zotero/storage/3BJJ8G2I/.zotero-ft-cache

NATURE. VOL. 220. NOVEMBER 2. 1968

Thermal Conductivity
Prelirninary determinations on matched blocks of well
oriented graphite composites show that parallel to the basal planes of the crystallites the thermal conductivlty 1s very high, and a t least twenty times greater than the value uarallel to their c axes. For uurc nearideal graphites this anisotropy ratio may reach about 200, depending on the defect conter~t'~.With regard t o thermal vibrations in these solids, it is interesting to find that thermal cor~ductancesrivalling the best natural metals arc attained even in the well oriented compositcs, despite their conglomeratc structure. Heat transport in pure graphite and in these composites is almost wholly by phonons. As is well known, phonon scattering effects lead to striking variations of thermal conductivity with temperature, but apparently a t ordinary temperatures the conglomerate structure does not produce much more marked scattering than in ncar-ideal graphite itself. Presumably the good parallelism of neighbouring graphite crystallites permits transmission of phonons across any intervening polymer molecules without much attenuation. Technological consequences of this finding are potentially very important.
Electrical Conductivity
Well oriented composites of graphite show unusual electronic behaviour. I n the direction of the composite a taxis, resistivity values for a particular material with 50 per cent of polymer showed a mean value of p, = 1.72 Q
a cm a t 295' K, rising to 2.05 crn at 77" K. I n the direc-
tion of the composite c axis for the same material, correspoIlding resistivity values were = 264.8 Q cm at 2950 K
a and 307'8 cm at 770 K. The large anisotropy ratio of
about 150 is in the sense to be expected if electrical conduction is controlled by the well oriented crystallites of graphite. I t may be compared with anisotropy ratios of only about 2 found in extruded polycrystalline graphitesl1. What is surprising is that the temperature coefficientof llas about the same small negative value in both directions. This suggests that some kind of activation of the charge carriers enabling them to cross a small energy gap (2-4 x 10-3 eV) intervenes in electrical conduction. Pos-
the charge carriers must tunnel through polper macromolecule barriers; if so the magnitude of the barrier is surprisingly low. A somewhat similar situation with negative temperature coefficient of resistance applies for electrical conduction in very thin deposits of gold or platinum on insulating substratcs of quartz glass or of

barium titanatel4. Electron transfer is thought to take
place between separated islands of the metallic deposit.
graphite com~ositeswith a variety of polymers show similar small negative temperature coefficients, and a general conduction phenomenon seeins
bc

Thermoelectric Power

I n pure mar-ideal graphite, the remarkable anisotropy of thermoelectric power raises problems in solid state
physics, as well as offering interesting potentialities in
high temperature technology15. Well oriented graphite composites show a corresponding anisotropy of thermoelectric power. As might be expected with this very sensitive property, the absolute magnitude of the thermoelectric pourc:ris somewhat dependent on t,hepolymer used. I n a typical instance ( 2 0per cent acrylonitrile copolymer) meen valuos u.crn approximately 3.3 yV/"C in the direction of the composite a axis, and approximately 6.2 yV/"C
in the direction of the composite c axis. Somewhat below room temperature the thermoelectric power changes
sign ; the equivalent band structure of these well orienttd composites is probably modified by charge transfer
effects to the polymer molecules. As is also the case for the electronic properties of carbons with conglomerate structure, and for molten conductors generally, there is a real need for new theoretical descriptions for collective
-" e n e r n levels in these condensed states of matter.

'Primak W. and Fuchs, L. H., Phys. Rea., 95, 22 ( 1 9 5 4 ) ; .Spain, I . L.,
~bbklohdcA. R. and Young D. A., Proc. Second Industrtal Carbon and Graphite ~Anfereics1,23 (~oc:Chem.Ind., London, 1965); Phil. Trans. fio.~.Soe.,262,345 (1967). B"mn. G. E.. .I. Appl. Chem., 6 , 477 (1956).

a Plrani, M., and Fehse, V., 2.Elektroehem., 29, 168 (1923).

4 Blackman, 1,. C , , Sa,lnders, G,, and Ubbelohde, A. R , , Proc, Roy, Sot.,

A , 264, 19 (1961). Tombrel, F . , and Rappeneau, J., Lea Carbonas, chap.

25 (Masson Ct Cie,

1966).

M ~ ~ & . c $ ~ ~ ~ ~ ~ ~ ~ , D"' A~" B$rit' lJ' A~pp~l. P'h'r;., ~ $ ~

~ ~ o o Ar .eW. Tbbelohde A. R . and Young, D. A,, Proc. Roy. SOC.,280, 153 ?1964).' ~bbelohd; A. R.: Endeavour, 24, 63 (1965).
' S P ; $ : ; ~ & . ~ $ ; ~ , A. R., and Young., D. A., Phil. Trans. Roy. Soc.,

8 IJbbelohde, A. R., P W C .ROY.SOC.A, , 304, 25 (1968).
'Rlacltman, J,. C. F.,Dundas, P. H., and Ubbelohde, A. R., Proc. Roy. Soc.,

A' 255' 293 (1960).

Reynolds, W. K.. P h ~ i c a Pl ropertus of Graphite (Elsevier Press, 1968).
" Juel, US Patent, 3,168,509(1966).

1s Hookcr, TJbbelohde, A. R., and Young, D. A., Proc. Roy. SOC.A, , 284, 17 (1965).

'"Mason, I. B., and Knibbs, R. H., J.Nuel. E n e r g ~ , l 8 , 3 1 1 ( 1 9 6 4 ) .

"Van Steensel, K . , Philips Res. R w . , 2 2 , 246 (1967).

1s

UbBblealcokhmdea'nA, .IR,. .6.aFnd.,

Orr ani

J. C . , Nature 179 193 Dundas, P. H., &ern.

(1957). Ubbelohde, A . R., and Indust., 595 (1959).

Expetimenls lo delermine lhe Force of Gravily on
Single Electrons and Posilrons

by FRED C. W l l T E B O R N WILLIAM M. FAIRBANK
Department of Physics, Stanford University, California

Two experimental methods are described for measuring the gravitational force on electrons falling through vertical metal tubes. A third method is being devised t o study the fall of positrons.

EXPERIMENTtSo determine the gravitational properties years. I n this article we will examine the motivation of electrons and positrons by the time of flight technique for thc experiments, the methods used, the principal have been under way a t Stanford University for several difficulties involved and the results obtained so far.

NATURE, VOL. 220. N O V E M B E R 2, 1968

Gravitational Properties of Elementary Particles

particles of very different mass (that is, between electrons

The obvious lack of symmetry in the abundance of matter over antimatter in the solar system, and perhaps much more of the visible universe, led Morrison and Gold192 to speculate that a gravitational repulsion exists between
matter and antimatter. Because both particles and ant,iparticles have positive inertial mass, they would fall ill opposite directions in a gravitational field if the speculation is correct. Thus one could distinguish between a gravitational field and an accelerating reference frame, in violation of the equivalence principle of general relativity. Tht: equivalence principle would hold in systems composed predominantly of matter or antimatter but not in a mixed system. So far, of course, the effects of general relativity have been cxarnined only in systems cornposed predominantly of matter.
Although the gravitational force on stable antiparticles

+ and protons or positrons and protons) was assumed to
have the magnitude q 2 6/4nk0r2. This model leads to a net force between two hydrogen atoms of - 26/4naor2,
where the negative sign indicates attraction. Swan11
+ showed that the net force between a hydrogen atom and
an antihydrogen atom was 26/4no0r2. But with this model a neutral mass would attract a proton with exactly
the same force as it would an electron. Each would be attracted with one half the force that ta hydrogen atom would feel. Because of the difference in inertial masses, the electron acceleration would be 1,836 times that of the proton. The latter would fall with an acceleration of 0.5g. Of course, it should be emphasized that Swann's proposal was speculative and largely intended to show
the importance of measuring the gravitational propertics of elementary particles.

has not beer1 directly measured, some indirect evidence

has been obtained from virtual and short lived antimatter. Experimental Method

Schiff3showed that the mass of virtual antimatter present
in nuclei of ordinary matter was sufficient to have been detected in the Eotvos experiment^',^ if virtual antimatter had been repelled by gravity. Good6showed t,llat
the KOand KOmesons (lifetime < s) must have the

The gravitational potential gradient for an electron a t
the Earth's surface is expected to be mg = 5.6 x lo-" eV rn-'. All electric and magnetic potential gradients must be
reduced below about lo-'' eV ni-' or measured to this
accuracy in an experiment intended to detect the gravita-

same gravitational properties. Thus virtual antimatter tional force. It would not be desirable to attempt the

and unstable antimatter have normal gravitational experiment inside an insulating box, because a single

properties. The arguments of Morrison and Gold involved electric charge trapped in the insulator even 5 m distant

stable, real antimatter. Indeed, they proposed that from the test region would exert a force on an electron

electromagnetic mass would be attracted by both matter greater than mg. To surround the experiment with a

and antimatter. I n this respect it should be added that metal container raises the problem of surface charge

positrons are not considered ideal test particles for determ- induced by the freely falling electron. But if tho metal

ining the sign of the gravitational force because a large is a long vertical cylinder, the induced surface charge

part of their mass is electromagnetic. It may be shown?*8, produces only a horizontal force on the electron.

however, that not all of the electron mass is electromag- The electrons are constrained to move along the axis

netic. I n the absence of a copious source of low energy of the cylinder by a coaxial magnetic field. Inhomo-

antinucleons, we felt that the positron was the best test geneities in the magnetic field AB will cause spatial

antiparticle.

variations in the magnetic potential

The necessity of a repulsive force to provide for the

separation of matter from antimatter has been largely

removed by Alfv6n0J0,who proposed a number of electro-

magnetic mechanisms for matter-antimatter separation.
There is no conclusive experimental evidence to show where pb= 6 x lo-@eV gauss-' is the Bohr magneton, 9% is a
whether such mechanisms have in fact led to separat,ion positive integer, s = f 4 is the spin, and y,= 2.0023 is the

in the observable universe.

spin gyromagnetic ratio. I n a region shielded by conven-

It seems that if positrons have the same gravitational tional materials, AB can be reduced t o about 0.01 gauss.

properties as electrons, there would be very little change This would lead to potential variations of 10-lo eV and

in physics except that future cosmological arguments will more for most electrons. Thus the magnetic potential

be unable to associate antigravity with antimatter. But variations would be larger than the expected gravitational

if positrons have even slightly different gravitational potential change in a 1 m fall except for those electrons

- properties (neglecting radiation reaction effects) very in the "gronnd staten-those, that is, having lz = 0 and
serious and far reaching consequences would result. s - 3. The ground state electrons experience magnetic

First, general relativity would have to be modified. potential variations of only about 10-l3 eV. To ensure Second, we would know that the Milky Way galaxy is that all of the "low energy" (E< eV) electrons are

composed chiefly of matter, for the stars in it appear to in the ground state, the cathode may bc placed in a

revolve around its centre. Third, we would have strong region of high magnebic field (3,000 gauss), so that all

reason to believe that somewhere outside our galaxy, electrons not in the ground state are accelerated as they

perhaps beyond our limits of observation, there is an leave the cathode region (Fig. 1). As the electrons arc

accumulation of antimatter.

emitted in pulses, those with low energy become spatially

If positrons or electrons or both were to display unex- separated from the others and reach the detector later.

pected gravitational properties, some clues about the Late arrivals consist entirely of ground state electrons

nature of gravity itself might be uncovered. For example, because all others are accelerated as they leave the

Swann speculated" on a mechanism for gravity which cathode.

would produce an attractive inverse square force A variety of techniques had to be used to reduce other

between two neutral ordinary particles or two neutral undesired forces. The cylinder diameter (5 cm) was

antiparticles but a repulsive force between a neutral accurate to 0.3 x

cm to avoid serious variations in

particle and a neutral antiparticle. Binding energy electric image potentials. The cylinder, made of oxygen

and electromagnetic energy were implicitly excluded free copper, was thermally isolated from its vacuum

from consideration. He used electrons and positrons conta nor except a t the bottom end. This was necessary

and their antiparticles as his "elementary" particles so as to reduce spatial temperature variations to below

and treated neutrons as gravitationally equivalent 10-6 degrees m-' and sufficiently minimize the Thompson

to hydrogen atoms. The long range force between e.m.f. the coefficient of which is of the order V degree-'.

elementary particles of equal inertial mass was assumed To reduce sufficiently the interactions with background

to have the magnitude of the Coulomb force g2/4no,r2 gases the pressure in the free fall region had to be less than

(MKS units). The corresponding force between elementary 10-l1torr. This was done with an ion pump by excluding

DETECTOR VACUUM CHAMBER
MOVABLE DRIFT TUBE
GUIDE SOLENOID

NATURE. VOL. 220. NOVEMBER 2. 1968
and over to produce a statistically reliable distribution of electron flight times.
If the moving electrons encountered only a constant force F the distribution of electron flight times would be
cut off a t time tmax = 2/2mh/lFI. Thus in the ideal cascs the force on the electron could bo dcterrnined directly from the time of flight distributiort. The gravitational
force is expectcd to be - mg. An additional vertical force
yE, (to be discussed later in this article) is expectcd from the walls of the metal cylinder; q is the charge of thc free falling particle. An adjustable force qEa may bc applicd by running a current vertically through thc drift tube walls. Thus

STATIONARY DRIFT TUBE

+ By finding tmaxfor several values of Ea one would expect
to be able to determine (mg qEw) and m for the electron or other particles tostcd. The actual data reduction is complicated by electric fringing ficlds, delayed dctector pulses caused by electron trapping and background noise in the detector.

- CATHODE
MAGNET
CATHODE
Fig. 1. Schematic diagram of the free fall apparatus: the wires labelled "s" are superconducting. The regulated current supply I, maintains both drift tubes at a negative (positive in positron experiments) voltage relative to the vacuum chamber. I, controls the relative potential of the two drlft tubes. In the first experiment the movable drift tube was positively biased so that electrons moved slowly only in the stationary tube. The current I, produces a uniform
electric field in the stationary drift tube.

all organic and volatile materials from the system and

cooling the entire free full region to 4.2" K.

Another sourco of potential variations in the cylinder

is the patch effect1=. This arises from the variations in

work function along a metal surface as a result of the

crystalline nature of the surface. Different crystal faces

have work functions which differ typically by 0.1 V. If

one assumes that the faces are encountered in a random

fashion on a metal surface, then spatial variations in

potential A@ may be estimated by A@=O.O6 (alr) eV

(ref. 13), where a is a characteristic patch dimension and

r is tho distance above the surface. This would lead to

potential variations of about

eV if a = 0.0045 cm (a

typical crystal size for oxygen free copper) and r = 2.5 cm.

Our drift tube was electroformed onto a polished alumin-

ium mandrcl which was later dissolved away. This

process is expected to leave an amorphous surface so that

the dimension a was much smaller than 0.0045 cm, but

other surface irregularities of macroscopic size surely

were present during our experiments. Preliminary

experiments performed with a pilot model free fall appara-

tus 2 cm in diameter indicated that a t 4.2O K the potentials
along the tube axis were uniform to about lo-* or 10-loeV

(ref. 13). We do not know what causes this apparent

reduction in potential irregularities. We speculate that

adsorbed gases may be smoothing out the variations.

Forces on the electrons are studied by a time of flight
techniquc. Initially a burst of about lo8 electrons is

emitted frorn the cathode. The arrival of each electron a t

the top of the tube causes the electron multiplier to

produce a pulse which is amplified and carried to a multi-

channel scaler. The multichannel scaler stores the number

of pulses arriving in each of 400 successive timc intervals

(typically 2.5 ms intervals) following the initial burst from

the cathode. Because of the mutual repulsion of electrons

in the drift tube, no more than one electron with energy

less than 10-loeV can be expected from the original burst

of electrons. Thus the experiment must be repeated over

Experimental Results

Data obtained in experiments with different applied

forces are shown in Fig. 2. By defining the "cut off"

as the lowest value o f t for which dNldt goes below the

flat last

portion of the 0.5 s), one may

curve (determined get crude values of

mbyanadvoefraFgi=ngmgth+e

+ q(E, Ea)from two distributions. The distributions in

+ Fig. 2 give m = 1.1x

kg and mg qE, = 1.3x 10-l1

V m-*. Thc sensitivity of the distributions to small

changes in E, was sufficient to confirm that the particles

forming the distributions were electrons. Further

informatiorl was deduced from the distributions by making

least squares fits of a theoretical distribution function in

which the force was one of sevcral adjustable parameters.

Tho other parameters accounted for background noise

and assumed power law forms for elcctron energy distribu-

tion and omission from potential traps. The parameters

were adjusted by a computcr optimization program.

The results, which wore reported elsewhere14, are sum-

marized in Fig. 3 and show that the only vertical forcc

present in the free fall region was the applied electric

field. Thus the gravitational force appears to be cancelled

by the electric field produced by the walls of the tube.

This result is in agreement with a calculation by Schiff

and Barnhill15which showed that the electrons in the walls

of a vertical metal cylinder would adjust their positions

just enough to produce an electric field mgle directed so as

t o oppose the gravitational force. Tho field would also

be present in the centre of the cylinder.

The electric field caused by ion displacement induced

by, gravity irk the cylinder walis was sh&n to be rltgligible

us-lrl"e the Schiff-Barrihill auuroach. but other theorists disagree. Dcssler et al.lBan4 ~ e r r i nc~lailm~ that a much
larger potential gradient of the order of lo-' eV m-l should

arise as a result of the ion lattice displacement. Thc ovcr-

lying weight of the drift tube causes tho bottom of the

tube to be compressed more than the top. This could

lead to a work function gradient and, according to ref. 16,

an electric field in tho tube. The question is still unre-

solved in spite of the apparent agreement between

Schiff and Barnhill's theory and the free fall experiment,

because the unknown mechanism that shields the patch

effect may also shield the lattice compression effect.

Further evidence that the time of flight distribution

curves did in fact arise from very low energy electrons

was obtained by Knightla. Hc used a modified version

of our pilot model electron free fall apparatus to measure

magnetic forces on the electrons by noting the change in

their time of flight distribution as the magnetic field

gradient was varied by about 1,000 gauss/cm-I over a

distance of a few cm. His ability to measure the anomal-

NATURE, VOL. 220, NOVEMBER 2, 1968

439

ous magnetic m o m e n t of the electron to a n accuracy of + 30 per cent demonstrated t h a t m a n y of the particles in his drift tube were ground state electrons with energies less than 10"8 eV.

APPLIED ELECTRIC FIELD WAS + 5 x 10"" VOLTS/METER

10!

10

10"

10-"

S», applied electric field (V/m)

Fig. 3. Measured force versus applied force. The vertical value is the force determined from analysis of the time of flight distribution curves. The horizontal value is the absolute magnitude of the deliberately applied electric field. The solid diagonal line represents F = \ eE&\ for a
particle having the electron's inertial mass.

slow electrons when the total potentials in the two drift tubes are equal. The potential of the upper tube relative to the lower is varied b y sending a highly regulated current (1 p a r t in 105) t h r o u g h a 1 0 - ' Q. resistor connecting t h e two tubes. Connexions to the tubes are made with superconducting wires to minimize Johnson noise. By increasing the distance between the two drift tubes the gravitational potential is altered. Any such potential change not compensated b y the field from the wall (only t h a t part predicted by Sehiff and Barnhill in this case) must be compensated by the applied voltage difference between

CASE I

0-25

0-50

Time of flight (s)

6

Fig. 2. Time of flight distribution curves. The horizontal scale in each graph is the time of flight of electrons. On the vertical scale the number of electrons the flight of which ended in each 2-5 ms time interval is plotted. In the histogram the values are averages of ten such intervals. These numbers represent the accumulated counts from about 80,000 pulses of electrons. The arrows point to the apparent cut off which is the flight time at which the distribution appears to flatten out into the background noise. The background noise is simply the average of the
last 0-50 s of data and is indicated by the dashed line.

Experiment with Movable Drift Tube
It is important to note t h a t the gravitational potential gradients of electrons and positrons could be compared by a different method even if the patch effect were not shielded. This method uses the movable drift tube shown in Fig. 1. Voltages are applied to t h e upper drift t u b e and to the chamber wall relative to the lower drift tube to achieve the potential profile shown in Fig. 4. The time of flight distribution should have the m a x i m u m n u m b e r of

f ' f IL \

\

*s

*

M

•
z. — i

< ho -
/ \\

CASE 2 / Jk A

*s

M

'
i '-2

\
-

Z, VERTICAL DISTANCE FROM CATHODE

Fig. 4. Potential versus height in movable drift tube apparatus. In

case 1 the total potential 3>M of the movable drift tube has been made

equal to #s, the total potential of the stationary drift tube, by adjust-

ment of the applied voltage between the tubes to the value Vi. In case 2

the movable tube has been moved higher by the amount z2 — Zi. The

applied voltage is readjusted to the value V2 which again makes

0M

=

*

s . The change caused by the

in total change

potential in height

energy z2 — zl

for a particle is just q(V2—

Io7f,)c. harge

q

NATURE. VOL. 220, NOVEMBER 2, 1968

., Fig. 5. Data from movable drift tube experiments. The horizontal
axis is the applied potential difference between the movable and stationary W i t tubes. The vertical axis is the ratio of the number of electrons with flight time between 25 and 50 ms to the number with flight times between 12.6 and 25 ms. Each ratio requires 10 to 16 h of
data accumulation. 0, Separation = 1 cm; separation = 31 em.

the tubes. Thus the gravitational potential change is

determined from the change in applied voltage required

to equalize the two total potentials.

Using this method with electrons afforded data that

were apparently affected much more than expected by

potential fluctuations of the vacuum chamber relative to

the drift tubes. This caused a spread in energies of elec-

trons entering the upper drift tube. As a result it took

10-15 h to get a usable distribution for a single potential

setting. Many settings were required to determine the

intrinsic relative potentials (primarily the contact poten-

tial difference) of the two tubes. Fig. 5 shows a sum-

mary of data taken in similar conditions a t drift tube

separations of 0 and 30 cm a t several potential settings.

Each point represents the ratio of "slow" electrons (those

taking between 25 and 50 ms to traverse the tubes) to

"fast" electrons (those taking from 12.5 to 25 ms). The

total potentials of the drift tubes are assumed equal a t the

maxima of these ratios. The maxima are 5 x

V

apart for 30 cm change in separation which indicates that

the total potential change experienced by electrons falling

through distance z was a little less than 30 per cent of mgz.

The accuracy of these data does not seem to be as good

as that taken in the single drift tube experiment ( f9 per

cent14)but may be improved if the electronic noise can be

reduced. The total potential change expected is zero for

electrons and 2 mgz for positrons, provided that both have

gravitational propertics consistent with general relativity.

The Positron Experiment
At present, Mr John Madey of Stanford University is doveloping a source of slow positrons with which to perform free fall experiments. The main problem is to reduce the energy spread of positrons to the extent where there is a reasonable probability of having a 10 loeV positron leave the bottom of the drift tube in a known 10 rns time interval.
We plan to use a four stage process to reduce the energy spread of positrons emitted from a radioactive source. I n the first stage the positrons impinge on a thin mica slab the opposite face of which has a thin metal coating on it. Cherryi8 has shown that when positrons pass through such a slab, a few of them (about 30 per mCi of source s-l) emerge in the energy range 0-10 eV. Madey has obtained similar results a t Stanford (private oommunication from J. M. Madey). The second stage, not yet tried, is to trap and store these positrons in a magnetic and electrostatic bottle, and then to release them a t desired intervals into the third stage. The third stage

will consist of a small diameter cylinder made of a resistive

material. I t will be coaxial with and placed just below

the same drift tube that was used in the free fall experi-

ments. The positrons are expected to lose energy to the

walls of the resistive medium by eddy currents (private

communication from J. M. Madey). Thus the positrons

will lose energy without the danger of annihilation.

Part of the resistive region will be maintained a t

V

below the drift tube potential, so that after a time estim-

ated as 10 s all of the positrons originally released from

the electromagnetic bottle will be in a

V trap. We

expect from one to ten positrons to be trapped in this

way. Further reduction of the energy spread by this

method is limited by the patch effect and by thermal

noise, so the fourth stage of reduction uses the drift tube

where these effects are very small. If the drift tube

potential were lowered instantaneously all the posit,rons

would escape from the trap together, with a

eV

energy spread. But if the drift tube potential is lowered

slowly enough, this energy spread can be enormously

reduced a t the cost of some loss of knowledge of the time

a t which the positrons leave the trap. Let @(t)be the

drift tube potential relative to the bottom of the trap,

and let E be the kinetic energy and v the velocity of a

trapped positron. When tho positron enters the drift

tube a t time te, its kinetic energy E becomes fixed a t

E- @(te). The trap has length I = 1 cm. The maximum

value

of

E

is

just

ern =

-

2 -

1-d-@ -,

a

s

v dt

21, - IS v

the

maximum

time

a particle can stay in the trap when Ew @(t). When the positron escapes EB @(t),so that V B . \ / r m Dlr2inside the

-d@

trap. Therefore smdt= - 21 .\/rn/2

Integration yields

If we are willing to let the escape time be uncertain by 0.01 s then the energy spread is reduced to only 2.5 x
eV. Every 2,500 pulses from the source should yield a t least one 10-lo eV positron. The positron time of flight distributions would be studied by one of the methods already used on electrons.
I n conclusion, we have used two methods to examine extremely small forces on electrons falling through vertical metal tubes a t low temperatures. Both methods indicate that the gravitational potential change is cancelled by an electrical potential to less than lo-" eV m-'. A method has been devised that is expected to produce enough low energy positrons to permit measurement
of their gravitational properties in free fall experiments. This work was supported by the US National A ~ O -
nautics and Space Administration.

'Morrison P. and Gold T Essays on Gravity 45 (Gravity Kesearch Fonndktio;, New ~ o s i o n , ' k e wHampshire, 19i7).

Morrison, P.. Amer. J . I'hys., 26, 358 (1958).

Schiff. L. I..
~ i i t v d $R, , ;.,

Proc. ~ck

US Nut. Acad. Sci.. 45. 69
a iD, ., and Peketc, k., ~ n

(,1959.).
nP.hysik,

88,11(1922).

6Roll, P. G., Krotkov, It., and Dicke, R. H., Ann. Phys. (fly), 26, 442 (1964).

Go'od, M. L., Phys. Rev.,l2l, 311 (1961).

Heitler, W., The Quantum Theory of Radiation, 3rd ed., 15, 16 (Oxford,

1954).

s ~ e y n m a nR, . P . , Leighton, R. B., and Sands, M., The Fe?/nmanLectures

on Phr~sicr,Vol. 11, 28 (Addison-Wesley Publishing Comp;my, Tnc., T.ondon, 1964).

AlfvCn, H., Revs. Mod. Phvn., 37, 662 (1965).

loAlfvCn, H., AScScientifiAc merican,216, 106 (April, 1967).
" Swann, TIT.17. G . , Astrophys. J.,183,783 (1961).

l2 Herring, C., and Niclrols, M. H . , Revs. Mod. Phys., 21, 185 (1949).

l 3\tTitteborn,F. C., thesis, Stanford Univ., 1965 (unpublislled).

l4Witteborn, I?. C., and Fairbank, W. &.I.,Phys. Rev. Lett., 19, 1049 (1967).

'5 Schiff, L. I., and Ramhill, M. V., Phys. Rev., 151, 1067 (1966).

Dessler, A. J., Michel, F . C., Rorschach, H. E., and Tran~mell,G. T., P h w .

Rev.,168, 737 (1068).

"Herring, C., Phys. Rev. (in the press).

Knight, L. V., thesis, Stanford Univ., 1965 (unpublished).
'* Cherry, W. H., thesis, Princeton T7niv.,1958 (unpublished).