1865.] Tlie Proposed Pendulum Operations for India. 255 



called, depends also on the state of the atmosphere, it is necessary for 

 its calculation, to record the readings of the barometer, when the 

 observations are taken in air. 



The last correction is for the height of the station of observation 

 above the mean sea level. The force of gravity varying inversely as 

 the square of the distance from the earth's centre, a pendulum swung 

 at a certain elevation above the sea, will make fewer oscillations in a 

 day than at the level of the sea, and a correction has to be added on 

 this account. Dr. Young, however, demonstrated that the correction 

 computed on this consideration alone, was too large, as it neglected 

 the attraction of the elevated mass itself, and he showed how this 

 might be approximately allowed for.* 



The general principle followed in determining the length of the 

 seconds pendulum, is to observe the number of vibrations made by a 

 pendulum of known length, in a mean solar day ; then the length of 

 the seconds pendulum is found by multiplying the length of the given 

 pendulum, by the square of the number of its vibrations in a day, and 

 dividing by the square of the number of seconds in a day. 



The number of vibrations is generally determined by the method of 

 coincidences. The detached pendulum is placed in front of a good 

 clock, and adjusted to such a length as to gain or lose, (the latter 

 generally) two beats upon the clock in some convenient time, 5 to 10 

 minutes. Suppose the pendulums to be started togethei, then the 

 longer one of the two will be left behind by the other, the distance 

 between them continually increasing, until at length they will be at 

 opposite extremities of their arcs of vibration at the same moment : 

 the longer pendulum has now lost one oscillation on the shorter one, 

 and both are apparently going at the same rate, but in opposite direc- 

 tions ; after a short time they will begin to approach each other, the 

 distance between them gradually diminishing, until they both appear 

 to coincide. It is clear that between two consecutive coincidences the 



* This correction is given by the formula — h x, where n denotes the num- 



r 



ber of oscillations in a mean solar day, r the radins of the earth at the given 

 station, h the height of the station above the mean level of the sea : «■ is an 

 unknown quantity determinable from theory ; on the assumption that the mean 

 density of the earth is 5.5 and that of the surface 2.5 Dr. Young (Phil. Trans- 

 actions 1819) showed that the correction for a station on a tract of table land 

 would be reduced by £rd or that the correction =|n h. 



