The systematic survey of the gravity field of the earth was given a
great impetus by the contributions of Capt. Henry Kater, F.R.S. In 1817,
he designed, constructed, and applied a convertible compound pendulum
for the absolute determination of gravity at the house of Henry Browne,
F.R.S., in Portland Place, London.[24] Kater's convertible pendulum
(fig. 11) consisted of a brass rod to which were attached a flat
circular bob of brass and two adjustable weights, the smaller of which
was adjusted by a screw. The convertibility of the pendulum was
constituted by the provision of two knife edges turned inwards on
opposite sides of the center of gravity. The pendulum was swung on each
knife edge, and the adjustable weights were moved until the times of
swing were the same about each knife edge. When the times were judged to
be the same, the distance between the knife edges was inferred to be the
length of the equivalent simple pendulum, in accordance with Huygens'
theorem on conjugate points of a compound pendulum. Kater determined the
time of swing by the method of coincidences (fig. 12). He corrected for
the buoyancy of the air. The final value of the length of the seconds
pendulum at Browne's house in London, reduced to sea level, was
determined to be 39.13929 inches.
The convertible compound pendulum had been conceived prior to its
realization by Kater. In 1792, on the occasion of the proposal in Paris
to establish the standard of length as the length of the seconds
pendulum, Baron de Prony had proposed the employment of a compound
pendulum with three axes of oscillation.[25] In 1800, he proposed the
convertible compound pendulum with knife edges about which the pendulum
could complete swings in equal times. De Prony's proposals were not
accepted and his papers remained unpublished until 1889, at which time
they were discovered by Defforges. The French decision was to experiment
with the ball pendulum, and the determination of the length of the
seconds pendulum was carried out by Borda and Cassini by methods
previously described. Bohnenberger in his _Astronomie_ (1811),[26] made
the proposal to employ a convertible pendulum for the absolute
determination of gravity; thus, he has received credit for priority in
publication. Capt. Kater independently conceived of the convertible
pendulum and was the first to design, construct, and swing one.
[Illustration: Figure 10.--HENRY KATER (1777-1835), English army officer
and physicist. His scientific career began during his military service
in India, where he assisted in the "great trigonometrical survey."
Returned to England because of bad health, and retired in 1814, he
pioneered (1818) in the development of the convertible pendulum as an
alternative to the approximation of the "simple" pendulum for the
measurement of the "seconds pendulum." Kater's convertible pendulum and
the invariable pendulum introduced by him in 1819 were the basis of
English pendulum work. (_Photo courtesy National Portrait Gallery,
London._)]
After his observations with the convertible pendulum, Capt. Kater
designed an invariable compound pendulum with a single knife edge but
otherwise similar in external form to the convertible pendulum[27] (fig.
13). Thirteen of these Kater invariable pendulums have been reported as
constructed and swung at stations throughout the world.[28] Kater
himself swung an invariable pendulum at a station in London and at
various other stations in the British Isles. Capt. Edward Sabine,
between 1820 and 1825, made voyages and swung Kater invariable pendulums
at stations from the West Indies to Greenland and Spitzbergen.[29] In
1820, Kater swung a Kater invariable pendulum at London and then sent it
to Goldingham, who swung it in 1821 at Madras, India.[30] Also in 1820,
Kater supplied an invariable pendulum to Hall, who swung it at London
and then made observations near the equator and in the Southern
Hemisphere, and at London again in 1823.[31] The same pendulum, after
its knives were reground, was delivered to Adm. Luetke of Russia, who
observed gravity with it on a trip around the world between 1826 and
1829.[32]
[Illustration: Figure 11.--THE ATTEMPT TO APPROXIMATE the simple
(theoretical) pendulum in gravity experiments ended in 1817-18 when
Henry Kater invented the compound convertible pendulum, from which the
equivalent simple pendulum could be obtained according to the method of
Huygens (see text, p. 314). Developed in connection with a project to
fix the standard of English measure, Kater's pendulum was called
"compound" because it was a solid bar rather than the fine wire or
string with which earlier experimenters had tried to approximate a
"weightless" rod. It was called convertible because it is alternately
swung from the two knife edges (_a_ and _b_) at opposite ends. The
weights (_f_ and _g_) are adjusted so that the period of the pendulum is
the same from either knife edge. The distance between the two knife
edges is then equal to the length of the equivalent simple pendulum.]
[Illustration: Figure 12.--THE KATER CONVERTIBLE PENDULUM in use is
placed before a clock, whose pendulum bob is directly behind the
extended "tail" of the Kater pendulum. A white spot is painted on the
center of the bob of the clock pendulum. The observing telescope, left,
has a diaphragm with a vertical slit of such width that its view is just
filled by the tail of the Kater pendulum when it is at rest. When the
two pendulums are swinging, the white spot on the clock pendulum can be
seen on each swing except that in which the two pendulums are in
coincidence; thus, the coincidences are determined. (Portion of plate 5,
_Memoires publies par la Societe francaise de Physique_, vol. 4.)]
[Illustration: Figure 13.--THIS DRAWING ACCOMPANIED John Goldingham's
report on the work done in India with Kater's invariable pendulum. The
value of gravity obtained, directly or indirectly, in terms of the
simple pendulum, is called "absolute." Once absolute values of gravity
were established at a number of stations, it became possible to use the
much simpler "relative" method for the measurement of gravity at new
stations. Because it has only one knife edge, and does not involve the
adjustments of the convertible pendulum, this one is called
"invariable." In use, it is first swung at a station where the absolute
value of gravity has been established, and this period is then compared
with its period at one or more new stations. Kater developed an
invariable pendulum in 1819, which was used in England and in Madras,
India, in 1821.]
While the British were engaged in swinging the Kater invariable
pendulums to determine relative values of the length of the seconds
pendulum, or of gravity, the French also sent out expeditions. Capt. de
Freycinet made initial observations at Paris with three invariable brass
pendulums and one wooden one, and then carried out observations at Rio
de Janeiro, Cape of Good Hope, Ile de France, Rawak (near New Guinea),
Guam, Maui, and various other places.[33] A similar expedition was
conducted in 1822-1825 by Captain Duperry.[34]
During the years from 1827 to 1840, various types of pendulum were
constructed and swung by Francis Baily, a member of the Royal
Astronomical Society, who reported in 1832 on experiments in which no
less than 41 different pendulums were swung in vacuo, and their
characteristics determined.[35] In 1836, Baily undertook to advise the
American Lt. Charles Wilkes, who was to head the United States
Exploring Expedition of 1838-1842, on the procurement of pendulums for
this voyage. Wilkes ordered from the London instrument maker, Thomas
Jones, two unusual pendulums, which Wilkes described as "those
considered the best form by Mr. Baily for traveling pendulums," and
which Baily, himself, described as "precisely the same as the two
invariable pendulums belonging to this [Royal Astronomical] Society,"
except for the location of the knife edges.
[Illustration: Figure 14.--VACUUM CHAMBER FOR USE with the Kater
pendulum. Of a number of extraneous effects which tend to disturb the
accuracy of pendulum observations the most important is air resistance.
Experiments reported by the Greenwich (England) observatory in 1829 led
to the development of a vacuum chamber within which the pendulum was
swung.]
The unusual feature of these pendulums was in their symmetry of mass as
well as of form. They were made of bars, of iron in one case, and of
brass in the other, and each had two knife edges at opposite ends
equidistant from the center. Thus, although they resembled reversible
pendulums, their symmetry of mass prevented their use as such, and they
were rather equivalent to four separate invariable pendulums.[36]
Wilkes was taught the use of the pendulum by Baily, and conducted
experiments at Baily's house, where the latter had carried out the work
reported on in 1832. The subsequent experiments made on the U.S.
Exploring Expedition were under the charge of Wilkes, himself, who made
observations on 11 separate occasions, beginning with that in London
(1836) and followed by others in New York, Washington, D.C., Rio de
Janeiro, Sydney, Honolulu, "Pendulum Peak" (Mauna Loa), Mount Kanoha,
Nesqually (Oregon Territory), and, finally, two more times in
Washington, D.C. (1841 and 1845).
Wilkes' results were communicated to Baily, who appears to have found
the work defective because of insufficient attention to the maintenance
of temperature constancy and to certain alterations made to the
pendulums.[37] The results were also to have been included in the
publications of the Expedition, but were part of the unpublished 24th
volume. Fortunately they still exist, in what appears to be a printer's
proof.[38]
The Kater invariable pendulums were used to investigate the internal
constitution of the earth. Airy sought to determine the density of the
earth by observing the times of swing of pendulums at the top and bottom
of a mine. The first experiments were made in 1826 at the Dolcoath
copper mine in Cornwall, and failed when the pendulum fell to the
bottom. In 1854, the experiments were again undertaken in the Harton
coalpit, near Sunderland.[39] Gravity at the surface was greater than
below, because of the attraction of a shell equal to the depth of the
pit. From the density of the shell as determined from specimens of rock,
Airy found the density of the earth to be 6-1/2 times greater than that
of water. T. C. Mendenhall, in 1880, used a Kater convertible pendulum
in an invariable manner to compare values of gravity on Fujiyama and at
Tokyo, Japan.[40] He used a "simple" pendulum of the Borda type to
determine the absolute value of gravity at Tokyo. From the values of
gravity on the mountain and at Tokyo, and an estimate of the volume of
the mountain, he estimated the mean density of the earth as 5.77 times
greater than that of water.
In 1879, Maj. J. Herschel, R.E., stated:
The years from 1840 to 1865 are a complete blank, if we except
Airy's relative density experiments in 1854. This pause was
broken simultaneously in three different ways. Two pendulums of
the Kater pattern were sent to India; two after Bessel's design
were set to work in Russia; and at Geneva, Plantamour's zealous
experiments with a pendulum of the same kind mark the
commencement of an era of renewed activity on the European
continent.[41]
With the statement that Kater invariable pendulums nos. 4 and 6 (1821)
were used in India between 1865 and 1873, we now consider the other
events mentioned by Herschel.
[Illustration: Figure 15.--ONE OF FRANCIS BAILY'S PENDULUMS (62-1/2
inches long), shown on the left, is now in the possession of the Science
Museum, London, and, right, two views of a similar pendulum (37-5/8
inches long) made in the late 19th century by Edward Kuebel, Washington,
D.C., which is no. 316,876 in the collection of the U.S. National
Museum. Among a large number of pendulums tried by Baily in London
(1827-1840), was one which resembles the reversible pendulum
superficially, but which is actually an invariable pendulum having knife
edges at both ends. The purpose was apparently economy, since it is
equivalent to two separate invariable pendulums. This is the type of
pendulum used on the U.S. Exploring Expedition of 1838-1842. It is not
known what use was made of the Kuebel pendulum.]