  f  p h a s e  r e s p o n s e  p h a s e  i  n  t  b y  h  e  p o i n t s ,  o  f  p h a s e  i n c r e a s e d  d e c r e a s e d  r e l a t i v e  i n s e r t i n g  f  o  o n e  a  r i n g ,  c o n d u c t o r  r v a r i o u s  t w o  t h e s e  m a x i m a .  v a l u e s  i n c h e s  t w o  t  p o i n t s  r e s i s t a n c e ,  w i t h  I  a m p l i t u d e  r e s i s t a n c e  d i s c o n t i n u i t y ,  a m p l i t u d e  b e t w e e n  a n d  b r a s s  m e a s u r e m e n t s  p o i n t  w i t h  f  d e t e r m i n e d  h  c o n s i d e r a b l y  a m p l i t u d e  t  a m p l i t u d e  h e a r  o  w a s  o  a n d  increasing  f r o m  a n d  w a s  t  # 4 .  o  f  t  h  h  e  r e s i s -  e  f o u n d  o t h e r  t h a t  t  h  i n c r e a s e d  t h a t  t  h  e  r e l a t i v e  r e s i s t a n c e ,  e  -31-  -32-  approximately p r o p o r t i o n a t e l y f o r both p o i n t s . The decrease o f amplitude response i s p a r t l y e x p l i c a b l e by Ohm's Law I~  > t h a t i s , an i n c r e a s e o f  impedance corresponds t o aiidecrease o f eddy c u r r e n t i n t e n s i t y , r e s u l t i n g i n a decrease o f secondary h o r i z o n t a l i n t e n s i t y . ^ i n t h i s case w i l l  be, t o a f i r s t  field  approximation  -//z*-+uJL When t h e r e l a t i v e response i s c a l c u l a t e d from z  this  and p l o t t e d as a f u n c t i o n o f R, however, t h e r e i s l i t t l e r e l a t i o n between t h i s and the experimental c u r v e s . Thus t h e r e must be o t h e r v a r i a b l e s c a u s i n g t h e decrease o f r e l a t i v e amplitude response than r e s i s t a n c e and inductance. S k i n e f f e c t c o u l d p o s s i b l y .produce t h i s d>is;c;repancyas the r e s i s t a n c e P  R was t h e t o t a l d.c. r e s i s t a n c e o f t h e conductor. From a l l simple t h e o r e t i c a l approximations o f s u r f a c e c u r r e n t f l o w , t h e phase curve should be f l a t ,  with  a 180 degree d i s c o n t i n u i t y e x a c t l y over t h e c e n t r e , as was c a l c u l a t e d i n s e c t i o n F , l , ( b ) . The p o s s i b i l i t y o f o t h e r i n d u c t i v e , r e s i s t i v e , and c a p a c i t a t i v e e f f e c t s due t o t h e p r o x i m i t y o f t h e v e r t i c a l s e a r c h c o i l , ' and the e f f e c t s o f conductor r e s i s t a n c e were not c o n s i d e r e d . The f o l l o w i n g mathematical  p r e s e n t a t i o n demonstrates  t h a t the l a s t  effect  i s not n e g l i g i b l e and must be c o n s i d e r e d . Examination o f t h e equations (1) and (2) above'ty* -^ 3  shows t h a t t h e v a r i a t i o n o f & , t h e phase o f t h e h o r i z o n t a l secondary f i e l d ,  depends on the r a t i o o f t h e imaginary and  r e a l p a r t s o f t h e e f f e c t i v e impedance o f the conductor.  Let Z  p  M  be the e f f e c t i v e impedance of the  conductor,  be the mutual inductance between conductor and  search  coil, Z  be the secondary  cu  be the a n g u l a r frequency of the  s  Then  ^  -  +  impedance, field.  *  I t w i l l be assumed t h a t the c a p a c i t a t i v e r e a c t a n c e of the conductor i s n e g l i g i b l e compared t o the i n d u c t i v e reactance, which i s due m a i n l y t o the s e l f inductance o f the Then, j?p= JCo^/ +• ft> where R, i s the conductor  conductor,//  resistance.  C o n s i d e r a t i o n of the c i r c u i t from the c o i l t o the input t o the vacuum tube v o l t m e t e r i s n e c e s s a r y t o d e t e r m i n e d . e q u i v a l e n t c i r c u i t may  An  be drawn as f o l l o w s .  :c  z  and,  Z=  j'^^-z  s  Where /  + #3  +  .  „  ,—  /  i s the s e l f inductance of the search  z  /?s i s the r e s i s t a n c e of the c a b l e and Cz  coil,  coil,  i s the c a p a c i t y of the c a b l e ,  /?z i s the i n p u t r e s i s t a n c e of the measuring £3  and uii are s m a l l i n comparison  of ^  z  and  AJ. , so t h a t  Z'/o -  -for, 9  #1 + ^ Z ? * =  w i t h the p a r a l l e l impedance  =  Thus the f o l l o w i n g equations  result,  +j(eul, *  +  apparatus.  t<JC tuli ) z  2  - 3 4 -  From v a r i o u s approximations, L/ was b e . M  t o be.tiSydt/, when the c o i l was  r e l a t i v e amplitude  calculated to  a t the maximum of the  curve, a n d - ^ x ^ at the p o i n t 2 i n c h e s  from the c e n t r e wherebthe second s e t of measurements of phase and amplitude were t a k e n . R  z  about for  4  0  0  0  a t t a i n e d a maximum o f  ohms f o r the f i r s t p o i n t and a minimum of  the second. When the v a l u e s at the r e l a t i v e  2 5 0  amplitude  maximum were s u b s t i t u t e d i n t o the equation ( 3 ) , a phase angle v a r i a t i o n v e r y s i m i l a r t o t h a t of the experimental was  results  o b t a i n e d . However c a l c u l a t i o n s f o r the p o i n t 2 i n c h e s  from the c e n t r e gave the same r e s u l t s . T h e r e f o r e , i t can be concluded t h a t the d i f f e r e n c e i n phase between the h o r i z o n t a l f i e l d and the v e r t i c a l i s at  l e a s t a f u n c t i o n of the inductance and the r e s i s t a n c e  of  the conductor. However, n e i t h e r the c u r v a t u r e of the  graphs  o f phase near the p o i n t of d i s c o n t i n u i t y , nor the.  i n c r e a s e of t h i s c u r v a t u r e w i t h conductor  resistance,i.e.  the i n c r e a s e o f phase d i f f e r e n c e between the two  points at  which measurements were taken, i s e x p l a i n e d by t h i s These p o s s i b l y a r e apparent s o l u t i o n o f the problem  treatment.;  o n l y from a much more d e t a i l e d  by Maxwell's equations.' T h i s more  d e t a i l e d s o l u t i o n might show v a r i a t i o n s i n phase of the eddy c u r r e n t s f o r d i f f e r e n t p e n e t r a t i o n s of the c u r r e n t below the s u r f a c e of the conductor, depending  on the r e s i s t a n c e ,  for  c u r r e n t f l o w at' v a r y i n g d i s t a n c e s from the edges o f  the  conductor.  and.  PLATE: 5  Coftt/vc/or-  6 a /  Conductor ^6 af Centre  Ce^frrS  Loo/>  21o  O—®-rxa  D/p 672°^ 4-"Be/o»£oa/>  fa)  Cb)  ISO  /So  07, Ob  90'  OS  •9o'-\ 04  04  •o 3, 1  • -jg  •7  '  \  £7  Conofvef»r*£ af Centre ' •It  I ^ B  I  1  V8o  /lise'asa - Otsfanee /'u r~eef fro*7 Circ fierr/>ce o-f loofi A/os?j a <J/o*ne?er Ofol/aafe- r7*/aAW Fhaae /n De-frees &*/af/yr Arnfi//-fac/e /'r~,e/</ um  VerT/oa/  «•/</  -36-  PLATE  6  ConJoe/bfe " f Centre Conductor *6 at'Ceriti-e ajt>4S*l*'f f,~£ "&e/o*"Loo/> Dip d\ -4"3<:/ov* loop  Conductor *£atCe»tre  :  Oip ^S'left^'ffe/o^lo^  .in,  (b) • IS  170  -.14  *  }  •zw  1  ,z i11  tto'f  # V>9~  1  -» j -egi  \'i  ..orj .<*{ m  IBO'  {  v. 't  1 *  1o  /So-  \  -0 I S  \Jr .  i  ger  9o  •03>  •ox  \  V  /  •J.OI J  6  ,e4!  7  • S-  47 Conductor gix, Centne-l/ne  Condvctor atCentre D/pZzi'left, 9 "Betonrloop  a'b , t*ffr/oyvIcojb  Z7o  /go'  r  l8o'\  \o? Ob  9o'  OS  L**&-*>— —=> A  Vo4 [•OS  9o  m  •of  fC7~-^  M OS  • •{  SB*""  •a I  o/  M  *'-r" sV'  sj/f  9'  6'<"  ft'  /ihsc/ssa - P/Ztonee in /err AJ^J, C/r-cw i*rr„ p ofloop a Zona a O/anrefer Ordinate- ffelatire Pi>o,e /In^te In Degrees t?o/ t/ue4r»p//S- de ^"'""tol freid r  a  u  Verri'mt/ P,e/d  -37-  8  PLATE  Cano/uctar / £ . A f Centre?  Z7o  tfio  9o  9«  C7™^"  'i>3 o/  4  Con e/i/e tor  Cona/uefor * 7 a , >/4/ CeitsC  *76.  ^} " ffe/ow ZTo  A f Cen tre  £00/3  cd)  !8o°  'So  09  A  OS 07/  07  •  •06  I  9o'  •OS  •04  i  •of  disc/tact - D/ifanre /n rl?et Oroide  CirPo*>ferrjtee o^^oa/0 A/oay a O/'a/ne/rr  -ffe/at,WPJ*,,e /„ 0e *e* — fie/a^W rlmfit/tuo'e 9  tZ^JtZ/ir^/j*  -38-  2.  R e c t a n g u l a r conductors w i t h i n t h e l o o p .  (a) Phase c u r v e s . The  curves are i d e n t i c a l w i t h those f o r c y l i n d r i c a l  conductors except f o r t h e f o l l o w i n g (i)  characteristics.  Maxima become rounded as depth of conductor i n c r e a s e s ( P l a t e s 5 and 6 )  ( i i ) P o s i t i o n of 1 & 0 degree d i s c o n t i n u i t y occurs over c e n t r e It/Jien  l i n e o f t h e conductor only/i d i p i s 0 o r 90 degrees. ( i i i ) P o s i t i o n o f ISO degree d i s c o n t i n u i t y v a r i e s w i t h d i p . ( i v ) Shape o f curves i s independent ( P l a t e s 6 ( e ) , 8 ( a ) , {b), (b) R e l a t i v e amplitude (i)  (c),  of conductivity. (d).)  curves  F o r 90 o r 0 degree d i p p i n g bodies, curves a r e s i m i l a r t o those f o r c y l i n d r i c a l  ( i i ) F o r 0 degree  conductors.  d i p p i n g r e c t a n g u l a r p l a t e s , maxima occur  v e r y c l o s e t o p o i n t s d i r e c t l y above the conductor boundaries. ( i i i ) Maxima occur s l i g h t l y o u t s i d e t h e edges o f such p l a t e s and a r e approximately equal over t h e s i d e s and ends, p r o v i d e d t h a t the r a t i o o f l e n g t h t o width i s n o t ' g r e a t e r than 5 . (iv)  F o r d i p p i n g conductors, maxima occur over the s l o p i n g surface and t h e acute a n g l e d edge.- The magnitude and p o s i t i o n o f t h e maximum over t h e s l o p i n g s u r f a c e depends on both the d i p and depth o f t h e conductor. ( P l a t e s 5, 6 ) !  The magnitude o f the o t h e r maximum depends on the d i p  -39-  -40-  a n d  d e p t h ,  b e i n g  o f  ( v )  e i t h e r  t h e  R a t i o  ( v i i )  i  ( P l a t e  1 0 ( a )  o v e r  h o l l o w  o n e s .  M a x i m a  a r e  M a x i m a  ( P l a t e  d  ( P l a t e s  ,  t h i c k n e s s  ,  f  c  g e o l o g i c a l  o  f  )  a n  ( d )  F r o m  r e l a t i v e  t h e  a  e d g e  o  q u i t e  f  o  f l o w s  c o m p l e t e l y  B u t  c u r r e n t  f  t h e  a s  t h o s e  o v e r  m e t a l l i c  o  f  p e r m e a b i l i t y .  a m p l i t u d e  f  w o u l d  t h e s e  d  m a x i m a  b e  r e s u l t s  a r o u n d  t h e  w i t h  t h o s e  f r o m  t h i s  i  t  p  w e r e  m a y  a r e  c u r v e s  p r o d u c e  s u r f a c e  u s e f u l  a r e a .  i  o b t a i n e d  i  s  e d g e ,  b e  k n o w n .  w o u l d  c u r r e n t  f  i  t h e s e  v e r y  s u r f a c e  a m p l i t u d e  m a x i m a  t h e  a f f e c t  I  c u r v e s  r e l a t i v e  h o r i z o n t a l  f i e l d  f  s a m e  t h i c k n e s s  c o m p l e x .  c o n f l i c t i n g  c a l c u l a t e d .  f  t h e  t h i s  t h e  s u r f a c e  o f  )  c u r v e s ,  o  f  e  o  a m p l i t u d e  i  b e  s  f u n c t i o n  )  b e t w e e n  v a r i a t i o n  o f  h  ( d )  o  m u s t  o  t  3(a)  c o n d u c t o r  v a r i a t i o n  e  r e l a t i v e  t h e s e  p l a t e  a p p r o x i m a t e  t h e  )  r a t i o  r e c t a n g u l a r  c a n  c o n s t a n t ,  i n s i d e  v a l u e d  i n c r e a s e  a n d  t h e  r  a n d  a n d  d i s t r i b u t i o n  f i e l d  a n d  8(c)  , a n d  i n t e r p r e t a t i o n  c u r r e n t  a  v a r i a t i o n  s i n c e  T h e  f o u n d  s l i g h t l y  d o u b l e  s h o w i n g  i n v e s t i g a t i o n  h o r i z o n t a l  r  i n d e p e n d e n t  w i t h  p h a s e  t h e  c o r r e s p o n d i n g  F u r t h e r  (  1 0 ( a ) .  i  c o n s i d e r a b l y  a  p  a  6 ( e )  ( P l a t e s  f r o m  P l a t e  a p p r o x i m a t e d  T h e  i  s  c o n d u c t o r s  d e c r e a s e  C u r v e s  p l o t t e d ,  o  e s s e n t i a l l y  )  s o l i d  8 ( b )  w i t h  i  e s s e n t i a l l y  I n f e r e n c e s  m a x i m a  r e m a i n s  a b o v e  m a x i m a  c o n d u c t i v i t y .  ( c )  s p o s i t i o n  c o n d u c t o r .  M a x i m a  ( v i i i )  t  d i r e c t l y  b e t w e e n  d i p .  ( v i )  b u t  f l o w  n  i  i  a s s u m e d  v a l u e s  n  n  p r a c t i c e .  a  t h a t  o f  e x p e r i m e n t a l l y  c a l c u l a t i o n ,  c o n f i g u r a t i o n  c a h  b e  a n  f o u n d .  -41-  T h e  c a l c u l a t i o n  F o r  s u r f a c e  e d g e ,  s u r f a c e ,  b e  e x t e n t  o f  w h e r e  d i s t a n c e s  v e r t i c a l  t h e  g i v e n  s e e n  t o  t h e  t h e  a l o n g  t h e  a c u t e  o v e r  t h e  s l o p i n g  d i s t r i b u t e d  o f  6,  r e l a t i v e  d e p e n d  o n  a m p l i t u d e  b o t h  t h e  a n d  d i s c u s s i o n  o f  s u r f a c e  o f  w h i c h  a ,  s e a r c h  t h e  i  t h e  e d g e  c u r r e n t  T h e n  i n t e n s i t y  o f  t h e  f l o w i n g  a s s u m i n g  a  c o n d u c t o r  t h r o u g h  H £  t h e  h o r i z o n t a l  s  D ,  1,'  x ,  a r e  a s  c u r r e n t ,  t h e n  a l t e r n a t i n g  p r o p o r t i o n a l  c o i l .  h o r i z o n t a l  n  f i e l d  t h e  f i e l d  c o n d u c t o r  i  n  t h e  x  b y  a l t e r n a t i n g  a m p l i t u d e  d i r e c t i o n ,  o f  i  d . c .  s h o w n .  i  f o r  s  o n l y  a  d i r e c t i o n  t h e  a n d  c o n d u c t o r .  h o r i z o n t a l  f l o w i n g  d i r e c t i o n  a n  t h e  5  c o n c e n t r a t e d  e v e n l y  t r e a t m e n t  C o n s i d e r  s  o f  P l a t e s  f l o w  c u r r e n t  i  m o r e  b e  b e  C a l c u l a t i o n  i  t o  c a n  c u r r e n t  I f  s e e m s  f r o m  d i s t r i b u t i o n  M a t h e m a t i c a l  t h e  ( d ) .  s h a r p n e s s  d e p t h  t h e  s e c t i o n  t h e  d i p  i n  n  b y  T h e  ( i )  t o  i  c o n d u c t o r s ,  i n d i c a t e d  m a x i m a .  a n d  m a d e  f l o w  a n d  a s  s  d i p p i n g  c u r r e n t  a n g l e d  ( d )  i  T o  f i e l d ,  f i n d  t h e  t h e  s h o w n  t h e  t h e  v a l u e  a b o v e  n  a b o v e  m a g n e t i c  t o  i  f i e l d  e . m . f .  o f  x  t h e  e q u a t i o n  i  n  m u s t  g i v e s  t h e  i n d u c e d  g i v i n g  e x p r e s s i o n  d i a g r a m .  x  i  n  m a x i m a  b e  t h e  - 4 2 -  d i f f e r e n t i a t e d  w i t h  e q u a l  T h e  t  g i v e n  A s  o  z e r o .  r e s p e c t  r e l a t i o n  a c c u r a t e  a p p r o x i m a t e  s o l u t i o n  s o l u t i o n s  1» a  »  »  D ,  s e c o n d ,  ^  t h e  m e a s u r e m e n t s  " o f  m e n t s  w e r e  1 2  3  b y  b e i n g  w i t h  v a r i a b l e s  s  i  s  e  t  t h e n  i n c h e s  i  s  g o o d ,  m a x i m a .  l a r g e r  F o r  a n d  q u i t e  b e  c o n d u c t o r ,  i  n  t h e  m o r e  s m a l l .  i  f  i  b e l o w  s h o w n  i  n  s u r f a c e .  o f  . 1 8 "  s e c o n d ,  e a s i l y  T h u s  t h e  g i v e n .  (7)  n  t h e  n  i  o  a n d  a p p l i e d  p r a c t i c e  o t h e r  d a t a  t h e  a n d  a b o v e  1 . 3 .  o f  c a s e  W i t h  c a n  t h e  t h e  b e  w e r e  . 3  o v e r  a n d  t h e  t  o  f r o m  c u r v e s ,  g i v e  t h e  g i v e n  b y  t h i s  d e p t h  a n d  a g r e e -  b y  m e a s u r e d  t h a t  i n c h e s  ( 1 )  d i s t a n c e  t h e  t h e  f r o m  c l o s e  a n  1 . 5  f i r s t ,  v e r y  t  m e a s u r e -  e x p l a i n e d  f e a s i b l e  o  o f .  a  f i e l d  d i a g r a m ,  x  o f  d i p p i n g  c a l c u l a t e d  r e a d i n g s  t  o  h o r i z o n t a l  d e t e r m i n e d  s e e m s  t  l o o p ,  v a l u e s  t h i s  s h o w n .  d a t a  t h e  w h e r e  t  d i r e c t i o n  V a l u e s  t  a l t h o u g h  i  c o m p l i c a t e d ,  c a s e s ,  t h e  e x p e r i m e n t a l  i n v e r t e d  t w o  a r e  w e r e  c o r r e s p o n d i n g  n o t  e x t r e m e l y  E x p e r i m e n t a l  a s  t o p  s  e x p e r i m e n t a l  d e g r e e s .  t a k e n  i  a n d  t a k e n  i n c h e s  r e s p e c t i v e l y ,  c o u l d  t h e  d e r i v a t i v e  z  #6,  i n a c c u r a c i e s  i s  t h i s  -34?V9-e +6Co*)  =  f o r m u l a e  f o u n d ,  m e n t  a n d  Jefu^If  =  T h e s e  9 0  x  t h e  a  t h e  4  r  1 ,  F o r  a n g l e  o  r  D,'  *  c o n d u c t o r  f  o  »  f i r s t ,  C o m p a r i s o n  f  1  t h e  ( 2 )  x  b e t w e e n  a ,  F o r  w e r e  o  b y  a n  ( i i )  t  t h e  i  s  t h e  e r r o r  f o r m u l a  o f  a  g e o l o g i c a l  m e t h o d s .  -43-  T h e  f o r m u l a e  (1).  a r e  , 0 4 6 8 i  f  C o r r e s p o n d i n g  r e l a t i v e  T h e r e  t h e  b e  h o r i z o n t a l  i  a  l a r g e  c u r r e n t  o v e r  s o m e  c u r r e n t  o f  f l o w  v e r y  d i s t a n c e  f l o w  a t  t h e  h o r i z o n t a l  t o  i n s i d e  t h e  h e r e ,  t h e  t h e  c o r n e r s  o f  e n d s .  c o u l d  t h e  a l o n g  A l s o ,  o  t h e s e  r  d i r e c t i o n  o f  t h e  .035  w e r e  i n d i c a t i n g  a r o u n d  f  m a x i m a  f i e l d  e d g e  f r o m  .11551  a n d  v a l u e s  u n i f o r m l y  n e a r  c a l c u l a t e d  (2)  d i c e c t i o n  d i s c r e p a n c y  c a n n o t  d i s t r i b u t e d  r  m a x i m a  e x p e r i m e n t a l  a m p l i t u d e  s  o  f i e l d  c l e a r l y  e d g e s , '  t h e  t h a t  b u t  s i d e s ,  m u s t  a n d  d i s t u r b a n c e s  p o s s i b l y  .031.'  a n d  c o n t r i b u t e  o f  t o  t h i s  d i s c r e p a n c y .  3.  R e c t a n g u l a r  T h e  a m p l i t u d e  t h e  l o o p  g e n e r a l  c u r v e s  P h a s e  ( i )  A  ( i )  l a r g e  p h a s e  o v e r  R e l a t i v e  o  r  t h e  t o  l o o p  o f  t h o s e  f  ( P l a t e  t h e  o  r  7)  p h a s e  a n d  c o n d u c t o r s  r e l a t i v e  w i t h i n  f o l l o w i n g .  d i s c o n t i n u i t y  e a c h  a  0  R a t i o  d e g r e e  a n d  o f  t o w a r d s  t h e  i n c r e a s e d ,  d i p p i n g  a r e  p l a t e ,  d i r e c t l y  i  s  l o o p ,  a n d  f r o m  1 8 0  d e g r e e s  a n t i s y m m e t r i c .  c m r v e s  o c c u r  m a x i m a  d i f f e r e n t  c o n d u c t o r .  a m p l i t u d e  e q u a l ,  ( i i )  s i m i l a r  G . u r v . e s o r a t e r a l l y d i s p l a c e d  F o r  t h e  c u r v e s  o c c u r s  ( b )  f  o u t s i d e  c h a r a c t e r i s t i c s  w e r e  e x c e p t i n g  ( a )  ( i i )  c o n d u c t o r s  t h e  o v e r  d i s t o r t e d  t h e  m a x i m u m  o t h e r  t h e  f  t w o  t h e  o  r  m a x i m a  e d g e s  o f  c o n d u c t o r s  n e a r e r  d e c r e a s e d .  t h e  a r e  t h e  n o t  p l a t e .  d i p p i n g  l o o p  b e i n g  -44-  PLATE Conductor  7  left£~dpeof / ' /?; ht£dfe aft £Conductor ' 9  Oots/cte Loofi, D'/i>£<?£ •4 deiffiA//-oo/>  /eff ^3 "ff-e/on/ Loop Z70  Z7o  •/80  Conductor 7(,Centre a? Z* Oofadeloo^O ^"Setour loa/> -z7o  oi,  9o  /Ibfe/ssa - £>tstanee tn r&ef- 0ui*''cte GrcumPerenee Ofd/rioife - /fetat/ye /°!f>a  ot/oofi  A/'nj a./D/anjefer  \ £>ej/-ees ——ffe/at/veA/r)fii''tude ^fr^/to/p/Wc/  -45-  ( i i i )  R a t i o  o f  m a x i m a  d e c r e a s e d  ( c )  D i s c u s s i o n  T h e  s i m i l a r  w i t h  A s  o  o f  r  f i e l d  s e c o n d a r y  h o r i z o n t a l  c o n d u c t o r  s h o u l d  t h e  o n  w i t h  t h e  w i t h i n  t h e  i n t e n s i t y  i  d u e  s  t o  i  t h e  p r o x i m i t y  l a r g e  d i s t a n c e  f i e l d  f r o m  d i s t r i b u t i o n  c o n d u c t o r s  d e c r e a s e  _  T h e  '  t h e  t h e  t h e  e d d y  p r o b a b l y  l o o p ,  b u t  t h e  l o o p .  o f  n e a r  f r o m  s  t h e  l o o p  l o o p ,  c u r r e n t s  i  T h i s  h a s  b e e n  t h e s i s  h a s  a i d e d  p r o p o r t i o n a t e l y .  r e s e a r c h  o f  a  m e a s u r e m e n t s  i  n u m b e r  p r e v i o u s l y  o f  p h a s e  a m p l i t u d e  t h e  f o u n d  i n t e r p r e t a t i o n  o f  f i e l d  r e s u l t s ,  c o n t i n u a t i o n  p l o t t e d  m a y  a l s o  m e a s u r e m e n t s  I t  t a k e n  h a d  f l o w e d  c o n c e p t  b e  w a s  o f  i  n  u s e  t h e  b e e n  p r o v e n  a p p r o x i m a t e  f  o f  i  n  o  t h e  t h e  n  p h a s e  q u a l i t a t i v e  i  n  m o s t  a r o u n d  i n c o r r e c t  r  i  a  c o n d u c t o r  b e  a n d  o f  n  p o i n t s .  h a v e  u s e  b e e n  i  n  o f  a m p l i t u d e  i n t e r p r e t a t i o n  c u r v e s  o f  f i e l d .  a s s u m e d  p r i n c i p a l l y  a n d  n  i  h o r i z o n t a l  w i l l  s h a p e s  i  t h e  c h a r a c t e r i s t i c s  T h e  c u r r e n t s  o f  t h e i r  r o u g h l y  n  u n c e r t a i n  o f  r e s e a r c h .  e d d y  a n d  t h i s  m a n y  s i m i l a r  t o  o f  n  m a d e , /  a n d  d u e  d i s c u s s e d  f i e l d  T h i s  a n d  t h e  s e c o n d a r y  c u r r e n t s  l o o p . '  '  u n d e r s t a n d i n g  A c c u r a t e  r  a w a y  a r e  c a s e .  S U M M A R Y  t h e  o  m a x i m a  f l o w  t h e  d e p e n d i n g  r a p i d l y  b e  f  o f  a l t h o u g h  d i p p i n g  c u r r e n t  f o r m  f o u n d  v e r t i c a l  u n a l t e r e d ,  c o n d u c t o r  g e n e r a l  t h a t  s  s u r f a c e  d e f o r m a t i o n  t h e  a  d e c r e a s e s  t o  V I  a  t o  f  i  p r e v i o u s  t h e  i  n  e x t r e m e l y  e d g e  m o s t  o f  w o r k  a  c a s e s  s i m p l i f i e d  t h a t  e d d y  c o n d u c t o r .  a n d  c a s e  o n l y  o f  a  -46-  h o r i z o n t a l sheet l i k e conductor. For a d i p p i n g conductor, such an approximation was found completely i n c o r r e c t , the surface current f l o w being d i s t r i b u t e d quite evenly over the s l o p i n g surface, and tending t o be concentrated near the a  cut?e-angled edge. As,most ore-bodies d i p a t some angle  other than 90 or 0 degrees, the assumption of concentrated current f l o w a t the edges of a conductor i s thus rendered invalid. The p r e v i o u s l y accepted concept that the h o r i z o n t a l and v e r t i c a l f i e l d s were i n quadrature was completely i n v a l i d a t e d by experimental and mathematical means. I t was found that a t the only p o i n t s where a measurable h o r i z o n t a l f i e l d e x i s t e d , t h i s f i e l d v/as e i t h e r i n phase or 180 degrees out of phase w i t h the v e r t i c a l component. With the exception of research done by L. B. S l i c h t e r i n 1932 ( 4 ) , p r a c t i c a l l y no other q u a n t i t a t i v e determinations of the c h a r a c t e r i s t i c s of phase and amplitude of the h o r i z o n t a l f i e l d had been made. I n the present research, the r e l a t i o n s between the p h y s i c a l dimensions and depth of a conductor and the form of the r e l a t i v e amplitude curves p l o t t e d aB p r o f i l e s taken d i r e c t l y above the conductor were q u a n t i t a t i v e l y discussed. Also, some explanations were given of the dependence of corresponding phase curves on the p h y s i c a l c h a r a c t e r i s t i c s of the conductor, and on p o s s i b l e i n t e r a c t i o n e f f e c t s of the measuring device. oooOooo  - 4 8 -  B i b l i o g r a p h y  B r u c k s h a w ;  H e i l a n d ,  J  C .  .  M c G . ,  A . ,  F .  A , ,  S l i c h t e r ,  M o d e l  L .  N e w  B . ,  J .  A . ,  M c G r a w - H i l l ,  r  c  ,  350,  1934.  p p 7 7 3 - 8 0 9 ,  p p .  29S-9,  193S.  a n d  T h e o r e t i c a l  C o n d u c t i n g  p p .  E l e c t r o m a g n e t i c  Y o r k ,  46,  1946.  M e a s u r e m e n t s ,  P r o s p e c t i n g ,  N e w  o  E x p l o r a t i o n ,  Y o r k ,  o f  P  Y o r k ,  O b s e r v e d  R e s p o n s e  G e o p h y s i c a l  S t r a t t o n ,  N e w  E l e c t r i c a l  M c G r a w - H i l l ,  S o c .  G e o p h y s i c a l  P r e n t i c e - H a l l ,  L a w s ,  P h y s .  1931.  S p h e r e s ,  443-459,  T h e o r y , "  E l e c t r o m a g n e t i c  A .  I.  M .  E . ,  1932.  p p .  488-90,  

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