264 The Proposed Pendulum Operations for India. [No. 4, 



3.77, and at Spitzbergen by (10.38 — 6.27) 4.11 vibrations. But the 

 acceleration between the stations would only be increased by the 

 difference between these numbers, or by 0.44 vibrations. It so happened, 

 however, that even this difference was too large, for in the deduction 

 of the temperature correction, the old buoyancy formula had of course 

 been used ; on applying a correction on this account, the above dif- 

 ference required to be reduced by 0.36 vibrations so that the whole 

 error on the acceleration of the pendulum between Sierra Leone and 

 Spitzbergen was only -4- .08 vibrations. 



On this scale a black streak was painted, in the middle of which a 

 space was left white, equal to the diameter of the coincidence cylinder, 

 so that when the pendulum was at rest, the cylinder exactly covered it. 

 Again, to the bottom of the clock pendulum a piece of blackened 

 paper was attached, in which a hole had been cut of such a size that 

 when both pendulums were at rest, it exactly coincided with the image 

 of the white space on the black streak : hence when the pendulums 

 were moving in coincidence, the coincidence cylinder was visible 

 through the hole, and completely eclipsed the white space. Bessel's 

 result was expressed in lines of the toise of Peru, the standard used in 

 the measurement of the Peruvian arc. 



In publishing these experiments, M. Besse! pointed out the true 

 correction for buoyancy, which he had investigated by swinging in air 

 two spheres of equal diameters, but of different densities, one being of 

 brass and the other of ivory, suspended by a fine steel wire ; and again 

 by swinging the same brass sphere first in air and then in water. 

 These experiments showed that the old formula for reducing observ- 

 ations in air to a vacuum gave too small a correction, and that it should 

 be multiplied by a factor. 



Mr. Francis Baily made a long series of experiments on the cor- 

 rection for buoyancy, which were published in the Philosophical 

 Transactions for 1832. He used about 80 pendulums, all differing in 

 form, weight, and mode of suspension. From these experiments he 

 deduced factors for pendulums of almost every description that have 

 ever been used, and computed also the weight of the air adhering to 

 each, in other words deduced the vibrating specific* gravity of the 



* "The vibrating specific gravity of a compound pendulum is ordinarily found 

 " as follows ; Let <!', d" d!" ... denote the distance of the centre of gravity of each 



