
























252 The Proposed Pendulum Operations for India. [No. 4 
all, with the exception of Sir George Everest,* approved of the 
proposed plan of carrying them out; several made very valuable 
suggestions. 
The Secretary of State in Council consequently sanctioned the 
experiments, and on Colonel Walker’s recommendation he directed 
Captain Basevi, R. E., who was then in England on furlough, to 
proceed to Kew to learn the use of the Pendulum and apparatus, with 
the view of his conducting the experiments in India. 
Before detailing the proposed operations, a sketch of the theory, and 
of what has hitherto been done in the way of Pendulum experiments, 
may be interesting. The application of Pendulum experiments to 
determine the figure of the earth, is based upon a theorem demonstrated 
by Clairaut, which may be stated thus, that the sum of the ellipticityt 
of the earth, and the fraction expressing the ratio of the whole increase of 
gravity to the equatorial gravity is a constant quantity, and is equal to 
& of the ratio of the centrifugal force to the force of gravity at the 
equator. Hence by ascertaining the difference between the polar and 
equatorial gravity, or, which is the same thing, the progressive increase 
in the force of gravity in going from the equator towards the pole, the 
ellipticity of the earth is at once determined. 
It is proved in mechanics that the forces of gravity, at any two 
stations on the earth’s surface, are proportional to the lengths of the 
seconds Pendulum at those stations, orto the squares of the number 
of vibrations made by the same pendulum in any given time, one 
solar day for instance. Here is at once an easy means of determining 
the variations in the force of gravity, and the solution of the problem 
of the earth’s ellipticity is reduced to the measure of the length of the 
seconds pendulum at a number of points on the earth’s surface, or, as 
has been most generally done, to the observation of the number of 
oscillations made by the same pendulum ina mean solar day. 
This theory, however, supposes the pendulum to bea ‘simple pen- 
dulum” that is, to consist of a material point suspended by a string 
without weight, which is, of course a practical impossibility ; but as 
* Sir G. Everest proposed to employ only the Pendulum of an astronomical 
clock, but this method is objectionable, as the Pendulum cannot be said to be 
acted on solely by gravity. 
+ The ellipticity or compression, as it is sometimes called, is the fraction whose — 
numerator is the difference between the polar and equatorial semi-diameters, 
and the denominator is the equatorial semi-diameter. ‘ 
