Figure 15.—One of Francis Baily’s pendulums (621/2 inches long), shown on the left, is now in the possession of the Science Museum, London, and, right, two views of a similar pendulum (375/8 inches long) made in the late 19th century by Edward Kübel, 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 Kübel pendulum.
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 [37] The results were also to have been included in the publications of the Expedition, but were part of the unpublished 24th volume.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 61/2 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.