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 recommendations 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 tbe figure of the earth, is based upon a theorem demonstrated 

 by Clairaut, which may be stated thus, that the sum of the ellipticityf 

 of the earth, and the fraction expressing the ratio of the increase of 

 gravity to the equatorial gravity is a constant quantity, and is equal to 

 J- 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, wbich 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, or to 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 in a mean solar day. 



This theory, however, supposes the pendulum to be a " 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. 



f 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. 



