18G5] The Proposed Pendulum Operations for India. 263 



out another expedition under Captain Duperrey. He was supplied 

 with two of Captain Freycinet's brass pendulums, viz. one with a 

 cylindrical rod, and the one on Kater's principle. He observed at six 

 stations, viz. Ascension, Mauritius, Port Jackson, Falkland Isles, 

 Toulon, and Paris. In deducing the ellipticity, he combined his 

 results with those of Freycinet only, and obtained values varying from 



T5~5 LU 2 90' 



During Ross's voyage to Baffin's Bay in 1818, some observations 

 were taken at Brassa, in the Shetlands, and at Hare Island, with a clock 

 fitted with an invariable pendulum vibrating on a knife edge, which 

 rested on hollow agate cylinders. Observations were repeated at these 

 stations, and a further set taken at Melville Island, on Captain Parry's 

 first voyage to the North Pole in 1819-20. Captain Sabine conducted 

 both these experiments, using the same instruments. 



The ellipticity deduced from the experiments at Captain Sabine's 

 stations was -2TT-z> from the same combined with Kater's ^rg-T an ^- 

 combined again with Biot's xts"-'? and from a general combination of 

 all of these, g-f-g-.y. The observations of the detached pendulums only 

 were used in these determinations ; for though the clock pendulums gave 

 closely coinciding values of ellipticity, still being acted on by other forces 

 than gravity, their results are less reliable, and are only valuable in so 

 far as they afford an independent corroboration of the other results. 

 Captain Sabine was not at first aware of the strict expression for the 

 reduction to a vacuum, but after the publication of Bessel's observ- 

 ations in 1828, he had an apparatus specially constructed, and ascer- 

 tained the proper correction practically, by swinging his pendulums 

 in air, and in vacuo. 



The error from this cause, however, proved to be trifling, owing to 

 his observations being strictly differential, so that only the differences 

 between the corrections by the old and new formula? entered. 



The most widely differing buoyancy corrections at any of his or 

 Captain Kater's stations of observation, computed by the old formula 

 were -J- 5.75 vibrations at Sierra Leone and -j- 6.27 vibrations at 

 Spitzbergen, in a mean solar day. These corrections, multiplied by 

 the proper factor, 1.65, to reduce them to the new formula became -4- 

 9.52 and -J- 10.38 vibrations, so that the number of vibrations in a 

 mean solar day at Sierra Leone required to be increased by (9.52 — 5.75) 



