While scientists who had used the Repsold-Bessel pendulum apparatus
discussed its defects and limitations for gravity surveys, Maj. Robert
von Sterneck of Austria-Hungary began to develop an excellent apparatus
for the rapid determination of relative values of gravity.[82] Maj. von
Sterneck's apparatus contained a nonreversible pendulum 1/4-meter in
length, and 1/2-second time of swing. The pendulum was hung by a single
knife edge, which rested on a plate that was supported by a tripod. The
pendulum was swung in a chamber from which air was exhausted and which
could be maintained at any desired temperature. Times of swing were
determined by the observation of coincidences of the pendulum with
chronometer signals. In the final form a small mirror was attached to
the knife edge perpendicular to the plane of vibration of the pendulum
and a second fixed mirror was placed close to it so that the two mirrors
were parallel when the pendulum was at rest. The chronometer signals
worked a relay that gave a horizontal spark which was reflected into the
telescope from the mirrors. When the pendulum was at rest, the image of
the spark in both mirrors appeared on the horizontal cross wire in the
telescope, and during oscillation of the pendulum the two images
appeared in that position upon coincidence. In view of the reduced size
of the pendulum, the chamber in which it was swung was readily portable,
and with an improved method of observing coincidences, relative
determinations of gravity could be made with rapidity and accuracy.
By 1887 Maj. von Sterneck had perfected his apparatus, and it was widely
adopted in Europe for relative determinations of gravity. He used his
apparatus in extensive gravity surveys and also applied it in the silver
mines in Saxony and Bohemia, by the previously described methods of
Airy, for investigations into the internal constitution of the earth.
On July 1, 1889, Thomas Corwin Mendenhall became superintendent of the
U.S. Coast and Geodetic Survey. Earlier, he had been professor of
physics at the University of Tokyo and had directed observations of
pendulums for the determination of gravity on Fujiyama and at Tokyo.
Supt. Mendenhall, with the cooperation of members of his staff in
Washington, designed a new pendulum apparatus of the Von Sterneck type,
and in October 1890 he ordered construction of the first model.[83]
Like the Von Sterneck apparatus, the Mendenhall pendulum apparatus
employed a nonreversible, invariable pendulum 1/4-meter in length and of
slightly more than 1/2-second in time of swing. Initially, the knife
edge was placed in the head of the pendulum and hung on a fixed plane
support, but after some experimentation Mendenhall attached the plane
surface to the pendulum and hung it on a fixed knife edge. An apparatus
was provided with a set of three pendulums, so that if discrepancies
appeared in the results, the pendulum at fault could be detected. There
was also a dummy pendulum which carried a thermometer. A pendulum was
swung in a receiver in which the pressure and temperature of the air
were controlled. The time of swing was measured by coincidences with the
beat of a chronometer. The coincidences were determined by an optical
method with the aid of a flash apparatus.
[Illustration: Figure 25.--MENDENHALL'S 1/4-METER (1/2-SECOND)
APPARATUS. Shown on the left is the flash apparatus and, on the right,
the vacuum chamber within which the pendulum is swung. The flash
apparatus consists of a kerosene lantern and a telescope, mounted on a
box containing an electromagnetically operated shutter. The operation of
the shutter is controlled by a chronograph (not shown), so that it emits
a slit of light at regular intervals. The telescope is focused on two
mirrors within the apparatus, one fixed, the other attached to the top
of the pendulum. It is used to observe the reflection of the flashes
from these mirrors. When the two reflections are aligned, a
"coincidence" is marked on the chronograph tape. The second telescope
attached to the bottom of the vacuum chamber is for observing the
amplitude of the pendulum swing.]
The flash apparatus was contained in a light metal box which supported
an observing telescope and which was mounted on a stand. Within the box
was an electromagnet whose coils were connected with a chronometer
circuit and whose armature carried a long arm that moved two shutters,
in both of which were horizontal slits of the same size. The shutters
were behind the front face of the box, which also had a horizontal slit.
A flash of light from an oil lamp or an electric spark was emitted from
the box when the circuit was broken, but not when it was closed. When
the circuit was broken a spring caused the arm to rise, and the shutters
were actuated so that the three slits came into line and a flash of
light was emitted. A small circular mirror was set in each side of the
pendulum head, so that from either face of the pendulum the image of the
illuminated slit could be reflected into the field of the observing
telescope. A similar mirror was placed parallel to these two mirrors and
rigidly attached to the support. The chronometer signals broke the
circuit, causing the three slits momentarily to be in line, and when the
images of the slit in the two mirrors coincided, a coincidence was
observed. A coincidence occurred whenever the pendulum gained or lost
one oscillation on the beat of the chronometer. The relative intensity
of gravity was determined by observations with the first Mendenhall
apparatus at Washington, D.C., at stations on the Pacific Coast and in
Alaska, and at the Stevens Institute, Hoboken, New Jersey, between March
and October 1891.
[Illustration: Figure 26.--VACUUM RECEIVER within which the Mendenhall
pendulum is swung. The pressure is reduced to about 50 mm. to reduce the
disturbing effect of air resistance. When the apparatus is sealed, the
pendulum is lifted on the knife edge by the lever _q_ and is started to
swing by the lever _r_. The arc of swing is only about 1 deg. The
stationary mirror is shown at _g_. The pendulum shown in outline in the
center, is only about 9.7 inches long.]
Under Supt. Mendenhall's direction a smaller, 1/4-second, pendulum
apparatus was also constructed and tested, but did not offer advantages
over the 1/2-second apparatus, which therefore continued in use.
In accordance with Peirce's theory of the flexure of the stand under
oscillations of the pendulum, determinations of the displacement of the
receiver of the Mendenhall apparatus were part of a relative
determination of gravity by members of the Coast and Geodetic Survey.
Initially, a statical method was used, but during 1908-1909 members of
the Survey adapted the Michelson interferometer for the determinations
of flexure during oscillations from the shift of fringes.[84] The first
Mendenhall pendulums were made of bronze, but about 1920 invar was
chosen because of its small coefficient of expansion. About 1930, Lt. E.
J. Brown of the Coast and Geodetic Survey made significant improvements
in the Mendenhall apparatus, and the new form came to be known as the
Brown Pendulum Apparatus.[85]
[Illustration: Figure 27.--THE MICHELSON INTERFEROMETER. The horizontal
component of the force acting on the knife edge through the swinging
pendulum causes the support to move in unison with the pendulum, and
thereby affects the period of the oscillation. This movement is the
so-called flexure of the pendulum support, and must be taken into
account in the most accurate observations.
In 1907, the Michelson interferometer was adapted to this purpose by the
U.S. Coast and Geodetic Survey. As shown here, the interferometer,
resting on a wooden beam, is introduced into the path of a light beam
reflected from a mirror on the vacuum chamber. Movement of that mirror
causes a corresponding movement in the interference fringes in the
interferometer, which can be measured.]
The original Von Sterneck apparatus and that of Mendenhall provided for
the oscillation of one pendulum at a time. After the adoption of the Von
Sterneck pendulum in Europe, there were developed stands on which two or
four pendulums hung at the same time. This procedure provided a
convenient way to observe more than one invariable pendulum at a station
for the purpose of detecting changes in length. Prof. M. Haid of
Karlsruhe in 1896 described a four-pendulum apparatus,[86] and Dr.
Schumann of Potsdam subsequently described a two-pendulum
apparatus.[87]
[Illustration: Figure 28.--APPARATUS WHICH WAS DEVELOPED IN 1929 by the
Gulf Research and Development Company, Harmarville, Pennsylvania. It was
designed to achieve an accuracy within one ten-millionth of the true
value of gravity, and represents the extreme development of pendulum
apparatus for relative gravity measurement. The pendulum was designed so
that the period would be a minimum. The case (the top is missing in this
photograph) is dehumidified and its temperature and electrostatic
condition are controlled. Specially designed pendulum-lifting and
-starting mechanisms are used. The problem of flexure of the case is
overcome by the Faye-Peirce method (see text) in which two dynamically
matched pendulums are swung simultaneously, 180 deg. apart in phase.]
The multiple-pendulum apparatus then provided a method of determining
the flexure of the stand from the action of one pendulum upon a second
pendulum hung on the same stand. This method of determining the
correction for flexure was a development from a "Wippverfahren" invented
at the Geodetic Institute in Potsdam. A dynamometer was used to impart
periodic impulses to the stand, and the effect was observed upon a
pendulum initially at rest. Refinements of this method led to the
development of a method used by Lorenzoni in 1885-1886 to determine the
flexure of the stand by action of an auxiliary pendulum upon the
principal pendulum. Dr. Schumann, in 1899, gave a mathematical theory of
such determinations,[88] and in his paper cited the mathematical methods
of Peirce and Cellerier for the theory of Faye's proposal at Stuttgart
in 1877 to swing two similar pendulums on the same support with equal
amplitudes and in opposite phases.
[Illustration: Figure 29.--THE GULF PENDULUM is about 10.7 inches long,
and has a period of .89 second. It is made of fused quartz which is
resistant to the influence of temperature change and to the earth's
magnetism. Quartz pendulums are subject to the influence of
electrostatic charge, and provision is made to counteract this through
the presence of a radium salt in the case. The bearings are made of
Pyrex glass.]
In 1902, Dr. P. Furtwaengler[89] presented the mathematical theory of
coupled pendulums in a paper in which he referred to Faye's proposal of
1877 and reported that the difficulties predicted upon its application
had been found not to occur. Finally, during the gravity survey of
Holland in the years 1913-1921, in view of instability of supports
caused by the mobility of the soil, F. A. Vening Meinesz adopted Faye's
proposed method of swinging two pendulums on the same support.[90] The
observations were made with the ordinary Stueckrath apparatus, in which
four Von Sterneck pendulums swung two by two in planes perpendicular to
each other. This successful application of the method--which had been
proposed by Faye and had been demonstrated theoretically to be sound by
Peirce, who also published a design for its application--was rapidly
followed for pendulum apparatus for relative determinations by
Potsdam,[91] Cambridge (England),[92] Gulf Oil and Development
Company,[93] and the Dominion Observatory at Ottawa.[94] Heiskanen and
Vening Meinesz state:
The best way to eliminate the effect of flexure is to use two
synchronized pendulums of the same length swinging on the same
apparatus in the same plane and with the same amplitudes but in
opposite phases; it is clear then the flexure is zero.[95]
In view of the fact that the symmetrical reversible pendulum is named
for Bessel, who created the theory and a design for its application by
Repsold, it appears appropriate to call the method of eliminating
flexure by swinging two pendulums on the same support the Faye-Peirce
method. Its successful application was made possible by Maj. von
Sterneck's invention of the short, 1/4-meter pendulum.
[Illustration: Figure 30.--THE ACCUMULATED DATA OF GRAVITY observations
over the earth's surface have indicated that irregularities such as
mountains do not have the effect which would be expected in modifying
gravity, but are somehow compensated for. The most satisfactory solution
to this still unanswered question has been the theory of isostasy,
according to which variations in the density of the material in the
earth's crust produce a kind of hydrostatic equilibrium between its
higher and lower parts, as they "float" on the earth's fluid core. The
metals of different density floating in mercury in this diagram
illustrate isostasy according to the theory of Pratt and Hayford.]