Rapport BIPM-82/9

THE NEFJTONIAN GRAVITATIONAL CONSTANT :

An Index of Measurements

George T. Gillies

Bureau International des Poids et Mesures Pavillon de Brereuil

F-92310 Ssvres, France

TABLE OF CONTENTS

Introductory Text................................................l

1. Measurements of the Absolute Value of G and Reports of Important Subsidiary Technology.............16

2. Important Comments and Reviews of Measurements of G...................................................45

3. Measurements of Gravitational Permeability or Absorption .......................................... 50

4. Measurements of the Local Directive Action of the Gravitational Force.............................57

5. Neasurements of the Dependence of G on the Physical State of Masses...............................58

6. Measurements of the Dependence of G on the Chemical State of W S S ~ S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ ~

7. Measurements of the Dependence of G on Temperature. ........................................... 61

8. Measurements of the Dependence of G on the Radioactivity of Masses ................................ 63

9. Measurements of the Dependence of G on the Electromagnetic Energy Content of Masses...............64

10. Measurements of the Dependence of G on Inter-mass Spacing ..................................... 66

11. Measurements of the Dependence of G on Time...............71

12. Measurements of Spontaneous Matter Creation...............79

13. Measurements of the Dependence of G on the State of Quantization of the Test Masses and Their Orientation with Respect to the "Fixed StarsW..........83

THE NEWTONIAN GRAVITATIONAL CONSTANT: AN INDEX

OF MEASUREMENTS

George T. G i l l i e s Bureau I n t e r n a t i o n a l des Poids e t Mesures

Pav i l l on de B r e t e u i l F-92310 SZvres, France

ABSTRACT

The Newtonian G r a v i t a t i o n a l Constant, "G", has probably been measured more o f t e n but , i n t e r e s t i n g l y , w i th l e s s p r e c i s i o n than any o t h e r phys ica l cons tan t of fundamental importance. I n an e f f o r t t h a t has spanned more than a century t o connect g r a v i t a t i o n t o t h e o t h e r fo rces of na tu re , over 200 experiments on G have been completed and repor ted ; bu t many of them have not been repor ted i n what would now be considered t o be t h e open l i t e r a t u r e . This paper is an at tempt t o c a r r y MacKenzie's and Poynting 's b ib l iog raph ie s forward from t h e 1800's t o t h e present ; and thereby inc lude a s many a s poss ib le of t h e experimental r e s u l t s on G t h a t have been obtained s i n c e 1900.

I. In t roduc t ion

I f one were t o ca ta logue t h e t o o l s of p rec i s ion measurement, a n unusual ly high number of t h e l i s t i n g s would claim a s t h e i r genes is t h e p rec i s ion measurement of t h e Newtonian G r a v i t a t i o n a l Constant, h e r e i n simply r e f e r r e d t o a s "G". These t o o l s would inc lude t h e t o r s i o n balance, t he o p t i c a l l e v e r , t h e qua r t z f i b e r , synchronous d e t e c t i o n techniques, u l t ra -h igh p r e c i s i o n r o t a t i o n s and many o thers . Yet G s t ands alone a s t h e only fundamental cons tan t c u r r e n t l y known t o l i t t l e b e t t e r than one p a r t i n a thousand although t h e r e a r e t h r e e measurements claiming accurac ies of one p a r t i n t e n thousand. I n p a r a l l e l with t h e s e e f f o r t s t o measure t h e a b s o l u t e va lue of G, t h e r e has a l s o been a wide v a r i e t y of experiments aimed a t l i n k i n g t h e g r a v i t a t i o n a l fo rce t o t h e o t h e r fo rces of nature. A l l such e f f o r t s t o d a t e have had t h e s i n g u l a r l y unique r e s u l t of demonstrating t h a t g r a v i t y , indeed, s t a n d s alone - t h e l a s t of t h e g r e a t c l a s s i c a l mechanisms - i n s p i t e of i t s modernized p re sen ta t ion v i a genera l r e l a t i v i t y .

C l a s s i c a l g r a v i t a t i o n a l physics has been l i k e t h i s , and foreseeably w i l l cont inue t o be l i k e t h i s . The reason why is t h a t , t o t h i s da t e , no one has succeeded i n i s o l a t i n g s u f f i c i e n t l y well t h e g r a v i t a t i o n a l i n t e r a c t i o n between l abo ra to ry masses t o t h e poin t where o t h e r d i s t u r b i n g fo rces o r experimental u n c e r t a i n t i e s do not dominate t h e measurement, a t l e a s t a t l e v e l s above those a t which o t h e r phenomena might be expected t o occur.

It is neve r the l e s s both i n t e r e s t i n g and important t o ca ta logue t h e l a r g e body of work done a l r eady i n t h e hope t h a t a thorough l i s t i n g of t h e experimental f a c t s concerning our knowledge of G w i l l s t i m u l a t e f u t u r e work on t h i s cons t an t and t h e f o r c e t h a t i t governs.

P a r t of t h e mot iva t ion f o r t h i s paper l i e s i n t h e f a c t t h a t much of t h e work on G w a s r epo r t ed obscurely i n s p i t e of t h e f a c t t h a t most experiments have been c a r e f u l l y designed and completed. It was, t h e r e f o r e , a cha l lenge t o e x t r a c t from va r ious l i b r a r i e s , a r ch ives and p r i v a t e c o l l e c t i o n s t h e e x i s t i n g d a t a t h a t , when c o l l e c t i v e l y viewed, w i l l he lp t o focus a t t e n t i o n on j u s t exac t ly what has been done and, more impor tan t ly , what has not been done i n t h i s f i e l d , -

This work is meant t o be a b ib l iography and, a t p re sen t , on ly t h a t . Owing t o t h e unusual ly l a r g e number of r e f e rences c i t e d , any thorough d i scuss ion of a l l t h e r e s u l t s would have taken up more space than w a s a v a i l a b l e here. Nevertheless , t h e r e is a smal l amount of anno ta t ion provided i n t h e fol lowing pages f o r each of t h e t h i r t e e n s e c t i o n s of t h e bibl iography. These a r e a s i n t o which t h e papers have been c l a s s i f i e d a r e l i s t e d below:

Measurements of t h e abso lu t e value of G and r e p o r t s o f important subs id i a ry technology.

Important comments and reviews of measurements of G. Measurements of g r a v i t a t i o n a l permeabi l i ty o r absorpt ion. Measurements of t h e l o c a l d i r e c t i v e a c t i o n of t h e

g r a v i t a t i o n a l force . Measurements of t h e dependence of G on t h e phys i ca l s t a t e of

masses. Measurements of t h e dependence of G on t h e chemical s t a t e of

masses. Measurements of t h e dependence of G on temperature. Measurements of t h e dependence of G on t h e r a d i o a c t i v i t y of

masses. Measurements of t h e dependence of G on t h e e lec t romagnet ic

energy content of masses. Measurements of t h e dependence of G on inter-mass spacing. Measurements of t h e dependence of G on time. Measurements of spontaneous ma t t e r c r e a t i o n ( r e l a t e d t o 11) . Measurements of t he dependence of G on t h e s t a t e of

q u a n t i z a t i o n of t h e t e s t masses and t h e i r o r i e n t a t i o n wi th r e spec t t o t h e "f ixed stars".

There a r e about 850 r e fe rences c i t e d i n t hese 13 sec t ions . There is some dup l i ca t ion , a s a few of t h e papers con ta in two o r more experimental r e s u l t s each i n a d i f f e r e n t a rea . Dupl ica te l i s t i n g s c o n s t i t u t e about 5% ( o r l e s s ) of t h e t o t a l , however. The r e fe rences a r e l i s t e d a l p h a b e t i c a l l y i n each s e c t i o n with a chronologica l s u b l i s t i n g f o r each au thor i n each sec t ion . The o rde r of t h e items i n each of t h e r e f e rences fol lows t h e IS0 recommendations a s c l o s e l y a s poss ib le . Abbreviat ions f o r t h e jou rna l t i t l e s follow the American I n s t i t u t e of Physics S t y l e Manual wherever poss ib le . For those journa ls no t l i s t e d

t h e r e , t h e abb rev ia t ions i n t h e IS1 Current Contents indexes have been used. Those l i s t i n g s t h a t have t h e a u t h o r ' s name(s) marked wi th an a s t e r i s k have not been consul ted a t t h e time of t h i s wr i t i ng . References t o e n t r i e s i n t h e va r ious a b s t r a c t i n g journa ls have not been given except f o r a few s p e c i a l cases where t h e a b s t r a c t e d a r t i c l e was judged t o be publ ished obscurely.

Not a l l of t h e l i s t i n g s i n t h e Mackenzie (1900) and Poynting (1894) b ib l iog raph ie s were repeated here. Some, l i k e those r e f e r r i n g t o t h e "Fr. B e r t i e r " Controversy of t h e l a t e 1700 ' s / ea r ly 1800f s , have l i t t l e s c i e n t i f i c merit and were omitted.

Sec t ions 11 and 12 con ta in s e v e r a l r e f e rences t o i n s t rumen ta l papers i n a d d i t i o n t o t hose a c t u a l l y quot ing s i g n i f i c a n t r e s u l t s . I n p a r t i c u l a r , t h e work a t t h e Un ive r s i t y of V i r g i n i a is l i s t e d i n d e t a i l .

11. Experimental S tud ie s and C r i t i c a l Analyses of G

1. Measurements of t h e Absolute Value of G and Reports of Important Subs id i a ry Technology

The h i s t o r y of t h e measurement of t h e u n i v e r s a l g r a v i t a t i o n a l cons tan t begins w i th geophysical s t u d i e s of a r e l a t e d phys i ca l q u a n t i t y , t he mean d e n s i t y of t h e ea r th . These e f f o r t s s t a r t e d with a t tempts t o measure t h e a t t r a c t i o n of i n d i v i d u a l mountains, measurements of s t r a t a of t h e e a r t h ' s c r u s t a s a func t ion of depth i n var ious mines, and they a r e cont inuing wi th measurements of t h e a t t r a c t i o n of l a y e r s of water i n l a r g e l eve l - con t ro l l ab l e l akes and i n t h e oceans.

Chronological ly , t h e t o r s i o n balance methods came next , and t h e s e gave the most r e l i a b l e r e s u l t s u n t i l t h e advent of t h e t o r s i o n pendulum technique. The balance-beam methods were s tud ied during t h e l a t e 1800's, and today a l l t h r e e of t h e s e methods a r e being developed i n experiments aimed a t accu rac i e s of one i n lo5.

Numerous miscel laneous methods have a l s o been developed. These inc lude resonant t o r s i o n pendulums, v e r t i c a l pendulums, near zone g r a v i t y wave d e t e c t o r e x c i t a t i o n , and long period h o r i z o n t a l pendulums. There have a l s o been s e v e r a l proposed s a t e l l i t e de te rmina t ions of G, but so f a r no such measurements have a c t u a l l y been made (al though s p a c e c r a f t have been important i n measuring t h e time r a t e of change of G and t h e geocen t r i c cons t an t , i . e . , G x M e a r t h ) '

The e a r l y works on G, p a r t i c u l a r l y those of Cavendish, Reich and Bai ly, have been reviewed hundreds of t imes, and t h e p r i n c i p a l papers of t h e s e workers a r e summarized and paraphrased i n most undergraduate textbooks on physics . There a r e , however, about 60 o t h e r de te rmina t ions of G t h a t a r e i n t h e open l i t e r a t u r e . Some of t hese a r e w e l l known too, p a r t i c u l a r l y those of Boys, Poynting, Braun, Hey1 and t h e Reams- Deslattes-Luther-Towler c o l l a b o r a t i o n between t h e Un ive r s i t y of V i r g i n i a and t h e U.S. Nat ional Bureau of Standards.

Of t h e l a t e s t works, t h e r e a r e t h r e e t h a t c la im accu rac i e s nea r one p a r t i n t e n thousand. They a r e summarized i n Table I. The agreement between t h e va lues is only f a i r , however, even a t t h e 10'~ l e v e l .

Table I

Experimental Author Year Technique (G + AG) x 1 0 ~ ~ m ~ k ~ ' l s ' *

Facy, P o n t i k i s 1972 Resonant Pendulum 6.6714 f 0.0006

Sagi tov e t a l . 1977 Torsion Pendulum 6.6745 + 0.0008

Luther , Towler 1982 Torsion Pendulum 6.6726 + 0.0005

A l l u n c e r t a i n t i e s quoted i n Table I a s wel l a s t h a t i n t h e CODATA value below rep resen t one s tandard devia t ion .

Even i f u l t i m a t e l y measured i n a drag-free s a t e l l i t e , where e x t e r n a l h o r i z o n t a l g r a v i t y g r a d i e n t s would not i n f luence t h e balance, measurements of G would s t i l l be l imi t ed by t h e u n c e r t a i n t i e s a r i s i n g from d e n s i t y g r a d i e n t s i n t h e m a t e r i a l s used. This would probably occur somewhere between t h e 10'~ and 10'~ l e v e l . A t t h a t po in t , a t o t a l l y d i f f e r e n t approach t o t h e measurement of G w i l l become necessary.

Our c u r r e n t l y accepted va lue , t h e CODATA value, i s from 1973:

G = (6.6720 + 0.0041) x 10'11 m3kg'1s'2.

2. Important Comments and Reviews of Measurements of G

There a r e fou r thorough reviews of t h e measurements of G: two d a t i n g t o t h e l a t e 1800's and two more r ecen t ones. Poynting and, l a t e r , MacKenzie summarized t h e contemporary knowledge of G and, f o r t h a t ma t t e r , a l l of g r a v i t a t i o n a l physics , i n books p r i n t e d i n 1894 and 1900, r e spec t ive ly . Sagi tov (1969) r e c e n t l y publ ished a s i m i l a r work on G, a l though he omit ted many r e fe rences t o experiments probably judged by him t o be of secondary importance. Most r e c e n t l y , de Boer (1982) has con t r ibu ted a review a r t i c l e which ca ta logues t h e r ecen t major experiments and p re sen t s t he r e s u l t s and u n c e r t a i n t i e s t o g e t h e r on e a s i l y readable graphs. There a r e s e v e r a l o t h e r reviews of t h e experiments, and these a r e l i s t e d i n t h e bibl iography. It should be mentioned t h a t each success ive e d i t i o n of t h e Encyclopedia Br i t ann ica a r t i c l e s on "Gravi ta t ion" con ta in i n t e r e s t i n g and r e l a t i v e l y thorough s e c t i o n s on G t h a t a r e very use fu l .

I n a d d i t i o n t o t h e review a r t i c l e s on G, t h e r e a r e a l a r g e number of papers , both o ld and new, t h a t comment on o r d i s c u s s c e r t a i n measurements of G, propose new measurement techniques, o r analyze probable experimental l i m i t a t i o n s . Some of t hese a r e worth consul t ing , s i n c e e r r o r s have occas iona l ly appeared i n t h e main papers of t h e p r i n c i p a l i n v e s t i g a t o r s . The t i t l e s of t h e papers i n t h i s s e c t i o n of t h e bibl iography usua l ly i n d i c a t e t h e relevance t o a c e r t a i n experiment o r c l a s s of experiments.

3 . Measurements of G r a v i t a t i o n a l Permeabi l i ty o r Absorption

Although not widely known, one of t he most thoroughly researched a s p e c t s of g r a v i t a t i o n a l physics i s t h e ques t ion of t h e ex i s t ence of a g r a v i t a t i o n a l analogue t o magnetic permeabil i ty . The p u r s u i t of t h i s ques t ion , i .e . , t h e dependence of G on t h e d e n s i t y of t h e ma t t e r i n t e rven ing between t h e i n t e r a c t i n g masses, began with a n u l l r e s u l t i n t h e l a t e 1800's. It cont inued u n t i l r ecen t t imes, always wi th n u l l r e s u l t s , but with ever- increasing accuracy. We now know t h a t i f g r a v i t a t i o n a l energy is, i n f a c t , absorbed by any in t e rven ing ma te r i a l , i t occurs a t a l e v e l such t h a t , when measured i n terms of G, t h e r e s u l t i s ( A G / G ) ~ ~ , < 10-16.

A t f i r s t t he se measurements were made by employing a Cavendish balance wi th a c y l i n d r i c a l s c reen s e p a r a t i n g t h e suspended dumb-bell from t h e a t t r a c t i n g masses. Each screen was made of a d i f f e r e n t type of m a t e r i a l , and a l l t h e ma te r i a l s had d i f f e r e n t d e n s i t i e s . The screens were s e q u e n t i a l l y changed and the measurements of G subsequent ly made were analyzed f o r a r e s u l t i n g e f f e c t . La t e r , Majorana began a long s e r i e s of experiments using a balance-beam and claimed t o have found a r e s u l t a t t h e 10'11 l e v e l , but subsequent work by himself and o t h e r s disproved t h i s . The most s e n s i t i v e measurements have been made i n r ecen t times by s e v e r a l workers s tudying t h e period s h i f t i n h o r i z o n t a l pendulums during a t o t a l s o l a r e c l i p s e . I n every case , however, t h e r e s u l t s have been n u l l except f o r t h e r e s u l t s of A l l a i s and, l a t e r , Sax1 and Allen which a r e seldom discussed.

Unless a new theory p r e d i c t s a permeabi l i ty e f f e c t s u b s t a n t i a l l y d i f f e r e n t from t h a t empi r i ca l ly sought s o f a r , i t i s d i f f i c u l t t o s e e where the motivat ion would a r i s e f o r new experiments i n t h i s area.. This i s e s p e c i a l l y so s i n c e r ecen t g r a v i t a t i o n a l analogues of electromagnetism p r e d i c t t h a t t h e " g r a v i t a t i o n a l permeabi l i ty of f r e e

16 xG space" is only - = m/kg (Forward, 1961), a very small e f f e c t c *

indeed !

4 . Measurements of t h e Local D i r e c t i v e Action of t h e G r a v i t a t i o n a l Force

Since so many p r o p e r t i e s of c r y s t a l l i n e ma te r i a l s depend upon t h e d i r e c t i o n of observa t ion (e.g. r e f r a c t i v e index, l o c a l d e n s i t y d i s t r i b u t i o n , thermal conduc t iv i ty , e t c . ) , i t seemed reasonable t o

ques t ion the constancy of G w i th in c r y s t a l l i n e m a t e r i a l s a s wel l . This was f i r s t done by MacKenzie, then l a t e r by Poynting al though no an iso t ropy i n t he va lue of G was found i n e i t h e r case a t = 10'~ and 10 '~ l e v e l s , r e spec t ive ly . Hey1 d id an exhaus t ive experiment i n t h i s a r e a i n 1924 and, by weighing c r y s t a l s from each of t he f i v e non-isometric groups, was a b l e t o put a l i m i t of (AGIG),, = thereby e f f e c t i v e l y

e l imina t ing any doubt about i t .

It has been suggested t h a t one should not expect t o f i n d such a n i s o t r o p i e s i n gene ra l because they would l e a d t o a v i o l a t i o n of conserva t ion of momentum. Nevertheless , t h e weakness of t h e g r a v i t a t i o n a l fo rce and t h e s i n g u l a r p r o p e r t i e s of some c r y s t a l s made t h i s , t emporar i ly a t l e a s t , an a t t r a c t i v e a r e a of research .

5. Measurements of t h e Dependence of G on t h e Phys ica l S t a t e of Masses

This ca tegory is a r a t h e r gene ra l one, a l though it is poss ib l e t o c l a s s i f y var ious types of experiments w i t h i n it. S p e c i f i c a l l y , t h e r e have been measurements of G involv ing t e s t masses and a t t r a c t i n g masses of var ious geometr ica l shapes. For example, spheres , cy l inde r s , rods, r i n g s , and i r r e g u l a r masses have been used. I n f a c t , a c y l i n d r i c a l con f igu ra t ion having t h e sphere- l ike f i e l d of a po in t source is p re sen t ly under s tudy. A t t r a c t i n g and t e s t masses i n t h e gaseous, l i q u i d and s o l i d s t a t e have been ( o r a r e being) s tud ied , as w e l l a s masses which undergo a change of s t a t e during t h e experiment. I n a l l c a ses , no depa r tu re from t r u e constancy of G has been observed, a t l e a s t wi th in the l e v e l s of t he experiments ' p rec is ion . When one cons iders t h a t t he sun, a plasma, and i t s p l a n e t s (gas , s o l i d and l i q u i d combinations) have o r b i t s which conform p r e c i s e l y t o t h e Inverse squa re law (with only minor r e l a t i v i s t i c c o r r e c t i o n s ) , it i s seen t h a t t h i s l a w is indeed we l l obeyed. The r e fe rences c i t e d he re a r e r e p r e s e n t a t i v e examples of var ious types of experiments involv ing gases , l i q u i d s and s o l i d masses of var ious shapes. Some of t hese c i t a t i o n s a r e l i s t e d i n o t h e r more appropr i a t e s e c t i o n s of t h e b ib l iography too.

6 . Measurements of t h e Dependence of G on t h e Chemical S t a t e of Masses

This a r e a of research i s usua l ly i n t e r p r e t e d a s being a t e s t o f t h e weak equivalence p r i n c i p l e of General R e l a t i v i t y , i .e . a de termina t ion of t h e equivalence of g r a v i t a t i o n a l and i n e r t i a l mass. The var ious searches f o r a non-zero E8tv3s r a t i o which t e s t t h i s equivalence a r e catalogued by W i l l (1981) and a r e not included h e r e , except f o r a few s p e c i a l ca ses given below.

The e a r l i e s t measurements i n t h i s a r e a involved pendulums of t h e same mass but made of d i f f e r e n t ma te r i a l s . E3tv3s and h i s contemporaries expanded t h i s t o inc lude t o r s i o n balances and balance- beams which had masses of d i f f e r e n t ma te r i a l s a t t ached t o them and which o s c i l l a t e d i n t he time-varying f i e l d of t he sun a s measured a t t h e s u r f a c e of t he ear th .

Severa l workers s tud ied t h e i n t e r e s t i n g ques t ion "Does G va ry while t h e t e s t mass undergoes a chemical r eac t ion?" but, i n a l l cases , e q u i l i b r a t e d o r r e a c t i n g , n u l l r e s u l t s have been obtained. This a r e a has not been without cont roversy , however. C.F. Brush claimed t o s e e a d i f f e r e n c e i n pendulum per iods between pendulums made of bismuth and those of zinc. H i s observa t ions were u l t ima te ly explained by a lack of i n c l u s i o n of t he buoyancy of a i r i n h i s c a l c u l a t i o n s .

Although not s t r i c t l y belonging t o t h i s category, t h e experiment of L. Kreuzer (1966), a t Pr ince ton , is included he re because it has been i n t e r p r e t e d by some a s providing evidence f o r a v a r i a t i o n of G over t h e elements of t h e p e r i o d i c t ab l e . This c laim was subsequently r e fu t ed , but caused some i n t e r e s t a t t h e time.

7. Measurements of t h e De~endence of G on T e m ~ e r a t u r e

Ear ly i n t h i s century , t h e r e were two a t tempts t o measure w i t h balance-beams a dependence of G on t h e temperature of t h e a t t r a c t i n g masses. They both produced n u l l r e s u l t s but were nonethe less open t o d iscuss ion . This was so f o r two reasons. F i r s t , t h e r e were well-known d i f f i c u l t i e s i n experiments wherein two masses a t d i f f e r e n t temperatures were used i n a high-precis ion balance; and second, t h e unknown thermal p r o f i l e of t h e e a r t h immediately below t h e balance would seem t o make an exac t r e p e t i t i o n of t h e experiment impossible, because any thermal dependence of g r a v i t y would presumably a f f e c t t h e e a r t h ' s f i e l d too (and how can one c o n t r o l t h e temperature of t h e e a r t h ? ) .

P ro fe s so r Shaw and h i s s tuden t s , t h e r e f o r e , cons t ruc ted a Boys- type balance i n which t h e a t t r a c t i n g masses could be heated. They measured G and analyzed t h e i r d a t a i n t h e form G = Go(l + aT). A t f i r s t

they found a = loe5 O C ' ~ . This r e s u l t c rea ted g r e a t i n t e r e s t and s e v e r a l papers were w r i t t e n d i scuss ing it. A c a r e f u l r e p e t i t i o n of t h e i r o r i g i n a l work showed, though, t h a t a f t e r removing troublesome convect ion e f f e c t s , a < 2 x 10'~ O C ' ~ , which e f f e c t i v e l y s e t t l e d t h e i s s u e i n t he negat ive . There do not seem t o have been any o t h e r experiments fo l lowing t h i s one. Perhaps t h i s is because it was r e a l i z e d t h a t t he l a r g e temperature d i f f e r e n c e between t h e e a r t h and sun, when compared wi th t h e much sma l l e r d i f f e r e n c e between t h e e a r t h and moon, should have h igh l igh ted t h e ex i s t ence of t he e f f e c t . I n s t ead , both o r b i t s serve only t o v e r i f y t h a t t h e inve r se square law is, i n f a c t , independent of temperature. I n ques t ions of t h i s type, however, s c a l e f a c t o r s may be important ; and even though Poynting's and Southerns ' balance-beam experiments ( l abo ra to ry s c a l e ) i n t h e e a r t h ' s f i e l d produced n u l l r e s u l t s a t t h e 10'~ l e v e l , Shaw's experiment wi th i s o l a t e d g r a v i t a t i o n a l fo rces ( a l s o a t l abo ra to ry s c a l e ) was 2 000 times l e s s s e n s i t i v e than e i t h e r of t h e i r s . So t h e r e may s t i l l , perhaps, be e f f e c t s t o be discovered.

8. Measurements of t h e De~endence of G on t h e Rad ioac t iv i tv of Masses

One very i n t e r e s t i n g a rea of r e sea rch i n t h i s century has been t h e sea rch f o r a connection between g r a v i t a t i o n and what we now know t o be

t h e nuc lear forces . S tud ie s i n t h i s a r ea have involved a wide v a r i e t y of experimental techniques. Seve ra l famous p h y s i c i s t s have worked i n t h i s a r e a , i nc lud ing G. Sagnac, P. Zeeman, A. Compton and J.J. Thornson, each lending t h e i r own s p e c i a l e x p e r t i s e t o t h i s d i f f i c u l t problem.

Compton, f o r i n s t ance , produced a l a r g e and c o n t r o l l a b l e pseudo- g r a v i t a t i o n a l ( c e n t r i f u g a l ) f i e l d by r o t a t i n g samples of radium a t high speeds. He concluded t h a t t h i s d id no t a f f e c t t h e r a d i o a c t i v i t y by more than Thompson's uranium-pendulum experiment ( c a r r i e d ou t i n more d e t a i l by Southerns) showed no g r a v i t a t i o n a l coupl ing t o t h e sample's r a d i o a c t i v i t y a t t h e l e v e l of 5 x 10". A l l o t h e r measurements a l s o produced n u l l r e s u l t s , except f o r t h a t of R. Geigel who claimed t o have seen a s m a l l weight change i n a nonradioac t ive sample hanging on a s e n s i t i v e balance when a radium salt sample w a s placed nearby. He i n t e r p r e t e d t h i s as an abso rp t ion of r a d i o a c t i v i t y which l ed t o a n i n c r e a s e i n t h e g r a v i t a t i o n a l p o t e n t i a l energy of t h e nonradioac t ive sample. W. Kaufmann s h o r t l y a f t e r , however, uncovered a thermal e f f e c t which explained t h e apparent weight change. No one s i n c e then h a s repea ted Geige l ' s experiment.

9. Measurements of t h e Dependence of G on t h e Electromagnet ic Energy Content o f Masses

A t t h e same time as the sea rches f o r a r a d i o a c t i v i t y - g r a v i t a t i o n a l f o r c e coupling were under way, t h e r e w a s a p a r a l l e l e f f o r t i n progress aimed a t f ind ing an e l ec t romagne t i c -g rav i t a t i ona l coupling.

These searches t y p i c a l l y involved weighing samples of s t e e l i n magnetized and unmagnetized s t a t e s o r charged and uncharged s t a t e s .

The very much l a r g e r s i z e of t h e e lec t romagnet ic fo rces always makes experiments of t h i s kind very d i f f i c u l t , and c a r e f u l a t t e n t i o n must be paid t o t h e s h i e l d i n g of undes i rab le e lec t romagnet ic coupl ings t o t h e l abo ra to ry which would o therwise make t h e r e s u l t s ambiguous. I n s p i t e of t h i s , n u l l r e s u l t s were always reported.

A t p r e sen t , J.F. Woodward is r epea t ing (with much h ighe r p r e c i s i o n ) t h e e a r l y work of Faraday and B lacke t t i n search of an e l e c t r o g r a v i t a t i o n a l e f f e c t , but i t is not c l e a r a t t h i s po in t what a p o s i t i v e r e s u l t i n t hese experiments would mean i n terms of t h e value of G o r t h e g r a v i t a t i o n a l i n v e r s e square law. H i s p re l iminary r e s u l t s a r e included i n t h i s b ib l iography anyway, f o r t h e sake of completeness. The r e fe rence s e c t i o n of h i s paper r e f e r s t he reader t o c i t a t i o n s of e a r l i e r work along t h a t s p e c i f i c l i n e .

10. Measurements of t h e Dependence of G on In te r -mass Spacing

The pas t decade has seen a g r e a t d e a l of research i n t h i s a r e a , and most of t he e f f o r t was motivated by t h e work of D. Long a t Eas te rn Washington Univers i ty . He claimed t h a t an a n a l y s i s of p a s t measurements of t he abso lu t e va lue of G showed a d i s t a n c e dependence, which he l a t e r

t e s t e d experimental ly . H i s p o s i t i v e r e s u l t produced g r e a t i n t e r e s t and motivated about t e n groups t o undertake experiments of t h e i r own, most of which now claim n u l l r e s u l t s . The fundamental importance of t h i s ques t ion has caused i t t o remain open, however, and both t h e o r e t i c a l and experimental work w i l l probably cont inue f o r some time t o come.

Here too , experiments have been done on many s c a l e s of d i s t a n c e , ranging from 2 cm up t o s e v e r a l ki lometers . There have been ana lyses of t he f r e e o s c i l l a t i o n s of t h e e a r t h i n terms of how they might be inf luenced by a non-zero G(R); and on t h e s t i l l l a r g e r s c a l e , t h e motion of t h e p l ane t s has been seen t o confirm t h e inve r se square law t o a n amazingly high p r e c i s i o n (except f o r t h e previously mentioned r e l a t i v i s t i c c o r r e c t i o n s ) .

The major i ty of t he l a t e s t experiments have been designed t o b e high s e n s i t i v i t y n u l l measurements, although t h e e a r l y work (and t h a t of Long) i n s t e a d involved measurements of t h e abso lu t e va lue of G a t two o r more d i f f e r e n t mass spacings. While a workable scheme i n p r i n c i p l e , t h e abso lu t e measurements a r e u sua l ly burdened with l a r g e d r i f t s and me t ro log ica l d i f f i c u l t i e s . This sometimes makes t h e i r r e s u l t s open t o ques t ion .

Measurements of t h e Dependence of G on Time

Perhaps no o the r a r e a of g r a v i t a t i o n i s of g r e a t e r i n t e r e s t t o t h e o r i s t s and cosmologists than t h e p o s s i b i l i t y of v a r i a t i o n s of G i n time. There have been many t h e o r i e s c a l l i n g f o r a time-varying G, each having i t s own impl i ca t ions on t h e behavior of ma t t e r and r a d i a t i o n a t t he e a r l y moments of t he universe.

Here again, the experiments f a l l i n t o t h e t h r e e f a m i l i a r c a t e g o r i e s of l abo ra to ry , geophysical and astronomical . I f such an e f f e c t e x i s t s , i t is agreed t h a t i t must be very, very small; probably on the order of E/G = 10'11 Few labora tory t e s t s of any kind have been done a t t h i s l e v e l , and i t is not s u r p r i s i n g t h a t t h e e x i s t i n g l a b o r a t o r t e s t s of t h i s e f f e c t a r e l imi t ed a t t h e l e v e l of E/G = 10q Severa l experiments wi th t e s t masses have been proposed f o r both ear th-sur face and o r b i t i n g l a b o r a t o r i e s which should be s e n s i t i v e t o t he p red ic t ed 10'11 changes, but none has y e t been completed.

The geophysical t e s t s have usua l ly involved s t u d i e s of t h e expansion of t he e a r t h o r i n v e s t i g a t i o n s of a pa leobio logic type. While t hese provide cor robora t ing evidence, they a r e not u sua l ly accepted a s hard proof because of t he many unce r t a in f a c t o r s involved. Wesson's con t r ibu t ions a r e t he most complete i n t h i s a r ea , and h i s book "Cosmology and Geophysics" (1978) should be consul ted f o r a thorough review of geophysical i n v e s t i g a t i o n s of e / ~ .

The t h r e e astronomical t e s t s of t / G a r e now i e l d i n g s i m i l a r r e s u l t s and seem t o show t h a t E/G - -(6 f 2) x year-1. These t e s t s include: (1) lunar l a s e r ranging from MacDonald Observatory i n

Texas, (2 ) r a d a r ranging of t h e inne r p l ane t s , and (3 ) l una r o c c u l t a t i o n s t u d i e s and de termina t ions of t h e moon's o r b i t .

There a r e some miscel laneous t e s t s of e / ~ a s we l l , although before t he ex i s t ence of t h i s e f f e c t i s accepted a s t r u l y proven, i t i s l i k e l y t h a t evidence from a l l t h r e e a r e a s ( l abo ra to ry , geophysical and as t ronomica l ) w i l l have t o be a v a i l a b l e and show good agreement.

12. Measurements of Spontaneous Mat te r Crea t ion

Most of the t h e o r i e s t h a t c a l l f o r a non-zero 6 / ~ a l s o r e q u i r e t h e spontaneous c r e a t i o n of mat te r . This is usua l ly t h e r e s u l t of a gauge condi t ion ; o r is i n response t o s a t i s f y i n g some phenomenological requirement, such as maintaining cons tan t d e n s i t y i n t h e universe. I n a Machian universe, t h e va lue of t h e g r a v i t a t i o n a l cons tan t and processes l i ke mat te r c r e a t i o n a r e presumably coupled i n such a way t h a t t h e va lue ( o r ex i s t ence ) of one a f f e c t s t h e o ther . Therefore, i t seemed appropr i a t e t o inc lude t h e known experimental t e s t s , t e s t s i n progress , and proposed t e s t s of t h i s e f f e c t i n t h i s b ib l iography too.

I n terms of ca t egor i e s , t h e f i l~ experiments a r e c l a s s i f i a b l e i n t h e same way a s t h e GIG experiments. There a r e s u b s t a n t i a l l y fewer of them, and only one l abo ra to ry experiment, t h a t of S. Cohen and J. King, has y ie lded a r e s u l t , which w a s n u l l a t t h e RIM = s-l l e v e l . The spinning-rotor measurement c u r r e n t l y i n progress a t t h e Un ive r s i t y of V i r g i n i a seems t o be t h e most promising experiment f o r t h e immediate f u t u r e , a l though o t h e r s a r e a l s o i n progress .

13. Measurements of t h e Dependence of G on the S t a t e of Quant iza t ion of t h e Tes t Masses and t h e i r Or i en ta t ion wi th R e s ~ e c t t o t h e "Fixed S t a r s "

There have been two proposals f o r measuring G i n terms of h, t h e Planck cons tan t . These experiments, i f ever done, w i l l be t h e f i r s t d i r e c t t e s t s of a quantum s t r u c t u r e of t he g r a v i t a t i o n a l f i e l d . One i n d i r e c t t e s t by D. Page and C. Gei lker has been c a r r i e d out but i s d isputed .

An apparatus has been cons t ruc ted a t the Cavendish Laboratory o f Cambridge Univers i ty i n England f o r t h e purpose of searching f o r a v a r i a t i o n i n G with r e spec t t o t he f ixed s t a r s . Although t h i s i s p re sen t ly i n a c t i v e , i t i s hoped t h a t such an experiment can be done eventua l ly , a s i t r e p r e s e n t s a kind of "universa l gravimetry" which, i f s e n s i t i v e enough, should y i e l d r e s u l t s of fundamental s ign i f i cance .

Summary of Sec t ion 11

The r e s u l t s of t he d i f f e r e n t searches f o r v a r i a t i o n s i n G a r e summarized i n Table 11. For each category, the experiment claiming h ighes t p rec i s ion i s quoted, un less otherwise s t a t e d .

Some r e s u l t s en tered i n Table 11 a r e dimensionless. I n t hese cases , t h e au tho r s l i s t e d had t r i e d t o s e t l i m i t s on some appropr i a t e dimensionless s c a l e f a c t o r . Their o r i g i n a l r e s u l t s (where necessary) have been t r a n s l a t e d i n t o t h e more f a m i l i a r AG/G format f o r p re sen ta t ion here .

Table I1

Author Year Resul t ( AG/G) E f f e c t

M. Caputo 1962 < 6 x 10'16 G r a v i t a t i o n a l permeabi l i ty o r abso rp t ion

P.R. Hey1 Di rec t ive a c t i o n of g r a v i t a t i o n a l fo rce

Dependence of G on phys i ca l and/or chemical s t a t e s of mat te r

For a review, s e e C. W i l l

Temperature dependence v i a a Cavendish balance

P .E. Shaw and N. Davy

Temperature dependence v i a a common balance

J.H. Poynting and P. P h i l l i p s

Grav i t a t i on / r a d i o a c t i v i t y coupling

P. Zeeman

Dependence of G on magnet izat ion of ma t t e r

M.G. Lloyd

Dependence of G on e l e c t r i f i c a - t i o n of ma t t e r

L. Simons

R.E. Spero, e t a l .

b / G (Astronomical)

For a review, s e e T. Van Flandern

e / ~ (Laboratory)

D.R.F. Curot t

f i / ~ (Laboratory)

S. Cohen and J . G . King

111. Closing

A s mentioned previous ly , t h i s work i s meant t o be a r e sou rce b ib l iography, not a c r i t i c a l review of t he s t a t u s of each of t h e va r ious a r e a s t r e a t e d here. It i s hoped t h a t t he r eade r s of t h i s b ib l iography w i l l b e n e f i t from the r e l a t i v e l y comprehensive l i s t i n g of r e f e rences

, given here. Fur ther , it is hoped t h a t r eade r s w i l l respond with missing r e fe rences i f poss ib le . This w i l l be t h e only way t h a t t h e "holes" can be f i l l e d , s i n c e t h e work t o b r ing t h e b ib l iography t o t h e present l e v e l has been more than one person should at tempt alone.

A s much u s e f u l in format ion as poss ib l e has been put i n t o each c i t a t i o n . References t o work done i n t h e Sovie t Union a r e harder t o g e t ( i n hard copy) than most o the r s . This i s because t h e r e does not seem t o be any d i r e c t exchange mechanism between Sovie t l i b r a r i e s and Western l i b r a r i e s . Nevertheless , probably most of t h e important works publ ished t h e r e have been obtained by t h e au tho r and appropr i a t e ly catalogued.

The r e fe rences have been recorded a t t h e BIF'M using computerized word processors . This makes i t poss ib l e t o seek, s o r t and l i s t them by au thor , da t e , journa l and key word(s). The f l e x i b i l i t y of t h i s system makes t h i s b ib l iography, i n f a c t , a g r a v i t a t i o n a l physics d a t a base. Searches of it by non-BIPM personnel can be made under s p e c i a l arrangement.

English t r a n s l a t i o n s of some non-English a r t i c l e s i n t h e b ib l iography (except those marked wi th an a s t e r i s k ) a r e a v a i l a b l e from the au thor , a l s o v i a s p e c i a l arrangement.

The addresses and telephone numbers of t h e research l i b r a r i e s t h a t have been most h e l p f u l i n t h i s work a r e given below.

L ib ra ry of t h e United S t a t e s Nat iona l Bureau of Standards U. S . Department of Commerce Washington, D.C. 20234 USA (301) 921-2318

Superintendant of Documents U.S. Government P r i n t i n g Of f i ce Washington, D.C. 20402 USA (202) 783-3238

National Technical Information Serv ice U. S . Department of Commerce 5285 P o r t Royal Road S p r i n g f i e l d , V i r g i n i a 22161 USA (703) 487-4650

The Library of Congress Photoduplication Service 10 First Street S.E. Washington, D.C. 20540 USA (202) 426-5000

Research Library Microreproduction Laboratory, Room 14-0551 Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, Massachusetts 02139 USA (617) 253-5668

The Science and Technology Information Center Clark Hall University of Virginia Charlottesville, Virginia 22901 USA (804) 924-7209

Centre de Documentation Scientifique et Technique 26, rue Boyer F-75971 Paris Cedex 20 France (1) 358-35-59

British Library Lending Division Boston Spa Wetherby West Yorks L523 7BQ United Kingdom (0937) 843434

The author shall continue to add to this bibliography as more work on G is done in the future and as other previous reports are uncovered and made available. It is possible that there may be, therefore, a future updating of the present bibliography if there is sufficient reason and demand.

IV. Acknowledeements

The staff of the Bureau International des Poids et Mesures, particularly Dr. T.J. Quinn, Dr. R.P. Hudson, Miss J. Monprofit, Mr. P. Carr6, Mrs. M. Petit, and Ms. D. Howell are thanked for their support and assistance. The Science and Technology Library of the University of Virginia was essential in many ways, and the efforts of Mrs. J. Kirwan, Ms. M. McMartin and Mr. R. Johnson are particularly appreciated. I also gratefully acknowledge the assistance of Mrs. D.B. Dillin of the Carnegie Institution.

Useful discussions were also held with my colleagues A.J.F. Metherell, J.W. Beams (deceased), J.E. Faller, H. de Boer, J.W. Miiller, R.C. Ritter, R.G.S. Clarke, D.R. Long, U. Bleyer, A. Marussi, W.-T. Ni, C. Speake, G. Jones, Mr. and Mrs. Y.T. Chen, and S. Cheung.

July 1982

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1. Measurenents o f t h e Absolute Value o f G and Reports o f Important Subs id i a ry Technology

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AGAFONOV, N. I . e t a l .* Torsion balance o s c i l l a t i o n f requenc ies i n t h e presence of rocking. I n : Problems of G r a v i t a t i o n a l Measurements, Moscow, VNIIOFI, 1 9 7 4 7

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AIRY, G.B. Report on t h e Harton experiments. Mon. Not. R. Astron. SOC 15 1855 : 125-126. .' -

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AIRY, G.B. E x t r a i t du r appor t p rgsen t s 3 l a 35e s6ance a n n i v e r s a i r e de l a Soc i6 t6 Royale Astronomique de Londres par l e Conse i l de c e t t e s o c i 6 t 6 , l e 9 f g v r i e r 1855. Arch. Sc i . Phys. Nat., 29 1855 : - 177-191.

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A I R Y , G.B. Supplement t o t h e 'account of pendulum experiments undertaken i n t h e Harton c o l l i e r y ' ; being an account of experiments undertaken t o determine t h e c o r r e c t i o n f o r t h e temperature of t h e pendulum. Ph i lo s . Trans. R. Soc. London, - 146 1856 : 343-355.

AIRY, G.B. Ueber die in der Kohlengrube von Harton zur Bestimmung der mittleren Dichte der Erde unternommenen Pendelbeobachtungen. Ann. Phys. (Leipzig), - 97 1856 : 599-605.

AIRY, G.B. Account of pendulum experiments undertaken in the Harton colliery for the purpose of determining the mean density of the earth. Philos. Mag., 12 1856 : 228-231.

AIRY, G.B. Supplement to the 'account of pendulum experiments undertaken in the Harton colliery'; being an account of experiments undertaken to determine the correction for the temperature of the pendulum. Philos. Mag., 1 2 1 8 5 6 : 467-468.

AIRY, G.B.* On the pendulum experiments lately made in the Horton colliery, for ascertaining the mean density of the earth. Am. J. Sci., 21 1856 : 359-364. - -

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4. Measurements of t h e Local D i r e c t i v e Action of t he Grav i t a t i ona l Force

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5. Measurements of t h e Dependence of G on t h e Phys ica l S t a t e o f Masses

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6. Measurements of the Dependence of G on the Chenical State of Masses

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7 . Measurements of t h e Dependence of G on Temperature

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8. Measurements of t he Dependence of G on the Rad ioac t iv i ty of Masses

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9. Measurements of t h e Dependence of G on t h e E lec t r anagne t i c E n e r ~ v Content of Masses

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