zotero/storage/CZ77RKTB/.zotero-ft-cache

3 STU D Y OF T H E C HA R GE SPEC T RU M O F TH E EXT RE M ELY HEAVY • , • 823

abundances. The major source of the heavy cosmic rays is supernova explosions in our galaxy.
(6) In order to study the extremely important charge region Z> 92, experiments with area-time factors much greater than 100 m2 days will be required.
ACKNOWLEDGMENTS
We would like to acknowledge the invaluable assistance given by the National Center for Atmospheric Research, whose personnel at Palestine, Texas launched

and tracked the balloons in two record-breaking flights and recovered the equipment. We acknowledge the invaluable assistance of Mary Herwig, Rose Maharaj, and Jennie Whitley in scanning the emulsion and of Cathy Burrow and Roger Thorne in measuring the tracks in the emulsion. The Bristol contribution was supported by grants from the Science Research Council and the Royal Society, London. The Berkeley contribution was supported in part by the U.S. Atomic Energy Commission, under Contract No. AT(04-3)-34.

PHYSICAL REVIEW D

VOLUME 3, NUMBER 4

15 FEBRUARY 1971

1970 Solar Eclipse as "Seen" by a Torsion Pendulum
ERWIN J. SAXL
Tensitron, Incorporated, Harvard, Massachusetts 01451
AND
MILDRED ALLEN
Mount Holyoke College, South Hadley, Massachusetts 01075 (Received 6 August 1970)

During the solar eclipse of 7 March 1970, readings were taken and recorded electronically of the times required for the torsion pendulum to rotate through a given fixed part of its path, involving both clockwise and counterclockwise motions, on its first swing from ·rest. Significant variations in these times were observed during the course of the eclipse as well as in the hours just preceding and just following the eclipse itself. Between the onset of the eclipse and its midpoint there is a steady increase in the observed times. After the midpoint the times decrease suddenly and level off promptly to values considerably greater than those observed before the eclipse. Furthermore, before the eclipse there is a periodic variation in these times. This strange periodicity was essentially repeated two weeks later at the same hours, though the actual values were somewhat greater than the earlier ones. These increases in actual values exceed by a factor of 106 those that can be explained by the attraction of the moon due to its change in position relative to the sun and earth. All this leads to the conclusion that classical gravitational theory needs to be modified to interpret these experimental facts.

INTRODUCTION
I N this paper a study is made of the variations in behavior of a torsion pendulum during the solar eclipse of 7 March 1970. The torsion pendulum is essentially the same as that used in studying the effect of added weights on its period, 1•2 but with modifications discussed later in this paper. With this setup, when the pendulum is started reproducibly from rest in a precisely defined release position, the time of traversing a constant portion of its path is timed accurately and recorded automatically. To do this, light from a fixed source is reflected from a mirror attached to the torus to fall on a photocell. Over a preamplifier the latter starts a crystal-controlled counter as the light beam travels clockwise across the photocell and stops it on its return counterclockwise trip, to record the times between these two passages of the light beam across the photocell. This gives recordings of the times used in
1 E. J. Sax! and M. Allen, J. Appl. Phys. 40, 2499 (1969). 1M. Allen and E. J. Sax!, J. Appl. Phys. 40, 2505 (1969).

traversing a constant fixed part of the total vibration path of the oscillating torus on the first swing from rest.
Some improvements had been made in the apparatus since the previous work, which increased its precision still further. Notably, a stronger light source was used which made it possible to narrow the vertical slit limiting the width of the light beam falling on the photocell. Preamplification of the signal received by the photocell and other minor changes (such as a constant voltage transformer for a uniform power supply and a nonferrous and nonmetallic manual release mechanism) were made to assure safe and reliable action of the electronic timing and printout mechanism. Earlier observations during other eclipses, taken before these needed improvements, agree qualitatively with the present results, but are not good enough for quantitative comparison.
Furthermore, it was possible to keep the temperature around the isoelastic Ni-Span "C" suspension wire at 21.7°C with a fluctuation of only ±0.6°C. This suspension has been kept under the given load for some 17

824

E. SAXL AND M. ALLEN

3

years so that possible creep should have reached the full line in Fig. 1. Each point in this figure is the

equilibrium. Moreover, the operation of the pendulum average of five consecutive grounded readings. The

was started at 4 a.m. EST while the critical readings limited vertical lines indicate the average deviations of

did not begin until 10:15 a.m. This long running-in the five readings from the average circled values. The

period should eliminate for the suspension wire any lack beginning of the eclipse at 12:31 p.m., its midpoint at

of stability due to repeated twisting or malfunction 1:40 p.m. and its end at 2:58 p.m. are also indicated on

arising from mechanical hysteresis or sudden slippage in the graph. It is to be noted that these observed time

its metallic structure or lack of temperature stability intervals level off to about 29.581 sec after the end of

inside the tube surrounding it. In another prolonged set the eclipse, whereas in the morning they had started at

of observations taken to study the effect of electric about 29.570 sec, an appreciable difference inasmuch as

charge on the period of the pendulum, there was no as the times can be read to 0.00001 sec and are signifi-

comparable change in the grounded period. Moreover, cant to about 0.0001 sec. The precision of the quartz-

the torsional elasticity of the suspension wire studied crystal-controlled oscillator in the Beckman EPUT

statically did not change with the position of the moon. (events per unit time) counter is one part in 108•

Furthermore, the wire was checked statically to see that The irregularities occurring before the start of the

it followed Hooke's law exactly as well as calculations eclipse might be considered accidental, exceptthat data

made to show that the margin of safety for operation taken two weeks later at the same hour of the day

within the elastic limit was substantial (1 :7). To avoid (dashed curve) show corresponding humps-an indica-

slipping, not only was the wire tightly clamped at both tion, by the way, that the observations are reproducible.

ends but three pointed set screws were driven, one These maxima and minima may indicate a kind of

above the other, solidly into the wire.

gravitational fine structure which is reproducible even

Observations in the present case were recorded when the positions of the sun and moon relative to the

alternately with the pendulum grounded and with it earth are quite different. This apparent wavelike struc-

charged to ±4900 V, but only the grounded results are ture has been observed over the course of many years

presented in this paper. Somewhat different, and at at our Harvard laboratory. It cannot be predicted on

times unexpected, effects were noted when the pendu- the basis of classical gravitational theory nor has it been

lum was charged electrically.

observed in the quasistationary experiments underlying

this theory (e.g., spring-operated gravimeters, seismo-

PROCEDURE

graphs, and interferometer devices).

Under these carefully guarded conditions, automatic recordings of the times during which the torus rotated through a constant angle were made from 10:15 a.m. until 3:40 p.m. EST on the day of the eclipse in the town of Harvard, Mass. The eclipse in Boston, some 20 m distant, was about 96.5% total.
Significant variations in the recorded times were observed during the course of the eclipse, as is shown by

Furthermore, the actual values of these observed times are greater at the later date. On that occasion the sun and moon were on the opposite sides of the earth, whereas during the eclipse they were in conjunction on the same side. This difference in relative position might well explain an increase in the observed times. These times are known to increase with increase in tension on the wire and therefore with gravitational attraction. Thus the moon pulling in the same direction as the

earth could be expected to increase the observed times.

6

4

2

..., 29.580

"C
.0C.,
ID

8 6

(/)

4

iwll

The difficulty is that this relative increase of about 2.7X lo-4 recorded here would require an increase in tension of 1.2 kg, as calculated from the results of our paper on the period of a torsion pendulum1 (see Fig. 5 therein). This is 5% of the total weight of the pendulum bob, 23.4 kg (51.5 lb), and is far greater than classical theories of gravitation can explain. Results of this order of magnitude have been consistently observed in

2

Harvard over a period of 17 years. The greatest possible

I

le

variation in g computed according to the older theories3

II 12 I 2 3 4 E.S.T.

for a given site on the earth's surface is 0.00016 cm/sec2
or 1.6Xl0-5%, so that our results are about 105 times as

F10. 1. Times required to traverse the fixed part of the path of oscillation (ordinates) vs the hour at which the observations were
made, from about 10 a.m. until nearly 4 p.m. (abscissas). The full line shows the observations made on 7 March 1970, the day of the total eclipse. The short vertical dashed lines, a, b, and c, show the times of onset, midpoint, and endpoint of the eclipse. The curved dashed line shows the data taken two weeks later, 21 March, when the sun and moon were on opposite sides of the
earth.

great. As shown in Fig. 1, the maximum average deviation of our results (which is a measure of our un-
certainty) is about 2.5x10-2%.
It is further to be noted that the greatest change
3 W. A. Heiskanen and F. A. Vening Meiness, The Earth and Its Gravity Field (McGraw-Hill, New York, 1958), p. 120.

3

1970 SOLAR ECLIPSE AS ''SEEN'' BY A TORSION PENDULUM

825

occurs between the onset of the eclipse and its midpoint. This agrees qualitatively with the work of Allais4 with a paraconical pendulum, where the change of azimuth ii;i.creased substantially in the first half of the eclipse of 30 June 1954. Both •these effects would seem to have a gravitational basis which cannot be explained by accepted classical theory.
Both our experimental findings and those of Allais cause one to question whether the classical laws of gravitation hold without modification.
CONCLUSION
Quantitative observations made with a precise torsion pendulum show, in agreement with many earlier, less precise recordings made at Harvard since 1953, that
'Maurice F. C. Allais, Aerospace Eng. 18, 46 (1959).

the times required to traverse a fixed fraction of its total angular path vary markedly during the hours before the eclipse and during its first half, i.e., up to its midpoint. Also the significant changes in these times do not coincide exactly with the astronomically determined onset, midpoint, and endpoint of the eclipse.
These variations are too great to be explained, on the basis of classical gravitational theory, by the relative change in position of the moon with respect to the earth and sun. This leads to the same conclusion arrived at by Allais-that classical gravitational theory needs to be modified to interpret his (and our) experimental results. Moreover, the findings with the torsion pendulum, the significant mass of which moves perpendicularly to the geogravitic vector, seem to indicate the possibility of a fine structure in these observations neither predicted nor recorded using •the orthodox methods of quasistationary gravitational investigations.

PHYSICAL REVIEW D

VOLUME 3, NUMBER 4

15 FEBRUARY 1971

Symmetry, Unitarity, and Geometry in Electromagnetic Scattering*
P. ,C. WATERMAN The MITRE Corporation, Be,dforit, Massachusetts 01730
(Received 11 August i970)
Upon defining vector spherical partial waves {~..} as a basis, a matrix equation is derived describing scattering for general incidence on objects of arbitrary shape. With no losses present, the scattering matrix
is then obtained in the symmetric, unitary form S= -Q'*a-, where (perfect conductor) Qis the Schmidt
orthogonalization of Q,.,.,= (k/,r)fda•[(VXRetk,.)X~,.,J, integration extending over the object surface. For quadric (separable) surfaces, Q itself becomes symmetric, effecting considerable simplification. A secular equation is given for constructing eigenfunctions• of general objects. Finally, numerical results are presented and compared with experimental measurements.

INTRODUCTION
I.N earlier work, a matrix description of acoustic scattering was given, based on the full HelmholtzKirchhoff integral formula plus interior continuation arguments.1 The present work constitutes the sequel for the vector electromagnetic case. Close parallels between the scalar and vector formalism are evident; we have attempted to accentuate them by using the same notation whenever possible.
Section I deals with derivation of the basic equations for the transition matrix. Incident illumination is constrained only .to have no singularities in the interior volume of the scatterer; both volume- and surface-type scattering are considered for objects of general geometry, the surface of which need not be smooth (i;e., have continuous-turning normal). In Sec. II the scattering matrix is defined, and symmetry and unitary constraints are introduced into the original equation to

obtain the solution in exactly symmetric, unitary form at any truncation. A secular equation is also discussed, from which one could alternatively proceed by constructing eigenfunctions appropriate to. the given object.. Our approach to the problem in terms of the scattering matrix in a spherical0wave basis is not new, incidentally, and has been described in some detail by Newton, for exarnple.2
In Sec. III. a closer look is taken at matrix elements required in the computation. Constraints arising from the object geometry are discussed, and an important reduction found for objects bounded by quadratic surfaces, i.e., coordinate surfaces in one of the 11 systems in which the scalar Helmholtz equation is separable. Finally, numerical' results are presented in· Sec. IV for bodies with rotational symmetry, and compared with experimental measurements, as well as the Rayleigh and geometrical-optics approximations.

* Work supported in part by the Advanced Research Projects 2 R. G. Newton, Scattering Theory of Waves anit Particles

Agency, under contract No. AF19 (628)5165.

(McGraw-Hill, New York, 1966), Chap. 2, pp. 101-104, pp.

1 P. C. Waterman, J. Acoust. Soc. Am, 45, 1417 (1969).

189-190.