1865.] The Proposed Pendulum Operations for India. 257 
time as the pendulum, so that their effect might be neglected in com- 
puting the length of the simple pendulum. When in use, the knife 
edge rested upon a steel plate. The number of vibrations per diem 
was ascertained by means of a clock, but Borda made a great improve- 
ment on the old method of counting the coincidences. He fixed a 
straight edge vertically, so as to coincide with the pendulum wire at 
rest, when seen through a teleseope placed opposite. A cross was 
made on the bob of the clock pendulum, and the observation consisted 
in noting the times when the wire and cross disappeared together 
behind the edge. After a series of coincidences had been observed, 
the length of the pendulum was measured by means of a horizontal 
steel plate, which was screwed up from below, so as just to touch® the 
ball : then the pendulum was removed, and a bar, whose length had 
been carefully compared with a standard, inserted in its place. The 
bar had a T head, of which the lower surface rested on the upper steel 
plate, and a graduated rod, sliding on the bar, was adjusted to contact 
with the lower plate. The diameter of the platinum ball was then 
measured by means of the same slider, by placing it on the steel plate 
for the purpose; the brass cap and wire were then weighed. The 
apparatus was enclosed in a glass case, and the temperature was care- 
fully recorded. All necessary corrections were applied, excepting the 
true one for buoyancy. The whole process, which required very great 
delicacy, had to be repeated, and the length of the corresponding 
simple pendulum computed after each series of observations. Borda’a 
pendulum was about 12 feet in length. 
His method was followed by M. M. Arago, Biot, and Chaix, at 
Formentera, the southernmost station of the French arc, with this 
exception that they used a pendulum of only 3 feet in length. These 
observations were extended by Biot in 1817 to Leith, and Unst in the 
Shetlands, and in conjunction with M. Mathieu, he observed at 
Dunkirk, Paris, Clermont, Bordeaux, and Figeac. From these opera- 
tions, Biot deduced an ellipticity of 53;. 
Tn about 1809, Captain Warren made some observations at the 
Madras observatory with a pendulum formed of a leaden ball suspended 
by a fibre made from the plantain leaf. The vibrations were counted 
and an assistant noted the times, from an astronomical clock. In order 
to measure its length, he attached some glass plates to a wall, and set 
