I860.] The Proposed Pendulum Operations for India. 201 



the detached pendulum vibrating slower than the clock one, the tail- 

 piece will be seen to pass across the diaphragm, followed by the 

 white disc ; at each succeeding vibration the disc follows closer and 

 closer, first touching it, and at last becoming completely eclipsed by 

 it. The exact time of this event, called a " disappearance," is noted; 

 after a few more vibrations, the disc will reappear preceding the tail- 

 piece ; the time of this event, called the " reappearance," is also noted ; 

 and the mean of the disappearance and reappearance, is taken as the 

 true time of coincidence. It is immaterial in this method of observ- 

 ation, whether the detached pendulum vibrates faster or slower than 

 the clock pendulum, but it is a sine qua non that its arc of vibration 

 be less. The result, introducing all corrections, except the true one 

 for buoyancy, was 39.13929 inches, which is still the received length, 

 although General Sabine in 1831, showed, by swinging the pen- 

 dulum in air and in vacuo, that the buoyancy correction was different, 

 according as the heavy weight was above, or below, the plane of 

 suspension. 



Captain Kater, in the following year, 1818, made a series of expe- 

 riments at the principal stations of the English Survey, from Shanklin 

 in the Isle of Wight, to Unst in the Shetlands. He used in these 

 observations a pendulum of a different pattern, known as " Kater's 

 invariable pendulum." With it, it is not possible, nor was it intended, 

 to determine the length of the seconds' pendulum, but it is essentially 

 a differential instrument, and is used for measuring the differences 

 in the number of vibrations at different stations. With these dif- 

 ferences, if at any one station the length of the seconds' pendulum 

 has been already determined, the corresponding lengths at the other 

 stations can be ascertained. The invariable pendulum, is of the same 

 dimensions as the convertible one, but is without the second knife 

 edge, and tail-piece, and the sliding weights. The mode of observation 

 is exactly the same. Captain Kater deduced values of the ellipticity, 

 from consecutive pairs of stations ; he considered ^ as a probable 

 value (the same as M. Biot's) ; but he remarks on the difficulty of 

 deriving a satisfactory determination, unless the extreme stations 

 comprise an arc of sufficient extent to render the effects of irregular 

 local attraction insensible. 



In 1821-22, some very good observations were made by Mr, 



