1865.] The Proposed Pendulum Operations for India. 259 
become tangents to the disc. Now, if both pendulums be set in motion, 
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 gud non that its are 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 $7 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. 
Bes 
