The Mining Magazine
M anaging Director a nd E ditor : W . F. W h i t e . A ssistants : S t. J. R. C. S h e p h e r d , A .R .S .M ., D.I.C.., F .G .S ., F . Hig h a m, A .R .S.M ., M .Sc., F.G .S.
P u b l i s h e d o n t h e 1 5 t h o f e a c h m o n t h b y M i n i n g P u b l i c a t i o n s , L i m i t e d , a t S a l i s b u r y H o u s e , L o n d o n , E . C . 2 .
T e l e p h o n e : M e tr o p o l i t a n 8 9 3 8 . T e l e g r a p h i c A d d r e s s : O lig o cla se. C o d e s : M c N e i l l , b o th E d i t i o n s , & B e n tle y . Br a n c h Of f i c e s j( N e w Y o r k : A m e r . I n s t . M . & M .E .
I C h ic a g o : 3 6 0 , N . M ic h ig a n B lv d . Su b s c r ip t io n j P e r a n n u m , in c lu d in g p o s ta g e . ( U .S .A ., S3 p e r a n n u m , in c l u d i n g p o s t a g e .
Vol. X L V 1 . No. 4. L O N D O N , A P R I L , 1932.
P R I C E O N E S H I L L I N GC O N T E N T S
Ed i t o r i a l
Notes ...
T h e I.M .M . B e n e v o l e n t F u n d A p p e a l ; “ M a v o r a n d C o u ls o n ” T r a v e llin g S t u d e n t s h i p s ; A p p o i n t m e n t s t o A d v is o r y C o m m itte e f o r th e M e ta llife r o u s M in in g I n d u s t r y ; Mr. S c o t t T u r n e r b e c o m e s P r e s id e n t o f th e A m e r ic a n I n s t i t u t e ; P r o f e s s o r S c h n e id e r h ö h n ’s V ie w s o n th e G e o l o g y o f N o r th e r n R h o d e s i a ; D r. C a m se ll o n I m p e r ia l M in er a l R e s o u r c e s .
The In stitu tio n M e e tin g ...
T h e p a p e r s p r e s e n t e d a t th e M arch m e e t i n g a r e r e v ie w e d .
Metallurgy and E n g in e e rin g ...
T h e p r e s id e n tia l a d d r e s s o f S ir H e n r y F o w l e r b e fo r e th e I n s t i t u t e o f M e ta ls i s d e a lt w ith .
The Developm ent of the K alahari . ..
T h e c o n s e q u e n c e s o f a s u r v e y fo r a p r o je c te d r a ilw a y lin k in g R h o d e s ia w i t h W a lv is B a y a r e d is c u s s e d .
PAGE
194
Re v i e w o f Mi n i n g ...
Ar t ic l e s
Electrical Prospecting for Auriferous Q uartz Veins and Reefs.
Helmer Hedstrom
T he a u th o r p a y s p a r tic u la r a t t e n t i o n t o p r o c e s s e s o f
“ e le c tr ic a l t r e n c h in g ,’ ’ w h ic h a r e u n d e r g o in g e x t e n s iv e t e s t s o n s e v e r a l g o ld f ie ld s .
Prospecting for Alluvial D eposits
A . F. SkerlIn th e lig h t o f h is o w n e x p e r ie n c e , th e a u t h o r m a k e s s p e c ia l r e fe r e n c e t o t h e N o r th e r n N ig e r ia n tin fie ld .
Gold in E cuador. . . . / / . L. Holloway
A b r ie f h is t o r y o f g o ld m in in g in E c u a d o r , w it h s o m e n o t e s o n t h e o r ig in o f t h e p la c e r d e p o s it s .
The I.M.M. Benevolent F u n d ...
Second L is t of S u b scrip tio n s.
Le t t e r s t o t h e Ed i t o r.
The Goldfields of D utch W est Borneo
P. M . Van BosseHydraulic Pipe-Lines . . F . W . Leighton
Bo o k Re v i e w sK egel’s " L eh rb u c h d er B e rg w irtsch aft ” S. / . Truscott Ne w s Le t t e r s
B ris b a n e ...
M o u n t I s a ; L a w n H ills C o n c e s s io n ; G o ld D i s c o v e r y in Q u e e n s la n d ; M u r d o c h C o p p e r P r o c e s s ; G r e a t B o u ld e r P r o p r ie ta r y ; T a x a t i o n o f D i v i d e n d s ; S h a le R e t o r t in g in T a s m a n ia .
4—3
194 196 196 198
201
213 219 223
223 224
224
226
P A G E
Johannesburg ... 227
L u ip a a r d ’s V l e i ; R a n d f o n t e in B la c k R e e f ; S a b ie G o ld M in e S o ld ; C o n g o C o p p e r D e v e l o p m e n t s ; G o ld S t r ik e s in R h o d e s ia ; R h o d e s i a ’s M in er a l R e s o u r c e s .
V ancouver... 228
P o r t la n d C a n a l ; S a lm o n R i v e r ; C a r i b o o ; O m in e c a D i s t r i c t ; P h illip s A r m ; B r id g e R i v e r ; W a lla c e M o u n ta in ; R e n o G o ld M in e s ; C e d a r C reek .
T o r o n to ... 231
P o r c u p in e ; K ir k la n d L a k e ; S u d b u r y ; R o u y n . Pe r s o n a l...
232
Tr a d e Pa r a g r a p h s...
232
E d g a r A llen-A llis-C halm ers V ib ra tin g Screen 233 V ickers P ro je ctio n M icroscope ... 234
Me t a l Ma r k e t s...
235
St a t i s t i c s o f Pr o d u c t i o n ...
237
Pr i c e s o f Ch e m i c a l s...
239
Sh a r e Qu o t a t i o n s ...
240
Mi n i n g Di g e s t T he Geology of th e C opper B elt, N o rth e rn R h o d esia ...H. Schneiderhohn 241 M agnetic S urveys over D ykes A . E . Eve and D. A . K eys 245 E xplosive C ru sh in g .it. S. Dean and J . Gross 247 T elluride M inerals a t K algoorlie Dr. F. L . Stillw ell 249 S hin y an g a D iam onds Fields Dr. E . O. Teale 251 M illing M ethods a t M inas de M atah am b re . S o u th A m erica . . A . R . Kirchner, J . V. Galloway, and W. P . Schoder 251 Sh o r t No t i c e s...
251
Re c e n t Pa t e n t s Pu b l i s h e d ...
252
Ne w Bo o k s, Pa m p h l e t s, e t c...
252
Co m p a n y Re p o r t s...
253
B a la g h & t G o l d ; C e n tr a l P r o v i n c e s M a n g a n e s e ; C h a m p io n R e e f ; C ity D e e p ; C r o w n M in e s ; D u r b a n R o o d e p o o r t D e e p ; E a s t P o o l ; E a s t R a n d P r o p r i e t a r y ; G e d u ld P r o p r ie ta r y ; G o v e r n m e n t G o ld M in in g A r e a s ; L a n g la a g te E s t a t e ; L o w e r B is ic h i (N ig e r ia ) T in ; M o d d e r f o n t e in D e e p ; M y s o r e G o ld ; N e w S t a t e A r e a s ; N u n d y d r o o g M in e s ; O o r e g u m G o ld ; R a n d f o n t e in E s t a t e s ; R e z e n d e M in e s ; R o b in s o n D e e p ; S im m e r a n d J a c k M i n e s ; T h a r s is S u lp h u r a n d C o p p e r ; T o y o T in ; T w e e f o n t e i n C o llie r y ; V a n R y n D e e p ; W it w a t e r s r a n d G o ld ; W itw a t e r s r a n d D e e p . Di v i d e n d s De c l a r e d...
256
Ne w Co m p a n i e s Re g i s t e r e d...
256
193
E D IT O R IA L
W H IL S T th e response to th e appeal of Mr. H ugh P icard for th e I.M.M.
B enevolent F u n d has n o t come up to our expectations, it is, perhaps, as m uch as one can hope for, in view of th e prevailing depression. I t is ce rtain ly gratifying to note from th is m o n th ’s list th a t th e appeal is receiving th e a tte n tio n of m ining com panies and th eir employees.
I T was announced la st m o n th th a t th e In stitu tio n of Mining Engineers has aw arded th e “ M avor and Coulson ” Travelling S tu d en tsh ip for 1932-33 to Mr.
E . J . K im m ins, of B irm ingham U niversity.
The stu d en tsh ip is w orth £300 and the successful candidate is required to devote one year to th e stu d y of coal m ining m ethods in G reat B ritain , th e C ontinent of E urope, and eith er C anada or th e U nited S tates.
S E V E R A L new appo in tm en ts to th e A dvisory Com m ittee for th e M etal
liferous Mining In d u stry were announced tow ards th e end of March. T he new chair
m an, to succeed th e late Mr. J . J . B urton, will be Mr. R. A rth u r Thom as, while Mr.
B u rto n ’s place as representative of th e iron and steel in d u stry will be tak en b y Mr. E . J.
Fox. T he new representative of th e owners of iron ore m ines and quarries is M ajor W. D.
B a rra tt and Mr. E. A rcher becomes secretary, following Mr. F. C. Starling.
T H E new president of th e A m erican In stitu te of Mining and M etallurgical Engineers is Mr. Scott T urner, D irector of th e U nited S tates B ureau of Mines. Mr.
T u rn er g rad u ated from th e U niversity of Michigan in 1902 and received his E.M . from th e Michigan College of Mines in 1904. Since then he has h ad extensive experience in various p a rts of th e world, n o ta b ly in Spitzbergen, and he was for several years consulting engineer to th e Mining C orpora
tion of C anada before joining th e B ureau of Mines.
E L S E W H E R E in this issue will be found a tran slatio n of certain ex tra c ts from a w ork b y Professor Schneiderhohn, of Freiburg,1 in w hich his views on th e geology of th e copper belt of N orthern R hodesia are
set out. The a u th o r has advised us th a t in th e p rep aratio n of th e m aterial quoted the literatu re published up to May, 1930, was taken in to consideration, b u t th a t no inform ation published since th a t date has induced him to a lte r his views w ith regard to th e genesis of th e copper deposits of N o rth ern R hodesia and th e K atanga.
A T th e annual convention of th e Canadian In stitu te of Mining and Metallurgy more light was shed by Dr. Charles Camsell on th e ever-green topic of th e m ineral position of th e B ritish E m pire. H e drew attention to a survey m ade b y th e U n ited States D e p a rtm e n t of Commerce w hich shows th a t th e E m pire considered as a u n it has com m ercial control over 21 out of 28 of the essential raw -m aterial m etals an d minerals.
In c o n tra st our own Im perial In stitu te in a recent rep o rt does n o t show th e Empire in such a favourable position, b u t then it views th e subject from th e standpoint of political control. T hus petroleum , which is included in th e form er, is excluded from th e la tte r. Dr. Camsell stressed th e need for th e com pilation of a consolidated state
m ent or m ineral balance-sheet for th e whole E m pire, w hich he said was in course of p reparation. W ith such evidence before th e governm ents of th e B ritish Common
w ealth a t th e forthcom ing O ttaw a conference th e cause of Im perial u n ity should be further strengthened.
T h e I n s titu tio n M e e tin g
T he w ork of Sir H aro ld C arpenter on th e in tern al stru ctu re of m etals is already well know n, b u t, alth o u g h th e greater part of his investigations have been devoted to finished m etallurgical products, it is not too m uch to say th a t m ining m en have tak en greater in terest in th e results of his labours since his atte n tio n has been turned to n ativ e m etals. In 1928 th e first-fruits of th is aspect of his research were presented to th e In stitu tio n of Mining and Metallurgy in th e form of a paper, w ritten in collabora
tion w ith Dr. S. T am ura, w hich embodied th e results of an application of metallo- graphic technique to th e stu d y of native m etals. A t th e tim e it w as only partially appreciated how m uch th e w ork was likely to be of im portance to economic geologists, although th e a u th o rs them selves realized th a t th e stru ctu re of th e m etals gave valuable
1 “ M ineralische B o d e n sch ätze im SüdlichenA frik a .” B e rlin : N em -V erlag.
194
A P R IL , 1932 195 indications as to their p ast history. The
subject was advanced a stage fu rth er in 1930, when, in conjunction w ith Dr. M. S. Fisher, Sir H arold once more brought th e m atter before th e In stitu tio n , th e investigation having been confined on this occasion to specimens of n ativ e copper. B y th is lim e it was generally realized how illum inating this type of research was likely to be as an aid to the elucidation of the problem s of ore genesis and during th e course of the discussion of th is paper Dr. H. C. Boydell suggested th a t a similar stu d y of specimens of native silver m ight be of even greater interest to practical geologists, as th e subject of the origin of th a t m etal was much more controversial th an th a t of n ative copper.
This suggestion was adopted and a t last m onth’s m eeting of the In stitu tio n th e first paper for presentation— “ A M etallographic Investigation of N ative Silver,” by the same authors—drew an interested audience of mining geologists as well as m etallurgists, and a second paper— “ The Volumetric Assay of Gold,” by Mr. W. B ranch Pollard—
proved an additional a ttractio n to the latter, the time available proving all too short for those eager to take p art in the discussions.
The stu d y of native silver em bodied in the paper by Sir H arold C arpenter and Dr. Fisher involved an exam ination of samples of the m etal from deposits in various parts of the world, the specimens being investigated by m etallographic m eans and by experiments in h eat treatm en t. The authors have realized th a t the reactions by which native silver has been formed are fairly well understood by geologists, and th a t the new data are m ainly useful for th e light th ey throw on existing theories and for th e help they m ay afford in determ ining the origin of any particular deposit. Briefly, th e y find that the m etal is deposited by aqueous solutions of either meteoric or hydrotherm al origin, and th a t when deposited by supergene or cool hypogene w aters the structure of m etals shows few, if any, traces of recrystallization. W hen, however, the structure is coarsely homogeneous, similar to th a t produced by annealing, it is con
sidered th a t the m etal has either been deposited from w aters a t a tem perature above th a t of recrystallization (about 200° C.) or th a t th e silver has subsequently been therm ally m etam orphosed. Most of the specimens seemed to show th a t more often than not the silver has been deposited from cool w aters, although examples from N orthern Rhodesia, Lake Superior, and
Cobalt were deposited from hot solutions.
A t Lake Superior, where th e silver is associated w ith native copper, it is interesting to note th a t b o th m etals have been formed a t a tem perature w ithin th e range of 200° C.
to 250° C. These notes will give some idea of the type of result which has been obtained from this work, and a t th e meeting, after th e paper had been introduced by Sir H arold C arpenter, who had som ething to say of th e differences between n ative copper and n ative silver, the discussion was opened by Dr. Desch, who, together w ith all th e la te r speakers, congratulated th e authors on the rem arkable m icrophotographs th e y had prepared. D r. Desch was followed by Dr. Sydney Sm ith, who com pared one of the au th o rs’ specimens w ith a sim ilar one collected by himself in Canada. Dr. W. R.
Jones, in his contribution to the discussion, welcomed the fixation of additional points on a geological therm om etric scale, although this speaker was rem inded by Dr. J. A. L.
Henderson th a t pressure conditions cannot be ignored in such research. O ther speakers included Professors B annister and M errett, Dr. Fisher being able to reply to certain of their questions.
The discussion of the first paper of the evening somewhat curtailed the tim e avail
able for Mr. Pollard to present his on the assay of gold, b u t th e subject is of such interest th a t th e w ritten discussion will surely be followed very closely. I t will suffice here to say th a t certain aspects of the m ethod described by the au th o r were first brought to the notice of m em bers by a paper read in 1923, the present work being an amplification of the procedure then developed. The a u th o r’s m ethod, which is employed a t th e Cairo Mint and in th e A lexandria Assay Office, originally involved solution of the assay in aqua regia, the gold being then precipitated as m etal by a stan d ard solution of mercurous nitrate.
Various refinem ents have now been incor
porated in the process, and it is considered th a t for certain purposes th e wet assay has advantages over the d ry m ethod, an opinion ten tativ ely shared by Dr. Sydney Sm ith, who opened th e discussion on the paper and told som ething of his experiences in carrying out an analysis by this means.
A t any rate, it is possible to agree w ith the
author th a t, in spite of the fact th a t it would
be hard to improve on the fire assay of gold
from the point of view of accuracy, the
economies of tim e and expense prom ised by
his m ethod m erit close exam ination.
196 T H E M IN IN G M AGAZINE
M e ta llu r g y a n d E n g in e e r in g
A t th e recent annual general m eeting of the In stitu te of Metals, on the occasion of his induction to the presidential chair, Sir H enry Fow ler m ade some rem arks which seem w orthy of atten tio n , p articu larly when he referred to the relations existing betw een m etallurgy and engineering. Sir H en ry from 1925 to 1930 occupied the position of chief m echanical engineer to th e L.M.S. Railw ay, which he relinquished on his ap p o in tm en t as assistant to th e vice-president for research and developm ent, an ap p o in tm en t which lends additional w eight to his pronounce
m ents. A fter referring to th e custom of the in stitu te, w hereby th e p resid en t’s chair is held successively by a producer of m etals, a research m etallurgist, and a user of m etal
lurgical products—a m ost satisfactory arrangem ent— th e new president dealt w ith th e connexion betw een engineering and m etallurgy, holding the view th a t no engineer can be said to be properly equipped for his w ork unless he has some knowledge of m etallurgy. In th is respect, of course, it will readily be ad m itted th a t th e engineer’s knowledge can hardly, in m ost cases at least, be expected to ex ten d beyond a w orking acquaintance w ith th e properties and stren g th of m aterials, w h eth er cast or m achined, and w ith th e effects produced by heat and m echanical tre a tm e n t. Sir H enry also em phasized the fact th a t no im p o rta n t discovery in m etallurgy has been m ade b u t th a t a resu ltan t advance in engineering practice soon becam e evident. The engineer is, in fact, co n stan tly w aiting on th e m e ta l
lurgist to provide him w ith those m aterials which m ake y e t fu rth e r conquests of the forces of n atu re possible. W itness, for exam ple, th e advance of the high-speed Diesel engine and the notable im provem ents in aero-engine design which m ade possible th e building of th e Schneider T rophy machines. M any m ore exam ples m ight be q uo ted tending to show th a t th e engineer will generally be able to find an im m ediate use for all the new m aterials the m etallurgist can find for him. The engineering profession, in fact, shows a definite tendency to recognize th a t its interests and those of th e m etal
lurgists run on parallel if not converging lines, as th e president was gratified to record.
Sir H enry Fowler had, in addition, som e
th in g to say ab o u t m odern facilities for th e teaching of m etallurgy, as he was in no doubt th a t th e advance of m etallurgical
education, as well as the grow ing im portance of m etallurgy generally, was largely responsible for th e creation of a better understanding betw een th e scientific and the so-called p ractical m an. N evertheless, it seems evident th a t th ere is a definite element of danger in th is grow th of educational facilities and th a t it has gone fa r enough, if not, indeed, alrea d y too far. I t is possible th a t th e sinking of available funds in the erection of teaching establishm ents which are really only a duplication of departm ents already in existence m ay sta rv e th e la tte r of endow m ents of which th e y are bad ly in need.
It is impossible to overlook th e fact that m unicipal pride is a p t to d em and at least an eq u ality in its educational facilities with those of its neighbour, b u t th ere should be a wider u nderstanding and it should be recognized th a t some of th e new institutions resulting from these processes of civic expansion are unnecessary, inasm uch as adequate accom m odation for stu d e n ts exists elsewhere.
T h e D e v e lo p m e n t o f th e K alah ari
The developm ent of C entral A frican com
m unications has alw ays received special a tte n tio n in these colum ns, th e m anner in which the traffic arteries have followed the pioneer, extending fa rth e r inland as mineral deposits have been discovered, throwing interesting light on th e factors affecting the advance of civilization. Now, therefore, th a t details are available concerning recon
naissances m ade last y ear to te st the possibilities of constructing a new railway link across th e n o rth of th e K ala h ari Desert it is possible once more to re tu rn to the subject. The projected line across the K alahari is in ten d ed to join th e railway system s of Southern R hodesia w ith those of South-W est Africa, th e re b y affording a direct o u tlet from th e in terio r to Walvis Bay. I t is sta te d th a t th e results of the survey have been so favourable th a t the project has a t last been bro u g h t into the realm of p ractical politics an d th e govern
m ents concerned have been urged to initiate a m ore extensive survey in order to confirm the results o btained b y th e first expedition and, more especially, to establish by boring operations the presence of ad eq u ate water supplies along th e route.
Reference to th e accom panying sketch
m ap will show th e route to be tak en by the
A P R IL , 1932 197 'S’ttipotti proposed new railw ay and it is im portant to
'Vas ba note th a t the results of this first engineering
°L5 It survey seem to show th a t a line could be ani constructed w ith an easier gradient and 'ev®tli4s which would have cheaper operating costs ttnitedg than those along the existing routes to Beira
^®1} and Lobito Bay. In fact, the engineer in charge has expressed th e view th a t W alvis 1 Hjot Bay would be a more economical route th a n }e funds c the other two even for traffic from N orthern limentsf Rhodesia and th e K atanga. It is im p o rtan t
°ldeparts to remember, however, th a t there is b u t faint nethe 1st, hope of the new line being able to develop ee badly I];
k the (art;
demand at!
d faciis here should!
it shouli new instit®
eesses of o inasmad r studentsei
the Kalalt ral African received sje , the mam ive followed llandaiK ' rered, tin actors aflec
Now, there oncerning k i to test
a new ni Kalahari ft 3 return 1»
line across oin the a’
,ia with tbs
much mineral traffic in its own area, judging
w afiordi®;by the present state of our knowledge of the
erior to® docal geology, and th e real raison d ’etre of
=
results ofthe new line lies in the hope, confidently irJl,|e (Jut expressed by the agricultural surveyors, th a t
ouiht
intui there exist am ple supplies of artesian w ater ndW below the desert sands. I t is hoped by the opening up of these resources of under- 'jftocoi ground w ater ultim ately to render the r 1 j country suitable for ranching purposes, and
F a : estim ates have been prepared which envisage j S ¿ir, the area carrying about 1,700,000 head of
cattle.
. 0 The developm ent of th e w estern edge of the K alahari since th e discovery of supplies
of artesian w ater has been extraordinarily rapid. In a recent paper read before the Geological Society of South A frica Mr. H. F.
From m urze has given a concise account of th e flowing bore-holes in th e R ehoboth, Gibeon, and Gobabis districts of South-W est Africa. T he first holes which gave flowing w ater in this area were drilled by the German W ater Boring D epartm ent, while th e y were endeavouring to find out w hether th e U pper K arroo sedim ents were coal-bearing. A fter th e W ar th e area was fu rth er tested by th e Irrigation D ep artm en t of th e South-W est
A dm inistration, m any more holes being drilled, as a result of which a strip of bush- covered sand, previously left to game and th e B ushm an, has been rendered habitable and potentially productive. The au th o r of this paper has draw n several interesting con
clusions as a result of his survey, among which it m ay be noted th a t he is of the opinion th a t a prom ising area for the striking of flowing w ater lies in th e southern portion of the Aminuis Reserve and in the ground extending eastw ards in to B echuanaland, an area which, if developed, will need such an outlet for its produce as the projected railw ay m ight provide.
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R E V IE W O F M INING
In tro d u ctio n .—Mining conditions during
the past m onth have shown little change. The decline in m etal prices, due to th e advance of sterling, has, however, proved som ew hat disconcerting. N evertheless, it is felt th a t at last m atters are on th e road to recovery, although it is recognized th a t it m ay be some tim e before th e y im prove to any appreciable ex ten t.
T r a n s v a a l—T he o u tp u t of gold on the
R an d for M arch was 914,017 oz. and in outside districts 46,018 oz., m aking a to ta l of 960,035 oz., as com pared w ith 914,102 oz.
in F eb ru ary , the M arch to ta l representing a new m onthly record. The num ber of natives em ployed on th e gold mines a t th e end of th e m o n th to talled 214,024, as com pared w ith 216,171 a t th e end of F ebruary.
The report of E a st Geduld Mines for 1931 shows th e ore reserves a t th e end of the year to have been 3,750,000 tons, averaging 6-9 dw t. in value over a stoping w idth of 58 in. Stoping operations were commenced on J u ly 1 last and up to th e end of th e year 231,700 tons of ore had been milled, the gold yield totalling 56,003 oz., w orth
£237,116. T he w orking loss for th e half- y e a r’s operations am ounted to £33,035, although profits have been earned since Septem ber. The mine is expected to be in full swing by th e middle of the year.
D uring 1931 the mill a t the W est R and Consolidated Mines crushed 1,066,000 tons of ore, yielding gold to th e value of
£1,217,901. W orking costs am ounted to
£984,879 and th e working profit to £233,022.
T he indebtedness of th e com pany to the General Mining and Finance Corporation, which a t th e end of 1930 am ounted to
£216,125, was repaid during th e year. The estim ated ore reserves a t the end of the period under review am ounted to 4,053,000 tons, averaging 5-6 dw t. in value over a stoping w idth of 45 in. T he fire which occurred at th e m ine in Ju n e last, which resulted in a stoppage in th e W est S haft section for six weeks, is responsible for the decrease of 21,000 tons in th e ore crushed.
The rep o rt of the Meyer and Charlton Gold Mining Com pany for 1931 shows the ore milled, 206,120 tons, to be 7,280 tons less th a n in th e previous year, owing to the stoppage in N ovem ber last caused b y the fire in th e C ity Deep. The value of th e gold produced was £207,868, while w orking costs am ounted to £186,886, leaving a w orking profit of £20,982. The ore reserves a t the
end of th e year were estim ated to consist m ainly of a few sm all blocks of South Reef, which have been opened up in claim s leased from th e C ity Deep, and, although certain high-grade pillars rem ain in th e mine, it is regarded as evident th a t th e end of its profitable 1 fe is n o t a long w ay off.
T he accounts of th e New Kleinfontein C om pany for 1931 show a w orking loss, after providing for developm ent expenses, of £11,622. The ore m illed totalled 611,200 tons and 124,487 oz. of gold was recovered, th e to ta l revenue being £531,993.
T he ore reserves a t th e end of th e year were estim ated to be 288,000 tons, averaging 4-93 dw t. in value over a stoping w idth of 53-01 in., as com pared w ith 286,100 tons, 5-01 dw t., and 51-75 in. a t th e end of 1930.
D evelopm ent in th e A pex m y n p ach t was resum ed during th e year an d w ork so far accom plished has provided ore reserves which more th a n replace th e tonnage mined from th e section.
D etails of th e rep o rts of th e companies of the Jo hannesburg Consolidated group for 1931 will be found elsew here in th is issue.
On th e R andfontein E sta te s th e development of th e principal section of th e mine is in a- very interesting stage, th e y e a r’s work having fully borne out th e expectations of a progressive flattening of th e dip of the reefs. I t is now believed th a t beds are in th e form of a large synclinal fold, which is cu t out to th e east b y th e W itpoortje fault, situ a te d considerably east of the present working.
An accident to th e rock hoisting engine a t th e No. 5 vertical sh aft of th e Consolidated Main R eef Mines, rep o rted on M arch 9, was expected to interfere w ith th e m onthly output.
T he accounts of R an d Mines, L td., for 1931 show a profit of £541,041, which, added to th e balance of £428,817 brought in and £378 in respect of forfeited dividends, gives an available to ta l of £970,236. Of th is am ount £409,030 has been distributed as dividends, equal to 80% , £63,083 expended in investm ents, and £31,412 has gone for tax atio n purposes, leaving a balance of
£466,711 to be carried forw ard.
The rep o rt of W itp o o rt Gold A reas for
1931 shows th e ore reserves to be 567,000
tons, of an average value of 6-2 dw t. over a
stoping w idth of 41 ins. T he position
developed during th e year shows th e company
to have been indebted to th e General Mining
198
A P R IL , 1932 199 and Finance C orporation to the ex ten t of
£90,000, while other com m itm ents, for stores, etc., were also heavy. As th e General Mining Corporation was disinclined to advance more money, th e agreem ent w ith B rakpan mines, already noted in these columns, was entered in to and at an ex trao rd in ary meeting held last m onth this was approved.
Shareholders of B rakpan Mines have been informed th a t in order to avoid appropria
tions from profits the board m ay decide to raise the funds required for the paym ents to the W itpoort com pany and for th e develop
ment of the new ly-acquired area by an issue of shares. F o r this purpose it will be necessary to increase th e capital of the company and a t m eetings to be held in Ju n e and Ju ly next it will be proposed th a t the directors be given power to do this up to a maximum of £1,150,000.
S outhern R h od esia.—The o u tp u t of gold
from Southern R hodesia during F ebruary was 45,032 oz., as com pared w ith 42,706 oz.
for the previous m onth and 42,818 oz. in February, 1931. O ther o u tp u ts for F eb ru ary last w e re : Silver, 6,380 o z ; coal, 44,928 to n s; chrome ore, 2,647 t o n s ; asbestos, 873 tons.
The report of th e Globe and Phcenix Company for 1931 shows th a t 72,512 tons of ore was crushed, the gold recovered totalling 65,588 oz. T he n et profit for the year, including £37,214 brought in, am ounted to £114,915. D ividends declared during the year absorbed £80,000, equal to 2s. per share, leaving a balance of £34,915 to be carried forward. The ore reserves a t the end of th e year were estim ated to be 124,000 tons, containing gold to th e value of £632,520, as com pared w ith 126,300 tons, valued a t £639,660, a t th e end of the previous year. The installation of new plant at the mine is said to be proceeding satis
factorily and it is hoped th a t it will be in full commission by th e m iddle of th e present year.
N orthern R hodesia.— Shareholders of the
R hokana C orporation were inform ed last m onth th a t th e concentrating mill had started running on D ecem ber 11 last and had been in successful operation ever since, m etallurgical results being satisfactory and th e tonnage capacity estim ated to be considerably greater th a n th e nom inal figure.
Smelting operations commenced on March 17, the first blister copper being shipped on March 21. Shareholders were rem inded th a t th e railw ay betw een N ’D ola and
N ’K ana was not com pleted u n til May 26, 1930, so th a t eighteen m onths only were required to com plete th e mill and bring it in to operation, while the first copper has been shipped in less th a n two years.
A circular to shareholders of th e Rhodesia- K atan g a Com pany gives details of the developm ent w ork carried out by diam ond drilling up to th e end of 1931. T his work is said to have fully confirmed the estim ates of ore previously m ade, th e grade having been raised from an average of 4'2% to 4'5%
copper. I t is fu rth er stated th a t pending an im provem ent in th e price of th e m etal, work on th e mine has been reduced to a m inim um , being confined to two drill shifts per day in th e n o rth p a rt of th e m ine, where th e ore-bodies are a t present undefined.
A u stralia.— I t was announced last m onth
th a t th e Sulphide Corporation h ad decided to resum e work on the Central Mine—which h ad been closed down since Ja n u a ry , 1931, owing to low m etal prices—on A pril 4.
Tow ards th e m iddle of March details becam e available of th e rep o rt of Mr. C. O.
Lindberg on the Lake View and S tar mine, w hich he visited on behalf of th e New Consolidated Gold Fields, L td. Mr. Lindberg states th a t he is im pressed by th e continued favourable developm ent results and the im provem ent in operating conditions. He points out th a t th e Chaffers sh aft is expected to be ready for service to the 1,600 ft. level in the present m onth and the cost of its enlargem ent, estim ated at betw een £55,000 and £60,000, has been m et out of profits.
The conversion of the mill from d ry to wet m ethods w ith flotation is expected to be com pleted shortly, when operating costs are expected to be reduced to 7s. 6d. per ton and to ta l costs to about 23s. 9d. per ton.
Mr. Lindberg adds th a t trib u te production is on th e decline and th a t it will probably cease entirely as th e p lan t goes into produc
tion a t th e new rate of 30,000 tons per m onth.
The M arch circular to shareholders of
th e W iluna Gold Corporation showed the
new ore-body on th e No. 2 W est lode to
have an indicated length of over 1,000 ft.,
the ore being free of antim ony. D riving
on th e lode had been started. A t th e end
of the m onth additional inform ation was
issued, a bore-hole west from th e W est lode
a t 554 ft. n o rth on th e 625 ft. level having
encountered ore 51 ft. wide, averaging
44s. 6d. in value. A t a point 342 ft. n o rth
driving on the lode h ad commenced and
200 T H E M IN IN G MAGAZINE been carried for 52 ft. in ore averaging
54s. 6d. over a w id th of 7 ft. 3 in., th e full w idth of ore not being exposed.
N ew G uinea.— I t was announced last
m onth by th e Consolidated Gold Fields of South A frica th a t th e dredge an d power plan t on th e p ro p e rty of Bulolo Gold Dredging h ad sta rte d w ork on M arch 21 and th a t th e y were working satisfactorily.
India.—A t e x trao rd in ary m eetings of
shareholders of th e B alaghat and N undy- droog com panies, held following th e annual m eetings th is m onth, th e sale of th e B alaghat p ro p erty to N undydroog was approved.
T he term s of sale involve th e paym ent of £40,000 in cash for th e leases, workings, a n d certain p lan t, th e paym ents to be spread over a period of nine m onths. F or m ining an d milling th e B alaghat ore reserves th e N undydroog Com pany will m ake a charge of 24s. per ton and, afte r deducting in addition from th e n et sale proceeds of bullion th e 5% ro y alty due to th e Mysore govern
m ent an d th e cost of keeping th e B alaghat m ine free of w ater, th e n e t profit will be divided as to 25% to N undydroog and 75% to B alaghat. T he form er com pany will tak e over th e assets and s ta rt w ork on the ore reserves on May 1 next.
C anada. — In th e Suprem e Court of
O ntario judgm ent was given last m onth in favour of th e representatives of B ritish shareholders in th e Y ukon Consolidated Gold Corporation, in an action against Mr. Treadgold, a form er president of the com pany. The judgm ent orders th e re tu rn to th e com pany for cancellation of 2,419,000 shares of th e common stock and 15,000 preferred shares held b y Mr. Treadgold and enjoins him from dealing in th e shares u n til th e cancellation is effected.
S p a in .—D uring
1931 th e Rio T into Com pany m ade a trad in g profit of £424,894, while th e n e t profit was £100,185. A fter adding the am ount of £384,367 brought in, th ere was an available to ta l of £484,552, of which £81,250 has been d istrib u ted as dividends, equal to 5s. per share, leaving a balance of £403,302 to be carried forw ard.
T he rep o rt points out th a t conditions in Spain have been increasingly difficult, although th e good relations betw een th e com pany and its Spanish em ployees have been m aintained.
M inerals S ep aration . — The report of
M inerals Separation, L td ., for 1931 shows a credit balance for th e year of £33,948, against £54,658 for 1930. The balance
brought forw ard was £28,972 and, after allowing for several oth er item s, there was an available to ta l of £72,462, of which
£30,000 was d istrib u ted as dividends, equal to 15%. No dividend was received from the A ustralian com pany during th e period under review, although an in terim paym ent has been received for th e cu rren t year.
M urex.—A t an e x trao rd in ary meeting
of Murex held th is m o n th th e increase of the capital from £200,000 in 10s. shares to £250,000 by th e creation of 50,000 preference shares of £1 each was approved. The new shares were offered to th e shareholders a t 21s. each.
V enture T ru st.—An ex tra o rd in ary m eet
ing of th e V enture T ru st is to be held this m onth, w hen shareholders will be asked to approve th e reduction of th e share capital by w riting 3s. 4d. off th e value of th e present 10s. shares. The reduced capital would th e n consist of 500,000 shares of 6s. 8d.
and it will th en be proposed th a t it be restored to £250,000 by th e creation of a fu rth e r 250,000 shares of 6s. 8d. each.
U n ion C orp oration .— T he accounts of
th e U nion C orporation for 1931 show a n et profit of £229,117, which, together w ith th e £111,017 brought forw ard from 1930, gives an available to ta l of £340,134.
A dividend equal to 2s. 6d. per share will absorb £126,162 and £100,000 is to be placed to a special reserve, leaving a balance of
£113,972 to be carried forward.
C on solid ated M ines S electio n . —
D uring 1931 th e Consolidated Mines Selection Com pany seriously felt th e absence of a dividend on its large holding in th e Anglo Am erican C orporation of S outh Africa.
The continued depreciation in th e market value of holdings has been p a rtly m et by the transference of £20,000 from th e reserve account, w hich is now exhausted. The book value of th e com pany’s holdings at th e end of th e year stood a t £503,005, against a m ark et value of £304,933, which th e directors consider to be m uch below the tru e value. T he profit and loss account shows th a t afte r w riting £32,917 off the value of shares held th e balance carried forw ard is £2,125.
C opper.— I t was announced last month
th a t a t a m eeting of copper producers held
in New Y ork it h ad been decided to reduce
th e o u tp u t for th e rem aining nine months
of 1932 to 20% of capacity. Shareholders
of th e com panies operating in N orthern
R hodesia have been inform ed th a t production
will be reduced accordingly.
ELECTRICAL PROSPECTING FOR AURIFEROUS Q U A R T Z VEINS AND REEFS
By H E L M E R H E D S T R O M
T h e a u th o r , w h o is c o n n e c te d w ith th e E le c tric a l P ro s p e c tin g C o m p a n y o f S to c k h o lm , p a y s p a r tic u la r a tte n tio n to p ro c e s s e s o f “ e le c tr ic a l tr e n c h in g ,” w h ic h a r e u n d e rg o in g e x te n s iv e te sts o n s e v e ra l g o ld field s.
In t r o d u c t i o n.
— D uring th e last few years a num ber of articles have appeared in mining periodicals on th e use of electrical m ethods when prospecting for base m etal ores. Very little has been published, however, on the application of these geo-electrical m ethods to other problem s of m ining geology, this being a com paratively recent developm ent.
The present article is intended as a brief description of p a rt of this new developm ent, nam ely of some new applications of those geo-electrical m ethods which are characterized by th e determ ination of electrical potentials. These “ p o tential methods ” have previously been used alm ost solely for th e locating of buried bodies of b etter electrical conductivity th a n the surroundings, for instance— pyritic ore- bodies. The new applications of these methods are used to locate or determ ine the distance to b oundary planes betw een different rock form ations. According to whether these boundary planes are nearly horizontal or nearly vertical, th e new applications m ay be divided into the following tw o classes :—
(1) “ E lectrical drilling,” which comprises the determ ination of thickness of overburden, depth to th e ground w ater table, dip of slightly inclined sedim entary beds at moderate depth, etc. This process, which might possibly be of more interest, in general, to the civil engineer or hydrologist th a n to the m ining engineer, has already been dealt w ith in several recent publications.1
1 O. H . Gisli : “ D e p th s of G round W a te r a n d o ther S ubsurface F e a tu re s in d ic a te d b y E a rth - R esistiv ity S u rv e y s,” Terrestr. M agnetism , 33, No. 3, 129-138 (1928).Irv in g B. C rosby a n d E . G. L eo n ard o n :
" E lectrical P ro s p ec tin g ap p lied to fo u n d atio n pro b lem s,” A .I.M .M .E ., Tech. Publ. 131 (1928).
E. L a n c a s te r Jo n es : " T he E a r th R e sistiv ity M ethod of E le ctrica l P ro s p e c tin g ,” Th e Min in g Ma g a z in e, J u n e a n d Ju ly , 1930.
G. F. T agg : “ T he E a r th R e sistiv ity M ethod of G eophysical P ro s p e c tin g ,” Th e Min in g Ma g a z in e, Septem ber, 1930.
E. G. L eo n ard o n : “ E le ctrica l E x p lo ra tio n Applied to G eological Pro b lem s in Civil E n gineering,” A .I.M .M .E ., T ech. P ubl. 407 (1931).
H ans L u n d b erg a n d Th. Z uschlag : A new D evelopm ent in E le ctrica l P rospecting, A .I.M .M .E., Tech. P u b l. 415 (1931).
(2) “ E lectrical trenching,” comprising the locating of hidden contacts, fault planes, q u artz veins, bankets, and reefs. This process should be of p articu lar interest to m ining m en in these tim es of increasing activ ity in th e field of gold prospecting. I t is this application of th e p otential m ethods which is th e special subject of th e present article.
Previously it has not been described in the literatu re, excepting in an article by G. F.
Tagg in th e
Ma g a z i n efor Septem ber, 1930, and in th e recent R eport of the Im perial Geophysical E xperim ental Survey, where th e problem of finding a vertical fault by th e use of a four-electrode system has been discussed theoretically.
F A U L T P L A N E
Fig. /.
Th e o r e t i c a l Co n s i d e r a t i o n s o f
"
El e c t r i c a l Tr e n c h i n g. ” —By “ electrical trenching ” an electric current is conveyed to th e earth by m eans of two power electrodes, one of which (A in Fig. 1) is grounded in th e area of investigation, while th e other electrode (B) is placed so far aw ay th a t it has practically no influence on the m easurem ents. The electrical p o ten tial a t the surface w ithin the area of investigation will th u s be caused solely by th e electric current entering th e ground a t A, and the following relations will apply :—
If the stren g th of the current is called
I and th e electrical resistivity of the ground
form ation is called p v it is easy to prove th a t
the electrode A will act as a “ point-source ”
202 T H E M IN IN G MAGAZINE
w ith a p o ten tial
E = ■Pi
If th e ground is hom ogeneous in all directions an d to g reat depths th e p o tential P a t a point in a distance 1 from th e electrode A will be
1 ~ 2wl 2.
The p o ten tial along a radius from A will th u s decrease in inverse proportion to th e distance from A. This “ norm al p o ten tial ” distribution, however, will be d istu rb ed by th e presence of a vertical bo u n d ary plane (contact) to an o th er form ation w ith a different electric resistiv ity
p 2,as shown in Fig. 1. T he ensuing anom alous p o te n tia l distrib u tio n in this case can be conveniently represented m ath em atically b y application of L ord K elvin’s and M axwell’s “ m ethod of im ages.”
B y optical analogy we im agine th a t th e b o u n d ary plane is acting as a m irror, p a rtly reflecting and p a rtly tra n sm ittin g light from th e point-source A. In th e m edium p1 th e expression for th e p o te n tia l will th u s be com posed of two p arts, the first one due to
p , - ? +
th e point-source E itself, and th e second one due to th e im age w hich we suppose to have th e stre n g th kE , w here k m ay be called th e “ reflection coefficient.” A t th e point P x in Fig. 1, th e p o te n tia l will th e n be
k . E
2a - l j ...
In th e m edium p 2 th e p o ten tia l a t any point will be th e sam e as if th e ground were hom ogeneous, b u t th e stre n g th of the point source changed from E to an o th er value E 1. (By optical analogy one m ay imagine th a t th e point source E is seen dim ly through th e b o u n d ary plane.) A t th e point P, in Fig. 1 th e p o te n tia l will th e n be
E 1
... 4.
P„ =
A t th e b o u n d a ry plane th e p o ten tial must be th e sam e w h eth er com puted from the expression 3 or 4. C onsequently :__
E k . E _ E 1 a a ~ aT
or
E 1 = (1 + k ) . E . . . . . 5 .
F u rth e r, th e com ponent of electric current
A P R IL , 1932 203 passing through a certain sm all p a rt of the
boundary plane m ust be th e same w hether computed from th e p r side or the p 2-side.
This current can be expressed as th e electric
dP . .
field -jj (the derivative of th e p o ten tial in respect to th e distance), divided b y th e resistivity. D erivating th e expressions 3 and 4 and p u ttin g lx = 12 = a, we then get :—
k ) = -
1 . ( 1
+ k )7 ' (1
P i PiPi
Pi
P i + P i
and, from th e expressions 3 and 4 :—
P i
l E:i _. _ P i ___________
L P i + P i 2 a — h
P i 7.
P 2
E
4 -( 1 +
P 2 P i + P i ’P iThe reflection coefficient k thus varies from + 1 to — 1, according to w h eth er the formation p 2 on th e back side of th e boundary plane offers a com paratively very high or a com paratively very low resistance to the
Ar\ £.n f,
passing of an electric current. In the first case th e b oundary plane acts as a to tally reflecting m irror, in th e second case as a to ta lly reflecting “ negative ” m irror (the image in this case being of opposite stren g th to th e point source E). F or th e same cases th e “ dim m ing coefficient ” (1 -f~ k) in expression 5 varies from 2 to 0. •
Faults and Contacts.— B y th e use of
th e equations 7 and 8 th e p o ten tial d istrib u tio n can be com puted along a profile of investigation th a t crosses a contact.
Fig. 2 shows th e results of such com putations p u t together in a diagram . T he b oundary surface in this figure is supposed to be at a distance of 100 units of length from the power electrode. The p o ten tial values com puted for observation points a t different distances from th e power electrode have been p lo tted against these distances, every value first having been m ultiplied b y th e corre
sponding distance. In other words, the
p lo tted values represent th e ratio betw een
th e com puted p otential and the norm al
p otential, and th u s represent th e m agnitude
204 T H E M IN IN G MAGAZINE of th e anom aly caused by th e presence of the
b o u n d ary plane. D ifferent curves correspond to different ratio s betw een th e resistivities
p 2 andon th e tw o sides of th e b o u n d ary plane.
The exam ination of th e simple Fig. 2 discloses an im p o rta n t fact related to th e m ethod of locating vertical faults and contacts electrically. I t shows th a t th e anom aly in th e p o ten tial a t th e b oundary plane will am ount to 50% of th e possible m axim um already for a resistiv ity ra tio of 3 : 1 , while for a resistiv ity ra tio of 10 : 1 the anom aly will reach 82% of th e possible m axim al value. This m eans th a t a p ractical
“ satu ratio n value ” of anom aly is reached already a t com paratively sm all resistiv ity ratios, and th a t th e m ethod consequently is very sensitive to sm all differences in resistivity on th e tw o sides of th e contact.
If, instead of th e p o tential, th e p o ten tial gradient or th e electric field (potential drop per u n it length), is calculated for th e same conditions as in Fig. 2, we get, by derivation from th e expressions 7 and 8, in respect to th e distance 1 :—
d P i 1 P2 — P i I q
E dl l2 p 2 + P l '(2 a - l)* ' ' '
and
- T - w ’ - T O + i N f ; ) ,o-
for th e conditions on th e “ front side ” and th e “ back s id e ” of th e b o u n d ary plane, respectively.
C om puting after th e expressions 9 an d 10 the electric field for different distances 1 and different values of th e resistiv ity ratio
— , and dividing th e com puted results w ith
Pl .
1
the norm al electric field -2- , we get curves as those draw n in Fig. 3. This figure th u s shows th e com puted electric field expressed in th e norm al electric field as u n it, th e value 1-00 representing th e norm al field and the other values th e m agnitude of “ anom aly ” caused by th e presence of th e contact. I t is readily seen th a t th e “ satu ra tio n effect ” discussed above appears also in this case, so th a t a com paratively large anom aly in the electric field is caused already for a com p aratively sm all difference in th e resistivities on th e tw o sides of th e contact. I t will be noted th a t the m agnitudes of these anom alies are th e same as the p o ten tial anom alies shown in Fig. 2. Fig. 3, however, in co n trast to Fig. 2, shows a discontinuity a t the
b oundary plane. Thus in passing over the contact betw een tw o m edia w ith a resistivity ratio of 1 : 3 , th e electric field suddenly changes from a value equal to one half of the norm al field to a value equal to 1-5 tim es the norm al.
Quartz Veins, Bankets, and R eefs.— If the
b oundary plane in Fig. 1 is replaced by a sheet, of thickness b an d resistiv ity
p z,as shown in Fig. 4, th e p o te n tia l distribution can be calculated in th e following way.
f/'gr. 4-,
T he “ reflection coefficient ” used above,
^ — —1 we call
p 21.The “ reflection
P 2 + Picoefficient ” of th e opposite side of the same b o u n d a ry surface, is th e n - - — — a n d may
Pi + Pz
accordingly be called p 12, equal to — pn . The corresponding “ dim m ing coefficients”
will be 1 + p 21 an d 1 — p 21.
In th e m edium p v th e p o ten tia l will be due to th e point source E an d a series of images of E in th e tw o bou n d ary planes.
Of these im ages th e first one will be of the
“ stre n g th ” E .p 31 an d will be placed at a distance a from th e first bo u n d ary plane in analogy w ith eq u atio n 6. The second one, w hich is “ dim m ed ” by th e first boundary plane, th e n reflected in th e second boundary plane an d again “ dim m ed ” when seen th ro u g h th e first b o u n d ary plane, will have th e stre n g th E . ( l + p31)
,p2Z.(1 + p13), and will be a t a distance (a -f- 2b) from the first b o u n d ary plane. T hrough double reflection of this second im age in th e tw o boundary planes a th ird image is added, which will have th e stre n g th E . (1 - f Psi) .p 23. (l + P
13) -P
13-P
23- a n d will be placed a t a distance (a + 4b) from th e first b o u n d ary plane.
B y rep eated reflection in th e tw o boundary
planes we th u s get an infinite series of images,
which gives th e following expression for the
p o ten tial in a point on th e surface of the
A PR IL , 1932 205
halloi;
5 ti%
1 oistribI ng way.
I 1! SH i
medium p 1 a t a distance x (numerically
< a) from th e first b oundary plane :—
+ (J P 3 l ) 2 -P23 a + x + 2b (1 P 3 l ) 2 ■ P23 • P l 3 • P 23
a + x + 4b ( 1 ~ P 3 l ) 2 - P 2 3 - P l 3 2 ■ P23
a + x + 6b
+
+ or
P i.
E
1 +
-P 31 a — x a + x/ 1
+ (1 — P 3 l ) 2 - P2
If Pl =
P l _ 1\ a + x + 2b P132 • P232
a + x + 6b
P2 1 '
+
P l3 • P 23 a + x + 4b+ )
+
E
+
a + xP311
+ i 1 — P s l ) 2 - P l 3 -
Pl3 ( a + x + 2b a + x + 4b
+
P13
a + x + 6b+
side«! tits i l l
PitP* 1
equal to
¿15 coelck
potential w.
E and a sffi
= t 1 + P31) ( a I
+ __ P-23____ L
+ x a — x + 2b P 2 3 • P l3+
P 23 • P 13 a + x + 2bP233 • P132
4b
+
P23 • P l 3~l + x + 4b
6b
+
+
13.If p 1
— p.2 P— (1 + P3l) ka + x a P 13
2b
+
P i s
+
P i sa + x + 2b a — x + 4b
P i 3
+
P13+
'■ )
14.a + x + 4b a — x + 6b
At the surface of the m edium p :! we get for a point a t a distance x ( > b) from th e first boundary plane :—
1
(1 + P31) (1 + P23)
+
11
.
P23~■ Pl3~
a + x + 4b
and if Pl = p 2 :—
+
a + x
P233 • Pl3J
a + x + 6 b
g -3 = (! - P132)
P is
(
1 +
Pl3~a + x a + x + 2b P2 3• P i 3
a 4- x + 2b
+ +
15.+
P isx + 4b a + x + 6b
+ )
16.12.
