A CONDUCTANCE INSTRUMENT FOR THE STANDARDIZATION OF VOLUMETRIC ANALYTICAL REAGENTS

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Xerox University Microfilms 300 North Z eeb R o a d Ann Arbor, M i c h i g a n 48106

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Vo8 e l < Alfred H 191$A conductance i n s t r u m e n t f o r the s t a n d a r d i z a t i o n o f v o l u m e t r i c ana­ l y t i c a l reagents o New Y o r k , 19i?0 iii,5 > U ty p ew ritten leaves* diagr tables,. 29cm„ T h e s i s (Ph„D„) - New York Univer­ s i t y , Graduate S c h o o l , 1 9 5 0 o B i b l i o g r a p h y : p«>5>3-5lj.. C57 6 2 1

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Xerox University Microfilms,

THIS DISSERTATION H A S

A n n Arbor, M i c h i g a n 48106

BEEN M I C R O F I L M E D E X A C T L Y AS R E C E I V E D .

LIBRARY OP NEW TORI UNIVERSITY ttNIVlRSITY HEIGHTS

A CONDUCTANCE INSTRUMENT FOR THE STANDARDIZATION OF VOLUMETRIC ANALYTICAL REAGENTS

ALFRED M. VOGEL

A D i s s e r t a t i o n i n th e Departm ent o f C hem istry S u b m itted in p a r t i a l F u l f il l m e n t o f th e R equirem ents f o r th e Degree o f D o c to r o f p h ilo s o p h y a t New York u n i v e r s i t y

A p r il, 1950

To P r o fe s s o r R alp h H. M u ller I w is h to acknowledge my g r e a t d e b t fo r s u g g e s tin g t h i s problem , f o r h is g u id a n c e and d i­ r e c t i o n , fo r h i s p o in t in g new ways in ch em ica l s c i e n c e ,

I w ould l i k e

t o thank

my f e l l o w s t u d e n t s f o r h e l p , f r e e l y g iv e n .

I d e d ic a t e t h i s to my w i f e , B e s s , w it h o u t whom t h i s work w ould n o t h a v e been p o s s i b l e .

iii

TABLE OF CONTENTS PAGE I II

INTRODUCTION PART I - CONCENTRATION-TEMPERATURECONDUCTANCE DATA A.

EXPERIMENTAL 1. 2.

B.

DIRECT READING OF NORMALITY

B.

TEMPERATURE COMPENSATION

8 9 12 14 15 17

D evelopm ent o f Network Therm istor C h a r a c t e r is t ic s C a lc u la tio n o f S and p

19

22 25 26

CONCOMITANT PROBLEMS 1. 2. 3. 4. 5. 6.

VI

C o n d u c tiv ity N o rm a lity E q u a tio n s Temperature R e s is ta n c e R e la t io n s Temperature C o e f f i c i e n t o f C onductance A Combined E q u a tio n Comparison w ith o th e r Data I n t e r n a t io n a l C r i t i c a l T ab le V alu es

A.

C.

V

3 7

PART I I - INSTRUMENT REQUIREMENTS

1. 2. 3.

IV

Apparatus and C h em icals Method o f M easurem ent

RESULTS AND DISCUSSION 1. 2. 3. 4. 5. 6.

III

1

Power C h a r a c t e r i s t i c s o f th e T h erm isto r Wagner G round Adjustment f o r C e l l C on stan t and R ea g en t Bridge B a la n c e I n d ic a t o r Quadrature B alan ce T herm istor C o a tin g s

30 31 32 33 34 34

SUMMARY

36

TABLES AND FIGURES

39

BIBLIOGRAPHY

53

I

I n tr o d u c tio n

E l e c t r o l y t i c c o n d u cta n ce m easurem ents have b een made f o r a p p ro x im a te ly th e l a s t s e v e n t y - f i v e y e a r s .

The te c h n iq u e s

o f the m easu rem en ts have been I n v e s t i g a t e d and Improved o v e r th e y e a r s , w i t h i n r e c e n t tim es by G r in n e ll Jon es and h is c o -w o r k e r s , u n t i l t h e y are c a p a b le o f a p r e c i s i o n u s u a l l y n o t a t t a in e d by m o st o th e r p u r e ly c h e m ic a l or p h y s i c a l c h e m ic a l m eth ods.

T h ese

co n d u c ta n c e te c h n iq u e s have b een a p p lie d t o a number o f p ro b ­ lem s and y i e l d e d e x c e l l e n t r e s u l t s , as I n t i t r a t i o n e n d p o in t s , c a l c u l a t i o n o f I o n i z a t i o n c o n s t a n t s , d e te r m in a tio n o f e x t e n t o f h y d r o l y s i s , s o l u b i l i t y o f some s a l t s , and o t h e r s . T . S h e d lo v sk y (1 ) p o i n t s out t h a t con d u ctan ce I s a l s o a s u f f i c i e n t l y s e n s i t i v e f u n c t io n o f c o n c e n tr a t io n to b e u s e f u l i n i t s q u a n t i t a t i v e d e te r m in a tio n .

He p o in t s o u t fu r th e r t h a t

s i n c e th e te m p e r a tu r e c o e f f i c i e n t i s ab ou t 2$ p er d e g r e e , good tem p er a tu r e r e g u l a t i o n i s needed fo r a c c u r a te w ork.

He s t a t e s

t h a t to make use o f conductance f o r c o n c e n tr a tio n d e t e r m in a t io n s , e i t h e r a c a l i b r a t i o n curve or som e a n a ly t ic f u n c t io n o f c o n c e n ­ t r a t i o n v e r s u s c o n d u cta n ce i s n e e d e d . B ecause o f th e se c h a r a c t e r i s t i c s , th e u s e o f co n d u c­ t a n c e f o r a n a l y t i c a l purposes h a s been s e v e r e ly l i m i t e d . t h e pu rp ose o f t h i s i n v e s t i g a t i o n

It is

to d e v is e an in str u m e n t w h ic h

w i l l be d i r e c t r e a d in g in n o r m a lity , tem p eratu re com p en sated ,

and ca p a b le o f a p r e c i s i o n needed f o r g e n e r a l a n a l y t i c a l pur­ p oses.

S p e c i f i c a l l y , t h i s in stru m en t s h o u ld b e c a p a b le o f

s t a n d a r d iz in g v o lu m e tr ic r e a g e n ts u se d I n a n a l y s i s . I t i s on ly w i t h i n r e c e n t y e a r s th a t te m p e r a tu r e com­ p e n s a tio n becam e p o s s i b l e .

S in ce th e te m p e r a tu r e c o e f f i c i e n t

of e l e c t r o l y t i c c o n d u cta n ce i s la r g e and n e g a t i v e , to c o m p en sa te , an e le m e n t w it h an e q u a l o r g r e a te r tem p eratu re v a r i a t i o n o f co n d u cta n ce i s n eeded. R e s is t a n c e e le m e n ts c a ll e d th e r m is t o r s

(2 ), w ith a

n e g a t iv e tem p era tu re c o e f f i c i e n t o f ab ou t 4$ p e r d e g r e e , rea ch ed a s u f f i c i e n t l y high s t a t e o f developm ent w ith in th e p a s t fo u r y e a r s to o f f e r the p o s s i b i l i t y o f tem p eratu re c o m p e n sa tio n . I n c o n n e c tio n w it h the developm ent o f t h i s equipm ent i t was n e c e s s a r y to have d e t a i l e d c o n d u c ta n c e - c o n c e n tr a t io n tem p eratu re r e l a t i o n s f o r

th e a n a l y t i c a l l y i n t e r e s t i n g ra n g es —

0 .0 9 t o 0 .1 1 Normal, and 1 5 ° to 35°C'. A thorough s e a r c h o f the r a th e r c o p io u s condu ctan ce l i t e r a t u r e y i e l d e d no in fo r m a tio n r e a l l y a p p lic a b le to t h e prob­ lem a t hand.

D e ta ile d c o n d u cta n ce d a ta f o r s o l u t i o n s o f e l e c ­

t r o l y t e s u s e f u l In a n a l y t i c a l ch em istry i n th e c o n c e n t r a t io n range 0 .0 9 - 0 .1 1 Normal w ere p r a c t i c a l l y n o n - e x i s t e n t , s in c e most c o n d u cta n ce work had b e e n done w ith an eye t o the s t a t e o f e le c t r o ly t e s in d ilu te s o lu t io n s . id e

( 3 ) and h y d r o c h lo r ic a c i d

Only f o r p o ta ssiu m c h l o r ­

(4) has any s y s t e m a t ic s t u d y o f

the te m p e r a tu r e c o e f f i c i e n t b een made. h o w ev er, f o r th e p r e s e n t p u r p o s e .

B oth w ere u s e l e s s ,

The e x p r e s s io n s g iv e n f o r

th e s e e l e c t r o l y t e s r e l a t e th e change o f c o n d u cta n ce w ith tem per­ a tu r e fo r a s o l u t i o n made u p as e it h e r 0 .1 Normal or 0 . 1 Demal

a t a p a r t i c u la r te m p e r a tu r e .

S in ce , f o r co m p en sa tio n p u r p o s e s ,

we are i n t e r e s t e d i n th e v a r ia t io n i n con d u cta n ce w ith tem p era­ t u r e of s o l u t i o n s t h a t a r e alw ays of t h e same c o n c e n t r a t io n , t h e s e two d i d not s e r v e our p u rp o ses. Because o f t h i s com p lete l a c k o f in fo r m a tio n i n th e l i t e r a t u r e i t became n e c e s s a r y f i r s t t o e x p e r im e n ta lly d eterm in e t h e c o n d u c ta n c e -c o n c e n tr a tio n -te m p e r a tu r e v a r i a t i o n fo r some e l e c t r o l y t e s , w ith g o o d p r e c i s i o n , b e f o r e b e in g a b le to p r o c e e d w it h the d ev elo p m en t o f th e in s tr u m e n t. The work c o v e r e d b y th is t h e s i s may b e d iv id e d i n t o two p a r ts .

Part I d e a l s w it h the a c cu m u la tio n o f the c o n c e n t r a t io n -

tem p a ra tu re v a r ia t i o n d a ta o f good p r e c i s i o n fro m w hich th e I n ­ stru m en t may be d e s ig n e d , and some r e l a t e d p r o b le m s.

P art I I

d e a l s w ith th e d e s ig n o f t h e in str u m e n t capable o f g iv in g c o n ­ c e n t r a t io n i n terms o f n o r m a lity by d i r e c t r e a d in g , and w it h no c o n s ta n t tem p era tu re b a th b e in g n e c e s s a r y .

P art I A. E xp erim en tal 1.

A pparatus and C h em ica ls To o b ta in t h e n e e d e d data, i t

was n e c e s s a r y to b u i l d

a con d u ctan ce b r id g e c a p a b le o f y i e l d i n g r e s u l t s o f b e t t e r th an a n a ly tic a l p r e c is io n .

A b r id g e was b u i l t f o l lo w in g th e d e s i g n

a s g iv en and d is c u s s e d by Jon as and J o se p h s ( 5 ) .

Some s i m p l i ­

f i c a t i o n was made s i n c e i t was d eterm in ed p r e v io u s ly th a t t h i s b r id g e n e e d n o t cover, th e extrem e r a n g e s of m easurem ent o f th e J o n e s and Josep h s b r i d g e , n o r was t h e r e any d e s i r e to meet th e

e x t r a o r d i n a r il y h ig h r eq u ire m en ts o f p r e c is io n im posed by t h e i r pu rp ose o f a b s o lu t e con d u ctan ce m easu rem en ts. The tw o r a t io arms o f th e b r id g e were made o f two I n t e r n a t i o n a l R e s i s t o r Company 1000 ohm p r e c is io n r e s i s t o r s o f 1$ t o le r a n c e s e l e c t e d fro m a b a tc h s o t h a t th e y m atched each o th e r to w it h in 0 .1 $ .

T hese are n o n - I n d u c t iv e ly wound r e s i s t o r s .

A s e t o f f iv e d eca d e r e s i s t a n c e s , T ype 5 1 0 , m an u factu red by th e G en eral Radio Company, were u sed f o r b r id g e . ohms.

th e v a r ia b le arm o f the

These g a v e a ran ge o f r e a d in g s from 0 .1 ohm to 1 1 ,1 1 1 The th o u s a n d s , h u n d red s, and t e n s d ecad es were i n t e r ­

c a l i b r a t e d a g a i n s t a 1000 ohm G en era l Radio Company Standard R e s is t a n c e Type 133G, S e r i a l # 8 8 3 , b y means o f a Type K p oten ­ tio m e t e r m an u factu red b y Leeds and N o rth ru p . i s d e s c r ib e d i n a number o f sta n d a r d t e x t s

The m ethod used

(6 ) .

The nominal

v a lu e s o f the lo w e s t d eca d es were u s e d s in c e ev en d e v ia t io n s t e n tim es g r e a t e r th a n th e maximum s p e c i f i e d by th e m anu factu rer would n o t a f f e c t th e r e s u l t s to w i t h i n th e r e q u ir e d t o l e r a n c e s . The c a l i b r a t i o n w as r e p e a te d on f o u r d i f f e r e n t days and the average v a lu e s u s e d .

An average p r e c i s i o n o f ab ou t one p art i n

tw enty th ou san d was a t t a in e d f o r th e h ig h e r v a l u e s . g iv e s t h e r e s u l t s o f th e c a l i b r a t i o n .

T able I

S in c e th e c a li b r a t i o n was

made b y means o f d i r e c t c u r r e n t a f i n a l check was made when th e b rid g e was a sse m b le d by "m easuring1* t h e r e s i s t a n c e o f th e S ta n ­ dard w it h the b r id g e u s in g a l t e r n a t i n g c u r r e n t.

T h is se rv ed to

check t h e b r id g e and the c a l i b r a t i o n a t the same tim e .

The

v a lu e s o b ta in e d w ere 1 0 0 0 .0 2 and 1 0 0 0 .0 7 ohms on two se p a r a te o c c a s io n s •

The b r id g e b a la n c e I n d ic a to r u s e d was one d e s c r ib e d byM u lle r , Garman and Droz ( 7 ) m o d ifie d o n ly s l i g h t l y to g a in s e n ­ s itiv ity .

When t h i s was d o n e , i t was p o s s i b l e , by means o f th e

b a la n c e i n d i c a t o r , to e s t im a t e to f h u n d re d th s o f an ohm f o r v a lu e s o f m easured r e s i s t a n c e l e s s th an 4 0 0 0 ohms.

For th e c o n ­

d u c t i v i t y m easurem ents, a Washburn ty p e c e l l was used w ith a c e l l c o n s t a n t o f about 3,7.

The e l e c t r o d e s w ere p la in u n p l a t i n ­

iz e d p la tin u m a p p r o x im a te ly one and one h a l f In ch es i n d ia m e te r . The s o u r c e of a l t e r n a t i n g cu r re n t was a Terman o s c i l l a t o r a d ­ ju ste d t o g iv e a pure s i n e wave as d e te r m in e d a g a in s t a J a ck so n audio o s c i l l a t o r Model # 6 5 5 by means o f th e L is s a jo u s p a t te r n on an o s c i l l o s c o p e .

I t w as c o n s t r u c te d to g i v e two p o s s ib le

f r e q u e n c ie s , one c lo s e t o 1000 and th e o t h e r c lo s e to 500 c y c l e s . I t was c o m p le te ly s h ie ld e d i n an I r o n b ox and p la ced a t a d i s ­ tance o f about 12 f e e t fr o m the c o n d u c t i v i t y b r id g e .

I t s o u tp u t

v o lt a g e was v a r ia b le a t w i l l . A c o n s t a n t tem p eratu re b a th was u s e d , r e g u la te d to to ,0 0 4 °C a t tem p er a tu r es f u r t h e s t fro m room tem p era tu re.

The

e x c u r s io n s of b a t h tem p eratu re were ch eck ed b y means o f a Beckmann therm om eter and a record o f th e v a r i a t i o n s kept w it h each c o n d u c t i v i t y m easurem ent.

The a c t u a l b a t h tem perature was

m easured by means o f a t o t a l im m ersion therm om eter g rad u ated from - 5 ° to 5 0 . 5 ° c .

The therm om eter was c e r t i f i e d by th e B ureau

of s ta n d a r d s i n 1 9 3 1 , C e r t i f i c a t e # 5 6 2 8 3 .

I t s c a lib r a t io n was

checked a t the tim e of t h e s e ex p erim en ts b o t h a t the i c e p o in t and t h e t r a n s i t i o n tem p eratu re o f t h e s y s te m sodium s u l f a t e d e c a h y d r a te-so d iu m s u l f a t e anhydrous (8 ) .

The read in gs a t t h e s e

check p o in ts a g r e e d p e r f e c t l y w it h the Bureau o f Standards C e r tific a te v a lu e s . For th e n eeds o f t h is w ork, I t was d e c id e d t h a t mea­ su rem en ts a t f i v e c o n c e n tr a tio n s and f i v e

tem p eratu res i n th e

narrow range o f a n a l y t i c a l i n t e r e s t w ould g iv e s u f f i c i e n t i n ­ in fo r m a tio n t o determ in e th e v a r ia t io n o f con d u ctan ce w ith both c o n c e n tr a tio n and te m p e r a tu r e . The f i r s t grou p s o f m easurem ents were made on p o t a s ­ sium c h lo r id e and p o ta s s iu m d ich ro m a te.

For t h i s purpose the

b e s t grad e o f r e a g e n ts o b t a in a b le was u s e d .

P o ta ssiu m c h l o r i d e ,

a n a l y t i c a l r e a g e n t g r a d e , made b y Merck, and Bureaa o f S ta n d a rd s p o ta ssiu m d ich ro m a te were u s e d .

The s o l u t i o n s w e r e made up by

w e ig h t c o n v e r te d to w e ig h t i n v a c u o , as d e s c r ib e d in T read w ell and H a l l ' s A n a l y t i c a l C h em istry ( 9 ) .

S in c e the m easurem ents

were p r im a r ily in te n d e d f o r g e n e r a l a n a l y t i c a l p u r p o s e s , th e r e a g e n t s were u se d d i r e c t l y from the f r e s h l y o p en ed b o t t l e s w ith o u t f u r t h e r p u r i f i c a t i o n .

However, a s a p a r t i a l. ch eck on

the r e l i a b i l i t y o f the m a t e r i a l, a m o istu r e d e te r m in a tio n was made o n the p o ta s s iu m c h lo r id e s e v e r a l w eek s f o l lo w in g t h e open­ in g o f the b o t t l e .

I t was found t o h a v e , a t t h a t tim e, l e s s

than on e p a r t I n fo u r th o u sa n d o f m o is tu r e .

Owen and Sw eeton

(4) fo u n d t h a t a n a l y t i c a l r e a g e n t grade h y d r o c h lo r ic a c id gave r e s u l t s th a t c h e c k e d th e m ost p r e c i s e c o n d u c t i v i t y measurements fo r t h a t c h e m ic a l m ost a d m ir a b ly . The w e ig h ts u s e d I n th e making o f the s o l u t i o n s were c a li b r a t e d a g a i n s t a Bureau o f sta n d a r d s c e r t i f i e d w eight t e s t "TW60016 a c c o r d in g to th e m ethods o u t l i n e d by R ic h a r d s ( 1 0 ) . F r e s h ly p rep ared e q u ilib r iu m w a te r w ith a s p e c i f i c con d u ctan ce o f

( 1 .4

k

0 . 2 ) x 10“6 r e c i p r o c a l ohms was u sed i n

m aking up th e s o l u t i o n s .

I t was made b y a d i s t i l l a t i o n o f a

d i l u t e a l k a l i n e permanganate s o l u t i o n , o n ly th e m id d le t h i r d of th e c o n d e n sa te b ein g u s e d .

The s o l u t i o n s were k e p t in w e l l

c le a n e d and ste a m ed ground g la s s s to p p e r e d p yrex f l a s k s .

The

n o r m a lity o f t h e p o ta ssiu m d ich rom ate s o l u t i o n was c a l c u l a t e d f o r o x id a t io n - r e d u c t io n u s e . 2.

Method o f M easurement The m easurem ents were made i n th e f o llo w in g m ann er.

A tem p eratu re w as s e t i n t o

the c o n s t a n t tem p era tu re b a th .

The

c o n d u c t iv it y c e l l was r i n s e d th r e e tim es and th e n f i l l e d w i t h th e s o l u t i o n o n which t h e m easurem ent was t o be m ade. was a llo w e d t o

come to th e bath te m p e r a tu r e .

The c e l l

The r e s i s t a n c e

was m easured an d then rem easured u n t i l th e r e was no ch an ge w ith t im e , I n d i c a t i n g c o n sta n c y o f te m p e r a tu r e .

The m easurem ent was

r e p e a t e d a t b o t h a v a ila b le f r e q u e n c i e s , ch eck r e s u l t s a c t i n g as a c h e c k on t h e in s tr u m e n t. A c t u a l l y , f o r e a c h f i n a l m easurem ent o b ta in e d , tw o s e p a r a t e m easurem ents w ere u sed , one w ith th e r a t i o arms i n p o s i t i o n , th e seco n d w ith th e r a t i o arms r e v e r s e d .

one

By t h i s

means one can e lim in a t e t h e need f o r two e x a c t l y e q u a l r a t i o arms i n the b r i d g e .

From th e b r id g e fo r m u la , th e tr u e r e s i s t a n c e

o f th e e l e c t r o l y t e in t h e c e l l i s g iv e n b y th e sq u are r o o t o f th e p rod u ct o f th e i n d iv i d u a l v a lu e s o b t a in e d .

S in c e the tw o

s e p a r a t e v a lu e s o b ta in ed w ere alw a y s q u ite c lo s e t o g e t h e r , I n ­ s t e a d o f ta k in g th e sq u a r e r o o t o f t h e p r o d u c t, an average o f th e two m easurem ents was ta k e n . th e average i n s t e a d of t h e

The e r r o r in tr o d u c e d by t a k in g

square r o o t was f a r l e s s than o n e

p a r t i n one h u n d red th o u sa n d .

At th e same tim e , the s p e c i f i c g r a v it y o f th e s o l u t i o n was ta k e n .

With t h i s in fo r m a tio n and the w e ig h t c o m p o sitio n o f

the s o l u t i o n , th e a c t u a l n o r m a lity o f the s o l u t i o n a t th e tem p er­ a tu r e o f th e "bath c o u ld be c a l c u l a t e d .

The m eth od was t o take

the s p e c i f i c g r a v it y o f th e s o l u t i o n and m u lt ip ly i t b y 1000 tim es th e w e ig h t o f one m i l l i l i t e r o f water a t t h a t te m p e r a tu r e . T h is w e ig h t o f one l i t e r was m u l t i p l i e d by the w e ig h t p e r cen t o f s o l u t e d eterm in ed from th e w e ig h t c o m p o sitio n of th e s o l u t i o n when made u p .

The n e t w eig h t o f s o l u t e was d i v i d e d b y th e e q u i­

v a le n t w e ig h t o f th e s o l u t e to g i v e th e n o r m a lity of th e s o l u t i o n a t th e tem p eratu re o f th e con d u cta n ce m easurem ent. At th e same tim e a r e c o r d o f q u adrature b a la n c e and Wagner ground s e t t i n g was kept f o r ea ch m easurem ent. T h is w hole p r o c e s s o f measurement o f co n d u cta n ce was r e p e a te d a t each o f th e fiv e - t e m p e r a t u r e s b e tw e e n 16° and 32° C f o r e a c h o f th e f i v e s o l u t i o n s .

B* 1,

R e s u lt s and D is c u s s io n

C o n d u c tiv ity -N o r m a lity E q u a tio n The f i r s t t h in g sou gh t was a r e l a t i o n b etw een norm al­

i t y and c o n d u cta n ce or r e s i s t a n c e , th e d e s ir e d in s tr u m e n t.

one that c o u l d be b u i l t in t o

By means o f a large s c a l e p l o t o f

n o r m a lity a g a in s t con d u ctan ce i t was se en that a s t r a i g h t lin e r e l a t i o n was c l o s e l y ap p roxim ated o v e r the rang© o f c o n c e n tr a t io n u sed .

B ased on t h i s , t h e method o f l e a s t s q u a r e s (11) was ap­

p l i e d to th e n o r m a l i t i e s , c a l c u l a t e d as above, v e r s u s th e r e c ip r o c a l o f th e c o r r e sp o n d in g m easured r e s i s t a n c e s .

From

t h e s e th e w e l l known s t r a i g h t l i n e r e l a t i o n of c o n d u c ta n c e

v e rsu s n o r m a lity was w e l l e s t a b l i s h e d fo r t h e whole r a n g e o f c o n c e n tr a tio n a n d at e a c h o f the te m p e r a tu r e s . T a b le s I I and I I I g iv e th e d a ta f o r p otassiu m c h lo r id e and p o ta s s iu m d ic h r o m a te .

For e a c h tem p era tu re th e a c t u a l nor­

m a lity and r e s i s t a n c e m easurem ent i s g iv e n . s u l t i n g from t h e

The e q u a tio n s r e ­

l e a s t sq u a r e s m ethod and t h e v a lu e s c a l c u l a t e d

from t h e e q u a tio n s are g iv e n to show agreem ent between e q u a t io n s and d a t a .

On t h e a v e r a g e , fo r a l l th e d a t a , th e v a lu e s c a l c u l a t e d

from t h e e q u a tio n s a g r ee w ith in 0 . 01$ fo r p o ta s siu m c h l o r i d e and t o

s l i g h t l y b e t t e r th a n 0 . 02$ f o r p o ta s siu m d ic h r o m a te .

w ill b e shown i n

it

Part I I th a t t h i s s t r a i g h t l i n e r e l a t i o n b e ­

tween c o n d u c ta n c e and n o r m a lity can be b u i l t In to the c o n d u c t i­ v it y b r id g e t o g i v e a r a t h e r s im p le d i r e c t r e a d in g in te r m s o f n o r m a lity , 2.

T em perature V a r ia tio n o f E l e c t r o l y t e R e s is t a n c e . These e q u a tio n s were u s e d to o b t a in th e tem p era tu re

c o e f f i c i e n t o f c o n d u c ta n c e .

From them th e r e s i s t a n c e o f

s o lu ­

tio n s o f rounded n o r m a lity v a lu e s a t each o f th e tem p er a tu r es was o b t a in e d .

The f i r s t th in g so u g h t was a d e te r m in a tio n a s t o

w hether the tem p er a tu r e c o e f f i c i e n t o f con d u cta n ce fo r s o l u t i o n s , alw ays a t the sam e n o r m a lity , rem ain ed c o n s t a n t over th e w hole c o n c e n tr a tio n r a n g e . The r a t i o o f t h e r e s i s t a n c e o f e a c h s o lu t io n a t ea ch tem p eratu re to t h e r e s i s t a n c e o f a s o l u t i o n o f e x a c tly t h e same n o r m a lity at one o f the te m p e r a tu r e s , ta k en a s a r e f e r e n c e , was c a lc u l a t e d f o r e a c h e l e c t r o l y t e .

These r a t i o s showed t h a t over

the e n t i r e c o n c e n t r a t io n range o f i n t e r e s t ,

th e tem p eratu re

c o e f f i c i e n t rem ain s v i r t u a l l y c o n s t a n t .

T h is holds f o r b o th

e le c tr o ly te s . T a b les IV and V g i v e th e r e s u l t s i n

a form w h ic h most

d i r e c t l y r e v e a ls t h i s f a c t f o r th e tw o su b s ta n c e s used s o f a r . The f i r s t colum ns g i v e the n o r m a lit y o f the s o l u t i o n s , w h ic h i s th e same fo r e a ch te m p e r a tu r e .

The rem aining columns g i v e

r a t i o s o f th e r e s i s t a n c e s o f th e s o l u t i o n s a t to th e

r e s i s t a n c e s o f th e s o l u t i o n s

the

tem perature t ° c

o f the sam e n o r m a lity a t

tem perature t g c , c l o s e to th e c e n te r o f the tem p erature i n t e r v a l . W hile t h e r e i s a s m a ll d r i f t e f f i c i e n t w ith c o n c e n tr a tio n i n d i c a t e d

in th e tem perature co­ by th e above d a t a , t h i s

d r i f t a t i t s maximum turns o u t to b e l e s s th a n 0,025 % fr o m the mean v a lu e f o r t h e e n t i r e r a n g e .

The fa c t t h a t t h is te m p er a tu r e

c o e f f i c i e n t i s v i r t u a l l y a c o n s t a n t over the w h ole range o f con­ c e n t r a t io n a llo w s f o r a r a th e r u n co m p lic a ted sy stem o f tem p er a ­ tu re co m p en sa tio n . S in ce i n th e cou rse o f d e s ig n in g t h e tem p eratu re com­ p e n s a tio n n etw o rk , a com p arison o f t h e tem p erature v a r i a t i o n o f e l e c t r o l y t i c r e s i s t a n c e would have t o be made w ith th a t o f the th e r m is to r r e s i s t a n c e , and s i n c e th e tem p eratu re v a r i a t i o n o f th e r m isto r r e s i s t a n c e s can be r e p r e s e n te d w i t h good ap p roxim a­ t i o n by an e x p o n e n t ia l e q u a tio n (2 ) ,

i t was th o u g h t a d v is a b le

to s e e w h eth er an e x p o n e n t ia l co u ld e x p r e ss t h e v a r ia t io n o f e l e c t r o l y t i c r e s i s t a n c e w ith te m p e r a tu r e .

An eq u ation o f

the

form r T = R0e* + ^ / T was so u g h t,

ftp i s

........................... *........................... (1)

th e r e s is t a n c e o f a s o l u t i o n o f known n o r m a lity

a t tem perature T°A; RQ i s the r e s i s t a n c e of a s o lu tio n o f

the

same n o r m a lity a t tem p eratu re T°A , a r e f e r e n c e tem p eratu re; ek

a n d # are c o n s t a n t s d e te r m in e d fro m the d a t a by t h e l e a s t

sq u a r es m eth od .

I t was fo u n d t h a t t h is e x p r e s s io n h ad an in ­

s u f f i c i e n t number of c o n s t a n t s to e x p r e ss th e d a ta w it h good p r e c is io n .

A t h i r d c o n s t a n t was added to s e e w h eth er an ade­

qu ate e x p r e s s io n of the d a t a w ould r e s u l t . An e q u a tio n o f t h e form Rrp s

R0 ( l + A e B /T )/c .................................... (2)

was u s e d . S in c e th e l e a s t sq u a r e s method c o u ld n o t b e a p p lied d i r e c t l y b e c a u s e o f C i n t h e e q u a t io n , a r b it r a r y v a lu e s o f were s u b s t i t u t e d and th e n

c

the l e a s t squares m ethod a p p lie d .

In

p r a c t i c e , th e l e a s t sq u a r e s m ethod was a p p lie d to th e eq u a tio n i n th e form Log (Rt /R q - k ) = a 4 b / T .......................... (3) S u c c e s s iv e a r b i t r a r y v a lu e s of k w ere u se d and the l e a s t sq u ares c a l c u l a t i o n s made.

For each v a lu e o f k , the sum

o f th e d e v i a t i o n s , of t h e v a lu e s c a lc u la t e d from t h e e q u a tio n , from the e x p e r im e n ta l v a lu e s was o b ta in e d .

A p l o t o f the d e v i­

a t i o n sums v e r s u s the v a l u e s of k was made f o r b o th p o ta ssiu m c h lo r id e and p o ta ssiu m d ic h r o m a te .

The v a lu e s o f k g i v in g the

minimum d e v i a t i o n sum i n e a c h c a s e was read o f f th e graph and ch o sen f o r th e e q u a tio n .

F ig u r e s I and I I g i v e t h e s e p lo t s f o r

p o ta ssiu m c h l o r i d e and p o ta s s iu m d ic h r o m a te.

A c t u a l l y , as can

be s e e n from t h e graphs, a range o f v a lu e s o f k w ith corresp on d ­ in g v a lu e s f o r

th e c o n s t a n t s a and b gave e q u a l l y g o o d r e s u l t s .

The e q u a tio n s o b t a in e d w ere*

f o r p o ta s siu m c h lo r id e % = R0 ( l 4 0 .0 0 0 7 5 2 6 6 8 2 4 1 5 .1 0 / T ) / 4 .0 1 2 7 ............... ( 4 ) fo r p o ta s s iu m d ich rom ate RT = R0 ( l 4 0 . 0 0 0 6 6 3 4 6 a 2 4 2 8 . 1 3 / T ) / 3#7 76 7 ................ ( 5 )

The r e f e r e n c e tem p erature f o r t h e s e e q u a tio n s was 2 9 1 .1 6 ° A . The a v e r a g e d e v ia t io n s o f th e v a lu e s of Rrp/R0 c a lc u ­ la t e d from th e s e e q u a tio n s a g a in s t th e a c tu a l v a lu e s u s e d i n th e l a s t sq u a r e s c a l c u l a t i o n s was l e s s

th an ,0 0 3 $ fo r 0 . 1 Normal

p o ta ssiu m c h l o r i d e , w ith no d e v i a t i o n la r g e r than 0 . 0 1 $ .

For

p o ta ssiu m d ich ro m a te the av era g e d e v ia t io n was 0 , 01$ w it h non© g r e a t e r th a n 0 ,0 2 $ f o r th e 0 .1 Norm al s o l u t i o n .

For b o th e l e c ­

t r o l y t e s o v e r the co m p lete tem p er a tu r e and c o n c e n t r a t io n r a n g e no d e v i a t i o n was g r e a t e r th a n 0 . 02$ . 3.

T em perature C o e f f i c i e n t o f C onductance I t has b e e n s a id th a t s i n c e th e co n d u cta n ce o f an i o n

depends on i t s r a t e o f movement, i t

seems r e a s o n a b le t o tr e a t

co n d u ctan ce i n a manner a n a lo g o u s t o th a t em ployed f o r oth er p r o c e s s e s ta k in g p la c e a t a d e f i n i t e r a te w h ich i n c r e a s e s w ith tem p eratu re

(1 2 ).

I f one th e n a p p l i e s the A rrh en iu s t y p e o f

e q u a tio n to t h i s p r o c e s s one o b t a in s fo r L, th e s p e c i f i c con d u c­ ta n ce , L a Ae-E/RT where A i s

..............................................................( 6 )

th e r a t e c o n s t a n t , E th e a c t i v a t i o n en erg y o f the

p r o c e s s w h ich d e te r m in e s t h e r a te o f movement o f the i o n s , R i s the m olar g a s c o n s t a n t and T i s th e a b s o lu te te m p e r a tu r e .

If

one d i f f e r e n t i a t e s t h i s e q u a tio n w i t h r e s p e c t to te m p e r a tu r e , one o b t a in s

This seem s to be t h e b a s is f o r the o c c a s io n a l l i s t i n g i n

the

l i t e r a t u r e o f some tem p eratu re c o e f f i c i e n t s o f s p e c i f i c conduc­ tiv it y as

(l/L )d l/d t.

Bremmer and Thompson (3 ) a p p lie d the v i r i a l

eq u ation t o t h e ir tem p eratu re d ata fo r th e con d u ctan ce o f a 0 .1 Demal s o l u t i o n , c a r r y in g th e e q u a tio n t o

the t h ir d d e g r e e .

In

a la t e r p a p e r Bremmer (13) d i f f e r e n t i a t e d th e v i r i a l e q u a tio n and rearran ged i t to g i v e an e x p r e s s io n f o r

( l / L ) dL/dT as a fu n c tio n

o f te m p e r a tu r e . ^Because o f such c o n s i d e r a t i o n s , a new l e a s t sq u a r e s c a l c u l a t i o n , b a s e d on the m ethods d e s c r ib e d a b o v e , was a tte m p te d , combining s p e c i f i c

c o n d u c t iv it y w ith tem p era tu re in an exponen­

t i a l form o f e q u a t io n .

I t w as hoped t h a t some s im ila r r e s u l t

g iv in g a s good agreem ent w it h th e d a ta m ig h t be o b ta in e d as w ith r e s is ta n c e .

F u r t h e r , i t o f f e r e d the p o s s i b i l i t y o f y i e l d i n g a

sim ple r e l a t i o n f o r tem p eratu re' c o e f f i c i e n t as a f u n c t i o n of tem p er a tu r e, nam ely L L ) dL -_ L (L-A) HT “ T2 ......................................................... (8 ) I t was f o u n d , h o w e v e r , th a t u s i n g th e same number of c o n sta n ts a s p r e v io u s ly in e q u a tio n ( 2 ) , agreem ent w ith e x p e r i­ m ental d a t a was p o o r e r by a f a c t o r o f a t l e a s t th r e e tim e s th a t obtain ed w it h the r e s i s t a n c e e q u a tio n . I f one d o e s take e q u a tio n (6 ) and s u b s t i t u t e s l/R ij fo r L one o b t a i n s ,

o n rearran gem en t,

D i f f e r e n t i a t i n g and r e a r r a n g in g one o b t a in s 1

dRrp

%

dT

E =

RT2

The same p r o c e s s when a p p lie d to the a c t u a l e q u a tio n used f o r p o ta s s iu m c h lo r id e and p o ta ssiu m d ich rom ate y i e l d s |

1 j dRrp

(R ip -K )

dT"

the form

-b = T2

The f a c t o r - b /T 2 may b e c o n sid e r e d a m easure o f th e tem p eratu re c o e f f i c i e n t f o r a range o f tem p era tu res and has t h e advan tage o f good p r e c i s i o n and g r e a t s i m p l i c i t y . 4.

A C om plete E q u a tio n . Y/hen th e s im p le s t r a i g h t l i n e r e l a t i o n s betw een c o n ­

d u c ta n c e and n o r m a lity are combined w i t h the tem p eratu re e q u a ­ t i o n s on e o b t a in s a co m p lete sta te m e n t o f th e v a r i a t i o n o f s p e c i f i c r e s i s t a n c e w ith n o r m a lity and tem p era tu re w ith in a s i n g l e f a i r l y sim p le e q u a tio n f o r ea ch s u b s ta n c e .

C a lc u la t io n s

a r e s im p le and r a p id ; t h i s typ e o f e q u a tio n sh o u ld be u s e f u l as an e m p ir ic a l e x p r e s s io n o f su ch d ata f o r many d i f f e r e n t e l e c ­ tr o ly te s .

T hese e q u a tio n s a r e :

f o r p o ta s siu m c h lo r id e ^

" ■b n r O T D T O T l j j l

+

0 .0 0 0 7 5 2 6 6 e 2 4 1 5 .1 0 /T )

f o r p o ta s siu m d ich rom ate ^

" (F T ^ T O S I S I l t1 * 0 .0 0 0 6 6 3 4 6 e 2428*13/T )

T h is g i v e s f o r p o ta s siu m c h lo r id e an a v e r a g e p r e c i s i o n o f b e t t e r th a n 0 .0 2 $ w ith th r e e d e v ia t io n s out o f 25 check v a lu e s a lm o st a s la r g e as 0 .0 5 $ , v ia tio n i s

For p o ta ssiu m d ic h r o m a te , th e a verage d e ­

j u s t about 0 .0 2 5 $ w ith 2 d e v i a t io n s o u t o f 25 b e in g

a s g r e a t a s 0 .0 7 $ , a l l th e r e s t b e in g under 0 .0 5 $ .

In making

th e c a l c u l a t i o n s f o r th e s e e q u a tio n s a c e l l c o n s t a n t o f 3 7 .4 3 1 ■was u sed b a sed on th e s p e c i f i c con d u ctan ce v a lu e s l i s t e d by Jones and Bradshaw (1 4 ). 5.

Comparison w ith Other i n v e s t i g a t o r s While th e r e s u l t s s o fa r h ave i n d ic a t e d a good amount

o f s e l f c o n s i s t e n c y , some e x t e r n a l m easure o f the r e l i a b i l i t y would b e d e s i r a b l e .

The o n ly u sa b le v a lu e s i n the l i t e r a t u r e

were t h o s e fo r p o ta ssiu m c h l o r i d e ,

J o n es and Bradshaw g iv e a

fig u r e f o r the " a b s o lu te 11 s p e c i f i c c o n d u cta n ce o f p o ta ssiu m c h lo r id e a t 18°C a s 0 ,0 1 1 1 6 6 7 r e c ip r o c a l ohms f o r a s o l u t i o n made up b y d i s s o l v in g 7 .4 1 9 1 3 grams o f p o ta ssiu m c h lo r id e i n 1000 grams o f s o l u t i o n .

J o n e s and P r e n d e r g a st (15) r e p o r t an­

o th er " a b so lu te " v a lu e o f 0 .0 1 1 1 9 1 9 a t 18°C f o r a s o l u t i o n o r i g i n a l l y d e s c r ib e d by K oh lrau sch a s h a v in g 7 .4 3 3 4 4 grams o f p o ta ssiu m c h lo r id e in 1000 gram s of s o l u t i o n .

As a ch eck on ray

work I d e c id e d to c a lc u l a t e th e c e l l c o n s ta n t b a sed on th e work o f each o f th e se a u th o rs and ob serve t h e m agnitude o f the de­ v ia tio n .

In ord er to u se t h e s e s o l u t i o n s , I had to c a l c u l a t e

th e n o r m a lity o f t h e i r s o l u t i o n s .

T h is was done by 1 ) d e ter m in ­

in g the s p e c i f i c g r a v i t i e s o f s o l u t i o n s o f th e s e c o m p o sitio n s from my own d a ta , 2 ) c a l c u l a t i n g the w e ig h ts o f l i t e r s o f such s o l u t i o n s , 3) from th e w e ig h t c o m p o sitio n as g iv e n a b o v e , d e­ ter m in in g th e w e ig h t o f p o ta s s iu m c h lo r id e i n a l i t e r

o f ea ch

su ch s o l u t i o n a t 18°C , 4 ) c a lc u l a t i n g th e n o r m a lit y , 5 ) d e­ term in in g my v a lu e s o f r e s i s t a n c e fo r th e s e n o r m a l i t i e s , and f i n a l l y , 6 ) c a lc u l a t in g th e c e l l c o n s t a n t s from my v a lu e s and t h e data o f th e se a u th o rs fro m K c LR.

From th e s e c a l c u l a t i o n s

I d e te r m in e d t h a t th e Bradshaw s o l u t i o n was 0 .0 9 9 8 5 6 Normal and th e K o h lrau sch s o l u t i o n 0 ,1 0 0 0 5 0 Norm al. S in ce a t 18°C the r e l a t i o n f o r n o r m a lity v ersu s r e s i s ­ ta n c e as d eterm in ed f o r my c e l l was N ■ -.0 0 5 7 1 1 + 3 5 3 .8 6 /R a t th e Bradshaw n o r m a lity , R ■ 3 ,3 5 2 .0 ohms, and a t the K o h l­ r a u sc h n o r m a lity , R ■ 3 ,3 4 5 .9 ohm s. Bradshaw »s v a lu e i s r a u sc h s o l u t i o n i s

The c e l l c o n s ta n t b a s e d on

3 7 .4 3 1 ; t h e c e l l c o n s ta n t b a s e d on t h e K oh l­ 3 7 .4 4 7 .

Another fo rm of e x t e r n a l c h e c k is th e com p arison o f my r a t i o o f c o n d u cta n ce a t two d i f f e r e n t te m p e r a tu r e s w ith t h a t a p p e a r in g i n th e l i t e r a t u r e f o r th e same s o l u t i o n .

In th e l i t ­

e r a t u r e one f in d s th e data g i v e n i n term s of c o n d u cta n ce a t v a r io u s tem p era tu res o f a s o l u t i o n made up as 0 . 1 Normal o r 0 . 1 Demal a t 18°C .

B e ca u se the r e s u l t s o f th e p r e s e n t work a r e g iv e n

f o r s o l u t i o n s of a s p e c i f i c n o r m a lit y a t a l l te m p e r a tu r e s , I t was n e c e s s a r y to r e c a lc u l a t e som e o f th e data o v e r to th e sy s te m u sed by th e se a u th o rs. c a lc u la tio n s .

This r e q u ir e d a n o th er s e r i e s o f le n g t h y

F i r s t , taking e a c h o f my s o l u t i o n s , i t was n e c e s ­

s a r y t o t a b u la te th e c a lc u la t e d n o r m a lity of e a c h s o l u t i o n a t ea ch te m p e r a tu r e .

S econ d , r a t i o s o f th e n o r m a lit ie s of e a c h

s o l u t i o n t o i t s n o r m a lity at 2 4 .1 2 ° C w ere c a l c u l a t e d .

T h ir d ,

f o r e a c h tem p eratu re i t was fo u n d t h a t t h e r a t i o s w ere c o n s t a n t to much b e t t e r th an 0 .0 1 $ .

F o u r t h , by t h e l e a s t sq u a r e s m ethod

an e q u a t io n was d e v e lo p e d fo r t h e v a r i a t i o n o f n o r m a lity w it h tem p era tu re^

I t was found t h a t a f i r s t d egree e q u a t io n d id n o t

g iv e a d eq u a te r e s u l t s , but t h a t a se co n d degree e q u a tio n d i d .

The r e s u l t i n g e q u a tio n g i v e s the n o r m a lity o f a s o l u t i o n o f p o ta s siu m c h lo r id e a t any te m p e r a tu r e f o r a s o l u t i o n 0 ,1 Normal a t 18°C: N a 0 .1 0 0 1 6 1 where t i s

th e tem perature i n

( 5 .0 0 2 x 1 0 “7 ) t 2

d eg r ee s c e n t ig r a d e .

F i f t h , th e

n o r m a lity o f the s o l u t i o n 0 . 1 Normal a t 18°C was c a l c u l a t e d a t 20°C and 25°C . a t 25°C .

T h ese came t o be 0 .0 9 9 9 6 a t 20°C and 0 .0 9 9 8 5 at

S i x t h , fro m the r e s i s t a n c e s f o r a s o l u t i o n 0 .0 9 9 9 6

Normal a t 20°C and f o r a s o l u t i o n 0 .0 9 9 8 5 a t 25°C , t o g e t h e r w ith th e v a lu e f o r a 0 . 1 Normal s o l u t i o n a t 18°C , th e r a t i o s o f th e c o n d u c ta n c e s i n d ic a t e d in T a b le VI w ere c a lc u l a t e d . colum n g i v e s the name o f t h e p a r is o n I s made.

The f i r s t

i n v e s t i g a t o r w it h whom th e com­

The r em a in in g colum ns g iv e th e r a t i o s o f

s p e c i f i c c o n d u c ta n c e s for t h e p airs o f tem p era tu res l i s t e d i n e a c h colum n f o r a p o ta ssiu m c h lo r id e s o l u t i o n 0 .1 Normal a t 18°C •

I t i s se en t h a t the r e s u l t s o b t a in e d i n th e p r e s e n t i n ­

v e s t i g a t i o n agree w ith the m o s t r e l i a b l e v a lu e s In th e l i t e r a t u r e to a b o u t on e part i n 4000.

The v a lu e s l i s t e d f o r Bremmer and

Thompson w ere c a lc u la t e d fr o m th e e q u a t io n g iv e n i n t h e i r a r t i c l e . 6.

i n t e r n a t i o n a l c r i t i c a l T a b le s . I n making u s e o f

some d i f f i c u l t y

t h e I n t e r n a t io n a l C r i t i c a l T a b le s

a r o s e w ith t h e v a lu e s l i s t e d t h e r e .

T h is stemmed

from th e manner o f l i s t i n g t h e data w h ic h i s c o n fu s in g t o s a y th e l e a s t .

The

d a ta i s l i s t e d there I n such a manner a s to le a d

one to u n d ersta n d t h a t the c o n d u c ta n c e s g iv e n a t each l i s t e d tem p era tu re are t h o s e fo r s o l u t i o n s w h ose n o r m a lity i s g i v e n a t the h ea d o f th e t a b l e .

This means a t c o n s ta n t n o r m a lity .

It

tu r n s o u t t h a t th e v a lu e s l i s t e d are a c t u a l l y th e c o n d u c ta n c e s ,

18 .

at t h e v a r io u s te m p e r a tu r e s o f a s i n g l e s o l u t i o n made up w ith the l i s t e d n o r m a lit y a t a p a r t i c u la r tem^ r a t u r e , u s u a l l y 18°C. To i l l u s t r a t e ,

a p o ta s siu m c h lo r id e s o l u t i o n 0 .1 Normal a t 18°C

tu rn s out to b e 0 ,0 9 9 8 5 Normal a t 25°C , and t h i s I s th e a c tu a l n o r m a lity o f t h e s o l u t i o n whose c o n d u cta n ce i s

l i s t e d as th a t

of a 0 . 1 Normal s o l u t i o n a t 25°C i n th e I n t e r n a t io n a l C r i t i c a l T a b le s .

For a s o l u t i o n made up a s 0 ,1 Normal a t 25°C u s e of

the d a t a l i s t e d w i l l l e a d to an e r r o r o f as much as 0 . 2 $ . conductance l i t e r a t u r e m ust be c a r e f u l l y rea d w ith t h i s i n mind.

A ll

part I I C o n d u c tiv ity m easurem ents may b e made by m eans o f d i ­ r e c t c u r r e n t (17) or more c o n v e n t io n a lly b y means o f a l t e r n a t i n g c u r r e n t a p p lie d t o a Yi/heatstone b r id g e .

On c o n s id e r in g th e

typ e o f in s tr u m e n t to b e b u i l t , i t was d e c id e d to u s e the b a s i c W h eatston e b r id g e , and f i t

th e d e s ig n i n t o i t s p a t t e r n .

The

b r id g e tu r n s out to be a d m ira b ly s u i t e d t o th e p u r p o s e .

The

d e s ig n c e n t e r s around two main f e a t u r e s ,

tiie f i r s t b e i n g th e d i ­

r e c t r e a d in g o f n o r m a lity from r e s i s t a n c e m easu rem en ts, the se c o n d b e in g th e te m p er a tu r e com p en sation d e v ic e d o in g away w ith the c o n s t a n t tem p eratu re b a t h .

W ith t h e s e two t h i n g s , s e v e r a l

c o n c o m ita n t r eq u ire m en ts a r i s e , and, t o g e t h e r with som e p r e v i ­ o u s ly c o l l e c t e d d a ta , th e b a s i s f o r a w orking model c a n be l a i d . The d i s c u s s i o n o f the p la n n e d in str u m e n t w i l l be c o n s id e r e d under t h e s e g e n e r a l c a t e g o r i e s . A.

D ir e c t R eading o f NormaL i t y

In a W heatstone b r i d g e , assu m in g pu rely r e s i s t i v e e le m e n ts i n the b r id g e , a t b a la n c e , th e unknown r e s i s t a n c e i s g iv e n b y th e f a m ilia r fo r m u la Rjj * R l ^ 2 / ^ 3 ..............................................................( D R^ and R2 are the r e s i s t a n c e s i n th e two arms o f th e b r id g e a d ­ j a c e n t t o th e arm c o n t a in in g th e unknown r e s i s t a n c e . r e s i s t a n c e i n th e arm o p p o s it e th e unknown r e s i s t a n c e ,

R3 i s

th e

i f we

te m p o r a r ily c o n s id e r R^ and R2 c o n s t a n t , we se e th a t Rg i s an in v e r s e f u n c t io n o f the v a lu e o f R j, We now r e tu r n to

th e fo r m u la , e s t a b lis h e d p r e v i o u s l y

by th e l e a s t sq u a res m eth o d , r e l a t i n g r e s i s t a n c e and n o r m a lit y .

In T a b le s I I and I I I i t

I s g iv e n I n th e form

N - - g * f /R

........................................................... (2 )

where N i s th e n o r m a lit y , g and f

are c o n s t a n t s determ ined from

th e d a t a by th e l e a s t sq u a r es m eth o d , and R i s o f th e s o l u t i o n o f th a t n o r m a lity *

t h e r e s is t a n c e

i f we r e a r r a n g e the e q u a tio n

we may o b ta in t h e form R = f/(N + g )

.........................................................(3 )

Here we see t h a t N i s an in v e r s e f u n c t io n o f R, th e r e s i s t a n c e o f th e s o lu t io n *

S in c e i t i s t h i 3 r e s i s t a n c e

t h a t a c t u a lly w i l l

be i n th e "unknown" arm o f the b r i d g e , we se e t h a t R3 from e q u a tio n (1) a n d N from e q u a tio n

( 3 ) are b o th in v e r s e f u n c t io n s

o f th e same t h i n g , th e r e s i s t a n c e o f th e s o l u t i o n i n which we are i n t e r e s t e d .

I f , t h e r e f o r e , a p o te n tio m e te r i s used a s a

v a r ia b le r e s i s t a n c e in t h e o p p o s it e arm t o th a t o f the s o l u t i o n , the p o t e n t io m e t e r can b e u sed t o e s t a b l i s h b a la n c e in the W heatstone b r i d g e .

The p o te n tio m e t e r can be c a lib r a t e d to r e a d

in term s o f n o r m a lit y d i r e c t l y .

I f a l i n e a r p o te n tio m e te r i s

ch o sen to g iv e b a la n c e , th en the s c a l e f o r r e a d in g n o r m a lity w i l l be a l in e a r one and n eed o n ly be c a l i b r a t e d i n t h r e e p o s i t i o n s fo r good c a l i b r a t i o n . When o n e s e l e c t s a l i n e a r p o te n tio m e te r o f s u f f i c i e n t p r e c i s i o n , i t m u st m eet th e s p e c i f i c a t i o n s s e t b y ch em ical a n a l y t i c a l p r o c e d u r e , I . e . , one p a r t i n a th o u sa n d .

As a m a tte r

o f f a c t , to be s u r e o f t h i s , a b e t t e r p r e c i s i o n i s d e s i r a b l e . I f we lo o k at T a b le s I I and I I I i n

P art I , we s e e th a t the t o t a l

v a r ia t io n in r e s i s t a n c e o f s o l u t i o n s f o r th e ra n g e 0 .0 9 - 0 .1 1 Normal I s about ilO $ o f th e r e s i s t a n c e o f a 0 .1 Normal s o l u t i o n . U sin g t h i s , we n e e d have a p o te n tio m e te r t h a t c o v e r s a ran ge o f

o n ly 20$ o f th e t o t a l r e s i s t a n c e , i . e . , e st.

th e range o f our i n t e r ­

For th e r e a d in g arm o f t h e b r id g e a com b in ation o f a fix e d

r e s i s t o r p lu s the p o te n tio m e te r ca n be u s e d and t h i s

com bina­

t io n m ust g iv e th e d e s ir e d p r e c i s i o n , A f u r t h e r r e s t r i c t i o n , a lth o u g h not a r i g i d o n e , i s p la c e d on the r e s i s t a n c e in t h i s v a r ia b le arm.

A c c o r d in g to

W heatstone b r id g e t h e o r y , th e g r e a t e s t s e n s i t i v i t y i n b a la n c in g the b r id g e i s a c h ie v e d when a l l arms a r e e q u a l.

For d e v ia t io n s

from t h i s c r i t e r i o n , s e n s i t i v i t y f a l l s o f f r a p id ly , w ith t h i s , s in c e i t

in lin e

turn ed o u t t h a t fo r tem p eratu re com p en sation

the a d ja c e n t arm w o u ld have a r e s i s t a n c e

value o f a b o u t 500 ohms,

i t was d ecid ed t h a t th e r e a d in g arm s h o u ld have a r e s i s t a n c e of the same m agn itu d e.

This would be g iv e n b y a c o m b in a tio n o f a

f i x e d r e s i s t o r o f 4 0 0 ohms and a 0 - 100 ohm l i n e a r p o t e n t i o ­ m e te r . The H e lip o t Company m akes p o te n tio m e te r s w it h a l i n e ­ a r i t y o f 0 .1 $ over th e e n t ir e r a n g e o f t h e p o te n tio m e te r . sta te m e n t o f 0 . 1$ l i n e a r i t y means th a t a t any p o i n t ,

This

th e v a lu e

o f th e r e s i s t a n c e a t th a t p o in t w i l l be o f f from what I t sh ou ld b e , a s a l in e a r f u n c t io n o f s c a l e , by no more than 0 . 1$ o f th e t o t a l r e s i s t a n c e o f th e p o t e n t io m e t e r .

X f such a 0 - 1 0 0 .. ohm

p o te n tio m e te r were o b ta in e d i n c o n j u n c t io n with th e 4 0 0 ohm r e s i s t o r , then th e l i n e a r i t y o f th e n o r m a lity s c a l e w ould be good t o 1 p a rt i n 5 0 0 0 , w e ll w i t h i n the r e q u ir e m e n ts .

One added

c o n d it io n fo r w o rk a b le r e s u l t s , t h a t th e tem p eratu re c o e f f i c i e n t o f r e s i s t a n c e o f th e w ire u sed i n making up the p o t e n tio m e te r must b e lo w , made I t im p o s s ib le t io m e t e r .

to o b ta in a 0 .1 $ l i n e a r p o te n ­

The b e s t p o te n tio m e te r ob tain ed ., made o f m anganin w ire o f low tem p eratu re c o e f f i c i e n t , was o n e gu aran teed t o 0 .5 $ l i n e a r i t y , w h ich c le a r l y was not q u ite good enough.

On t e s t i n g

th e p o t e n t io m e t e r , h o w ev er, the l i n e a r i t y b a s e d on th e m id­ p o in t r e s i s t a n c e v a lu e was found t o be, e x c e p t fo r th e l a s t t h i r t i e t h o f t h e p o te n tio m e te r (w h ich can b e n e g le c te d i n t h e c o n s t r u c t io n o f th e in str u m e n t) b e t t e r th a n 0 .1 7 $ over a l l p o in ts .

When combined w it h the f i x e d r e s i s t o r o f 400 ohm s, a lso

made o f m angan in, the l i n e a r i t y o f the n o r m a lity s c a l e w i l l be g o o d , a t any p o in t to a t l e a s t on e part i n

3 0 0 0 , and p r a c t i c a l l y

everyw here g o o d t o about one p a r t i n 6000.

The t e s t o f l i n e ­

a r i t y was r e p e a te d on two s e p a r a te days and a l l m easurem ents made f o r th e same s e t t i n g s a greed t o one t e n t h of an ohm o r b e t t e r , a l l a lo n g th e p o t e n t io m e t e r .

A s e t o f t y p i c a l m easu re­

m ents and v a lu e s needed f o r p e r f e c t l i n e a r i t y i s g iv e n i n T ab le V I I .

A c t u a l l y , m easurem ents were made at e v e r y f i v e d i ­

v i s i o n s ou t o f th e t o t a l o f 300 s c a l e d i v i s i o n s .

At random,

some v a lu e s a t e a c h p o in t on the s c a l e b e tw e e n some o f t h o s e ta k en above w ere a ls o u s e d f o r a l i n e a r i t y c h e c k .

T h ese , t o o ,

f e l l I n to th e g e n e r a l p a t t e r n o f t h e v a lu e s i n d ic a t e d in T able V I I . B. 1.

Tem perature C om p en sation

D evelop m ent o f the N etw ork. The s e v e r e s t l i m i t a t i o n on the w id e r u se o f c o n d u c t i­

v i t y i n a n a l y t i c a l c h e m is tr y has b e e n the f a c t th a t good tem p era­ tu r e r e g u la t i o n was n e e d e d .

The h e a r t o f t h e in stru m en t t o be

b u i l t i s t h e r e f o r e the tem p era tu re com p en sation d e v ic e .

S in c e

th e tem p eratu re c o e f f i c i e n t of r e s i s t a n c e o f th e th e r m is to r i s a b o u t tw ic e t h a t o f e l e c t r o l y t i c r e s i s t a n c e , a co m b in a tio n o f the th e r m is to r w it h r e s is t a n c e o f low tem p era tu re c o e f f i c i e n t i n some way m ight b e u s e d t o match t h a t o f t h e e l e c t r o l y t i c r e s is ta n c e . The f i r s t a tte m p t at m atch in g was made w it h a combina­ t i o n of a th e r m is to r and a r e s i s t o r i n s e r i e s , w ith p o o r r e s u l t s . The se co n d a ttem p t was w ith a th e r m is to r In co m b in a tio n w ith a p a r a l l e l r e s i s t o r , and t h i s too p r o v e d in a d e q u a te .

The n e x t

co m b in a tio n o f a r e s i s t o r and th e r m is to r i n s e r i e s , w i t h a se co n d r e s i s t o r i n p a r a l l e l w ith t h i s to be g o o d .

s e r i e s c o m b in a tio n , proved

T h is c o n c lu s io n was b a s e d on t h e f o llo w in g s

L et th e r e s i s t a n c e of the t h e r m is t o r be d e s ig n a te d by T , th e v a lu e o f t h e r e s is t a n c e i n

s e r i e s w it h th e th e r m is to r

by S , and the v a lu e o f th e r e s i s t a n c e in p a r a l l e l w it h th e two , b y P.

Then

th e r e s i s t a n c e o f the w h o le n etw o rk i s g iv e n by r = P (S 4 T ) / ( P 4 S 4 T)

I f T]_

i s the r e s i s t a n c e o f the th e r m is to r a t t £ c and T0 th e r e ­

s is ta n c e

o f th e t h e r m is t o r a t t°c t h e n the r a t i o o f th e r e s i s ­

ta n c e o f the n etw ork a t t°C to t°c I s g iv e n b y P(S 4 TX) / ( P 4 S 4 T].) (S 4 T ^ P 4 S 4 T0 ) P(S 4 T0 ) / ( P 4 S 4 T0 ) " (S +“ t 0 ) ( P 4 S 4 Tx ) At th e same tim e , th e r e s i s t a n c e o f a n e l e c t r o l y t e i n s o l u t i o n may be d e s ig n a te d by R^, f o r the r e s i s t a n c e a t tem p eratu re t°C and R0 f o r the r e s i s t a n c e o f a s o l u t i o n o f t h e same c o n c e n tr a ­ t i o n a t tem p eratu re t ° C . e le c tr o ly te

The r a tio o f the r e s i s t a n c e o f the

a t t j c t o t h a t a t t°C w i l l be g i v e n by R^j/Rq. R^

may b e c o n s id e r e d as e q u a l

t o some f a c t o r R^ tim es RQ;

r^

- R-jR0 .

S in c e we want th e t h e r m is t o r and i t s

network to m atch

th e change

in r e s i s t a n c e o f th e e l e c t r o l y t e , we can e q u a te t h e s e

two r a t i o s

as a

s ta te m e n t o f th e p ro b lem ,

RlHp _ (S 4 Tx)(P 4 S 4 T0 ) R0 (S 4 T0 )(P 4 S 4 TX) ...................... (4) S o lv in g t l i i s e q u a tio n fo r P, th e v a lu e o f p a r a l l e l r e s i s t a n c e we have „

'

(Rj. - 1 ) ( S + TX)(S t T0 ) (S t - K i ( S t T0 J .............................. ( 5 )

T ak in g an oth er tem p era tu re tgC and r e p e a t in g t h e above p r o c e s s we have

B _ (R2 - l ) ( s 4 T2 )(s 4 T0 ) = (s > Tg) -_R2 (S 4 T0 ) E q u a tin g e q u a tio n s

(6)

(5 ) and (6 ) we g e t

(Rg - 1 ) (S 4 Tg) ^ (RX - 1 ) ( S 4 TX) (S 4 Tg)-Rg(S-4 T0 )‘ (S 4 T ^ - R ^ S 4 T0 )

............................(7 )

S o lv in g t h i s e q u a t io n , f o r S i n term s o f the o t h e r q u a n t i t i e s we g e t

4

s _ T0£ T ;iR g (R i-l) - T gR ^ (R g -l)

TgRgCRx-l) - TxRxCRg-l)

T iT g (R 2 -R l3

4

T 0 (Rb-Ri) . . . . ( 8 )

I f f o r th e t h e r m is to r we c o n s id e r T^, th e r e s i s t a n c e o f th e t h e r m is to r a t t | ,

a s composed o f a f a c t o r

tim e s T0 , th e r e ­

s i s t a n c e o f th e th e r m is t o r a t t £ c , t h e n Tx r % T 0

and

T2 = AgT0

S u b s t it u t in g th e s e tw o fo rm u la e i n e q u a tio n ( 8 ) we o b ta in

_ T0 [AlR2(Rl-l) - A2R1 (H2 - 1 ) + A^Ag (R2-R]_ jj S ' AgRglR].-!)"- AjR^Rg-1) t (Rg-Rj)

■

and r e a r r a n g in g we g et

T jT

■*■0

2.

-R]Rg(Ag-A3_) j R gA j^ A g-l) t RjAgCl-A-^) “ HnRgtAg-Ai)" - R g fA g -i) - R1 (i-A ^ )

(9 )

C h a r a c t e r i s t i c s o f t h e t h e r m is t o r In o r d e r to use t h i s fo r m u la , i t i s ,

o f c o u r s e , nec­

e s s a r y t o d eterm in e the c h a r a c t e r i s t i c s of t h e th e r m is to r to he used f o r th e com p en sation n etw o rk .

To do t h i s , the r e s i s t a n c e

o f th e t h e r m is t o r , Type 25A s e l e c t e d as b e s t f o r the p u r p o se , was m easured by means o f t h e b r id g e p r e v io u s l y d e s c r ib e d , at a number o f d i f f e r e n t tem p era tu res i n b a th .

th e c o n s t a n t tem perature

I t s c h a r a c t e r i s t i c s were d eterm in ed w i t h the th e r m is to r

p o s i t i o n e d in th e c o n d u c t iv it y c e l l t o be u s e d f o r the i n s t r u ­ m ent, and c o a te d w ith the m a t e r ia l i n s u l a t i n g

i t e le c tr ic a lly

from th e s o l u t i o n . A fte r th e m easurem ents o f t h e r m is to r r e s i s t a n c e had been m ade, an e q u a tio n r e p r e s e n t in g i t s

c h a r a c t e r i s t i c s was ob­

ta in e d i n th e same manner a s d e s c r ib e d in P a r t I for t h e d e te r ­ m in a tio n o f th e te m p e r a tu r e -r e s i s t a n c e c h a r a c t e r i s t i c s o f the e le c tr o ly te s o lu tio n s .

Some d i f f i c u l t y arose I n a c h ie v in g the

d e s ir e d r e s u l t s , and a number of e x t r a m easurem ents had t o be made t o a t t a i n t h e p r e c i s i o n e x p e c t e d .

Table VXH shows th e

agreem ent b etw een th e m easvirem ents, I n terms o f r a tio s r e f e r r e d to th e th e r m is t o r r e s i s t a n c e a t 2 4 .2 5 ° C , and t h e corresp on d in g v a lu e s c a l c u l a t e d from th e e q u a t io n . check ed to 0 ,0 3 $ . method was

The a v e r a g e agreem ent

The e q u a tio n o b ta in e d by t h e

le a s t s q u a r e s

Log (a p /lfc * 0 .0 2 )

S

- 5 .5 5 5 2 6

a

1 6 5 4 .8 0 / t

w h ere Rq, I s th e v a lu e o f th e r m is to r r e s i s t a n c e a t T°A and t h e r e s i s t a n c e o f th e th e r m is to r a t 24,25°C la tte r is 3.

( 2 9 7 .4 1 ° A ).

is The

3 3 6 .1 0 ohms,

C a lc u la t io n o f S and P The e q u a t io n determ ined f o r the t h e r m is t o r was u se d

to

c a lc u l a t e t h e r a t i o o f th e r e s i s t a n c e o f t h e th e r m isto r a t

v a r io u s te m p e r a tu r e s to i t s r e s i s t a n c e

at 1 8°C .

The r a t i o s of

r e s i s t a n c e a t th e same tem p eratu res t o the r e s i s t a n c e a t 18°C w e re a ls o c a l c u l a t e d f o r p o ta ssiu m c h lo r id e an d p o ta ssiu m d i chrornate from e q u a tio n s (4 ) and (5 ) I n Part I . T h ese w ere u sed I n e q u a tio n v a lu e s o f

s/T 0 .

( 9 ) , p a r t I I , t o g iv e

I t I s i n t e r e s t i n g to n o te t h a t the v a lu e s o f

S / t 0 c a lc u l a t e d from th e r a t i o s o f one p a ir o f tem p era tu res v a r i e d fro m t h a t c a lc u l a t e d from th e r a t i o s te m p e r a tu r e s .

o f another p a ir o f

About a dozen o f t h e s e v a lu e s w ere c a l c u l a t e d ,

a n d an a v e ra g e o f th e s e was tak en frcm th e v a l u e o f S/T 0 . T a b le IX g i v e s t h e s e v a lu e s. I f we ta k e e q u a tio n (5 ) I n P a rt I I , it

we may r e a r r a n g e

t o the form

„ . (E^-l) (S/T0 + l ) ( S / T n t A i) ' (S /T 0 4 Ax) - R i l s / i o + 1) b y fa c to r in g

1 /T 0

S / T 0 and v a lu e s o f

a fte r s u b s titu tin g A

R^

^

- T0T;i_.

The r a t i o

were s u b s t i t u t e d In t h i s eq u a tio n and f o r

e a c h tem p eratu re a v a lu e o f P/T0 was o b ta in e d #

The a v e ra g e o f

t h e s e v a lu e s w as c a lc u l a t e d .

Then u s in g

_ (P /T 0 + S/T 0 + 1 ) ( S / t 0 + AX) 1 " ( p/ * 0 + s / t 0 * A1 ) (S /T (? 4 IT o b ta in e d from e q u a tio n ( 4 ) P a r t I I , a f t e r s u b s t i t u t i n g Aq s T^Tq , and f a c t o r in g l / T 0 v a lu e s o f R^ were c a lc u l a t e d to ch eck t h e e f f e c t i v e n e s s o f the th e r m is to r netw ork as a tem per­ a tu r e c o m p e n sa to r . tju a te .

I t w as fo u n d th a t th e agreem ent was not a d e -

At one p o in t , 3 4 °C , th e d e v ia t io n r o s e to as much as 1

p a rt i n 700.

B ecause o f t h i s , and b e c a u s e some p r e v io u s p r e lim ­

in a r y c a l c u l a t i o n s had shown t h a t a b e t t e r match was a t t a i n a b l e , some a d ju stm e n t was made i n th e v a lu e o f S /T 0 .

T his a d ju stm e n t

was b a s e d on o b s e r v a t io n o f the average s / l ^ v a lu e and th e v a lu e s o f S/T 0 i n v o l v i n g 34°C i n T a b le IX.

T h is was done f o r b o th

p o ta s s iu m c h lo r id e and p o ta s s iu m d ic h r o m a te .

The v a lu e s o f

S /T 0 t a k e n , a f t e r a s m a ll amount o f t r i a l and e r r o r , w ere f o r p o ta s s iu m c h lo r id e S/T 0 = 0 .4 6 0 } f o r p o ta ssiu m dichrom ate S/T 0 = 0 .4 8 5 . The c o r r e sp o n d in g v a lu e s o f P /T 0 o b ta in e d b y c a l c u l a t i o n , as p r e v io u s ly d e s c r ib e d , w ere f o r p o ta ssiu m c h lo r id e P/T q = 3 .1 3 7 ; f o r p o ta ssiu m dichrom ate P/T q = 3 .2 0 5 . I n T ab le X we h a v e the r e s i s t a n c e . p a t i o s f o r the e l e c t r o l y t e s com pared w ith th e m atching v a lu e s o f th e th e r m isto r n e tw o r k .

We s e e th a t on th e a v e ra g e the agreem ent i s good t o about 0 .0 4 $ w ith the w o r st m atch good t o 1 p a r t i n 1 5 0 0 . Prom th e v a lu e o f the r e s i s t a n c e o f th e th e r m is to r a t 18°C which was ta k e n as th e r e f e r e n c e ,

th e v a lu e s o f the r e s i s ­

ta n c e f o r the t h e r m is to r tem p eratu re co m p en sa tio n netw ork are c a l c u l a t e d to b e , f o r p o ta ssiu m c h lo r id e S ■ 2 0 4 ,6 0 ohm s, P ■ 1 3 9 5 ,3 ohms; f o r p o ta ssiu m d ich rom ate S * 2 1 5 .7 2 ohm s, P a 1 4 2 5 .5 ohms. To b u ild th e co m p en sa tin g netw ork in t o th e b r i d g e , the r e s i s t a n c e S , i n s e r i e s w ith th e t h e r m is t o r , can be made up o f a f i x e d p r e c i s i o n r e s i s t o r o f 200 ohms and a 0 - 100 ohm, 0 . 1 $ , t e n tu r n lin e a r p o t e n t io m e t e r .

S in c e th e t o t a l r e s i s t a n c e i n

S i s abou t 210 ohms and th e l i n e a r i t y o f th e p o te n tio m e te r i s g u a r a n te e d to b e t t e r th a n th e n e a r e s t 0 .1 ohm, f o r p e r f e c t s c a l e s e t t i n g s , the t o t a l r e s i s t a n c e w i l l be good to b e t t e r th a n one p a r t I n two th o u sa n d .

B ecause o f a f a i r l y h ig h tem p eratu re

c o e f f i c i e n t f o r t h e r e s i s t a n c e w ir e o f th e p o te n tio m e te r , a t ­ t e n t i o n must be p a id to how room te m p er a tu r e v a r ia t i o n m ig h t a f f e c t th e v a lu e o f S .

The f i x e d p r e c i s i o n r e s i s t o r i s made o f

m anganin Y/hich h a s a n e g l i g i b l e tem p era tu re c o e f f i c i e n t . p o te n tio m e te r h a s a c o e f f i c i e n t o f 0 .0 0 0 7 7 .

The

For a ten d e g r e e

change i n room tem p er a tu r e the v a lu e o f th e p o te n tio m e te r r e ­ s i s t a n c e w i l l change b y 0 .7 7 $ .

S in c e th e r e l a t i v e amoun-t o f

r e s i s t a n c e u sed from th e p o te n tio m e te r i n S I s j u s t about one t w e n t ie t h o f the t o t a l , th e maximum e r r o r due to t e n d egree c h a n g e s i n room tem p er a tu r e w i l l b e l e s s th a n 0 .0 4 $ .

For the p a r a l l e l r e s i s t o r

P, s p e c i f i c a t i o n s w i l l he met

by t a k in g a f ix e d p r e c i s i o n r e s i s t o r o f 1000 ohms and a 0 - 5 0 0 ohm, 0 .1 $ , l i n e a r p o t e n t io m e te r in s e r i e s .

For a p e r f e c t

s c a l e s e t t i n g the r e s i s t a n c e v a lu e w i l l be w it h in 0 .5 ohms out o f a t o t a l o f about 1400 ohm s, or g o o d to 1 p a r t I n 2500 a t i t s w o r st.

S in ce the p o t e n t io m e t e r i s made o f m angan in, room tem ­

p e r a tu r e v a r ia t io n may be n e g l e c t e d . The method u sed i n e v a lu a t in g th e m agn itu d es o f S and P g a v e no Id ea o f t h e a llo w a b le In d e p e n d en t v a r i a t i o n in t h e i r v a lu e s w h ile s t i l l m a in ta in in g s u f f i c i e n t l y good com pensation from th e a n a l y t i c a l p o in t o f v iew .

In o rd er to d eterm ine

th is ,

a s e t o f c a lc u l a t io n s were c a r r ie d out u s in g a r b it r a r y v a r i a ­ t i o n s i n th e s e t t i n g s o f th e s e r i e s and p a r a l l e l r e s i s t o r s c a l e s . T hese were a p p lie d t o th e v a lu e s o f netw ork com p en sation w h ich were p o o r e s t in t h e i r agreem ent w ith the e l e c t r o l y t e v a lu e s. Those s e l e c t e d were f o r p o ta ssiu m d ic h r o m a te . a t io n s were u sed ,

A l l p o s s i b l e v a r i­

A v a r ia t i o n o f 0 . 4 $ was t r i e d on the s e r i e s

r e s i s t o r and a t th e same tim e one o f 0 .0 7 $ on th e p a r a l l e l r e s is to r .

Table XI g i v e s th e r e s u l t s o f t h e s e c a l c u l a t i o n s .

w o r st r e s u l t o b ta in e d gave ag reem en t to 1 p a r t i n 7 0 0 .

The

I f we

assume o p era to r s c a l e s e t t i n g s to p lu s or m inus th e n e a r e s t h a lf d i v i s i o n , th e erro r I n the v a lu e o f S w i l l b e l e s s than 0 .0 2 5 $ . The same s c a le s e t t i n g e r r o r on th e p a r a l l e l r e i i s t o r w i l l g iv e an e r r o r o f l e s s th an 0 .0 2 $ . t r o u b le from t h i s a n g l e .

There s h o u ld , t h e r e f o r e , be no

C ase 5 , T a b le X I, i l l u s t r a t e s t h i s .

C oncom itant problem s 1,

Power C h a r a c t e r is t ic s o f th e T h erm isto r The th e r m is to r r e s i s t a n c e I s a f u n c t i o n o f the te m ­

p e r a tu r e o f i t s su r r o u n d in g s o n ly when the r a t e w ith w h ich the I 2R e n erg y g e n e r a t e d in t h e t h e r m is t o r i s m atch ed by the r a t e o f d i s s i p a t i o n to i t s

su r r o u n d in g s.

An e q u ilib r iu m s t a t e I s

a t­

t a i n e d w h ich i n v o l v e s the t h e r m i s t o r , the h e a t g en e ra ted i n i t and th e d i f f e r e n c e i n tem p eratu re b etw een th e th e r m isto r a n d i t s s u r r o u n d in g s .

T h is s ta te o f e q u ilib r iu m depend s on the c u r r e n t

th ro u g h th e th e r m is t o r and th e tem p erature o f th e s o l u t i o n in th is ca se.

W hile making m easu rem en ts of th e th e r m is to r c h a r a c ­

t e r i s t i c s , a r e c o r d of th e v a r i a t i o n o f th e r e s i s t a n c e o f t h e r m is to r w ith pow er d i s s i p a t e d I n i t was t a k e n .

th e

A c tu a lly ,

t h i s was done by ta k in g th e r e s i s t a n c e m easurem ent of the th e r m is to r a t s e v e r a l d i f f e r e n t v o l t a g e s im p r e s s e d across b r id g e .

By a c q u ir in g th e s e f i g u r e s , i t was p o s s i b l e to s e l e c t

an in p u t v o l t a g e b e lo w w h ich f a i r l y

la r g e c h a n g e s i n b r id g e

e . m . f . gave v a r i a t i o n s of t h e r m is t o r r e s i s t a n c e in 3 0 0 0 .

th e

l e s s than 1 part

T h is e . m . f . o f 1 . 5 v o l t s w as s e l e c t e d from th e d a t a

o f w h ich T a b le X II g iv e s a r e p r e s e n t a t iv e sam p le*

The r e a d in g s

ta k e n a t 1 . 0 v o l t s vary fro m th o se a t 1 ,5 v o l t s b y le s s t h a n 1 p a r t in 3 3 0 0 , and on the a v e ra g e b y 1 p a r t i n 4 0 0 0 . B ecau se o f the pow er d i s s i p a t i o n p r o b le m , care m u st be t^c en i n b u i l d i n g the I n str u m e n t t h a t the v o l t a g e a c r o s s the b r id g e does n o t v a r y to so la r g e an e x te n t t h a t th e ch an ges in th e r m is to r c h a r a c t e r i s t i c s a r e enough to a f f e c t tem p eratu re c o m p e n sa tio n .

In lo o k in g f o r an o s c i l l a t o r t o su p p ly the a . c .

b r id g e o f the in s tr u m e n t, i t

Y/as found t h a t th o se commonly u s e d

v a r y t h e i r v o l t a g e ou tp u t a c c o r d in g t o

th e lo a d .

S in c e i t was

e s t im a t e d t h a t th e o v e r a l l r e s is t a n c e o f th e b r id g e would v ary fro m about 200 ohms to 350 ohm s, d ep en d in g on e l e c t r o l y t e co n ­ c e n t r a t i o n and te m p e r a tu r e , i t was n e c e s s a r y to c u t o f b r id g e s u p p ly w ith lo a d .

th is v a r i a t i o n

I t was fo u n d th a t a Terman o s c i l ­

l a t o r , su ch as was u se d f o r t h e o r ig in a l m easurem ents o f P art I , p a s s in g on i t s

o u tp u t th r o u g h a cathode f o llo w e r s t a g e , gave a

v a r i a t i o n i n o u tp u t o f ab ou t ^10$ from a mean v a lu e f o r a change i n lo a d su ch a s i s g iv e n a b o v e .

This am ount can b e t o le r a t e d

s i n c e I t f a l l s w e l l w ith in th e lim it s e s t a b l i s h e d b y th e v a lu e s i n T able X I I , 2.

Wagner Ground. A b r id g e s u p p lie d w ith a l t e r n a t i n g c u r r e n t i s s u b j e c t

to much c a p a c l t a t i v e c o u p lin g o f i t s b r a n c h e s .

T hose c o u p lin g s

b etv /een o s c i l l a t o r le a d s or th o s e b etw een th e d e t e c t o r lea d s have no h a r m fu l e f f e c t on p o s i t i o n o f b r i d g e b a la n c e .

C ou p lin gs

a r e p o s s i b l e w h ich may d i s t u r b the b a la n c e o f the b r i d g e . p a th s w i l l ten d t o n e u t r a l i z e each o t h e r .

Some

I f , h o w e v e r , a l l a re

n o t n e u t r a liz e d i n one way o r anoth er, b r i d g e r e a d in g s w i l l d e ­ pend on th e p o s i t i o n o f the u n i t s in th e b r i d g e ,

p r e c i s e m eas­

urem ents are n o t p o s s ib le u n l e s s the c a p a c l t a t i v e c o u p lin g s a re n e u t r a l iz e d by b e in g made sym m etric w ith r e s p e c t to th e te r m in a ls o f th e d e t e c t o r . ground (1 8 )

(5 )

T h is i s a cco m p lish ed b y means o f th e Tffagner (1 9 ).

In th e c o u r se o f making the m easurem ents d e s c r ib e d i n P a r t I , a r e c o r d was k ep t o f th e s e t t in g s o f the Wagner ground* The r e c o r d s show th a t th ese rem ained p r a c t i c a l l y c o n s t a n t w hether

th e e l e c t r o l y t e was p o ta s s iu m c h lo r id e or p o ta s siu m d ic h r o m a te , w h eth er th e r e s i s t a n c e w a s h igh or lo w , w hether th e tem p erature was h ig h or lo w .

The o n l y th in g th a t c a u se d ch an ges i n Wagner

g round s e t t i n g was change i n freq u en cy a p p lie d to th e b r id g e . T a b le X I I I g i v e s the r e c o r d s th a t b ear o u t t h i s c o n s t a n c y . S in c e th e in s tr u m e n t vi 11 have a f i x e d fr e q u e n c y im ­ p r e s s e d on th e b r id g e , a l l th a t i s n eed ed w ith r e s p e c t to th e Wagner ground i s

some sem i-p erm a n en t manner o f s e t t i n g i t .

When

th e in s tr u m e n t i s b u i l t , t h e Yfagner ground may be g iv e n an o r i g i n a l s e t t i n g and f u r t h e r changes n e c e s s i t a t e d b y r e p la c in g p a r t s , change o f c o n d u c t iv it y c e l l , e t c . , may be made by screw d r iv e r a d ju stm e n t.

Checks may be made from tim e t o tim e .

There

i s no n e c e s s i t y f o r a d j u s t i n g the Wagner ground p o s i t i o n s w ith e a c h m easurem ent made, 3.

A djustm ent f o r C e ll C o n sta n t and R eagen t The fo u r t h arm o f the b r id g e i s a v a ila b le

ta n c e s e t t i n g t h a t w i l l d ep en d on two t h i n g s .

fo r a r e s i s ­

The f i r s t i s th e

v o lu m e tr ic s o l u t i o n to be s t a n d a r d iz e d , th e seco n d i s s t a n t o f the c o n d u c t iv it y c e l l *

th e con ­

T h is arm, whose r e s i s t a n c e ra n g e

s h o u ld b e 100 to 1000 ohms t o in c lu d e p r a c t i c a l l y a l l th e e l e c ­ t r o l y t e s o f a n a l y t i c a l i n t e r e s t , m ust be composed o f a group o f f o u r d e c a d e s i n o rd er to g u a r a n te e a s e t t i n g p r e c i s i o n o f a t l e a s t 1 p a r t p er 100 0.

To d eterm in e th e v a lu e to be s e t in t o

t h i s arm f o r ea ch e l e c t r o l y t e , a s o l u t i o n o f p o ta s s iu m c h lo r id e i s made up by w e ig h t to be 0 . 1 Normal a t room te m p e r a tu r e , then I t I s p la c e d In th e c e l l o f t h e in s tr u m e n t, th e r e a d in g arm i s s e t f o r a s e le c t e d p o s itio n t o

r e p r e s e n t 0 .1 Norm al, and th e d e ca d es

a d j u s t e d u n t i l th e b r id g e i s b a la n c e d .

T h is v a lu e o f decade

r e s i s t a n c e t o g e t h e r w ith the r e l a t i o n b etw een th e s p e c i f i c c o n d u cta n ce o f p o ta ssiu m c h lo r id e and each o f th e o th e r e l e c ­ t r o l y t e s w i l l g i v e th e s e t t i n g v a lu e s fo r t h i s arm f o r t h e s e s o lu tio n s . p e a te d ,

W ith e v e r y change i n c e l l , th e p r o c e ss must be r e ­

To c a l i b r a t e th e s c a l e f o r any' e l e c t r o l y t e , th r e e s o lu ­

tio n s a r e made up b y w e ig h t, t h e i r n o r m a lity c a lc u la t e d from s p e c i f i c g r a v it y m easurem ents and th e s e t t i n g f o r b a la n c e f o r each o b t a in e d .

S in c e we have a l i n e a r s c a l e , we need o n ly d i ­

vide t h e s c a l e In p r o p o r tio n a l p a r t s . 4,

B r id g e B a la n ce i n d ic a t o r . The o rd er o f th e s e n s i t i v i t y o f th e b r id g e b a la n c e in ­

d ic a t o r may b e c a lc u l a t e d from th e v a lu e s u se d so f a r i n th e d e s c r i p t io n o f th e b r id g e .

An e x a c t c a l c u l a t i o n i n v o lv e s the

use o f K i r c h o f f ' s lav/s and a good d e a l o f a r it h m e t ic .

An ap­

p ro x im a te v a lu e w h ich sh o u ld be q u i t e s a t i s f a c t o r y may be e v a lu ­ ated b y th e f o llo w in g s t e p s .

The r a n g e o f 0 .0 9 to 0 .1 1 Normal

i s c o v e r e d b y 100 ohms o f b a la n c in g p o te n t io m e t e r . th o u sa n d th o f a u n i t o f n o r m a lity i s 0 ,5 ohms o f th e p o te n tio m e t e r .

Each te n

a p p r o x im a te ly e q u iv a le n t to

In o r d e r to be on th e s a f e s id e ,

l e t u s assum e t h a t i t I s d e s ir e d to ”s e e w a d if f e r e n c e o f 0 .2 5 ohms w i t h th e b r id g e b a la n c e i n d i c a t o r .

The r e s i s t a n c e o f the

branch b e tw e e n th e In p u t arms w i l l b e about one th ou san d ohms. To " see"

0 .2 5 ohms o u t o f 1000, th e b r id g e b a la n c e i n d ic a t o r

must b e s e n s i t i v e t o one four th o u sa n d th o f th e In p u t v o l t a g e . I f th e in p u t v o l t a g e i s 2 v o l t s , th e i n d ic a t o r must be a b le to d e te c t f i v e t e n t h s o f a q i i l l i v o l t .

It is

in ten d ed t h a t th e b r id g e b a la n c e in d ic a to r be

m o d eled a f t e r th e one d e s c r ib e d b y Garman and K inney (2 0 ), h a s th e a d v a n ta g e of v i s u a l i n d i c a t i o n .

It

The a u th o r s s t a te t h a t

t h e in d ic a t o r i s capable o f r e sp o n d in g to a s i g n a l o f 100 m ic r o ­ v o l t s , which i s

much more th a n enough fo r th e p r e s e n t p u rp o ses.

E x p er ie n c e w i t h the same ty p e o f c i r c u i t more than b e a r s out t h e i r c la im .

Some m o d if ic a t io n i s

in te n d e d , t o s i m p l i f y the

c ir c u it. 5.

Q uadrature B alan ce. A r e c o r d of q u a d ra tu re b a la n c e was k e p t f o r a l l c o n ­

d u c t i v i t y r e a d in g s made on th e s o l u t i o n s .

U n f o r t u n a t e ly , no

r e a l r u le c o u ld be e s t a b l i s h e d w h ich would be u s e f u l f o r i n s t r u ­ m e n ta l p u r p o s e s .

As a r e s u l t , i n th e in s tr u m e n t i t w i l l be

n e c e s s a r y to make quadrature s e t t i n g s w ith e a c h measurement b y m eans o f th e u s u a l v a r ia b le c o n d e n ser in p a r a l l e l w it h the decade r e s i s t o r s . T h e o r e t i c a l l y , a t b a la n c e , c a p a c it o r s e t t i n g has no e f f e c t on th e r e s i s t i v e b a la n c e o f th e b r id g e , and so one m ig h t be in c lin e d t o

le a v e i t o u t .

H owever, sh a r p n e s s o f balan ce i s

l o s t and the l o s s in s e n s i t i v i t y I s p r o h i b i t i v e . 6.

T h erm isto r C o a tin g s. S in c e th e t h e r m is t o r 25A, and a l l o t h e r p o s s ib ly u s e ­

f u l f o r co m p en sa tio n p u r p o s e s , are n o t c o a te d w it h any I n s u la t in g m a t e r i a l , i t w as n e c e s s a r y to f i n d some e l e c t r i c a l i n s u l a t io n f o r th e t h e r m is t o r .

The prob lem was one o f o b t a i n in g a c o a tin g

w i t h th e a b i l i t y to w ith s ta n d d i l u t e a c id and a l k a l i w ithout d e t e r i o r a t i o n , w ith good e l e c t r i c a l i n s u l a t i n g p r o p e r t i e s , and

good th e rm a l c o n d u c ta n c e .

The l a s t two a r e ju s t a b o u t m u tu a lly

e x c l u s i v e , and so a compromise i s

n e c e s s a r y on th erm a l ch arac­

te r is tic s . Many d i f f e r e n t m a t e r ia ls were t r i e d , su ch a s metha­ c r y l a t e la c q u e r s , p o ly s ty r e n e la c q u e r s , p o ly s ty r e n e p o ly m e rize d on th e th e r m is to r and o t h e r s . were u n s a t i s f a c t o r y . by th e

u.

For one r e a s o n or a n o th e r th e s e

T ygon Rack C o a tin g L acq u er, m anu factu red

S , Stonew are Company, w h ich i s u s e d in t h e p la t in g

i n d u s t r y , was fo u n d to b e v e ry s a t i s f a c t o r y . B ecau se the c o a t i n g had t o be r a t h e r t h ic k fo r good e l e c t r i c a l i n s u l a t i o n , som e th erm al la g was in tr o d u c e d in to t h e t h e r m is to r p r o p e r t ie s .

T h e se are n o t s e r i o u s h o w ev er.

Equi­

lib r iu m seem s to be r e a c h e d by a llo w in g a b o u t a m in u te for e a c h degree o f d i f f e r e n c e in tem p er a tu r e b e tw e en th e th e r m is to r a n d th e s o l u t i o n .

S in c e t h i s w i l l i n m ost c a s e s not b e more th a n

two o r t h r e e d e g r e e s , th e tim e l a g d o es n o t cause t o o much i n ­ c o n v e n ie n c e .

SUMMAEf

The d e s ig n o f an in s tr u m e n t capable o f s t a n d a r d iz in g v o lu m e tr ic r e a g e n ts was c a r r ie d th r o u g h ste p by s t e p .

T h is r e ­

quired a n accu m u la tio n o f co n d u cta n ce data la c k in g in th e l i t ­ e r a t u r e , from w h ich r e l a t i o n s n e c e s s a r y fo r the d e s ig n o f the in s tr u m e n t were e s t a b l i s h e d . Prom th e d a ta i t was shown th a t over s m a ll r a n g e s o f c o n c e n tr a t io n , 0 .0 9 - 0 .1 1 Normal, a s t r a ig h t l i n e r e l a t i o n hold s b e tw e e n co n d u cta n ce and n o r m a lity to a d e g r e e d eterm in ed i n the m ain, in t h i s c a s e , by th e p r e c i s i o n o f th e m easurem ents, one p a r t i n f i v e

th o u sa n d .

An e x p o n e n t ia l e q u a tio n w as ob tain ed b y th e l e a s t sq uares m ethod w h ich gave th e v a r i a t i o n o f s p e c i f i c r e s i s t a n c e o f a s o l u t i o n w it h tem p er a tu r e,

Prom t h i s e q u a tio n i t was p o s­

s i b le t o d e f in e a tem p eratu re c o e f f i c i e n t 1

cLRqi

Rjji-K dT

b T2

which w o u ld h o ld fo r th e range o f tem p era tu re e x p lo r e d . An e x a m in a tio n o f th e r e l i a b i l i t y o f th e accu m u lated d a ta was made b y com p arison w ith th e work o f some o f the' a c k ­ n ow ledged le a d e r s in th e f i e l d .

A f t e r e x te n s iv e r e c a l c u l a t i o n ,

agreem ent to b e t t e r th an 0 .0 4 $ was d em o n stra ted , th is , i t

i n l i n e w ith

was shown t h a t t h e I n t e r n a t i o n a l C r i t i c a l* T a b les were

c o n fu s in g i n t h e i r p r e s e n t a t io n o f con d u ctan ce d a t a and c a u t io n was u r g e d In th e r e a d in g o f c o n d u cta n ce data to p r e v e n t t h i s c o n f u s io n .

Prom t h e s t r a i g h t l i n e r e l a t i o n b etw een n o r m a lity and con d u ctan ce i t w as shown t h a t i n th e p ro p o sed in str u m e n t a lin e a r s c a l e c o u l d be u sed to g iv e d i r e c t r e a d in g s i n n o r m a lit y , o b v ia t in g the n e e d o f any graphs or c h a r ts f o r th e m easurem ents. F u r th e r , by e q u a tio n and c a l c u l a t i o n I t was shown t h a t a th e r m is to r i n a s s o c i a t i o n w it h two r e s i s t o r s , one in s e r i e s w ith th e t h e r m is t o r , the o th e r i n p a r a l l e l w ith th e s e r ie s com­ b i n a t io n , would g i v e adequate tem p era tu re com p en sation fo r a range o f te m p e r a tu r e s from 15°C to 35°C .

In l i n e w ith t h i s ,

H. K. Moneypenny (2 1 ) p u b lis h e d a r e c e n t a r t i c l e i n which he made u s e o f a t h e r m is to r as a com p en satin g d e v ic e i n an a l t e r ­ n a tin g c u r r e n t b r id g e u sed f o r th e d e te r m in a tio n o f carbon i n s te e l.

H is th e r m is to r i s a s s o c i a t e d w ith a p a r a l l e l r e s i s t o r

a lo n e , and the v a lu e o f th e p a r a l l e l r e s i s t a n c e i s

s e t m a n u a lly

by v a r y in g the tem p era tu re and w a tc h in g th e b r id g e b alan ce u n t i l com p en sation i s

a c h ie v e d .

In t h i s manner co m p en sa tio n f o r a

v ery l i m i t e d r a n g e i s a c h ie v e d .

To c a l c u l a t e th e v a lu e s n e e d e d

fo r co m p en sa tio n i t was n e c e s s a r y t o d eterm in e th e tem p e r a tu r e r e s i s t a n c e c h a r a c t e r i s t i c s o f th e th e r m is to r s e l e c t e d fo r t h i s com p en sation n e tw o r k .

The c o n c o m ita n t problem o f power g e n e r a ­

tio n and d i s s i p a t i o n was a n a ly z e d w ith r e s p e c t to th e t h e r m is t o r , and i t was shown t h a t below a c e r t a i n p o in t an e q u ilib r iu m was e s t a b l i s h e d where th e c h a r a c t e r i s t i c s o f th e th e r m is to r w ou ld not be t o o s e n s i t i v e to f l u c t u a t i o n s i n o u tp u t e . m . f . of th e b r id g e o s c i l l a t o r * I t was th e n shown t h a t , f o r a p a r t i c u la r bridge c o n ­ s t r u c t i o n , s e t t i n g s o f th e Wagner ground rem ain s u f f i c i e n t l y c o n s ta n t r e ^ A r d le s s o f te m p e r a tu r e , ty p e o f s o l u t i o n or c o n c e n ­ t r a t i o n , to a llo w f o r sem i-perm anent a d ju s tm e n t. o f th e Wagner

ground.

T h is i s p o s s i b l e o n ly w ith a f ix e d fr e q u e n c y a l t e r n a t i n g

c u r r e n t im p r essed o n the b r id g e . The method, fo r c a l i b r a t i n g th e p ro p o sed b r id g e has been d e s c r ib e d .

A b r id g e b a la n c e i n d i c a t o r w ith a s e n s i t i v i t y o f

0 . 5 m i l l i v o l t s was shown to be a d eq u a te fo r t h e p u rp oses a t hand. The e le m e n ts n e c e s s a r y fo r th e d e s ig n of an In stru m en t ca p a b le o f s ta n d a r d iz in g v o lu m e tr ic r e a g e n ts b y means o f conduc­ ta n c e m eausrem ents, w hich w ould a ls o be d i r e c t r e a d in g , tem pera­ t u r e com p en sating, and c a p a b le o f th e p r e c i s i o n u s u a l l y a s s o c i a t e d w ith c o n v e n t io n a l ch e m ic a l a n a l y t i c a l p roced ure has b e e n d e s c r ib e d .

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TABLE X III Wagner Ground S e t t i n g s *

t°C

C e ll R e s is ta n c e

C a p a c ita n c e i n Wagner Ground i n M icro fa ra d s 1000 C y c le s 500 C y c le s

P otassiu m C h lo r id e 1 6 .7 °

3 ,8 0 0

.0 0 2 6

.0 0 1 7

2 0 .4 °

3 ,3 5 0

.0 0 2 6

.0 0 1 7

2 4 .1 °

2 ,9 5 0

.0 0 2 5

.0 0 1 6

2 7 .8 °

2 ,6 3 0

.0 0 2 6

.0 0 1 7

3 1 .8 °

2 ,3 5 0

.0 0 2 6

.0 0 1 7

P otassiu m D ichrom ate 1 7 .2 °

1 2 ,0 5 0

.0 0 2 +

.0 0 1 *

2 1 .0 °

1 0 ,7 0 0

.0 0 1 9

.0 0 1 7

2 4 .2 °

9 ,5 5 0

.0 0 1 9

.0 0 1 7

2 7 .7 °

8 ,4 0 0

.0 0 1 9

.0 0 1 7

3 1 .8 °

7 ,5 0 0

.0 0 1 9

.0 0 1 7

The se co n d s i g n i f i c a n t f ig u r e in Wagner ground c a p a c ita n c e s e t t i n g was n o t sh a r p ly d e f in e d and c a n only b e c o n s id e r e d a g r o s s a p p r o x im a tio n . ■» The s e t t i n g s o f th e r e s i s t i v e e le m e n t of th e Wagner ground w ere c o n sta n t to 12 % .

52.

KCI

34

as F iji

DEV. SUM

2 0

12

L

j.

j.

.27

.28

ARBITRARY

.29

.30

CONSTANT

80

DEV.

70

Flo 2

SUM

XIO*