1865.] The Proposel 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 acorrection has to be added on 
this account. Dr. Young, however, demonstrated that the correction 
computed on tis 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 numher 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 together, 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 lenger 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 
n 
_  * This correction is given by the formula (-) h w, where m denotes the 
r 
number of oscillations in a mean solar day, 7 the radius of the earth at the given 
station, h the height of the station above the mean level of the sea: wis an 
unknown quantity determinable from theory ; on the assumption that the mean 
density of the earth is 5.5 and that of the surface 2.6 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 = 3 7 h. 
